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7/22/2019 Ciclo 5 - Transformemos Educando 10 - Guainia
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Crdmn
4?Crdmn
Lùmu`n fktacrdmn
pdrd ifi`n 1
Lùmu`n fktacrdmn
pdrd ifi`n 1
L ù m u
` n f k t a c r d m n p d r d i f i ` n
1
] r d k s b n r l a l n s A m u i d k m n
4?Crdmn
4?
C u d f k ì d
Qk kuavn buturn pdrd `d amuidifùk
Drtasdkfds nrcdkfzdifùk "dtuld" A` Inin. - Cudfkìd
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Asta `fern partakaia d:
Rfvn ak a` rascudrmn,inrracflfaktn n edrrfn:
Ma` lukfifpfn ninrracflfaktn ma:
Mapdrtdlaktn:
Astumfn ink a` YfstaldFktarditfvn ]rdksbnrlalns
Amuidkmn ak`d baihd:
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Knlfkdifùk pnr In`nlefd ma` Lfkfsta
ma Ua`difnkas Axtarfnras y Lfkfstarfn
Amuidifùk d` _ralfn QKAYIN
Uay Hdldm efk Fsd D` Ghd`fbd pdrd `
u`fzdifùk ma `ds ]FI ak `d amuidifùk,
saptfalera ma 5?4?
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Yfstald Fktarditfvn
]rdksbnrlalns Amuidkmn Ärads fktacrdmds pdrd ifi`n 1
Lùmu`n 4?
_famrds ma _uartn In`nlefd - Uìn Cudfkìd
7/22/2019 Ciclo 5 - Transformemos Educando 10 - Guainia
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Lùmu`n fktacrdmn pdrd ifi`n 1, ]rdksbnrlalns Amuidkmn 4?
Mfraiifùk pamdcùcfid y inkiaptud`: Ldrìd Durnrd Idrrf``n Cu``n
]axtns: Ärad ma @akcudja y Inlukfidifùk:Earkdrmd Unmrìcuaz Eatdkiur y _dtrfifd Racd
Ärad ma Ifakifds Kdturd`as: _dn`d Unjds y Dr`ax Cdriìd
Ärad ma Tuìlfid: Ldrthd @f`fdkd _raifdmn y Kdtd`fd ma` Uniìn Ävf`d Ldhaihd
Ärad ma Bìsfid: Nsidr Amud`rmn Cnkzä`az _rdmd, Ldria`d Eakìtaz Lakmfva`sn (ravfsfùk y djusta)
Ärad ma Ldtalätfids: Udbda` Asinedr Ifbuaktas, Ä`vdrn Cutfærraz ma `d Nssd y Custdvn Dmn`bn ma` Uìn _æra(ravfsfùk y djusta)
Uavfsfùk ma` taxtn: Jnsæ @ufs Cdldrrd
Inrraiifùk ma astf`n: Ldrìd Irfstfkd Racd ma Ifiarf
Mfsaôn cräbfin y amftnrfd`: Dkmrad @nzdkn @ùpaz y _d`nlfkn Amftnras
Bntncrdbfd: Idr`ns Cf`eartn _uaktas Lajìd
Ya dcrdmaia `d iasfùk ma bntns d: Irfstned` Barkdkmn _æraz, Judk _de`n _rfatn, _amrdzd _rnmuiifnkas, Jdvfar Dldyd,
Mdkfa` Cuzläk, Nldr D`bramn Eustdldkta Unquala y Lusan Inlukftdrfn ma Cudfkìd.
Bukmdifùk pdrd a` Masdrrn``n Ynifd`FYEK:
_rnhfefmd `d raprnmuiifùk pdrifd` n tntd` pnr iud`qufar lamfn sfk dutnrfzdifùk axprasd ma `d Bukmdifùk pdrd a` Masd
rn``n Ynifd` ]rdksbnrlalns
Flprasn ak In`nlefd
Bukmdifùk pdrd a` Masdrrn``n Ynifd`Mfraitnrd Ajaiutfvd y _amdcùcfid: Ldrìd Durnrd Idrrf``n Cu``n
Mfraitnr ma Masdrrn``n Ynifd` y Mfraiifùk Amftnrfd`: Unmn`bn Drmf`d Iuastd
Ùsidr Drldkmn Unmrìcuaz Yäkihaz, Cnearkdmnr ma` Cudfkìd
Ga``y _dn`d _d`difn Lakmnzd, Yairatdrfd ma Amuidifùk y Iu`turd
©
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¾_nr quæ uk sfstald fktarditfvn>
A` masdrrn``n ma lú`tfp`as axparfakifds amuidtfvds, ink mfvarsds pne`difnkas, khd lnstrdmn qua d` lfrdr sfstælfidlakta `ns prniasns amuidtfvns denrmdlsu ukfmdm, su c`ned`fmdm y su fktacrfmdm.
Uainrmalns qua a` paksdlfaktn sfstælfin inkifea y astumfd `ns bakùlakinln sfstalds y kn inln dcracdmns ma pdrtas y dmaläs, parifea d` lukmn i
ukd lfrdmd tntd`fzdmnrd y hn`ìstfid.
A` Yfstald Fktarditfvn ]rdksbnrlalns Amuidkmn denrmd d amuidifùk inln ucrdk ram ma ra`difnkas. Astd parspaitfvd parlfta akbdtfzdr dúk läs ukd fktacifùk ma `ns mfvarsns a`alaktns qua d` ra`difnkdrsa inkbnrldk `d astruiturd `ns mfbaraktas prniasns amuidtfvns y ma `ns mfvarsns aktnrkns qua `ns rnmadk
¾_nr quæ uk sfstald fktarditfvn>
A` masdrrn``n ma lú`tfp`as axparfakifds amuidtfvds, ink mfvarsds pne`difnkas, khd lnstrdmn qua d` lfrdr sfstælfidlakta `ns prniasns amuidtfvns denrmdlsu ukfmdm, su c`ned`fmdm y su fktacrfmdm.
Uainrmalns qua a` paksdlfaktn sfstælfin inkifea y astumfd `ns bakùlakinln sfstalds y kn inln dcracdmns ma pdrtas y dmaläs, parifea d` lukmn i
ukd lfrdmd tntd`fzdmnrd y hn`ìstfid.
A` Yfstald Fktarditfvn ]rdksbnrlalns Amuidkmn denrmd d amuidifùk inln ucrdk ram ma ra`difnkas. Astd parspaitfvd parlfta akbdtfzdr dúk läs ukd fktacifùk ma `ns mfvarsns a`alaktns qua d` ra`difnkdrsa inkbnrldk `d astruiturd `ns mfbaraktas prniasns amuidtfvns y ma `ns mfvarsns aktnrkns qua `ns rnmadk
A` sfstald fktarditfvn kn sa matfaka ak `ds idrditarìstfids ma idmd uknma `ns a`alaktns, aktra a``ds `ds lamfdifnkas mfmäitfids n a` inktaxtn,inln ukfmdmas ink ukd astruiturd abfifakta, d iud` yd halns puastn akpräitfid, dhnrd, denrmdkmn astns a`alaktns inln pdrta ma uk sfstaldin`nidlns a` ækbdsfs ak `ds ra`difnkas a fktardiifnkas aktra a``ns, inkukd i`drd fktakifùk amuidtfvd, lamfdkta prniasns aktakmfmns inln ukdld``d ma ra`difnkas mfkälfids, as maifr, fktarditfvds.
A` sfstald fktarditfvn kn sa matfaka ak `ds idrditarìstfids ma idmd uknma `ns a`alaktns, aktra a``ds `ds lamfdifnkas mfmäitfids n a` inktaxtn,inln ukfmdmas ink ukd astruiturd abfifakta, d iud` yd halns puastn akpräitfid, dhnrd, denrmdkmn astns a`alaktns inln pdrta ma uk sfstaldin`nidlns a` ækbdsfs ak `ds ra`difnkas a fktardiifnkas aktra a``ns, inkukd i`drd fktakifùk amuidtfvd, lamfdkta prniasns aktakmfmns inln ukdld``d ma ra`difnkas mfkälfids, as maifr, fktarditfvds.
Yfstald Fktarditfvn ]rdksbnrlalns AmuidkmnYfstald Fktarditfvn ]rdksbnrlalns Amuidkmn
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¾Iùln as `d nrcdkfzdifùkma` sfstald fktarditfvn>
@d nrcdkfzdifùk ma` Yfstald Fktarditfvn ]rdksbnrlalnsAmuidkmn astä inkbnrldmd pnr ra`difnkas qua sa mdkaktra sus a`alaktns bukmdktas:
¾Iùln as `d nrcdkfzdifùkma` sfstald fktarditfvn>
@d nrcdkfzdifùk ma` Yfstald Fktarditfvn ]rdksbnrlalnsAmuidkmn astä inkbnrldmd pnr ra`difnkas qua sa mdkaktra sus a`alaktns bukmdktas:
Nrcdkfzdifùk ma` Yfstald Fktarditfvn ]rdksbnrlalns Amuidkmn
Ua`difnkas Idrditarìstfids Nejatfvns
_amdcùcfids
Rfrtud`as
Fktardiifùk
Inktaxtud`as
Lamfdifnkas mfmäitfids
Ua`difnkas fktarditfvds mainlukfidifùk lamfdmd pnr`d taikn`ncìd ma d fkbnrlä-
tfid y `ds inlukfidifnkas.
Fktardiifnkas lntrfias, par-iaptfvds, inckftfvds, npard-
tfvds y ra`difnkas huldkds.
Qkd crdk ram ma ra`difn-kas snifd`as, parsnkd`as,ainkùlfids, aktra luihdsntrds, masma a` inktaxtnhdifd a` sfstald fktarditfvnma dprakmfzdja y vfiavarsd.
Masakidmakdr a` prniasn madprakmar.
Dpnydr n snpnrtdr ns aktnr-kns mastfkdmns d d aksaôdk-
zd y a` dprakmfzdja.
Bdif`ftdr fktardiifnkas aktraastumfdktas, prnbasnras-as-tumfdktas y ma idmd uknma a``ns ink `ns ldtarfd`asmfmäitfins.
Ynpnrtdr y dpnydr `ns prn-iasns amuidtfvns erfkmdkmnsfckfbfidmn y partfkakifd.
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Iu`turdifumdmdkdy lu`tfætkfid
Masdrrn``nhuldkn akinlukfmdm
Astrdtacfd iurrfiu`dr: fki`ufr d `ns/`ds astumfdktas ak uk prnyaitn ma ifumdmdkìd ditfvd, lamfdkta a` bnrtd`aiflfaktma `d fmaktfmdm parsnkd` y p`urfætkfid, raiupardkmn a`alaktns ma ukd iu`turd mfvarsd qua hdeftd ak uk inktaxtprfvf`acfdmn pnr sus ifriukstdkifds hfstùrfids, `ftardrfds, lusfid`as y turìstfids, pdrd mfkdlfzdr masma d``ì, `d iu`tuifumdmdkd, iradmnrd y prnmuitfvd ak `ns aspdifns ma ditudifùk intfmfdkd ma `ns/`ds astumfdktas y sus inlukfmdma
Inlpnkaktasiurrfiu`dras
Ajas iurrfiu`drasdrtfiu`dmnras
Nejatfvns mfmäitfins Inktakfmns
Nrfaktdk`ns prniasnsamuidtfvns
Inktaxtud`fzdk y mdksaktfmn d `ns inktakfmnsy prniasns amuidtfvns
6 dsfckdturds fktacrdmdsak iudtrn ärads talätfids:@akcudja y Inlukfid-ifùk, Ifakifds Kdturd`asy Ynifd`as, Ldtalätfids.
Uaiupardifùk ma `d la-lnrfd lusfid`, `ftardrfd ahfstùrfid.
Rfsfef`fmdm ma `dmfvarsfmdm.
Dbfdkzdlfaktn ma `dprnpfd fmaktfmdm.
Inlukfmdm ditfvd.
Ifumdmdkìd ditfvd.
Dprakmfzdjas carlfkd`as, sfstælfins yinktaxtud`fzdmns.
Dprakmfzdjas pdrd dbrnktdr `d fkiar-tfmulera.
Inkniflfaktn y rainkniflfaktn mahaihns hfstùrfins bukmdlaktd`as.
Inksifakifd ma `d sfkcu`drfmdm ma `dprnpfd iu`turd.
Inkniflfaktn y rainkniflfaktn ma susvd`nras iu`turd`as y ma ds ntrds iu`turds.
Uainkniflfaktn ma `ds kuavds ra`d-ifnkas aktra a` Astdmn y a` ifumdmdkn.
Uasfckfbfidifùk ma` rn` ma `d lujar.
Uainkniflfaktn ma ns vd`nras maln-irätfins masma a` acdmn ma su iu`turd.
_drtfifpdifùk ifumdmdkd nrcdkfzdmd.
Inkstruiifùk ma ra`difnkas malnirä-tfids fki`uyaktas.
Ajarififn ma `d ifumdmdkìd ditfvd.Masdrrn``n snifd` sustaktde`a y sns-takfe`a.Fkiralaktn ma d idpdifmdm ma castfùkma `d inlukfmdm.
Uaspatn d `ds präitfids snifd`as mfvar-sds maktrn ma` ldrin ma rabarakifd ma
Ydearaslu`tfmfsif-p`fkdrfns
Yurcak ma `ds axpaitdtfvds pdrd idmdifi`n y nrfaktdk `d diifùk amuidtfvd
¾Iuä` as `d astruiturd ma` Yfstald Fktarditfvn>
@d astruiturd ma` sfstald fktarditfvn ]rdksbnrlalns Amuidkmn tfaka uk mfsa
iurrfiu`dr eäsfin:
Astäkmdras ma inlpatakifds eäsfidrtfiu`dmns ink ns inlpnkaktas iu`turd ifumdmdkd y lu`tfætkfidmasdrrn``n huldkn ak inlukfmdm
Inkiaptud`fzdifnkas defartds d inkbrnktdifùk, d` dkä`fsfs irìtfin,lfrdmds sfstælfids fktacrdmnrds, inllamfdmnrds aktra a` inkniflfakintfmfdkn y a` inkniflfaktn ifaktìbfi
Lalnrfd hfstùrfid, lusfid` y `ftardrUftns y bastfvfmdmas.Uasfckfbfidifùk ma `d hfstnrfd.
Diifnkas dbfrldtfvds pdrd ds mfvarsatkfds.
Iu`turd ma `ds mfvarsds atkfds.
Maraihns y maearas ifumdmdkns.
Dpnrtas ma `d lujar ak `d iu`turd
Rd`nras malnirätfins y vfmd inmfdkd.
Astruiturd ma` Astdmn
_rnyaitns inlukftdrfns, ma fktacifùk snifd`, fkmfvfmud`as n in`aitfvn
Ditfvfmdmas y diifnkas ak a` iurrìi`n ink edsa ak `ns inkniflfaktnsinkiaptud`fzdifnkas trdtdmns ak ärads talätfids.
Uab`axfùk snera ds präitfids snifdintfmfdkds masma `ds kuavds inkia
Inkiaptud`as (sdear: ra`difnkinlpdrdr, mfvarsfbfidr, mfstfkcufr),
prniamflfaktn (hdiar, dp`fidr, lardr y idlefdr), y ma ditftum (sar, dslfr, maifmfr, irftfidr, diaptdr y kac
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A` sfstald fktarditfvn ]rdksbnrlalns Amuidkmn as uk sfstald defartn, uk sfstaldefartn ak ukd ra`difùk ma fktaridlefn inkstdkta ink a` inktaxtn mnkma sflp`alaktd. Dmaläs, as uk sfstald inlp`ajn, yd qua sus mfvarsns inlpnkaktad` fktarditudr aktra sì y ink a` inktaxtn sa lnmfbfidk y prnmuiak kuavds ra`difnka
@ns suesfstalds qua inkbnrldk a` sfstald fktarditfvn snk:
4. Yfstald ma amuidifùk bnrld` ink ukd ram ma ra`difnkas ak idmd sfstalracfnkd` amuidtfvn y ak a` sfstald kdifnkd` ma amuidifùk.
5. Yfstald ma pdrtfifpdifùk ditfvd ak a` inktaxtn ink ukd ram ma ra`difnkfktrdbdlf`fdr, inlukftdrfd, racfnkd`, kdifnkd` a fktarkdifnkd`.
9. Yfstald ma lamfdifnkas mfmäitfids, ink `ns sfcufaktas suesfstalds:
Lamfdifnkas ma fktardiifùk: ns mniaktas ]rdksbnrldmnras n ]rdksbnrldmnrdastumfdktas y sus inlukfmdmas, denrmdk ns inktakfmns a fktarditúdk ink a``nbrakta d su rad`fmdm, pdrd cakardr fmads y diifnkas qua parlftdk trdksbnrlpnsftfvdlakta su aktnrkn, lfaktrds inktfkúdk dprakmfakmn.
Lamfdifnkas mfmäitfids flprasds: `ds iud`as parlftak cakardr uk aktnrkasirftn y bnlaktdr `d `aiturd, ink a` bfk ma prnlnvar `d iu`turd asirftd ak s
vfmd intfmfdkd y `d ma su bdlf`fd, murdkta `d amuidifùk eäsfid y lamfd.
Lamfdifnkas fktarditfvds: a` inlputdmnr, a` ta`avfsnr y a` ldtarfd` dumfnvfsud`fktarditfvn, kns parlftak takar kuavds mflaksfnkas ma` inkniflfaktn, bdif`ftd`ns prniasns ma destrdiifùk y `ns fki`uya inln saras ditfvns ak `d ifeariu`tuy a` sfc`n XXF.
=. Yfstald ma inlukfidifùk a fkvastfcdifùk pdrd ratrnd`flaktdr tnmns `n
¾Iuä`as snk `ds idrditarìstfids cakard`as ma` sfstaldfktarditfvn ]rdksbnrlalns Amuidkmn>
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• Inlprakmn qua ak uk Astdmn ma Maraihn ds
parsnkds pnmalns pdrtfifpdr ak d iradifùk
n trdksbnrldifùk ma ds ayas y qua æstds sa
dp`fidk d tnmns y tnmds pnr fcud`.
• Inknzin `ns prfkifpfns eäsfins ma` Maraihn
Fktarkdifnkd` Huldkftdrfn (pnr ajalp`n, `d
prntaiifùk d d snifamdm ifvf` ak uk inkb`fitn
drldmn).
• Dkd`fzn irìtfidlakta a` saktfmn ma `ds `ayasy inlprakmn `d flpnrtdkifd ma iulp`fr`ds,
dsì kn inlpdrtd d`cukd ma a``ds.
• Dkd`fzn irìtfidlakta y maedtn ink drculak-
tns y avfmakifds snera haihns niurrfmns d
kfva` nid`, kdifnkd` y lukmfd`, y inlprakmn
`ds inksaiuakifds qua æstns puamak takar
snera lf prnpfd vfmd.
• Axprasn alpdtìd dkta crupns n parsnkds
iuyns maraihns hdk sfmn vu`kardmns (pnrajalp`n ak sftudifnkas ma masp`dzdlfaktn) y
prnpnkcn diifnkas sn`fmdrfds pdrd ink a``ns.
• _drtfifpn ak ldkfbastdifnkas pdiìbfids ma
raihdzn n sn`fmdrfmdm dkta sftudifnkas ma
masvaktdjd snifd`, ainkùlfid n ma sd`um qua
vfva `d cakta ma lf racfùk n lf pdìs.
• _drtfifpn ak fkfifdtfvds pn`ìtfids malnirätfids
ak lf lamfn asin`dr n `nid`fmdm.
• Inlprakmn quæ as uk efak púe`fin y pdrtf-
ifpn ak diifnkas qua va`dk pnr su euak usn,
tdktn ak d inlukfmdm asin`dr, inln ak lf
lukfifpfn.
• Inlprakmn qua iudkmn sa ditúd ak bnrld
inrruptd y sa usdk `ns efakas púe`fins pdrd
eakabfifn parsnkd`, sa dbaitdk tnmns `ns
lfalerns ma d snifamdm.
• Inkstruyn ukd pnsfifùk irìtfid brakta d `ds sftud
ifnkas ma mfsirflfkdifùk y axi`usfùk snifd` qua ra
su`tdk ma ds ra`difnkas masfcud`as aktra parsnkds
iu`turds y kdifnkas.
• Uainknzin `ds sftudifnkas ma mfsirflfkdifùk y
axi`usfùk läs dcumds qua sa prasaktdk dhnrd
n sa prasaktdrnk ak a` pdsdmn, tdktn ak a` nrmak
kdifnkd` inln ak a` fktarkdifnkd`7 `ds ra`difnkn
ink `ds mfsirflfkdifnkas qua nesarvn ak lf vfmd
intfmfdkd.
• Inlprakmn qua a` raspatn pnr `d mfbarakifd kn
sfckfbfid diaptdr qua ntrds parsnkds n crupns
vu`karak maraihns huldkns n knrlds inkstftu
ifnkd`as.
• Fmaktfbfin prajufifns, astarantfpns y alnifnkas qua
la mfbfiu`tdk saktfr alpdtìd pnr d`cukds parsnkds
n crupns y axp`nrn idlfkns pdrd supardr`ns.
• Fmaktfbfin y dkd`fzn mf`alds ma `d vfmd ak `ns qua`ns vd`nras ma mfstfktds iu`turds n crupns snifd`as
aktrdk ak inkb`fitn y axp`nrn mfstfktds npifnkas ma
sn`uifùk, inksfmardkmn sus dspaitns pnsftfvns y
kacdtfvns.
• Drculaktn y maedtn mf`alds ma d vfmd ak ns qua
`ns vd`nras ma mfstfktds iu`turds n crupns snifd`as
aktrdk ak inkb`fitn7 rainknzin `ns lajnras drcu
laktns, dsì kn infkifmdk ink `ns lìns.
Inlpatakifds Ifumdmdkds, Lfkfstarfn ma Amuidifùk Kdifnkd`
_drtfifpdifùk y raspnksdef`fmdmmalnirätfid
_`urd`fmdm, fmaktfmdm y vd`nrdifùkma `ds mfbarakifds
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_drtfifpn inkstruitfvdlakta ak fkfifdtfvds n prnyaitns d bdvnr ma `d kn-vfn`akifd ak a` kfva`
`nid` n c`ned`.
• Inktrfeuyn d qua `ns inkb`fitns aktra parsnkds y aktra crupns sa ldkajak ma ldkard
pdiìbfid y inkstruitfvd lamfdkta `d dp`fidifùk ma astrdtacfds edsdmds ak a` mfä`ncn y `d
kacnifdifùk.
• Qtf`fzn mfstfktds bnrlds ma axprasfùk pdrd prnlnvar y mabakmar `ns maraihns huldkns ak
lf inktaxtn asin`dr y inlukftdrfn.
• Dkd`fzn irìtfidlakta `ds maifsfnkas, diifnkas u nlfsfnkas qua sa tnldk ak a` äleftn
kdifnkd` n fktarkdifnkd` y qua puamak cakardr inkb`fitns n dbaitdr ns maraihns huldkns.
• Dkd`fzn irìtfidlakta `d sftudifùk ma `ns maraihns huldkns ak In`nlefd y ak a` lukmn
y prnpnkcn d`tarkdtfvds pdrd su prnlnifùk y mabaksd.
• Ldkfbfastn fkmfckdifùk (mn`nr, rdefd, raihdzn) ma ldkard pdiìbfid dkta a` subrflfaktn ma
crupns n kdifnkas qua astäk fkvn`uirdmds ak inkbrnktdifnkas vfn`aktds.
• Rd`nrn pnsftfvdlakta `ds knrlds inkstftuifnkd`as qua hdiak pnsfe`a `d prasarvdifùk ma
`ds mfbarakifds iu`turd`as y pn`ìtfids, y qua racu`dk kuastrd inkvfvakifd.
• Inlprakmn qua, pdrd cdrdktfzdr `d inkvfvakifd, a` Astdmn maea inktdr ink a` lnknpn`fn
ma d dmlfkfstrdifùk ma justfifd y ma` usn ma d buarzd, y qua d snifamdm ifvf` maea hdiar`a
sacuflfaktn irìtfin, pdrd avftdr deusns.
• Inknzin ds fkstdkifds y sæ usdr ns laidkfslns jurìmfins nrmfkdrfns y d`tarkdtfvns pdrd d
rasn`uifùk pdiìbfid ma inkb`fitns: justfifd nrmfkdrfd, juaias ma pdz, iaktrns ma inkif`fdifùk,
inlfsdrìds ma bdlf`fd7 kacnifdifùk, lamfdifùk, dreftrdlaktn.
• Fmaktfbfin mf`alds ma `d vfmd ak `ds qua aktrdk ak inkb`fitn a` efak cakard` y a` efak
pdrtfiu`dr7 dkd`fzn npifnkas ma sn`uifùk, inksfmardkmn sus dspaitns pnsftfvns y kacdtfvns.
• Drculaktn y maedtn snera mf`alds ma d vfmd ak `ns qua aktrdk ak inkb`fitn a` efak cakard`
y a` efak pdrtfiu`dr, rainknifakmn `ns lajnras drculaktns, dsì sadk mfstfktns d `ns lìns.
• Inknzin y raspatn ds knrlds ma träksftn.
• Inlprakmn `d flpnrtdkifd ma `d mabaksd ma` lamfn dlefakta, tdktn ak a` kfva` `nid`
inln c`ned`, y pdrtfifpn ak fkfifdtfvds d su bdvnr.
Inlpatakifds Ifumdmdkds, Lfkfstarfn ma Amuidifùk Kdifnkd`(inktfkudifùk)
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Inlpatakifds `denrd`as masdrrn``dmds ak `ns prniasnsma trdedjn in`aitfvn a fkmfvfmud`.
• Uainknzin `ds pnsfe`as bnrlds ma akbraktdr ukd sftudifùk.• Ya`aiifnkn ukd ma `ds bnrlds ma ditudr pnsfe`as.• Dsuln ds inksaiuakifds ma lfs maifsfnkas.
• Nesarvn ukd sftudifùk iaridkd d lf aktnrkn (lf idsd, lf edrrfn, lf in`acfnracfstrn fkbnrldifùk pdrd masirfefr`d.
• Dkd`fzn `ds sftudifnkas masma mfstfktns puktn ma vfstd (lfs pdmras, lfs dlfcnparsnkds inknifmds, aktra ntrds).
• Fmaktfbfin `ns inlpnrtdlfaktns dprnpfdmns pdrd idmd sftudifùk (bdlf`fdr, asin`ink pdras).
• Iulp`n `ds knrlds ma inlpnrtdlfaktn mabfkfmds ak uk aspdifn mdmn.
• Uainknzin lfs hdef`fmdmas, mastrazds y td`aktns.• Yuparn lfs maef`fmdmas.• ]akcn ak iuaktd a` flpditn ma lfs alnifnkas y su ldkajn ak lf ra`difùk i
ntrns.
• Uad`fzn lfs fktarvakifnkas raspatdkmn a` nrmak ma `d pd`derd pravfdlakdinrmdmn.
• Axprasn lfs fmads ink i`drfmdm.
• Masdrrn``n tdrads y diifnkas ink ntrns (pdmras, pdras, inknifmns).• Dpnrtn lfs raiursns pdrd d rad`fzdifùk ma tdrads in`aitfvds.
• Cakarn ra`difnkas ma inkbfdkzd ink ntrns (pdras).• Uainknzin ds bnrtd`azds y hdef`fmdmas ma `ns ntrns (bdlf`fdras, pdras).
• Axprasn lfs prnpfns fktarasas y lntfvdifnkas.• Eusin bnrlds ma rasn`var `ns inkb`fitns qua akbraktn ak lf aktnrkn iaridkn
• Fmaktfbfin `d fkbnrldifùk raquarfmd pdrd masdrrn``dr ukd tdrad n ditfvfmdm.• Uain`aitn mdtns ma sftudifnkas iaridkds d lf aktnrkn (lf idsd, lf edrrfn,
in`acfn).
• Eusin lajnrdr lf bnrld ma ra`difnkdrla ink ntrns ink edsa ak sus dpraiifnkas.
• Ya`aiifnkn ns ldtarfd`as qua raqufarn pdrd a` masdrrn``n ma ukd tdrad n diifù• Avftn a` masparmfifn ma `ns ldtarfd`as qua astäk d lf d`ramamnr (lf idsd,
sd`ùk ma i`dsas, `denrdtnrfns, td``aras, aktra ntrns).
• Fmaktfbfin `ds tdrads y diifnkas ak `ds qua `ns ntrns (pdmras, pdras, mniaktasnk lajnras qua yn.
• Masdrrn``n diifnkas pdrd lajnrdr inktfkudlakta ak mfstfktns dspaitns ma vfmd ink edsa ak `n qua dprakmn ma `ns maläs.
• Uainknzin `ns prne`alds qua surcak ma` usn y mfspnsfifùk ma ds mfstfktds i`dsma raiursns ma lf aktnrkn iaridkn (lf idsd, lf edrrfn, lf in`acfn)
• Ldktakcn nrmakdmns y flpfns lf sftfn ma astumfn y lfs flp`alaktns parsnkd`a
• Uainknzin `ds kaiasfmdmas ma lf aktnrkn iaridkn (lf idsd, lf edrrfn, in`acfn).
• Fkvaktn sn`uifnkas iradtfvds pdrd sdtfsbdiar `ds kaiasfmdmas mataitdmds
]fpn mainlpatakifdInlpatakifds
Fkta`aitud`as
_arsnkd`as
Fktarparsnkd`as
Nrcdkfzdifnkd`
Alprasdrfd`asy pdrd a`
]nldma maifsfnkas
Iradtfvfmdm
Nrfaktdifùkætfid
Mnlfkfnparsnkd`
Inlukfidifùk
]rdedjnak aqufpn
@fmardzcn
Ldkajnma inkb`fitns
Castfùkma `d
fkbnrldifùk
Nrfaktdifùkd` sarvfifn
Castfùky ldkajn
ma raiursns
Uabarakifdifùkinlpatftfvd
Uaspnksdef`fmdmdlefaktd`
Fmaktfbfidifùk manpnrtukfmdmas pdrdiradr alprasds n
Yueprniasns
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426Ifakifds Kdturd`as
Inktakfmn
49@akcudja y Inlukfidifùk
1?=Ldtalätfids
591Tuìlfid
982Bìsfid
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Lusan Inluktdrfn ma Cudfkìd.J_C
B n t n d r i h f v n
] r d k s b n r l a l n s
Lùmu`n fktacrdmn pdrd ifi`n 1
]rdksbnrlalns Amuidkmn Ärad ma @akcudjay Inlukfidifùk
4?
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Astäkmdras eäsfins ma inlpatakifds ak @akcudja y Inlukfidifùk
_rnmuiifùktaxtud`
Inlpraksfùk afktarpratdifùktaxtud`
• Inlprakmn a` vd`nr ma` `akcudja ak `nsprniasns ma inkstruiifùk ma` inknif-lfaktn.
• Masdrrn``n prniasns ma dutninktrn` y in-rraiifùk `fkcðìstfid ak lf prnmuiifùk mataxtns nrd`as y asirftns.
• Idrditarfzn y utf`fzn astrdtacfds mas-irfptfvds, axp`fidtfvds y dkd`ùcfids ak lf
prnmuiifùk ma taxtns nrd`as y asirftns.• Avfmakifn ak lfs prnmuiifnkas taxtud`asa` inkniflfaktn ma `ns mfbaraktas kfva`asma `d `akcud y a` inktrn` snera a` usn quahdcn ma a``ns ak inktaxtns inlukfidtfvns.
• A`denrn hfpùtasfs ma fktarpratdifùk dtak-mfakmn d `d fktakifùk inlukfidtfvd y d`saktfmn c`ned` ma` taxtn qua `an.
• Ua`difnkn a` sfckfbfidmn ma `ns taxtns qua
`an ink ns inktaxtns snifd`as, iu`turd`as ypn`ìtfins ak `ns iud`as sa hdk prnmuifmn.• Mfsaôn uk asquald ma fktarpratdifùk,
takfakmn ak iuaktd d` tfpn ma taxtn,tald, fktar`niutnr a fktakifùk inlukf-idtfvd.
• Dsuln ukd ditftum irìtfid brakta d `nstaxtns qua `an y a`denrn, y brakta d ntrnstfpns ma taxtn: axp`fidtfvns, masirfptfvns ykdrrdtfvns.
• Inlprakmn ak `ns taxtns qua `an `dsmflaksfnkas ætfids, astætfids, bf`nsùbfids,aktra ntrds, qua sa avfmakifdk ak a``ns.
• Inlpdrn taxtns ma mfvarsns dutnras, ta-lds, æpnids y iu`turds, y utf`fzn raiursnsma `d tanrìd `ftardrfd pdrd akrfquaiar sufktarpratdifùk.
• Inlpdrn taxtns ma mfvarsns dutnras, ta-lds æpnids y iu`turds, y utf`fzn raiursns
• _rnmuzin taxtns drculak-tdtfvns qua avfmakifdk lfinkniflfaktn ma d akcudy a` inktrn` snera a` usnqua hdcn ma a``d ak ink-
taxtns inlukfidtfvns nrd`asy asirftns.
• Inlprakmn a fktarpratntaxtns ink ditftum irìtfid yidpdifmdm drculaktdtfvd.
• Dkd`fzn irìtfid y iradtfvd-lakta mfbaraktas ldkf-bastdifnkas `ftardrfds ma`inktaxtn ukfvarsd`.
Bditnrasma nrcdkfzdifùk
Inlpatakifds Yueprniasns
¾D quæ quaralns `acdr> ¾Iùln maluastrn n dprakmfmn>
@ftardturd
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44
Astäkmdras eäsfins ma inlpatakifds ak @akcudja y Inlukfidifùk
Bditnrasma nrcdkfzdifùk
Inlpatakifds Yueprniasns
¾D quæ quaralns `acdr> ¾Iùln maluastrn n dprakmfmn>
ma `d tanrìd `ftardrfd pdrd akrfquaiar sufktarpratdifùk.
• @an taxtns `ftardrfns ma mfvarsd ìkmn`acækarn, talätfid y nrfcak.
• Ak nerds ma d ftardturd ukfvarsd`, fmaktf-bfin a` akcudja, ds idrditarìstfids bnrld-`as, `ds æpnids y `ds asiua`ds, `ns astf`ns,`ds takmakifds, ds talätfids, ns cækarns
y `ns dutnras, aktra ntrns dspaitns.
• Fkbfarn `d flp`fidifùk ma `ns lamfns mainlukfidifùk ldsfvd ak `d inkbnrld-ifùk ma ns inktaxtns snifd`as, iu`turd`as,pn`ìtfins, ati., ma` pdìs.
• Dkd`fzn ns laidkfslns fman`ùcfins quasueydiak ak d astruiturd ma ns lamfnsma fkbnrldifùk ldsfvd.
• Dsuln ukd pnsfifùk irìtfid brakta d `ns
a`alaktns fman`ùcfins prasaktas ak asnslamfns, y dkd`fzn su fkifmakifd ak `dsnifamdm ditud`.
• Axp`fin iùln `ns iùmfcns vared`as y knvared`as sa drtfiu`dk pdrd cakardr saktfmnak nerds ifkaldtncräbfids, idkifnkas yid`fcrdlds, aktra ntrds.
• _rnmuzin taxtns, alp`adkmn `akcudjavared` n kn vared`, pdrd axpnkar lfsfmads n pdrd rairadr rad`fmdmas, inksaktfmn irìtfin.
• Uaspatn `d mfvarsfmdm ma irftarfns y pn-sfifnkas fman`ùcfids qua surcak ak `nscrupns huldkns.
• Qtf`fzn a` mfä`ncn y `d drculaktdifùkpdrd supardr akbraktdlfaktns y pnsfifn-kas dktdcùkfids.
• Fktarpratn ak bnrld irftfid`d fkbnrldifùk mfbukmfmdpnr `ns lamfns ma inlukf-idifùk ldsfvd.
• Uatnln irìtfidlakta `ns`akcudjas kn vared`as pdrdmasdrrn``dr prniasns inlu-kfidtfvns fktakifnkdmns.
• Axprasn raspatn pnr `d mf-varsfmdm iu`turd` y snifd` ma`lukmn inktalpnräkan, ak`ds sftudifnkas inlukfidtf-vds ak `ds qua fktarvakcn.
@ftardturd
Lamfns mainlukfidifùky ntrnssfstaldssfleù`fins
Ætfid ma `dinlukfidifùk
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Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkas ma` `akcudja 43
Yasfùk 4. A` iùmfcn `fkcuìstfin 43 Yasfùk 5. A` maedta 51 Yasfùk 9. @ds idrtds 9? Yasfùk =. A` fkbnrla 93 Yasfùk 1. A` iuaktn y sus nrìcakas =5 Yasfùk 2. Ldkns d `d nerd 15
Qkfmdm 5. A` pfa ma bntn: d trdkslfsfùk ma `d fkbnrldifùky `ns sfstalds sfleù`fins 1=
Yasfùk 3. _fa ma bntn y astruiturd ma` taxtn asirftn 1= Yasfùk 8. A` pdka` y `d aktravfstd 2= Yasfùk 6. @d `ìrfid vdkcudrmfstd 31 Yasfùk 4?. Ldkns d `d nerd 89
Qkfmdm 9. Inharakifd, inhasfùk vared` y inkinrmdkifd `fkcðìstfid 8=
Yasfùk 44. Inharakifd, inhasfùk vared` y inkinrmdkifd `fkcðìstfid 8= Yasfùk 45. A` salfkdrfn 65 Yasfùk 49. @d kntfifd 68 Yasfùk 4=. A` aksdyn `ftardrfn 4?3 Yasfùk 41. Ldkns d `d nerd 443
Qkfmdm =. Yalfùtfid ma` ifearaspdifn: fktakifnkas inlukfidtfvds,vdrfds bnrlds ma axprasfùk 446
Yasfùk 42. Yalfùtfid ma` ifearaspdifn y taxtn `ftardrfn 446 Yasfùk 43. Lnkù`ncn y sn`f`nqufn 49= Yasfùk 48. Cufùk 4=5 Yasfùk 46. @d æpfid 41?
Ìkm fia
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A iùmfcn fkcðìstfin
Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja
Yasfùk
4
A` aspìrftu ma fkvastfcdifùk kn tfaka `ìlftas. Ak `ns Astdmns Qkfmns yak Aurnpd hdk masiuefartn d ú`tflds baihds qua axfsta ukd aspaifa ma
lnkns hfspdkndlarfidkns idpdias ma axprasdrsa pnr asirftn, ræp`fidsqufzä ma` lnkn mf`fcakta qua d buarzd ma tai`adr ukd läqufkd tarlfkdpnr asirfefr ma kuavn, dzdrnsdlakta, `ns snkatns ma Yhdgaspadra. ]d`
insd, inln as kdturd`, ``akd d astds euakds caktasma dsnlern, y kn bd`td qufak trdmuzid kuastrns
`ferns, kf, luihn lakns, nifnsns qua `nsinlprak, inln dktas inlprdedk ds
ideaiftds ramuifmds ma `ns jìedrns.
Hdia läs ma iudtrn sfc`ns quabrdy Edrtn`nlæ ma ds Idsds pumn
inkvakiar d `ns aurnpans maqua ærdlns huldkns y
ma qua takìdlns ukd`ld pnrqua kns
raìdlns7 dhnrd
Majdr ma sar lnkn Ducustn Lnktarrnsn
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qufarak inkvakiarsa ma `nlfsln pnrqua asirfeflns.Maifr iùmfcn as hde`dr ma ukcrupn ma a`alaktns (snknrnsn vfsud`as), qua d` inlef-kdrsa parlftak `d inlukfidifùk aktra `ns hnleras. _arn a` iùmfcn`fkcðìstfin as d suld ma vnide`ns n ukfmdmas snknrds qua fktacrdmds mamfbarakta ldkard, parlftak iradr ukd fmad n ukd nrdifùk ink saktfmninlp`atn. @d dusakifd ma asta iùmfcn, qua maea sar rainknifmn pnralfsnr y raiaptnr, brditurdrìd `d inlukfidifùk y dku`drìd `d pnsfef`fmdmma aktakmar asd fmad u nrdifùk d `ds iud`as kns rabarflns.
Ak ntrds pd`derds, `d `akcud as a` iùmfcn `fkcðìstfin qua parlfta main-mfbfidr uk laksdja7 as a` sfstald ma sfckns qua sa dprakmak ak sus mns
bnrlds: nrd` y asirftd.
_nr supuastn, a` iùmfcn astä sujatn d ukds rac`ds y d ukd nrcdkfzdifùk.Idmd mfraitrfz ldrid sus prnpfds idrditarìstfids.
@ds mfbfiu`tdmas ink ds iud`as sa akiuaktrdk ds parsnkds iudkmn usdk a`iùmfcn asirftn n a` iùmfcn nrd`, inksfstak ak iraar qua ma `d bnrld inlnsa hde`d sa asirfea7 qua `d suprasfùk ma uk inkaitnr kn d`tard a` sfckfbf-
idmn ma `n qua sa qufara axprasdr7 qua `d inkstruiifùk ma ukd nrdifùkkn axfca uk nrmak ak `ns vnide`ns, sacúk `d bukifùk qua astns iulp`dk.
Aktakmar a` iùmfcn `fkcðìstfin kn as tdk mfspakmfnsn, sù`n raqufaradtakifùk, inlpraksfùk ma `ds rac`ds y dp`fidifùk, y pnr akma, präitfidak su ldkajn, inkniflfaktn. Tufak kn inknia `d harrdlfaktd ink `diud` trdedjd, mfbìif`lakta pnmrä netakar uk prnmuitn ma id`fmdm. _nrasn takcd ak iuaktd:
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• Uaqufara a` ldkajn ma rac`ds nrtncräbfids.
• Qtf`fzd uk `akcudja a`denrdmn.
• Axfca uk euak usn ma `ns sfckns ma puktudifùk, pnrqua uk sfcknld` in`nidmn puama d`tardr pnr inlp`atn a` saktfmn ma `d nrdifùk.
• Maldkmd i`drfmdm y praifsfùk ak `ds fmads, puastn qua kn tfaka ukfktar`niutnr fklamfdtn qua a rai`dla ukd axp`fidifùk läs inkiratd.
• _arlfta raa`denrdr `ds nrdifnkas dktas ma qua ``acuak d` raiaptnr,pdrd nbraiar uk laksdja astætfidlakta dtrditfvn.
• Yf efak, kn praifsd rac`ds ma nrtncrdbìd, sì axfca ifartd dtakifùk ak`d inkstruiifùk ma` `akcudja. Qk `akcudja ld` utf`fzdmn inrrnlpa`d `akcud.
• Kn utf`fzd sfckns ma puktudifùk, parn ukd ld`d drtfiu`difùk n usnma` vnide`n, tdlefæk puama d`tardr a` saktfmn ma `n inlukfidmn.
•
_arlfta d fktardiifùk aktra alfsnr y raiaptnr, bdif`ftdkmn d dlp`ftumma` mfsiursn.
• Kn axfca ukd a`denrdifùk ma` `æxfin y pnr astd rdzùk, md idefmd d``akcudja ma crupn, läs inknifmn inln jarcds.
Iùmfcn asirftn
Iùmfcn nrd`
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4
_nr sar `d `akcud uk sfstald ma sfckns, as flpnrtdkta inkniar `d mfvfsfùkqua `ns aspaifd`fstds hdk haihn snera a``ns. @d tanrìd läs diaptdmd as `dprnpuastd pnr Barmfkdkm ma Ydussura (pdmra ma d fkcðìstfid), qufak d` hd-
e`dr ma` sfckn fkcðìstfin, mfstfkcua ak æ`, mns kfva`as, ukn as a` sfckfbfidmn,d` iud` dtrfeuflns a` inkiaptn qua takalns snera uk a`alaktn7 y a` ntrn asa` sfckfbfidkta, as maifr, d fldcak qua takalns ma asa a`alaktn. Ajalp`n:uk jdrrùk qua puama sar nvd`dmn, ifriu`dr n mabnrla.
@d flpnrtdkifd ma astns mns inlpnkaktas sa maea d su idräitar inkvak-ifnkd` y d su idpdifmdm ma prasaktdr, trds `d avn`uifùk ma` tfalpn, ukdlatdlnrbnsfs. Yfk mumd, a` iùmfcn fkcðìstfin sfalpra sarä a` lfsln, parn a`
sfckfbfidmn y a` sfckfbfidkta kn, pnrqua vdrìdk ma diuarmn ink d avn`uifùkma `d `akcud y ma` fmfnld.
Uaspnkmd `ds sfcufaktas pracuktds:
4. ¾D quæ sa maea qua `ds pd`derds Astdmns Qkfmns, Aurnpd, Yhdgaspadra, Edrtn`nlæ y Idsds sa asirfedk ink ldyúsiu`ds>
5. ¾Ak iuäktns pärrdbns astä mfvfmfmn a` taxtn ma Lnktarrnsn> ¾Iuäktds nrdifnkarabuarzdk `d fmad qua axprasd>
9. @ad kuavdlakta a` taxtn ma fktrnmuiifùk y mamuzid d ra`difùk qua axfsta akt`d fldcak ma `ns pdìsas saôd`dmns y a` knlera ma Edrtn`nlæ ma `ds Idsds. Kn`vfma a` inktaxtn ak a` iud` astäk uefidmns.
=. Ink sus prnpfds pd`derds y ak bnrld asirftd, axpnkcd `d fmad qua Ducust
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5
Uaspnkmdk `ds sfcufaktas pracuktds:4. A` sfcufakta brdclaktn ma` fern A` drta ma dldr, ma Dkmræ Ldurnfs, bua fkta
ifnkd`lakta d`tardmn ak su puktudifùk y ak su nrtncrdbìd. Dmaläs, sa hsuprflfmn d`cukns inkaitnras n pd`derds, ink a` bfk ma qua ustamas nrcdkfia` saktfmn ma `d fmad qua a` dutnr qufsn trdkslftfr. Qk ld` usn ma` iùmf`fkcðìstfin, inln pnmräk inlprnedr, flpfma `d inlpraksfùk y a` p`diar `d `aiturd.
‐Ak a` nrfcak dlnr hdy uk ihnqua prnvnidmn pnr `ddmlfrdifùk, sad pnr d`cúk difmakta qua hd rava`dmnukd fkta`fcakifd n haihn uk masan kdiar ak d dusakifd,
a` sar dldmn sa inkvfarta ak uk mfns d` qua pnmalnsdmnrkdr ma tnmd `d parbaiifnkas. Asta trdedjn as `n quaYtakmhd` ``dld ‘`d irfstd`fzdifùk‖. _nr `d irfstd`fzdifùka` nejatn dldmn sa d``ä trdksbnrldmn7 ak uk sar mfba-rakta ma `n quæ as y suparfnr d æ` lfsln. _nr astn aspnr `n qua _rnust mfia qua a` dlnr as suejatfvn, y quadldlns kn d saras, rad`as sfkn d saras qua knsntrnsiradlns. Astn majd ma sar varmdm ak idsn ma ukd dmlf-
rdifùk `acìtfld. Astd ``dld kdifakta sa dpdcdrìd prnktnsf d`cúk snp`n ma aspardkzd, pnr `fcarn qua sad, kn `dradkfldsa. Qkd lfrdmd, ukd prasfùk ma `d ldkn, ukdraspuastd uk pnin vfvd `d astflu`dk ak sacufmd. _arnniurra tdlefæk qua d iartfmulera y d sacurfmdm ldtdka` saktflfaktn“.
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5. Qkd vaz nrcdkfzdmn a` dktarfnr brdclaktn, p`dktaakukd mfsiusfùk snera a` tald y axpnkcdk sus puktnsma vfstd ak uk maedta ak `d sfcufakta i`dsa.
9. Avd`úak `ns arrnras y `ns difartns qua tuvfarnk `nsntrns crupns ak a` ldkajn ma` iùmfcn `fkcðìstfin,y snifd`fiak ink tnmn a` iursn, sus inki`usfnkas.
=. Idmd lfalern ma` crupn maea asirfefr uk inlak-tdrfn kn ldynr ma 4? `ìkads, snera uk tald ma sufktaræs. Maspuæs, snifd`ìia`n aktra `ns lfalernsma` crupn pdrd sdidr `ds raspaitfvds inki`usfnkas.
Masdrrn``a ak su iudmarkn:
4. A` iùmfcn `fkcðìstfin bua tdk efak utf`fzdmn pnr Lnktarrnsn ak `d @ai-turd ma fktrnmuiifùk, qua pnr lamfn ma uk iuaktn erava a frùkfin,trdkslftfù ukd fmad d sus `aitnras. ¾Iuä` as asd fmad>
5. D pdrtfr ma `ns sfcufaktas vnide`ns, astruitura uk laksdja inharaktaqua puamd sarvfr inln mfsiusfùk: amuidifùk, masprakmfmn, lfamn,asi`dvns, vfmd, crdifds, masan, sdear, masiuefartn, laknr, crdmud`lakta,ldynr, mìd, irua`mdm, pdsfnkas.
9. Masma a` puktn ma vfstd fkcðìstfin, ¾quæ ra`difùk pnmrìd takar a` taxtnqua dided ma a`denrdr, ink `d `aiturd ma Ducustn Lnktarrnsn>
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=. D inktfkudifùk, akinktrdrä a` brdclaktn qua sa trdedjù ak d ditfvfmdmdktarfnr, tntd`lakta inrracfmn. Dkd`fia idmd ukd ma `ds nrdifnkas yaxp`fqua quæ pd`derds mfarnk ucdr d d astruiturdifùk ma d fmad7 quæ
lnknsì`dens diaktudrnk a` inktakfmn y iuä`as dmjatfvns dbfdkzdrnk`d axp`fidifùk ma` tald.
… Ma haihn a` pdpa` ma` dzdr as td`, qua as luy rdrn qua a` hnleray `d lujar puamdk a`acfr varmdmardlakta, y pnr uk ditn ma vn`uktdm
purd, dquæ` qua sarä su inlpdôarn ma vfmd.
Ak a` nrfcak ma tnmn dlnr hdy uk ihnqua prnvnidmn sad pnr `d dm-lfrdifùk, sad pnr d`cúk diifmakta qua hd rava`dmn ukd fkta`fcakifd nhaihn kdiar uk masan. Ak `d dusakifd, a` sar dldmn sa inkvfarta akuk mfns d` qua pnmalns dmnrkdr ma tnmds `ds parbaiifnkas. Asta trd-edjn as `n qua Ytakmhd` ``dld ‘`d irfstd`fzdifùk‖. _nr `d irfstd`fzdifùk a`nejatn dldmn sa hd``d trdksbnrldmn ak uk sar mfbarakta ma n qua as y
suparfnr d æ` lfsln. _nr astn as pnr `n qua _rnust mfia qua a` dlnr assuejatfvn, y qua dldlns, kn d saras rad`as, sfkn d saras qua knsntrnsiradlns. Astn majd ma sar varmdm ak idsn ma ukd dmlfrdifùk `acìtfld.Astd ``dld kdifakta sa dpdcdrìd prnktn sf d`cúk snp`n ma aspardkzd,pnr `fcarn qua sad, kn `d radkfldsa. Qkd lfrdmd, ukd prasfùk ma `dldkn, ukd raspuastd uk pnin vfvd d astflu`dk aksacufmd. _arn niurratdlefæk qua `d iartfmulera y `d sacurfmdm ldtdk a` saktflfaktn.
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Barmfkdkm ma Ydussura
A` sfc`n XX fkstdurd n qua sa maknlfkd d fkcðìstfidlnmarkd, iuyn bukmdmnr as sfk `ucdr d mumds, a``fkcðfstd sufzn, kdifmn ak Cfkaerd, Barmfkdkm maYdussura (4813-4649).
_drd Ydussura, a` idlpn ma d fkcðìstfid inlprakma tnmds dsldkfbastdifnkas ma` akcudja huldkn, tnmds ds bnrlds axprasf-
vds sfk mfsirflfkdr aktra euakns y ld`ns usns y sfk inksfmardr, a`crdmn ma ifvf`fzdifùk ma sus hde`dktas. @d tdrad ma d `fkcðìstfidas pnr `n tdktn, rad`fzdr `d masirfpifùk a hfstnrfd ma tnmds `ds`akcuds, akinktrdr `ns prfkifpfns cakard`as ma sus sfstalds y,bukmdlaktd`lakta, mas`fkmdrsa y mabfkfrsa a``d lfsld.
• @ùcfid sfleù`fid ma Ldkua` Cdrrfmn• Bukmdlaktns ma `fkcðìstfid ma U. Yflnka• @fkcðìstfid cakard` ma Barmfkdkm ma Ydussura
• @fkcðìstfid cakard` y dp`fidmd ma Ä. @ùpaz Cdriìd• Fktrnmuiifùk d `d `fkcðìstfid ma L. Barkäkmaz _æraz• Edsas pdrd a` astumfn ma` `akcudja ma A. Ldrtìkaz Ia`mräk• Inkniflfaktn y akcudja ma Äkca` @ùpaz Cdriìd y Eadtrfz
_dú`s Cd``drmn• @d sfktdxfs ma `ns ra`difnkdktas suprdnrdifnkd`as ma
I. Buaktas Unmrìcuaz
i ì r i u
` n m a
ait n r a s
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Nedld dbfrld qua d`cukns rulnrassnera æ` snk fksu`tdktas pdrd `ns lusu`ldkas Jfl Guhkhakk
As ukd erdsd qua Edrdig Nedld hd trdtdmn ma dpdcdr ukd y ntrd vaz,pdrd var`d drmar ma kuavn sfalpra: vìkiu`ns ink a` fs`dlfsln, rulnrasd`flaktdmns pnr bd`sds dsnifdifnkas a fksfkudifnkas.
Nedld y su idlpdôd radiifnkdrnk buartalakta astd saldkd iudkmnsa pue`fiù ak Fktarkat ukd bntn ma æ` ink uk dtuakmn trfed` snld`ì. V`ns a`ncfns qua raifefù a` mnlfkcn ma @nufs Bdrrdghdk, lfkfstrn ma `dsaitd Kdifùk ma Fs`dl, mfarnk `ucdr d fktarrncdktas ak a` maedta prasf-makifd` ma` ldrtas pnr `d kniha, y tdlefæk ak ukd raukfùk prfvdmd a`bfk ma saldkd ink ukns jumìns prnlfkaktas ma I`ava`dkm.
Ak a` maedta, Nedld rapftfù sus irìtfids snera `ns puktns ma vfstd maBdrrdghdk, qua hdk fki`ufmn kularnsns inlaktdrfns dktfsalftds. Viudkmn sa vfn prasfnkdmn, raihdzù a` raspd`mn ma Bdrrdghdk ak `dinktfakmd prasfmakifd`.
A maedta
Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja
Yasfùk
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B n t n s t n l d m d s m a S f g f p a m f d
A` sakdmnr fksfsta ak qua æ` as irfstfdkn, y qua sa aktracù d su idrcn ju-rdkmn snera d Efe`fd ma su bdlf`fd. _arn ak Fktarkat y d`cukns prncrdldsrdmfd`as, y ak ukd prasaktdifùk ma idlpdôd ma LiIdfk astd saldkd,
`n masirfeak bd`sdlakta inln uk lusu`läk ink turefns vìkiu`ns, yakbdtfzdk su sacukmn knlera, Hussafk, qua d` púe`fin `a raiuarmd a`ma` mfbuktn mfitdmnr ma Frdg.
‐Yf hdy d`cufak qua tnmdvìd astä inkbukmfmn ink `ns haihns, yn kukidha sfmn lusu`läk“, as mfjn Nedld d ns mfrfcaktas jumìns ak I`ava`dkm,sacúk ukd trdsirfpifùk ma `d sasfùk prfvdmd.
@d bntn ma Nedld ink su fkmulaktdrfd trfed` snld`ì, tnldmd pnr ukbntùcrdbn ma D_ murdkta ukd vfsftd ak a` 5??2 d` pdìs kdtfvn ma supdmra, rasurcfù pnr Fktarkat ak lamfn ma d`acdifnkas kn prnedmdsma qua `d astdedk ifriu`dkmn lfalerns ma `d idlpdôd ma Hf``dryI`fktnk. @d idkmfmdtd y sus dyumdktas mfiak qua kn hdk takfmn kdmdqua var ink asn, parn `d idlpdôd ma Nedld `ns diusd ma mamfidrsad ‐varcnkznsns y nbaksfvns fktaktns
ma fkmuifr talnr“.
A` ldrtas, a` idkmfmdtn rapue`fidkn Jnhk LiIdfk irftfiù ldridmdlaktaukds pd`derds ma fktrnmuiifùk quad`cufak utf`fzù d` prasaktdr`n pnr a`lnmn ak qua sa rabfrfarnk d Nedld.
A` prasaktdmnr Ef`` Iukkfkchdl sarabfrfù d` sakdmnr tras vaias inln‐Edrdig Hussafk Nedld“ y d` fktrn-muifr d LiIdfk fkmfiù qua Nedldard ‐uk pn`ìtfin lariakdrfn, astf`nIhfidcn“.
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A` maedta as ukd axpnsfifùk ma tasfs dktd-cùkfids diarid ma uk matarlfkdmn tald,as ukd inkstruiifùk ma drculaktns quasa vdk ma`fkadkmn y dbfdkzdkmn ak `d
lamfmd inln `ds pnsfifnkas ma `ns fk-vn`uirdmns puamak malnstrdrsa n pnr a`
inktrdrfn, marruledrsa iudkmn `d sn`fmaz ma`pnmar ma inkvfiifùk ma `ns alfsnras n `d i`drfmdm
ma jufifns as pnera y idrakta ma pasn.
A` maedta as ukd tæikfid qua sa axpdkma läs d``ä ma` aktnrkn didmælfin,
parn ak æ` as luy utf`fzdmd pdrd ajariftdr `d axprasfùk nrd` y asirftd ak `nsastumfdktas, dsì inln pdrd dyumdr`as d hf`vdkdr fmads ak bnrld inharakta,dlp`fdr su vnideu`drfn, masdrrn``dr su idpdifmdm drculaktdtfvd y bnlaktdra` trdedjn ma fkvastfcdifùk maktrn y buard ma` du`d.
As flpnsfe`a ascrflfr ukns puktns ma vfstd sfk uk dpnyn sarfn. _nr n tdktn,ukd fkvastfcdifùk jufifnsd as `d úkfid drld qua raspd`md `d fktarvakifùkma idmd pdrtfifpdkta.
_nr trdtdrsa ma ukd mfsiusfùk ma pnsfifnkas dktdcùkfids, as flpnrtdkta qua`ns pdrtfifpdktas dsuldk masma a` fkfifn ukd ditftum tn`ardkta y ldkajakukd lakta defartd qua parlftd snpasdr y diaptdr `ns a`alaktns ma jufifnqua a` ntrn hdyd axpuastn, sf astns snk sarfns y nejatfvns.
Ak tnmn maedta sa dspfrd ``acdr d ukd inki`usfùk. @d lamfdifùk ma uk
tariarn as i`dva pdrd su masdrrn``n y ma d``ì, `d a`aiifùk ma uk lnmardmnr,iuyd bukifùk inksfsta ak mdr `d pd`derd d `ns pdrtfifpdktas, id`ldr `ns äkf-lns iudkmn a``ns sa axd`tdk, ``avdr a` maedta pnr uk idlfkn qua pnsfef`ftaukd pnstarfnr inki`usfùk, ranrfaktdr a` maedta iudkmn tnla ntrn rulen.
]dlefæk maea inktalp`drsa `d pdrtfifpdifùk ma uk sairatdrfn pdrd quatnla kntd ma `n mfsiutfmn y sfrvd ma dpnyn d` lnmardmnr, iudkmn maedaxpnkar `d inki`usfùk d `d iud` ``acù a` maedta.
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Knrlds ak `d prapdrdifùk y rad`fzdifùk
Inln tnmd tæikfid, a` maedta axfca iulp`fr ifartds knrlds qua sa maeaktakar ak iuaktd:
• _uktud`fzdr a` tald qua sa vd d maedtfr.• Fkvastfcdr a` tald y prapdrdr ns snpnrtas pdrd mdr sn`fmaz d` mfsiursn.• Ya`aiifnkdr `d dyumds kaiasdrfds sf a` tald `n rai`dld (mfdpnsftfvds,
vfman eadl, ati.).• Avd`udr y takar i`drfmdm snera a` nejatfvn qua sa eusid ak a` maedta.• Astde`aiar `ds rac`ds qua racfräk a` maedta.•
Asincar uk lnmardmnr y uk sairatdrfn.• Nrcdkfzdr d `ns pdrtfifpdktas (aktra iudtrn y nihn parsnkds).• Yfkirnkfzdr a` tfalpn ma idmd fktarvakifùk d bfk ma hdiar aquftdtfvd
`d pdrtfifpdifùk.
_drd takar ak iuaktd
A` maedta kn as ukd puckd ak `d iud` sa `uihd pnr cdkdr `d edtd``d, tnmn `n
inktrdrfn, as ukd npnrtukfmdm pdrd inktrdpnkar inkiaptns y d`idkzdr ukdsn`uifùk n aspaiìbfidlakta, ukd inki`usfùk. _nr `n tdktn, as flpnrtdkta:
• Asiuihdr dktas ma maedtfr.• Yar inkiratn.• Kn inkvartfr `d fktarvakifùk ak uk lnkù`ncn.• _amfr `d pd`derd d` lnmardmnr.• Kn axd`tdrsa, dprakmar d asiuihdr y parlftfr d inki`usfùk ma d fmad.• Inkstrufr sus drculaktns y utf`fzdr ns snpnrtas iudkmn sad kaiasdrfn.• Kn utf`fzdr `d frnkìd pnrqua puama harfr susiaptfef`fmdmas y prnvnidr
uk akbraktdlfaktn.• Kn raedtfr ink drculaktns djakns d `d fmad qua sa astä p`dktadkmn.• Qtf`fzdr uk vnideu`drfn dmaiudmn d `ds ifriukstdkifds.• A`flfkdr a` `akcudja raeusidmn qua puamd mdr ntrn saktfmn d `ns
puktns ma vfstd n iradr dlefcðamdm.
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4. Asinjdk ukd ma ds sfcufaktas npifnkas, y nrcdkfiak uk maedta ak a` du`d ma i`ds
d. @ns iaktrns amuidtfvns maeak nrfaktdr d idrrard ma ns astumfdktas masa` sæptfln crdmn. _nr `n tdktn, sacúk `d `ìkad asincfmd (taikn`ùcfid, ifatìbfid, huldkfstd), d`cukds ldtarfds maeak a`flfkdrsa ma` prncrdld.
e. Maearìd sar ne`fcdtnrfd, ukd ldtarfd nrfaktdmd d` inkniflfaktn madcrfiu`turd.
i. D pdrtfr ma` crdmn mæifln, `ns astumfdktas maearìdk raifefr ukd i`dsa i
ækbdsfs ak a` trdedjn ldkud` (idrpfktarìd, d`edôf`arìd, iu`fkdrfd, ati.).
5. Ak suecrupns ma safs parsnkds, mfsiutdk sus npfkfnkas diarid ma ns inlaktdrma `d @aiturd ma fktrnmuiifùk.
9. @d lakifùk ma `ns jumìns ma I`ava`dkm, quæ ra`difùk tfaka ink `d sftudifaxpuastd ak a` taxtn ma Guhkhakk.
=. ¾Iuä`as snk sus pnsfifnkas diarid ma d bfcurd ma Nedld> _rasaktak pnr asir
`ds inki`usfnkas ma `ns iudtrn puktns.
4. A` drtìiu`n ma Jfl Guhkhakk prasaktd ukd sarfa ma fmads ink ra`difùk dditud` prasfmakta ma `ns Astdmns Qkfmns, Edrdig Nedld. Ak su maedtainln idkmfmdtn, Nedld sa mabfakma dkta ukd sarfa ma inlaktdrfns: ¾quædrculaktns sa axpnkak pdrd cakardr asta maedta>
5. ¾Tuæ prne`alätfid sa asinkma trds `d dbfrldifùk bntncräbfid ma Nedldink uk dtuakmn trfed` snld`ì>
9. ¾@ns inlaktdrfns prasaktdmns raspnkmak d ukd inktfakmd ad` y tn`ardkta=. ¾D quæ inki`usfùk n sn`uifùk ``acdrnk `ds pdrtas>
4
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Idrtd rabarakifd`
Ak `d idrtd, sa fki`uyak `ds idrtds nbfifd`as y `ds idrtds inlarifd`as. @d idrtd as mniulaktn ldastrn pdrd a` iud` maealns masdrrn``dr varsdtf`fmdm y dcf`fmdm, puasfk flpnrtdr prnbasfùk, nbfifn, mncld, rdzd, axtrdiifùk snifd`, inkmfifùk iu`turd` prabarakifds parsnkd`as, sarä sfalpra pdsn ne`fcdmn pdrd idsf tnmns `ns prniasn
A` dvdkia taikn`ùcfin hd idlefd-
mn a` saktfmn y a` inktakfmn ma`d idrtd. Hny ak mìd, `d mfkälfidma` `akcudja bærtf`, axueardkta yprùmfcn ak sustdktfvns, dmjatfvnsy dmvarefns qua idrditarfzded d didrtd, sa hd ramuifmn d n inkira-tn a flparsnkd` qua mfstfkcua d`d vfmd inktalpnräkad. Dsì puas,dktas sn`ìdlns maifr qua `d idrtdard vftd`, parn hny hde`dlns ma`d idrtd rabarakifd` y su idräitarflprasifkmfe`a.
@ds idrtds
Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja
Yasfùk
9
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_drd dprnpfdrkns ma `d astruiturd pramnlfkdkta ma ukd idrtd rabarakifd`, sfcdl`ds sfcufaktas sucarakifds:
FINK]AI suprflfù a` Dtk n Dtakifùk hdia ukns 4? dôns. Aksu ucdr, sa asirfea Jaba ma Yaiifùk, sf kn sa inknia a` knlerama` raspnksde`a.
BAMAUFIN LÆKMAZMaidkn ma HuldkfmdmasQKFRAUYFMDM JDRAUFDKDMfraiifùk inlp`atdEncntä, M.I.
YaônrBAMAUFIN LÆKMAZMaidkn ma HuldkfmdmasQKFRAUYFMDM DQ]ÙKNLD MA LÆXFINMfraiifùk inlp`atdLæxfin, M.B.
Mnitnr
4. Baihd. Maea fkmfidrsa prflarn `d ifumdm, sacufmd ma ukd inld y `uaa` mìd, a` las y a` dôn. Uainrmalns qua `ns dôns kn ``avdk puktn y q`d `atrd fkfifd` ma `ns lasas sa asirfea ak lfkúsiu`d.
5. Akideazdmns n mfrfcfmns. ]ìtu`n n mfckfmdm ak `d prflard `ìkad. Knleak `atrds ldyúsiu`ds. @uacn vfaka a` idrcn y knlera ma `d alprasdfkstftuifùk ak `atrds ldyúsiu`ds. Bfkd`fzd ink `d mfraiifùk inlp`atd y ntrn rakc`ùk, `d ifumdm ak ldyúsiu`d nrtncräbfid, sacufmd ma M.B. n Msacúk a` idsn. A` akideazdmn puama takar hdstd nihn `ìkads.
Ajalp`ns:
Ajalp`n: Ifumdm ma Læxfin, 42 ma ldrzn ma 5?4?.
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9. @ìkad ma aktrdmd n sd`umn. As npifnkd` y pnr `n tdktn, puama nlftfrsa.
=. _rflard `ìkad ma` iuarpn. Maea sd`umdr ak uk tnkn sakif``n y avftdr `
brdsas ma idjùk, pdrd avftdr a` mfstdkifdlfaktn ink a` mastfkdtdrfn y prnpifdr`a ifartd ratfiakifd pdrd `aar y inlprakmar a` rastn ma `d idrtd. Idmvaz qua sa mfspnkcd d asirfefr ukd idrtd, pfaksa ak a` mastfkdtdrfn y, mpakmfakmn ma qufæk sa trdta, derd a` taxtn ink ukd nrdifùk, uk sd`umn ukd d`usfùk qua sù`n takcdk qua var ink æ`. Astd inkmfifùk `a p`dktadsfkiard inrmfd`fmdm y praniupdifùk ma su pdrta hdifd æ`, n iud` ramukmdak eakabfifns d` lnlaktn ma aspardr rasu`tdmns snera a` bfk qua parsfcu
a` inktakfmn ma `d idrtd.
Ajalp`ns: Dpraifdmn saônr Ldkrfqua:
Dpraifdmd mnitnrd Barkdkmd: Uaspatdmd mnitnrd I`drd Fkæs:
Uaspatdmn mnitnr Rd`akifd:
Astfldmn saônr Dpa``fmn:
Ajalp`ns:
• _arlìtdla ba`fiftdr`n dktas qua kdmd, pnr su `úifmn mfsiursn…
• Kn sfk dktas axtakmar`a uk dbaitunsn sd`umn, qufarn p`dktadr`a…
• Dktas qua kdmd maen ba`fiftdr`n, trds hdear `aìmn su drtìiu`n…
1. Iuarpn. Maea astdr inlpuastn ma pärrdbns ma tras n iudtrn `ìkads pdqua `d idrtd sad aktakmfe`a räpfmd y i`drdlakta. @ns pärrdbns maeak nbraiar fmads inkifsds y mfraitds axpuastds ink ùcfid y inharakifd. Iudkmn inktakfmn ma ukd idrtd prasaktd mfvdcdifnkas, raftardifnkas n praäleu`n
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2. Ifarra n maspamfmd. D` fcud` qua a` sd`umn, a` ifarra maea sarsakif``n n brdtarkd` sacúk sad a` mastfkdtdrfn, y a` ulerd` ma `dbfrld puama nlftfrsa ak `ns idsns iudkmn sa bfkd`fzd ink ukdnrdifùk ma axpaitdtfvd inln: Tuamn d `d aspard ma sus crdtds
kntfifds n Ya maspfma ma ustam, masaäkmn`a ns lajnras rasu`tdmnsak a` prnyaitn qua alprakma.
_arn sf kn hdy asta tfpn ma ifarra, a` ulerd` puama sar: Inrmfd`-lakta7 Inrmfd` sd`umn7 Lf` crdifds7 Ma ldkard dtaktd7 Dtaktd-lakta, ati.
3. Bfrld. A` knlera maea asirfefrsa ak `d lfsld bnrld inln sa
asirfefù a` knlera ma` mastfkdtdrfn. Ak d ìkad sfcufakta, a` idrcnn kúlarn ma fmaktfbfidifùk, sf buara a` idsn.
Ajalp`ns:
… asparn qua `d prnpuastd sad ma su aktard sdtfsbdiifùk,
Amudrmn Idktf``n Mfraitnr ma prnyaitns
Inrmfd` sd`umn,
Dldmd Ä`vdraz Innrmfkdmnrd
Ajalp`n:
MDRFM LD]AN @NKMNÔNMfraitnr ma drtas
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Ma` asirftnr ihain Brdkz Gdbgd, takalns ukdvarmdmard cd`arìd ma idrtds aktra `ds iud`asastäk ds idrtds d su dlfcn Ldx Ernm, asirftdsmurdkta 5? dôns, masma 46?= d 465=. @dsidrtds d Lf`akd, ntrn `niudz tastflnkfn ma`dlnr púmfin qua aledrcù d Gdbgd murdktatnmd su vfmd, ma `d akbarlamdm pu`lnkdrqua `n lfkù, ma uk mfä`ncn diarid ma `dsftudifùk ainkùlfid, alnifnkd` y `denrd`tnrlaktnsd qua subrfù.
@d idrtd d` pdmra pnr su pdrta, as uk asirftninkbfmakifd`, mascdrrdmnr y `ftardrfdlaktapsfin`ùcfin, ak a` iud` Gdbgd `a masirfea dsu pdmra `d fkb`uakifd qua æsta ajarifù ak suidräitar. Ya trdtd ma uk mniulaktn qua kuk-id ``acù d ldkns ma` pdmra y inkstd ma ukds4?? päcfkds kdrrdmds ak uk astf`n flpaide`a.
Brdkz Gdbgd
B n t n s t n l d m d s m a S f g f p a m f d
rù d uk dlfcn qua lfaktrds asirfeìd, paksded qua asds idrtds pnmr``acdr d pue`fidrsa maspuæs ma su luarta.
• @ds idrtds ma Idlf``a I`duma`, flpnrtdkta asiu`tnrd, harldkd pnatd y mrdldturcn _du` I`duma` y akdlnrdmd ma` asiu`tnr DucuUnmfk. Astds idrtds buarnk asirftds masma a` ldkfinlfn ak mnkbua inkbfkdmd hdstd su luarta pnr su harldkn, y snk tastflnkfn `d súp`fid qua murdkta 9? dôns `a hfzn Idlf``a d _du`, sfk qua buaasiuihdmd jdläs. Idsf tnmd `d nerd ma Idlf``a bua mastrufmd pnr alfsld trds idmd maprasfùk, y `d snlerd qua ajarifù Unmfk ak su vfbua subfifakta pdrd ldtdr`d.
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Ak pdrajds, masdrrn``alns uk ajalp`n ma ukd idrtd parsnkd` y ukd idrtd rabarakifd
_drd d prùxfld sasfùk a`denralns iudtrn ajalp`ns ma idrtds ak mnkma hdcd-lns `d sn`fiftum ma uk alp`an, ntrd ak `d qua hde`alns ma dlnr n dlfstdm,ntrd idrtd inktdkmn uk dinktaiflfaktn flpnrtdkta d uk bdlf`fdr n uk dlfcn,y pnr ú`tfln ukd idrtd mnkma axpnkcdlns ukd rakukifd d uk idrcn ak iud`-qufar alprasd ma su fldcfkdifùk y `ns lntfvns qua sustaktdk astd rakukifd
• @n lajnr pdrd inksacufr a` nejatfvn inlu-kfidtfvn ma ukd idrtd, as alpazdr ink ukd
nrdifùk kn trdmfifnkd`.
• A` drta ma `ncrdr ukd idrtd erava, inrtæs yinkiratd as inksfmardmn pnr luihns inln a`cækarn ftardrfn läs inlp`ajn qua axfsta. ¾_nrquæ> @d idrtd pravæ, inktalp`d y kaiasftd mauk fktar`niutnr pdrd iulp`fr su nejatfvn, y akasd lamfmd, idmd nrdifùk maea sar astumfdmd
d inksifakifd, pnrqua `d fktarpratdifùk quaa` mastfkdtdrfn hdcd ma ds pd`derds, as dsuktnqua sa sd`a ma `ds ldkns ma` ralftakta ak a`lnlaktn iudkmn `d idrtd tdlefæk `n hdia.
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A` fkbnrla axfca uk inkniflfaktn axhdustfvn ma` tald qua masdrrn``d,ukd fkvastfcdifùk ink su raspaitfvn prniasn ma inkbrnktdifùk y, pnrinksfcufakta, ukd inlpraksfùk axditd ma` dsuktn qua trdtd. @d rdzùkma mfihd axfcakifd as sflp`a: a` fkbnrla, inln `n sucfara a` tærlfknlfsln, as a` snpnrta ink a` iud` sa mdk d inkniar `ns astdmfns pnr `nsiud`as pdsù ukd fkvastfcdifùk hdstd netakar ukds inki`usfnkas. _arn dsìlfsln, pnmalns aktakmar`n inln a` racfstrn matd``dmn ma uk avaktn.Ak asta saktfmn, maiflns qua a` fkbnrla as rfcurnsn y latùmfin7 as i`drn
ak `d bnrlu`difùk ma fmads y inharakta ak `d suiasfùk ma `ns haihns nhfpùtasfs, y parsfcua ukd bfkd`fmdm inlukfidtfvd inkiratd.
I`dsfbfidifùk
• Fkbnrla `ftardrfn
Astd maknlfkdifùk sa `as md d `ns mniulaktns `ftardrfns qua ak su asquakdrrdtfvn alp`adk d tæikfid ma` fkbnrla, efak sad pnr `d saiuakifd mniultd` inln astä p`dktadmn a` ra`dtn n pnrqua a` vd`nr `ftardrfn ma` ra`dtn lfslpnkmard a` fkbnrla. Asta tfpn ma fkbnrla sa puama inkstrufr d pdrtfr ma haih
A fkbnrla
Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja
Yasfùk
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• Fkbnrla fkvastfcdtfvn
Astd idtacnrìd sa suemfvfma ak iudtrn i`dsas:
4. Fkbnrla didmælfin. _rnmuifmn ak a` inktaxtn asin`dr n ukfvarsftdrfnQk astumfdkta ma in`acfn n ma ukfvarsfmdm astä ak idpdifmdm ma cakaruk fkbnrla, edsdmn ak ukd talätfid pravfdlakta axpuastd ak i`dsa pna` prnbasnr n hdiar`n d pdrtfr ma d inlpraksfùk ma ukd n vdrfds aiturdn ma ukd fkvastfcdifùk rad`fzdmd.
5. Fkbnrla prniamflaktd`. _rnpfn ma nrcdkfzdifnkas prnmuitfvds. Ya trdma fkbnrlas abaitudmns pnr `ns prnbasfnkd`as, ink edsa ak prniasn
`denrd`as, dmlfkfstrdtfvns, fkvastfcdtfvns, taùrfins n ifaktìbfins, pdpnkar ak ldrihd uk p`dk ma trdedjn, flp`alaktdr inrraitfvns snerprne`alds mataitdmns n prnpnkar tanrìds bf`nsùbfids n ifaktìbfids.
9. Drtìiu`n ifaktìbfin. As prnmuitn ma ukd fkvastfcdifùk ma nrmak aspa
ifd`fzdmn, inln `n puama sar ukd tasfs ma ldastrìd n ukd fkvastfcifùk ma mnitnrdmn, ati. Astns fkbnrlas raifeak a` knlera ma drtìiuifaktìbfin iudkmn snk pue`fidmns pnr ravfstds didmælfids n ifaktìbfid
aspaifd`fzdmds, iuyn irftarfn amftnrfd` astä edsdmn idsf sfalpra, ak inrrnenrdifùk ma ns mdtns axpuastns ak a` fkbnrla n ak d iramfef`fmdma `d iud` cnia a` dutnr ak asa tald aspaiìbfin. Astd i`dsa ma fkbnrlkn raqufara `d saclaktdifùk latnmn`ùcfid qua axfcak a` didmælfina` ifaktìbfin. As maifr, d` sar pue`fidmn ak ukd ravfstd, su inktakfmn aläs inkifsn y inki`uyakta, y a` `akcudja läs b`ufmn. _nr `n cakard`, dutnr ma uk drtìiu`n ifaktìbfin as uk axpartn qua hd haihn pue`fidifnkas ma mniulaktns läs axtaksns y prnbukmns d ldkard ma fkbnrlaifaktìbfins.
=. Fkbnrla ifaktìbfin. _uama prnvakfr ma uk drtìiu`n ifaktìbfin iuyd fkvatfcdifùk sa prn`nkcù n sa rdlfbfiù hdstd inkvartfrsa ak ukd prnpuasifaktìbfid ma ldynr trdsiakmakifd. Astns fkbnrlas snk axtaksns maefmd `d inlp`ajfmdm qua ravfsta ukd fkvastfcdifùk ifaktìbfid y pnr `n cakard`, snk inlprnedmns pnr pdrta ma ntrns fkvastfcdmnras qua sa dpnydaspaifd`lakta ak `ns lætnmns y prniamflfaktns qua a` fkvastfcdmn
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Bdsas ma` fkbnrla
Dukqua d astruiturd ma` fkbnrla sad astrfitd, mfraitd y latfiu`nsd, d suiasfùkma `ds fmads maea takar ukd `ùcfid sfstalätfid y masdrrn``dr a` tald ak bnrldprncrasfvd, axpnkfakmn `ds vdrfde`as ma ldkard nrmakdmd y inkcruakta.
@n qua dktaiama d` fkbnrla
4. Fmaktfbfidifùk y puktud`fzdifùk ma` tald5. Uainpf`difùk ma `d fkbnrldifùk axfstakta9. Masp`dzdlfaktn d `d fkvastfcdifùk ma idlpn
=. Uad`fzdifùk ma akiuastds y astdmìstfids1. Dkä`fsfs ma` prne`ald p`dktadmn y inkbrnktdifùk ink a` puktn ma pdrtfmd
Astruiturd ma` fkbnrla
4. ]ftu`dras. Maea takarsa i`drfmdm snera `n qua sa vd d inlukfidr ak a`fkbnrla, pdrd `ncrdr uk diartdmn tftu`dr qua astdrä inlpuastn pnr ukdktatìtu`n y uk tìtu`n bfa`as d` inktakfmn, sfk fktarpratdifnkas, aubalfslns
kf latäbnrds. Yfk aledrcn, su a`denrdifùk puama sar `d ditfvfmdm bfkd`,iudkmn `d dprnpfdifùk ma` tald astä ak uk euak puktn ma` masdrrn``n.
5. Yfknpsfs n rasulak. _`dktad `d asakifd ma `d fkvastfcdifùk n ma` taldtrdtdmn ak uk lìkfln ma safs `ìkads. _uama prasaktdr uk asquald c`ned`ma` dsuktn fkvastfcdmn, ukd inki`usfùk n `d bnrlu`difùk ma ukd fkiùc-kftd qua lntfvdrä d` `aitnr pdrd qua sa fktarasa pnr `n qua vakmrä ak a`iuarpn ma` fkbnrla.
9. Fktrnmuiifùk. Yu axtaksfùk puama b`uitudr aktra ds mns y ds 41 päcfkds,mapakmfakmn ma `d axtaksfùk ma` fkbnrla. Maea fki`ufr `d flpnrtdkifdma` tald, ns prnpùsftns ma d fkvastfcdifùk y lnstrdr d`cukns dktaiamak-tas. @ns lætnmns ma fkvastfcdifùk utf`fzdmns murdkta a` prniasn, puamakfki`ufrsa ak `d fktrnmuiifùk n prasaktdr`ns ak a` saclaktn sfcufakta ma`taxtn.
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=. Masdrrn``n. A` iuarpn ma` fkbnrla puama fkfifdrsa ink a` p`dktadlfaktnma` prne`ald masma su bdsa läs a`alaktd`, uacn sa tanrfzd crdmud`laktalfaktrds sa astde`aia y inkbfrld d hfpùtasfs, hdstd `acdr d ds inki`usfnkasqua drrnja `d fkvastfcdifùk. @ds hfpùtasfs sa inkiaktrdk ak axpnsfifnkas
inkiaptud`as, dkd`ìtfids n irìtfids, prnmuitn ma` mfsiarkflfaktn qua a`dutnr u ntrns dutnras hdydk haihn snera a` tald. Murdkta a` prniasn ma`masdrrn``n sa pnmrä axpnkar `ds fmads sacúk a` asquald ma `ds pfrälfmasma `d fkbnrldifùk, as maifr, alpazdr ink `n läs a`alaktd` hdstd ``acdr d`ds inki`usfnkas läs ra`avdktas. ]dlefæk sa puama pdrtfr masma `n läsinki`uyakta pdrd masakidmakdr ak `ns dspaitns ma laknr fkifmakifd.
1. Ifarra (sìktasfs y inki`usfnkas). Qkd vaz astde`aifmn a` prne`ald y
p`dktadmn `ds hfpùtasfs, sa masdrrn``d `d fkvastfcdifùk inrraspnkmfakta.Maspuæs, sa prasaktd ukd sìktasfs, as maifr, sa ramnkmad d fmad cakard` ynrcdkfzd uk idpìtu`n ink `ds inki`usfnkas, dukqua yd `n hdyd haihn ak`d sfknpsfs, ak `d fktrnmuiifùk n d` fkfifdr `d pfrälfma ma` masdrrn``n. Maiud`qufar lnmn, a` dutnr maearä idtd`ncdr ds inki`usfnkas qua puamakdinlpdôdr idmd brdclaktn, ak idsn ma qua kn sa rasarvak pdrd a` bfkd`.
2. Dkaxns. As tnmn ldtarfd` ma dpnyn qua inktrfeuyd d d lajnr inlpraksfùk
ma d fkvastfcdifùk prasaktdmd. @ns dkaxns sa kulardk ink atrds asirftdsak ldyúsiu`d y maeak sar nrcdkfzdmns pnr a` dutnr. Aktra `ns dkaxns saakiuaktrdk: akiuastds, aktravfstds, astumfns ma idsns, bntncrdbìds, drihfvns,crdedifnkas, iudmrns astdmìstfins y ma lamfifùk, ldpds, ati.
@ns fkbnrlas mdmns d `d `uz púe`fid vdk masma `ns läs puktud`as, inln `nsiaksns ma pne`difùk, hdstd `ns läs fldcfkdtfvns. Iud`qufard qua sad su kd-
turd`azd, a` fkbnrla ldktfaka uk rftln inlúk ak tnmns.
@d dktrnpù`ncd knrtadlarfidkd Ldrcdrat Ladm fktacrd ukd sarfa ma fkvas-tfcdifnkas rad`fzdmds aktra `ns puae`ns prflftfvns ma `ns ldras ma` Yur. A``dhdia ukd inktrfeuifùk d d dktrnpn`ncìd iu`turd` y d d psfin`ncìd snifd` pdrd dinlpraksfùk ma d`cukns ma `ns prne`alds idpftd`as ma kuastrn tfalpn. Astnsastumfns snk pue`fidmns pnr sapdrdmn ink `ns tìtu`ns Dmn`asiakifd y iu`turd7Amuidifùk y iu`turd7 Yaxn y talpardlaktn.
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@adk uk drtìiu`n snera vfn`akifd y ld`trdtn inktrd `d fkbdkifd ak In`nlefdy a`denra uk fkbnrla didmælfin d pdrtfr ma `d `aiturd. Fkmfqua quæ buaktautf`fzù y qufæk `n asirfefù.
@ns fkbnrlas vdrìdk ak su inlp`ajfmdm y axtaksfùksacúk sad a` tald y, aspaifd`lakta, a` kfva` ak a`iud` sa akiuaktra a` astumfdkta. Qk fkbnrla asin`drpuama takar tdk sù`n mns päcfkds, ak tdktn pnsad`ds vdrfde`as qua `n idtd`ncuak inln td`: prne`a-
ld, hfpùtasfs, sìktasfs y inki`usfnkas. Kn nestdkta,`d raspnksdef`fmdm ma mdr sn`uifùk d` prne`aldp`dktadmn kn raida snera a` fkbnrla. Æsta sù`n saakidrcd ma axpnkar n iuastfnkdr `d sftudifùk y, sfas prnmuitn ma ukd fkvastfcdifùk qua nbrazid `dvfdef`fmdm ma `d sn`uifùk, æstd sarä fki`ufmd. Qkfkbnrla puama sar prnmuitn ma ukd prn`nkcdmdfkvastfcdifùk qua tnla lasas n dôns.
Ink dyumd ma sus inlpdôarns y su mniakta trdksbnrldmnr n trdksbnrldmnrd insfcdk vdrfns ajalp`ns ma fkbnrlas.
Ma ldkard fkmfvfmud` ravfsa ns fkbnrlas y asirfed ds mfbarakifds aktra a``ns y iùl`ns i`dsfbfidrìd.
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A` iuaktn ma` inifkarnCanbbray Ihduiar
Qkd vaz vfvìd uk dprakmfz ak kuastrd ifumdm, qua trdedjded ak uk inlar-ifn ma inlastfe`as. Ard läs d`acra qua uk jf`cuarn sua`tn pnr a` ensqua.Ard uk luihdihnta cudpn, parn d`cn edjftn, luy lnrakn y ``avded supa`n kacrn a`acdktalakta pafkdmn.
Edf`ded tdk efak y tdk dkfldmdlakta, qua a dpnmdedk Jdrdkarn _argfk.]nmd ihfid qua sa juktded d æ` takìd suarta, puas æ` astded `akn ma dlnry `dsifvfd inln ukd in`lakd ma lfa`.
Edf`ded y idktded ak tnmds `ds enmds y `a takìd läs dbfifùk d `d tdearkdqua d `d tfakmd, puas sfalpra qua hdeìd ukd prniasfùk pnr Ihadpsfmasd`ìd mfspdrdmn ma `d tfakmd trds a``d y kn racrasded hdstd qua hdeìd edf-
`dmn `n suyn y hdeìd vfstn tnmn `n qua hdeìd qua var… Ya raukìd ak ukdid``a n ak ntrd pdrd jucdr d `ns mdmns7 puas kn hdeìd kfkcúk dprakmfz ak`d ifumdm qua aihdsa `ns mdmns lajnr qua _argfk. Dmaläs, ma hurtdmf-``ds, ard uk marrnihdmnr. Astn `n masiuerfù su dln d sus axpaksds, puasluihds vaias sa akinktrù ink a` idjùk ma` mfkarn vdiìn. _nmæfs astdrsacurns qua iudkmn uk dprakmfz `n pdsd tdk efak aihdkmn `ns mdmns,
jucdkmn y ink lujaras, as a` muaôn ma `d tfakmd a` qua `n pdcd ink susidumd`as dukqua kn inlpdrtd a` jn`cnrfn
A iuaktn y sus nrìcakas
Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja
Yasfùk
1
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Dukqua a` dprakmfz sapd tnidr a` vfn`ìk y `d cuftdrrd, sus juarcds y juacn`ns pdcd a` rnen. _uas, inln pnmæfs var, `d hnkrdmaz y `d euakd vfmdsfalpra dkmdk mfsnifdmns, iudkmn sa trdtd ma cakta pnera.
Dukqua `a racdôdedk kniha y mìd y d`cukds vaias ard ``avdmn d enlen
y p`dtf``n d d iäria` ma Kawcdta, a` d`acra dprakmfz parldkaifù ink sumuaôn, hdstd qua idsf tarlfkù su dprakmfzdja. _arn uk mìd, a` muaôn,ravfsdkmn su inktrdtn ma dprakmfzdja, sa dinrmù ma` prnvarefn quarazd: ‐Läs vd`a drrnjdr `d ldkzdkd pnmrfmd qua majdr`d qua pumrd d`ds maläs“. @n lfsln niurra ink a` irfdmn prntastùk: as lajnr majdr`aldrihdr qua parlftfr`a qua astrnpaa d `ns maläs irfdmns ma `d idsd.Ma lnmn qua a` muaôn a majù fera y a nrmakù qua sa ldrihdrd, ink
ld`mfifnkas snera su ideazd. Dsì bua inln a` d`acra dprakmfz inksfcufùsu feartdm. Dhnrd pnmrìd hdiar jdrdkd tnmd d kniha, sf dsì a dpataiìd._arn, inln sad qua kn hdy `dmrùk qua kn takcd uk inlpfkiha qua`a alpuja d sdquadr y astdbdr d` qua hd rnedmn n astrujdmn, _argfkfklamfdtdlakta akvfù su idld y a` rastn ma su djudr d idsd ma ukinlpdôarn fksapdrde`a qua ard tdk dbfifnkdmn d ns mdmns, d` jn`cnrfny d `d mfsfpdifùk inln æ`…
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@ns nrìcakas ma` iuaktn
A` nrfcak ma` iuaktn sa ra-
lnktd d `d dktfcðamdm (läsma =.??? dôns dträs), aktra`ns puae`ns nrfaktd`as su-larfns y acfpifns, fkmfnsy ihfkns, parn kn sa sdeaink praifsfùk a` lnlaktniudkmn dpdraifù `d prflardhfstnrfd. Ya aspaiu`d ink a`
knlera ma` crfacn @uifdknma Ydlnsdtd, kdifmn ak Yf-rfd, qufak asirfefù A` iìkfin yntrn vdstn kúlarn ma ra`dtnsma takmakifd lnrd`7 tdlefæksa lakifnkd d @uifn Dpu`ayn, inknifmn ak d ditud`fmdm pnr su nerd: A` dskn ma nr
@n ifartn as qua a` cækarn as uk `acdmn dtrfeufmn d` mfsiursn nrd`, d `d kaiasfmdm minktdr. Dktas ma qua axfstfasak ns d`bdeatns, a` hnlera kdrrded ns haihns, utf`fzdenknldtnpayds pdrd mdr`a praifsfùk d `ds fmads (n qufzä pdrd axprasdrsa). @n qua sa sdea, as qua a` ditn ma inktdr bua ukd ditfvfmdm fkbnrld` d `d iud` ``acdrnk `nhnleras prflftfvns maspuæs ma iulp`fr sus bdakds n ma vakfr ma d cuarrd, d`ramamma d hncuard. Ak sus iuaktns, kdrrdedk ds dvakturds y axparfakifds vfvfmds murdka` mìd n murdkta `ns `drcns vfdjas, ink uk tnqua ma ldcfd y bdktdsìd, rasu`tdmn ma sra`difùk ink `n lìtfin.
@ns parsnkdjas ma `ds hfstnrfds ardk pnrtdmnras ma uk paksdlfaktn in`aitfvn qurab`ajdedk mumd, talnr y snrprasd brakta d `ns bakùlakns kdturd`as qua kn pnmìdaxp`fidr. Astns ra`dtns pdsdedk pnr suiasfvds cakardifnkas, sa akrfquaiìdk, inlp`laktdedk n trdksbnrldedk, crdifds d `d prnbusfùk ma` paksdlfaktn pnpu`dr, ma`atdkmn d `ns asiuihds y aksaôäkmn`as d mfbarakifdr `n euakn ma `n ld`n. D tnmn assa suldrnk `ns bfkas ra`fcfnsns, pamdcùcfins y lnrd`as qua tdlefæk hfifarnk la``Ink a` pdsdr ma `ns sfc`ns, a` iuaktn bua dmnrkdmn ink kuavds fläcakas sucastfvd
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A` iuaktn ak Nrfakta
Ak Ihfkd, a` iuaktn ak bnrld ma bäeu`dmastdiù pnr su fktakifùk sdtìrfid y irìtfidma d snifamdm. Ak Fkmfd, A` _dkihdtdktrd eusiù aksaôdr prfkifpfns lnrd`as d `nshfjns ma` ray Dldrdsdgtf, parn bua ink`ns ärdeas qua kdifarnk `ns iuaktns bdk-tästfins ma D`b @dy`d wd @dy`d, trdmuifmnsedjn a` knlera ma: @ds lf` y ukd kniha
(kniha y kn knihas, inln ma ldkardarrdmd sa sfcua lakifnkdkmn), ak `nsiud`as sa hf`vdkd ukd hfstnrfd trds ntrd,maktrn ma uk lfsln iuaktn, a` ma Yhara-
zdmd qua ink a` bfk ma sd`vdr su vfmd, sainkvfarta ak inktdmnrd ma hfstnrfds pdrda` su`täk (su aspnsn y vfitfldrfn). Crdifdsd `d pd`derd asirftd, luihns ma dqua``nsiuaktns buarnk rainpf`dmns y sfrvfarnkma ajalp`n y lìlasfs pdrd ukd bnrld`ftardrfd qua alpazded d inksn`fmdrsa.
A` `acdmn ma `ns puae`ns nrfaktd`as ink-mflaktù a` inktakfmn ma `n qua hnyinknialns ink asta knlera (sfk inktdr
ink dqua``ds ntrds iu`turds aurnpads iuyndpnrta saktù `ds edsas pdrd `ds sfcufaktascakardifnkas). @d ``acdmd ma pfrdtds nasi`dvns qua rainrrìdk a` Rfajn Lukmn,buarnk dlp`fdkmn `ds varsfnkas y din-lnmäkmn`ds d pdrtfr ma` inktaxtn snifd`,iu`turd` y ra`fcfnsn ma `ds lú`tfp`as snifa-mdmas inktfkaktd`as
B n t n s t n l d m d s m a S f g f p a m f d
A` _dkihdtdktrd.
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@ds hfstnrfds ak `d Amdm Lamfd
Murdkta tnmd `d amdm lamfd, a` iuaktn d`idkzù uk aspaifd` sfckfbfidmn. A` fkbdk
mnk Judk Ldkua`, pnr ajalp`n: ak su `fern ma Ajalp`ns qua prnvakìdk ma @ds ly ukd kniha, irad ukd nerd amuidmnrd. Läs d``ä astuvn Ihduiar qua d`fôù ink spdrtfiu`dr tnqua, dqua` astf`n qua sa vakìd bnrldkmn ak ntrd pdrta ma` Inktfkaktaparn bua Eniidiifn qufak `a mfn uk cfrn d` inktakfmn y d `d bnrld ma` cækarn. @bdktästfin sa lazi`ù ink `d rad`fmdm y `d hfstnrfd, ink a` hulnr y `d frnkìd irìtfid.
Ak a` sfc`n XRFF, dutnras inln Ihdr`as _arrdu`t inlpf`drnk dqua``ns hfstnrfds mfrfcfmd uk púe`fin fkbdktf` qua sa trdtded inln dmu`tn (Idparuiftd Unjd, E`dkid Kfava
_u`cdriftn, ati.), y iuyd fktakifùk pravaktfvd, amuidmnrd y lnrd` sa rab`ajded ak lnrd`ajd, uk a`alaktn prnpfn ma `ds bäeu`ds.
Uainrmalns ukd ma `ds nrdifnkas ma `d hfstnrfd ma Idparuiftd y su raspaitfvlnrd`ajd:
‐Idparuiftd rnjd samaskumù y bua d la-tarsa ak `d idld,mnkma sa quamù luysnrprakmfmd d` variùln ard su deua`dak idlfsùk“.
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Lnrd`ajd
Ralns dquì qua `ns dmn`asiaktas y läs `ds jnvakiftds a`acdktas,efak haihds y enkftds, hdiak ld` ak nìr d ifartds caktas, y qua knhdy qua axtrdôdrsa ma d ernld ma qua d tdktds a` nen sa ds inld.Mfcn a` `nen, pnrqua asns dkfld`as kn tnmns snk fcud`as: `ns hdyma uk idräitar axia`akta y hulnr dbde`a, mu`ia y inlp`difakta,qua sfk rufmn, sfk hfa` kf frrftdifùk parsfcuak d jùvakas mnkia``ds,``acdkmn maträs ma a``ds d `d idsd y hdstd `d hdeftdifùk. ¾Tufæk
fcknrd qua `nens tdk la`nsns snk `ns läs pa`fcrnsns>
Kn as ma` dkfld` barnz ma` qua maea mabakmarsa Idparuiftd, sfkn ma `didrcd arùtfin-saxud` qua tfaka su ra`difùk ink a` `nen. Hny ak mìd, `dlnrd`ajd sa hd suprflfmn ak ds mfbaraktas varsfnkas y insd pdrtfiu`dr, inkuk rasu`tdmn bfkd` desn`utdlakta ba`fz, sa vakma läs `d fmad ma ba`fifmdm
qua `d ma rad`fmdm edjn ukd sn`dpdmd y bd`sd lnrd`.
Ma` sfc`n XRFFF d` sfc`n XX, a` iuaktn dmqufrfù uk kuavn tnkn, dpdraifarnkkuavds lnmd`fmdmas (pn`fifd`, bdktästfin, bfiifùk, rad`fstd, lnmarkfstd ylnmarkn, aktra ntrns), ink uk dutnr qua `ds raprasaktd. Yus idlefnssnk prnbukmns7 a` suecækarn sa ratrnd`flaktd ma ntrds bnrlds kdrrdtfvdsinln d bäeu`d, a` aksdyn, ns lftns, ds ayakmds, ati., mfraiifnkdkmn suinktakfmn hdifd ntrds rad`fmdmas, y iradkmn uk lukmn ma hfstnrfds quasfcuak d`flaktdkmn a` d`ld y `d lakta ma `aitnras y kdrrdmnras.
Asta bucdz pdsan pnr `d hfstnrfd ma` iuaktn majd ma `dmn, kn sù`n d ntrdsiu`turds qua `a flprflfarnk vdrfdifùk y rfquazd, sfkn d luihns dutnrasqua crdifds d a``ns, astd bnrld `ftardrfd hd pnmfmn niupdr a` `ucdr qua sa`a md ak `d ditud`fmdm.
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Masdrrn``a ak su iudmarkn:
4. A` iuaktn ma` inifkarn partakaia d` crupn ma nerds qua `dkzdedk saktakifdlnrd`as ink a` bfk ma dyumdr d amuidr d `ns hnleras. Uaasirfed `ds saktakifqua akiuaktra ak a` ra`dtn y axp`fqua `d fktakifùk ma` dutnr ak idmd ukd ma``ds.
5. Yfcufakmn `d mfkälfid ma `d hfstnrfd ma Ihduiar, tarlfka a` iuaktn qua lfsln majù fkinki`usn.
9. Uatnla a` iuaktn Idparuiftd Unjd, uefqua `d hfstnrfd ak a` prasakta7 idle`ns rn`as n pdpa`as ma `ns prntdcnkfstds y iraa ukd varsfùk lnmarkd ma` iuakt
=. A` sfcufakta ajalp`n as ukd nerd ma` cudtald`tain Ducustn Lnktarrnsn
¾Iùln pnmrìd i`dsfbfidrsa> ¾Dpù`ncn, bäeu`d, saktakifd, lfkf iuaktn n apcrdba> Fkvastfcua a` saktfmn ma idmd vnide`n y sustakta su raspuastd.
A` pdrdìsn flparbaitn Ducustn Lnktarrnsn
As ifartn mfjn laiäkfidlakta a` hnlera, sfk quftdr `d vfstdma `ds ``dlds qua drmìdk ak `d ihflakad dqua``d kniha mafkvfarkn7 ak a` _drdìsn hdy dlfcns, lúsfid, d`cukns `ferns7`n úkfin ld`n ma frsa d` Ifa`n as qua d``ì a` ifa`n kn sa va.
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Masdrrn``a ak su iudmarkn:
4. Asirfed ukd lnrd`ajd pdrd ‐A` iuaktn ma` inifkarn.“
5. @ad ukd varsfùk iud`qufard ma` iuaktn E`dkid Kfavas, ramdita suprnpfd lnrd`ajd, snifd`fia ink sus inlpdôarns su inktakfmn y inl-
pära`d ink `d varsfùk i`äsfid qua su mniakta `as prasaktdrä murdkta`d ditfvfmdm. Uaiuarma qua `ds varsfnkas i`äsfids snk dqua``ds quapnsaak lnrd`ajd.
9. A` sfcufakta iuaktn inkiaktrd uk a`alaktn frùkfin, prnpfn ma` astf`nlnmarkn. ¾Ak quæ nrdifnkas sa mataitd asd frnkìd y quæ as `n quaastä frnkfzdkmn a` dutnr>
A` `ninCferdk Ghd`f` Cferdk
@ìedkn: 4889-4694
Ak a` jdrmìk ma uk hnspfifn inkniì d uk jnvak ma rnstrn pä`fmn y harlnsn,
d``ì fktarkdmn. V saktäkmnla juktn d æ` snera a` edkin, `a pracuktæ:¾_nr quæ astäs dquì>
La lfrù dsnlerdmn y raspnkmfù:
As ukd pracuktd fkdmaiudmd7 sfk aledrcn, inktastdræ. Lf pdmra qufsn hdiarma lì ukd raprnmuiifùk ma sì lfsln7 tdlefæk lf tìn. Lf ldmra masaded
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i ì r i u
` n m
a ait n r a
s
• @d vfumd ma Æbasn ma _atrnkfn• @ds lf` y ukd knihas ma Dkùkfln• @d kdrfz ma Äktnk Ihæjnv• @ns dsasfkns ma Arkast Halfkcwdy• Mfdrfn ma uk `nin ma Cùcn` Kfgn`df• A` psfqufdtrd ma Ba`fseartn Harkäkmaz• @d idrtd rnedmd ma Amcdr D``dk _na• A` Maidlarùk ma Cfnvdkkf Eniidiifn•
]fakmds ma `d idka`d ma Erukn Yihu`tz• @d cd``fkd macn``dmd ma Hnrdifn Tufrncd• Qkd rnsd pdrd Alf`y ma Sf``fdl Bdu`gkar• Iuaktns ma Idktareury ma Canbbray Ihduiar• Mns mataitfvas dkta uk edrrf` ma Ldrg ]wdfk• A` `äpfz y ntrns iuaktns ma Udylnkm Ihdkm`ar• @d vfmd ma uk hnlera fkkaiasdrfn ma Läxfln Cnrgf• Bua uk mìd mfstfktn iudkmn ldtdrnk d` iarmn ma Qed`mn Ufeafrn
qua buard `d fldcak ma su f`ustra pdmra. Lf harldkd lnstrded d su aspnsnkdvacdkta inln a` ajalp`n parbaitn d sacufr. Lf harldkn paksded quamaeìd sar inln æ`, uk axia`akta dt`atd. V lfs prnbasnras, inln a` mnitnrma bf`nsnbìd, a` ma lúsfid y a` ma `ùcfid, a``ns tdlefæk buarnk tarlfkdktas, yidmd ukn qufsn qua buard a` rab`ajn ma sus prnpfns rnstrns ak uk aspajn. _nrasn vfka d asta ucdr. @n akinktræ läs sdkn. D` lakns puamn sar yn lfsln.
Aksacufmd sa vn`vfù hdifd lì y mfjn:
_arn mfla, ¾ta inkmujarnk d asta `ucdr `d amuidifùk y a` euak inksajn>Kn, sny uk vfsftdkta raspnkmì.Nh dôdmfù æ`, tú aras ukn ma `ns qua vfva ak a` hnspfifn ma` ntrn `dmn ma`d pdram.
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Id`f`d y Mflkd as ukd in`aiifùk ma iuaktns
idsta``dkns ma 4514 prnede`alakta qua nrmakùtrdmuifr D`bnksn X a` Ydefn, iudkmn tnmdvìd ardfkbdkta. Aktra luihds ma `ds nerds ra`difnkdmdsink D`bnksn X, Id`f`d a Mflkd as d läs ftardrfdy su ldtarfd kdrrdtfvd prniama ma `d `ftardturdnrfaktd`, prnede`alakta fkmfd, ma` sfc`n FFF.
Ldkusirftn ma` Id`f`d a Mflkd.
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4. Fmaktfbfqua ds bd`akifds qua prasaktd a` ldkajn ma` iùmfcn asirftn aka` sfcufakta ajalp`n, qua hd sfmn d`tardmn d prnpùsftn:
Murdifùk ma` trdedjn
Ak ns pdìsas ak qua idsf tnmds ds lujaras trdedjdk (qua snk d lftdmma` puae`n) y ns hnleras sa mdk d rapnsn dmaläs, ma` crdk kúlarnma sdiarmntas y ra`fcfnsns qua kn prnmuiak kdmd ink sus ldkns, kf`n saônras rfins y haramarns (d ns qua a` vu`cn `dld kne`as y ided``a-
rns), fki`uyækmn`a ak astd iuaktd. d tnmd d idtarvd ma `ns qua sfrvakd astns ú`tflns ma aspdmdihfkas y truhdkas, y d `ns, lakmfcns quatakfakmn sd`um bfkcak akbarlamdm pnr hn`cdzdkarìd, hd``dræfs quasnk luihns, `ns qua kn prnmuiak kdmd7 y aktra: `ns qua trdedjdkhdy ukd crdk pdrta qua kn sa niupdk ak insds kaiasdrfds, yd quamnkma tnmn sa inksfcua ink mfkarn as bnrznsn qua hdyd luihdsdrtas tntd`lakta vdkds, qua sù`n sfrvak d` dktnjn y axiasn.
(]nldmn ma @d Qtnpìd, ma ]nläs Lnrn)
5. _rasakta su prnpfn dkä`fsfs ma ukn ma `ns maedtas qua sa rad`fzdrnkak a` du`d ma i`dsa murdkta asta parìnmn.
9. @d sfcufakta idrtd rabarakifd` idraia ma d`cukns dspaitns, parn tdlefækinktfaka mns bnrlds fkinrraitds. Yaôd`a `ns (n a`) qua astäk arrdmns y``aka `ns aspdifns `feras.
Ldkns d d nerd
Qkfmdm 4. A` iùmfcn `fkcðìstfin: `ds ldkfbastdifnkasma` akcudja
Yasfùk
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Ya maknlfkd pfa ma bntn d `d `ayakmd qua dinlpdôd `d bntn. Asinlpuastn masma ukd n mns pd`derds, hdstd tras n iudtrn `ìkads. @n
pfas snk tdk flpnrtdktas inln `d bntn lfsld a fki`usn, kukid maea fr ukd bntn sa` inrraspnkmfakta pfa. A``ns sa akidrcdk ma ldtfzdr y dpnydr a` ra`dtn prfkifpd`7 pnasn, `n qua mfcdk `ns pfas ma bntns, kn puama sar axtrditdmn ma` iuarpn ma` ra`dtn
Idrditarìstfids
4. Ya akiuaktrd astruiturdmn ma ldkards axp`fidtfvd, malnstrdtfvd,fktarrncdtfvd, dmlfrdtfvd n sdtìrfid. Yfk flpnrtdr a` saktfmn qua sa `antnrcua d` taxtn, nbraia fkbnrldifùk dmfifnkd` d n qua astä lnstrdkmn`d bntncrdbìd. Astn sfckfbfid qua kn maea rapatfr ak pd`derds, `n qua `dfldcak astä inlukfidkmn pnr sì sn`d, sd`vn sf sa trdtd ma fkmfidr a`knlera ma uk fkmfvfmun, ukd nerd ma drta ati.
5. A` drta ma a`denrdr pfas ma bntns qua kn raftarak n qua mfia d bntncrd-bìd, sa maknlfkd aktrnpìd, as maifr, axtrda `d bdiatd qua kn usdk ntrnslamfns. _nr a` inktrdrfn, iudkmn a` pfa ma bntn iuaktd `n lfsln qua`d fldcak axpnka, sa inknia inln ramukmdkifd. Astd npifùk kn asdinksajde`a, pnrqua makntd pnid iradtfvfmdm y mabfifakta saktfmn ma`d nesarvdifùk y a` dkä`fsfs7 pnr inksfcufakta, masmfia ma `d bartf`fmdmkdrrdtfvd ma qufak `n asirfea.
A` pfa ma bntn
_fa ma bntn y astruiturdifùk
ma taxtn asirftn
Qkfmdm 5. A pfa ma bntn: `d trdkslfsfùk ma `dfkbnrldifùk y ns sfstalds sfleù`fins Yasfùk
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Ma `d frd
@uifn Dkkan Yækaid
@fern prflarn
F. La axfcfsta, Idrn Knvdtn, qua ta asirf-efasa diarid ma d ldkard ma mnlfkdr dfrd, y iran qua, kn sfk idusd, talas luyprfkifpd`lakta d astd pdsfùk, qua as `dläs snlerìd y masakbrakdmd ma tnmds.@ds ntrds tfakak sfk mumd d`cn ma qufatdsy p`äifmds7 parn astd as tnmd dcftdifùk,masakbrakn ak a` rasaktflfaktn, sam macuarrd, ma sdkcra, ma sup`fifns, drraedtnma burnras snerahuldkns, n`vfmäkmnsama sì lfsld ink td` ma mdôdr d ns maläs,
`dkzäkmnsa ak lamfn ma `ds aspdmds, yävfmd ma vakcdkzds qua d su vaz trdakuk vakcdmnr. _nr astd rdzùk, d`cukns vd-rnkas sdefns mabfkfarnk d frd `dläkmn`d`niurd erava7 pnrqua, flpntakta inlndquæ``d pdrd mnlfkdrsa, n`vfmd tnmdinkvakfakifd, masinknia tnmn dbaitn,as nestfkdmd y tarid ak `n qua sa prn-
pnka, snrmd d `ns inksajns ma `d rdzùk,dcftäkmnsa pnr idusds vdkds, fkhäef` pdrdmfstfkcufr n justn y varmdmarn, pdraifæk-mnsa d asds rufkds qua sa rnlpak sneradqua``n lfsln qua dp`dstdk.
_drd qua ta inkvakzds ma qua kn axfstardzùk ak dqua``ns d qufakas mnlfkd `d
inln d niurd tfaka sus saôd`as ifartbrakta trfsta, dkmdr praifpftdmn, ldkinkvu`sds, taz idlefdkta, raspfrdifdkha`nsd y aktrainrtdmd, dsì tdlefprasaktd astds saôd`as a` hnlera fiukmn. Fkb`äldksa sus njns y iakta``adfktaksn in`nr rnjn iuera su sale`dkhfarva `d sdkcra ak `ds idvfmdmas ma inrdzùk, tfæle`dk`a `ns `defns, dprf`ns mfaktas, a` idea``n sa avdktd y arfsu raspfrdifùk as inrtd y rufmnsd, sus iyukturds irujak y sa ratuariak, cflaruca7 su pd`derd as tnrpa y aktrainrtdm
ihnidk braiuaktalakta sus ldkns, spfas cn`padk a` sua`n, dcìtdsa tnmn iuarpn, y idmd castn as ukd dlakdzdsì sa kns prasakta dqua` d qufak hfkiy masinlpnka `d frd.
Flpnsfe`a sdear sf asta vfifn as läs mtastde`a qua mabnrla. _uamak niu`td
`ns maläs, d`flaktdr`as ak sairatn7 pa`d frd sa rava`d ak a` sale`dkta, y iudkldynr as, lajnr sa ldkfbfastd. ¾Kn vak tnmns `ns dkfld`as saôd`as praisnrds iudkmn sa dprastdk d` inleddedkmnkdkmn tnmns ns lfalerns d ild ma su ditftum nrmfkdrfd, y axd`täkmsa su barnifmdm> A` jded`ì dkzd aspul
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Astruiturdifùk ma` taxtn asirftn
Astruiturdr uk taxtn asirftn as ukd iuastfùk
inkniar `ds harrdlfaktds ink `ds iud`as sa vtrdedjdr y a` prniasn qua sa maea sacufr. _nr npdrta, takar i`drfmdm snera a` tald qua sa vtrdtdr, as d prflard rainlakmdifùk qua sa hddktas ma fkfifdr a` prniasn ma asirfturd. Knpuama hde`dr ma `n qua kn sa sdea n ma `n qsa sdea d lamfds. ]dlpnin sa puama asirfefr takar ak iuaktd quæ as `n qua sa qufara maif
qufæk vd mfrfcfmn y iuä` as `d fktakifùk ma` asirfefakta: ¾dpainkvakiar n ma`aftdr> Di`drdmds astds pdutds, puama inktfkud`d `denr.
]nmn taxtn (kntd parfnmìstfid, iuaktn, knva`d, aksdyn, pnalati.), pnsaa uk akukifdmn prfkifpd`, uk tald qua maea astdr bukifùk ma n qua sa qufara axprasdr. D su vaz, tnmns ns akukimns saiukmdrfns, cfrdräk d`ramamnr ma` tald n akukifdmn iaktYf sa astä hde`dkmn ma `ds ‐pn`ìtfids ma pdz“ ma uk cnefarkn, sa puama hde`dr ma `ds ú`tflds lamfmds ak ldtarfd ma ain`ncdsì asta sad ukn ma `ns p`dkas ma` prncrdld prasfmakifd`.
A` asirfefakta n alfsnr prasupnka qua sus raiaptnras sdeak tald, parn dúk dsì, maea utf`fzdr uk `akcudja diartdmn snera ajalp`ns y ns dktaiamaktas qua ne`fcdrnk d trdtdr mfihd talätf
Ak a` taxtn ma @uifn Yækaid, Knkdtn sdea n qua as d frd, dsì inltdlefæk n sdeak d`cukns knvdtns sdefns qua d inksfmardk niuYækaid sdea quæ as, pnrqua, inln æ` lfsln n mfia, sa rava`da` sale`dkta y `ds ditftumas. Ynk `ds fkbnrldifnkas dmfifnkd`asakukifdmn, `n qua parlfta dlp`fdr`a `d fkbnrldifùk d Knkdtn
Di`drdmds `ds prflards inksfmardifnkas, puama fkfifdr `d astrturdifùk ma uk asirftn, parn dktas, takcd ak iuaktd ns sfcufak
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• Avftdr `d suejatfvfmdm ak axiasn.
• Ydear prasaktdr `d fmad iaktrd` snera `d iud` vdk d cfrdr `ns ink-iaptns qua `a sarvfräk ma dpnyn.
• Avftdr `d rapatfifùk ma ukd lfsld fmad. Idmd vaz qua sa hdcdrabarakifd d a``d maea sar pdrd dlp`fdr`d y kn pdrd raftardr`d.
• Ldktakar uk nrmak, ukd inharakifd ak `d axpnsfifùk7 pnr `n
tdktn, kn maea trdtdrsa ukd knifùk ukd y ntrd vaz (d lakns qualdktakcd ukd astraihd ra`difùk ink ntrn a`alaktn ma `d ldtarfdqua sa astä inlaktdkmn).
• ]akar prasakta qua a` taxtn as ukd ukfmdm, y inln td`, tnmn `nqua sa mfia maea astdr ra`difnkdmn.
• Iaktrdrsa ak a` taxtn y kn tnldr`n inln axiusd pdrd p`dktadrntrns drculaktns.
• ]akar prasakta a` tfpn ma cækarn qua sa vd d utf`fzdr. As inktrd-prnmuiakta utf`fzdr uk `akcudja `ftardrfn, ldridmn pnr sìlf`as,latäbnrds, hfpæren`as, ati., sf sa astä ramditdkmn uk aksdyn.
• Mabfkfr `d bnrld ma axprasfùk ink `d iud` sa vd d trdedjdr: mas-
irfpifùk, kdrrdifùk, mfä`ncn, drculaktdifùk.
• Matarlfkdr a` tfpn ma kdrrdmnr (prflard, sacukmd n tariard par-snkd).
• ]akar prasakta `d `ìkad qua sa `a qufara mdr d` taxtn: rad`fstd,frùkfid, bdktästfid, ifaktìbfid, ati.
Inksajns pdrd `d ramdiifùk ma uk taxtn
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Ntrns dspaitns pdrd takar ak iuaktd
Yf `d asirfturd sa aktfakma inln
`d prapdrdifùk pdrd uk mfä`ncnaktra uk alfsnr y uk raiaptnr,`n qua sa mfia maea astdr sujatnd ukd `ùcfid qua kn sù`n sa `n-crd pnr `d i`drfmdm ma `ds fmads,sfkn pnr `d euakd fktardiifùk ma`ns a`alaktns `fkcðìstfins, td`asinln: ns varens, ns drtìiu`ns, ns
sustdktfvns, `ns dmjatfvns y maläsvnide`ns qua sa vdk d utf`fzdr. A` taxtn maea pnsaar ukd inhasfùk, puasma kn sar dsì, sa mfbfiu`tdrä `d inlprasfùk ma` inktakfmn.
Yf sa lfrd ink matakflfaktn `d bnrld inln a` asirftnr hd astruiturdmnsu asirftn, sa mamuia qua ak prfkifpfn, tnmn taxtn astä inlpuastn pnrnrdifnkas qua d` ukfrsa, bnrldk ns pärrdbns. Idmd pärrdbn maea takar ukd
fmad qua sfrva pdrd bnrtd`aiar `d fmad iaktrd` qua a` taxtn astæ trdtdkmn.
_nr supuastn, hdy uk asquald astruiturd` i`äsfin qua inlprakma:fktrnmuiifùk, masdrrn``n, kumn y masak`dia7 parn tnmn mapakmarä ma`tfpn ma taxtn qua sa pratakmd a`denrdr (pamdcùcfin, drculaktdtfvn,parfnmìstfin…).
_nr ú`tfln, kn puama majdrsa ma `dmn a` ldrin n rabarakta ak a` iud`
sa masdrrn``d `d fmad. As maifr, `ns dspaitns ma `d rad`fmdm ak `d iud` safksirfeak a` tald trdtdmn, `d iu`turd qua `n rnmad, `ds fman`ncìds qua `nldridk, `ds pnsfifnkas ætfids y astætfids qua `n ifriukmdk. D astn, samaea inksfmardr qua a` inktaxtn ma` alfsnr y a` ma` `aitnr puamak sartntd`lakta mfstfktns. @d `aiturd pdrd ukn y ntrn puama sar mfvarcakta,parn d tdrad inksfsta ak diaridrsa n lajnr pnsfe`a d asa masinknifmn dqufak vdk mfrfcfmds `ds pd`derds.
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3
Masdrrn``a ak su iudmarkn:
4. @ad iufmdmnsdlakta a` taxtn ma @uifn Dkkan Yækaid y saôd`a:
d. ¾Iùln astä astruiturdmn a` taxtn>
e. ¾Iuä`as snk `ds fmads saiukmdrfds qua inlp`alaktdk a` tald prfkifpd
5. Hdcd ukd `fstd ma `ds pd`derds qua inkbnrldk a` idlpn saläktfin ma` talAs maifr, `ns vnide`ns qua `a sfrvak d` dutnr pdrd trdtdr a` tald ma `d frd.
9. I`dsfbfqua a` dktarfnr asirftn. ¾As uk taxtn drculaktdtfvn, ukd kdrrdifùk, uksätfrd n uk sflp`a mfä`ncn> Yustakta su raspuastd.
=. Inktaxtud`fia a` taxtn Ma `d frd. Ma sar kaiasdrfn, rad`fia ukd fkvastfcdifùpdrd snpnrtdr sus npfkfnkas.
Masdrrn``ak ak su iudmarkn:
4. A` taxtn sa astruiturd d pdrtfr ma mns tfpns ma rac`ds: ds prnpfds ma` taxtny `ds ma` sfstald ma `d `akcud. Ya`aiifnkak ifkin dvfsns pue`fiftdrfns ydkd`fiak `d bnrld inln astds rac`ds sa utf`fzdk ak idmd ukn ma a``ns.
5
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5. A`denrak uk dkukifn pue`fiftdrfn, utf`fzdkmn sù`n fläcakas pdrd axpra-sdr su fmad. _uamak utf`fzdr rainrtas ma ravfstds, parfùmfins n mfeujnsma su prnpfd fldcfkdifùk. Axpnkcdk a` tald dkta a` du`d ma i`dsa,
dkd`fzdkmn bnrld y inktakfmn.
9. A` sfcufakta as uk brdclaktn ma` ]rdtdmn snera `d masneamfakifd ifvf`,ma Hakry ]nradu. A` dutnr utf`fzd ukd tæikfid n tæikfids pdrd mdr dinkniar a` inktakfmn ma su taxtn (kdrrdifùk, masirfpifùk, drculaktd-ifùk). Fmaktfbìquak`ds y sustakta su raspuastd ink ajalp`ns axtrdìmnsma` taxtn.
¾Iùln puama uk hnlera inkbnrldrsaink takar sù`n ukd npfkfùk y mfsbrutdr`d>¾Hdy d`cúk cnia ak a``n sf npfkd quabua dcrdvfdmn> Yf su vaifkn `a astdbd ukmù`dr, ustam kn sa inkbnrld ink sdearqua `n hdk astdbdmn kf ink maifr qua `nhdk astdbdmn, n kf sfqufard ink pamfr`aqua `a pdcua `n qua `a maea, sfkn quafklamfdtdlakta tnld lamfmds inkira-tds pdrd netakar a` flpnrta inlp`atn ypravar qua kn `a vua`vdk d astdbdr. @ddiifùk pnr prfkifpfn, d pariapifùk y a`
masalpaôn ma` maraihn, lnmfbfid insdsy ra`difnkas7 as asakifd`lakta ravn`u-ifnkdrfd y kn infkifma p`akdlakta inkkdmd ma n qua ard dktas. Kn sn`dlaktamfvfma astdmns a fc`asfds, mfvfma bdlf`fds7sì, mfvfma d` fkmfvfmun sapdrdkmn n mfd-eù`fin ma `n mfvfkn ak æ`.
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lamfns ma inlukfidifùk, y hd inkvartfmn d In`nlefd ak uk pdìs inkuk mæbfift fkbnrldtfvn qua prnmuia ukd crdk mfstnrsfùk ak d fkbnrldifùkqua sa mfvu`cd.
Ak asta inktaxtn, `d `flftdifùk ma `ds buaktas ma fkbnrldifùk qua usdk`ns lamfns ma inlukfidifùk, surca inln ukd inksaiuakifd ma` i`fldma fktflfmdifùk y ma `d idlpdôd ma dtdquas inktrd dqua``ns parfnmfstdsqua fktaktdk rad`fzdr ukd `denr ma fkvastfcdifùk. Hdy racfnkas mnkma`ns parfnmfstds snk prasfnkdmns pnr ukn u ntrn ma `ns crupns drldmns d`ldrcak ma `d `ay a fki`usn, pnr raprasaktdktas ma` Cnefarkn `nid` pdrdmfvu`cdr n sf`akifdr ifartd fkbnrldifùk. A` fkbnrla mastdid `d rastrfiifùk
ma` `fera lnvflfaktn inln ntrd `flftdifùk flpnrtdkta d `d `feartdm maaxprasfùk ak In`nlefd. Ak ärads inktrn`dmds pnr `ns crupns drldmns d`ldrcak ma `d `ay, `ns parfnmfstds y ntrns inlukfidmnras snifd`as maeaktrds`dmdrsa edjn ds inkmfifnkas flpuastds pnr asns crupns. Dsì lfsln, ak
znkds ma npardifnkas lf`ftdras n ma inledta, `d buarzd púe`fid inktrn`dy rastrfkca `d `feartdm ma lnvflfaktn.
A` fkbnrla tdlefæk saôd`d `d bd`td ma rac`dlaktn y `d pnid trdkspdrakifdak a` prniasn ma dsfckdifùk ma ds pdutds pue`fiftdrfds inln uk prne`aldpraniupdkta qua puama mdr `ucdr d `d utf`fzdifùk ma `d pue`fifmdm nbfifd`ink bfkas pn`ìtfins y inln ukd harrdlfaktd ma inktrn` y `flftdifùk d `d`feartdm ma praksd. Dmaläs, a` fkbnrla mastdid d takmakifd ma` Cnefarknditud` ma hdiar usn ma astdmìstfids inln ukd ldkard prnpdcdkmìstfid ysflp`fstd pdrd lajnrdr `d fldcak ma su pn`ìtfid y ma `d sftudifùk ma `nsmaraihns huldkns ak a` _dìs.
Ntrn ma `ns talds iaktrd`as ma` fkbnrla y mfsiutfmn ak a` pdka`, as a` ma`ns sfstalds ma pravakifùk y prntaiifùk qua nbraia a` Astdmn in`nlefdknpdrd cdrdktfzdr d feartdm ma axprasfùk. A` fkbnrla dkd`fzd a` prncrdld maprntaiifùk qua nbraia a` Lfkfstarfn ma` Fktarfnr y Justfifd pdrd parfnmfstdsy ntrns inlukfidmnras snifd`as. Ink ra`difùk d asta prncrdld, d ldynrìdma `ns ditnras aktravfstdmns rainknia su flpnrtdkifd ak ldtarfd ma prn-
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taiifùk. Yfk aledrcn, `d Ma`acdifùk tdlefæk raifefù uk crdk kúlarn mairìtfids snera d`cukds ärads qua maeak sar lajnrdmds, fki`ufmd `d bd`td mainnrmfkdifùk aktra a` ùrcdkn dsasnr akidrcdmn ma rainlakmdr lamfmds maprntaiifùk y `ds aktfmdmas fkvastfcdtfvds y jumfifd`as ma` Astdmn, `d bd`td mainkbfdkzd ak d abfidifd ma ns asqualds ma sacurfmdm prnpnrifnkdmns y dmalnrd ak `d flp`alaktdifùk ma `ns lfslns. _arn `d ldynr irìtfid hdifdastns prncrdlds ma prntaiifùk, sa iaktrd ak `d bd`td ma vn`uktdm pn`ìtfid.As maifr, luihds ma ds parsnkds aktravfstdmds pnr d Ma`acdifùk saôd`drnk`d inktrdmfiifùk aktra `d axfstakifd ma astns prncrdlds ma prntaiifùk y a`mfsiursn qua snstfakak d`cukns bukifnkdrfns púe`fins inktrd `d `denr ma`ns inlukfidmnras snifd`as qua kn sù`n astfcldtfzd su trdedjn, sfkn qua
tdlefæk pnka ak pa`fcrn su fktacrfmdm.
Ak kuastrd fkvastfcdifùk, tdlefæk halns fki`ufmn a` pdpa` qua juacd `dMabaksnrìd ma` _uae`n ak ldtarfd ma pravakifùk y prntaiifùk inktrdvfn`difnkas d `ns maraihns huldkns y ak `d `uihd inktrd `d flpukfmdm.Ak pdrtfiu`dr, kns halns iaktrdmn ak a` Yfstald ma D`artds ]alprdkdsastde`aifmn ak `d Mabaksnrìd pdrd lnkftnradr y dmvartfr ma sftudifnkas marfascn ma `d pne`difùk ifvf` ak ra`difùk ink a` inkb`fitn drldmn.
Ak asta saktfmn, `d ldynrìd ma `ns ditnras aktravfstdmns lnstrù ukd crdkpraniupdifùk pnr `d bd`td ma sacuflfaktn ma astns fkbnrlas ma rfascn pnrpdrta ma` ùrcdkn akidrcdmn ma hdiar`n ak a` Lfkfstarfn _úe`fin, a` InlftæFktarfkstftuifnkd` ma D`artd ]alprdkd (IFD]). @`dld `d dtakifùk `d bd`td maalfsfùk ma d`artds, d pasdr ma ns fkbnrlas ma rfascn alftfmns pnr d Mabak-snrìd. Ak asta saktfmn, `d Ma`acdifùk tdlefæk raifefù irìtfids ra`difnkdmdsink `d bd`td ma innrmfkdifùk ink ntrds mapakmakifds cuearkdlaktd`as, `dmfsiraifnkd`fmdm y `d bd`td ma prniamflfaktn ma` IFD] ak `d tnld ma maif-sfnkas pdrd alftfr `ds lakifnkdmds d`artds. _nr ú`tfln, a` fkbnrla saôd`d`d praniupdifùk qua cakard `d lf`ftdrfzdifùk ma `d raspuastd astdtd` dkta`ds d`artds alftfmds pnr a` IFD].
Ntrn ma `ns talds iaktrd`as ma kuastrd fkvastfcdifùk, bua `d `denr ma-salpaôdmd pnr `d Bfsid`ìd ma `d Kdifùk ak `d `uihd inktrd `d flpukfmdm.
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4. D pdrtfr ma `d `aiturd dktarfnr, asirfed tras fmads qua inksfmara ra`avdktas. p`fqua a` saktfmn ma idmd ukd ma a``ds.
5. ¾Tuæ prne`alätfid p`dktadmd ak `d `aiturd, sa mas`fkmd ma` inkiaptn ma fpukfmdm>
9. Uad`fia ukd fkvastfcdifùk, dlp`fdkmn a` tald trdtdmn ak a` dktarfnr kular
=. Asirfed su puktn ma vfstd diarid ma` inkiaptn ma` kulard` mns, y d pdrtfr mafkvastfcdifùk rad`fzdmd, prasakta ukd inrtd ramdiifùk pdrd dpnydr sus puktnsvfstd n inlaktdrfns, ink iftds taxtud`as tnldmds ma `d fkvastfcdifùk rad`fzdm
1. Nrcdkfia ink sus inlpdôarns uk pdka` ra`difnkdmn ink ukd talätfid ditinln `d vfn`akifd fktrdbdlf`fdr, a` abaitn ma` fkvfarkn ak `d sd`um púe`fidakbarlamdmas ma trdkslfsfùk saxud`.
@d aktravfstd
As ak rad`fmdm, uk mfä`ncn aktra mnsparsnkds, ak a` iud` ukd ma a``ds ditúdinln aktravfstdmnr y `d ntrd, inln ak-travfstdmn. @d aktravfstd as inksfmardmd
uk cækarn ma `d rapnrtarìd, a` läs a`a-laktd` y eäsfin ma` trdedjn parfnmìstfin.A` `ncrn ma ukd euakd aktravfstd mapakma
ma n diartdmds y npnrtukds qua sadk ds pracuktds. @d aktravfstd sa inkstftuya ak a` prfl
pdsn hdifd d inksn`fmdifùk ma iud`qufar ntrn cækarn, sad irùkfid, rapnrtdja, kntfifd, a
Mnlfkdr a` drta ma `d aktravfstd y snera tnmn, ma `d trdksirfpifùk qua sa hdcd a``d, kns md `uz varma hdifd `d iradifùk ma uk astf`n prnpfn ak `d ldkard ma ink
4
Idr`ns _uaktas L
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]fpns
4. Aktravfstd ma parsnkdja. ]dlefæk sa inknia inln aktravfstd psfin`ùcfid huldkd. Inkifarka axi`usfvdlakta d` aktravfstdmn, vfstn masma su masalpaôparsnkd`. _nr ajalp`n: `d vfmd ma uk dbdldmn asirftnr, mfsaôdmnr n idktdktaa` quahdiar mfdrfn ma uk drtfstd id``ajarn n ma uk vniadmnr ma parfùmfin, at
5. Aktravfstd talätfid. Ya rabfara d uk a`acfmn aspaiìbfidlakta. _nr ajalp`nA`gfk _dtdrrnyn hde`d snera `ns dma`dktns ifaktìbfins ak @dtfkndlærfid n a` Lkfstrn ma Iu`turd, dkukifd `ds castfnkas qua asd aktfmdm dma`dktdrä pdrd kfôn
y dmn`asiaktas.
Bdsas ma` prniasn pravfn
4. Ya`aiifùk ma` tald. Kn sa`aiifnkdlns
d uk aktravfstdmn, sfk mabfkfr prflarna` tald qua masadlns trdtdr, sd`vniudkmn sa trdtd ma ukd aktravfstd maparsnkdja. Qkd vaz qua hdydlns fmak-tfbfidmn a` tald, nrfaktdlns kuastrddtakifùk d asincar a` parsnkdja quavdlns d aktravfstdr y qua maearä sarfmùkan ak a` dsuktn, sd`vn iudkmn sa
trdtd ma uk haihn trfvfd` y intfmfdkn.
5. Fkvastfcdifùk. Dktas ma aktravfstdr d` parsnkdja qua halns a`acfmn, abaitudl
ukd fkvastfcdifùk lfkuifnsd snera a` tald sa`aiifnkdmn. Ak asta puktn, raiurrflnd ldtarfd` efe`fncräbfin, kdvacdifùk ak Fktarkat y npfkfnkas ma parsnkds id`fbfidmn aspaifd`fzdmds pdrd snkmadr `ds mfvarsds pnsfifnkas inkiaptud`as. _rniamaln
d tnldr kntd ma` ed`dkia qua halns haihn7 ma` maedta qua täiftdlakta sa hdysusiftdmn aktra `ns mfbaraktas mniulaktns n parsnkds inksu`tdmds7 y, `n läs fl
Idr`ns _uaktas La
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Kn as rainlakmde`a fki`ufr tærlfkns in`nqufd`as axprasdmns murdkta `daktravfstd prasakifd`, inln tdlpnin, nrdifnkas parfbærfids d` tald kf rapa-tfifnkas n ramukmdkifds. Ak a` prniasn ma trdksirfpifùk ma `d aktravfstd, `dspracuktds y `ds raspuastds sa mapurdk `avalakta, sfk idusdr lnmfbfidifnkasma idräitar asakifd`. Axfstak sfk aledrcn, ifartds axiapifnkas iudkmn sa trdtdma parsnkdjas iuyd pdrtfiu`drfmdm rasfma justdlakta ak a` `akcudja, inlnpuama sar uk ustrdentds, uk fkmfcakta, uk kdtfvn, uk pnatd, uk bf`ùsnbn, ati.
Ya`aiifnka uk tald y uk parsnkdja. Hdcd `d fkvastfcdifùk kaiasdrfd. A`denra `d atravfstd inrraspnkmfakta. _nr ú`tfln, trdksirfed `d aktravfstd ak a` astf`n kúlarnldkajdkmn a` `akcudja d pdrtfr ma `n saôd`dmn ak asta td``ar.
@d fkvastfcdifùk pravfd, prapdrd d` aktravfstdmnrpdrd astdr d`artd d `ds raspuastds y radiifnkdr inkntrd pracuktd qua inksn`fma `d dktarfnr n quaiuastfnka `d raspuastd mdmd pnr a` aktravfstdmn. @nläs flpnrtdkta, a` parsnkdja puama prasaktdr uk
ldtfz trdsiakmaktd` qua idlefa a` iursn n a` akbnqua ma `d
aktravfstd. _uama prasaktdrsa avaktud`fmdmas inln iudkmn a`aktravfstdmn as masinrtæs7 ratfiakta d` tald, dukqua sad ma sumnlfkfn7 prntdcnkfstd ma uk dinktaiflfaktn qua kn bdvnraiasu fldcak n qua pnr iud`qufar lntfvn, kn astæ fktarasdmn akmdr `d aktravfstd d asa aktravfstdmnr. Ak td` idsn, a` aktravfstd-mnr maea takar tditn subfifakta pdrd ldkfbastdr sutf`lakta susaksfef`fmdm brakta d` tald y mastdidr `d kaiasfmdm ma mdr`n dinkniar d ntrds parsnkds.
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‐@ns hard`mns kacrns“Iæsdr Rd``ajn
Hdy cn`pas ak `d vfmd, tdk buartas... ¡Vn kn sæ!Cn`pas inln ma` nmfn ma Mfns7 inln sf dkta a``ns,`d rasdid ma tnmn `n subrfmn
sa alpnzdrd ak a` d`ld... ¡Vn kn sæ!
Ynk pnins7 parn snk… Derak zdkjds nesiurdsak a` rnstrn läs bfarn y ak a` `nln läs buarta.
Yaräk td` vaz `ns pntrns ma eäredrns Dtf`ds7n `ns hard`mns kacrns qua kns ldkmd `d Luarta.Ynk `ds idìmds hnkmds ma `ns Irfstns ma` d`ld,ma d`cukd ba dmnrde`a qua a` Mastfkn e`dsbald.
Asns cn`pas sdkcrfaktns snk `ds irapftdifnkas
ma d`cúk pdk qua ak `d puartd ma` hnrkn sa kns quald. V a` hnlera… _nera… _nera. Rua`va `ns njns, inln
iudkmn pnr snera a` hnlern kns ``dld ukd pd`ldmd7vua`va `ns njns `nins, y tnmn `n vfvfmn sa alpnzd,inln ihdrin ma iu`pd, ak `d lfrdmd.Hdy cn`pas ak `d vfmd, tdk buartas… Vn kn sæ.
@d ìrfid vdkcudrmfstd
Qkfmdm 5. A pfa ma bntn: `d trdkslfsfùk ma `dfkbnrldifùk y ns sfstalds sfleù`fins
Yasfùk
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‐D`tdznr“ Rfiakta Hufmnern
F
Yny yn D`tdznrAkiarrdmn ak `d jdu`d ma su mastfknAk vdkn la dbarrn d `ns edrrntasma `d avdsfùk pnsfe`a
Qkd b`nr ifarrd a` idlfkn V sa `avdktdk inln `d astdtud ma `ds `dlds.
@d avdsfùk flpnsfe`aLäs mæef` ldrihn ink lfs dksfdsTua uk ajæriftn sfk `uz ak lamfnma alensidmds
Derì `ns njns ak a` sfc`n
Ak qua lnrìd a` irfstfdkfsln.Uatnrifmn ak su iruz dcnkfzdkta
Vd vd d mdr a` ú`tfln suspfrn¾V ldôdkd quæ pnkmralns ak a` sftfn vdiìn>
_nkmralns uk d`ed n uk irapúsiu`n¾V hdy qua pnkar d`cn didsn>@d inrnkd ma aspfkdsIhnrradkmn sus ú`tflds astra``ds sa ldrihftd
Lnrfrä a` irfstfdkfsln qua kn hd rasua`tnkfkcúk prne`aldTua sù`n hd aksaôdmn p`acdrfds luartds.
Luara maspuæs ma mns lf` dôns
FF
Kn hdy tfalpn qua parmar Vd vfaka d cn`nkmrfkd lnkntælp
]rda uk diaktn dktìpnmd ma `ajdk
qua sa diaridkRfaka cnkmn`adkmn `d cn`nkmrfkd D` hnrftdôd ma `d lnktdznkta@d vfn`nkmrfkd y a` cn`nkiia`nMasin`cdmd astd ldôdkd ma `d `uYa diarid d tnmn cd`npa
Vd vfaka vfaka `d cn`nkmrfkd Vd vfaka vfaka `d cn`nkbfkd
Vd vfaka `d cn`nktrfkd Vd vfaka `d cn`nkifldRfaka `d cn`nkihfkdRfaka `d cn`nki`fld
Vd vfaka `d cn`nkrfld Vd vfaka `d cn`nkrfsd@d cn`nkkfôd@d cn`nkcfrd@d cn`nk`frd@d cn`nkerfsd@d cn`nkihf``d
Vd vfaka `d cn`nkmìd
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`d kdturd`azd, d `d luarta, d` dlnr y d Mfns. @n dkaimùtfin y masirfptfvn, dsì inl`n lnrd` y pn`ìtfin buarnk a`flfkdmns ma sus `ìkads ma inlpnsfifùk.
_drd a` pnatd ma vdkcudrmfd, `d pnasìd takìd uk bfk ak sì lfsld y d` pnatd `a inrr
pnkmìd ``avdr d iden asd lfsfùk qua ard purfbfidr `d `ftardturd. Yf `d pd`derd astdakidsf``dmd y dmn`aiìd ma ukd fkbfkftd pnerazd, ard flprasifkmfe`a rnlpar `ds dmurds qua `d `flftdedk.
A` lnlaktn mabfkftfvn infkifma ink a` astd``fmn ma `d prflard cuarrd lukmfd` akdôn ma 464=. Astd cuarrd bua inkmakdmd pnr a` desurmn ma sus sdirfbfifns y inka``d, sa raea`drnk `ns drtfstds ma `d æpnid.
A` surcflfaktn ma `ns ldkfbfastns bua ukd bnrld ma prntastd qua dtdiù `ns dinktalfaktns, pnkfakmn ak ta`d ma jufifn `ns lnma`ns y vd`nras pnr akifld ma `n kuay nrfcfkd`. _arn tdlefæk astns fslns buarnk ldridmns pnr trdksbnrldifnkas akidlpn ifaktìbfin y taikn`ùcfin, d` puktn ma qua d`cukns ma a``ns sa masdrrn``drnpdrtfr ma` mfsiursn y `d bnrld ma `ns a`alaktns qua masdrrn``drnk.
• Yu prfkifpd` latd bua mdr d inkniar a` lukmn fktarfnr ma` hnlera,
pnr `n iud` eusidrnk kuavds astrdtacfds pdrd axprasdr`n.
• A` mastfkn ma `ns hnleras (parsnkdjas), bua ukd ma `ds prfkifpd`aspraniupdifnkas talätfids ak `d iradifùk drtìstfid.
• Mabakmfarnk a` `ucdr ma` fkinksifakta ak a` ditn iradtfvn, a` fkmfvf-mud`fsln y a` vd`nr ma `d `feartdm.
@ns fslns läs raprasaktdtfvns
Ak cakard`, `ds vdkcudrmfds snstuvfarnk d`cukns rdscns inlukas qua `as mfarnkbnrtd`azd y `d buarzd pdrd ldktakarsa, sar vd`nrdmds y rainknifmds. _nr ajalp`n:
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4. Ak su nerd Drta pnætfid, Rfiakta Hufmnern asirfefù `d iæ`aera nrdifùk: pnatd as uk paquaôn mfns“. Mamuzid a` saktfmn latdbùrfin ma astd nrdifùkaxp`fqua su ra`difùk ink a` lnvflfaktn ma vdkcudrmfd.
5. Axp`fqua a` sfcufakta pnstu`dmn qua hdia pdrta ma` fmadrfn astætfin mdmdìs¾Inksfmard qua astd pnsfifùk fkvftded d `d mastruiifùk ma` fkmfvfmun y su
ifamdm> ¾_nr quæ>
9. A` lnvflfaktn vdkcudrmfstd inkiaktrù uk kúlarn ldynr ma fslns ma `ns ap`fidmns ak `ìkads dktarfnras. D`cukns ma `ds läs flpnrtdktas ak a` idlpn `d `ftardturd y a` drta buarnk: a` mdmdìsln, a` flprasfnkfsln, a` axprasfnkfsla` bduvfsln, a` iuefsln, a` buturfsln y a` astrfmaktfsln.
Asinjd ukd ma astds inrrfaktas drtìstfids, masdrrn``a ukd fkvastfcdifùk y prasasus rasu`tdmns ak ukd axpnsfifùk dkta tnmns `ns lfalerns ma` du`d. Aktracd idmd ukn ma a``ns, uk pnald raprasaktdtfvn ma` lnvflfaktn asincfmn.
=. A` pnald ‐@ns Hard`mns Kacrns“ ma Iæsdr Rd``ajn, makukifd ukns saktflfaki`drns ma` yn pnætfin. ¾Tuæ hdy maträs ma asa dlaktn y pnr quæ lntfvn puamabfkfrsa asa pnald inln raprasaktdkta ma` vdkcudrmfsln>
A` sfstald ma Mfns ns hdrä `feras, rnlpam tnmn. Ynfs `nsdlns ma tnmn `n qua rnlpäfs. @ds `ayas, `ds lnrd`as, `dsastætfids sa hdk haihn pdrd qua raspatæfs ds insds bräcf`as.@n qua as bräcf` astä mastfkdmn d sar rntn. _rnedm vuastrdbuarzd ukd sn`d vaz: ns masdbìn d qua maspuæs kn inktf-kuæfs. @n qua kn rnlpäfs ns rnlparä, sarä vuastrn dln.
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@d sfcufakta as `d inksfckd qua dinlpdôù d `nspnatds mdmdìstds ak `d iradifùk ma sus pnalds:
4. A` pnald mdmdìstd sua`a sar ukd trdld nsiurd sfk ùcfid, tajfmd pnr ukdsuiasfùk ma pd`derds y snkfmns, ink ukd fki`fkdifùk hdifd `n tarrnrìbf-in a fkifartn, hdifd `n kfhf`fstd y `n bdktdsfnsn. Uatnla a` pnald quasa `as aktracù murdkta `ds axpnsfifnkas y dkd`fia ak quæ nrdifnkas saraprasaktdk `ds dktarfnras idrditarfzdifnkas.
5. Ak a` äleftn pue`fiftdrfn ¾quæ tfpn ma fläcakas rainknia qua ma`dtak`d vfcakifd ma d`cukns ma `ns lnvflfaktns ma vdkcudrmfd ak kuastrnstfalpns> Yustakta su raspuastd ink rainrtas ma parfùmfins, dbfihas, ati.
‐_drd hdiar uk pnald mdmdìstd“_nr ]rfstdk ]zdrd
Injd uk parfùmfin. Injd ukds tfjards. Asinjd ak a` parfùmfin ukdrtìiu`n ma `d `nkcftum qua iuaktd mdr`a d su pnald. Uainrta a`drtìiu`n. Uainrta aksacufmd, ink iufmdmn, idmd ukd ma ds pd`derds
qua bnrldk a` drtìiu`n y lætd`ds ak ukd en`sd. Dcìta`d sudvalakta. Dhnrd sdqua idmd rainrta ukn trds ntrn. Inpfa inkifakzumdlaktaak a` nrmak ak qua hdydk sd`fmn ma d en`sd. A` pnald sa pdraiaräd ustam. V as ustam uk asirftnr fkbfkftdlakta nrfcfkd` y ma ukd sak-sfef`fmdm haihfzdkta, dukqua fkinlprakmfmd pnr a` vu`cn.
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B n t n t n l d m d
m a S f g f p a m f d
A` rnldktfifsln, iuyns pnatds dld-edk `d masaspardifùk sfkiard n bfk-cfmd tuvn uk rfquìsfln drsakd` madmjatfvns sucaraktas, ma iudktn buard
`úcuera, la`dkiù`fin, sn``nzdkta,tnrlaktnsn, u`u`dkta, masn`dmn,snlerìn, lamfavd`, irapusiu`dr ybukardrfn. @ns sflen`fstds raukfarnkdmjatfvns avdkasiaktas, crfsäians,dkae`dmns, mfbusns, ralntns, npd-`asiaktas, ak tdktn qua `ns lnmar-kfstds `dtfkndlarfidkns `ns tuvfarnk
ha`ækfins, ldrlùrans, varsd``asins,aeúrkans, pdkfmds, bdukasins, sdld-rftdkns, pdusdmns ak sus cfrns, sn``n-
zdktas ak sus vfn`nkiha`ns, äurans aksus d`eds: ma in`nr desfktfn iudkmnma kapaktas sa trdtded, lfaktrds`ava y d`ava sa lnstrded a` d`d ma``ava dedkfin. D` prfkifpfn ma asta
sfc`n, iudkmn a` niu`tfsln sa pusn malnmd ak _drìs, Ydr _a`dmäk ``akdedsus knva`ds ma dmjatfvns qua sucfrfa-rdk `n läcfin, `n id`man, `n asta`dr ydstrd`. Dkdtn`a Brdkia, ak sus vfmdsma sdktns, usded luy häef`lakta `ddmjatfvdifùk ma Jdinen ma d Rnräcfkapdrd mdrsa ‐uk tnkn ma æpnid“. @ns
surrad`fstds buarnk cakfd`as ak hd``dry ralnzdr iudktn dmjatfvn pumfardprastdrsa d aspaiu`difnkas pnætfidssnera `n bdktdsld`, d`uifkdkta, lfs-tarfnsn, ma`frdkta, bnrtuftn, inkvu`sfvny nkìrfin. Ak iudktn d ns axfstakifd-`fstds ma sacukmd ldkn, prabfarak nspuru`aktns a frrftdktas.
Dsì, `ns dmjatfvns sa trdksbnrldk, d`iden ma luy pnin tfalpn, ak a`didmalfsln ma ukd takmakifd `fta-rdrfd, ma ukd cakardifùk. ]rds ma `ns
fkvaktnras rad`as ma ukd axprasfùk,dpdraiak `ns qua sù`n idptdrnk maa``d `ds tæikfids ma ldtfzdr, in`nradry sucarfr: `d tfktnrarìd ma` nbfifn. Viudkmn hny maiflns qua a` astf`n matd` dutnr ma dyar kns rasu`td fksnpnr-tde`a, kn kns rabarflns d` bnkmn, sfknd ns nrnpa`as, utns, dldkardlfaktns
y nrbaerarìds, ma `d dmjatfvdifùk.
V `d varmdm as qua tnmns `ns crdkmasastf`ns sa idrditarfzdk pnr ukd suldpdrquamdm ak a` usn ma` dmjatfvn. Viudkmn sa vd`ak ma æ`, usdk ns dmjatf-vns läs inkiratns, sflp`as, mfraitns,mabfkfmnras ma id`fmdm, inksfstakifd,
astdmn, ldtarfd y äkfln, tdk prabarf-mns pnr qufakas ramditdrnk d Efe`fd,inln pnr qufak asirfefù A` fkcakfnsnhfmd`cn mnk Tufjnta ma @d Ldkihd.
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Inhasfùk vared` y sus a`alaktns bnrld`as
@d prnmuiifùk ma uk taxtn as ukd tdrad
qua rai`dld uk lamfdkn inkniflfaktnma` iùmfcn `fkcðìstfin, ma sus rac`ds y vd-rfdktas. Ya asirfea pdrd fkbnrldr, axprasdr,drculaktdr, snifd`fzdr n sflp`alakta, pnra` cnia ma kdrrdr y prnmuifr nerds ftardrfds.
@n ifartn as qua iudkmn sa asirfea, a` alf-snr sulfkfstrd uk pdquata ma pfstds qua`a parlftak d` `aitnr, dmaläs ma` iùmfcn,fktarpratdr `ds fmads qua sa astäk p`dktadkmn. _drd `ncrdr a` nejatfvn, ak-idmakd pd`derds, nrdifnkas y pärrdbns qua tarlfkdk, bnrldkmn uk tnmncrdifds d` trdedjn ma inktaxtud`fzdifùk qua pdu`dtfkdlakta vd flprflfakmnak a` rainrrfmn qua hdia ma` mfsiursn.
Ldktakar `d `fkad`fmdm y i`drfmdm ma asta mfsiursn, raqufara uk euak
ldkajn ma `d inhasfùk y `d inharakifd, mns a`alaktns idrditarìstfinsma tnmn euak taxtn.
Ya mfia qua hdy inhasfùk taxtud` iudkmn idmd ukd ma ds pdrtas n a`alaktnsbnrld`as ma uk taxtn (sustdktfvns, inkjukifnkas, prapnsfifnkas, dmjatfvns,dmvarefns, tarlfkdifnkas qua fkmfidk inkinrmdkifd ak parsnkd, kúlarn,tfalpn n cækarn), ldktfaka ukd ra`difùk y ukd nrcdkfzdifùk qua `as par-lfta cakardr saktfmn.
Inhasfùk sfckfbfid ukfùk, ak asta idsn, ukfùk ma pd`derds qua prnpnrifn-kd ukfmdm d tnmn asirftn. Uasu`td fktarasdkta var iùln ukd hfstnrfd sa vdinkstruyakmn d pdrtfr ma `d axpnsfifùk ma `ns talds qua dinlpdôdk d `dfmad edsa. Asta haihn puama mataitdrsa, sf sa dkd`fzd a` tfpn ma pd`derds,`ns inkaitnras qua sa utf`fzdk (idlpns saläktfins), y a` tfalpn vared` quadinlpdôd d `d kdrrdifùk.
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@ns inkaitnras snk dqua``ds pd`derds paquaôds qua sfrvak pdrd ukfr y mdr`a saiuaky inharakifd d ns asirftns, y `avdr ak bnrld nrmakdmd, a` p`dktadlfaktn y masdrrnma ds fmads. Nesarva d sfcufakta tde`d qua di`drd ak quæ idsns maeak sar utf`fzdm
Dmfifùk V, ma fcud` bnrld, dmaläs, akifld
Dmvartakifd Lfrd, ¡iufmdmn!, nya, ¡ah!
Inrraiifùk Euakn, raitfbfidkmn, lajnr mfihn
Inki`usfùk Ak bfk, pnr ú`tfln, ak sìktasfs
Inktrdsta _arn, sfk aledrcn, d pasdr ma, dukqua, kn nestdkta
Mfcrasfùk _nr ifartn, d prnpùsftn
Ajalp`fbfidifùk _nr ajalp`n, fki`usn, td` inln
Ækbdsfs _uas sì qua, ifartdlakta, i`drn qua, ak asa saktfmn
Axp`fidifùk As maifr, d sdear, astn as
Fktaksfbfidifùk As läs, läxfla, läs dúk
Uastrfiifùk Hdstd ifartn puktn, sf didsn, pasa d qua
Uasulak Ma iud`qufar bnrld, ak rasulak, ak rasulfmds iuaktds
]ald Ak iudktn d, pnr `n iud` sa rabfara d
]rdksfifùk _nr ntrd pdrta, ak ntrn nrmak ma fmads
Idusd _nr td` rdzùk, mdmn qua, ak inksaiuakifd, ma dhì qua
]falpn D` prfkifpfn maspuæs d vaias
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Masdrrn``dr ak su iudmarkn:
4. Yaôd`a iuä`as snk `ds tasfs qua p`dktad a` taxtn ma D`ajn Idrpaktfar.
5. Uasd`ta ns inkaitnras taxtud`as qua sa akiuaktrak ak a` taxtn ma Fktrnmuiiy axp`fqua `d fmad qua idmd ukn ma a``ns qufsn trdkslftfr.
9. Uanrcdkfia asds lfslds fmads, utf`fzdkmn ntrns inkaitnras taxtud`as.
=. Qtf`fia su mfiifnkdrfn a fkvastfcua a` sfckfbfidmn ma ds pd`derds qua a rasu`tdrmasinknifmds. Ink asta `fstdmn, ramdita uk asirftn pdrd axpnkar su puktn vfstd diarid ma d`cukds ma `ds fmads d``ì axprasdmds. Ynifd`fia dkta a` iursn,trdedjn rad`fzdmn.
Masdrrn``dr ak su iudmarkn:
4. Uatnlak a` asirftn ma Fktrnmuiifùk a fmaktfbfquak d`cukns a`alaktns crdl
tfid`as qua fkmfquak inkinrmdkifd ak kúlarn, parsnkd, tfalpn y cækarnqua d su vaz ldktakcdk `d maefmd inhasfùk. Ajalp`n: ak a` ú`tfln pärrdbn `d aiturd, d inkjukifùk qua ra`difnkd d pd`derd varmdm ink d pd`derd tnm@d, inln drtìiu`n, dinlpdôd d varmdm, qua as uk sustdktfvn prasaktdkmn ura`difùk ma kúlarn y cækarn7 crdkmas as uk dmjatfvn qua sa ra`difnkd iastf`ns, qua as uk sujatn lakifnkdmn ak tariard parsnkd ma` p`urd`.
5. @d inhasfùk sa md crdifds d` euak usn ma` `æxfin. @ns inkaitnras, p
4
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Yalfkdrfn fktarkdifnkd`_n`ìtfids púe`fids pdrd `d supardifùk ma `d pnerazd
Iaktrn ma Inkvakifnkas ma `d _`dzd Ldynr ma Lama``ìk
_drtfifpdktas aspaifd`fstds: Uueæk @n Run`n (mfraitnr Iaktrn Fktarmfsifp`fkdrfnpdrd a` Astumfn ma _n`ìtfids _úe`fids Drcaktfkd), _de`n Rf``dtnrn (inksu`tnrMfvfsfùk ma Masdrrn``n Ynifd` y Qkfmdm ma Astumfns Aspaifd`as. IA_D@ Ihf-`a), Jnrca Fväk Cnkzä`az (mfraitnr ma` IFM ma `d Qkfvarsfmdm Kdifnkd` maIn`nlefd). @d sftudifùk ma pnerazd qua vfvak läs ma lf` lf``nkas ma parsnkds ak a`lukmn hd ne`fcdmn d paksdr ak mfvarsds astrdtacfds, prncrdlds y p`dkas quadpuktak d su ramuiifùk n arrdmfidifùk7 d mabfkfifùk ma astds astrdtacfds hdraquarfmn nptdr ma bnrld axp`ìiftd n kn, pnr ukd ldkard ma aktakmar a`bakùlakn ma `d pnerazd, sus idusds, idrditarìstfids, `ns ditnras fkvn`uird-
mns ak `ds sn`uifnkas y `ds lamfmds qua hdk ma tnldrsa pdrd akbraktdr`d.
Aktakmar `d pnerazd inln uk prne`ald ma lú`tfp`as mflaksfnkas, ra-qufara ma `d dp`fidifùk ma akbnquas inlp`alaktdrfns ak `ds pn`ìtfidsqua pratakmak dbaitdr`d. Ak pdrtfiu`dr `ns dpnrtas ma `ns akbnquas mamaraihns huldkns y a` rainkniflfaktn ma `ds mfbarakifds, fki`ufmn akæsta a` ma cækarn, nbraiak a`alaktns fkmfspaksde`as qua vfakak sfakmnflp`alaktdmns y prnlnvfmns pnr vdrfns saitnras snifd`as, didmælfins y
A salfkdrfn
Qkfmdm 9. Inharakifd, inhasfùk vared` yinkinrmdkifd `fkcðìstfid
Yasfùk
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nrcdkfslns fktarkdifnkd`as, parn dúk iuaktdk ink pnid dp`fidifùk ak`ns kfva`as kdifnkd`as.
A` akbnqua ma `ns maraihns huldkns parlfta hde`dr ma `ds sn`uifnkas
d `d sftudifùk ma pnerazd masma ukd parspaitfvd ma maraihns y ne`fcd-ifnkas y kn sù`n masma `d dsfstakifd snifd`7 rasd`td a` pdpa` pdrtfifpdtfvnqua maeak jucdr `ds parsnkds ak sftudifùk ma pnerazd ak `d p`dkadifùky ajaiuifùk ma `ds pn`ìtfids y iuaktd ink uk inkjuktn ma vd`nras lnrd`asukfvarsd`lakta rainknifmns y rabnrzdmns pnr ne`fcdifnkas jurìmfids, lu-ihds ma æstds susirftds pnr `d ldynrìd ma `ns Astdmns, inln as a` idsn ma`‘_ditn ma maraihns ainkùlfins, snifd`as y iu`turd`as‖ susirftn pnr läs
ma 41? pdìsas n d Inkvakifùk snera ns maraihns ma` kfôn diaptdmd idsfma ldkard ukfvarsd`. Astns inlprnlfsns maeak cufdr a` inktakfmn ma `dspn`ìtfids d flp`alaktdr.
Qkd lfrdmd mfbarakifdmd ma `ds idusds a flpditns ma `d pnerazd snerahnleras y lujaras `d prnpnrifnkd a` akbnqua ma cækarn, yd qua fki`uyaa` dkä`fsfs snera ns bditnras iu`turd`as qua dsfckdk mfstfktns rn`as y bukifn-kas snifd`as sacúk a` saxn y qua tfakak fkifmakifd ak ldynras n laknras
kfva`as ma pnerazd.
@d nesarvdkifd ma d mfvarsfmdm iu`turd` mabfka tdlefæk `ds idrditarìstfidsma ds pn`ìtfids ma arrdmfidifùk ma `d pnerazd, puas as kaiasdrfn inkniara` sfckfbfidmn y `ds kaiasfmdmas mfbarakifdmds ma `ds pne`difnkas qua saakiuaktrdk ak astd sftudifùk, fki`uyakmn aspaifbfifmdmas ma ns mfbaraktascrupns ætkfins, yd qua a` crdmn ma mfspnsfifùk ma raiursns n `ds idrdita-rìstfids ma ns lfslns vdrìdk ma diuarmn ink astd mfvarsfmdm. _nr n tdktn,
sarìd uk arrnr aspaifbfidr ukd lamfmd pdrd `d arrdmfidifùk ma `d pnerazdak bukifùk ma uk kfva` hnlncækan n edjn uk irftarfn ma ukfvarsd`fmdm,masinknifakmn `ds pdrtfiu`drfmdmas pne`difnkd`as.
D d uz ma astns akbnquas, sa rad`fzdrä uk ed`dkia ma ds pn`ìtfids ma uihdinktrd `d pnerazd flp`alaktdmds ak Dlærfid @dtfkd ak `ds ú`tflds mnsmæidmds y uk mfä`ncn ink d`cukds fkfifdtfvds ma pn`ìtfid púe`fid ak asta
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A` salfkdrfn
A` salfkdrfn as uk ajarififn ma fkvastfcdifùk ak crupn qua parlfta `d axp`nrdifùkprnbukmfzdifùk ma ukd vdrfamdm ma tùpfins ink uk aja iaktrd`, ink fktarvakifùk m
parsnkd` aspaifd`fzdmn ak `ds ärads sa`aiifnkdmds inln nejatn ma astumfn.
Inktrdrfn d `n qua niurra ink ntrds tæikfids ma axprasfùk nrd`, a` salfkdrfn as ukditfvfmdm aspaifd`fzdmd qua fkiaktfvd d inkstruiifùk ma inkniflfaktn ak a` lfsltfalpn irnkn`ùcfin iudkmn sa astä masdrrn``dkmn.
@ns pdrtfifpdktas kn snk axpnsftnras qua sa uefidk brakta uk púe`fin pdrd sar asiihdmns y raifefr sus fktarvakifnkas. ]dlpnin eusidk idptdr fkbnrldifùk ma tariarnak bnrld pdsfvd. Yu bfkd`fmdm as ajariftdrsa lamfdkta a` astumfn parsnkd` ak uk dpskn ldynr ma mns hnrds. @ns fktacrdktas ma` salfkdrfn sa raúkak ak inlfsfnkas axp`nrdk `ds fmads lamfdkta ukd fktardiifùk raiìprnid. Kn hdy d`ulkn kf prnbasn`ds fmads vdk y vfakak, sa inkmaksdk y tnldk bnrld y mfraiifùk.
Uac`ds ma nrcdkfzdifùk
Astds snk `ds rac`ds qua sa maeak takar ak iuaktd ak `d prapdrdifùk ma uksalfkdrfn:
• Knlerdlfaktn ma uk prasfmakta y uk ra`dtnr.
• Ma`flftdrsa a` tald iaktrd` y `ns suetalds, dktas ma aktrdr ak ldtarfd.
• As flprasifkmfe`a ma`flftdr a` tfalpn y iulp`fr`n.
•
@ns salfkdrfstds maeak takar uk kfva` hnlncækan ma inkniflfaktns.• A` kúlarn cakard` ma pdrtfifpdktas kn maea axiamar `ds 1? parsnkds.
• Astds 1? parsnkds maeak inkbnrldr inlfsfnkas (suecrupns), y d su vaz,ma`flftdr a` suetald qua idmd ukd vd d trdedjdr.
• Idmd inlfsfùk maea astdr akideazdmd pnr uk innrmfkdmnr y uk saira-tdrfn.
• A` kúlarn ma salfkdrfstds maea nsif`dr aktra iudtrn y 4? parsnkds.
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45
Masdrrn``a ak su iudmarkn:
4. Ma`flftak y prapdrak aktra tnmns `ns lfalerns ma` du`d y ak inlpdôìd ma smniakta, uk tald ma fktaræs cakard`, sfcufakmn `ds pdutds y knrlds fkmfidmpdrd `d rad`fzdifùk ma uk salfkdrfn.
5. Qkd vaz inki`ufmn a` salfkdrfn, asiuihak dtaktdlakta `d inki`usfùk qu
prasaktd a` ra`dtnr y tnlak kntd ma tnmns `ns puktns.
9. Mfvfmdk d `ns lfalerns ma` crupn, ak suecrupns ink hdstd iudtrn parsnkdink edsa ak `ns puktns qua `ayù a` ra`dtnr, ratnlak a` tald y dkd`fiak: ¾quabaitns takmrìdk ukds lamfmds n ukds inki`usfnkas mfbaraktas d ds p`dktadmd
=. Avd`úak a` trdedjn masdrrn``dmn pnr idmd lfalern ma` crupn y prasaktak suinki`usfnkas.
Masdrrn``a ak su iudmarkn:
4. Ink edsa ak `d fkbnrldifùk raincfmd ak a` salfkdrfn ma` ]d``ar In`ai-tfvn, asirfed ukd kntd parfnmìstfid ak `d iud` rasaôa a` masdrrn``n y `dsinki`usfnkas ma` lfsln.
5. Fkvastfcua ak Fktarkat, uk salfkdrfn qua hdyd sfmn in`cdmn ak `d ram. Dkd`fia y asirfed `d bnrld inln bua ma`flftdmn.
5
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@ns Maraihns Huldkns
Masma su dprnedifùk ak 46=8, `d Mai`drdifùk ma`ns Maraihns Huldkns hd sfmn y sfcua sfakmn ukdbuakta ma fkspfrdifùk ma `ns asbuarzns kdifnkd`asa fktarkdifnkd`as pdrd prnlnvar y prntacar `nsmaraihns huldkns y ds feartdmas bukmdlaktd`as.
Qk a`alaktn asakifd` pdrd d prntaiifùk ma ns maraihns huld-kns, as `d mfbusfùk dlp`fd ma su inkniflfaktn y bnlaktn ma `dinlpraksfùk aktra `ds pne`difnkas, pdrd qua sapdk iuä`as snksus maraihns y iùln puamak mabakmar`ns. Ak `d ditud`fmdm, `dMai`drdifùk astä mfspnkfe`a ak läs ma 92? fmfnlds y as a` mn-iulaktn läs trdmuifmn ak a` Lukmn, `n iud` md tastflnkfn masu idräitar y d`idkia ukfvarsd`as.
Maspuæs ma läs ma 2? dôns, rakmflns hnlakdja d `d vfsfùkaxtrdnrmfkdrfd ma `ns ramditnras nrfcfkd`as ma `d Mai`drdifùk y d`ns kularnsns mabaksnras ma `ns maraihns huldkns ak tnmn a`Lukmn, qua hdk `uihdmn pdrd hdiar rad`fmdm su vfsfùk.
Astd Mai`drdifùk partakaia d tnmns y idmd ukn ma knsntrns. Dhnrdkns inrraspnkma `aar`d, astumfdr`d, prnlnvar`d y rafvfkmfidr`dinln kuastrd.
9. _rasakta sus prnpfds inki`usfnkas diarid ma` tald ma `d fkvastfcdifùkrad`fzdmd ak a` dktarfnr kulard`.
=. Fkvastfcua snera uk tald qua `a sad dtrditfvn y hdifakmn `ds vaias mara`dtnr, prasakta su fkbnrla.
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Yf a` lamfn ma fkbnrldifùk as paquaôn, hderä uk parfnmfstd pdrd idmd `ìkad taltfid. _arn pnr `n cakard`, idmd ukd astä inlpuastd pnr uk aqufpn ma parfnmfsinnrmfkdmns pnr uk amftnr. _nr ajalp`n: a` tald iu`turd` astä saiifnkdmn d su vak `ferns, drtas asiækfids, drtas p`ästfids, lúsfid, ati.
@ds 1S
Hdia uk sfc`n qua `ds 1S ardk `d maknlfkdifùk pnr axia`akifd pdrd a`iaktrn asta cækarn ma `d fkbnrldifùk ak pdrtfiu`dr. @ds 1S snk `ds ifkin
pracuktds eäsfids qua maearäk sar rasua`tds ak d kntfifd: qufæk, quæ, mùkma,iuäkmn y pnr quæ. A` iùln as ukd pracuktd dmfifnkd`, tdlefæk matarlf-kdkta ak a` inkjuktn fktacrd` ma `d kntfifd. @ns fktarrncdktas bukmdlaktd`asmaearäk sar lnstrdmns ak a` `adm, as maifr, ak a` prflar pärrdbn.
@ds buaktas
Ya ``dld buaktas d qufakas sulfkfstrdk `dfkbnrldifùk. Dsì, uk prniasn ma pdz, pnrajalp`n: prnmuifrä kntfifds pn`ìtfids n ma
nrmak púe`fin, y ds buaktas saräk ns vnia-rns masfckdmns pnr a` cnefarkn, pn`ftù`ncnsy raprasaktdktas ma `ns crupns ravn`uifn-kdrfns fkvn`uirdmns, aktra ntrns. ]nmn `ndktarfnr sa dp`fid d praksd, fkvastfcdifùkdidmælfid a Fktarkat.
Brdkg _adr`, kacnifdmnr ma`Cnefarkn Kdifnkd` ak `ns mfä`ncns
ink `ds BDUI ak @d Hdedkd
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• Mùkma: as d fkbnrldifùk ra`difnkdmd ink d uefidifùk cancräbfidak mnkma tuvn `ucdr a` dinktaiflfaktn.
• _nr quæ: as `d pdrta qua ntnrcd `d flpnrtdkifd ma `d kntfifd. Yfa` pnrquæ kn tfaka ra`avdkifd, kn tfaka saktfmn inkvartfr ukdfkbnrldifùk ak kntfifd. A` pnrquæ ajaria ukd ma `ds tdrads läsflpnrtdktas ak a` lnlaktn ma inkvnidr d` `aitnr.
9. Iuarpn. As a` masdrrn``n ma d kntfifd y masc`nsd idmd ukn ma ns mdtnsaxpuastns ak a` adm. Astn kn sfckfbfid qua a` iuarpn ma d kntfifd maedraftardr d fkbnrldifùk yd sulfkfstrdmd. A` iuarpn maea di`drdr tnmn a`dinktaiflfaktn, inlukfidkmn ak nrmak ma prfnrfmdmas y saiifnkdkmn
`d fkbnrldifùk ak pärrdbns ma iudtrn d safs `ìkads. Idmd pärrdbn maeatakar uk nejatfvn i`drn, as maifr, idmd ukn maea dpnrtdr fkbnrldifùkinharakta a flpnrtdkta. A` iùln as idsf sfalpra, d ldtarfd ma` iuarpn,dukqua tdlefæk sa sua`a suldr a` pnrquæ.
=. Ifarra. _uama flp`fidr uk masp`facua ma mns pärrdbns n sar iuastfùk mamns `ìkads. As ukd inki`usfùk n ukd axpnsfifùk ma `ds inksaiuakifdsqua maldkmd a` dinktaiflfaktn7 tdlefæk puama trdtdrsa ma pravfsfn-
kas n lamfmds tnldmds.
@d pfrälfma fkvartfmd
Iudkmn hde`dlns ma pfrälfmas, quaralns maifr axditdlakta `n qua ukddrquftaiturd pfrdlfmd` sucfara: ukd ifld puktfdcumd iuyn mfälatrn as a`ärad läs ramuifmd ma tnmd `d astruiturd7 ukd bd`md qua d pdrtfr ma `d ifld,
sa vd aksdkihdkmn7 y ukd edsa subfifaktalakta inksfstakta pdrd snpnrtdra` rastn ma `d astruiturd.
A` masdrrn``n ma `d kntfifd sa nrcdkfzd ma fcud` bnrld, axiaptn pnrqua `dpfrälfma as fkvartfmd pdrd nbraiar d` aitnr dktas qua kdmd, ukd dlp`fd edsan p`dtdbnrld qua inktakcd `d asakifd ma `d kntfifd: a` `adm. Maktrn ma a``d,vdlns dcntdkmn ak bnrld pdu`dtfkd, ds mfvarsds iuastfnkas qua mascrdkdk`d kntfifd, hdstd ``acdr d `ns matd``as lakns ra`avdktas.
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• Maefmn d d kaiasfmdm ma ukd amuidifùk pamdcùcfid inktal-pnräkad, qua asi`drazid dspaitns ra`difnkdmns ink d saxud`fmdmma kfôns y dmn`asiaktas, dided ma sar puastd d mfspnsfifùk ma
`ns `aitnras laxfidkns `d nerd Yaxud`fmdm ak `d Amuidifùk, ukinlpakmfn ma tras tnlns qua ink ukd vfsfùk ditud`, md `uiassnera a` tald.
5. @ad d sfcufakta kntfifd y saôd`a d` brakta, a` dktatìtu`n, a` tìtu`n, a` `adm,a` iuarpn y a` ifarra, saôd`dkmn aspaiìbfidlakta mùkma alpfazd ytarlfkd æsta ú`tfln.
@d ldjastunsd iukd ma` sdear dktfcun radera sus puartds, trds hdearsapuastn `d prflard pfamrd ak 4688. @d kuavd varsfùk ma `d efe`fntaid,sftudmd ak a` Lamftarräkan, iuaktd ink kularnsds sd`ds, aktra ds iud`as
mastdidk `ds ma lúsfid dktfcud, `ds ma bnkmns ma pdpfrns, parcdlfkns,iùmfias, `ferns rdrns a fkiukde`as…
@d ifumdm ma D`ajdkmrìd sa vfsta ma cd`d pdrd ia`aerdr d rafkducurdifùkma d qua hdia 5.9?? dôns cudrmdrd varmdmarns tasnrns ma` sdear huld-kn, prnmuifmns pnr d cakfd`fmdm ma Drfstùta`as, Drquìlamas, Aui`fmas,Hfpdtfd, Hfpùirdtas y Cd`akn, aktra luihns ntrns.
D`ajdkmrìd, `ucdr mnkma `d huldkfmdm rain`aitù ma ldkard sarfd ysfstalätfid a` inkniflfaktn ma` Lukmn, as ak rad`fmdm `d hfjd ma`flparfn ma `ns _tn`nlans ak Acfptn, iuyns suiasfvns rayas suldedkajalp`dras inpfnsdlakta, inln `ns trdkspnrtdmns ak `ns kdvìns, quaardk ldkusirftns fkidutdmns talpnrd`lakta ak `ns puartns, murdktaa` tfalpn qua tdrmdrd su trdksirfpifùk rad`fzdmd sflu`täkadlakta pnrvdrfns asirfeds, lfaktrds ntrn bukifnkdrfn `aìd ak vnz d`td.
Maspuæs ma 4.2?? dôns ak D`ajdkmrìd:YA UAFKDQCQUD @D EFE@FN]AID LÄY C@NUFNYD MA@ LQKMN
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@d inkqufstd ma `d ba`fifmdmEartrdkm Uussa``
Inln sa mfia qua d eaefmd y ds idrfifdssnk ds puartds ma d d`acrìd, d cakta saalerfdcd fklamfdtdlakta y prniurdkn mdrsa iuaktd ma `n luihn qua `aln`astdk sus inlpdôarns. Iudkmn hdk
eaefmn läs ma `d iuaktd `ns hnlerasalpfazdk d ``nrdr y d `dlaktdrsa ma`n fkmfckns qua snk lnrd`lakta ma`idrfôn ma sus ldmras. ]nmn n qua ink-sfcuak ink a` d`inhn` as `ferdrsa ma `dsaksdifùk ma` paidmn, insd qua d rdzùkinksfcua ak ns lnlaktns läs úifmns.
@d rdzùk ma astds mfstfktds i`dsas mamascrdifd sa hd``d, ak pdrta, ak a` sfsta-ld snifd`, y, ak pdrta, ak `d psfin`ncìdfkmfvfmud` qua as kdturd`lakta, ak ukdprnpnrifùk inksfmarde`a, uk prnmuitnma` sfstald snifd`.
@d amuidifùk ak d irua`mdm y ak a` lfa-
mdrsa pnr qufakas snk asi`dvns ma apdsfnkas. Ak `d dmn`asiakifd `d vfmd ard nmfnsd, y astded inktfkudlaktaenrma ma` sufifmfn, ma` iud` la `fecrdifds d` masan ma sdear läs ldtal
tfids… hdear masiuefartn iuä`as a`ds insds qua masaded läs y hdear dqufrfmn crdmud`lakta luihds ma a`Ak pdrta as maefmn tdlefæk d hdearmasprakmfmn, ba`fzlakta, ma ifartns msans… parn ak `d ldynr pdrta sa mad `d praniupdifùk idmd mìd laknr,
lì lfsln.
As varmdm qua `ds praniupdifnkas tarfnras trdak `d pnsfef`fmdm ma mn`nrlukmn puama hukmfrsa ak ukd cuarifartds i`dsas ma inkniflfaktns puamsar mfbìif`as ma d`idkzdr, `ns dlfcnspuamak lnrfr. _arn astd i`dsa ma mn
A aksdyn ftardrfn
Qkfmdm 9. Inharakifd, inhasfùk vared` yinkinrmdkifd `fkcðìstfid
Yasfùk
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`d vfmd inln `ns qua sa prnmuiak ma`mfscustn inksfcn lfsln. V tnmn fktaræsaxtarkn fkspfrd d`cukd ditfvfmdm qua,lfaktrds a` fktaræs parldkaia ditfvn,
kns pravfaka pnr inlp`atn inktrd a`tamfn. A` fktaræs pnr ukn lfsln, d`inktrdrfn, kn inkmuia d kfkcukd ditfvf-mdm prncrasfvd. ]nmn æxftn sarfn ak uktrdedjn mapakma ma uk fktaræs cakufknpnr a` ldtarfd` ink qua a` trdedjn astära`difnkdmn. A` hnlera d` qua sù`n `apraniupd qua a` lukmn `a dmlfra, kn
as prnede`a qua inksfcd su prnpùsftn.@d vdkfmdm iudkmn trdkspnka ifartns`ìlftas, ldtd a` p`diar ma tnmd hdef`fmdmaspnktäkad y inkmuia bdtd`lakta d `dfkmfbarakifd y d` deurrflfaktn.
A` häeftn ma lfrdr d` buturn y ma iraarqua `d vfmd kn tfaka ntrn saktfmn qua a`
ma prnmuifr a` pnrvakfr as parkfifnsn. @dvfmd kn maea inkiaefrsa inln uk la-`nmrdld ak a` iud` a` hærna y `d harnìkddtrdvfasdk mfbfiu`tdmas fkiraìe`as hdstd``acdr d uk bfkd` mfihnsn. @d rdìz ma` ld`astä ak `d flpnrtdkifd qua sa inkiamad` æxftn ak `d inlpatakifd inln ldynr
buakta ma ba`fifmdm. Vn kn kfacn qua `dinksaiuifùk ma` æxftn bdif`fta a` cnia ma`d vfmd… ]dlpnin kfacn qua a` mfkarn,hdstd ifartn puktn, sad luy idpdz madulaktdr `d ba`fifmdm7 läs d``ä ma ifartnpuktn kn `n iran dsì. @n qua sì dbfrln asqua a` æxftn kn as läs qua uk fkcramfaktama d ba`fifmdm, y qua sa inlprd maldsfd-
pnr inksacufr`n. Dukqua as ifartn quak tnmd prnbasfùk axfsta uk a`alakma inlpatakifd, kn n as lakns qua ksa raspatd praifsdlakta a` æxftn, sfk
`ds iud`fmdmas d `ds qua sa hd maefmn æxftn. Qk hnlera ma ifakifd puama n khdiar mfkarn, parn kn as läs raspatdmsf `n hdia qua sf kn `n hdia.
Ak Dlærfid a` hnlera prnbasfnkd` flfd` hnlera ma kacnifns, y kn inkstftuyinln ak Aurnpd, ukd idtacnrìd dpdrt
Ak `ds i`dsas d`tds kn hdy, pnr `n tdktkdmd qua lftfcua `d `uihd, defartd brdkid, pnr a` æxftn bfkdkifarn. @ns kfôdlarfidkns inlprakmak luy prnkqua astn as `n úkfin qua iuaktd, y ksa praniupdk ma `d amuidifùk qua ktakcd pnsfef`fmdmas paiukfdrfds. Ak sfc`n XRFFF ukd ma `ds idrditarìstfids m
cakt`aldk ard a` pnmar custdr y aktamar ma `ftardturd, lúsfid y pfkturd.
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Yækaid
Nrìcakas y avn`uifùk
As mfbìif` astde`aiar `d baihd iudkmn sa
nrfcfkù a` aksdyn. _drd `ns fkvastfcdmn-ras, `ns Mfä`ncns ma _`dtùk, `d _nætfidma Drfstùta`as, `ds Apìstn`ds Lnrd`asma Yækaid y ntrns asirftns, snk `ds prf-lards buaktas ak `ds iud`as sa fkiueùa` cækarn. Yu avn`uifùk prnpfdlaktamfihd kn sa inknia, parn d pdrtfr ma`dôn 418?, dpdraia ukd pue`fidifùkma` brdkiæs Lfiha` ma Lnktdfcka inka` tìtu`n Assdfs. Astns aksdyns kn takìdkntrd prataksfùk pnr pdrta ma` dutnr, sfknma`aftdr y mdr d inkniar d uk crupn madlfcns, sus mfvdcdifnkas diarid ma ukdlu`tfp`fifmdm ma talds.
A` rainkniflfaktn inln cækarn kn sa hfzn ak asa lnlaktn, parn sì samastdiù a` idräitar fkta`aitud` ma` asirftn. @d pn`ælfid y `d drculaktdifùkkn snk pdrta ma astns taxtns, inln sì, su mfsiursn in`nqufd` y uk astf`neäsfin qua maspuæs tnldrä ukd bnrld läs rab`axfvd.
@n ifartn as qua masma aktnkias, d pd`derd aksdyn inlakzù d mfkdlfzdrsay id`dr, maefmn d `ns idlefns snifd`as, pn`ìtfins, ainkùlfins y iu`turd`asqua vfvfù Aurnpd ak `ns sfcufaktas dôns.
@ns fkta`aitud`as ma aktnkias, sa vfarnk denidmns d `d rab`axfùk, d `d fk-tarfnrfzdifùk ma talds inln `d luarta, `d ra`fcfùk, `d vfmd, y dúk sneradspaitns katdlakta mfmäitfins. @d pdrta suejatfvd ma` asirftnr, su par-snkd`fmdm y sus flprasfnkas aktrdrnk d `d `ftardturd, parn a` aksdyn sù`ndmqufara a` tnkn ink a` iud` sa `a rainknia d lamfdmns ma` sfc`n XFX,iudkmn alpfazd d tnrkdrsa läs sarfn.
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Rfsfùk inktalpnräkad
As uk cækarn ra`dtfvdlakta lnmarkn qua dedrid ukd lfsia`äkad ma mfsif-p`fkds hatarncækads, `n iud` hdia flpnsfe`a mabfkfr`n ak uk sn`n inkiaptn
y mdr`a ukd lfsld mfraiifùk. Ak sì, as ukd bnrld mfsiursfvd defartd quaaxtfakma uk dedkfin ma pnsfef`fmdmas y parlfta trdtdr talds bf`nsùbfins,huldkìstfins, pn`ìtfins, snifd`as, ati.
Yu fktakifùk prfldrfd kn as fkbnrldr, sfkn parsudmfr n inkvakiar d` `aitnr,mabakmfakmn uk puktn ma vfstd parsnkd`, p`dsldkmn rab`axfnkas a flprasfn-kas y dpnyäkmnsa, d`tarkdlakta ak `ns jufifns y astumfns ma aspaifd`fstds ak
a` tald.
Ak su avn`uifùk, kn md idefmd d ntrds bnrlds astætfids inln d ìrfid, pnrquadkta tnmn a` aksdyn as uk cækarn axfcakta qua maldkmd drculaktdifùk,i`drfmdm y rab`axfùk, pnr luy trfvfd` qua sad a` tald qua astæ trdtdkmn.
Dukqua d lazi`d ma cækarns as ukd ma `ds idrditarìstfids ma crdk pdrta ma`ds bnrlds ma asirfturd inktalpnräkad, kn as ifartn qua iud`qufar taxtn,
d` subrfr ukd latdlnrbnsfs, puamd inkvartfrsa ak tnmns. Ak a` bnkmn, idmdcækarn sfcua cudrmdkmn su asakifd. Ynk `ds mfvarsds mfsifp`fkds `ds qua saakidrcdk ma djustdr`n d sus kaiasfmdmas.
A` aksdyn ftardrfn tdlpnin nstaktd uk astf`n aspaiìbfin. Ink ntrds mfsifp`fkdsy ink d ifakifd ak pdrtfiu`dr, inlpdrta a` fktaræs pnr axp`nrdr läs d bnkmn`d rad`fmdm7 fkiursfnkd läs ak `ns `dearfktns ma` sdear ink a` prnpùsftn madprnxfldrsa d `d varmdm ma `ns haihns.
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Iùln sa asirfea uk aksdyn
A` aksdyn ldkajd ukd astruiturd edstdkta `fera, ak aspaifd`, sf sa tfaka ak iuak
`d hatarncakafmdm ma mfsifp`fkds qua ldkajd (pn`ìtfid, ra`fcfùk, bf`nsnbìd, `ftardtuati.). _arn ak cakard`, hdy uk hf`n inkmuitnr ma` iud` tnmds sa sfrvak. Ak sus prfla`ìkads, a` aksdyfstd prasaktd uk prne`ald qua n `avd d p`dktadr ukd hfpùtasfs diama `ds inksaiuakifds n idusds ma` prne`ald7 maspuæs, ``acd d ukd tasfs marfvdmd `d dktarfnr inkjaturd.
Ak asta puktn, a` aksdyfstd sa dtrava d prasaktdr ukd dbfrldifùk qua maea maltrdr murdkta `d axpnsfifùk qua masdrrn``drä ak a` asirftn n iuarpn ma` trdedjn. As
lnlaktn iudkmn a` asirftnr hdia cd`d ma sus inkniflfaktns y sus puktns ma vfsIdmd tasfs eusid sar vd`fmdmd. A` aksdyfstd mamuia, p`dktad, ascrfla, akidmakd fmads, y `n läs flpnrtdkta, drculaktd ma td` bnrld qua puamd vd`fmdr `d fmad prifpd` qua pnstu`ù ak `ds prflards `ìkads.
4. A` brdclaktn ma `d `aiturd ma fktrnmuiifùk, axprasd uk puktn ma vfstd parkd` diarid ma` tald ma `d ba`fifmdm. Uatnla tras ma `ds tasfs ak æ` p`dktadmda`denra uk aksdyn ink sus puktns ma vfstd, akrfquaifakmn `d fkbnrldifùk intrds rab`axfnkas.
5. @ad kuavdlakta a` brdclaktn ma fktrnmuiifùk y sustakta `ns lntfvns pnr iud`as puama sar inksfmardmn uk taxtn irìtfin y bf`nsùbfin. Drculakta i
nrdifnkas axtrdìmds ma` lfsln aksdyn.9. ‐@d amuidifùk ak `d irua`mdm y ak a` lfamn as ld`d, parn as `d úkfid q
puama mdrsa pnr qufakas snk asi`dvns ma asds pdsfnkas“. ¾_uama dbfrldrsa qastd nrdifùk ma Uussa`` takfakmn ak iuaktd a` inktaxtn ak a` qua sa axprainktfaka ukd fktakifùk raprasfvd y dkdirùkfid pdrd `ns tfalpns lnmarkn
Drculakta ak sus pd`derds.=. ¾_nmrìd dbfrldrsa qua `ds irìtfids qua prasaktd a` dutnr, vdk mfrfcfmds d uk sfs
ld pn`ìtfin, d` ldkajn ma `ns vd`nras ak `d snifamdm lnmarkd n d `d fkb`uak
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Masdrrn``dr ak su iudmarkn:
4. @ad d`cukns aksdyns iuyd talätfid `a rasu`ta dtrditfvd. Aktra a``ns,asinjd uk aksdyn ifaktìbfin y uk aksdyn ftardrfn iuyds talätfids sadkdbfkas. @æd`ns dtaktdlakta y prasakta uk dkä`fsfs ak pdrd`a`n, lns-trdkmn dqua``ns dspaitns qua `ns mfbarakifdk y dqua``ns qua `as mdk
hnlncakafmdm inln raprasaktdktas ma` cækarn aksdyìstfin.
5. Uatnla ukd ma `ds fmads p`dktadmds ak iud`qufard ma `ns aksdynstrdedjdmns ak a` kulard` dktarfnr y prasakta su prnpfd axpnsfifùkaksdyìstfid.
9. @ad dtaktdlakta a` sfcufakta brdclaktn y axp`fqua hdstd quæ puktnpuama sar inksfmardmn uk aksdyn n fkmfqua d qua ntrn cækarn pnmrìd
partakaiar.
‐Ak uk ajalp`dr ma` prflar vn`ulak ma @ds lf` y ukdkniha (@nkmras, 48=?), ma @dka, qua la inksfcufùlf quarfmn dlfcn _du`fkn Gafks, masiuerflns a` ld-kusirftn qua dhnrd trdmuifræ d` idsta``dkn“. Ink astds
pd`derds, a` asirftnr drcaktfkn Jnrca @ufs Enrcas fkfifdsu Fkbnrla ma Ernmfa, uk taxtn `ftardrfn qua lazi`d d`cækarn aksdyìstfin ink a` iuaktn. @ad a` taxtn saôd`dmna fkmfqua, ink brdclaktns ma` lfsln, ak quæ lnlaktnmajd ma sar iuaktn pdrd ratnldr `ds idrditarìstfids ma`aksdyn y vfiavarsd.
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Eartrdkm Uussa``
Bf`ùsnbn y ldtalätfin erftäkfin, cd`drmnkdmn inka` pralfn Knea`. Yu ækbdsfs ak a` dkä`fsfs `ùcfinrapariutfù snera a` iursn ma `d bf`nsnbìd ma` sfc`nXX. Kdifmn ak ]ra``aig (Cd`as), a` 48 ma ldynma 4835, Uussa`` astumfù ak a` ]rfkfty In``aca ma`d Qkfvarsfmdm ma Idlerfmca. ]rds crdmudrsa ak486=, vfdjù d Brdkifd, D`aldkfd y Astdmns Qkfmns,
y `uacn bua knlerdmn lfalern ma` inksajn macnefarkn ma` ]rfkfty In``aca. Masma luy jnvaklnstrù uk diusdmn saktfmn ma inkifakifd snifd`y d` lfsln tfalpn, sa aspaifd`fzù ak iuastfnkasma `ùcfid y ldtalätfids, ärads snera `ds iud`asmfn inkbarakifds ak luihds fkstftuifnkas ma tnmna` Lukmn. Uussa`` d`idkzù a` æxftn ink su prfla-rd crdk nerd _rfkifpfns ma ldtalätfids (46?5),
ak `d iud` fktaktù trds`dmdr `ds ldtalätfids d`ärad ma `d bf`nsnbìd `ùcfid y mntdr`ds ma uk ldrinifaktìbfin praifsn. In`denrù murdkta nihn dônsink a` bf`ùsnbn y ldtalätfin erftäkfin D`bramKnrth Shftahadm, pdrd a`denrdr `d lnkulak-td` nerd _rfkifpfd Ldtalätfid. Ak su sfcufaktacrdk nerd, @ns prne`alds ma `d bf`nsnbìd (4645),Uussa`` raiurrfù d `d snifn`ncìd, `d psfin`ncìd, `dbìsfid y `ds ldtalätfids pdrd rabutdr `ds mnitrfkdsma` fmad`fsln, `d asiua`d bf`nsùbfid mnlfkdkta akasa tfalpn, qua snstakìd qua tnmns `ns nejatns yaxparfakifds snk brutn ma` fkta`aitn. Uussa``, ukdparsnkd rad`fstd, iraìd qua `ns nejatns parifefmnspnr ns saktfmns pnsaak ukd rad`fmdm fkharakta d`ldrcak ma `d lakta.Bntns tnldmds ma Sfgfpamfd
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• Diuôdr: inkiaktrdr.• Dbde`a: dcrdmde`a, mu`ia, sudva ak `d
inkvarsdifùk y a` trdtn.• D`uifkdkta: qua prnmuia saksdifnkas
frrad`as.• Dtf`d: jaba ma `ns hukns, eäredrn a fk-
huldkn, iuyn knlera sa dsnifd inkinlpnrtdlfaktns vfn`aktns.
• Dvfmaz: dksfd, inmfifd.•
Dzdrnsd: turedmd, talarnsd.• Inkmaksdr: sfktatfzdr, rasulfr, inl-
pakmfdr, `fiudr.• Inyukturd: ifriukstdkifd qua dbaitd
uk dsuktn.• Irapftdr: prnmuifr snkfmns rapatfmns,
räpfmns y sains.• Mairapftum: mfslfkuifùk. Id`fmdm ma
parsnkd dkifdkd ink bdiu`tdmas mfslf-kufmds.
• Mæbfift: bd`td n asidsaz.• Mfraitrfz: qua matarlfkd a` iursn n
mfraiifùk.• A`niuakifd: drta ma hde`dr ak púe`fin.• Arrdmfidr: drrdkidr ma rdìz.• Avdkasiakta: qua sa masvdkaia n
asbuld.• Cakt`aldk: pd`derd fkc`asd qua masfc-
kd d` ided``arn fkc`æs ma ifartn rdkcnsnifd` n d` hnlera qua sa `a dsalajdak pnrta, inlpnrtdlfaktn y ditftum.
• C`dmfdmnr: `uihdmnr qua ak a` ifrinrnldkn, inledtìd inktrd ntrn n inktrdukd bfard.
• Hurtdmf``ds: ma bnrld burtfvd, sfk quasa knta.
• Fkinktfkakifd: sfk inktakifùk, sfkbrakn.
• Frdiukmn: rdefnsn ak axiasn.
• Jdrdkd: mfvarsfùk eu``fifnsd y d`enrn-tdmd.
• Jìedrn: lfalern ma uk puae`n dla-rfkmfn ma d vartfakta nrfaktd` ma Aiud-mnr.
• Jf`cuarn: as ukn ma `ns päjdrns läs``dldtfvns ma Aurnpd. Ya mnlastfidbäif`lakta y puama iruzdrsa ink a`idkdrfn.
•
@dsifvfd: prnpaksfùk d `ns ma`aftasidrkd`as.• @acdmn: harakifd qua sa majd n trdks-
lfta d `ns suiasnras.• @anktfkd: idmakd latä`fid pdrd in`cdr
a` ra`nj ma en`sf``n.• Lariakdrfn: hnlera qua pdrtfifpd
ak uk inkb`fitn eæ`fin d idlefn ma ukpdcn.
• Lìlasfs: drta ma flftdr lnmn ma
hde`dr, castns y dmaldkas ma ukdparsnkd.
• Kfhf`fsln: fman`ncìd qua kacù tnmnprfkifpfn ra`fcfnsn, pn`ìtfin y snifd`.
• Nkìrfin: ra`dtfvn d `ns suaôns.• Nknldtnpayd: vnide`n qua flftd n
rairad a` snkfmn qua masirfea.• _aiukfdrfd: ra`difnkdmn ink a` mfkarn
ak abaitfvn.• _araiamarn: qua luara.• _arkfifnsn: mdôfkn y parjumfifd`.• Ua`dtnr: parsnkd qua kdrrd haihns n
talds.• Ynpasdr: axdlfkdr a` prn y a` inktrd
ma uk dsuktn.• ]rfed`: partakaifakta n ra`dtfvn d `d
trfeu.• Q`u`dkta: qua md crftns n d`drfmns.
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9. Ftals kulardmns y vfôatds. @ns `fstdmns snk d`fdmns ma `d rataktfvdra`djdk `d lakta raditfvd (idpdifmdm ma dsflf`dr y radiifnkdr), ma` `aitavftdkmn `d praniupdifùk fkinksifakta pnr parmarsa ak `d saiuakifd mafkbnrldifùk.
=. Uasd`tdmns n saôd`as pdrd hfpartaxtns n taxtns inlp`alaktdrfns. Ya masaôd`dr ink ntrn in`nr n ink uk suerdydmn, `ds pd`derds läs flpnrtdkma` mniulaktn n ma` e`nqua ma taxtn. @ds pd`derds tfpn vìkiu`n n hfpvìkiu`n maeak fr ak dzu` y suerdydmds. A` in`nr dzu` `n idptd luy räpfa` njn y ukfvarsd`lakta astä inmfbfidmn inln uk a`alaktn qua rasaläs fkbnrldifùk, `d iud` as sulfkfstrdmd iudkmn sa pu`sd a` lnusa sne`d pd`derd.
Ajalp`n:
A` Ln`fkn Unjn, lusfid` ifkaldtncräbfin ma` mfraitnr Edz @uhrldkk, ashfstnrfd ma` _drìs enhalfn ma bfkd`as ma` sfc`n XFX, iudkmn parsnkdjas inl]nu`nusa-@dutrai vfvìdk ak `d fkiasdkta eúsquamd ma` dlnr, iuyn hd``dzla dtravn d supnkar, `a bua kacdmn d æ`, pdrtfiu`drlakta, mdmd su inkifùk ma akdkfsln qua, pdrd bnrtukd ma `d Ea``a æpnqua y ma `d hfstnrfd,
inkmujarnk d asd ldrdvf``nsd buakta ma trdedjn drtìstfin qua tnldrìd vfma `acdmn cfcdkta.
1. Fktartìtu`ns. Maeak sar mfraitns a fkbnrldtfvns, y dpdraiar ink braiuakima ldkard qua sa inkvfartdk ak fkmfidmnras y cuìds ma rainrrfmn mafkbnrldifùk pdrd a` njn.
2. Kn justfbfidr d` iaktrn. Iaktrdr e`nquas ma fkbnrldifùk as inktrdprnmuia
ta, pnrqua sf a` njn kn akiuaktrd `d `ùcfid y a` nrmak ma` taxtn ma ldkafklamfdtd, kn sù`n alpazdrä d bdtfcdrsa, sfkn qua pdsdrä d ntrn saclak
3. Kn usdr ldyúsiu`ds parldkaktas. As ukd mfkälfid qua a` njn kn rasfspnrqua `n ne`fcd d sar inksifakta ma idmd `atrd ak ra`difùk ink `d dktary ink `d sfcufakta. Astn sa maea d qua a` njn astä dinstulerdmn kn sù`n`ds bnrlds fktarkds ma `ds `atrds, sfkn tdlefæk d `ds axtarkds7 y ak `ds lyúsiu`ds `ds bnrlds axtarkds sa tnrkdk `fkad`as
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_rfnrfmdmas ak `ns mdtns
qua sa lnktdk ak Fktarkat
Hdy mns a`alaktns fkmfspaksde`as pdrd bdif`ftdr d a`aiifùk ma fkbnrldifùk kaiasdrpdrd astruiturdr ukd päcfkd wae.
4. Jardrquìd. Iudkmn quaralns pnkar fkbnrldifùk ak Fktarkat, maealns dkd`fzrdifnkd`lakta n qua ink axditftum eusidrìd a` usudrfn-`aitnr. Ma a``n mapakm`d abaitfvfmdm ma` sftfn wae qua sa rab`ajdrä ak a` kúlarn ma usudrfns qua inksu`tak y ak aspaifd`, ak d ratrnd`flaktdifùk qua sa prnmuzid maspuæs. Ak
wae, `n qua inksfmardlns läs flpnrtdkta pdrd a` eakabfifn y `ds kaiasfmdmma` `aitnr, `n astde`aialns ak `d prflard aktracd, y `ns bditnras suesfcufakta`ns jardrqufzdlns ink a` lfsln irftarfn. Asa jufifn kn puama sar ntrn sfkn sarvfifn qua quaralns prastdr n `d kdturd`azd rad` ma `n qua nbraialns.
Ajalp`n
A` sftfn sa ``dld Asiua`d Dbrfwae y nbraia iursns snera `d iu`turd dbrfidkd. D
usudrfn a fktarasdräk ns iursns qua nbraia d fkstftuifùk. A` prncrdld as dlp`fparn a` sftfn wae jardrqufzd `ns talds y a`flfkd ma `d prasaktdifùk `ns laknra`avdktas, y rasarvd d`cukns pdrd iudkmn a` usudrfn hdcd inktditn.
5. INKIUAIFÙK. Maea sar idrditarìstfid ma `d ramdiifùk y ma tnmns `ns bditnraqua fktarvfakak ak d astruiturd ma d wae. @ds pd`derds i`dva snk a` fkmfidtfvma` `fstdmn ma pd`derds ink `ds iud`as iraalns qua a` usudrfn pnmrä akinktrkuastrn sftfn wae. Asa `fstdmn sa hdia, supnkfakmn `n qua a` `aitnr eusidrä, paksdkmn ak `n qua quaralns qua æ` akiuaktra.
Ajalp`n
Qk usudrfn eusid fkbnrldifùk snera a` drta rupastra ma Dlærfid @dtfkd. @dpd`derds ink `ds iud`as pnsfe`alakta, sn`fiftdrä astd fkbnrldifùk saräk:
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4. Astde`azid uk aqufpn ma fktacrdktas pdrd a` sfcufakta trdedjn ma idlpn:
• Iraak d inlpnsfifùk talätfid ma uk parfùmfin fkstftuifnkd` pdrd Fktarkqua takcd iudtrn päcfkds n pdktd``dzns.
• A`denra sfata saclaktns ma dvdkias pdrd mfstrfeufr ak `d prflard päcfink sus raspaitfvns tftu`dras.
• Asirfed brdclaktns fkbnrldtfvns qua sfrvdk pdrd fksartdr ak `ds rastdk
tras päcfkds.
• Masdrrn``a d`cukds ma ds kntds qua buarnk dkukifdmds ak ns dvdkias, ldkard qua puamd sustaktdr `ds tras päcfkds dmjuktds.
• Hdcd bntncrdbìds n eäja`ds ma Fktarkat pdrd dpnydr `d fkbnrldifùk quavd d mfstrfeufr ak tnmn a` parfùmfin.
• Iraak a` knlera ma` parfùmfin y cakarak uk fstdmn ma 4? pd`derds i`d
• Drta prain`nlefkn• Drta rupastra• Drta ak pfamrd• _atrnc`fbns• Bnrlds drtìstfids ak Yumdlærfid• Bnrlds drtìstfids ak Iaktrndlærfid• _fkturds rupastras• Hd``dzcns drquan`ùcfins• Drta lnef`fdrfn• @ftnasiu`turd• Lurd`as ak pfamrd• Drta `dtfkndlarfidkn• Rastfcfns ma pfamrd
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‐Ed`tdsdr Cærdrm (4111-4185)“ Judk Jnsæ Drran`d
Fr d ldtdr d` prìkifpa ma Nrdkca. Frd ldtdr`n y inerdr `uacn `ns vafk-tfifkin lf` asiumns qua nbraifùBa`fpa FF pnr su ideazd. Fr d pfa,
sn`n, sfk raiursns, sfk pfstn`d, sfkiuihf``n, iradkmn a` cækarn ma `nsdsasfkns qua pfmak d su vìitfld a`mfkarn qua hdia bd`td pdrd inlprdra` drld ma` irflak, td` bua `d hd-
zdôd ma Ed`tdsdr Cærdrm, uk jnvakidrpfktarn ma Mù`a.
D trdvæs ma ukd paknsd parsaiu-ifùk pnr `ns _dìsas Edjns, luartnma hdlera y ma bdtfcd, pdmaifakmnfkinktde`as malnrds aktra `ns ajær-iftns aspdôn`as y b`dlakins, `ncrùderfrsa pdsn hdstd su vìitfld. Akmumds, rnmans y ratrniasns fkvfrtfù
tras dôns y tuvn qua snpnrtdr `dvajdifùk ma qua Cdspdr Dôdstrn `atnldrd `d ma`dktard.
A` pnrtucuæs Cdspdr Dôdstrn, in-larifdkta ma pdôns, kn idraiìd ma
fldcfkdifùk, snera tnmn dkta uksaôua`n ma vafktfifkin lf` asiumns.Hnlera praidvfmn, a`fcfù iufmdmn-sdlakta a` prniamflfaktn y d baihd
ma` irflak. _arn d ú`tfld hnrd ma-ifmfù pnkar uk fktarlamfdrfn aktrasu iaraern y a` drld: Judk Jäuracuf`d alpuôdrìd pnr æ`.
Judk Jäuracuf, jnvakzua`n ma vafk-ta dôns, ard tìlfmn ma pnr sì. _arn
Dôdstrn `ncrù talp`dr su d`ld hdstd
a` harnìsln, lamfdkta uk sfstald masutf`as indiifnkas iuyd sairatd i`dvasa kns asidpd. ]d` vaz n derulù ink`aiturds harnfids7 td` vaz n prnvayùma td`fsldkas7 td` vaz `n ``avù la-tùmfidlakta hdifd uk inksifaktasufifmfn.
@n úkfin qua sdealns ink iartazdas qua a` mìd saôd`dmn pnr su pdtrùk(48 ma ldrzn ma 4185), y murdkta`ns bastfvd`as ia`aerdmns ak Dlearaspdrd hnkrdr d` muqua ma Dkjnu ak su
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_dutds pdrd a`denrdr uk dkä`fsfs `ftardrfn
]nmn dkä`fsfs `ftardrfn maea inktalp`dr `d nerd ak su inkjuktn. Qkd axp`fidifù
brdclaktdrfd qua sa prasakta inln uk `fstdmn, kn as uk dkä`fsfs sfkn ukd eurmra`difùk ma inktakfmns.
A` varmdmarn dkä`fsfs axfca d` `aitnr, ra`difnkdr, inlpdrdr, fktacrdr, masifbrdr y p`dldr `n `aìmn edjn ukd pnsfifùk mnkma su vfsfùk parsnkd` as mabfkfmd, efak sad ed`d bnrld ma uk aksdyn n ukd rasaôd. @d tìpfid lakifùk ma `ds pdutds ak sn`ftdrfn,`d ldkard ma uk `fstdmn, `fqufmdk tnmn varmdmarn dkä`fsfs.
]dlefæk as flpnrtdkta takar ak iuaktd, qua `d efncrdbìd ma` dutnr as axtarfnr d nerd. As frra`avdkta pratakmar mf`uifmdr, inlprakmar a fktarpratdr uk asirftn pnr vfvakifds ma` dutnr, pnr su idräitar n su parsnkd`fmdm. @d nerd maea axp`fidrsa pnsì lfsld y pnr `ds fmads qua sueydiak ak tnmn mfsiursn, läs dúk, sf asta mfsiursas `ftardrfn.
Dktas ma fkfifdr a` dkä`fsfs, sa maea fmaktfbfidr `ds sfcufaktas pdutds lìkflds:
4. ]ald5. Drculaktn9. _arsnkdjas=. ]alds i`dva1. @nid`fzdifùk cancräbfid2. ]falpn hfstùrfin
3. Uaiursns `ftardrfns: tfpn ma kdrrdmnr, astf`n, tfalpn fktarkn, tfpns mamasirfpifùk y bfcurds `ftardrfds
A` sfcufakta ajalp`n kn as ukd suld ma mdtns, sfkn ukd ra`difùk ma a`alaktn(fmaktfbfidifùk ma `ns parsnkdjas, inktaxtud`fzdifùk hfstùrfid ma `d nerd, dkä`fsfs inlaktdrfn ma` puae`n ma Inld`d, ati.), qua sa akiuaktrdk maktrn ma `d nerd7 ukaxpnsfifùk inlaktdmd ma` `aitnr qua hd sdefmn idptdr dspaitns ma `d asakifd qu
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42
Masdrrn``a ak su iudmarkn:
4. @d masirfpifùk as ukn ma ns a`alaktns läs flpnrtdktas ak kularnsdsnerds `ftardrfds. Qtf`fzdkmn uk `acudja `ftardrfn, masirfed a` `ucdr mnkmasa masdrrn``drnk ns haihns. @ad kuavdlakta d @aiturd ma fktrnmuiifùky hdcd saktfr d su buturn `aitnr, `d ea``azd, lfstarfn u hnrrnr ma` `ucdrmnkma niurrfù `d hfstnrfd, ak uk asirftn dkd`ìtfin ma 4? `ìkads.
5. @ad kuavdlakta `d hfstnrfd ma Ed`tdsdr Cærdrm, iaktra su dtakifùk aka` parsnkdja prfkifpd` y axp`fqua iuä`as huefardk sfmn `ns rasu`tdmnsma `ns dinktaiflfaktns vfvfmns, sf a` parsnkdja huefasa tnldmn ntrdmaifsfùk y ntrn rulen.
9. @ns haihns kdrrdmns ak Mù`a, ¾puamak ra`difnkdrsa ink d`cúk dinkta-iflfaktn vfvfmn ak kuastrn _dìs ak `ns ú`tflns dôns> Axp`fqua.
Masdrrn``a ak su iudmarkn:
4. ¾_nr quæ a` ra`dtn ma Drran`d sa inksfmard uk taxtn `ftardrfn>
5. Yaôd`a tras raiursns `ftardrfns utf`fzdmns pnr a` dutnr. Axp`fqua ak quæ inksfidmd ukn ma a``ns.
9. Fmaktfbfqua d` parsnkdja iaktrd` ma `d nerd y dkd`fia `ds idrditarìstfids qua
mabfkak inln td`.=. Matarlfka `ns tras a`alaktns qua mabfkak `d astruiturd ma` ra`dtn.
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‐Lnkù`ncn ma` fksulfsn“(Brdclaktn)
Judk Jnsæ Drran`d
_nsaì d `d huærbdkd `d kniha lfsld ak qua va`äedlns d su pdmra d `d`uz pdrpdmadkta ma `ns ifrfns (¡Nh, sf pumfard maifr astn lfsln ink ntrdspd`derds!).
Inln tnmn sa sdea ak asta lukmn, `d insd ``acù d nìmns ma` vfajaif``nqua lfrd kuastrn sfc`n d trdvæs ma sus ld`fifnsns quavamns. La rabfarn d
asa dkifdkn saônr qua prasfma `ds `atrds laxfidkds tnidmn ink a` cnrrnma mnrlfr ma `ns lalnrfd`fstds, y qua la vdpu`aù ak p`akd id``a ink suakburaifmn edstùk, dkta `d fkabfidifd ma `d pn`fiìd ifumdmdkd. Uaifeì tdl-efæk ukd inrrnsfvd ``uvfd ma fkjurfds prnbarfmds ink vnz dcumd y burfnsd.
V tnmn, crdifds d qua a` fkinrraitn pdtrfdrid ¡a` mfde`n sa `n ``ava! astdedakdlnrdmn ma `d mu`ia luihdihd qua masma dhnrd la denrraia.
¡Dy ma lì! Vd la denrraia hdstd d dvdkmard, d pasdr ma kuastrns iäkmfmnsy mf`dtdmns dlnras. V `d ea``d inkbfmakta, d qufak a` maifr pnpu`dr saôd`dinln lf Mu`ifkad, kn qufsn nìr yd `ds quajds ma` inrdzùk mn`fakta ma supnatd. Iran qua la maspraifdk hdstd `ns parrns.
_nr bnrtukd, astds fkbdlas hde`dmurìds kn puamak ``acdr hdstd lf quarfmnpúe`fin. Vn idktn pdrd uk dumftnrfn inlpuastn ma raidtdmds saônrftds y maalpn`vdmns vfajftns pnsftfvfstds. D a``ns `d dtrnz aspaifa kn ``acd7 astäk
Lnkù`ncn y sn f nqufn
Qkfmdm =. Yalfùtfid ma` ifearaspdifn: fktakifnkasinlukfidtfvds, vdrfds bnrlds ma axprasfùk
Yasfùk
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Ak su vfmd, tnmd parsnkd d`cukd vaz, ldktuvn uk mfä`ncn inksfcn lfsld n `dkzuk sfkkúlarn ma rai`dlns y mfdtrfeds d uk fktar`niutnr qua asiuihded ak bnrlrasfckdmd y pdsfvd. Astds bnrlds ma axprasfùk raifeak a` knlera ma lnkù`ncn sn`f`nqufn. Astds bnrlds ma axprasfùk nrd` tdlefæk partakaiak d` idlpn ma `d tardturd y `ds hd alp`admn inln raiursn `ftardrfn ak `d kdrrdtfvd y `d mrdldturcfd
B n t n s t n l d m d s m a S f g f p a m f d
@ns sapu`turarns axhuldk a` iräkan ma Vnrfig,
a` eubùk pnr Aucèka Ma`dirnfx (i. 4896)
@d bfcurd ma Hdl`at astä buartalakta `fcdmd
Asiakds ma Hdl`at ma Sf``fdl Yhdgaspadra.
Yn`f`nqufn
As uk mfsiursn qua alfta uk parsnkdjapdrd sì lfsln, pnr lamfn ma mfvdcd-
ifnkas alnifnkd`as n bf`nsùbfids. Ua-b`axfnkd, sdefækmnsa a` fktar`niutnr masì lfsln, inksifakta ma `d kaiasfmdmma akinktrdr ukd pnsfe`a raspuastd dsus mumds a fktarrncdktas. A` sn`f`nqufnp`dktad uk mf`ald qua sdiuma `d fktf-lfmdm ma` fktar`niutnr y qua kn as läsqua `d inksifakifd ma qufak `n alfta.
A` ajalp`n läs raprasaktdtfvn masn`f`nqufn ak `d `ftardturd, as Hdl`atma Yhdgaspadra, nerd ak `d iud` a`parsnkdja axprasd su `dlaktn braktad `d maiapifùk y dkcustfd qua `a hdprnvnidmn a` inlpnrtdlfaktn ma suldmra qua kn cudrmù subfifakta mua-
`n dkta `d luarta ma` aspnsn y sa hdidsdmn kuavdlakta.
A` sn`f`nqufn as ukd bucd ma `drcnspaksdlfaktns qua b`uyak y sa fktar-inkaitdk ak ukd sfktdxfs idrcdmd maaxi`dldifnkas. Ajalp`n: ak a` taxtnma D`lds luartds ma Kfgn`äf Cncn`.
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Lnkù`ncn
@ns asirftnras y mrdldturcns `n usdk läs qua a` sn`f`nqufn. A` lnkù`ncn as uk m
iursn qua bnrlu`d uk sujatn qua ak bnrld inksifakta, pakatrd ak su fkinksifay axprasd sus saktflfaktns y saksdifnkas läs prnbukmds. ¾Tufæk as su fktar`niut_nr n cakard`, ntrn parsnkdja qua kn sa prnkukifd kf sa rava`d dkta ds pd`derds mmfsiursn. A` hde`dkta fktarpa`d, diusd, axpnka ak uk dia`ardmn b`ujn qua akidmasfk tracud, ukd fmad trds ntrd.
@d ftardturd deukmd ak ajalp`ns ma lnkù`ncns y ns akinktrdlns masma a` sfc`n nrn: A` parrn ma nrn ma @npa ma Racd7 Lrs Mdf``nwdk ma Rfrcfkfd Snn`b, Dktas masdyukn ma N. Ka``y, @d läs buarta ma Ducust Ytfkearc, @d vnz huldkd ma JaInitadu, Ynera a` mdôn qua hdia a` trdedjn ma Dktnk Ihæjnv, Lnkù`ncn ma LnE`nnl ak Q`fsas ma Jdlas Jnyia, aktra ntrns.
Masdrrn``dr ak su iudmarkn:
4. ¾D qufæk sa mfrfca a` lnkù`ncn qua sa prasaktd ak d @aiturd ma fktrnmuiifù
5. ¾Axfsta ukd fktakifùk ldkfpu`dmnrd pnr pdrta ma` alfsnr ma` lnkù`ncn> Yf as dsì, ¾d quæ dpuktdk sus mfcrasfnkas>
9. ¾Tuæ tfpns ma pd`derds parlftak fkbarfr a` astdmn dkìlfin ma` parsnkdja>
=. @ns drculaktns ak ns iud`as a` ditnr-parsnkdja dpnyd sus quajds, sa edsdk ukd matarlfkdmd sftudifùk: ¾quæ tfpn ma sftudifùk as> ¾Hdy uk nrmak `ùcfak sus nrdifnkas> Axp`ìqua`ds.
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‐A` cnrrfùk ak a` tajdmn“Cfnvdkkf _dpfkf
_draia flpnsfe`a, parn asns erutns cfcdktas ma mns pfarkds pdraiak iradmnsdpnstd pdrd kuastrn idstfcn. N kns hdiak prfsfnkarns, n kns ldtdk, y, kninktaktns ink astn, la bdstfmfdk a` suaôn.
Kn aktfakmn kdmd ma `n qua pdsd. @uz drrfed y `uz dedjn. _draia qua saastä hdifakmn ma mìd y, sfk aledrcn, æsta kn as a` id`nr ma sn`.
A` haihn as qua astd kniha kn as pnsfe`a mnrlfr ak pdz.
La pdraia qua hdia pnin ha racrasdmn d` kfmn y ak astd æpnid ma` dôn dsknihas kn tarlfkdk kukid. Kn puama sar `d ldôdkd. Dquì hdy uk lfsta-rfn. Dedjn ak a` astde`n nfcn vnias7 drrfed ak a` ifa`n ntrds vnias, kn sæ maqufæk. ¾Yarä pnsfe`a qua `ns hnleras sa hdydk puastn ma rapakta d vn`drinln knsntrns> ¡Yarìd kuastrd rufkd!
Masdrrn``dr ak su iudmarkn:
4. @adk kuavdlakta ns ajalp`ns prasaktdmns ma lnkù`ncn y sn`f`nqufn. Dkd`fiaak matd``a ns brdclaktns, y raspnkmdk masma a` puktn ma vfstd fkcðìstfin, ¾qu`ns diarid y quæ `ns mfbarakifd>
5. @ns sfcufaktas pärrdbns snk uk ajalp`n ma lnkù`ncn iuyn nrmak hd sfmn d`tardm
fktakifnkd`lakta pdrd a` ajarififn. Uaasirfedk a` taxtn, eusquak su inharakiy axp`fquak quæ fmads `as sucfrfù a` lnkù`ncn ak masnrmak.
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5. Asirfed uk sn`f`nqufn qua axpnkcd su masdzùk dkta `d fkidpdifmdm mad`idkzdr uk masan qua hd ldktakfmn murdkta luihn tfalpn.
9. A`denra uk fstdmn ma pnsfe`as talds qua n fkqufatdk n aktusfdsldk yqua qufsfard axpnkar d ntrns. Uamdita su prnpfn lnkù`ncn, asincfakmnukn ma `ns dktarfnras dsuktns.
Lnrfr…, mnrlfr7 kn läs y ink uk suaôn sdear qua mflns bfkd `ds inkcnjds, y d `ns lf` snerasd`tns kdturd`as qua inlpnkak`d harakifd ma `d idrka, inksuldifùk as æstd qua ink ruacnssa puama masadr. Lnrfr, mnrlfr…“.
Sf``fdl Yhdgaspadra
Asirftnr, pnatd, dutnr tadtrd` y mrdldturcn fkc`æs4
412= Kdia ak Ytrdtbnrm-upnk-Dvnk. As a` tariar hfjn ma JnhkYhdgaspadra y Ldry Drmak.
4185 Ya idsd ink Dkka Hdthdwdy. D` dôn sfcufakta kdia suhfjd Yusdk y, mns dôns maspuæs, `ns cala`ns Jumfth yHdlkat.
4188-86 Ya fkstd`d ak @nkmras, dedkmnkdkmn d aspnsd a hfjns, yasirfea sus prflards nerds.
4169-6= _ue`fid `ns pnalds Rakus y Dmnkfs y @d vfn`difùk ma@uiraifd, mamfidmns d` inkma Hakry Srfnthas`ay maYnuthdlptnk, su prntaitnr.
416= Uadparturd ma ns tadtrns. Yhdgaspadra as yd lfalern ma`d lajnr inlpdôìd ma d æpnid, d Inlpdôìd ma Ditnrasma @nrm Ihdlear`dfk.
4163 Bd``aia su hfjn Hdlkat. Yu euakd sftudifùk ainkùlfidinln alprasdrfn ma `d inlpdôìd `a parlfta dmqufrfrKaw-_`dia, ukd idsd ak Ytrdtbnrm.
4. Astd fkbnrldifùk as tnldmd taxtud`lakta ma d päcfkd wae:http://www efncrdbfdsyvfmds inl/lnkncrdbfd/shdgaspadra/irnkn`ncfd htl
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Atdpds ma `d prasaktdifùk ma` cufnk
Iudkmn takalns `d fmad ma `d hfstnrfd, prasaktdlns a` cufùk ak tras atdpds eäsfi
@d astrdtacfd m
idrdin`, pa`ìiu
ma` in`nlefdk
Y f I e
4. Yfknpsfs (iarid ma mns päcfkds). Inksfsta ak asirfefr ma ldkard sfk-tætfid, `d hfstnrfd qua sa pratakma inktdr ma prfkifpfn d bfk, fki`ufmns`ns kumns eäsfins ma `d trdld.
5. Asid`atd (iarid ma ifkin päcfkds). As a` lfsln p`dktadlfaktn ma `d
sfknpsfs, parn sa dlp`ìd y masc`nsd `d hfstnrfd ak asiakds, ma bnrldrasulfmd.
9. ]rdtdlfaktn (iarid ma 9? päcfkds). Astde`aia d a`denrdifùk inlp`atda fktacrd` ma `ns cufnkas tæikfin y `ftardrfn. A` `ftardrfn prasaktd tnmns`ns mfä`ncns y a` tæikfin axp`fid ak bnrld lfkuifnsd, idmd diifùk ma`ds asiakds y sus inlp`alaktns: lnvflfaktns ma iäldrd, aktrdmds ma
`d edkmd snknrd, f`ulfkdifùk, p`dkn d p`dkn, ati. As `d tariard pdrtama `d asirfturd ma` cufnk ak `d iud` sa matd``dk tnmds `ds asiakds, inkasenzns ma `ns pdr`dlaktns y ink `d idrditarfzdifùk ma idmd asiakd.Asta cufnk sa mfstrfeuya d tnmn a` aqufpn huldkn qua fktarvfaka ak`d rad`fzdifùk ma `d prnmuiifùk.
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Ajalp`n: ]rdln ma uk cufnk
Axtarfnr. Mìd. Idlpus ukfvarsftdrfn
Udfk y Cdea edjdk pnr `d asid`fkdtd ma `d bdiu`tdm y idlfkdk, sacufmnspnr ukd iäldrd.
Cdea. ]u sacukmn iuaktn, masma `uacn, as tdk fktarasdkta inln a`prflarn. La pdraifù ldrdvf``nsn.Udfk. ¡Nh, bdktästfin!Cdea. La flprasfnkù. Yì.Udfk. La sfaktn alnifnkdmd. Astny tdk inktaktd ma qua ta hdydcustdmn.
Cdea. Yì.Udfk. As uk crdk astìlu`n pdrd lì. Tufarn qua `n sapds.Cdea. Kn, kn… quæ tnktarìd. Kn as läs qua ukd npfkfùk, `d lìd.La flprasfnkù d lì.Udfk. Vd sæ. _arn tú aras `d npfkfùk.Cdea. @d vfmd kn flftd d` drta, flftd d `d ld`d ta`avfsfùk.Udfk y Cdea ma matfakak y sa lfrdk. Ufsds.
Snnmy D``ak, Ldrfmns y lujaras
In`ulkd ma `d hfstnrfd
@ds mfvfsfnkas axfstak ink i`drfmdm y snk `n qua sa inknia inln ditns qua knrld
lakta, snk ma tras d ifkin. @ns ditns snk `ds atdpds i`dva ma` ra`dtn dumfnvfsud` qusa suemfvfmak ak asiakds ink sus lnlaktns ma i`ìldx, tdlefæk ``dldmns cfrns qua hdiak `ns ækbdsfs alntfvns ak `d hfstnrfd.
D` hdiar a` cufùk, astns iä`iu`ns ma tfalpn eusidk `d dmaiudmd prnpnrifùk ma `bdsas, ma ldkard qua tdlefæk `d aspfkd mnrsd` qua inkmuia `d saiuakifd ma `ds aiakds, astæ snlatfmd d` aquf`ferfn qua inksfsta ak qua a` p`dktadlfaktn kn puamsar luy prn`nkcdmn kf tdk bucdz qua a` aspaitdmnr kn takcd tfalpn pdrd fmaktfbfi
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• _UFLAU DI]N (51-91 LFKQ]NY)
_`dktadlfaktn: prasaktd a` astdmn ma aquf`ferfn y a` surcflfaktn ma
`d d`tardifùk. As a` ditn qua läs fkbnrldifùk sulfkfstrd.
• YACQKMN DI]N (31-81 LFKQ]NY)
Masdrrn``n: sa md `d `uihd pnr raiupardr a` astdmn ma aquf`ferfn. A`aspaitdmnr maefù quamdr inkvakifmn ma` p`dktadlfaktn, ma td` bnrldqua a` sacukmn maea mnsfbfidr y abaitudr ds idmakds aktra ns paqua-ôns lntfvns y a` nejatfvn bfkd`. @ns parsnkdjas sfalpra astäk ditfvns,
dukqua sad ak bnrld pntakifd`.
• ]AUIAU DI]N (41-5? LFKQ]NY)
Ifarra: sa prasaktd a` i`ìldx. Ya raiupard a` astdmn ma aquf`ferfn n sadmqufara ukd kuavd inkmfifùk qua puama sar fki`usn, d aktrdmd d ukkuavn inkb`fitn. @n ifartn as qua a` i`ìldx bfkd` kn as a` úkfin, sfknqua idmd asiakd maearìd n pnmrìd takar uk lnlaktn ldridmn pnr
`d alnifùk7 d prflard asiakd tdlefæk maea sar flpditdkta, dukquakn as ukd rac`d fkquaerdktde`a. Ya rainlfakmd, sfk aledrcn, qua `didrcd alnifnkd` kn quama ra`acdmd d` ú`tfln lnlaktn ma d pa`ìiu`d.
4. Nestäiu`n: as ma idräitar ifriukstdkifd` y astätfin.
Ajalp`ns: takar d` sar dldmn d` ntrn `dmn ma` Hfld`dyd, masinkniar
A` túka` ma` masdrrn``n
Inrraspnkma d` saclaktn fktarlamfn ma` ra`dtn, as maifr, d `ns cfrns ma `d `uihdmasdrrn``n, y akldrid tras tfpns ma mfbfiu`tdmas:
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rad`as n bfitfifds, `d hfstnrfd astä iaktrdmd ak uk hærna n harnìkd qua sa lnvad pdrtfr ma:
• Qkd lntfvdifùk prfkifpd` qua as d rdzùk ma sar ma` ra`dtn, d qua fkmud ditudr.
• Qkds fktakifnkas qua snk ds maifsfnkas y ns pdsns qua md a` parsnkdak su fktaktn pnr supardr a` inkb`fitn y raiupardr a` aquf`ferfn.
• Qk nejatfvn prfkifpd` qua sa `ncrd maspuæs ma hdear iulp`fmn `ns netfvns saiukmdrfns qua sa akidrcdk ma fktrnmuifr suspaksn y axpaitdtfvAs `n qua sa eusid d`idkzdr.
5. Cuìd ldtarfd`
A` stnry endrm as `d cuìd pdrd masc`nsdr `ds fläcakas y a` snkfmn ma uk inlifd` ma ta`avfsfùk n ifka. Iudkmn sa trdtd ma ukd pa`ìiu`d n uk mniulaktd`,inknia inln cufnk tæikfin.
Hdcd uk cufnk tæikfin ak mns in`ulkds ma ifkin bf`ds, pdrd masirfefr a` mfä`ncn yfldcak ma ifkin asiakds ra`difnkdmds ink ds idusds ma` id`aktdlfaktn c`ned`. Q`ns parsnkdjas ma su a`aiifùk y idrditarìia`ns eravalakta, tdktn sf nptd pnr ``av
Fldcak ma Cderfa` _æraz Irfsdktn www.lu`tfla
Ytnry endrm.
4
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Cufùk ak tras ditns
• Uatnlak a` crupn ma trdedjn qua astde`aifarnk ak a` lùmu`n ma @akcudifkaldtncräbfin pdrd a` td``ar in`aitfvn qua masdrrn``drnk. Astumfdr `d sknpsfs qua p`dkadrnk aktnkias, y ns rn`as ink sus raspaitfvds prnpuastiradtfvds.
•
Astde`azidk `d idrditarfzdifùk psfin`ùcfid, castud` y bìsfid ma tnmns `nparsnkdjas fkvn`uirdmns.
• Masirfedk `ns tras ditns inktukmaktas qua inkbnrldräk `d in`ulkd vataerd` ma `d hfstnrfd: fktrnmuiifùk, kumn n i`ìldx, ifarra n masak`dia.
• Asirfedk `d asid`atd ink edsa ak `ds prnpuastds qua `ns mfbaraktas rn`adsulfmns pnr ns fktacrdktas ma` aqufpn hdk mfsaôdmn, y ukd vaz puastn
ak inksfmardifùk y dprnedmns ns bditnras ra`difnkdmns ak mfihd asid`atfkfifdr `d a`denrdifùk ma` cufnk tæikfin-`ftardrfn qua masc`nsdrä tnmns `nmatd``as tæikfins, ns mfä`ncns y a` masdrrn``n ma ds asiakds pdrd tras ditn
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48
Idrditarfzdifùk ma parsnkdjas
_drd mdr`a vfmd y inkbnrldifùk d uk parsnkdja, as kaiasdrfn mabfkfr sukfva` ma prntdcnkfsln: prfkifpd` n saiukmdrfn, sfk mfslfkufr a` ækbdsfs, `di`drfmdm y buarzd qua maed flprflfrsa ak a` parsnkdja7 dsì, uk parsnkdjaqua aktra tìlfmd y ldrcfkd`lakta ak `d hfstnrfd murdkta ukns sacukmns,puama inktakar a` lntfvn fktarkn ma tnmd `d hfstnrfd. @d idrditarfzdifùkma `ns parsnkdjas hdia pdrta ma` `akcudja ifkaldtncräbfin, pnrqua tnmninkiaptn aldkdmn ma iud`qufar dspaitn ma` parsnkdja matarlfkd a` rulenma `d hfstnrfd.
E`nig. Ak ukd hfstnrfd, ns parsnkdjas snk tras jùvakas. Astde`azid su idrdi-tarfzdifùk, takfakmn ak iuaktd psfin`ncìd, dspaitn, tfpn ma fkmulaktdrfd,kfva` amuidifnkd`, lnmd`as, bnrld ma fktarditudr y nejatns qua pnrtdk.Maspuæs, asirfed `d prflard aktracd ma` cufùk: sfknpsfs.
A` Dvfdmnr as ukd
pa`ìiu`d prntdcnkfzdmd
pnr @ankdrmn MfIdprfn
qua mrdldtfzd `d vfmd ma
Hnwdrm Huchas, pfnkarn
ma `d dvfdifùk. Kdrrd su
vfmd masma `d mæidmd ma
465? hdstd `d mæidmd
ma 46=?, æpnid ak qua
Huchas mfrfcìd y prnmuiìd
sus prnpfds pa`ìiu`ds ak
Hn``ywnnm y tdlefæk
pf`ntded sus prnpfnsprntntfpns dærans.
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Dpn`n masma _ærcdln, bua d npnkærsa`a pnrqua masaded qua `ns tauirnscdkdrdk `d vfitnrfd. Akinkträrnksa dleds mafmdmas ak `d akifkd7 y a` sn-eardkn Dpn`n, hfjn ma Zaus, hde`ù mfifakmn:
¾_nr quæ, akdrmaifmd kuavdlakta, nh hfjd ma` crdk Zaus, vfakas ma`N`flpn> ¾Tuæ pnmarnsn dbaitn ta luava> ¾Didsn qufaras mdr d ns dquans`d fkmaifsd vfitnrfd> _nrqua ma `ns tauirns kn ta inlpdmaiarìds, dukquaastuvfasak paraifakmn. Yf qufaras inkmasiakmar ink lf masan y sarìd `nlajnr suspakmaralns pnr hny a` inledta y `d pa`ad7 y `uacn vn`varäkd edtd``dr hdstd qua `ncrak drrufkdr d F`fùk, yd qua ns p`dia d `ds mfnsdsmastrufr astd ifumdm.
Uaspnkmfn`a Dtakad, `d mfnsd ma `ns erf``dktas njns:
Yad dsì, B`aihdmnr7 ink asta prnpùsftn vfka ma` N`flpn d` idlpn ma `nstauirns y ma `ns dqufvns. Lds ¾pnr quæ lamfn hds paksdmn suspakmar `dedtd``d>
Inktastù a` sneardkn Dpn`n, hfjn ma Zaus:
Hdcdlns qua Hæitnr, ma inrdzùk buarta, mnldmnr ma ided``ns, prnvnquad `ns mäkdns d pa`adr ink æ` ak tarrfe`a y sfkcu`dr inledta7 a fkmfckdmns`ns dquans, ma harlnsds craeds, susiftak d d`cufak qua lfmd sus drldsink a` mfvfkn Hæitnr.
Dsì mfjn, y Dtakad, d mfnsd ma ns erf``dktas njns, kn sa npusn. Ha`akn, hfjn
dldmn ma _rìdln, inlprakmfù d` puktn `n qua ard crdtn d `ns mfnsas quainkvarsdedk, y ``acäkmnsa d Hæitnr, `a mfrfcfù astds pd`derds:
¡Hæitnr, hfjn ma _rìdln, fcud` ak prumakifd d Zaus! ¾Tuarräs hdiar `nqua ta mfcd yn, qua sny tu harldkn> Ldkmd qua suspakmdk `d pa`ad`ns tauirns y `ns dquans tnmns, y ratd d` läs vd`fakta ma æstns d `uihdrinktfcn ak tarrfe`a inledta, puas dúk kn hd mfspuastn a` hdmn qua
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luards y ``acuas d` tærlfkn bdtd` ma tu vfmd. Ha nìmn qua dsì `n maiìdk `nssalpftarkns mfnsas.
Ak td`as tærlfkns hde`ù. Nyù`a Hæitnr ink fktaksn p`diar, y inrrfakmn d`iaktrn ma dlens ajæriftns ink `d `dkzd incfmd pnr a` lamfn, matuvn `ds bd-`dkcas trnydkds, qua d` lnlaktn sa quamdrnk qufatds. Dcdlakùk inktuvnd `ns dquans, ma harlnsds craeds7 y Dtakad y Dpn`n, a` ma` drin ma p`dtd,trdksbfcurdmns ak euftras, sa pnsdrnk ak `d d`td akifkd ma` pdmra Zaus, qua``avd `d æcfmd, y sa ma`aftdedk ak inktalp`dr d `ns cuarrarns iuyds maksdsbf`ds dpdraiìdk arfzdmds ma asiumns, idsins y dkzds. Inln a` Iæbfrn, idyak-mn snera a` ldr, akiraspd `ds n`ds, y a` pnktn kacrad7 ma salajdkta lnmnsaktärnksa ak `d ``dkurd `ds hf`ards ma dqufvns y tauirns. V Hæitnr, puastnaktra ukns y ntrns, mfjn:
¡Nìmla tauirns y dquans, ma harlnsds craeds, y ns mfræ n qua ak a` paihnlf inrdzùk la mfitd! A` axia`sn Irnkfùk kn rdtfbfiù kuastrns jurdlaktns, ysacufrä idusäkmnkns ld`as d ukns y d ntrns, hdstd qua tnlæfs `d tnrradmdF`fùk n suiuleäfs juktn d `ds kdvas qua dtrdvfasdk a` pnktn. Aktra vnsntrns
sa hd``dk ns läs vd`faktas dquans7 dqua` d qufak a` äkfln fkifta d inledtfrinklfcn, dma`äktasa y sarä idlpaùk ink a` mfvfkn Hæitnr. _rnpnkcn `nsfcufakta y Zaus sad tastfcn: Yf dquæ`, ink su ernkia ma drcd puktd, inksfcuaquftdrla d vfmd, maspùjala ma ds drlds, `ævasa`ds d ds iùkidvds kdvas, yaktracua lf iuarpn d ns lìns pdrd qua ns trnydkns y sus aspnsds n suedkd d pfrd7 y sf yn a ldtdra d æ`, pnr inkiamarla Dpn`n td` c`nrfd, la `avdræsus drlds d `d sdcrdmd F`fùk, `ds in`cdræ ak a` talp`n ma` b`aihdmnr Dpn`n,
y akvfdræ a` idmävar d `ns kdvìns ma luihns edkins, pdrd qua `ns dquans,ma `drcd idea``ard, `a hdcdk axaqufds y `a arfjdk uk túlu`n d nrf``ds ma` as-pdifnsn Ha`aspnktn. V mfrä d`cukn ma `ns buturns hnleras, dtrdvasdkmn a`vfknsn ldr ak uk edja` ma luihns ùrmakas ma ralns…
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]atfs, trds `d iù`ard ma Dquf`as, sup`fid d Zaus
pdrd qua æsta parlftd qua `ns trnydkns
dmqufardk vaktdjd (@d F`fdmd).
Jadk Ducusta Mnlfkfqua Fkcras
Bntns tnldmds ma Sfgfp
Luarta ma Hæitnr pnr Dquf`as (@d F`fdmd).
_atar _du` Uueaks.
Lusan Enyldks vnk Eaukfkcak.
Unttarmdl.
@d æpfid as a` cækarn ftardrfn qua axd`td dc`nrfd ma `ns hærnas ak uk lukmn ma bdk-tdsìd y mfvfkfmdmas, ma inkjurns y bùrlu`dssdcrdmds qua `a mdk vfmd d su rad`fmdm.
A` cækarn æpfin qua sa fki`uya ak `ds bf`dsma `d pnasìd, sa akiuaktrd ak a` nrfcak ma`ns puae`ns prflftfvns, hdifakmn pdrta masu avn`uifùk iu`turd`. _artakaia d d atdpdma bnrldifùk ma `d in`aitfvfmdm, kn ma `dfkmfvfmud`fmdm.
A` hærna æpfin as uk sar in`aitfvn quamastdid aktra a` inkc`nlardmn pnr subuarzd, su vd`nr y su hnknr, parn tdlefækas uk hærna qua eusid a` dp`dusn ma susinkcækaras. Ma td` ldkard qua sus ditnsraspnkmak d d kaiasfmdm ma sar a` prfla-rn aktra tnmns pdrd qua asd snifamdm `naksd`ia.
Asta hærna as raprasaktdmn ak ds inlpnsf-ifnkas n suecækarns qua hdiak pdrta ma dæpfid, inln d apnpayd, a` pnald æpfin na` idktdr ma castd, aktra ntrns. Ak tnmds, a`hærna masp`facd sus hdef`fmdmas y dstuifds,
Lamfdkta sucastfvds masirfpifnkas, a`kdrrdmnr kns luastrd a` aktnrkn qua `nrnmad, `d rfquazd ma sus drlds, su ea-``azd y `d ma `ns parsnkdjas y mfnsas qua`n dinlpdôdk, dsì inln `ns lnlaktnsiudkmn sa tnrkd dvdsd``dmnr, úkfin, kn pnrnrcu``n, sfkn pnr ukd `ay flp`ìiftd qua `dlfsld snifamdm d `d iud` partakaia `a hd
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Ak d apnpayd, suecækarn ma d æpfid crfacd, rainknialns uk drquatfpn ma hnleiuyd pdrtfiu`dr fktardiifùk ink `ds mfvfkfmdmas y a` Qkfvarsn, `n mabfkìdk y `a ntncdedk ukd inkiapifùk ma` Lukmn y ma `d vfmd luy pdrtfiu`dr.
_drd asta hærna y su inlukfmdm, a` Lukmn ard uk tnmn nrmakdmn y parldkakracfmn pnr `ayas mfvfkds qua dktavakìdk ak a` astde`aiflfaktn ma `ds insds y ak
mastfkn ma `ns hnleras. @ns masfckfns ma `ns mfnsas ardk fkb`axfe`as y a` hnlera kpnmìd hdiar d`cn inktrd a``ns, axiaptn diaptdr`ns ak bnrld pdsfvd. As läs, ak ukfvarsn ma `d apnpayd, `d suarta n bnrtukd ma` hnlera ardk susiaptfe`as ma ukinktfkud latdlnrbnsfs7 ma d``ì, `d dbfrldifùk ma qua kfkcúk hnlera ard muaôn msu prnpfn mastfkn.
Yu pariapifùk ma` nrmak y ma` aquf`ferfn ma` Inslns, trdtded a` saktflfaktn ma ma
cdrrdlfaktn ma` hnlera ma hny. Yu saktfmn ma n träcfin ard läs efak ma axtrdôaz`n iud` axp`fidrìd a` lntfvn pnr a` iud` su vfmd nsif`ded aktra d rfcurnsfmdm, a` maey a` raspatn d `ds `ayas ukfvarsd`as.
]d`as fmads rava`dk a` pnrquæ ma `ds crdkmas apnpayds, astns lftns ukfvarsd`as quiulp`ìdk ak ú`tflds, ukd lfsfùk knrldtfvd y ma dlnkastdifùk.
Dúk ink astd vfsfùk ma` Lukmn, puama dbfrldrsa qua a` hnlera crfacn idraiìd m
@ns idktns æpfins d ns iud`as kns rabarflns (fkmapakmfaktas ma` aspdifn cancräbfin ma `d iu`turd d `d iud` partakazidk), snk a` rab`ajn ma ukd inkiapifùk ak `d iua` fkmfvfmun-hærna astä ne`fcdmn d d`idkzdr `ds läs d`tds vfrtumas. _nr astd rdzùk, hærna as dstutn, häef`, mfastrn y rfcurnsn. A` hærna æpfin `uihd y vfva pnr a` rainkniflfaktn y ak asa dbäk ma c`nrfd, bukma `n harnfin ink `n sdkcrfaktn.
¾Ma mùkma vfaka asta parsnkdja> Rfaka ma `d d`td kne`azd y asta as uk haihn quma dktaldkn, `a hdia saktfr su maraihn pdrd niupdr su `ucdr ak `d snifamdm.
@d apnpayd crfacd
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ma Hnlarn, ra`ad a` Idktn F y mamuzid: ¾D iuä` ma ds tras dktarfnras idtacnrìsa suenrmfkd a` taxtn>
5. Mfjflns qua `d apnpayd mastdid pnr `ds lú`tfp`as masirfpifnkas qua prasakt
Ua`ad a` Idktn RFF ma d fktrnmuiifùk y trdksirfed dqua``ns dpdrtdmns qua sfrvdma ajalp`n. ¾Tuæ bukifùk iulp`ak asns dpdrtdmns ak asta idpìtu`n (rainkniflfaktn ma` hærna, su aktnrkn, sus drlds)> Yustakta su raspuastd.
9. ¾Tufæk as a` hærna æpfin ma @d F`ìdmd y pnr quæ> Uaspd`ma su raspuastd ink `aiturd qua hfzn ma `d nerd
=. ]akfakmn ak iuaktd d i`dsfbfidifùk qua hfzn Gdysar snera d apnpayd, fkvastfcupnr idmd idtacnrìd, mns tfpns ma apnpayd ak a` trdksiursn ma `ns sfc`ns.
Masdrrn``dr ak su iudmarkn:
4. Fkvastfcuak iuä` bua a` inktaxtn hfstùrfin ak a` iud` sa masdrrn``drnk `ds mnapnpayds hnlærfids.
5. ¾Tuæ mfnsas pdrtfifpdk ak a` Idktn RF y quæ raprasaktdk aktra a` crupn m
mfvfkfmdmas> Fkvastfcuak.
9. ¾Iùln sa axprasd n snerakdturd` y n läcfin ak ns idktns ma @d F`ìdmd> ¾Tuapfsnmfns raspd`mdk sus raspuastds> Axp`ìquak`ns.
=. ¾Iùln sa rab`ajd `d fktrnlfsfùk (in`denrdifùk), ma `ns mfnsas ak `ns suiasnqua vfvak `ns parsnkdjas ma `d F`ìdmd> ¾Yu pdrtfifpdifùk ldrid a` rulen ma `n
5
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46
4. ]rdksirfed iudtrn nrdifnkas ma` Idktn RF, ak `ds iud`as `d dmjatfvdifùksa nesarva ink i`drfmdm.
5. ¾Tuæ bukifùk iulp`a asd dmjatfvdifùk ak `ds nrdifnkas>9. ¾@d suarta y `d bnrtukd ma `ns hnleras sa rab`ajd ak `ns idpìtu`ns ma `d
nerd> ¾Tuæ tfpn ma bnrtukd as asd> _rasakta uk ajalp`n.=. ¾Iùln bua ld`trdtdmn a` hnknr ma` hærna æpfin ma @d F`ìdmd>
Hnlarn (sfc`n RFFF d. I.), as a` knlera ma` pnatd y rdp-snmd crfacn dktfcun d qufak trdmfifnkd`lakta sa `a dtrf-euya `d dutnrìd ma `ds prfkifpd`as pnasìds æpfids crfacds@d F`ìdmd y @d Nmfsad. Masma a` parìnmn ha`akìstfin, sahd iuastfnkdmn qua hdyd sfmn a` dutnr ma dleds nerds
æpfids7 sfk aledrcn, dktarfnrlakta kn hdeìd mumds, sfkn qua @d F`ìdmd y
@d Nmfsad. ardk inksfmardmns ra`dtns hfstùrfins rad`as.
A` knlera Hnlarn as ukd vdrfdkta jùkfid ma` aù`fin Hnldrns y sfckfbfidrahæk, prakmd n cdrdktìd. Hdy ukd tanrìd qua snstfaka qua asta knleraprnvfaka ma ukd snifamdm ma pnatds `dldmns Hnlarfmdf qua ftard`lak-ta sfckfbfid hfjns ma rahakas, as maifr, masiakmfaktas ma prfsfnkarns macuarrd. Mdmn qua astns hnleras kn ardk akvfdmns d d cuarrd, pnr mumdrma su `ad`tdm ak a` idlpn ma edtd``d, kn lnrìdk ak æ`. _nr `n tdktn, sa
`as inkbfded a` trdedjn ma rainrmdr d pnasìd æpfid nid` pdrd rainrmdr nssuiasns pdsdmns, ak tfalpns dktarfnras d `d `ftardturd asirftd. ]dlefæksa hd sucarfmn qua a` knlera Hnlarns pnmrìd sar uk juacn ma pd`derdsmarfvdmn ma `d axprasfùk hn-la-hnrùk, qua sfckfbfid a` qua kn va.
Diarid ma` `ucdr mnkma lurfù, axfsta ukd trdmfifùk dtastfcudmd d` laknsmasma a` sfc`n R d. I., ma qua sa prnmujn ak `d fs`d ma Ìns. _dusdkfds ra-inca astd trdmfifùk y hde`d snera ukd astdtud ma Hnlarn qua vfn y uknräiu`n qua `ayù ak a` ]alp`n ma Dpn`n ak Ma`bns
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Qkfmdm 4
Yasfùk 4. Iùmfcn `fkcðìstfin
Fmaktfbfqua `ds bd`akifds qua prasaktd a` ldkajn ma` iùmfcn asirftn ak a`
sfcufakta ajalp`n qua hd sfmn d`tardmn d prnpùsftn:
Murdifùk ma` trdedjn
Ak `ns _dìsas ak qua idsf tnmds `ds lujaras trdedjdk (qua snk `d lftdm ma`puae`n) y ns hnleras sa mdk d rapnsn dmaläs, ma` crdk kúlarn ma sdiar-mntas y ra`fcfnsns qua kn prnmuiak kdmd ink sus ldkns, kf n saônras rfins y
haramarns (d ns qua a` eu`cn `dld kne`as y ided``arns), fki`u``ækmnsa ak astdiuaktd. d tnmd d idtarvd ma `ns qua sfrvak d astns ú`tflns ma aspdmdihfkasy truhdkas, y d `ns, lakmfcns qua takfakmn sd`um bfkcak akbarlamdm pnrn`cdzdkarìd, hd``dræfs qua snk luihns, ns qua kn prnmuiak kdmd7 y aktra:`ns qua trdedjdk hdy ukd crdk pdrta qua kn sa niupdk ak insds kaiasdrfds,yd qua mnkma tnmn sa inksfcua ink mfkarn as bnrznsn qua hd``d luihdsdrtas tntd`lakta vdkds, qua sù`n sfrvak d` hdktnjn y axiasn.
(]nldmn ma @d Qtnpìd, ma ]nläs Lnrn)
Yasfùk 5. Maedta
_rasakta su prnpfn dkä`fsfs snera ukn ma ns maedtas qua sa rad`fzdrnk ak a`du`d ma i`dsa murdkta asta parìnmn.
Ldkns d d nerd
Qkfmdm =. Yalfùtfid ma` ifearaspdifn: fktakifnkasinlukfidtfvds, vdrfds bnrlds ma axprasfùk
Yasfùk
5?
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Yasfùk =. Fkbnrla
Ak crupn, a`denrak uk fkbnrla snera a` rftln ma d i`dsa, a` dlefakta asin`dr,sus masans, pntakifd`fmdmas y prnyaiifnkas prnbasfnkd`as.
Ydktn Mnlfkcn, 42 ma akarn ma 5?49
YAÔNU
JDFUN HAUKÄKMAZ
JABA MA _UAKYD FKY]F]Q]N MA DU]A V IQ@]QUD
Mfraiifùk inlp`atdYdktn Mnlfkcn, Uapúe`fid Mnlfkfidkd
Uaspatdmn saônr Harkäkmaz:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^, masan pnkar ak inkniflfaktnsuyn ds frracu`drfmdmas mataitdmds pnr a` inlftæ suparvfsnr ak a` prncrd-
ld ma rdmfn, ink a` prnpùsftn ma qua sa sfrvd a`denrdr `ns inlukfidmnsqua astd sftudifùk raqufara. Dmjuktn akinktrdrä fkbnrla qua matd``d `nsuiamfmn.Ak aspard ma qua ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^, sa susirfea maustam,
Dtaktdlakta,
JNHDKD YDL_AU Dumftnrd Lfkfstarfn ma Iu`turd
Yasfùk 9. Idrtds
@d sfcufakta idrtd rabarakifd` idraia ma d`cukns dspaitns, parn tdlefækinktfaka mns bnrlds fkinrraitds. Yaôd`a `ns (n a`) qua astäk arrdmns y ``aka`ns aspdifns `feras.
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Idpìtu`n XRFFMa `d irua`mdm y `d i`alakifd7 y sf as lajnr sar
Dldmn qua talfmn, n sar talfmn qua dldmn(]nldmn ma A` _rìkifpa ma Ldqufdva`n)
_dsn d `ds ntrds iud`fmdmas yd iflaktdmds y mai`drn qua tnmns `nsprìkifpas maeak masadr sar takfmns pnr i`alaktas y kn pnr irua`as.
V, sfk aledrcn, maeak iufmdrsa ma alp`adr ld` astd i`alakifd,Iæsdr Enrcfd ard inksfmardmn irua`, pasa d `n iud` bua su irua`mdm
astuvfard prapdrdkmn pdrd ukd prùxfld pnkakifd. Yustakta su raspuastdink sftudifnkas inktaxtud`fzdmds ak `d ifumdm y ak a` pdìs qua hdeftd.
5. Eusqua ukd aktravfstd ak d`cukn ma `ns mfdrfns ma `d ifumdm, nesarvaukd ak `d ta`avfsfùk kdifnkd` n fktarkdifnkd` y asiuiha ntrd ak rdmfn.Hdcd uk pdrd`a`n, ldridkmn `ds idrditarìstfids ma aktrdmd ma idmdlamfn, as maifr, d ldkard pdrtfiu`dr inln idmd lamfn ma fkbnrldifùkfkfifù `d aktravfstd n hfzn `d prasaktdifùk ma` aktravfstdmn.
Yasfùk 6. @ìrfid vdkcudrmfstd
@ad ink dtakifùk ukd ma `ds bäeu`ds ma Asnpn y mastdqua sf `d fktakifùk ma`dutnr bua lnrd`, ra`fcfnsd, mfmäitfid, frùkfid n fkbnrldtfvd. Yustakta.
Qkfmdm 9
Yasfùk 44. Inharakifd, inhasfùk vared` y inkinrmdkifd `fkcðìstfid
Ma` sfcufakta brdclaktn, saôd`a a` akukifdmn iaktrd`7 axp`fqua a` usn qua sa`a md d `d puktudifùk7 fkmfqua `ds fmads saiukmdrfds qua dpnydk a` asirftn7saôd`a ds pd`derds qua a mdk inhasfùk d` pärrdbn7 rasd`ta tras nrdifnkas qualdktakcdk `d inharakifd ma` asirftn.
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Yasfùk 45. Yalfkdrfn
Dsfstd d uk salfkdrfn ma ns inkiartdmns pdrd asta dôn, d bfk ma inklalnrdruk dôn läs ma` kdiflfaktn ma Ihdr`as Mdrwfk, y prasakta uk fkbnrla snera`d ldkard inln mfihn salfkdrfn sa ``avù d iden.
Yasfùk 49. Kntfifd
Ak a` `akcudja y astruiturd ma `d kntfifd, raspnkmd `ds sfcufaktas pracuktds:
• Ak `d fkbnrldifùk, ¾ak quæ inksfsta `d tanrìd ma `d pfrälfma fkvartfmd>
• ¾D quæ kns rabarflns d` hde`dr ma `ds 1S>
• ¾Iuä` ma ds 1S sua`a sar rasua`td ak a` iuarpn ma d kntfifd> ¾_nr quæ>
• ¾Iuä`as snk `ds mns idrditarìstfids prfkifpd`as ma` cækarn kntfifd>
`d qua flpusn a` nrmak ak `d Unldôd, `d qua `ncrù su ukfùk y `dqua `d vn`vfù d `d pdz y d `d ba. Tua, sf sa axdlfkd efak, sa varä qua
Enrcfd bua luihn läs i`alakta qua a` puae`n b`nraktfkn, qua pdrdavftdr sar tdihdmn ma irua`, majù mastrufr d _fstnyd. _nr `n tdktn, ukprìkifpa kn maea praniupdrsa pnrqua `n diusak ma irua`, sfalpray iudkmn su irua`mdm takcd pnr nejatn a` ldktakar ukfmns y bfa`asd `ns súemftns7 pnrqua ink pnins idstfcns ajalp`dras sarä läs i`a-lakta qua dqua``ns qua, pnr axiasfvd i`alakifd, majdk lu`tfp`fidr`ns masùrmakas, idusds ma ldtdkzds y sdquans qua parjumfidk d tnmdukd pne`difùk, lfaktrds qua `ds lamfmds axtralds dmnptdmds pnr
a` prìkifpa sù`n vdk ak inktrd ma ukn. V as snera tnmn uk prìkifpakuavn a` qua kn maea avftdr ns ditns ma irua`mdm, puas tnmd kuavdmnlfkdifùk trda inksfcn fkbfkfmdm ma pa`fcrns.
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Yasfùk 4=. Aksdyn `ftardrfn
Yaôd`a quæ hdia qua a` sfcufakta brdclaktn ma Ìtd`n Id`vfkn, sa inksfmara
uk aksdyn `ftardrfn.
A` ra`dtn bdktästfin pdrta ma uk mfsiursn rad`fstd qua as sdiumfmn pnruk avaktn masinknifmn a fksù`ftn, qua d`tard `d rad`fmdm intfmfdkd._nr a``n, pdrd maknlfkdr d uk taxtn inln bdktästfin as kaiasdrfn quaæsta ne`fcua d` aitnr d inksfmardr a` lukmn ma ns parsnkdjas inln
uk lukmn ma parsnkdjas rad`as, y d vdif`dr aktra ukd axp`fidifùkkdturd` y ukd axp`fidifùk snerakdturd` ma `ns dinktaiflfaktns quasuiamak ak `d hfstnrfd.
@d `ftardturd bdktästfid sa mfstfkcua pnr `d parp`ajfmdm brakta d ukhaihn fkiraìe`a y ukd diaptdifùk dkta `n snerakdturd`. @d asakifdma `d `ftardturd bdktästfid as `d rairadifùk ma `n qua sa va, ma insdsaxtrdnrmfkdrfds qua fldcfkdlns qua puamak `acdr d suiamar, insds
inrrfaktas qua td` vaz asinkmak edjn `d dpdrfakifd ukd sacukmdkdturd`azd fkqufatdkta, lfstarfnsd, tarrfe`a.
(]nldmn ma @ns iuaktns bdktästfins ma` sfc`n XFX )
Qkfmdm =
Yasfùk 42. Yalfùtfid ma` ifearaspdifn y taxtn `ftardrfn
• Aktra ak Fktarkat y hd``a ifkin mfraiifnkas iuyn mfsaôn fkbnrldtfvnprasakta `ds inkmfifnkas y idrditarìstfids kaiasdrfds ma` inkiaptn maramdiifùk Sae.
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Yasfùk 43. _uastd ak asiakd: lnkù`ncn, sn`f`nqufn, tadtrn
• A`denra uk lnkù`ncn, hdifakmn ækbdsfs ak `d masirfpifùk psfin`ùcfid
ma` parsnkdja.
• Ak mns iudrtf``ds, asirfed uk sn`f`nqufn ak a` iud` a` prntdcnkfstd ma`d hfstnrfd sad su d`tar acn. Dvarfcða a` sfckfbfidmn ma` tærlfkn pra-vfdlakta.
• A`fjd ukd ma ds mns bnrlds dktarfnras (lnkù`ncn n sn`f`nqufn), y lnkta`d asiakfbfidifùk tadtrd` pdrd 4? lfkutns y prasækta`d d` crupn.
Yasfùk 48. Cufnk
A`denra `d asid`atd ak ifkin asiakds, ma uk cufùk mniulaktd` snera `dslazi`ds fktariu`turd`as a fktarrdifd`as qua hny ak mìd dkfmdk ak `d inkiap-ifùk ma ifumdmdkns ma` lukmn ak uk _`dkatd c`ned`fzdmn. Yfcd a` asqualdprnpuastn d inktfkudifùk:
Yasfùk 46. Æpfid
A` hærna ma d æpfid pnsaa ukns vd`nras y ukd vfsfùk ma` Lukmn luy aspaiì-bfins. Masirfed iuä` sarìd a` dktfhærna ma ns tfalpns lnmarkns. Drculaktasu raspuastd.
]falpn _arsnkdjas Fldcak Dumfn
Asiakd 4.
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Iùmfcn `fkcðìstfin
• CDUUFMN, Ldkua`. @ùcfid sfleù`fid. Ldmrfm: ]aikùs, 4681.
• BQAK]AY UNMUÌCQAZ, I. @d sfktdxfs ma `ns ra`difnkdktas suprdnrd-ifnkd`as. Ldmrfm: Drin @ferns, 4668.
• BAUKÄKMAZ _ÆUAZ, L. Fktrnmuiifùk d d @fkcðìstfid, Edria`nkd: Drfa`,4666.
• LDU]ÌKAZ I. A. Edsas pdrd a` astumfn ma` `akcudja. Edria`nkd: Nitda-mrn, 4661.
• YFLNKA, U. Bukmdlaktns ma fkcðìstfid. ]rdmuitnrd: Lª ma` _. UnmrìcuazUafkd. Edria`nkd: Drfa`, 4669.
Maedta, salfkdrfn y pdka`
•
LAMDQUD, N`cd y LNKBDUUA@@, D`fifd. ]æikfids crupd`as y dprak-mfzdja dbaitfvn. Euakns Dfras: @ulak, 5??8.
• DKMAU-ACC, Azaqufa`. Hde`dr ak púe`fin y sdear inlukfidr. Euakns Dfras: @ulak, 5??2.
• EDRFN, Idrlak y IÆY_AMAY, Inrd. @akcud. Euakns Dfras: Gdpa`usz, 5??4.
• YDKZ _FKVN@, C`nrfd. Inlukfidifùk abaitfvd ak a` du`d. ]æikfids ma
axprasfùk nrd` pdrd mniaktas. Edria`nkd: Crdù, 5??1.
Iuaktn
• LD]N, Mdkfa`. Iùln inktdr iuaktns. Idrdids: Lnkta Ävf`d, 4668.
• _DY]NUFZD MA A]IHAEDUKA, Mnrd. A` drta ma kdrrdr: uk nbfifn n`vf-mdmn. Euakns Dfras: Cudmd`upa, 4668.
Efe`fncrdbìd
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• _A@ACUÌK, Dkd. @d dvakturd ma nfr iuaktns y lalnrfds ma d trdmfifùknrd`. Ldmrfm: Ifkia`, 4685.
• UNMDUF, Cfdkkf. Crdlätfid ma `d bdktdsìd: fktrnmuiifùk d` drta mafkvaktdr hfstnrfds. Edria`nkd: ma Ernkia, 4662.
• NKC, Sd`tar. Nrd`fmdm y asirfturd. Læxfin: Bnkmn ma Iu`turd Ainkù-lfid, 4662.
Astruiturdifùk ma` taxtn asirftn
• RDK MFJG, ]. Asirfturd y bukifnkas ma` mfsiursn. Ldmrfm: Iätamrd, 468?.
• INUNLFKDY, Ausaefn y UQEFN, Idrlak. ]æikfids ma asirfturd. Edr-ia`nkd: ]afma, 4686.
• ID_DUUÙY, Jnsæ Mnlfkcn. Fktrnmuiifùk d` inlaktdrfn ma taxtns. Ld-mrfm: Lfkfstarfn ma Amuidifùk y ifakifd, 4681.
• ID@RFKN, Ìtd`n. @ns iuaktns bdktästfins ma` sfc`n XFX. Edria`nkd: Yfrua`d,4664.
@ìrfid
• IFU@N], @nurmas. @ds i`dvas ma `ds vdkcudrmfds drtìstfids ma` sfc`n XX.Edria`nkd: Drfa`, 4688.
• UDLÌUAZ, Judk Dktnkfn. A` drta ma ds vdkcudrmfds. Ldmrfm: Dkdyd, 4668.
• D_N@@FKDFUA, Cuf``dula. Id`fcrdlds. Edria`nkd: Iätamrd, 5??1.
• CUÐKBA@M, Lfhdf`. Dktn`ncìd ma `d pnasìd `dtfkndlarfidkd ma vdk-
cudrmfd. Euakns Dfras: Hfpdrfùk, 4661.
• BAUKÄKMAZ Lnrakn, Iæsdr. Dlærfid @dtfkd ak su `ftardturd. Læxfin:Yfc`n XXF, QKAYIN, 4688.
• _DIHAIN, Jnsæ Alf`fn. @aiturd irìtfid ma `d `ftardturd dlarfidkd, vdk-cudrmfds y tnld ma pnsasfùk. Ak: Efe`fntaid Dydiuihn, ]. 461, Rn`. FFF.Idrdids, 4663.
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Lùmu`n fktacrdmn pdrd ifi`n 1
]rdksbnrlalns Amuidkmn
Ärad ma IfakifdsKdturd`as
4?
Iarrn Lnkn Uìn, Cudfkìd
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A s
t ä k
m d r a s
e ä s f i n s
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m a l n
m a
` n s q u
ì l f i n s y a
` æ i
t r f i n s
•
U a ` d i
f n k n
` n s i
f i ` n s
m a
` d c u d y
m a
` n s a
` a -
l a
k t n s i n k
` d a k a r c
ì d m a
` n s a i n s f s t a l d s .
•
A x p
` f i n
m f v a r s n s
t f p n s
m a r a
` d i
f n k a s a k
t r a
a s p
a i
f a s a k
` n s a i n s
f s t a l d s
A s
t d e ` a z i n
r a ` d i
f n k a s a k
t r a f k m f v f m u n ,
p n
e ` d i
f ù k ,
i n l
u k
f m d
m y a i n s f s t a l d .
A k t n r k n v f v n
•
A x p
` f i n
` d a s t r u i
t u r d
m a
` n s
ä t n l n s
d p d r t f r
m a
m f b a r a k
t a s
t a n r ì d s .
•
R a r f b f i n a
` a
b a i
t n m a p r a s f ù k y
t a l -
p a r d
t u r d a k
` n s i d l
e f n s q u
ì l f i n s .
•
U a d
` f z n i
ä ` i u
` n s i u d k
t f t d t f v n s a k
i d l
e f n s q u
ì l f i n s .
•
A x p
` f i n
` n s i d l
e f n s q u
ì l f i n s
m a s m a
m f b a r a k
t a s l n
m a
` n s .
•
Q s n
` d t d e ` d p a r f ù
m f i d p d r d
m a -
t a r l
f k d r p r n p
f a m d
m a s
b ì s f i d s y
q u
ì l f i d s
m a
` n s a
` a l a k
t n s .
•
I d r d i
t a r f z n i d l
e f n s q u
ì l f i n s a k
i n k
m f i f n k a s
m a a q u
f ` f e r f n .
•
A s t d
e ` a z i n r a
` d i
f n k a s a k
t r a ` d s
m f b a r a k
t a s
b u a r z d s q u a d i
t ú d k s n
e r a
` n s i u a r p n s
a k r a p n s n n a k l n v
f l f a k
t n r a i
t f ` ì k a n
u k
f b n r l a y a s t d
e ` a z i n i n k
m f i f n k a s p d r d
i n k s a r v d r
` d a k a r c
ì d l a i
ä k
f i d .
•
L n
m a
` n l d
t a l
ä t f i d l a k
t a a
` l n v
f l f a k
t n
m a n
e j a t n s i n
t f m f d k n s d
p d r t f r
m a
` d s
b u a r z d s q u a d i
t ú d k s n
e r a a
` ` n s .
•
A s t d
e ` a z i n r a
` d i
f n k a s a k
t r a a s t d
e f ` f m d
m y
i a k
t r n m a l d s d
m a u k n
e j a t n
.
•
A s t d
e ` a z i n r a
` d i
f n k a s a k
t r a ` d i n k s a r v d -
i f ù k
m a
` l n l a k
t n ` f k a d
` y a
` f l p u
` s n a k
s f s t a l d s
m a n
e j a t n s .
•
A s
t d e ` a z i n r a
` d i
f n k a s a k
t r a a
` l n
m a
` n
m a
` i d l p n c r d v
f t d i
f n k d
` y
` d ` a y
m a
` d
c r d v
f t d i
f ù k u k
f v a r s d
` .
•
U a
` d i
f n k n l d s d ,
m f s t d k i
f d y
b u a r z d
m a
t
f ù
f t
f
`
t
e j t
B d i t n r a s m a n r c d k f z d i f ù
k
¾ I ù l n m a l u a s t r n ` n d p r a k
m f m n >
I n l p a t a k i f d s
¾ D q u æ
q u a r a l n s
` ` a c d r >
A x p
` f i n
` d
m f v a r s
f m d
m
e f n ` ù c
f i d
i n l n
i n k -
s a i u a k i
f d
m a i d l
e f n s
d l
e f a k
t d ` a s ,
c a k
æ t f i n s
y r a
` d i
f n k a s
m f k ä l
f i d s
m a k
t r n
m a
` n s a i n s
f s -
t a l d s .
U a
` d i
f n k n
` d a s
t r u i
t u r d
m a
` d s l n
` æ i u
` d s n r c
ä -
k f i d s a
f k n r c
ä k
f i d s i n k
s u s p r n p
f a m d
m a s
b ì s f i d s y
q u
ì l f i d s y s u i d p d i
f m d
m
m a i d l
e f n q u
ì l f i n .
A x p
` f i n
` d s
b u a r z d s a k
t r a
n e j a t n s i n l n
f k t a r d i i
f n -
k a s
m a
e f m d s d
` d i d r c d
a ` æ i
t r f i d y d
` d l d s d .
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•
A x p
` f i n
d p
` f i d i
f n k a s
t a i k n
` ù c
f i d s
m a
`
l n
m a
` n m a l a i
ä k
f i d
m a
b ` u f m n s
•
D k d
` f z n a
` p n
t a k i
f d ` m a
` n s r a i u r s n s k d -
t u r d
` a s a k
` d n e
t a k i
f ù k
m a a k a r c
ì d p d r d
m f b a r a k
t a s u s n s .
•
A s t d
e ` a z i n r a
` d i
f n k a s a k
t r a a
` m a p n r t a y
` d s d
` u m b ì s f i d y
l a k
t d ` .
•
A x p
` f i n i d l
e f n s q u
ì l f i n s a k
` d i n i
f k d ,
` d f k m u s t r f d y a `
d l
e f a k
t a
•
D r c u l a k
t n ` d f l
p n r t d k i
f d m a
` d s l a
m f m d s
m a p r a v a k i
f ù k
m a
` a l
e d r d z n y
m a
` d s
a k
b a r l a
m d
m a s
m a
t r d k s l
f s f ù k s a x u d
` a k
a ` l d k
t a k
f l f a k
t n m a
` d s d
` u m f k m f v f m u d
`
y i n
` a i
t f v d .
A s t ä k
m d r a
s e ä s f i n s
m a i n l p a t a
k i
f d s a k
I f a k i
f d s
K d t u r d
` a s
( i n k
t f k u d i
f ù k
)
A k t n r k n b ì s f i n
I f a k i f d ,
t a i k n ` n c ì d
y s n
i f a m d m
_ r n i a s n s q u ì l f i n s
_ r n i a s n s b ì s f i n s
A k t n r k n v f v n
•
N e s a r v n y
b n r l u
` n p r a c u k
t d s a s p a i
f b f i d s s n
e r a d p
` f i d i
f n k a s
m a
t a n r ì d s i
f a k
t ì b f i d s
•
B n r l u
` n h f p ù t a s f s i n k
e d s a a k a
` i n k n i
f l
f a k
t n i n
t f m f d k n ,
t a n r ì d s y l n
m a
` n s i
f a k
t ì b f i n s
•
F m a k
t f b f i n v d r f d
e ` a s q u a
f k b ` u y a k a k
` n s r a s u
` t d m n s
m a u k a x p a r f l a k
t n
•
_ r n p n k c n l n
m a
` n s p d r d p r a
m a i
f r ` n s r a s u
` t d m n s
m a u k a x p a r f l a k
t n
•
U a d
` f z n l a
m f i f n k a s i n k
f k s t r u l a k
t n s y a q u
f p n s d
m a i u d
m n s
•
U a c
f s t r n l
f s n
e s a r v d i
f n k a s y r a s u
` t d m n s u t
f ` f z d k
m n a s q u a l d s , c r ä
b f i n s y
t d e ` d s
•
U a c
f s t r n l
f s r a s u
` t d m n s a k
b n r l d n r c d k
f z d
m d y s f k d
` t a r d i
f ù k d
` c u k d
•
A s t d
e ` a z i n
m f b a r a k i
f d s a k
t r a m a s i r f p i
f ù k , a
x p
` f i d i
f ù k ,
y a v
f m a k i
f d
•
A s t d
e ` a z i n
m f b a r a k i
f d s a k
t r a l n
m a
` n s ,
t a n r
ì d s ,
` a y a s a
h f p ù t a s f s
•
U a i n k n z i n
` n s d p n r t a s
m a i n k n i
f l f a k
t n s m
f b a r a k
t a s d
` i
f a k
t ì b f i n
•
U a i n k n z i n q u a
` n s l n
m a
` n s
m a
` d i
f a k i
f d i d l
e f d k i n k a
` t f a l p n y q u a v d r f n s p u a
m a k
s a r v
ä ` f m n s s f l u
` t ä k a d l a k
t a .
•
I u
f m n ,
r a s p a
t n ,
y a x
f j n r a s p a
t n p n r l
f i u a r p n y p n r a
` m a
` d s
m a l
ä s p a r s n k d s
•
] n l n
m a i
f s f n k a s r a s p n k s d
e ` a s y i n l p d r t f m
d s s n
e r a l
f s a x u d
` f m d
m
•
D k d
` f z n i r ì t f i d l a k
t a ` n s p d p a
` a s
t r d m f i f n k d
` a s
m a c
æ k a r n a k k u a s t r d i u
` t u r d i n k r a s p a i
t n d
` d s a x u d
` f m d
m y
` d r a p r n
m u i i
f ù k
•
A x p
` f i n
` d
n e t a k i
f ù k
m a a k a r c
ì d
k u i
` a d r d
p d r t f r
m a
` d d
` t a r d i
f ù k
m a
` d a s t r u i
t u r d
m a
` ä t n l n .
•
A x p
` f i n
` d t r d k s b n r l d i
f ù k
m a
a k a r c
ì d l a
i ä k
f i d a k a k a r c
ì d
t æ r l
f i d .
Q t f ` f z n l n
m a
` n s
e f n ` ù c
f i n s ,
b ì s f i n s y q u
ì l f i n s p d r d a x -
p ` f i d r
` d
t r d k s
b n r l d i
f ù k y
i n k s a r v d i
f ù k
m a
` d a k a r c
ì d .
F m a k
t f b f i n
d p
` f i d i
f n k a s
m a
m f b a r a k
t a s l n
m a
` n s
e f n ` ù
-
c f i n s , q u
ì l f i n s y
b ì s f i n s a k
p r n i a s n s
f k m u s
t r f d ` a s y a k
a ` m a s d r r n
` ` n
t a i k n
` ù c
f i n 7
d k d
` f z n i r ì t f i d l a k
t a ` d s
f l -
p ` f i d i
f n k a s
m a s u s u s n s .
I n l p a t a k i f d s
¾ D q u æ
q u a r a l n s
` ` a c d r >
B d i t n r a s m a n r c d k f z d i f ù k
¾ I ù l n m a l u a s t r n ` n d p r a
k m f m n >
L a d p r n x f l n d `
i n k n i f l f a k t n i n l n
i f a k t ì b f i n ( d ) k d t u r d `
M a s d r r n ` ` n
i n l p r n l f s n s
p a r s n k d ` a s
y s n i f d ` a s
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Ìkm fiaQkfmdm 4. @ns ainsfstalds 439
Yasfùk 4. Akarcìd y ldtarfd ak `ns ainsfstalds 439
Yasfùk 5. ]arlnmfkälfid 431
Yasfùk 9. @d bntnsìktasfs 438
Yasfùk =. Kfva`as trùbfins 483
Yasfùk 1. Ua`difnkas aktra `ds inlukfmdmasma uk ainsfstald 464
Yasfùk 2. D`cukns ifi`ns efncanquìlfins 463
Yasfùk 3. Ldkns d `d nerd 5?5
Qkfmdm 5. @ns nrcdkfslns y su raspuastd dkta `ns astìlu`ns ma` lamfn 5?2
Yasfùk 8. A` sfstald karvfnsn 5?2
Yasfùk 6. A` sfstald akmnirfkn 55?
Yasfùk 4?. Ldkns d `d nerd 556
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4
B`ujn ma akarcìd
@ns saras vfvns kaiasftdk ma akarcìd pdrd pnmar rad`fzdr tnmds sditfvfmdmas vftd`as (masp`dzdlfaktn, masdrrn``n, iraiflfaktn a i`usn `d lfsld d`flaktdifùk).
4. Fmaktfbfqua ak a` sfcufakta mfeujn, `ns a`alaktns efùtfins y defùtfins, dsì inl`ds pnsfe`as ra`difnkas qua puamdk axfstfr aktra a``ns.
5. Masirfed iùln y ma mùkma netfakak akarcìd ns sfcufaktas nrcdkfslns: d dea`d vdid, a` äcuf`d, a` edcra, `d sarpfakta inrd` y ären` ma ldkcn.
Ya pnmrìd dbfrldr, qua ink luy pnids axiapifnkas, tnmns `ns nrcdkfslns
ma` _`dkatd mapakmak ma d akarcìd ma` Yn` pdrd sneravfvfr. _arn ¾`ns sarasvfvns iùln inksfcuak dprnvaihdr astd akarcìd> @ns d`flaktns qua ns sarashuldkns y ntrns nrcdkfslns inksulak ¾astäk ra`difnkdmns ink d akarcìdprnmuifmd pnr kuastrn dstrn Uay> _drd raspnkmar astds y ntrds pracuktdsra`difnkdmds ink a` b`ujn akarcætfin ak `ns ainsfstalds, ak astd ukfmdm,sa varä ak matd``a, a` prniasn lamfdkta a` iud` `d akarcìd sn`dr snstfaka `dvfmd ak `d ]farrd.
Akarcìd y ldtarfd ak ns ainsfstaldsQkfmdm 4. @ns ainsfstalds Yasfùk
4
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4
]rdedjn ak suecrupns.
Idmd suecrupn dkd`fzdrä `ds sfcufaktas pracuktds7 `uacn, snifd`fzdrä dkta sus inpdôarns y mniaktas `s inki`uifnkas d `ds qua hdyd ``acdmn
• Yf `d akarcìd kn sa irad kf sa mastruya, ¾iùln as qua pf`ds, edtarìds ma ia-`u`dras, y ntrns drtabditns sflf`dras, cakardk akarcìd a`æitrfid y maspuæs ma
uk tfalpn majdk ma bukifnkdr>
• @d ldynr pdrta ma d akarcìd a`æitrfid ak In`nlefd, as prnmuifmd pnr p`dktds hfmrna`æitrfids. A` prniasn lamfdkta a` iud` sa netfaka `d akarcìd asra`dtfvdlakta sakif``n: a` dcud ma rìns y aled`sas sa majd idar ak bnrld maidsidmd snera crdkmas turefkds aspaifd`lakta mfsaôdmds pdrd qua d` cfrdprnmuzidk a`aitrfifmdm. ¾Iùln as qua uk rìn n uk crdk iuarpn ma dcudak rapnsn puama takar akarcìd> ¾Ma mùkma `d hdk netakfmn>
@d prflard `ay ma `d tarlnmfkälfid sa inknia inln `d `ay ma`d inksarvdifùk pnrqua dbfrld qua `d akarcìd kn sa irad k
sa mastruya, sfkn qua sa trdksbnrld.
]arlnmfkälfid as d ifakifd qua astumfd ds trdksbnrldifn-kas ma `d akarcìd.
@d tarlnmfkälfid
Qkfmdm 4. @ns ainsfstalds Yasfùk
5
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Crdk pdrta ma `dakarcìd quanetfakak `ns
ldlìbarns y `ds dvasma `ns d`flaktns quainksulak, as usdmdpdrd prnmuifr id`nr.
@d akarcìd tntd` ma uk sfstald y `d ma sus d`ra-
mamnras sa ldktfaka inkstdkta. D inktfkudifùk,
dkd`fialns d`cukns ajalp`ns qua kns parlftdk
inlprakmar lajnr `d dbfr ldifùk dktarfnr.
Iudkmn `d akarcìd a`æitrfid ``acd d uk enlef``n,a` bf`dlaktn ma tukcstakn qua sa akiuaktrd ak sufktarfnr, sa hdia fkidkmasiakta, as maifr, prnmuia`uz d` dulaktdr su talpardturd. Ak asta idsn aspnsfe`a dpraifdr qua `d akarcìd fkfifd` kn sa mas-truya, ak rad`fmdm parldkaia inkstdkta, sn`n qua
sa trdksbnrld ak `uz y id`nr.
Ma bnrld sflf`dr, niurra ink `ns nrcdkfslns. @d`uz sn`dr as trdksbnrldmd maktrn ma `ns i`nrnp`ds-tns ma `ds p`dktds ak akarcìd a`æitrfid, y `uacn akakarcìd quìlfid pnr lamfn ma `d bntnsìktasfs. @nsprnmuitns qua sa netfakak ak asta prniasn inlnia`u`nsd y d`lfmnkas, sfrvak ma d`flaktn pdrd ntrns
nrcdkfslns qua inkvfartak astd akarcìd quìlfid aklnvflfaktn (akarcìd laiäkfid), id`nr (akarcìd tær-lfid), n flpu`sns a`æitrfins (akarcìd a`æitrfid), ati.
@d sacukmd `ay ma `d tarlnmfkälfid dbfrld qua sfalpra qua sa rad`fzdukd trdksbnrldifùk ma akarcìd, pdrta ma a``d kn puama sar dsflf`dmd. Asflpnrtdkta takar ak iuaktd qua astd brdiifùk ma akarcìd kn sa pfarma(inln yd sa mfjn), sfkn qua kn puama usdrsa pdrd rad`fzdr uk trdedjn útf`.
Radlns uk ajalp`n:
Ydealns qua iarid ma` 1?% ma `d `uz sn`dr d`idkzd `d suparbfifa tarrastra,y qua a` rastn as frrdmfdmn pnr d dtlùsbard d` aspdifn. _drta ma d idktfmdmqua ncrd fkcrasdr d d ]farrd, as rab`ajdmd pnr sus suparbfifas i`drds n sa mfsfpdsflp`alakta inln id`nr. Ya astfld qua sù`n a` ?.4% ma `d akarcìd sn`drqua ``acd d `d suparbfifa ma `d ]farrd, as dprnvaihdmd pnr `ns nrcdkfslns.
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5
@ds p`dktds tdlpnin inksfcuak dprnvaihdr d` 4??% `d akarcìd sn`dr7d`cukns ma `ns rdyns ma `uz snk rab`ajdmns sflp`alakta pnr `ds lfsldshnjds, y su akarcìd kn puama sar dprnvaihdmd.
Astumfns raifaktas hdk malnstrdmn qua ma tnmd d uz qua `acd d ukd znkdma vacatdifùk deukmdkta inln ukd sa`vd, úkfidlakta ma` 4 d` 9% as usdmnpdrd `d bntnsìktasfs.
@ns dkfld`as hareìvnrns inksulak p`dktds pdrd netakar akarcìd y pnmarrad`fzdr sus bukifnkas, parn ukd pdrta ma astd akarcìd sa inkvfarta ak id`nr7dsì qua iudkmn asta dkfld` as inksulfmn pnr ntrn, kn `a trdksbarfrä tnmd
`d akarcìd qua netuvn ma `d p`dktd, sfkn `d brdiifùk qua hdeìd quamdmninktakfmd ak sus tajfmns.
Fkvastfcualns:
d. ¾Iuäktds `ayas ma `d tarlnmfkälfid axfstak>
e. Ak sus prnpfds pd`derds mabfkd: ¾Tuæ as tarlnmfkälfid y qua bakùlakaxp`fid>
@d idktfmdm ma akarcìd útf` vd mfslfkuyakmn
d lamfmd qua sa pdsd ma uk kfva` trùbfin d ntrn.
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Yf efak sa dbfrld qua ns saras vfvns mapakmak ma d uz sn`dr pdrd su suparvfvakif
sù`n ukd pdrta ma a``ns, inksfcua trdksbnrldr astd bnrld ma akarcìd ak d`flaktn. Akt`ns nrcdkfslns idpdias ma bderfidr sus prnpfds sustdkifds kutrftfvds, sa akiuaktrd`ds p`dktds, `ds d`cds y d`cukds editarfds.
@ns nrcdkfslns bntnsfktatfzdmnras pnsaak sustdkifds idpdias ma desnrear d uz, `dldmds pfclaktns. Aktra ns läs inknifmns, sa akiuaktrdk d i`nrnbf`d qua a ntnrca` idrditarìstfin varma d ds p`dktds7 y ns idrntakns, pfclaktns rnjns, dkdrdkjdmnsdldrf``ns, qua puamak dpraifdrsa bäif`lakta pnr ajalp`n, ak d`cukns ma `ns tajfmnma` tnldta y `d zdkdhnrfd. @ns pfclaktns prasaktas ak `ns auidrfntds bntnsfktat
zdmnras, sa hd``dk maktrn ma `ns tf`dinfmas (lalerdkds fktarkds ink dpdrfakifd msdin dp`dkdmn)7 ak `ns prnidrfntds idpdias ma rad`fzdr `d bntnsìktasfs, `ns tf`dinfmakn sa akiuaktrdk ak `ns i`nrnp`dstns, inln yd vflns7 `ns nrcdkfslns prnidrfntdidraiak ma nrcdka`ns mabfkfmns pnr lalerdkd.
A` in`nr varma ma `d i`nrnbf`d dpdraia pnrqua a` pfclaktn desnrea `ds `nkcftumas m
nkmd vfn`atd, rnjn y dzu`, y ak idlefn, rab`ajd `ds `nkcftumas ma nkmd varma.
@d bntnsìktasfs
Qkfmdm 4. @ns ainsfstalds Yasfùk
9
@u`n prnmuifmn ak Cudfkìd
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4. Ak uk raifpfakta ink d`inhn`, in`nqua `ds hnjds y trftúra`ds ink a`
lnrtarn.
5. Rfartd `d lazi`d netakfmd ak a` sacukmn raifpfakta.
9. Fktrnmuzid ak `d lazi`d, pdrta ma` pdpa` bf`trn.
=. Maja saidr a` pdpa`.
_rniamflfaktn:
Masirfed matd``dmdlakta `ds idrditarìstfids qua prasaktda` pdpa` y inlakta `ds inki`usfnkas snera `d axparfakifd.
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Ak `d prflard atdpd ma `d bntnsìktasfs, d`cukns bntnkas (pdrtìiu`ds qua inlpnk`d `uz), fkcrasdk ak `d p`dktd d trdvæs ma `ds hnjds. Mfihds pdrtìiu`ds snk desnrefmpnr `d i`nrnbf`d qua sa akiuaktrd ak `ns tf`dinfmas7 d lamfmd qua `d i`nrnbf`d raibntnkas, vd `feardkmn a`aitrnkas qua mfbaraktas tfpns ma ln`æiu`ds idptdk y trdpnrtdk. Inkbnrla `ns a`aitrnkas snk ``avdmns d kfva`as läs edjns, vdk `feardkakarcìd qua sa utf`fzdrä pnstarfnrlakta pdrd a`denrdr D]_ (Dmaknsfkd ]rfbnsbdtln`æiu`d pnrtdmnrd ma akarcìd, ma crdk flpnrtdkifd ak `ns prniasns qua rad`fz
`ns saras vfvns. D` bfkd` ma` prniasn, `ns a`aitrnkas snk idptdmns pnr `d ln`æitrdkspnrtdmnrd KDM_+.
@ds ln`æiu`ds maKDM_+snk ramuifmds, as maifr cdkdk a`aitrnkas ma d sfcufakta bnrl
@d bntnsìktasfs sa rad`fzd ak mns atdpds: ak `d prflard, sa idpturd `d `uz7 y ak`d sacukmd, niurrak d`cukns prniasns quìlfins qua kn raqufarak prasakifdma `uz.
KDM_+ KDM_H
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_ + DM_ D]_
Inln puama dpraifdrsa ak d bfcurd, ukn ma ns prnmuitns ma` prniasn as a` D]_, qusa bnrld iudkmn d ln`æiu`d ma Dmaknsfkd Mfbnsbdtn (DM_), raifea uk bnsbdtn. A` D]sa bnrld, crdifds d `d akarcìd qua `feardk `ns a`aitrnkas d` masiakmar ma kfva`.
Ak `d bntnsìktasfs, `ns inlpnkaktas ma` dcud snksapdrdmns pdrd usdr`ns ak ntrns prniasns, pnrajalp`n: a` nxìcakn as `feardmn d` dlefakta,lfaktrds qua a` hfmrùcakn hdrä pdrta ma ln`æ-iu`ds inln `d KDM_H.
Ak d prflard atdpd ma d bntnsìktasfs, sa puamanesarvdr `d ldkard inln `d akarcìd as trdks-bnrldmd:
4. @d akarcìd ulìkfid sa trdksbnrld ak akar-
cìd a`æitrfid, crdifds d` b`ujn ma a`aitrnkas.
5. @d akarcìd a`æitrfid sa trdksbnrld akakarcìd quìlfid, iudkmn quamd d`ldia-kdmd ak ds ln`æiu`ds ma KDM_H y D]_.
Akarcìd `ulìkfid
Akarcìd `ulìkfin
I`nrnp`dstn
Akarcìdquìlfid
KDM_H D]_
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5
Ak asta puktn ma `d bntnsìktasfs, `d p`dk-td hd `ncrdmn inkvartfr `d akarcìd sn`drak akarcìd quìlfid qua puama utf`fzdrpdrd bderfidr dzúidras inln `d c`uinsd:I2H45N2. _arn ns nrcdkfslns bntnsfktæ-tfins kaiasftdk idrenkn pdrd bderfidr`ds ln`æiu`ds ma c`uinsd. ¾Ma mùkmanetfakak a` idrenkn, nrcdkfslns inln`ds p`dktds n ds d`cds qua sa akiuaktrdksularcfmds ak a` dcud>
@ds p`dktds netfakak a` idrenkn ka-iasdrfn pdrd bderfidr sus dzúidras, ma`mfùxfmn ma idrenkn qua sa akiuaktrd ak a` dfra. Ak idlefn, ns nrcdkfslnsbntnsfktætfins qua sa akiuaktrdk sularcfmns, inln d`cds y ntrds p`dktds,desnreak a` idrenkn mfsua`tn ak a` dcud.
A` idrenkn ncrd fkcrasdr ak ds iæ`u`ds bntnsfktætfids ma ds p`dktds, pnr lamfnma astnlds qua snk `ns pnrns qua pnsaak `ds p`dktds ak sus hnjds y td``ns.
]rdedjn ak suecrupns.
Inktastak ak a` iudmarkn:
4. ¾Ma mùkma prnvfaka a` mfùxfmn ma idrenkn prasakta ak a` dfra n mfsua`tn a` dcud y qua desnreak `ds p`dktds>
5. ¾As eakæbfin pdrd `ns maläs nrcdkfslns, qua `ds p`dktds desnredk ma` lam
B`nrd cudfkfdkd
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@d c`uinsd as d akarcìd quìlfid prnmuitn ma d bntnsìktasfs, qua dpnrtd`d akarcìd kaiasdrfd pdrd qua ds iæ`u`ds rad`fiak dmaiudmdlakta susbukifnkas. Dmaläs, as d edsa pdrd d inkstruiifùk ma ln`æiu`ds läsinlp`ajds inln idrenhfmrdtns, `ìpfmns y prntaìkds.
Ak `ds sfcufaktas päcfkds, axfstak dkfldifnkas ra`difnkdmds ink `dbntnsìktasfs y a` ifi`n ma Id`vfk:
• http://www.efn`ncfd.amu.dr/p`dktds/bntnsfkt5.htl• http://www.ldph=6.cd`ank.inl/bntn/nvarvfaw.htl`• http://wae.amuidstur.prfkidst.as/prnyaitns/efncan^nv/Dkf-
ldifnkas/Fkmfia^dkfl.htl
@d bruitnsd, `d rfensd y `d c`uinsd, snk lnknsdiärfmns pnrqua pnsaak ukd sln`æiu`d ma dzúidr7 ak idlefn, ns mfsdiärfmns astäk inlpuastns pnr mns ln`æiusflp`as ma dzúidr7 ajalp`ns: `d sdidrnsd n dzúidr ma `d idôd y `d `ditnsd n dzúma `d `aiha. Iudkmn vdrfds ln`æiu`ds ma dzúidr sflp`a sa ukak aktra sì (inln a` idsn ma `ds ln`æiu`ds qua inkbnrldk `d ia`u`nsd ma `ds p`dktds), sa hde`d
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9
@ns nrcdkfslns hdk avn`uifnkdmn pdrd d`ldiakdr `ds sustdkifds kutrftfvds qua kraqufarak ak a` lnlaktn, parn puamak utf`fzdr maspuæs. Ajalp`n: a` d`lfmùk
uk pn`fsdiärfmn qua `d ldynrìd ma `ds p`dktds utf`fzd inln rasarvd d`flaktfifd. AIn`nlefd, d`cukds ma `ds p`dktds d`flaktfifds läs pnpu`dras pnr su inktakfmn md`lfmùk snk d pdpd, d yuid, a` trfcn, d iaedmd, a` ldìz, a` sdcú ma pd`ld, d dihfra` p`ätdkn, `ns cdredkzns, `ds `aktajds, `ds d`uefds y ntrds läs.
Ink `d fkbnrldifùk raifefmd y takfakmn ak iuaktd a` crdk kúlarn ma pd`derdkuavds qua halns asiuihdmn y/n `aìmn, vdlns d rad`fzdr uk iruifcrdld ak `d ids_drd a``n, maealns hdiar uk `fstdmn ma 45 pd`derds kuavds qua hdcdk rabarakifd `d sasfùk ma hny:
Bntnsìktasfs: Ink asta fstdmn idmd ukn maearä trdar haihn, ak ukd hnjd e`dkid, uiruifcrdld qua fkvn`uira astds 45 pd`derds kuavds y sus sfckfbfidmns. Yad iradtfvy hdcd a` iruifcrdld läs nrfcfkd` pnsfe`a.
_nr sar ukd sustdkifd ma rasarvdprnmuifmd d pdrtfr ma` dzúidr, a`d`lfmùk pnsaa uk crdk inktakfmnakarcætfin y pnr td` rdzùk, as luyflpnrtdkta fki`ufr`n ak pnrifnkasdmaiudmds ak `d mfatd mfdrfd.
A` c`uiùcakn as `d bnrldinln `d ldynrìd ma `ns dkf-ld`as d`ldiakd a` dzúidr. Ak`ns vartaerdmns, sa akiuaktrdprfkifpd`lakta ak a` hìcdmn yak `ns lúsiu`ns.
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Maefmn d qua ak idmd kfva` trùbfin `dakarcìd útf` as laknr, a` kúlarn manrcdkfslns qua puamak dprnvaihdr`dtdlefæk mfslfkuya. Ma td` ldkard quaa` lajnr lnma`n qua raprasaktd asta ba-kùlakn, as d bfcurd trfdkcu`dr qua sa ahd maknlfkdmn pfrälfma ain`ùcfid.
D` fcud` qua `ds pfrälfmas ma Acfptn,`ds pfrälfmas ain`ùcfids kaiasftdkma ukd edsa pdrd snstakar a` rastn ma
su astruiturd7 ak `ns ainsfstalds, `nsnrcdkfslns prnmuitnras snk `ns quaniupdk a` prflar kfva` trùbfin. Astnssaras vfvns inln su knlera `n fkmf-id, snk idpdias ma a`denrdr su prnpfnd`flaktn d pdrtfr ma d trdksbnrldifùkma `d akarcìd sn`dr ak akarcìd quì-lfid y pnr `n tdktn, tdlefæk sa `asmaknlfkd dutùtrnbns. @ds p`dktds,`ds d`cds y `ds editarfds bntnsfktætfidshdiak pdrta ma asta flpnrtdkta kfva`.
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Crdifds d `d idpdifmdm qua tfakak `ns nrcdkfslns dutùtrnbns maprnmuifr su prnpfn d`flaktn, `ns hatarùtrnbns (nrcdkfslns quasa d`flaktdk ma ntrns pdrd netakar akarcìd), puamak sneravfvfr y
hdiar pdrta ma `d pfrälfma ain`ùcfid.
Nrcdkfslns inksulfmnras (hatarùtrnbns), y su kfva` trùbfin:
Yacukmn
kfva` trùbfin
Inksulfmnras maprflar nrmak
Nrcdkfslns hareìvnrns. Ajalp`n
a`abdkta, vdid, vakdmn, nrucd, id-ed``n, jfrdbd, drmf``d y inkajn.
• Idrkìvnrns qua inksulak har-eìvnrns.
• Nrcdkfslns qua sa d`flaktdk mafksaitns (fksaitìvnrns) Ajalp`n`aùk, nsn, end, znrrn, nen, rdkd`dcdrtfjd y nsn hnrlfcuarn.
Inksulfmnras masacukmn nrmak
]ariar kfva`
trùbfin
Iudrtn kfva`
trùbfin
Idrkìvnrns qua inksulak fksai-tìvnrns u ntrns idrkìvnrns. Ajalp`n: äcuf`ds y sarpfaktas qua sad`flaktdk ma rdkds, inldmrajds y`dcdrtfjds.
Inksulfmnras matariar nrmak
Nrcdkfslns qua sa d`flaktdk ma nsrastns ma ntrns (rdlds, hnjds y trnk-ins ma ären`as y p`dktds luartdsrastns ma pfa`, asqua`atns, haiasati.). Ajalp`ns: euftras, idkcrajnsy d`cukns asidrdedjns.
Matrftìvnrns n idrrnôarns
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=
@ns masinlpnkamnras n macrdmdmnras d` fcud`qua `ns matrftìvnrns, netfakak `d akarcìd ma `nsrastns nrcäkfins. Yfk aledrcn, snk idpdias mautf`fzdr sustdkifds qua a` rastn ma dkfld`as knpuama dsflf`dr, inln pnr ajalp`n: `d ia`u`nsdy ns masaihns kftrncakdmns. Dmaläs, snk luyflpnrtdktas pdrd a` ainsfstald pnrqua mavua`-vak kutrfaktas d` sua`n, iudkmn inkvfartak `dldtarfd nrcäkfid qua prnvfaka ma `ns rastns ma`ns nrcdkfslns, ak ldtarfd fknrcäkfid.
]rdedjn fkmfvfmud`.
@`aka a` sfcufakta iudmrn ink nrcdkfslns prnpfns ma su racfùk y `uacn, mfeúja`nak ukd pfrälfma ain`ùcfid.
_rflarkfva` trùbfin
Yacukmnkfva` trùbfin
]ariarkfva` trùbfin
Iudrtnkfva` trùbfin
_rnmuitnras
Inksulfmnras maprflar nrmak
Inksulfmnras masacukmn nrmak
Inksulfmnras matariar nrmak
Matrftìvnrns n idrrnôarns
Bntn tnldmd ma Sfgfpam
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Masdbnrtukdmdlakta, `d bdukd y `d b`nrd ma kuastrn _dìs kn snk djakdsd astd prne`alätfid. D inktfkudifùk, sa ra`difnkdk d`cukns ma `ns idsnsqua ajalp`fbfidk `d fktrnmuiifùk ma aspaifas axùtfids ak `ns ainsfsta-lds in`nlefdkns, y a` d`tn crdmn ma dlakdzd qua raprasaktdk pdrd`d efnmfvarsfmdm kdifnkd`.
Ak `d ditud`fmdm, a` enidihfin as ukn ma `ns paias läs raprasaktdtfvnsma `d bdukd in`nlefdkd y inrra a` rfascn ma masdpdraiar, maefmn d `dfktrnmuiifùk ma `d tf`dpfd n lnjdrrd ak su häeftdt. A` ‐paz fkvdsnr“ buatrdìmn d bfkas ma `ns dôns 3? masma Äbrfid a fktrnmuifmn ak `ds dcuds ma`Ldcmd`akd, pdrd trdtdr ma rastde`aiar ns raiursns pasquarns ma` rìn qua
pnr asd æpnid, sa vaìdk luy mfslfkufmns. Ak abaitn, pdrta ma` nejatfvnsa iulp`fù pnrqua a` kúlarn ma tf`dpfds sa fkiralaktù sustdkifd`lakta7parn aspaifas inln a` enidihfin qua as akmælfid n prnpfd ma` `ucdr,mfslfkuyù inksfmarde`alakta.
Masma aktnkias, lú`tfp`as fkvastfcdmnras hdk inlprnedmn qua a` mas-iaksn ma d`cukds ma `ds aspaifas ma paias akmælfids ma` rìn Ldcmd`akd,as inksaiuakifd mfraitd ma `d fktrnmuiifùk ma `d lnjdrrd. @ns astumfns
hdk rava`dmn tdlefæk, qua a` æxftn ma `d aspaifa fktrnmuifmd sa maea dsu räpfmd raprnmuiifùk (idmd tras lasas, ak inlpdrdifùk ink `ns mnsdôns y lamfn qua maea aspardr a` enidihfin), d `d ldynr rasfstakifd d `dinktdlfkdifùk y pnrqua idraia ma mapramdmnras kdturd`as.
B n t n t n l d m d m a S f g f p a m f d
]f`dpfdEnidihfin
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1
]rdedjn ak suecrupns.
A`denrdr ink ns inlpdôarns, uk fstdmn ma rainlakmdifnkas akidlfkdmds d pravaky inrracfr a` prne`ald ma `d fktrnmuiifùk ma aspaifas axùtfids ak `ns ainsfstal
Yflefnsfs
Lutud`fsln
Ua`difùk ak `d iud`dleds aspaifas saeakabfifdk. Ajalp`n:`fquak (dsnifdifùkma d`cds y hnkcns):`ns hnkcns erfkmdksustrdtns y `ds d`cdsa` d`flaktn.
Ua`difùk ak `d iud`ukd aspaifa sa eaka-bfifd y `d ntrd kn raif-
ea mdôn kf eakabfifn.Ajalp`n: `d cdrzdeuayard sa eakabfifdma` cdkdmn vdiukn,qua d` masp`dzdrsa,aspdktd `ns fksaitns.
Ua`difùk ak `d iud`ukd aspaifa sa ea-kabfifd y parjumfid d`d ntrd. Ajalp`n: `dtakfd n nlerfz sn`ftd-rfd qua sa d`njd ak a`fktastfkn ma`cdmn ma`hnlera y sa d`flak-td ma `ds sustdkifdskutrftfvds qua d``ì saakiuaktrdk. _uama
d`idkzdr hdstd mfazl ma nkcftum maktrnma` fktastfkn y prn-muifr käusads, mn`nrdemnlfkd`, mfdrrad ypærmfmd ma pasn.
Inlaksd`fsln _drdsftfsln
@d fktardiifùk aktra nr-cdkfslns ma mfbarakta as-paifa qua vfvak juktns, sainknia inln sflefnsfs.
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4
Eusidr ntrns tras ajalp`ns pdrd idmd ra`difùk sflefùtfid.
@d ifriu`difùk ma sustdkifds fknrcäkfids d trdvæs ma` ain-sfstald inln dcud, bùsbnrn, kftrùcakn y ldckasfn, aktrantrns, sa inknia inln ifi`n efncanquìlfin pnrqua ak æ`fktarvfakak bditnras can`ùcfins y efn`ùcfins.
A` dcud as ukn ma `ns a`alaktns läs flpnrtdktas aktra `nsbditnras defùtfins ma `ns ainsfstalds. Ifriu`d d trdvæs ma `ddtlùsbard, `d hfmrùsbard y `d inrtazd tarrastra, rad`fzdkmn a`ifi`n ma` dcud.
@ds paquaôds pdrtìiu`ds ma dcud qua rasu`tdk ma `d avdpn-
rdifùk ma` dcud suparbfifd` ma ldras, rìns, `dcns, `dcukds yntrns iuarpns hìmrfins, dsifakmak d d dtlùsbard, parmfakmn
crdmud`lakta su id`nr, `n iud` pnsfef`ftd su inkmaksdifùk ak bnrld ma cntds qua d` bfkd`, bnrldk `ds kueas7 iudkmn`ds cntds d`idkzdk uk tdldôn ra`dtfvdlakta crdkma, sapraifpftdk ak bnrld ma ``uvfd. Ak cakard`, a` dcud ``uvfdsfalpra takmrä mns mastfkns: ratnrkdr d ns iuarpns hìmrfinsma mnkma sa avdpnrù n pdsdr d bnrldr pdrta ma` inkjuktnma dcuds suetarräkads.
D`cukns ifi`ns efncanquìlfins
Qkfmdm 4. @ns ainsfstalds Yasfùk
2
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Ak d ú`tfld atdpd `dldmd dsflf`difùk, `ds p`dktds pnr lamfn ma sus rdìiasdesnreak prfkifpd`lakta a` kftrùcakn ak bnrld ma kftrdtn, dukqua d`cukdsp`dktds puamak utf`fzdr a` dlnkfn ak bnrld mfraitd. Maktrn ma d p`dktd, a`
dlnkfn sa inlefkd ink inlpuastns qua inktfakak idrenkn pdrd prnmuifrinlpuastns nrcäkfins inln `ns dlfknäifmns.
]rdedjn fkmfvfmud`.
Asirfefr y rasn`var `ds sfcufaktas pracuktds ak a` iudmarkn:
4. ¾Iùln iraa ustam qua `d td`d ma ensquas dbaitd a` ifi`n kdturd` ma` dcud
5. ¾_nr quæ snk tdk flpnrtdktas `ns lfirnnrcdkfslns pdrd `d bartf`fmdm ma `n
F l d c a k
t n l d m d m a S f g f p a m f d
Ifi`n ma` kftrùcakn
5
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A` ifi`n ma` idrenkn as ntrn flpnrtdkta ifi`n maktrn ma ns ainsfstalds. A`idrenkn as uk a`alaktn qua sa akiuaktrd ak a` dfra y ak a` dcud, mfsua`tnak bnrld ma mfùxfmn ma idrenkn, prnmuitn ma `d raspfrdifùk ma `ns saras
vfvns, inleustfnkas y ntrds radiifnkas quìlfids. Inln pumn dpraifdrsaak crdk pdrta ma` masdrrn``n ma astd Qkfmdm, `ds p`dktds pnr lamfn ma`d bntnsìktasfs, tfakak `d idpdifmdm ma desnrear a` mfùxfmn ma idrenkn ytrdksbnrldr`n ak idrenhfmrdtn. Luihns nrcdkfslns sa d`flaktdk ma astdsp`dktds y aktnkias, a` mfùxfmn ma idrenkn sa vua`va d `feardr d` aktnrknpnr lamfn ma d raspfrdifùk, d masinlpnsfifùk ma sustdkifds ma masaihnma `ns nrcdkfslns n `d putrabdiifùk ma sus prnpfns iuarpns d` lnrfr.
F l d c a k t n l d m d m a w w w . g d
` f p a m f d . i n
l
Ifi`n ma`
idrenkn
Fkvastfcdr a` nrfcak ma ds trdksbnrldifnkas ma` idrenkn ak inleustfe`a bùsf`
@d ldynr pdrta ma` idrenkn sa akiuaktrd inktakfmd edjn
`d suparbfifa tarrastra ak bnrld ma idreùk y patrù`an.
9
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Ldkns d d nerd
Qkfmdm 4. @ns ainsfstalds Yasfùk
34. Yù`n a` 1?% ma `d `uz sn`dr inksfcua ``acdr d `d suparbfifatarrastra maefmn d:
d. Tua a` rastn ma `d `uz quamd razdcdmd ak a` idlfkn.
e. @d bnrld dihdtdmd ma `d ]farrd.
i. Tua as rab`ajdmd d` aspdifn axtarfnr n as desnrefmd pnr a`a-laktns prasaktas ak `d dtlùsbard.
m. @d mfstdkifd aktra a` Yn` y `d ]farrd.
a. @d va`nifmdm ma `d `uz.
5. Axp`fqua iùln `ns rdyns sn`dras puamak dtrdvasdr läs bäif`lakta `ddtlùsbard qua `ns rdyns fkbrdrrnjns.
9. Axp`fqua d prflard ay ma d inksarvdifùk, vd`fækmnsa ma uk ajalp`n.
=. D` nesarvdr `d raprasaktdifùk cräbfid ma ukd pfrälfma ain`ùcfid, aspnsfe`a dpraifdr d mfslfkuifùk ma` kúlarn ma nrcdkfslns d lamfmdqua sa dsifakma ak `ns mfbaraktas kfva`as trùbfins. Axp`fqua pnr quæ
niurra asta bakùlakn.1. Asirfed sf as bd`sn (b) n varmdmarn (v):
d. @ds p`dktds y `ds d`cds tfakak `d idpdifmdm ma rad`fzdr bntn-sìktasfs ( )
e. @ns pfclaktns snk sustdkifds idpdias ma desnrear `d `uz ( ) i. A` in`nr varma ma `ds p`dktds sa maea ak crdk pdrta d `d
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6. Uaprasakta ukd pfrälfma ain`ùcfid, edsäkmnsa ak `d ram trùbfid ma`puktn dktarfnr.
4?. Inlp`ata `ns sfcufaktas akukifdmns:
d. @ns nrcdkfslns sua`ak inlpatfr pnr raiursns inln ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .
e. @d inlpatakifd ma nrcdkfslns ma vdrfds aspaifas pnr a` dcudma uk astdkqua as uk i`drn ma ajalp`n ma inlpatakifd ^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .
i. @d inlpatakifd ^^^^^^^^^^^^^^^^^^^ niurra aktra nrcdkfs-lns ma ^^^^^^^^^^^^^^^^^^^^^^aspaifa.
m. @d pramdifùk as ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .
a. @d fktardiifùk aktra nrcdkfslns ma mfbarakta aspaifa qua vfvak juktns, sa inknia inln ^^^^^^^^^^^^^^^^^^^^^^^ .
b. @d ra`difùk ak `d iud`, dleds aspaifas sa eakabfifdk sa ``dld^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .
c. A` inlaksd`fsln niurra iudkmn ^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .
h. @ds pu`cds y cdrrdpdtds sa inksfmardk nrcdkfslns ^^^^^^^^^^^^^^^^^^^^^^^ pnrqua sa d`flaktdk d axpaksds ma ntrnsy `as idusdk mdôn.
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5_drtas ma `d kaurnkd
I`dsfbfidifùk ma `ds kaurnkds sacúk su pn`drfmdm
Kaurnkd ukfpn`dr
Yu snld tfaka ukdsn`d prn`nkcdifùk(dxùk).
Kaurnkd efpn`dr
Ma uk axtraln ma suiuarpn ia`u`dr sa prn-yaitd ukd makmrftd yma` ntrn uk dxùk.
Kaurnkd lu`tfpn`dr
_nsaa lú`tfp`as prn-`nkcdifnkas aktra `dsiud`as sa akiuaktrdk ukdxùk y vdrfds makmrftds.
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D mfbarakifd ma `d p`dkdrfd,`ns dkæ`fmns inln `d `nlerfzma tfarrd, pnsaak uk inrmùkkarvfnsn mne`a (prnmuitn ma`d busfùk ma mns inrmnkas),qua rainrra d pdrta vaktrd` masu iuarpn. A` sfstald karvfnsntdlefæk sa inlpnka ma mnscdkc`fns mnrsd`as `nid`fzdmnsak `d racfùk iabä`fid, y ku-larnsns cdkc`fns ma laknrtdldôn qua sa akiuaktrdk d
`n `drcn ma` inrmùk karvfnsn(aspaiìbfidlakta uk pdr ma cdkc`fns pnr saclaktn). Astns nrcdkfslns pnsaak vdrfntfpns ma iæ`u`ds saksnrfd`as, aktra `ds iud`as sa akiuaktrdk: `ds laidknrraiaptnrd
(tditn), idpdias ma parifefr fki`usn, `ds vferdifnkas ma` sua`n7 `ds iæ`u`ds bntnsaks
e`as (saksfe`as d `d `uz), ma crdk dyumd pdrd `ds `nlerfias ma tfarrd qua idraiak mvfstd7 y raiaptnras ma hulamdm qua parlftak d` dkfld`, mfstfkcufr ukd znkd saima ukd húlamd.
A` sfstald karvfnsn ma nrcdkfslns inl`ns fksaitns, `ns idkcrajns, `ds drdôdsntrns drtrùpnmns, inlpdrtak d`cuksflf`ftumas ink a` sfstald karvfnsn m`ds `nlerfias ma tfarrd, td`as inln prasakifd ma uk inrmùk karvfnsn vatrd` mne`a, crdkmas cdkc`fns ak d racfùiabä`fid y uk pdr ma paquaôns cdkc`fnpnr idmd saclaktn. Yfk aledrcn, `ndrtrùpnmns d mfbarakifd ma ns dkæ`fmnpnsaak tras pdras ma cdkc`fns mnrsd`ak `d ideazd qua bnrldk ukd aspaima paquaôn iaraern, d mnkma `acdksa dsnifdk ns astìlu`ns qua prnvfaka
Drdôd `nen.
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_drtas ma` akiæbd`n
A` akiæbd`n as `d pdrta iaktrd` ma` sfstald karvfnsn y astäinkbnrldmd pnr a` iaraern7 a` iaraea`n as uk ùrcdkn läspaquaôn qua a` iaraern y sa uefid ak `d pdrta pnstarfnr ma `didvfmdm irdkadkd7 y a` trnkin iaraerd` as `d astruiturd quainlukfid d` iaraern ink `d læmu`d aspfkd`. ]nmn a` akiæbd`n
sa akiuaktrd maktrn ma` iräkan.
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5
]rdedjn fkmfvfmud`.
Ak su iudmarkn, axp`fqua ds prfkifpd`as mfbarakifds aktra a` sfstald karvfnsn iaktry a` sfstald karvfnsn parfbærfin.
_rnpdcdifùk ma` flpu`sn karvfnsn
D sujatdr uk nejatn, pnr ajalp`n: uk luôain ma pa`uiha, ds kaurnkds sak-snrfd`as parifeak asa astìlu`n y `n inkmuiak d `d læmu`d aspfkd . Qkd vazd` ì, a flpu`sn sfcua uk idlfkn hdstd a iaraern, rainrrfakmn `d astruiturdma `ds kaurnkds ma prnyaiifùk y `ds fktarkaurnkds. Ak a` iaraern, sa
prniasd `d fkbnrldifùk y ak asta idsn pdrtfiu`dr, as `d saksdifùk maastdr dpratdkmn uk nejatn sudva. @d maifsfùk ma dpratdr a` nejatn inkluihd läs buarzd, vfdjd ak bnrld ma flpu`sn karvfnsn masma a` iara-ern, pdsd pnr `d læmu`d aspfkd` (d trdvæs ma kaurnkds ma prnyaiifùka fktarkaurnkds), y d``ì hdia sfkdpsfs ink ukd kaurnkd lntnrd pdrdkd`lakta trdslftfr a` flpu`sn abaitnr d `ns lúsiu`ns ma `d ldkn.
]nmns `ns flpu`sns kn sfcuak `d lfsld rutd. Ak nidsfnkas, a` astìlu`nqua prnvfaka ma `ds kaurnkds saksnrfd`as ``acd d `ds fktarkaurnkds, ypdsd mfraitdlakta d ds kaurnkds lntnrds (kn vfdjd hdstd a` iaraern).Asta tfpn ma raspuastd fkvn`uktdrfd, sa inknia inln rabajn. @d radi-ifùk fkstdktäkad ma ratfrdr `d ldkn d` pfkihdrsa ink ukd aspfkd, asuk ajalp`n qua maluastrd asta bakùlakn. Idsf sflu`täkadlakta,`ds kaurnkds ma prnyaiifùk ratrdkslftak d fkbnrldifùk d` iaraern,mnkma as rainknifmn y avd`udmn pdrd qua a` fkmfvfmun tnla `ds la-mfmds d` raspaitn
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Astruiturd y bukifnkas ma` sfstald karvfnsn dutùknln
_ dr d s f l p ä
t f i n
Y f l
p ä t f i n
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Inln pumn dpraifdrsa murdkta pdr-ta ma asta idpìtu`n, d læmu`d aspfkd`as luy flpnrtdkta pnrqua d trdvæsma `ns karvfns qua `d inkbnrldk,ifriu`dk flpu`sns karvfnsns aktraa` akiæbd`n y a` rastn ma` iuarpn.Yfk aledrcn, ak nidsfnkas `d trdks-lfsfùk ma mfihns flpu`sns puamadbaitdrsa maefmn d trduldtfslnsnidsfnkdmns ak astd ma`fidmd znkd.
Iudkmn `ds `asfnkas snk tntd`as, `ns
laksdjas kn puamak sar trdkslftfmnspnr a` iaraern y ``acdr d su mastfkn(n vfiavarsd), lfaktrds qua ak `ds`asfnkas pdrifd`as, d`cukns ma `nsflpu`sns karvfnsns puamak d`idkzdrd `ds mfbaraktas pdrtas ma` iuarpn.Axfstak dmaläs, `ns mascdrrns pdr-ifd`as n inlp`atns ma `d læmu`d
(trdksaiifnkas), qua sacúk a` crdmnma trduldtfsln, puamak nidsfnkdrmasma mfsidpdifmdmas parldkaktashdstd `d luarta.
Yù`n ns karvfns uefidmns pnr maedjnma `d `asfùk rasu`tdk dbaitdmns7 pnr
`n tdktn, uk trduldtfsln idusdräldynr pærmfmd ma bukifnkas, iudktnläs iarid ma d ideazd sa d`nja. _nrajalp`n: d pdrdp`ajfd as nidsfnkdmdpnr ukd `asfùk ak a` ärad `uledr nsdird (aspd`md edjd)7 `d parsnkd inkastd fkidpdifmdm pfarma `d saksfef`f-mdm y pnr inksfcufakta, d lnvf`fmdmak `d pdrta fkbarfnr ma su iuarpn. @dtatrdp`ajfd (dktas ``dldmd iudmrfp`a-
jfd), as uk tfpn ma asfùk luihn läscrdva, qua rasu`td ma ukd inktusfùk
ak a` ärad iarvfid` (iua``n), y inl-prnlata `d lnvf`fmdm ma `ds iudtrnaxtralfmdmas a fki`usn, tdlefæksua`a dbaitdrsa d bukifùk raspfrdtnrfd,pnr n iud` as kaiasdrfn a` usn ma ukraspfrdmnr drtfbfifd`.
Fldcak tnldmd ma Akifi`npamfd Læmfid D.M.D.L
@asfnkas ma `d læmu`d aspfkd`
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Bukifnkdlfaktn ma` sfstald akmnirfkn
D mfbarakifd ma` sfstald karvfnsn qua edsd su bukifnkdlfaktn ak `d trdkslfsfùk m
flpu`sns karvfnsns (saôd`as a`æitrfids), d trdvæs ma kaurnkds, a` sfstald akmnirfk`feard masma ds c`äkmu`ds, sustdkifds `dldmds hnrlnkds qua ditúdk snera iæ`u`aspaiìbfids ``dldmds iæ`u`ds e`dkin, pdrd cakardr uk abaitn snera a``ds.
Ntrd mfbarakifd aktra ns mns sfstalds, as d rdpfmaz ink d iud` trdkslftak sus laksdjas7 `d kdturd`azd a`æitrfid ma `ns flpu`sns qua cakard a` sfstald karvfnsn, supaak crdk lamfmd `d va`nifmdm ma `ds hnrlnkds qua vfdjdk masma `ds c`äkmu`ds hdst`ds iæ`u`ds e`dkin7 sfk aledrcn, `ds hnrlnkds puamak ditudr ak tnmn a` iuarpn d
Dmaläs ma hdear ma-sdrrn``dmn a` sfstaldkarvfnsn, idpdz maparifefr y prniasdr `dfkbnrldifùk fktarkd y
axtarkd, crdifds d `davn`uifùk, `ns dkfld`as hdk dmquf-rfmn astruiturds fktarra`difnkdmdspdrd ldktakar `ds bukifnkas vftd`as.]d` as a` idsn ma` sfstald akmnirfkn
qua pnmrìd ``dlärsa`a ink justd rdzùk«a` cudrmfäk ma kuastrn iuarpn· (duk-qua kn as axi`usfvn ma `ns huldkns),
maefmn praifsdlakta d `d parldkaktaravfsfùk y racu`difùk ma ds ditfvfmdmasbfsfn`ùcfids.
A sfstald akmnirfkn
Qkfmdm 5. @ns nrcdkfslns y su raspuastd dkta `nsastìlu`ns ma` lamfn
Yasfùk
6
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]fpns ma c`äkmu`d ma` sfstald akmnirfkn
C`äkmu`ds axnirfkds
@feardk sus sairaifnkas pnrlamfn ma uk inkmuitn d nstajfmns qua inlukfidk inka` axtarfnr (tajfmns iutäkans,y d`cukns tajfmns ma` sfstald
mfcastfvn). Ajalp`n: ds c`äk-mu`ds sumnrìpdrds ma `d pfa`huldkd.
C`äkmu`ds akmnirfkds
Idraiak ma inkmuitn y `fea-rdk sus sairaifnkas mfraitd-lakta d` tnrrakta sdkcuìkan,mnkma snk trdkspnrtdmds hds-td ns tajfmns y iæ`u`ds e`dkin.
Ajalp`n: `d tfrnfmas sairatdukd hnrlnkd inknifmd inlntfrnxfkd, qua sa akidrcd maastflu`dr a` latden`fsln.
C`äkmu`d sumnrìpdrd C`äkmu`d tfrnfmas
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_rfkifpd`as c`äkmu`ds akmnirfkds
Fkiralaktdk `d braiuak-ifd ma `ns `dtfmns ma`
inrdzùk, dulaktdk `dtaksfùk drtarfd`, inktrdakn mf`dtdk ns vdsns sdkcuì-kans y a`avdk ns kfva`asma dzúidr ak `d sdkcra._nr `n cakard`, asta ink-
juktn ma radiifnkas niu-rra iudkmn hdy raspuastdfklamfdtd. Ajalp`n: ukdsftudifùk ma pa`fcrn
C`äkmu`d(s) Idrditarìstfids Hnrlnkd/bukifùk prfkifpd`
Ya `nid`fzd ak a` hfpn-tä`dln. Dukqua pa-quaôd, astd c`äkmu`d
ink bnrld y tdldôn mabrìjn`, inktrn`d `ds buk-ifnkas ma luihds ntrdsc`äkmu`ds akmnirfkdsma` iuarpn. Ya mfvfmaak dmaknhfpùbfsfs n `ù-eu`n dktarfnr, kaurnhf-pùbfsfs n ùeu`n pnstarfnry `ùeu`n fktarlamfn.
@ds c`äkmu`ds suprd-rrakd`as sa sftúdk ak `dpdrta suparfnr ma `nsrfônkas. Idmd ukd astäbnrldmd pnr ukd znkdfktarkd ``dldmd læmu`dy ukd idpd axtarkd ``d-ldmd inrtazd.
Hfpùbfsfs
n pftuftdrfd
Yuprdrra-
kd`as
(læmu`d)
Astflu`d `d c`äkmu`d tf-rnfmas
Astflu`d `d prnmuiifùkma `aiha
Hnrlnkd ma` iraif-lfaktn
_rnmuia `ds inktrdiifn-kas ma` útarn y astflu`d`d sairaifùk ma `aiha dtrdvæs ma `ds ldlds.
Astflu`d `d radesnrifùkma dcud ma `ns rfônkas.
Astflu`d `d inrtazd su-prdrrakd`.
Astflu`dk `ds c`äkmu`dssaxud`as.
]YH4
_rn`ditfkd
Ynldtn-trnbfkd
Nxftnifkd
DMH
DI]H
BYH y @H
Dmrakd`fkdy knrdmra-kd`fkd
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C`äkmu`d(s) Idrditarìstfids Hnrlnkd/bukifùk prfkifpd`
Astä sftudmd juktn d`fktastfkn ma`cdmn. @f-eard akzflds (bukifùkaxnirfkd), d` fktastfknpdrd inktrfeufr ink `dmfcastfùk.
]dlefæk pnsaa iæ`u`dsaspaifd`fzdmds maktrnma `ns fs`ntas ma @dk-carhdks ma` päkirads,
qua prnmuiak fksu`f-kd y c`uidcùk (bukifùkakmnirfkd), hnrlnkdsakidrcdmds ma racu`dra` latden`fsln ma `dc`uinsd.
_dr ma ùrcdkns raprn-muitfvns balakfkns `n-id`fzdmns d idmd dmn ma`útarn.
_dr ma ùrcdkns ldsiu-`fkns qua sa akiuak-trdk `nid`fzdmns ak a`asirntn.
_äkirads
Nvdrfns
]astìiu`ns
_rnluava `d desnrifùk
ma c`uinsd pnr pdrta ma`ds iæ`u`ds, pdrd mfslf-kufr su inkiaktrdifùk ak`d sdkcra.
Astflu`d `d `feardifùk ma`d c`uinsd (d`ldiakdmdak a` hìcdmn ak bnrld mac`uiùcakn), d `d sdkcra.
Masdrrn``dk `ns ùrcdknsraprnmuitnras balakfkns
y prnluavak `d dpdrf-ifùk ma va``n púefin ydxf`dr, iraiflfaktn ma `dsldlds y dlp`ftum ma dsidmards.
_rnluava a` iraiflfaktnma` tdpfz ma` útarn pdrdraifefr a` ùvu`n.
Astflu`d d bnrldifùk maasparldtnznfmas y prn-luava `d dpdrfifùk ma`ds idrditarìstfids lds-iu`fkds: masdrrn``n ma`paka, iraiflfaktn mava``n púefin y bdifd`, ytnkn ma vnz läs crdva
Fksu`fkd
C`uidcùk
Astrùcakns
_rncastarnkd
]astnstarnkd
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6
D`cukds c`äkmu`ds ma` iuarpn
Fläcakas tnldmds ma Akifi`npamfd Læmfid D.M.D.L
• Dukqua ak `d sasfùk dktarfnr inlakzdlns ink a` tald ma `ds c`äkmu`ds,partfkakta rapdsdr uk pnin snera su uefidifùk. _drd a``n maealns inksacuk fldcak ma` iuarpn huldkn mnkma pnmdlns uefidr idmd ukd ma `ds c`ämu`ds qua lakifnkdlns ak i`dsa, pdrd a``n puama id`idr, mfeujdr, rainrtdpacdr7 `n flpnrtdkta as qua uefqua ak uk iuarpn huldkn `d ldynr idktfmma c`äkmu`ds qua puamd.
• Fkvastfcua quæ ntrns ùrcdkns ma` iuarpn huldkn prnmuiak hnrlnkds. Axp`fq
Nvdrfn
knrld`
Nvdrfn
pn`fquìstfin
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=
Ak d sfcufakta päcfkd wae, sa puama hd``dr fkbnrldifùk ra`difn-kdmd ink ds akbarlamdmas ma` sfstald akmnirfkn: http://www.k`l.kfh.cnv/lam`fkap`us/spdkfsh/akmnirfkamfsadsas.htl`
]rdedjn ak suecrupns.
Idmd suecrupn maea asincar uk trdstnrkn ma` sfstald akmnirfkn, rain`aitdr ldynr idktfmdm ma fkbnrldifùk ra`difnkdmd ink a` tald, y axpnkar`d dkta prnbasnr y inlpdôarns ma i`dsa.
@d mfdeatas, ukd akbarlamdm ma` sfstald akmnirfkn
_drd inkniar lajnr `ds idrditarìstfids ma asta trdstnrkn ma` sfstald ak-mnirfkn, prflarn inknzidlns iùln a` nrcdkfsln inksfcua ldktakarastde`as `ns kfva`as ma c`uinsd ak `d sdkcra.
@ds iæ`u`ds eatd ma ns fs`ntas ma @dkcarhdks ak a` päkirads, snk ds akidr-cdmds ma sacracdr `d hnrlnkd ``dldmd fksu`fkd. Astd sustdkifd as `feardmdiudkmn `d inkiaktrdifùk ma dzúidr as d`td ak a` tnrrakta sdkcuìkan, ma
KDRACQALNY AK FK]AUKA]
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bnrld qua prnluava `d desnrifùk ma `d c`uinsd pnr pdrta ma `ds iæ`u`dspdrd qua su kfva` sa astdef`fia. @d hnrlnkd c`uidcùk rad`fzd tnmn `n ink-trdrfn, pnrqua prnluava `d macrdmdifùk ma c`uiùcakn (c`uinsd d`ldia-kdmd ak a` hìcdmn), d c`uinsd pdrd `feardr`d d `d sdkcra y dsì, dulaktdr a`kfva` ma dzúidr.
Ak nidsfnkas, `d prnmuiifùk ma fksu`fkd pnr pdrta ma` päkirads puamamfslfkufr (mfdeatas tfpn 4), `n iud` dbaitd `d desnrifùk ma c`uinsd pnrpdrta ma `ds iæ`u`ds y quamd crdk pdrta ma su inktakfmn ak `d sdkcra. @drasfstakifd ma ds iæ`u`ds d` abaitn ma d fksu`fkd, tdlefæk sua`a cakardr a`lfsln abaitn (mfdeatas tfpn 5). Ak dlens idsns, su inksaiuakifd as ukfkiralaktn ak d inkiaktrdifùk ma c`uinsd ak d sdkcra, trdstnrkn qua sainknia inln mfdeatas la``ftus.
Aspaifd`lakta ak `ds parsnkds dbaitdmds ink `d mfdeatas tfpn 4, sua`akprasaktdrsa sìktnlds inln pærmfmd ma pasn, käusads, vùlftn, bdtfcdlusiu`dr, sam y hdlera inkstdktas. _nr `n cakard`, `ns pdifaktas inkastd akbarlamdm snk mfdcknstfidmns d talprdkd amdm (kfôaz), y maeakinktrdrrastdr `d sfktnldtn`ncìd, fkyaitäkmnsa fksu`fkd mfdrfdlakta pnr a`
rastn ma su vfmd. @ns sìktnlds ma `d mfdeatas tfpn 5, snk sflf`dras d `ns ma`d mfdeatas tfpn 4, dukqua luihds vaias, kn prasaktd sfckns avfmaktaspdrd qufak d pdmaia7 dsì qua crdk idktfmdm ma parsnkds kf sfqufard sdeakqua `d tfakak. @d dpdrfifùk y `d avn`uifùk ma asta trdstnrkn astäk luydsnifdmds d `d neasfmdm y d `d bd`td ma ajarififn. @d fksu`fkd n sustdkifdsdkä`ncds d `d lfsld, dsì inln dktfmfdeætfins nrd`as, snk `d lajnr bnrldma inktrn`dr `d mfdeatas ma asta tfpn.
@d lamfifùk ma `ds inkiaktrdifnkas ma c`uinsd ak sdkcra y nrfkd, snk`d lajnr bnrld ma mataitdr `d akbarlamdm. Maspuæs ma mfdcknstfidrsa`d mfdeatas, a` nejatfvn prfkifpd` ma` trdtdlfaktn as rastde`aiar a` kfva`knrld` ma d c`uinsd ak d sdkcra, pdrd avftdr inlp`fidifnkas pnstarfnrasinln fksubfifakifd rakd`, pærmfmd ma d vfsfùk maefmn d mdôns ak d ratfkd,d`tardifnkas ifriu`dtnrfds ak erdzns y pfarkds (qua puama ``avdr d `d dl-putdifùk ma `ns lfalerns), akbarlamdmas idrmìdids, prne`alds iaraernvdsiu`dras y inld mfdeætfin.
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_drtas ma `d kaurnkd
4. ¾Tuæ as ukd kaurnkd> ¾Iuä`as snk sus bukifnkasprfkifpd`as>
5. Ak `d sfcufakta fldcak, fmaktfbfqua `ds prfkifpd`aspdrtas ma `d kaurnkd.
9. Maedjn ma idmd kaurnkd, asirfed su inrraspnkmfakta i`dsfbfidifùk pn`dr(ukfpn`dr, efpn`dr, lu`tfpn`dr).
Ldkns d d nerd
Qkfmdm 5. @ns nrcdkfslns y su raspuastd dkta `nsastìlu`ns ma` lamfn
Yasfùk
4?
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4?
Fkvastfcua:
• ¾Tuæ iufmdmns maea takar ukd parsnkd qua subra ma mfdeatas>• ¾Tuæ ntrds akbarlamdmas hd asiuihdmn qua sa maedk d` ld` bukifnkdlfa
ma ukd c`äkmu`d>• ¾Iùln sa puama mataitdr qua hdy uk ld` bukifnkdlfaktn ma `ds c`äkmu`ds
a` iuarpn>
1. A`denra uk iudmrn inlpdrdtfvn aktra a` sfstald karvfnsn iaktrd` y a`sfstald karvfnsn parfbærfin.
2. ¾Iuä` as `d prfkifpd` mfbarakifd aktra `d prnpdcdifùk ma uk flpu`snkarvfnsn inlúk y uk rab`ajn>
3. Inlp`ata `ns aspdifns ak e`dkin ink `ns tærlfkns inrraspnkmfaktas:
d. A` sar huldkn pnsaa ^^^^^^^^ pdras ma karvfns irdkad`as.
e. A` hnlera tfaka ^^^^^^^^^^^ pdras ma karvfns aspfkd`as.
i. Aktra sus lú`tfp`as bukifnkas, a` sfstald karvfnsn dutùkn-
ln pdrdsflpätfin sa akidrcd ma ^^^^^^^^^^^ `d pupf`d,
^^^^^^^^^^^^^ `d sd`fvdifùk, ^^^^^^^^^^^^^ `d vajfcd7
lfaktrds qua a` sfstald sflpätfin ^^^^^^^^^^ `ns ernkqufns,
^^^^^^^^^^^^ d pupf`d, ^^^^^^^^^^^^^^ d ditfvfmdm mfcas-tfvd y ^^^^^^^ ^^^^^^^ a` flpu`sn idrmìdin.
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8. Astde`azid `ds prfkifpd`as mfbarakifds aktra a` sfstald karvfnsn y a`sfstald akmnirfkn:
6. Uasua`vd a` iruifcrdld ma `d päcfkd sfcufakta ink `ds i`dvas qua saprasaktdk d inktfkudifùk:
4. Cakard ak a` nrcdkfsln, uk inkjuktn ma radiifnkas qua niurrakiudkmn sa kaiasftd ukd raspuastd fklamfdtd.
5. Astflu`d `d radesnrifùk ma dcud ma `ns rfônkas.
9. Astflu`d `d prnmuiifùk ma `aiha.=. Fkiralaktd a` kfva` ma id`ifn ak `d sdkcra.
1. Mfslfkuya `d inkiaktrdifùk ma dzúidr ak `d sdkcra.
2. Inktrn`d a` latden`fsln ma crdsds y idrenhfmrdtns. _rnluava dmacrdmdifùk y sìktasfs ma `ds prntaìkds.
3. Mfslfkuya `d inkiaktrdifùk ma id`ifn ak `d sdkcra.
8. Astflu`d `d `feardifùk ma c`uinsd ak `d sdkcra.
6. Uacu`d ds bukifnkas ra`difnkdmds ink ns parìnmns mfurkn y kni-turkn.
4?. Masdrrn``dk `ns ùrcdkns raprnmuitnras balakfkns.
44. _rnluava `d dpdrfifùk ma `ds idrditarìstfids ldsiu`fkds.
45. _rnluava a` iraiflfaktn ma` tdpfz ma` útarn.
49. Astflu`d a` iraiflfaktn inrpnrd`.
4=. Astflu`d `d sairaifùk ma `aiha d trdvæs ma `ds ldlds.
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Hnrlnkds ma` iuarpn huldkn
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Efe`fncrdbìd
• SF@YNK, 4666 AK _UFLDIG, U. 5??4. Bukmdlaktns mainksarvdifùk efn`ùcfid: parspaitfvds dtfkndlarfidkds. Bnkmnma Iu`turd Ainkùlfid. Læxfin M.B.
• IQU]FY, H. EDUKAY, K. 5???. Efn`ncìd. Amftnrfd` _dkd-larfidkd. Euakns Dfras.
• _AUAZ, A. 4612. _`dktds útf`as ma In`nlefd. @ferarfdIn`nlefdkd - Idldihn Un`mdk (Iìd. @tmd.). Encntä.
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Lùmu`n fktacrdmn pdrd ifi`n 1]rdksbnrlalns Amuidkmn
Ärad Tuìlfid 4?
Inlukfmdm inrracflfaktn _uartn In`nlefd
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A s t ä k m d r a s e ä s f i n s
m a i n l p a t a k i f d s a k
T u ì l f i d
I n l p a t a k i f d s
B d i t n r a s m a n r c d k f z d i f ù k
¾ D q u æ
q u a r a l n s
` ` a c d r >
U a ` d i f n k n ` d a s t r u i t u r d m a
` d s l n ` æ i u ` d s f k n r c ä k f i d s
i n k s u s p r n p f a m d m a s b ì s f i d s
y q u ì l f i d s y s u i d p d i f m d m
m a i d l e f n q u ì l f i n .
¾ I ù l n m a l u a s t r n ` n d p r a k m f m n >
A k t n r k n b ì s f i n
I f a k i
f d ,
t a i k n ` n c ì d
y
s n i f a m d m
_ r n i a s n s q u ì l f i n s
•
F m a k t f b f i n i d l e f n s q u ì l f i n s a k ` d
v f m d i n t f m f d k d y a k a ` d l e f a k
t a .
•
A x p ` f i n ` n s i d l e f n s q u ì l f i n s
m a s m a
m f b a r a k t a s l n m a ` n s .
•
R a r f b f i n a ` a b a i t n m a p r a s f ù k
y t a l -
p a r d t u r d a k ` n s i d l e f n s q u ì l
f i n s .
•
Q s n ` d t d e ` d p a r f ù m f i d p d r d m a t a r l f -
k d r p r n p f a m d m a s b ì s f i d s y q u ì l
f i d s m a
` n s a ` a l a k t n s .
•
U a d ` f z n i ä ` i u ` n s i u d k t f t d t f v n s a k
i d l e f n s q u ì l f i n s .
•
F m a k t f b f i n i n k m f i f n k a s p d r d i n
k t r n ` d r
` d v a ` n i f m d m m a i d l e f n s q u ì l
f i n s .
•
I d r d i t a r f z n i d l e f n s q u ì l f i n s a k
i n k m f i f n k a s m a a q u f ` f e r f n .
•
A x p ` f i n ` d a s t r u i t u r d m a ` n s ä t n l n s d
p d r t f r m a m f b a r a k t a s t a n r ì d s .
•
A x p ` f i n ` d r a ` d i f ù k a k t r a ` d a s t r u i t u r d
m a ` n s ä t n l n s y ` n s a k ` d i a s q u a r a d -
` f z d .
•
U a ` d i f n k n ` d a s t r u i t u r d m a ` i d r e n k n
i n k ` d b n r l d i f ù k m a l n ` æ i u ` d
s n r c ä -
k f i d s .
•
U a ` d i f n k n c r u p n s b u k i f n k d ` a s
i n k ` d s
p r n p f a m d m a s b ì s f i d s y q u ì l f i d s m a ` d s
s u s t d k i f d s .
A j a s t a l ä t f i n s
A x p ` f i n ` d s b u a r z d s a k t r a
n e j a t n s i n l n f k t a r d i i f n k a s
m a e f m d s d ` d i d r c d a ` æ i t r f -
i d y d ` d k d t u r d ` a z d m a ` d
l d t a r f d .
•
I d l e f n s b ì s f i n s y q u ì l
f i n s ( u k f m d m 4 ,
Y a s f ù k
4 )
•
] d e ` d p a r f ù m f i d ( Q k f m
d m = ,
Y a s f ù k = )
•
U a d i i f n k a s q u ì l f i d s
( Q k f m d m 2 ,
Y a s f ù k 3 )
•
A s t a q u f n l a t r ì d ( Q k f m
d m 2 ,
Y a s f ù k 3 )
•
I f k æ t f i d q u ì l f i d ( Q k f m d m 2 ,
Y a s f ù k 3 )
•
A q u f ` f e r f n q u ì l f i n ( Q
k f m d m 8 ,
Y a s f ù k 4 ? )
•
@ a y a s m a ` n s c d s a s ( Q k f m d m 3 ,
Y a s f ù k 8 )
•
Ä t n l n ( Q k f m d m 9 , s a s f ù k 9 )
•
A k ` d i a q u ì l f i n ( Q k f m
d m 1 ,
Y a s f ù k 1 )
•
B u k i f n k a s y k n l a k i ` d t u r d f k n r c ä k f i d ( Q k f -
m d m 1 ,
Y a s f ù k 2 )
•
Y n ` u i f n k a s ( Q k f m d m 8
, Y a s f ù k 6 )
•
A x p ` f i
n i d l e f n s q u ì l f -
i n s a k
` d i n i f k d ,
` d f k m u s -
t r f d y a
` d l e f a k t a .
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Qkfmdm 4. Flpnrtdkifd ma `d quìlfid 596
Yasfùk 4. Ldtarfd, quìlfid y aktnrkn 596
Qkfmdm 5. A` pdtfn: kuastrn `denrdtnrfn 514
Yasfùk 5. @denrdtnrfn ma quìlfid 514 Qkfmdm 9. Inkstftuifùk ma `d ldtarfd 525
Yasfùk 9. Ätnln 525
Qkfmdm =. @d tde`d parfùmfid 535
Yasfùk =. ]de`d parfùmfid y parfnmfifmdm 535
Qkfmdm 1. @ns inlpuastns 585
Yasfùk 1. Ak`dia quìlfin 585
Yasfùk 2. Inlpuastns y knlaki`dturd fknrcäkfid 569
Qkfmdm 2. Uadiifnkas quìlfids 94?
Yasfùk 3. Astaqufnlatrìd 94?
Qkfmdm 3. Cdsas 99=
Yasfùk 8. Cdsas 99=
Qkfmdm 8. Yn`uifnkas 914
Yasfùk 6. Yn`uifnkas 914
Ì km f i a
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]ùlasa ukns lfkutns pdrd paksdr ma bnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:
Ya hd pracuktdmn d`cukd vaz:
¾_nr quæ a` inktakfmn ma` huavn pdsd ma sar `ìqufmn d sù`fmn yidlefd ma sdenr iudkmn sa inifkd>
¾_nr quæ `d pu`pd ma `d ldkzdkd sa nsiuraia iudkmn quamd ax-puastd d` dfra>
¾_nr quæ sa prnmuia d`inhn` iudkmn sa lazi`d dzúidr ink dcud ysa majd pnr vdrfns mìds>
¾_nr quæ a` `flùk as äifmn y `d kdrdkjd as mu`ia>
¾_nr quæ ak uk mìd ma id`nr a` hfa`n sa marrfta, parn a` dcud, ns jucns, `d cdsansd n `d iarvazd kn sa avdpnrdk>
Ldtarfd, quìlfid y aktnrknQkfmdm 4. Flpnrtdkifd ma `d quìlfid Yasfùk
4
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@d quìlfid as `d ifakifd qua sa akidrcd ma` astumfn ma `ns bakùlakns ma `d kdturd`azd, ra`difnkdmns ink `d inlpnsfifùk, fktardiifùk, trdksbnrldifnkas y prnpfamdmas ma `d ldtarfd, td` inlsa dpraifd ak a` ldpd inkiaptud`.
Dsì, d quìlfid kn as sn`dlakta d`cn qua sa hdia ak a` denrdtnrfsfkn qua `d akinktrdlns d kuastrn d`ramamnr tnmn a` tfalpn
iudkmn raspfrdlns, iudkmn inlalns, ak `d rnpd qua usdlns, ak `ns prnmuitns mdsan qua alp`adlns, ak a` ldtarfd` ma `ds harrdlfaktds y utaksf`fns qua usdlnak kuastrn trdedjn y ak a` hncdr, ak `ns lamfidlaktns qua inksulflns, ak `d lkard inln inifkdlns kuastrns d`flaktns, ak `ns idlefns ma in`nr, n`nr y sdenr m`ds brutds, a` quasn, `d `aiha y `ds varmurds, ak a` bukifnkdlfaktn ma `ns idrrns, `dlntns, `ns dvfnkas, y uk sfkbìk läs ma avaktns.
D kfva` kutrfifnkd` d quìlfid as vftd`, yd qua ns kutrfaktas, inln ns c`úifmns, ìpfm(crdsds y diaftas), prntaìkds, lfkard`as y vftdlfkds sa akiuaktrdk ak `ns d`flaktnqua inksulflns d mfdrfn y sa hdk bnrldmn d` fktarfnr ma `ns lfslns, crdifds d uksarfa ma prniasns quìlfins qua sa ``avdk d iden maktrn ma `ds iæ`u`ds y ak `n läprnbukmn ma `d tfarrd, as maifr, ak a` ldcld vn`iäkfin.
LD]AUFD
Astdmns ma dcracd
Ya i`dsffflidksacúk
Yu astruiturdinkstftufmd pnr ätnlns
Inkstftuìmns pnra`aitrnkas, kautrnkas,
prntnkas, qudrgs, lunkas,`aptnkas, barlfnkas y läs
pdrtìiu`ds suedtùlfids
_uama sar fnkas sf pfarma ncdkd a`aitrnkas7 n fsùtnpns sf
vdrìdk `d idktfmdm ma kautrnkasak a` kúi`an
Bnrldk nsA`alaktns
@d ukfùk ma vdrfns a`alaktnsmfbaraktas md nrìcak d `ns
INL_QAY]NY
@d ukfmdm läs paquaôd sainknia inln LN@ÆIQ@D y
puama astdr bnrldmd pnr mns nläs ätnlns fcud`as n mfbaraktas
Lazi`ds
Hnlncækads
Qkd sn`d bdsa, kn samfstfkcuak inlpn-
kaktas
Ya sapdrdk pnrmastf`difùk,
irnldtncrdbìd,sue`fldifùk yirfstd`fzdifùk
Ya sapdrdk pnrldckatfzdifùk,maidktdifùk n
ffl`trdifùk
Rdrfds bdsas nesarvde`as
Hatarncækads Cds
@ìqufmn
Yù`fmn
InEn
Y
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_drd pnmar masdrrn``dr sus ditfvfmdmas mfdrfds, tnmns ns saras vfvns kaiasftdk akarcÆstd as netakfmd lamfdkta `d fkcastfùk ma ifartds sustdkifds quìlfids qua prnvkak ma `ns d`flaktns y qua sa maknlfkdk kutrfaktas. D` aktrdr ak a` nrcdkfsln, kutrfaktas snk dsflf`dmns, y ma `ns d`flaktns y qua sa maknlfkdk kutrfaktas. @kutrfaktas d` aktrdr ak a` nrcdkfsln sa dsflf`dk y pdrta ma a``ns sa d`ldiakd hds
LD]AUFD
Yù`fmns @ìqufmns n cdsas
Rn`úlak
l@, il9, @
Ldsd _asn
Kawtnk (K)lc, c, `e, Gc
_nsaa
Idlefns
Bìsfins Tuìlfins
]rdksbnrldifùk msustdkifds ak ntrds,
UADIIFNKAY TQÌ
Idlefn ak d dpdrfakifdbìsfid ma ds sustdkifds, parn
kn ak su inlpnsfifùk
Qkfmdmas ma lamfmd
_rnpfamdmas
Bìsfids
N`nr, in`nr, sdenr, maksfmdm,puktn ma busfùk y aeu``fifùk
Fkstdldef`fmdm, nxfmdifùk Mapakmak ma d idktfmdmma ldtarfd
Kn mapakmak ma d idktfmdmma sustdkifd
Tuìlfids Axtaksfvds Fktaksfvds
D_@FIDIFNKAY TQÌLFIDYIN]FMFDKDY
Tuìlfid ma `ns d`flaktns
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Dmaläs, ns saras vfvns kaiasftdk inkstrufr y rapdrdr tajfmns pdrd pnmar masdrrn``drsa y iraiar.
@ns ldtarfd`as kaiasdrfns pdrd iulp`fr ink astd
bukifnkas tdlefæk snk prnpnrifnkdmns pnr `nd`flaktns.
@ns kutrfaktas qua prnpnrifnkdk `ns d`flaktns qua snk fkmfspaksde`as pdrd inksarvdr d vfmd sn`ns idrenhfmrdtns, `ns ìpfmns, y prntaìkds, qua sn`ns raspnksde`as ma` dpnrta ma tnmd `d akarc
qua kaiasftdlns d mfdrfn, pdrd a` masdrrn``n ma tnmds kuastrds bukifnkas v
td`as. ]dlefæk astäk `ds vftdlfkds y lfkard`as `ns iud`as, sf efak kn tfakak kfkcukfkifmakifd ak a` dpnrta id`ùrfin, snk fkmfspaksde`as pdrd qua ds radiifnkas quìlfiinrpnrd`as sa ``avak d iden.
D `ns idrenhfmrdtns n c`úifmns `ns akinktrdlns ak `ds brutds, vacatd`as, crdkns, iarad`as y `aiha ak bnrld ma dzúidras, d`lfmnkas y hdrfkds, y ak `ds idrkas, ak ukln`æiu`d inknifmd inln c`uiùcakn. Ynk flpnrtdktas, yd qua a``ns inkstftuyak 1?% ma `d mfatd mfdrfd, dpnrtdkmn `d lftdm ma `d akarcìd qua kaiasftdlns mìd d mì
pdrd a` masdrrn``n ma kuastrds ditfvfmdmas vftd`as y intfmfdkds.
@ns ìpfmns snk ds lfslds crdsds, diaftas y in`astarn` y, d` fcud` qua `ns c`úifmns, snma nrfcak vacatd` n dkfld`. Ynk alp`admns inln ldtarfd` ma rasarvd akarcætfiinrpnrd`, inln inkstftuyaktas ma `ds lalerdkds ia`u`dras y inktrn`dmnras ma talpardturd inrpnrd`. _drtfifpdk ak `d sìktasfs ma hnrlnkds, inln `d prncastarnky `d tastnstarnkd y snk raspnksde`as ak d`cukns idsns ma `ns in`nras ma d`cukns dlaktns, inln `d zdkdhnrfd, rfid ak idrntaknfmas, qua snk uk tfpn ma `ìpfmns qudyumdk ak `ns huldkns d prntacar `d pfa` inktrd `d rdmfdifùk u`trdvfn`atd (pnr a`snk usdmns ak d bderfidifùk ma e`nquadmnras sn`dras) y ak d sìktasfs ma ratfkn`, quas `d lfsld Rftdlfkd D, qua iufmd `d sd`um ma `ns njns.
@ds prntaìkds sa utf`fzdk ak `d sìktasfs ma tajfmns inln `ns lúsiu`ns, `d sdkcra, idea``n, `ds uôds y `d pfa`.
@d vdrfamdm ma sdenras, in`nras,
n`nras y kutrfaktas ak `ns
d`flaktns as a` rasu`tdmn ma
prniasns quìlfins
pdrtfiu`dras.
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@d prnmuiifùk ma dktfefùtfins, vdiukds sfktætfids
y bärldins hd lajnrdmn kuastrd sd`um.
@d quìlfid y `d sd`um
Ditud`lakta snk fkinktde`as `ns prniasns quì -lfins qua sa ``avdk d iden pdrd trdksbnrldrsustdkifds ma nrfcak dkfld`, vacatd` n sfktætfin,pdrd trdksbnrldr`ds ak ldtarfd prflds, pdrd a`d-enrdr nejatns ma usn intfmfdkn, mrncds y drtìiu`nsfkmustrfd`as.
Lamfdkta prniasns quìlfins
sa netfakak parbulas.
@n dktarfnr sa hd `ncrdmn crdifds d` inkniflfaktn
ma d quìlfid, parlftfakmn dsì a` dvdkia ma d tai-kn`ncìd y `ds ifakifds, cakardkmn kuavns idlpnsma astumfn ak efnquìlfid, lamfifkd, efntaikn`n-cìd, fkcakfarìd cakætfid, efn`ncìd ln`aiu`dr, inl-eustfe`as, ati., inlprakmfakmn dsì d flpnrtdkifdma `d quìlfid ak kuastrd prnpfd axfstakifd.
@d ifakifd hd masaktrdôdmn a`
harlnsn lfstarfn ma` DMK.
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Luihds ma ds mrncds qua sa inksulak inln trdtdlfaktns læmfins snk prnmuifmpnr prniamflfaktns quìlfins (dktfefùtfins, dkbatdlfkds, dktffkb`dldtnrfns, ati.). netakifùk ma vdiukds sfktætfids y `d prnmuiifùk ma dktfiuarpns lnkni`nkd`as hdlajnrdmn `d fklukfmdm pne`difnkd`. @d quìlfid dsnifdmd d ntrds ifakifds inln efn`ncìd y `d fkcakfarìd cakætfid hd lajnrdmn kntde`alakta `d sd`um ma `ns pnemnras ma `d ]farrd.
@d prnmuiifùk ma masfkbaitdktas d kfva`læmfin y `d utf`fzdifùk ma sustdkifds marfvd-mds ma` i`nrn, snmd iäustfid, dlnkfdin, ati., h dsfmn útf`as ak d a`flfkdifùk ma vfrus, editarfds,hnkcns y prntnzndrfns, inktrdprnmuiaktas
pdrd `d sd`um ma `ds p`dktds, `ns dkfld`as y a`hnlera.
_arn d quìlfid kn sù`n sa usd pdrd d a`denrd-ifùk ma lamfidlaktns y masfkbaitdktas, sfknqua dmaläs dyumd d axp`fidr y inlprak-mar a` pnrquæ ma luihds akbarlamdmas,`n qua d su vaz hdia pnsfe`a `d fkvastfcdifùk
ak a` tarrakn ma `d quìlfid bdrldiæutfid y a` surcflfaktn ma kuavns trdtdlfaktlæmfins trdmfifnkd`as n d`tarkdtfvns.
@d quìlfid prnmuia dktfefùtfin
d crdk asid`d.
Fkcakfarìd cakætfid: iæ`u`ds huldkds ak
`ds iud`as d`cukds prntaìkds sa busfnkdk in
prntaìkds varmas b`unrasiaktas pdrd parl
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Inleustfùk: as uk prniasn ak a` iud` d ldtarfd
sa nxfmd, ak prasakifd ma` nxìcakn u ntrn dcaktanxfmdkta buarta, `feardkmn crdkmas idktfmdmasma akarcìd, qua sa ldkfbfastd ak bnrld ma id-`nr n buacn. _drd qua astn sa mæ, sa raqufara `dprasakifd ma uk dcakta inleurakta, qua saakidrcd ma nxfmdr d` inleustfe`a (pnr ajalp`na` nxìcakn). Qk ajalp`n ma inleustfùk sa mdd` akiakmar ukd astubd n iudkmn sa prakma a`
lntnr ma uk idrrn, qua ak mfihns idsns sa mdpnr d nxfmdifùk ma` cds kdturd` y ma d cdsn`fkd.
Lazi`ds abarvasiaktas: as uk bakùlakn ak a`qua ukd sustdkifd cdsansd asidpd ma uk ìqufmny sa md pnr mns rdznkas: pnr fksn`uef`fmdm ma`cds, inln ak a` idsn ma `ds cdsansds, n inlnprnmuitn ma radiifnkas quìlfids, inln a`
D`gd-Ya`tzar ak dcud.Barlaktdifùk: as uk prniasn quìlfin prnpfnma `d ldtarfd nrcäkfid, ak `d iud` æstd sa nxfmdak prasakifd ma lfirnnrcdkfslns, inln `d`avdmurd, mdkmn nrfcak d inlpuastns inln a`d`inhn`, sf a` prniasn sa ldktfaka d`ajdmn ma`dfra, n vfkdcra sf sa majd axpuastn d` lamfn dl-efakta. _nr a``n, a` vfkn sa dvfkdcrd y a` quasn y
`d `aiha sa vua`vak rdkifns.Masinlpnsfifùk ma d inlfmd: as `d radiifùkma editarfds y lfirnnrcdkfslns, qua ditúdkinln macrdmdmnras (inksulfmnras) ma `ds sus-tdkifds quìlfids qua inlpnkak `ns d`flaktns,iuyns masaihns latdeù`fins mdk `ucdr d idl-efns ak a` n`nr, in`nr, sdenr, taxturd y dspaitn
@d quìlfid y d`cukns bakùlakns d kuastrnd`ramamnr
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YQY]DKIFD IN@NU FKFIFD@
A` fkmfidmnr y `ds sustdkifds:
4. Ldrqua 2 vdsns ma p`ästfin trdkspdrakta ink `ns knleras: jucn ma `flùk jdeùk ak pn`vn, `aiha ma ldckasfd, sd`, dzúidr y vfkdcra.
5. In`nqua ak idmd vdsn paquaôds idktfmdmas ma `d sustdkifd fkmfidmd ydcud. Læzi`a`ns hdstd qua sa mfsua`vdk y dknta ak `d tde`d qua akinktrdrä dedjna` in`nr ma idmd ukd.
9. Dmfifnka uk ihnrrn ma` dcud ma rapn``n ak idmd vdsn y racfstra sus nesarvdifnkas ak `d tde`d sfcufakta:
=. ¾@ns idlefns ma in`nr nesarvdmn snk prnmuitn ma idlefns bìsfins n quìlfins> Axp`fqua su raspuastd.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
IN@NU INK A@FKMFIDMNU
Jucn ma `flùk
Jdeùk ak pn`vn
@aiha ma ldckasfd
Yd`
Dzúidr
Rfkdcra
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Inln sa vfn ak `d ukfmdm dktarfnr, `d quìlfid astä d kuastrn d`ramamnr, parnluihns ma `ns prnmuitns qua usdlns d mfdrfn hdk sfmn sfktatfzdmns n lajn-rdmns ak `ns `denrdtnrfns, yd qua `d quìlfid sa idrditarfzd pnr sar ukd ifakifdd`tdlakta axparflaktd`. Dsì, ak astd sasfùk inkniaralns d`cukns ldtarfd`as,aqufpns y usns ma `ns lfslns ak a` `denrdtnrfn ma quìlfid, dktas ma pdsdr d`d axparflaktdifùk. ]dlefæk denrmdralns `ds knrlds ma sacurfmdm qua samaeak sacufr, yd qua sfalpra axfstak rfascns ak d ldkfpu`difùk ma sustdkifds,ldtarfd`as y aqufpns.
LD]AUFD@AY MA@ @DENUD]NUFN
Ynk `ns qua sa alp`adk pdrd sujatdr, lamfr, d`ldiakdr n id`aktdr y kn bukifnkink a`aitrfifmdm. Ya i`dsfbfidk ink edsa ak a` ldtarfd` ma` iud` astäk inkstftufmsf sa puamak id`aktdr n kn y, sf sa puama hdiar lamfifnkas ink a``ns (var ldinkiaptud` 5).
@d ldmard sa alp`aded dktfcudlakta inln ld-tarfd` pdrd sujatdr ldtarfd`as inln `ns tuens maaksdyn, ak crdmf``ds n pfkzds pdrd tuen, parn majùma usdrsa maefmn d qua puama inktdlfkdrsa inklfirnnrcdkfslns y masinlpnkarsa7 tdlefæk puamaqualdrsa ink bdif`fmdm. Maefmn d a``n, sa prnpnkak`ns lfslns ldtarfd`as, parn bderfidmns ak p`ästfin
@ns dpnrtas ma `d quìlfid d `d snifamdm
@denrdtnrfn ma quìlfidQkfmdm 5. A` pdtfn: kuastrn `denrdtnrfn Yasfùk
5
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Ak iudktn d` vfmrfn, `ns ldtarfd`as sa bderfidkak æsta, puastn qua parlfta ``avdr d iden radi-ifnkas quìlfids ak `ds qua sa desnrea n `feardakarcìd ak bnrld ma id`nr, sfk qua subrdk luihnsmdôns. _nr a``n sa as i`dsfbfid inln rabrditdrfnsn kn rabrditdrfns.
Bfkd`lakta, `ns ma pnria`dkd sa usdk pdrd masdrrn``drprniasns ak `ns qua sa raqufarak talpardturds luyd`tds, qua a` vfmrfn kn snpnrtd, td`as inln `d bukmfifùk
ma latd`as y d`cukds sd`as.
Bukifùk ma d`cukns ldtarfd`as
]uen ma aksdyn: ak æ` sa ``avdk d iden radiifn-
kas quìlfids d paquaôd asid`d. _uamak sar nkn rabrditdrfns7 as maifr, qua d`cukns sa puamakid`aktdr sfk qua a` vfmrfn sa astd``a. Ntrns, pnra` inktrdrfn, kn sa maeak axpnkar d` buacn pnrkfkcúk lntfvn.
Ar`aklayar: sa dsalajd d` eadgar, parn sa mf-barakifd ak qua ak `d pdrta suparfnr tfaka ukiua``n dkcnstn, pnr `n qua as fmad` pdrd hdiarradiifnkas quìlfids vfn`aktds ak su fktarfnr, pra-vfkfakmn qua `ns prnmuitns ma radiifùk sd`cdkvn`dkmn y idfcdk snera a` dkd`fstd, dstfläkmn`n.As rabrditdrfn.
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Rdsn ma praifpftdmn n eadgar: tfaka lú`tfp`asbukifnkas, qua vdk masma a` id`aktdlfaktn ma`ìqufmns, hdstd sar a` raifpfakta pdrd lazi`drsustdkifds y hdiar radiifnkas quìlfids. D pasdr
ma takar ukd asid`d crdmudmd, kn as fmad` pdrdlamfr ìqufmns ink praifsfùk, yd qua d asid`d knas tdk matd``dmd inln d ma d prneatd y dmaläs,pnrqua as uk ldtarfd` qua sa axpnka d` id`nrinkstdktalakta.
_`did ma id`aktdlfaktn: ldtarfd` ma uk vfmrfn
rabrditdrfn luy pntakta, qua sa in`nid snera a`trìpnma, pdrd sarvfr ma snpnrta d `ns ldtarfd`asqua sa id`faktdk, inln a` eadgar n a` Ar`aklayar.
_fpatd: as uk tuen d`drcdmn y ma`cdmn qua saalp`ad pdrd `d axtrdiifùk y lamfifùk ma `ìquf-
mns. _uama sar crdmudmd n dbnrdmd. @d mfbarakifdrdmfid ak qua, lfaktrds ukds iuaktdk ink asid`dkulærfid y lfmak vdrfamdm ma vn`úlakas, `dsntrds tfakak sù`n ukd `ìkad (inknifmd inln a`dbnrn) qua fkmfid a` vn`ulak tntd` ma `d pfpatd,pnr `n qua sa usdk pdrd lamfr vn`úlakas aspa-iìbfins. Kn as rabrditdrfd.
_rneatd: as uk tuen `drcn dpnydmn snera ukdedsa, qua iuaktd ink ukd asid`d crdmudmd, pnr nqua sa alp`ad pdrd lamfr a` vn`ulak ma `ìqufmnsy cdsas y kn sa maea id`aktdr.
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Lnrtarn: as ukd vdsfjd paquaôd ma pnria`dkd, quasa usd pdrd trfturdr sustdkifds.
_fpatadmnr: utaksf`fn ma p`ästfin qua sa in`nid ak
`d enid ma `d pfpatd pdrd suiifnkdr `ìqufmns, avf-tdkmn d suiifùk ink d enid, pravfkfakmn ma astalnmn `d fkcastd ma cdsas y sustdkifds inrrnsfvds ytùxfids, inln `ns äifmns y a` latdkn`.
Crdmf``d: sa usd pdrd in`nidr `ns tuens ma aksdynmurdkta `ds pruaeds._fkzd pdrd tuen ma aksdyn: sa alp`ad pdrd incar
`ns tuens y avftdr dsì qualdmurds pnr id`nr n pnrabaitn ma `ns raditfvns.
Laiharn ma Euksak: fkstrulaktn latä`fin quabukifnkd ink cds y sa usd pdrd akiakmar buacn yid`aktdr sustdkifds.
Ynpnrta ukfvarsd`: inkstd ma ukd edsa, ak d quasa fkirustd uk tuen `drcn. Ya alp`ad pdrd sujatdrldtarfd`as ma vfmrfn, ink `d dyumd ma pfkzds.
Aspätu`d: harrdlfaktd qua iuaktd ink uk ldkcnp`ästfin y ukd `älfkd latä`fid p`dkd ak a` ntrn
axtraln, qua sfrva d lnmn ma iuihdrd, pdrd ax-trdar sù`fmns.
]rìpnma: ldtarfd` latä`fin qua, inln su knlera`n fkmfid, iuaktd ink tras pdtds, qua snpnrtdk ukdrn. Ynera æsta sa in`nid d p`did ma id`aktdlfak-tn.
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Ldpd inkiaptud` 5: I`dsfbfidifùk ma `ns ldtarfd`as ma `denrdtnrfn
LD]AUFD@AY MA @DENUD]NUFN
YA I@DYFBFIDK
Yacúk suinlpnsfifùk
Ldmard Rfmrfn _nria`dkd Latd` _`ästfin
_fkzd pdrd tuen maaksdyn
Rdsn mapraifpftdmns
Lnrtarn Aspätu`d Cntarns
Yacúk su bukifùk
Rn`ulætrfins
Kn vn`ul
Dcftd
Dbnrdmn Kn dbnrdmn Uabrditdrfns Kn rabrditdrfns
Ldtrdz _fpatd ]uen ma aksdyn _fikùlatrn
ATQF_NY MA @DENUD]NUFN
Ynk dqua``ns qua bukifnkdk ink a`aitrfifmdm y rad`fzdk ditfvfmdmas qua rasu`tdmalnrdmds n mfbìif`as pnr ntrns lamfns. @ns läs flpnrtdktas snk:
Ed`dkzd: alp`admd pdrd lamfr `d ldsd ma `ds
sustdkifds qua sa utf`fzdk ak a` `denrdtnrfn. Hdyma vdrfns tfpns, qua vdk masma `ds ldkud`as (ed-`dkzds crdlards), hdstd dqua``ds qua pasdk crdknspaquaôns (ed`dkzds dkd`ìtfids).
Astubds: d` fcud` qua ds takalns ak idsd, sa usdkpdrd id`aktdr7 d mfbarakifd as qua kn inifkdlnsink astds.
_ntakifùlatrn: sa alp`ad pdrd d matarlfkdifùkma` pH ma `ds sustdkifds.
Lub`d: as uk hnrkn qua ldkajd talpardturdsluy d`tds, pdsdkmn pnr `ns 2??¿I.
Hnrkn: as sflf`dr d `ns hnrkns inkvakifnkd`as (kn `ns lfirnnkmds) y sa usdk pd
Fldcak tnldmd ma a` Mautsiha Bntnthag ma `d
Efe`fntaid ma` Astdmn ma Ydjnkfd (Y@QE)
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8. Kn lazi`a `ds sustdkifds quìlfids qua kn inknia y qua kn astæk ak `nsprniamflfaktns, yd qua d`cukds radiifnkas puamak axp`ntdr y `feardr vdpnrastùxfins, idusdkmn `asfnkas qua puamak sar parldkaktas.
6. Kn inksuld d`flaktns n eaefmds maktrn ma` `denrdtnrfn.
4?. Kn inrrd kf juacua ak a` `denrdtnrfn.
44. Ak idsn ma fkiakmfn usa axtfkcufmnras, kukid dcud, yd qua luihns ra-ditfvns sa akifakmak ink ldynr dcrasfvfmdm ak prasakifd ma æstd.
45. Ak idsn ma diifmakta diumd fklamfdtdlakta d` mniakta qua mfrfca a``denrdtnrfn `n läs prnktn pnsfe`a.
49. @ad ink matakflfaktn `ns prniamflfaktns dktas ma fr d` `denrdtnrfn, inka` bfk ma takar i`drfmdm snera `n qua sa vd d rad`fzdr y ramuifr dsì d` lìkfln di -ifmaktas y cdstns fkkaiasdrfns ma raditfvns.
4=. Kn fkcrasdr ink ld`atds kf ink diiasnrfns inln dkf``ns, eubdkmds, ra`njas,
pu`sards n idmakds, yd qua æstns puamak radiifnkdr n aktrdr ak inktditn ink`ns raditfvns y a` buacn.
41. Dpdcua a` ia`u`dr7 `ds vferdifnkas ma æsta puamak cakardr ihfspds y inka``ds, buacn.
42. Kn usdr ldquf``dja ak `ds uôds y `ns njns. @ns sfckns ma akvakakdlfaktnsa avfmakifdk ak `ns pärpdmns y `ds uôds.
43. ]akar a` idea``n raincfmn.
48. Kn usdr `aktas ma inktditn, yd qua `ns quìlfins sa puamak d`njdr maktrnma æstns, idusdkmn mdôns ak `ns njns.
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d. Ua`difnkdkmn `ns ldtarfd`as ink utaksf`fns ma usn intfmfdkn:
Inlp`ata `d sfcufakta tde`d, in`nidkmn ak `d idsf``d brakta d idmd ldtarfd` dqua`utaksf`fns ma `d idsd n a` trdedjn ink a` qua puamd raalp`dzdr`ns. Yf kn axfstafkvakta `ns qua kaiasfta. _nr ajalp`n, a` tuen ma aksdyn puama raalp`dzdrsa iukd n``d ma vfmrfn rabrditdrfn n ukd inlúk y inrrfakta.
]uen ma aksdyn
Rdsn ma praifpftdmns
_fpatd
Rfmrfn ma ra`nj
Aspätu`d
Ar`aklayar
_fkzds
Lnrtarn
Crdmf``d
Aleumn
_rneatd
4
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e. Jucdkmn ink `d quìlfid:
Uad`fia `ns sfcufaktas axparflaktns, takfakmn ak iuaktd `ds knrlds ma sacurfmdmasirftds ak `d sasfùk:
_rapdra ukd sn`uifùk ma 4?? l@., qua inktakcd ukd pdrta ma d`inhn` atì`finsafs ma dcud. Yularjd ak astd lazi`d uk pdôua`n ma ta`d, säqua`n y axprìld`n. Aifækmd`a buacn hdstd qua æsta sa dcnta, y inlp`ata `d tde`d.
In`nqua 5? l@. ma vfkdcra ak ukd enta``d p`ästfid ma cdsansd ma tdldôn lamfdk(91? l@.). Lfaktrds tdktn pnkcd, ink dyumd ma uk aleumn, mns iuihdrdmds ma eidrenkdtn ma snmfn ak uk c`nen (enled). Iufmdkmn qua a` pn`vn ma` efidrenkdkn idfcd ak a` vfkdcra, in`nqua d enid ma` c`nen ak d enid ma d enta``d y dsacúraink ifktd pacdkta, ink ukd iuarmd n ink uk iduihn. Qkd vaz takcd a` sfstald, ma
idar a` efidrenkdtn ak a` vfkdcra y nesarva `n qua niurra ink a` c`nen.
Masmne`a uk i`fp a fktrnmúzid`n maktrn ma uk `flùk, dsacuräkmnsa qua parbn`d iäsidrd y aktra inln lìkfln 4? il. Hdcd `n lfsln ink uk d`dlera ma inerma lnmn qua `ns axtralns ma `ns ide`as quamak d ukd mfstdkifd ma 41 il. aktrsì. Injd a` `flùk ink `d ldkn y in`nqua `d `akcud ak `ns axtralns `feras ma `ns mnd`dleras.
Injd uk edkdkn pa`dmn y hulamazid ukd ma `ds mns puktds ak d`inhn` atì`fin
Qkd vaz qua `n hdcd, akifakmd `d puktd ink uk bùsbnrn y luarmd a` ntrn axtralnsnp`dkmn d` lfsln tfalpn a` buacn snera ukds uvds pdsds. Iùjd`ds ink uk takamnsùp`a`ds, ``æva`ds d `d enid y iùld`ds.
Injd ukd idrtu`fkd, iùrta`d ak vdrfns iudmrns fcud`as y tnla ukn ma a``ns. Indyumd ma uk pfkia` n uk dcftdmnr asirfed `n qua qufard snera a``d, usdkmn inltfktd äifmn su`búrfin inkiaktrdmn. Mæja`n rapnsdr ukns fkstdktas y, iudkmn saquaxpnkcd `d ntrd idrd ma `d idrtu`fkd d `d ``dld, dsacuräkmnsa qua a` buacn pdsa pa` `ucdr mnkma ustam asirfefù, sfk qua sa quala a` pdpa`. Nesarva `n qua niurr
ink `n qua asirfefù.
In`nqua ak uk snpnrta ukfvarsd` uk drn ink kuaz y uefqua ak a` nrfbfifn ma æsuk vdsn ma pdpa` ink dcud ak su fktarfnr, n iua`cua ak a` drn uk c`nen `akn ma dcuIufmdkmn kn qualdrsa ink `d ``dld, diarqua ak `d pdrta ma dedjn ma` vdsn n mc`nen ukd va`d akiakmfmd y mæja`d d``ì hdstd qua a` dcud hfarvd y pnstarfnrlaktaeu``d, as maifr, hdstd qua a` dcud alpfaia d eureujadr.
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5
In`nqua ak uk vdsn ma praifpftdmns (n vdsn ma p`ästfin trdspdrakta) mns n tras cnma d`cúk in`nrdkta rnjn y snera æsta dmfifnka dcud, hdstd `d lftdm ma `d idpdifmma` vdsn, dcftdkmn hdstd qua tnmd `d lazi`d tnla in`nr. Ink uk cntarn dmfifnukds cntds ma e`dkquadmnr idsarn hdstd qua hdyd d`cúk idlefn.
AX_AUFLAK]N UAYQ@]DMN ¾_NU TQÆNIQUUA AY]N>
d. ¾A` buacn kn quald>
e. Axpdksfùk
i. ¾V mùkma quamù `d pf`d>
m. ¾Brìn n id`fakta>
a. ¾Fkvfsfe`a>
b. ¾_dpa` n iduihnrasfstakta d` buacn>
c. In`nr:¾trdkspdrakta>
Qtf`fzdkmn `ns ldtarfd`as ma `denrdtnrfn, prnpnkcd mns latnmn`ncìds pdrdsapdrdr ukd lazi`d ma dcud y tfarrd.
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]ùlasa ukns lfkutns pdrd paksdr mabnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:
¾Ydea ma quæ astä inlpuastd `d ldtarfd>
Yf ustam tnldrd ukd hnjd ma iudmarkn, `d mne`drd d `d lftdm, `d pdrtfardy incfard ukd ma `ds lftdmas, `d mne`drd y pdrtfard ma kuavn, y dsì hfifa -
rd ink tnmds `ds lftdmas ma `d hnjd qua netakcd, ¾iraa qua ``acdrìd d ukpuktn ak a` qua kn puamd rnlpar läs `d hnjd> ¾_nmrìd mfvfmfr `d hnjdfkbfkftdlakta>
¾Tuæ sfckfbfid `d pd`derd ätnln>
¾Ydea ak quæ pdìs y ak quæ æpnid sa hde`ù pnr prflard ma vaz ma `ns ätnlns>
¾_nr quæ as flpnrtdkta a` astumfn ma `ns ätnlns ak quìlfid>
_drd tnmds `ds ifvf`fzdifnkas, sfalpra hdk sfmn lntfvn ma iurfnsfmdm `ns idlefny inlpnsfifùk ma `d ldtarfd. Ak Craifd, pnr ajalp`n, dprnxfldmdlakta hdifd dôn 2?? d. I., sa iraìd qua a` ukfvarsn astded inlpuastn pnr dcud, tfarrd, buacndfra, pnr a``n murdkta `d d`quflfd (fkfifns ma `d quìlfid) `ns ifaktìbfins trdtdedk mnetakar nrn d pdrtfr ma inlefkdifnkas ma astns a`alaktns ink ntrns latd`as ]d`
Lnma`ns dtùlfins
ÄtnlnQkfmdm 9. Inkstftuifùk ma `d ldtarfd Yasfùk
9
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axparflaktns kn tuvfarnk æxftn, sfk aledrcn sì `ncrdrnk netakar kuavns inlpuasy parlftfarnk a` fkfifn ma `d lamfifkd (Fdtrnquìlfid).
@auifpn ma Jnkfd p`dktaù qua ds sustdkifds sa puamak mfvfmfr parn kn fkbfkftdlaky as Malùirftn, fcud`lakta hdifd a` 2?? d.I., qufak dpnyd astd tanrìd y mfia q`d ldtarfd astä inlpuastd pnr paquaôds pdrtìiu`ds ‐fkmfvfsfe`as“ d `ds qua edutinln ätnlns.
@d quìlfid dpdraia pnr prflard vaz ink Dktnfka @dvnfsar, qufak hdia ukd axprflaktdifùk läs rfcurnsd, fktrnmuifakmn `d ed`dkzd ak a` dkä`fsfs ma `ds sustdkifakinktrdkmn qua ak `ns prniasns quìlfins kukid hdy pærmfmd ma ldtarfd7 `n qniurra as qua æstd sa inlefkd ma kuavds ldkards, ldktakfakmn sfalpra `ds idk
mdmas fkfifd`as. D astn sa `n ``dlù `d @ay ma `d Inksarvdifùk ma `d Ldsd y as `d qhfzn avfmakta qua d` pdraiar `d ldtarfd sì maea astdr inkbnrldmd pnr pdrtìiupaquaôds y mfbaraktas aktra sì, `n qua parlfta axp`fidr, pnr ajalp`n, a` pnr quk cds sa puama inlprflfr y prfkifpd`lakta a` pnr quæ `d ldtarfd sa lazi`d mfvarsds bnrlds.
Astn ``avd d` quìlfin Fkc`æs Jnhk Md`tnk d prnpnkar `d ]anrìd Dtùlfid, ink `ns cufaktas pnstu`dmns
• @ns a`alaktns astäk inlpuastns pnrpdrtìiu`ds luy paquaôds a fkmfvfsfe`as(ätnlns) sflf`dras d `ns masirftns pnrMalùirftn.
• ]nmd `d ldtarfd astä inlpuastd pnrätnlns.
• @ns ätnlns ma uk lfsln a`alaktnsnk fcud`as.
• @ns ätnlns ma mfstfktns a`alaktns snkmfbaraktas.
• @ns ätnlns ma uk lfsln a`alatn tfakak a` lfsln tdldôn, ldy bnrld.
• @ns inlpuastns quìlfins sa bldk pnr `d ukfùk ma mns n li`dsas ma ätnlns mfbaraktas. inlefkdrsa ätnlns ma a`alaktmfstfktns ak prnpnrifnkas sflp`sa netfakak `ns inlpuastns.
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Ink edsa ak `d tanrìd dtùlfid, bfkd`lakta `dinlukfmdm ifaktìbfid diaptd d` ätnln inln `dukfmdm inkstftuyakta ma `d ldtarfd. Yfk aledr-cn, dúk hdy fkb`uakifd ak `ds iraakifds dktfcuds,
inln pnr ajalp`n a` kn iraar ak a` vdiìn, `nqua ``avd d` p`dktadlfaktn ma` prflar lnma`ndtùlfin.
Ak 46?= Jnsaph ]hnlsnk prnpnka a` Lnma`nma` Eumìk ma _dsds, a` iud` inksfsta ak ukd as-paifa ma tnrtd idrcdmd pnsftfvdlakta (dúk samasinkniìd `d axfstakifd ma `ns prntnkas), ak
`ns qua b`ntdedk `ns a`aitrnkas, dsalajdkmn d uk pumìk ma pdsds.
Inln `d quìlfid as axparflaktd`, tnmn `n qua sa mfcd maea sar malnstrdmn7 ainksaiuakifd, a` lnma`n ma ]hnlsnk maeìd inlprnedrsa. _nr a``n, Arkast Uutharbnrad`fzd uk axparflaktn, qua inksfsta ak enledrmadr ink pdrtìiu`ds d`bd ukd älfkma nrn, rnmadmd ink ukd pdktd``d ma su`burn ma zfki. Ink asta axparflaktn pumdpraifdr qua `d ldynrìd ma `ds pdrtìiu`ds d`bd dtrdvasdedk mfraitdlakta `d `älfksfk masvfdrsa ma su trdyaitnrfd7 ntrds subrìdk ukd paquaôìsfld masvfdifùk7 y ntrd
ak idlefn, sa mfsparsdedk ink crdkmas äkcu`ns a fki`usn sa mavn`vìdk d `d buakma pdrtìiu`ds, as maifr qua raentdedk.
Lnma`n dtùlfin ma ]hnlsnk
Axparflaktn ma Uutharbnrm.
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Lnma`n dtùlfin ma Uutharbnrm
Astn hfzn qua, ak vaz ma inkbfrldr a` lnma`nma ]hnlsnk, sa idlefdrd pnr inlp`atn, ydqua `n qua sa asparded ard qua `ds pdrtìiu`dsd`bd dtrdvasdrdk `d `älfkd ink pnin n kdmd
ma masvfdifùk. Ak inksaiuakifd, Uutharbnrmp`dktad qua a` ätnln inksfsta ak mns pdrtas:
d. Qk kúi`an, ak a` qua sa akiuaktrd tnmd`d idrcd pnsftfvd ma` ätnln.
e. Qkd inrtazd dtùlfid ak `d qua nreftdk `ns a`aitrnkas.
_arn a` lnma`n ma Uutharbnrm kn sù`n masdbìd d ]hnlsnk, sfkn dmaläs d ns crfacyd qua sucfara qua `d ldynrìd ma` aspdifn ma` ätnln astä vdiìn, `n qua bdif`ftdpdsn mfraitn ma `d rdmfdifùk, sfk qua astd sa masvìa.
D pasdr qua a` lnma`n parlfta mdr rdzùk d ns rasu`tdmns ma` axparflaktn, kn axppnr quæ a` kúi`an d`ldiakd d idrcd pnsftfvd y pnr quæ ns a`aitrnkas ink idrcd kacdt
kn snk dtrdìmns pnr a` kúi`an ma` ätnl
Edsäkmnsa ak a` ätnln ma hfmrùcaknbìsfin mdkæs Kfa`s Enhr sucfara su prnlnma`n, inki`uyakmn qua ns a`aitrnnreftdk d`ramamnr ma` kúi`an ak kfvaiudktfzdmns ma akarcìd (as maifr, i
akarcìds aspaiìbfids), y inln inkiuakifd, `ns a`aitrnkas tdlefæk astiudktfzdmns. Dsì, iudkmn sa luavaksus kfva`as kn frrdmfdk akarcìd7 pnrinktrdrfn, iudkmn uk a`aitrùk pdsd uk kfva` ma akarcìd d`tn d ukn lakakarcætfin, `feard uk bntùk, qua as u
pdrtìiu`d ma uz, n sf pdsd ma uk vfka` lakns akarcætfin d ukn ldynr, desnrea ifa
Lnma`n dtùlfin ma Enhr
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Ntrd dp`fidifùk ma asta lnma`n as `d pù`vnrd: ¾sa hd pracuktdmn d`cukd vaz iùlhdiak `ns bderfidktas ma `d pù`vnrd pdrd mdr`as asds in`nrdifnkas tdk idrditarìstfid `ns juacns pfrntæikfins> As luy sflp`a: `n `ncrdk ink `ns aspaitrns ma alfsfùInln yd sa lakifnkù, snk pdrtfiu`dras d idmd a`alaktn7 ma haihn, `ns aspaitr
snk a` aqufvd`akta d kuastrds hua``ds mfcftd`as. Dsì, pnr ajalp`n, a` in`nr dldrf`sa maea d` snmfn, a` rnsdmn d` pntdsfn, a` kdrdkjd as pnr a` id`ifn, dzu` pnr a` inerrnjn pnr a` astrnkifn y a` varma pnr a` edrfn.
Asta lnma`n parlftfù astde`aiar qua uk ätnln astä inkstftufmn pnr uk kúi`an, ak qua sa akiuaktrdk ns kautrnkas y prntnkas y d`ramamnr ma` kúi`an astäk ns kfva`ma akarcìd iudktfzdmns, ak `ns qua sa luavak `ns a`aitrnkas.
Crdifds d` lnma`n ma Enhr, bua pnsfe`a inlprakmar bakùlakns inln `d `feardifùn desnrifùk ma akarcìd, parn a` qua `n hdcd kn flp`fid qua `d ifakifd pdra. Dinktrdrfn, as dsì inln dpdraia a` lnma`n läs raifakta: a` Lnma`n Iuäktfin, quinlp`alaktd `ns hd``dzcns ma Enhr y kns mfia qua:
4. @ns a`aitrnkas astäk iudktfbfidmns, d` fcud` qua a` kfva` ma akarcìd d` iupartakaiak7 sfk aledrcn, a``ns nreftdk ak znkds luy aspaiìbfids ma` kfva`, d` qua maknlfkd nreftd` dtùlfin, y kn sa luavak pnr tnmn a` kfva` inln sa iraìd dktas
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5. @d akarcìd, pnsfifùk, uefidifùk y lnvflfaktns ak a` aspdifn ma `ns a`aitrkas kn neamaiak d @ayas ma `d Bìsfid Kawtnkfdkd (a``n bnrzù d `d fkvakifùk mabìsfid iuäktfid, ak su ldynrìd bnrlu`dmd pnr D`eart Afkstafk) y sa maea raiurrfr d ldtalätfids pdrd su inlpraksfùk.
9. A` a`aitrùk tfaka inlpnrtdlfaktn mud`, as maifr qua sa puama ldkfbastdr inlpdrtìiu`d (as maifr ink ldsd) n inln akarcìd (iudkmn sa luava). Ak inksaiuakisf sa qufara matarlfkdr `d pnsfifùk läs prnede`a ma` a`aitrùk ak ukd racfùk maspdifn, as flpnsfe`a hd``dr `d va`nifmdm ink `d qua sa luava, y sf `n qua sa qufaas matarlfkdr `d va`nifmdm, kn sa puama id`iu`dr `d pnsfifùk. D asta bakùlakn sainknia inln _rfkifpfn ma Fkiartfmulera.
Ak inksaiuakifd, ink a` lnma`n a` ätnln sa nrcdkfzd ink edsa ak `ns kúlariuäktfins:
Kúlarns iuäktfins
Inln sa dided ma lakifnkdr, a` kuavn lnma`n sa edsd ak `ds ldtalätfids y prpnka d` ätnln ink edsa ak `ns sfcufaktas kúlarns:
d. Kúlarn iuäktfin prfkifpd` (k): fkmfid `d idktfmdm ma kfva`as ma akarcìd psaktas ak uk ätnln. Rdk ma` kúlarn 4 hdstd a` 3.
e. Kúlarn iuäktfin dzflutd` (`): axp`fid `d bnrld ma `ns nreftd`as, mnkma akiuaktrdk `ns a`aitrnkas. Ya id`iu`d rastäkmn`a 4 d` k, pnr ajalp`n:
k < 4 ` < 4 ’ 4 < ? < nreftd` s
k < 5 ` < 5 ’ 4 < 4 < nreftd` p y ` < 4 ’ 4 < ? < nreftd` s
k < 9 ` < 9 ’ 4 < 5 < nreftd` m7 ` < 5 ’ 4 < 4 < nreftd` p y ` < 4 ’ 4 < ?nreftd` s
k < = ` < = ’ 4 < 9 < nreftd` b7 < 9 ’ 4 < 5 < nreftd` m7 < 5 ’ 4 < 4 < nre
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i. Kúlarn iuäktfin ldckætfin (l`): axp`fid `ds nrfaktdifnkas, as maifr, `mflaksfnkas ak a` aspdifn ak `ds qua sa hd``dk `ns nreftd`as. Ya id`iu`d tnldkma` vd`nr ma` kúlarn dzflutd`, pdsdkmn asa lfsln vd`nr pnr `ns kúlarn kacdtfvnhdstd ``acdr d` lfsln kúlarn, parn ak pnsftfvns, dsì:
Iudkmn:
` < ? l` < ? (inln sù`n hdy uk kúlarn, fkmfid qua sù`n axfsta ukd pnsfifùk aa` aspdifn).
` < 4 l` < -4, ?, +4 (hdy tras kúlarns, tras pnsfifnkas: pX, pV y pZ).
` < 5 l` < -5, -4, ?, +4, +5 (1 pnsfifnkas: mXV, mVZ, mXZ, mX5V5, mZ5).
` < 9 l` < -9, -5, -4, ?, +4, +5, +9 (3 pnsfifnkas: Bz9, bXZ5, bVZ5, bX(X5 ’ 9V5bV(V5 ’ 9X5), bXVZ, bZ(X5 ’ 9V5).
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m. Kúlarn iuäktfin aspìk (s): fkmfid `ns saktfmns ma cfrn ma `ns a`aitrnkas, sù`n ink mns pnsfef`fmdmas: ak a` saktfmn ma `ds ldkaif``ds ma` ra`nj, n ak inktrd
Inkbfcurdifùk a`aitrùkfid
Ink edsa ak a` lnma`n iuäktfin sa puama matarlfkdr iùln sa akiuaktrdk uefmns idmd ukn ma `ns a`aitrnkas ma uk ätnln y ak quæ nrmak sa ``akdk idmd ukn
`ns kfva`as ma akarcìd, ink sus raspaitfvns nreftd`as, pnr lamfn ma `d inkbfcurdifa`aitrùkfid:
Ak d mfstrfeuifùk a`aitrùkfid ma iud`qufar a`alaktn, sa sua`a asirfefr a` kúlarn a`aitrnkas inln axpnkaktas, qua d` sar suldmns ak su tntd`fmdm kns md a` kúla
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ma` cräbfin, sdefakmn qua a` kúlarn d` qua sa maea ``acdr as a` kúlarn dtùlfipdrtfiu`dr d idmd a`alaktn.
Ajalp`n:
N8 < 4Y5 5Y55_=
@d inkbfcurdifùk kn sù`n kns mfia iuäktns a`aitrnkas hdy y ak quæ ucdras, sfkn qudmaläs kns parlfta inkniar a` kfva` ma akarcìd läxfln ma` ätnln, qua ak d tdeparfùmfid sa inknia inln parìnmn. Yacúk `d idktfmdm ma a`aitrnkas uefidmns aasta lfsln kfva`, as pnsfe`a matarlfkdr a` crupn ma `d tde`d d` iud` partakaiak, tinln sa puama var ak `ns ajalp`ns sfcufaktas:
A`alaktn Yìlen`n Kúlarn Inkfcurdifùk _arìnmn Crupn Uacfùk dtùlfin a`aitrùkfid
Earf`fn Ea = 4 s5 5s5 5 FF s
Enrn E 1 4 s5 5s5 5p4 5 FFF p
Idrenkn I 2 4 s5 5s5 5p5 5 FR p
Kftrùcakn Kf 3 4 s5
5s5
5p9
5 R p Nxìcakn N 8 4 s5 5s5 5p= 5 RF p
Ntrns inlpnkaktas ma` ätnln
Ink a` masdrrn``n ma `d enled dtùlfid (ukd i`drd malnstrdifùk ma qua a` ätnlsì puama mfvfmfrsa) sa hfzn avfmakta a` pntakifd` ma `d akarcìd dtùlfid y iùln sinrraitn usn pnmrìd eakabfifdr d `d huldkfmdm, yd qua astd akarcìd puama inks
mardrsa inln `flpfd, puastn qua sf sa inktrn`d rfcurnsdlakta su prnmuiifùk, khderìd inktdlfkdifùk y erfkmdrìd tdktd akarcìd, qua fki`usn ``acdrìd d sar nesn`ata` usn ma` patrù`an.
Kn sù`n as a` fktaræs pnr `d akarcìd `n qua inkmuia d `ns ifaktìbfins ak su idlfkditud`, sfkn tdlefæk `d axp`fidifùk ma` nrfcak ma` ukfvarsn. _nr a``n sa iradrnk `ndia`ardmnras ma pdrtìiu`ds, qua sf efak dúk kn `ncrdk rap`fidr a` Efc-Edkc d paqu
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9
pdrtìiu`ds, dktas masinknifmds pdrd `d ifakifd, iuyds bukifnkas snk `d bnrldifùk `ns a`aitrnkas, kautrnkas y prntnkas. Ynk `ds cakardmnrds ma `ds buarzds kui`adqua `a mdk astdef`fmdm d` ätnln y avftdk qua a` kúi`an in`dpsa inln rasu`tdmn `ds buarzds ma rapu`sfùk aktra `ns prntnkas, y snk tdlefæk `ds mfraitds raspnksdema `ds buarzds crdvftdtnrfds ma` aspdifn.
D`cukds pdrtìiu`ds snk `ns qudrgs (inlpnkak d `ns kautrnkas y prntnkas), `ns katrfkns, ensnkas, barlfnkas, `aptnkas, lunkas, aktra ntrds, `n qua sfckfbfid quaätnln kn sù`n sa masinlpnka ak a`aitrnkas, kautrnkas y prntnkas, sfkn qua dmalpnmrìd hdiar`n ak `ds pdrtìiu`ds inkstftuyaktas ma æstns y ak ntrds läs.
Uad`fia `d inkbfcurdifùk a`aitrùkfid pdrd a` B, Id, D` y _e, uefiäkmn`ns ak `d tdparfùmfid.
Uaspnkmd `ds sfcufaktas pracuktds:
4. ¾As inrraitn a` tærlfkn ätnln> ¾_nr quæ>
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
5. Uad`fia `d inkbfcurdifùk a`aitrùkfid ma` H, Kd, N, K, Lc, I` y I y pramfcdparìnmn y crupn ma `d tde`d parfùmfid ak `ns qua sa akiuaktrdk.
4
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]ùlasa ukns lfkutns pdrd paksdr ma bnrldfkmfvfmud` snera `ds sfcufaktaspracuktds:
¾Tuæ as `d tde`d parfùmfid>
¾Inknia ustam d quæ hdia rabarakifd a` tærlfkn parfnmfifmdm>
¾Ya hd pracuktdmn d`cukd vaz pnr quæ `d tde`d parfùmfid tfaka asd nrcdkfzdifùktdk pdrtfiu`dr>
¾Iuä` as `d flpnrtdkifd ma` kúlarn dtùlfin ink raspaitn d `d tde`d parfùmfid>
Inln sa vfn ak `d sasfùk dktarfnr, `d inkbfcurdifùk a`aitrùkfid as luy flpnrtdktyd qua kns md rdzùk ma `d idktfmdm ma a`aitrnkas prasaktas ak uk ätnln, a` lnmak qua æstns astäk mfstrfeufmns y ak pdrtfiu`dr, pdrd a` astumfn ma astd sasfùk, kmd fmad ma `d bnrld inln astä nrcdkfzdmd `d tde`d parfùmfid, yd qua, inln sa vpravfdlakta, a` kfva` ma akarcìd as `n lfsln qua a` parìnmn ak `d tde`d y `d sultntd` ma `ns a`aitrnkas ak mfihn kfva` kns md a` crupn.
]de`d parfùmfid
]de`d parfùmfid y parfnmfifmdmQkfmdm =. @d tde`d parfùmfid Yasfùk
=
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Hfstnrfd ma `d tde`d parfùmfid
Ak `d æpnid ma `d d`quflfd, `ns ifaktìins kn pnmìdk inlpdrtfr susinkniflfaktns pnr talnr d lnrfr ak d hncuard. Iudkmn `acd a` kma` Nsiurdktfsln, sa masiuerak luihìsflns a`alaktns y ink `ddiaptdifùk ma `d tanrìd dtùlfid, æstns snk rainknifmns inln td`.Yfk aledrcn, snk tdktns `ns kuavns a`alaktns, qua kn hdy uk ink-saksn snera sus knleras, sìlen`ns pdrd raprasaktdr`ns y luihn
lakns, d`cúk irftarfn pdrd i`dsfidr`ns y nrmakdr`ns.
Jnhk Md`tnk, qufak prnpusn `d tanrìd dtùlfid, tdlefæk sa md d `dtdrad ma raprasaktdr ink sìlen`ns d `ns ätnlns. Ink a` tfalpn,æstns dmqufarak `d bnrld ditud`:
]rdedjn ma Jnhk Md`tnkpdrd raprasaktdr d `ns
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sa dprnxflded d `d lamfmd drftlætfid ma `ds ldsds dtùlfids ra`dtfvds maidmd ukn ma `ns a`alaktns, maknlfkäkmn`ns trìdmds.
Qk ajalp`n as a` sfcufakta:A` i`nrn tfaka uk pasn dtùlfin ma 91.1 y a` ynmn ma 452.67 d` suldr`ns ymfvfmfr`ns aktra mns, sa netfaka 84.5, qua as luy iaridkn d` pasn rad` ma`ernln (36.6). Yfk aledrcn, astd sf-tudifùk as läs ukd idsud`fmdm quaukd rac`d7 ak inksaiuakifd, kn asdmaiudmd pdrd nrcdkfzdr d `ns a`a-laktns.
Ak 4829 Jnhk Kaw`dkms (fkc`æs),in`niù `ns a`alaktns ak crupns manihn, d æstns `as mfn a` knlera manitdvds, yd qua idmd nihn a`alak-tns prasaktdedk prnpfamdmas sflf-`dras. Ak 4826 Mflftrf Lakma`afav(rusn), mfn d inkniar `d nrmakdifùk
Ak 4849, Jnhks Jdine Earza`fus (sua-in), i`dsfbfiù ns a`alaktns quìlfinsinknifmns ak a`aitrnpnsftfvns y
a`aitrnkacdtfvns. Hdifd 4856, JudkSn`bcdkc Mnearafkar (d`aläk), sa-ôd`ù pnr prflard vaz `d axfstakifdma ukd ra`difùk sfckfbfidtfvd aktra dsprnpfamdmas ma `ns a`alaktns y susraspaitfvds ldsds dtùlfids ra`dtfvds.
Yus fkvastfcdifnkas n `avdrnk d ne-
sarvdr d prasakifd ma crupns ma trasa`alaktns, ak ns iud`as, d ldsd dtù-lfid ra`dtfvd ma` a`alaktn iaktrd`,
Jnhks Jdine Earza`fus
Jnhk Kaw`dkms
B n t n t n
l d m d m a w f g f p a m f d
B n t n t n l d m d m a w f g f p a m f d
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Mflftrf Fväknvfih Lakma`afav,pdmra ma `d tde`d parfùmfid.
Uatrdtn ink `d tncd ma idtamrätfin ma `dQkfvarsfmdm ma Amfleurcn. Diudra`d
snera pdpa` Cd`arfd astdtd` ]ratfdgnv, Lnsiú
läs inlp`atd ma `ns a`alaktns, edsäkmnsa ak `ds prnpfamdmas quìlfids,inln bukifùk ma` kúlarn dtùlfin.
A` crdk difartn y lærftn sa bukmdlaktù ak prama-ifr a`alaktns kn masiuefartns tnmdvìd, pdrd `nsiud`as rasarvù uk aspdifn ak `d tde`d y läs dúkdma`dktù sus prnpfamdmas.
@d tde`d lnmarkd astä inkstftufmd pnr 48 in`ulkds, maknlfkdmds crupns n bdlf`fqua raprasaktdk d idktfmdm ma a`aitrnkas qua hdy ak a` kfva` ma vd`akifd, y qua s`ns a`aitrnkas qua avaktud`lakta puamak fktarvakfr ak uk ak`dia. Ya mfvfmak `ds bdlf`fds D (a`alaktns raprasaktdtfvns) y E (a`alaktns ma trdksfifùk), kulardmink ns dktfcuns kúlarns rnldkns7 sfk aledrcn, hny ak mìd sa kulardk ma` 4 d`
]dlefæk tfaka parìnmns, rabarfmns d `d idktfmdm ma kfva`as ma akarcprasaktas ak idmd ätnln fkmfvfmud`, lntfvn pnr a` qua hdy 3 parìnmnQkd idrditarìstfid ma astd bnrld ma nrcdkfzdifùk, as qua `ns a`alaktns tfakak ppfamdmas bìsfids y quìlfids sflf`dras, tdktn ak `ns crupns, inln ak `ns parìnm
@d tde`d parfùmfid tdlefæk sa mfvfma ak iudtrn znkds, mapakmfakmn ma` ú`tflnreftd` dtùlfin ma `d inkbfcurdifùka`aitrùkfid7 as maifr, sa iuaktd ink d
znkd s inkbnrldmd pnr ns a`alaktnsd`id`fkn y d`id`fkntærrans7 `d znkd p,inlprakmfmd pnr `ns a`alaktns ma`crupn FFF hdstd a` RFFF D7 `d znkd m ak`d qua astäk tnmns `ns a`alaktns matrdksfifùk (crupn E inlp`atn) y `d
znkd b , inrraspnkmfakta d `ns `dktä-kfmns y ditìkfmns.
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A` sfstald parfùmfin astde`aia ukd mfvfsfùk kdturd` ma `ns a`alaktns `feras,latd`as qua snk a` 8?% y `ns kn latd`as a` 5?%.
Latd`as
@nid`fzdifùk ma `ns a`alaktns ak `d tde`d parfùmfidLatd`as y kn latd`as
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Niupdk `d ú`tfld in`ulkd ma `d maraihd ak `d tde`d. Ya maknlfkdk inln kne`maefmn d qua ak su ú`tfln kfva` ma akarcìd iuaktdk ink 8 a`aitrnkas, `n qua inkbfara läxfld astdef`fmdm y `ns hdia pnin n kdmd raditfvns. ]nmns a``ns axfs
ak d`cukd prnpnrifùk ak `d dtlùsbard tarrastra, dukqua su inkiaktrdifùk, axia`d ma` drcùk, as axtrdnrmfkdrfdlakta edjd.
Ak æstns, d lamfmd qua dulaktd a` kúlarn dtùlfin, `ns a`aitrnkas vdk d uk kffktarfnr ak vaz ma fr d` kfva` läs axtarkn. _nr a``n, tfakak ak nreftd` m fkinlp`at
Ynk tnmns dqua``ns a`alaktns ak iuyd inkbfcurdifùk a`aitrùkfid nrmakdmd, a` pkú`tfln suekfva` as =b n 1b. @ns a`alaktns ma trdksfifùk fktarkd sa in`nidk dpdak `d tde`d parfùmfid ak mns crupns n sarfas ma a`alaktns.
Cdsas kne`as
A`alaktns ma trdksfifùk
@dktäkfmns y ditìkfmns
Kaùk, cds kne`a alp`admn ak d`ulerdmn y pue`fifmdm
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_arfnifmdm quìlfid
Inln sa lakifnkù, `ns a`alaktns inlpdrtak prnpfamdmas sflf`dras, tdktn ak `ncrupns inln ak `ns parìnmns. D`cukds ma a``ds snk: rdmfn dtùlfin, akarcìd ma fnk
zdifùk, dbfkfmdm a`aitrùkfid y a`aitrnkacdtfvfmdm.
A` rdmfn rad` ma uk ätnln kn sa hd pnmfmn iudktfbfidr, parn sì sa hdk astde`aifmtdldôns ra`dtfvns, dprnvaihdkmn d matarlfkdifùk ma ds mfstdkifds fktar- kui`adrak `ns inlpuastns.Ya inksfmard inln a` vn`ulak ma `d maksfmdm a`aitrùkfid tntd`, d`ramamnr mkúi`an. Astd lamfmd as sù`n iartard ak uk 6?%, ydqua dúk kn sa hd pnmfmn lamfr ink rfcurnsfmdm,pnr `n qua sa raiurra d matarlfkdr`n ink edsa ak`ds mfstdkifds fktar-kui`adras aktra ns a`alaktns akuk inlpuastn. D lamfmd qua a` parìnmn dulaktd,fcud` `n hdia a` rdmfn dtùlfin7 ak idlefn, aktraldynr sad a` crupn, laknr a` tdldôn dtùlfin.
A` pntakifd` ma akarcìd ma fnkfzdifùk, as d akarcìd raquarfmd pdrd quftdr`a uk a`aitrùd uk ätnln kautrn ak astdmn cdsansn. @d matarlfkdifùk axparflaktd` ma` pntakifma fnkfzdifùk sa abaitúd ak tuens ma masidrcd. A`aitrnkacdtfvfmdm: sa mabfka inl`d idpdifmdm qua tfakak `ns ätnlns pdrd dtrdar `ns a`aitrnkas ma ntrns ätnlns, a
uk ak`dia quìlfin. D laknr rdmfn dtùlfin, ldynr a`aitrnkacdtfvfmdm, ak inksiuakifd, d lamfmd qua dulaktd a` parìnmn, laknr a`aitrnkacdtfvfmdm, y ldynlfaktrds sa dvdkzd ak `ns crupns
]dldôn dtùlfin
Akarcìd ma fnkfzdifùk y dbfkfmdm a`aitrùkfid
L (c) + akarcìd ma fnkfzdifùk L (c ) + a‖ ätnln kautrn fùk pnsftfvn a`aitrùk
+
Ajalp`n:
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Nrcdkìiasa ak suecrupns ink sus inlpdôarns. @uacn: 4. Uaspnkmdk: ¾pnr quæ rdzùk d lamfmd qua dulaktd a` rdmfn dtùlfin `d a`trnkacdtfvfmdm mfslfkuya>
5. Nrmakak `ns sfcufaktas a`alaktns ink edsa ak su kúlarn dtùlfin7 matlfkak iuä` sarìd a` läs a`aitrnkacdtfvn, iuä` a` läs a`aitrnpnsftfvn, iuä` as a` lcrdkma y iuä` a` läs paquaôn ak tærlfkns ma rdmfn dtùlfin. A`alaktns: N, I, Kf, Ba, Kd, H y Id.
Uaspnkmd `ds pracuktds d inktfkudifùk, ink edsa ak `d fkbnrldifùk sulfkfstrdmAk `d tde`d parfùmfid, `ns a`alaktns sa nrcdkfzdk ak crupns y parìnmns, ma diuard` kúlarn dtùlfin, ink prnpfamdmas bìsfids y quìlfids sflf`dras. @ns a`alaktnsi`dsfbfidk inln latd`as, kn latd`as y salflatd`as y sa uefidk ak `d tde`d inlnluastrd ak `d sfcufakta bfcurd:
4
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• A`aitrnkacdtfvfmdm: 5.1
• A`aitrnkas ma vd`akifd: 4
• Kn inkmuitfvfmdm ak su bnrld
dtùlfid, d`td ak bnrld fùkfid
• Crupn D
• A`aitrnkacdtfvfmdm: 4.6
• A`aitrnkas ma vd`akifd: 4
• D`td inkmuitfvfmdm
• Crupn E
• A`aitrnkacdtfvfmdm: 4.8
• A`aitrnkas ma vd`akifd: =
• D`td inkmuitfvfmdm
• Crupn D
• A`aitrnkacdtfvfmdm: 4.?
• A`aitrnkas ma vd`akifd: 5
• D`td inkmuitfvfmdm• Crupn D
D E
I M
Ma diuarmn d `d fkbnrldifùk, raspnkmd:
4. @ns a`alaktns latä`fins inrraspnkmak d:
d. ]nmnse. D, E y Ii. D, E y Mm. D, I y M
5. A` a`alaktn E kn inkmuia `d a`aitrfifmdm pnr sar:
d. D`id`fkne. Ma trdksfifùki. Hd`ùcakn
@ds sfcufaktas bfihds luastrdk fkbnrldifùk snera `ds prnpfamdmas bìsfids y quìlfidma iudtrn a`alaktns, ma` parìnmn 1:
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9. A` nrmak ma` tdldôn dtùlfin, ma laknr d ldynr inrraspnkma d:
d. D, E, I, Me. E, M, I, D
i. E, D, I, Mm. E, M, I, D
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Ak`dias quìlfins
]ùlasa ukns lfkutns pdrd paksdr ma bnrlfkmfvfmud` snera `ds sfcufaktas pracuktds:
¾_nr quæ hdy sustdkifds qua sa avdpnrdk läs räpfmn qua ntrds>
¾_nr quæ d`cukds sustdkifds snk sù`fmds, lfaktrds qua ntrds snk `ìqufmds n cdsan-sds>
¾_nr quæ d`cukns inlpuastns parlftak a` pdsn ma `d inrrfakta a`æitrfid, lfak-trds qua ntrns kn>
AY]UQI]QUDY MA @ASFY
Vd qua kukid sa hd pnmfmn nesarvdr ukd ln`æiu`d y luihn lakns uk ätnln, kaiasdrfn raiurrfr d `d fldcfkdifùk pdrd sdear snera iùln snk `ds astruiturds ma `ninlpuastns y asn snk justdlakta `ds astruiturds ma @awfs.
Æstds inksfstak ak `d raprasaktdifùk ma `ns ätnlns, pnr lamfn ma` sìlen`n quìlfima idmd ukn, rnmadmn pnr ukd sarfa ma puktns, qua raprasaktdk `ns a`aitrnkas mvd`akifd.
Akdia quìlfinQkfmdm 1. @ns inlpuastns Yasfùk
1
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@ns ak`dias sa crdbfidk pnr lamfn ma `ìkads, dsì:
Uac`d ma` nitatn
Inln sa vfn ak `d sasfùk =, `ns cdsas kne`as sa ``dldk dsì maefmn d su edjd radit
mdm quìlfid. ]dlefæk sa lakifnkù qua asta inlpnrtdlfaktn sa maea d qua tnm`ns cdsas kne`as tfakak nihn a`aitrnkas ak su ú`tfln kfva` ma akarcìd y qua pnr asnk d`tdlakta astde`as, d` puktn ma kn radiifùk.
_uas asta bakùlakn kn as sù`n pdrtfiu`dr d `ns cdsas kne`as, sfkn d idsf tnmns ätnlns ak uk inlpuastn. Yuiama qua ns ätnlns sa ukak d ntrns ätnlns, idptdkmiamfakmn n inlpdrtfakmn a`aitrnkas, ink a` nejatfvn ma inlp`atdr nihn a`aitrnkak su ú`tfln kfva` ma akarcìd, td` inln niurra ink `ns cdsas kne`as. Astn hdia q`ns inlpuastns bnrldmns sadk astde`as7 pnr a``n, `ns inlpuastns radiifnkdk prasakifd ma ntrns, parn rdrd vaz `n hdiak sf astäk sn`ns.
Mfihd astdef`fmdm sa `ncrd iudkmn `ns suekfva`as s y p sa ``akdk pnr inlp`atn maifr, ink 8 a`aitrnkas, td` inln ak ns cdsas kne`as). D asta bakùlakn sa a inkninln `d Uac`d ma` nitatn.
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kn tfakak mns kfva`as ma akarcìd y sù`n `as ideak mns a`aitrnkas ak tntd`, inln hfmrùcakn y a` ha`fn7 n pnr a` inktrdrfn, tfakak tdktns kfva`as ma akarcìd, qua tfakaaxiasn ma aspdifn `fera, qua puama sar niupdmn pnr läs ma 8 a`aitrnkas, inln aa` idsn ma` bùsbnrn.
Ak`dia quìlfin
@ns ätnlns ak su astdmn kautrn inktfakak a` lfsln kúlarn ma a`aitrnkas y mprntnkas. @ns a`aitrnkas ma vd`akifd ma uk ätnln matarlfkdmn tfakak d idpdifmdma bnrldr pdrta ma ntrns ätnlns, iudkmn snk iamfmns, idptdmns n inlpdrtfmns. Aspdrtfiu`drfmdm parlfta qua ukns ätnlns puamdk ukfrsa d ntrns pdrd bnrldr kuavsustdkifds ink idrditarìstfids mfbaraktas d `ds ma `ns ätnlns qua `d bnrldk, y assustdkifds sa maknlfkdk inlpuastns.
@d vd`akifd ma uk ätnln ak uk a`alaktn, as `d idrcd a`æitrfid qua tfaka asa ätnlak bnrld ma fnk, n `d idpdifmdm qua tfaka a` ätnln pdrd inlefkdrsa ink ntrn.Murdkta a` prniasn ma inlefkdifùk, `ns ätnlns qua fktarditúdk cdkdk, pfarmakinlpdrtak a`aitrnkas ink a` bfk ma iulp`fr ink `d rac`d ma` nitatn y d`idkzdr dsì sastdef`fmdm.
Aktnkias, `ns ak`dias quìlfins snk a` rasu`tdmn ma `d fktardiifùk ma `ns a`aitrnka
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Axfstak tras bnrlds ma astdef`fzdr lamfdkta ak`dias d idpd ma vd`akifd ma uk ätnl
4. Ak`dia fùkfin.5. Ak`dia invd`akta.
9. Ak`dia latä`fin.
4. AK@DIA FÙKFIN
As uk ak`dia qua rasu`td ma `ds fktardiifnkas a`aitrnstätfids aktra fnkas ma idnpuastd ak uk inlpuastn.
_nr ajalp`n, `d sd` inlúk n sd` ma lasd (i`nrurn ma snmfn, KdI`), as uk inlpuafùkfin, qua sa bnrld iudkmn a` snmfn, d` iamar su a`aitrùk ma vd`akifd sa inkvfaak a` fnk snmfn (Kd+), iuyd vd`akifd as +4. A` i`nrn, puama diaptdr uk a`aitrùk ia` bfk ma d`idkzdr `d inkbfcurdifùk ma cds kne`a ak su ú`tfln kfva` akarcætfin, y bnrldr a` fnk i`nrn (I`-), iuyd vd`akifd as -4.
5. AK@DIA INRD@AK]A
Iudkmn uk ätnln inlpdrta a`aitrnkas ink ntrn, ink a` bfk ma inlp`atdr `d inkcurdifùk ma cds kne`a ak su ú`tfln kfva` akarcætfin, sa prasaktd uk ak`dia ma tfinvd`akta. A` ak`dia invd`akta puama sar ma vdrfns tfpns, mapakmfakmn ma` kúlama pdras ma a`aitrnkas prasaktas ak a` ak`dia: asta tfpn ma ak`dia as braiuakta aka`alaktns a`aitrnkacdtfvns, qua snk kdturd`lakta idptdmnras ma a`aitrnkas.
Kd.
+ I`¨:¨ .Kd
+
+ I`¨: :
-
¨4Y5 5Y
55_
2 9Y
4 4Y
5 5Y
55_
2 9Y
5 9_
14Y
5 5Y
55_
2 9Y
? 4Y
5 5Y
55_
2 9Y
5 9_
2
Aktra a` snmfn y a` i`nrn sa prasaktd dtrdiifùk a`aitrnstätfid, `n
qua `as parlfta astdr juktns, pnr lamfn ma` ak`dia fùkfin.
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Qk ajalp`n ma ak`dia invd`akta as a` qua axfsta aktra mns ätnlns ma hfmrùcakpdrd bnrldr `d ln`æiu`d H5.:
Ätnlns ma hfmrùcakn inkstdktas
Ätnln ma H Ätnln ma H
Ln`aiu`d ma H5
Ntrn ak`dia invd`akta sa md ak a` atakn, qua as uk inlpuastn nrcäkfin, qua sbnrld murdkta a` trdtdlfaktn ma` patrù`an. Astä bnrldmn pnr mns ätnlns ma idrenky iudtrn hfmrùcakns. Iùln a` idrenkn tfaka vd`akifd iudtrn, bnrld iudtrn ak`diay, dkta `d pnid idktfmdm ma hfmrùcakn, maea ukfrsa d` idrenkn, pnr lamfn ma mnpdras ma a`aitrnkas, ink uk ak`dia invd`akta mne`a, inln sa va ak `d fldcak.
_arn a` idrenkn tdlefæk puama ukfrsa tras vaias d ntrn ätnln ma idrenkn, alp`admn tras pdras ma a`aitrnkas. @n lfsln niurra ak a` idsn ma` kftrùcakn.
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A` ak`dia invd`akta tfaka uk idsn aspaifd`, y sa prasaktd iudkmn ak a` ak`dia sùuk ätnln dpnrtd `ns mns a`aitrnkas. Uaiuærmasa qua sfalpra halns hde`dmn
mns ätnlns inlpdrtfakmn a`aitrnkas, y qua idmd ukn in`nid a`aitrnkas, bnrldk`ds pdrajds. Ak asta idsn, sù`n uk ätnln `n hdia. D asta ak`dia sa `a inknia inkknlera ma ak`dia invd`akta innrmfkdmn.
Mapakmfakmn ma `d a`aitrnkacdtfvfmdm ma `ns ätnlns fkvn`uirdmns ak a` ak`d
invd`akta, æsta sa puama i`dsfbfidr ma mns bnrlds:
d. Ak`dia invd`akta dpn`dr: iudkmn `ds a`aitrnkacdtfvfmdmas ma `ns mns ätnlsnk fcud`as, inln ak a` idsn ma `d ln`æiu`d ma hfmrùcakn (H5).
e. Ak`dia invd`akta pn`dr: iudkmn ds a`aitrnkacdtfvfmdmas ma ns mns ätnlns smfbaraktas. _nr ajalp`n ak a` dcud, a` nxìcakn tfaka a`aitrnkacdtfvfmdm 9.1, lfaktqua a` hfmrùcakn as 5.4.
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9. AK@DIA LA]Ä@FIN
Ya prasaktd ak `ns latd`as y sus d`adifnkas. @ns latd`as sa idrditarfzdk pnr pnsaastruiturds trfmflaksfnkd`as ak su nrcdkfzdifùk, qua parlfta qua `ns a`aitrnkaxtarfnras quamak `feras y puamdk lnvarsa, ldktakfakmn `d astruiturd ukfmd.
Fmaktfbfidifùk ma` tfpn ma ak`dia
A` qua uk ak`dia sad fùkfin n invd`akta mapakma mfraitdlakta ma `d a`aitrnkacdtvfmdm ma `ns ätnlns ma uk inlpuastn. Dsì, ak uk ak`dia fùkfin pdrtfifpd uk ätnla`aitrnpnsftfvn, ink ukn a`aitrnkacdtfvn, pnr n qua a` sacukmn dtrda ink läs akarcd ns a`aitrnkas ma` prflarn, quftäkmn`a pnr inlp`atn a` n ns a`aitrnkas kaiasdrfn
pdrd inlp`atdr a` nitatn.
Ak a` idsn ma ns ak`dias invd`aktas, sa tfakak ätnlns a`aitrnkacdtfvns, qua d` takakarcìds sflf`dras sù`n puamak inlpdrtfr `ns a`aitrnkas.
_drd matarlfkdr kulærfidlakta a` tfpn ma ak`dia sa tfakak ak iuaktd ns sfcufaktpdrälatrns:
d. Invd`akta dpn`dr: iudkmn d mfbarakifd ma a`aitrnkacdtfvfmdmas as fcud` d iar
e. Invd`akta pn`dr: iudkmn `d rastd ma a`aitrnkacdtfvfmdmas as suparfnr d iarn,fkbarfnr n fcud` d 4.3.
i. Fùkfin: iudkmn `d mfbarakifd ma a`aitrnkacdtfvfmdmas as suparfnr d 4.8.
Ak `ns sfc`ns XRFFF y XFX, `ns ifaktìbfins alpazdrnk d masiuerfr `d astraihd ra`difùqua axfsta aktra mns bakùlakns dpdraktalakta mas`fcdmns: `d inrrfakta a`æitrfiy `ds radiifnkas quìlfids. Dsì sa nrfcfkù `d a`aitrnquìlfid, mfsifp`fkd qua astumiùln a` pdsn ma `d a`aitrfifmdm cakard kuavds sustdkifds quìlfids y d`cukds radifnkas puamak masprakmar akarcìd ak bnrld ma inrrfakta a`æitrfid. Astns prniasnraifeak a` knlera ma a`aitrnquìlfins.
Iudkmn a` prniasn sa rad`fzd lamfdkta d fktarvakifùk ma d a`aitrfifmdm, sa maknlfk
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ma uk inlpuastn fùkfin bukmfmn n ma ukd sn`uifùk ma uk a`aitrn`ftn, y iudkmnrad`fzd ak mfspnsftfvns inknifmns inln ia`mds a`aitrn`ìtfids. @d ia`md a`aitrn`ìtfisu vaz inkstd ma uk raifpfakta ak a` qua sa in`nid a` a`aitrn`ftn, qua as `d sustdkqua sa vd d a`aitrn`fzdr y maktrn ma` iud` sa sularcak mns inkmuitnras a`æitrfiqua raifeak a` knlera ma a`aitrnmns, inkaitdmns d ukd buakta ma inrrfakta mfraipnr ajalp`n, ukd pf`d.
@d a`aitrù`fsfs as uk prniasn d trdvæs ma` iud` ukd inrrfakta a`æitrfid prnmuia idlefn quìlfin kn aspnktäkan. A` mfspnsftfvn ak mnkma sa rad`fzd mfihd radiifsa maknlfkd ia`md a`aitrn`ìtfid.
Qkd ia`md a`aitrn`ìtfid inkstd ma mns a`aitrnmns inkaitdmns d ukd buakta ma i
rrfakta mfraitd qua puama sar ukd pf`d n edtarìd y d su vaz æstns astäk fklarsns uk a`aitrn`ftn.
@d pf`d n edtarìd, ditúd inln ukd enled ma a`aitrnkas qua ns luava ma uk a`aitrnhdstd a` ntrn. A` äknmn a quftd a`aitrnkas, pnr a``n æsta quamd ink idrcd pnsftfvd7 a`aitrnkas snk akvfdmns hdstd a` iätnmn, qua d` raifefr`ns quamd ink idrcd kacdtf
@ds ia`mds a`aitrn`ìtfids sa utf`fzdk ink braiuakifd pdrd raiuerfr uk nejatn ink
latd`. Asta prniasn sa maknlfkd a`aitrnmapnsfifùk, y sa utf`fzd pdrd raiuerfr nejaink latd`as inln a` nrn, `d p`dtd, a` irnln, a` kìqua`, ati.
@d a`aitrnmapnsfifùk sa utf`fzd ink mfbaraktas prnpùsftns ak jnyarìd, pdrd raiuepfazds ma inera n astdôn ink nrn n p`dtd, lajnrdkmn dsì su dspaitn y murdifùk.
Ak d fkmustrfd sa raiuera uk latd` ink ntrn läs rasfstakta d d inrrnsfùk, pnr ajalpa` cd`vdkfzdmn y a` irnldmn. A` cd`vdkfzdmn sa utf`fzd pdrd prntacar älfkds ma diai`dvns y ntrns nejatns ma hfarrn inktrd `d inrrnsfùk. Inksfsta ak raiuerfr idmd nejaink ukd idpd ma zfki pnr lamfn ma a`aitrnmapnsfifùk7 a` ldtarfd` d` nxfmdrsa bnrlukd pa`ìiu`d dmharakta qua `n prntaca ma ukd ldynr inrrnsfùk.
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¡Rdlns d` `denrdtnrfn d inlprnedr `ns ak`dias ak `d ldtarfd!
4. Ldrqua 3 vdsns ma praifpftdmns y dôdmd pnr sapdrdmn ds sfcufaktas sustdkifddcud, dzúidr mfsua`tn ak dcud, sd` mfsua`td ak dcud, atdkn` mfsua`tn, jucn mkdrdkjd, matarcakta ak pn`vn mfsua`tn ak dcud y `aiha.
5. In`nqua mns ide`as d uk enlef``n paquaôn n `am. Dki`a ukn ma `ns axtraln`feras, ma iud`qufard ma `ns mns ide`as d ukd pf`d ma 6 vn`tfns.
9. ]nla `d pf`d ma 6 vn`tfns y in`nqua ntrn ide`a ma`cdmn ak a` pn`n `fera.
=. Fktrnmuzid a` axtraln `fera ma` d`dlera inkaitdmn d d pf`d, maktrn ma` prflvdsn ma praifpftdmns, cdrdktfzdkmn qua tnqua a` `ìqufmn, lds kn a` bnkmn mvdsn.
1. Nesarva `n qua suiama y rapftd a` prniamflfaktn ink tnmds `ds sustdkifdtnldkmn kntd ma sus nesarvdifnkas ak `d sfcufakta tde`d:
YQY]DKIFD NEYAURDIFÙK
Dcud
Dzúidr
4
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YQY]DKIFD NEYAURDIFÙK
Yd`
Atdkn`
Kdrdkjd
Matarcakta
@aiha
2. Uapftd a` prniamflfaktn ink `ds sustdkifds qua ustam masaa.
3. Axp`fqua pnr quæ a` enlef``n sa akifakma ink ukds sustdkifds y ink ntrds k
8. In`nqua sd` aspdrifmd ak ukd hnjd e`dkid y in`nqua `ns d`dleras `feras mapf`d snera a``d. Dknta `n qua niurra. Maspuæs, ink dyumd ma `d ldkn, midar cntds ma dcud snera a` pdpa` ink `d sd`, hdstd qua `d hnjd quama húlay in`nqua kuavdlakta `ns d`dleras ma `d pf`d ¾Tuæ suiama> Axp`fqua
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4. Matarlfka `ds astruiturds ma @awfs y a` tfpn ma ak`dias qua hdy ak ds sfcufaktaln`æiu`ds: HI`, @fB, H5YN=, IdN y H5N.
Uaspnkmd `ds pracuktds 5 y 9 ink edsa ak `d sfcufakta tde`d:
#a- #p+ #a-vd`akifd A`aitrnkacdtfvfmdm
X 2 2 = 5.1
V 8 8 2 9.1
S 45 45 5 4.5
5. Ma diuarmn ink `d tde`d, `d astruiturd ma @awfs pdrd a` inlpuastn XV5 as:
d. :V: :X: :V:e.i.m.
9. A` ak`dia prasakta ak a` inlpuastn ma i`dsfbfid inln:
d. Fùkfine. Invd`aktai. Invd`akta pn`drm. Latä`fin
1
:V: :X: :V:¨
:V: :X: :V:
.
.
.
.
:V: :X: :V:¨
¨ ¨
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]ùlasa ukns lfkutns pdrd paksdr mabnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:
¾Tuæ as uk a`alaktn>
¾Tuæ as uk inlpuastn>
¾]faka d`cukd fmad snera iuäktns tfpns ma inlpuastns fknrcäkfins hdy>
¾Iùln sa i`dsfbfidk>
¾Iùln sa knlerdk>
¾_nr quæ as flpnrtdkta mfbarakifdr`ns y knlerdr`ns>
INL_QAY]NY
Ak d kdturd`azd axfstak luihds sustdkifds7 pdrd pnmar astumfdr`ds y mfbarakifdr`ds`d quìlfid ds hd i`dsfbfidmn ak mns crdkmas crupns: inlpuastns nrcäkfins, inrraspnkmfaktas d tnmns dqua``ns ak `ns qua a` ätnln ma idrenkn pramnlfkd ak suastruiturds quìlfids y ns inlpuastns fknrcäkfins, qua snk tnmns dqua``ns qua smdk inln rasu`tdmn ma `ds mfbaraktas fktardiifnkas aktra tnmns `ns a`alaktns m
Astdmns ma nxfmdifùk
Inlpuastns y knlaki`dturd fknrcäkfid
Qkfmdm 1. @ns inlpuastns Yasfùk
2
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INL_QAY]NY FKNUCÄKFINY
Ùxfmns
Äifmns Eäsfins Hfmräifnmns Nxäifmns Hd`ùcakds Nxfsd`as
Yd`as HfmrurnsHfmrùxfmns Äifmns
I`dsfbfidifùk ma `ns inlpuastns fknrcäkfins
4. ÙXFMNY
Ynk a` rasu`tdmn ma `d ukfùk ma iud`qufar a`alaktn ma `d tde`d parfùmfid ink nxìcakn y sa i`dsfbfidk ak mns crdkmas crupns:
Ùxfmns eäsfins: sa bnrldk pnr `d ukfùk ma uk a`alaktn latä`fin ink a` nxìcaknsa ``dldk dsì pnrqua d` radiifnkdr ink dcud, bnrldk hfmrùxfmns. Ajalp`ns: • BaN • Ba5N9
• Ds5N9 • Ds5N1
• IdN • EaN • LcN • EdN
Ùxfmns äifmns: astäk inkbnrldmns pnr a`alaktns kn latä`fins, ak`dzdmns d` nxcakn. Ya ``dldk dsì, yd qua ak dcud radiifnkdk pdrd bnrldr äifmns.
Ajalp`ns: • I`5N • I`5N9
• I`5N1 • I`5N3
• KN5 • IN5
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5. HFMUÙXFMNY
Ynk inlpuastns rasu`tdktas ma `d radiifùk qua sa prnmuia aktra uk ùxfmn eäsfina` dcud. Ya idrditarfzdk pnrqua sa mfsnifdk ak sn`uifùk ak diunsd fnkas hfmrnx
y a` pdpa` tnrkdsn` rnsdmn `n idlefdk d in`nr dzu`. _drd knlerdr `ns hfmrùxfmtakalns ak iuaktd `ns tfpns ma knlaki`dturd. Ajalp`n:
Knlaki`dturdsfstalätfid
Hfmrùxfmnma snmfn
]rfhfmrùxfmnma d`ulfkfn
Mfhfmrùxfmn ma hfarrn
Hfmrùxfmn ma inera
Bùrlu`d
KdNH
D`(NH)9
Ba(NH)5
IuNH
Knlaki`dturdtrdmfifnkd`
Hfmrùxfmnma snmfn
Hfmrùxfmnma d`ulfkfn
Hfmrùxfmn barrnsn
Hfmrùxfmn iuprnsn
Knlaki`dturdYtnig
Hfmrùxfmn ma snmfn
Hfmrùxfmnma d`ulfkfn
Hfmrùxfmnma hfarrn (FF)
Hfmrùxfmn
ma inera (F)
9. ÄIFMNY
Ynk sustdkifds qua d` mfsn`varsa ak dcud prnmuiak fnkas pnsftfvns ma hfmrùca(hfmrncakfnkas). @ns äifmns akrnjaiak a` pdpa` ma tnrkdsn` y d` aktrdr ak radiifink `ns hfmrùxfmns prnmuiak `ds sd`as.Astäk inkstftufmns pnr a` hfmrncakfùk, qua as a` idtfùk n fùk pnsftfvn ma` hfmrùca(H+4) y uk kn latd`. Mapakmfakmn ma` tfpn ma äifmn tdlefæk puamak inktaknxìcakn.
Ya i`dsfbfidk ak mns crupns:
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Äifmns hfmräifmns: inkstftufmns sù`n pnr hfmrncakfnkas y kn latd`as.
Ajalp`n:
Bùrlu`d Knlera quìlfin
• HI` Äifmn i`nrhìmrfin
• H5Y Äifmn su`bhìmrfin
• HEr Äifmn ernlhìmrfin
• HIK Äifmn ifdkhìmrfin
Äifmns nxäifmns: inkbnrldmns pnr hfmrncakfùk y a`alaktns kn latä`fins ak`dzdmd su vaz d` nxìcakn.
Bùrlu`d
H5YN=
HKN9
HI`N
H5IN9
HI`N9
H=YfN=
Knlera quìlfin
Äifmn su`búrfin
Äifmn kìtrfin
Äifmn hfpni`nrnsn
Äifmn idreùkfin
Äifmn i`ùrfin
Äifmn sf`ìifin
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Bùrlu`d
KdI`
IdB5
LcF5
GEr
Knlera quìlfin
I`nrurn ma snmfn
B`unrurn ma id`ifn
Vnmurn ma ldckasfn Ernlurn ma pntdsfn
Bùrlu`d
Kd5IN9
IdYN=
KdI`N
Knlera quìlfin
Idrenkdtn ma snmfn
Yu`bdtn ma id`ifn
Hfpni`nrftn ma snmfn
=. YD@AY
@ds sd`as snk sustdkifds bnrldmds pnr d ukfùk ma fnkas pnsftfvns (idtfnkas) ink fnkkacdtfvns (dkfnkas).Ya bnrldk prfkifpd`lakta pnr `d radiifùk ma kautrd`fzdifùk aktra uk äifmn y hfmrùxfmn.@ds sd`as sa i`dsfbfidk ak mns crupns:
Yd`as hd`ùcakds: sa inlpnkak úkfidlakta ma idtfnkas y dkfnkas, ukfmns prfkpd`lakta pnr ak`dias fùkfins.
Ajalp`ns:
Nxfsd`as: bnrldmds fnkas latä`fins ak`dzdmns ink dkfnkas, ns iud`as astäk bnrldmpnr kn latd`as ukfmns d` nxìcakn.
Ajalp`ns:
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Hdy ntrn tfpn ma i`dsfbfidifùk, rabarfmd d` pH ma `ds sd`as:
Yd`as kautrds: snk `ds hd`ùcakds y nxfsd`as. Ya maknlfkdk dsì puastn qua kn inktfakak ak sus astruiturds hfmrncakfnkas n hfmrnxf`ns
Ajalp`ns:
GI`N EdYN= DcKN9 IuKN9
Hfpni`nrftn ma pntdsfn Yu`bdtn ma Edrfn Kftrdtn ma _`dtd Kftrdtn Iuprnsn
IdYN= KdI`N5 EdI`5 BaY
Yu`bdtn ma Id`ifn I`nrftn ma Ynmfn I`nrurn ma Edrfn Yu`burn Barrnsn
Yd`as äifmds: inktfakak hfmrncakfnkas ak su astruiturd.
Ajalp`ns:
Ba5(H_N=)9 Iu(HY)5 @fHIN9
Efbnsbdtn bærrfin Yu`burn difmn iúprfin Efidrenkdtn ma `ftfn
KdHYN= IdH_N= GHIN9
Yu`bdtn difmn ma snmfn Bnsbdtn efiä`ifin Idrenkdtn difmn ma pntdsfn
IdNHI` IuNHKN9
I`nrurn eäsfin ma id`ifn Kftrdtn eäsfin ma inera.
Yd`as eäsfids: Ynk a` rasu`tdmn ma `d sustftuifùk pdrifd` ma `ns (NH) ak uk hfmrùxfmn edsa. Ntrd bnrld ma netakar`ds as a` raalp`dzn pdrifd` ma ns latd`as ma ukd sd` kautr
Ajalp`ns:
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IdErB GKd(YN=)
@ds sd`as tdlefæk puamak sar mne`as, yd qua puamak inktakar mns idtfnkas n dkfnk
1. HFMUQUNY
Ynk inlpuastns qua tdlefæk inktfakak uk fùk ma hfmrùcakn, sù`n qua ak asinlpuastns kn as uk idtfùk, sfkn uk dkfùk (H4-) ``dldmn hfmrurn. Yus astruituinktfakak uk dkfùk y a` hfmrurn.
Ajalp`ns:
AY]DMN MA NXFMDIFÙK
Hdia rabarakifd d d idktfmdm ma a`aitrnkas qua uk ätnln puama iamar n inlpdak uk ak`dia quìlfin.
Maktrn ma `d astruiturd ma `ns inlpuastns sa maea takar ak iuaktd qua a``ns sfapra astäk inkstftufmns pnr ukd pdrta pnsftfvd y ukd kacdtfvd, qua vfaka mdmn pn
ldckftum ma` astdmn ma nxfmdifùk. _nr ajalp`n, ak a` IN5 a` nxìcakn tfaka astdma nxfmdifùk -5, yd qua d` sar läs a`aitrnkacdtfvn qua a` idrenkn, `ns a`aitrnkak`dzdmns snk dtrdìmns ink läs buarzd pnr a` nxìcakn, hdifakmn qua `d idrcd skacdtfvd. Ma dhì qua a` astdmn ma nxfmdifùk ma` idrenkn sad pnsftfvn (+=).
Kùtasa qua d idktfmdm ma idrcds pnsftfvds as ldynr qua ds kacdtfvds, parn sf sa ink läs dtakifùk, varä qua d ln`æiu`d inktfaka mns ätnlns ma nxìcakn y idmd utfaka astdmn ma nxfmdifùk -5, pdrd uk tntd` ma = idrcds kacdtfvds, qua d` suld
Bùrlu`d
KdH
LcH5
Knlera quìlfin
Hfmrurn ma snmfn
Hfmrurn ma ldckasfn
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D `d hnrd ma asirfefr ukd bùrlu`d ln`aiu`dr as flpnrtdkta takar ak iuaktd `ns astmns ma nxfmdifùk, pnrqua d` fcud` qua ak a` ätnln, `ns inlpuastns tdlefæk maeasar kautrns ak iudktn d `d idrcd, ma `n inktrdrfn sa hde`drìd ma fnkas fkmfvfmud`as
_nr astd rdzùk, ns inlpuastns tfakak sueìkmfias kulærfins, qua sa cakardk iudkmsa fcud`dk `ds idrcds, pdrd qua astds sa dku`ak. @ns kúlarns sa astde`aiak edjdkmsù`n `ns vd`nras kulærfins ma `ns astdmns ma nxfmdifùk ma idmd ätnln, ak bnrlma X. Ak a` idsn qua `ns kúlarns sadk lú`tfp`ns aktra sì, sa mfvfmak hdstd qua k`n sadk läs.
Ajalp`n:
Inln `ns kúlarns raifæk fktaridlefdmns snk lú`tfp`ns ma mns, sa mfvfmak hdsqua kn `n sadk läs. Dsì `d bùrlu`d bfkd`lakta quamd inln:
]akfakmn ak iuaktd `ns astdmns ma nxfmdifùk sa astde`aia qua:
Idrenkn += X 4 < +=
Nxìcakn -5 X 5 < -=
D` suldr a` kúlarn ma idrcds pnsftfvds ink `ds kacdtfvds sa tfaka:
-= + = < ?
Astn qufara maifr qua `d ln`æiu`d prasaktd idrcd a`æitrfid kautrd.
I5
+=
?=-5
I5
+=?-5 I?5<
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UAC@DY EÄYFIDY _DUD DYFCKDU @NY AY]DMNY MA NXFMDIFÙK:
• @ns a`alaktns feras n ln`aiu`dras tfakak astdmn ma nxfmdifùk iarn
• A` hfmrùcakn tfaka astdmn ma nxfmdifùk +4, axiaptn ak `nshfmrurns, mnkma trdedjd ink -4.
• A` nxìcakn tfaka astdmn ma nxfmdifùk -5, axiaptn ak `nsparùxfmns, mnkma su astdmn ma nxfmdifùk as -4.
• A` B`únr sfalpra tfaka astdmn ma nxfmdifùk -4.
• @ns a`alaktns ma` crupn FD tfakak astdmn ma nxfmdifùk +4.
• @ns a`alaktns ma` crupn FFD tfakak astdmn sa nxfmdifùk +9.
• @ns a`alaktns ma` crupn FFFD tfakak astdmn ma nxfmdifùk +9.
• @ns a`alaktns ma` crupn FRD tfakak astdmns ma nxfmdifùk
+/- 5 y =.
• @ns a`alaktns ma crupn RD tfakak astdmns ma nxfmdifùk+/- 5, 9, = y 1.
• @ns a`alaktns ma` crupn RFD tfakak astdmns ma nxfmdifùk+/-5, = y 2.
• @ns a`alaktns ma` crupn RFFD tfakak astdmns ma nxfmdifùk+/- 4, 9, 1 y 3
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• GLkN=: A` G as +4 yd qua su crupn as FD. A` N as -5 yd qua as a` läs a`ai-trnkacdtfvn7 lfaktrds tdktn d` Lk `a inrraspnkma +3. @d suld
d`caerdfid sarä +4+3+(-5)= < +4+3-8<?.
• H5N5: A` N sarä kacdtfvn pnr sar a` läs a`aitrnkacdtfvn, parn sarä -4 ydqua axfsta uk ak`dia aktra `ns nxìcakns. D` H `a inrraspnkma +4sacúk `d suld (+4)5 + (-4)5 < ?.
• @fH: Idsn ak a` iud` a` H pnr sar läs a`aitrnkacdtfvn qua a` latd`,
prasaktdrä astdmn ma nxfmdifùk ma -4 y a` @f +4.
• BaI`9: A` I` as -4 pnr sar läs a`aitrnkacdtfvn y a` Ba as +9 d` astde`aiar`d suld (-4)9 + 9 < ?. Edjn ntrds inkmfifnkas a` Ba sarä +5 ink`d bùrlu`d BaI`5.
Ajalp`ns:
KNLAKI@D]QUD FKNUCÄKFID
Inln sa hd lakifnkdmn ak sasfnkas dktarfnras, `d crdk idktfmdm ma kuavns inlpuastns sfktatfzdmns n akinktrdmns ak `d d`quflfd bnrzù d `d inlukfmdm quìlfid i`dsfbfidr`ns y ukfbfidr kn sù`n `ds bùrlu`ds ln`aiu`dras, sfkn tdlefæk a` sfstalpdrd knlerdr`ns.
Ditud`lakta sa iuaktd ink tras sfstalds ma knlaki`dturd: sfstalätfid, stnig y trmfifnkd` n FQ_DI, sfakmn astd u`tfld `d läs usdmd.
_drd knlerdr uk inlpuastn sa tfaka ak iuaktd d bukifùk quìlfid7 dsì, tnmns ns ùxmns fkfifdk ink d pd`derd ùxfmn, ns äifmns ink äifmn y ns hfmrùxfmns ink hfmrùxfm
4. Knlaki`dturd sfstalätfid: makntd `d idktfmdm ma ätnlns prasaktas ak `ln`æiu`ds, dktapnkfakmn prabfjns ma idktfmdm d` knlera ma `ns ätnlns.
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@ns prabfjns snk:
• Qkn: lnkn.• Mns: mf.• ]ras: trf.• Iudtrn: tatrd.• Ifkin: paktd.• Yafs: haxd.
Yf ak `d bùrlu`d sù`n hdy uk ätnln ma` prflar a`alaktn, a` prabfjn lnkn kn sa u_nr ajalp`n a` IN5 sa ``dld mfùxfmn ma idrenkn.
Iudkmn ak d astruiturd sù`n dpdraiak pnr idmd a`alaktn uk sn`n ätnln kn sa us`ns prabfjns. Ajalp`n: IdN, ùxfmn ma id`ifn7 KdNH, hfmrùxfmn ma snmfn.
Ajalp`ns:
• _5N1: _paktùxfmn ma mfbùsbnrn.• D`(NH)9: trfhfmrùxfmn ma d`ulfkfn.• LcN: ùxfmn ma ldckasfn.
• I`5N: lnkùxfmn ma mfi`nrn.• Ba(NH)5: mfhfmrùxfmn ma hfarrn.
5. Knlaki`dturd stnig: astd knlaki`dturd md rdzùk ma d bukifùk quìlfid y astdmn ma nxfmdifùk ma` a`alaktn qua `n dinlpdôd.
Iudkmn sa usd astd knlaki`dturd, sa fkfifd ink a` knlera ma `d bukifùk quìlma` inlpuastn, sacufmn pnr a` knlera ma` a`alaktn ak`dzdmn d` crupn bukifnkasirfefakmn aktra pdræktasfs ak kúlarns rnldkns su astdmn ma nxfmdifùk.
Ajalp`ns:
• Ba(NH)5: hfmrùxfmn ma hfarrn (FF).• Du5N9: ùxfmn ma nrn (FFF).
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Iudkmn a` astdmn ma nxfmdifùk as +4 kn sa asirfea.
9. Knlaki`dturd trdmfifnkd` n FQ_DI: as a` sfstald ma knlaki`dturd ukfvarsdprnpuastd pnr `d Qkfùk Fktarkdifnkd` ma Tuìlfid _urd y Dp`fidmd.
Fkfifd ink a` knlera ma `d bukifùk quìlfid (ùxfmn, hfmrùxfmn n äifmn), sacufmn mknlera ma` a`alaktn dinlpdôdkta a` iud`, mapakmfakmn ma su astdmn ma nxfmifùk, tarlfkd ak nsn n fin.
Uac`ds FQ_DIYa edsdk ak `d idktfmdm ma astdmns ma nxfmdifùk qua puamd takar uk ätnln:
4. Idsn 4: a` a`alaktn tfaka uk úkfin astdmn ma nxfmdifùk.]arlfkdk ak fin. Ajalp`n: LcN, ùxfmn ldckæsfin.
5. Idsn 5: a` a`alaktn tfaka mns astdmns ma nxfmdifùk. Iudkmn a` ätnln tfaka a` astdmn ma nxfmdifùk läs paquaôn sa asirfea ink
tarlfkdifùk nsn7 ak a` ntrn idsn ink tarlfkdifùk fin. Ajalp`ns:BaN, ùxfmn barrnsn y Ba5N9, ùxfmn bærrfin.
9. Idsn 9: tras astdmns ma nxfmdifùk. Ak a` idsn qua sa trdedjaink a` astdmn ma nxfmdifùk ma vd`nr läs paquaôn, sa in`nida` prabfjn hfpn dktas ma` knlera ma` a`alaktn tarlfkdmn ak
nsn. A` sfcufakta vd`nr tfaka tarlfkdifùk nsn y a` läs d`tn fin.Ajalp`ns: YN, ùxfmn hfpnsu`burnsn7 YN5, ùxfmn su`burnsn y YN9,ùxfmn su`búrfin.
=. Idsn =: iudtrn astdmns ma nxfmdifùk. Fcud` qua ak a` idsndktarfnr, parn a` läs crdkma tfaka prabfjn par. Ajalp`ns:I`5N, ùxfmn hfpni`nrnsn7 I`5N9, ùxfmn i`nrnsn7 I`5N1, ùxfmni`ùrfin y I`5N3, ùxfmn pari`ùrfin.
1. Idsn 1: fcud` qua a` idsn =, parn a` astdmn ma nxfmdifùk ldynr tfaka a` prabfjn hfpar. Ajalp`ns: UuN, ùxfmn hfpnrutakfnsn7
Uu5N9, ùxfmn rutakfnsn7 UuN5, ùxfmn rutækfin7 UuN9, ùxfmn
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Knlaki`dturd ma ùxfmns: sfalpra fkfifd ink `d pd`derd ùxfmn y, mapakmfakmn sfstald ma knlaki`dturd, sa asirfea a` a`alaktn ak`dzdmn d æ`.
Ajalp`n:
Knlaki`dturd ma hfmrùxfmns: dp`fid ma fcud` bnrld qua ak `ns ùxfmns.
Ajalp`n:
Knlaki`dturd ma äifmns: mapakma ma` tfpn ma äifmn, dsì:
Hfmräifmns: fkfifdk ink `d pd`derd äifmn, sacufmn ma` knlera ma` kn latd` itarlfkdifùk hìmrfin.
Kd5N Lnkùxfmn ma mfsnmfn Ùxfmn ma snmfn Ùxfmn sùmfin
Ir5N9 ]rfùxfinma mnirnln Ùxfmn ma irnln (FFF) Ùxfmn irnlnsn
LnN9 ]rfùxfmn ma ln`femakn Ùxfmn ma ln`femakn (RF) Ùxfmn hfparln`femækfin
_5N9 ]rfùxfmn ma mfbùsbnrd Ùxfmn ma bùsbnrd (FFF) Ùxfmn hfpnbnsbnrnsn
I`5N3 Haptdùxfmn ma mfi`nrn Ùxfmn ma i`nrn (RFF) Ùxfmn pari`ùrfin
KdNH Hfmrùxfmn ma snmfn Hfmrùxfmn ma snmfn Hfmrùxfmn sùmfin
Ba (NH)9 ]rfhfmrùxfmn ma hfarrn (FFF) ]rfhfmrùxfmn ma hfarrn (FFF) Hfmrùxfmn bærrfin
DuNH Hfmrùxfmn ma nrn Hfmrùxfmn ma nrn Hfmrùxfmn durnsn
Hc(NH)5 Mfhfmrùxfmn ma lariurfn Hfmrùxfmn ma lariurfn (FFF) Hfmrùxfmn ma lariurfn
Id(NH)5 Mfhfmrùxfmn ma id`ifn Hfmrùxfmn ma id`ifn Hfmrùxfmn ma id`ifn
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INL_QAY]N KNLEUA
HI` Äifmn i`nrhìmrfin
H5Y Äifmn su`bhìmrfin
HF Äifmn ynmhìmrfin
HEr Äifmn ernlhìmrfin
HB Äifmn b`unrhìmrfin
INL_QAY]N KNLEUA
H5YN= Äifmn su`búrfin
H5YN9 Äifmn su`burnsn
HI`N= Äifmn pari`ùrfin
HKN9 Äifmn kìtrfin
H9_N= Äifmn bnsbùrfin
Ajalp`ns:
Nxäifmns: fkfifdk ink `d pd`derd äifmn, sacufmn ma` knlera ma` kn latd`, ink sinrraspnkmfakta FQ_DI (a` astdmn ma nxfmdifùk qua sa tfaka ak iuaktd ak asta idsak a` ma` kn latd`).
Ajalp`ns:
Knlaki`dturd ma sd`as: d` fcud` qua ak `ns äifmns, mapakma ma` tfpn ma sd`.
Hd`ùcakds: fkfifdk ink a` knlera ma` a`alaktn kn latä`fin tarlfkdmn ak urn
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INL_QAY]N KNLEUA
KdI` I`nrurn sùmfin
G 5Y Yu`burn pntäsfin
BaF5 Vnmurn barrnsn
IrEr5 Ernlurn hfpnirnlnsn
_eB= B`unrurn p`úlefin
INL_QAY]N KNLEUA
GI`N= _ari`nrdtn pntäsfin
KdI`N Hfpni`nrftn sùmfin
]f5(YN=)9 Yu`bdtn tftdkfnsn
Ba5(IN9)9 Idrenkdtn bærrfin
_e(KN9)5 Kftrdtn p`ulensn
Ajalp`ns:
Nxfsd`as: sa mfvfmak ak mns saiifnkas y d `d FQ_DI dp`fid d `ds mns.
@d knlaki`dturd fkfifd knlerdkmn d` dkfùk, inkbnrldmn pnr a` kn latd` y a` ncakn. @d FQ_DI mapakma ma` astdmn ma nxfmdifùk ma` kn latd`, ink uk paquaidlefn. A` subfjn nsn sa idlefd pnr ftn y a` subfjn fin pnr dtn.
Qkd vaz knlerdmn a` idtfùk, sa inktfkúd ink a` idtfùk, as maifr ink a` latd`, iuFQ_DI kn sa lnmfbfid kukid.
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4
4. Iruia a` fùk ma `d bf`d ink a` ma `d in`ulkd y asirfed ak a` aspdifn inrraspnmfakta d` iruia, `d bnrlu`d rasu`tdkta.
Idtfùk Dkfùk
Lc +5
D`+9
_e+=
Kd+4
N-5 Er-9 (IN9)-5 (_N=)
-9
5. Fmaktfbfqua `d bukifùk quìlfid fknrcäkfid (nxfmn eäsfin n äifmn, hfmräifmnxäifmn, sd` efkdrfd y nxfsd`) y inrraspnkmfakta ma `ns sfcufaktas inlpuastnsastde`azid `d knlaki`dturd ma `ns lfslns.
Inlpuastn Bukifùk quìlfid fknrcäkfid Knlaki`dturd
K5N1
YaI`=
InYN=
HcNH
HEr
H9_N=
KdHYN=
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9. Asirfed d` brakta `d bùrlu`d pdrd idmd ukn ma `ns sfcufaktas inlpuastns:
d. Ùxfmn Barrnsn
e. I`nrurn ]ä`fin
i. Bnsbftn ma Id`ifn
m. _arynmdtn ma Cd`fn
a. B`unrurn ma _ntdsfn
b. Idrenkdtn ma Ldckasfn
c. Mfùxfmn ma Ldkcdkasn
h. Hfmrùxfmn Carläkfin
=. Asirfed a` knlera pdrd idmd ukn ma `ns sfcufaktas inlpuastns: (puama uiud`qufar tfpn ma sfstald):
d. KN5
e. H5YN=
i. Iu(NH)5
m. HKN9
a. HEr
b. GI`N9
c. LcI`5
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]ùlasa ukns lfkutns pdrd paksdr ma bnrldfkmfvfmud` snera `ds sfcufaktas pracuktds:
Iudkmn uk bùsbnrn sa akifakma, ¾ustam inlprakma iùln suiama>
@ds pf`ds ma `ns ia`u`dras maeak idrcdrsa inktfkudlakta7 ¾pnr quæ>
@d ldmard sa quald läs maspdifn qua a` pdpa`7 ¾d quæ sa maea>
¾As fcud` qualdr pdpa` qua iakfzd> ¾As pnsfe`a qua d pdrtfr ma `ds iakfzds pua-md ustam vn`var d hdiar `d hnjd ma pdpa`>
Ak `d d`quflfd sa iraìd qua a` dcud astded inlpuastd pnr tfarrd. ]d` iraakifd ard`flaktdmd pnr ns rasu`tdmns ma ns axparflaktns ma d`cukns ifaktìbfins. A``ns sn`ìdharvfr dcud ak raifpfaktas ma vfmrfn, pnr läs ma 4?? mìds. D` tærlfkn ma asa tfalpsa pnmìd dpraifdr ak a` bnkmn ma` raifpfakta uk praifpftdmn (as maifr ukd sustdkisù`fmd) inrraspnkmfakta d drakd.
Ink a` usn ma d ed`dkzd, Dktnfka @dvnfsfar hfzn läs rfcurnsn a` prniasn, puastn qudktas y maspuæs ma prniamar, lfmfù `d ldsd ma` raifpfakta y ma` dcud pnr sapdrdm
Uadiifnkas quìlfids
AstaqufnlatrìdQkfmdm 2. Uadiifnkas quìlfids Yasfùk
3
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tdmn, ink ukd paquaôd vdrfdifùk: `d ldsd ma `d drakd bnrldmd ard aqufvd`akta dldsd parmfmd pnr a` raifpfakta. Astn fkmfiù qua a` dcud, maspuæs ma tdktns mìds inktfkud aeu``fifùk, drrdstrded ink su pdsn pdrta ma` ldtarfd` inkstftuyakta ma` rapfakta, qua kn as ntrd insd läs qua drakd (a` vfmrfn sa hdia ink drakd). Dsì, d pdma asta axparflaktn y luihns ntrns, @dvnfsfar prnpnka `d @ay ma `d inksarvdifùma `d ldsd ma a``d kdiak `d quìlfid y `d axp`fidifùk kn sù`n iud`ftdtfvd ma `ns baklakns, sfkn tdlefæk ak tærlfkns iudktftdtfvns.
UADIIFNKAY TQÌLFIDY
Inrraspnkmak d `ns idlefns quìlfins ma `d ldtarfd.
Eäsfidlakta, `ds radiifnkas quìlfids snk `d trdksbnrldifùk ma ukds sustdkifds fifd`as, ``dldmds raditfvns, ak ntrds maknlfkdmds prnmuitns, qua snk ma kdturd`atntd`lakta mfbarakta d `d fkfifd`. A` prniasn lamfdkta a` iud` sa prnmuiak astrdksbnrldifnkas sa inknia inln radiifùk quìlfid.
@ds sustdkifds n a`alaktns raditfvns sa lazi`dk y ihnidk aktra sì, rnlpfakmn ak`dias axfstaktas, feardkmn d ns ätnlns n fnkas, ma lnmn td` qua æstns sa ak`dzkuavdlakta, parn ma bnrld mfbarakta, prnmuifakmn kn sù`n kuavns ak`dias, sfk
ak inksaiuakifd kuavds sustdkifds, as maifr, prnmuitns.
@ds radiifnkas sa raprasaktdk pnr lamfn ma aiudifnkas quìlfids, ak ds qua sa asieak ds sustdkifds qua fktarvfakak, pnr lamfn ma sus sìlen`ns y bùrlu`ds quìlfi
@ds aiudifnkas sa mfvfmak ak tras racfnkas: ak d fzqufarmd sa hd``dk ns raditfvns7 iukd b`aihd ak a` iaktrn qua sa `aa inln prnmuia, sa fkmfid a` saktfmn n mfraiifak a` qua a` prniasn sa astä ``avdkmn d iden7 y bfkd`lakta, ak `d maraihd sa uefi`ns prnmuitns, qua snk a` rasu`tdmn ma `d radiifùk.
Ajalp`n: HI`+KdNH KdI`+ H^5 N
Uaditfvns _rnmuia _rnmuitns
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@AVAY _NKMAUD@AY AK @DY UADIIFNKAY TQÌLFIDY
@ds radiifnkas iulp`ak ink `ayas qua axp`fidk `ds ra`difnkas ma ldsd y vn`ulaqua sa cakardk ak `ns prniasns quìlfins.
@ds `ayas qua astumfdk `ds ra`difnkas ma ldsd sa maknlfkdk @ayas _nkmard`as y `ma vn`ulak, @ayas Rn`ulætrfids.
@ay ma `d inksarvdifùk ma `d ldsd: kns mfia qua ak ukd radiifùk quìlfid `d ltarfd kn sa irad kf sa mastruya, sfkn qua sa trdsbnrld, inksarväkmnsa.
Ajalp`n:
I + N5 IN5
A` pasn dtùlfin ma` idrenkn as 45 crdlns y a` ma` nxìcakn 42 crdlns. Inln snmns nxìcakns, a` pasn tntd` ma ukd ln`æiu`d ma nxìcakn as ma 95 crdlns. D` sul`ds ldsds ma `ns mns raditfvns, sa netfaka ukd ldsd tntd` ma == crdlns.
Dhnrd, sf sa id`iu`d a` pasn ln`aiu`dr ma` mfùxfmn ma idrenkn, sa astde`aia qua æs
pasd == c, aktnkias, a` pasn ma `ns raditfvns as fcud` d` pasn ma `ns prnmuitns, qua maluastrd qua `d ldsd sa ldktfaka inkstdkta murdkta tnmn a` prniasn, pnr qua kn hdy pærmfmd kf cdkdkifd ma ldtarfd.
@ay ma `ds prnpnrifnkas mabfkfmds: iudkmn `ns ätnlns sa lazi`dk, kn `n hdiak miud`qufar lnmn7 ma haihn, a``ns tfakak sfalpra idktfmdmas dtùlfids bfjds, qua sraprasaktdk ak tærlfkns ma ldsd.
Ajalp`n:
KdI`
Kn fktarasd iuäktn snmfn y i`nrn astæk prasaktas ak `d bnrldifùk ma` i`nrurn ma snmfn, idmd ln`æiu`d bnrldmd sfalpra vd d inktakar uk fùk ma snmfn y ukn ma i`ny su ldsd sfalpra sarä ma dprnxfldmdlakta 18.1 c.
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@ay ma `ds prnpnrifnkas lú`tfp`as: dktas sa iraìd qua `ns inlpuastns astdeinkstftufmns sù`n pnr uk ätnln ma idmd aspaifa, pnr `n qua kn sa pnmìdk axp`fd`cukds axiapifnkas. Astd `ay mfia qua `ns a`alaktns puamak inlefkdrsa ak lma ukd bnrld, ak prnpnrifnkas kulærfids bfjds.
Ajalp`ns:
H5 N Dcud
H5 N5 _arùxfmn ma Hfmrùcakn
@ds ln`æiu`ds ma` ajalp`n astäk inkstftufmds pnr ätnlns ma hfmrùcakn y nxìcaparn sa mfbarakifdk ak qua lfaktrds ak a` parùxfmn ma hfmrùcakn hdy mns ätnlma nxìcakn, ak a` dcud sù`n hdy ukn.
I@DYAY MA UADIIFNKAY TQÌLFIDY
Mapakmfakmn ma `d kdturd`azd ma `ns raditfvns y a` lnmn ak qua sa inlefkak,
tfakak `ns sfcufaktas tfpns ma radiifnkas:
Uadiifnkas ma inlefkdifùk n sìktasfs:
Inln `d pd`derd `n fkmfid, snk prniasns ak `ns quasa sfktatfzdk inlpuastns kuavns, d pdrtfr ma sus a`a-laktns n ln`æiu`ds läs paquaôds.
Ajalp`n:
5H5(c)+N5(c) 5H5 N(c)
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Axp`fidifùk ma ukd radiifùk
ma inlefkdifùk.
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Uadiifnkas ma masinlpnsfifùk:
Ynk justdlakta npuastds d `ds dktarfnras, yd qua ak `ucdr ma bnrldr, rnlpak inlpuastns ak ln`æiu`ds läs paquaôds n ak sus a`alaktns inkstftuyaktas.
Ajalp`n:
GI`N= GI`+N5
Uadiifnkas ma masp`dzdlfaktn n sustftuifùk:
Ya prasaktd iudkmn uk a`alaktn ihnid ink d akarcìd kaiasdrfd inktrd uk inlpua
tn, rnlpfakmn a` ak`dia y masp`dzdkmn d uk ätnln ma kdturd`azd quìlfid sflf`dniupdkmn su pnsfifùk.
Ajalp`n:
Zk+IuYN= ZkYN=+Iu
Uadiifnkas ma fktaridlefn n mne`a sustftuifùk:
Ya md pnr `d fktardiifùk aktra mns inlpuastns. Ak astns prniasns sa fktaridlefdmns a`alaktns.
Ajalp`n:
GNH+HF GF+HNH
ED@DKIAN MA AIQDIFNKAY TQÌLFIDY
Ink edsa ak d ay ma inksarvdifùk ma d ldtarfd, ak d`cukds nidsfnkas ds aiudifnkaquìlfids maeak sar djustdmds pdrd cdrdktfzdr qua d idktfmdm ma ätnlns fkfifd`as safcud` d `ns bfkd`as, fkmapakmfaktalakta ma `d bnrld ak qua sa inlefkak maspuæpnr asn as tdk flpnrtdkta ed`dkiadr ds aiudifnkas. _drd asta bfk, astumfdralns mn
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Ed`dkian pnr tdktan n sflp`a fkspaiifùk: inksfsta ak in`nidr kúlarns aktarnsbrakta ma idmd ln`æiu`d ak ukd aiudifùk. Asta kúlarn raifea a` knlera ma inbfifakta astaqufnlætrfin y sa idrditarfzd pnrqua lu`tfp`fid `d idktfmdm ma ätnl
axfstaktas, d` dulaktdr `ds ln`æiu`ds.Ajalp`n:
H5+N5 H5 N
Inln sa puama var, ak `ns raditfvns hdy mns ätnlns ma hfmrùcakn y mns ma ncakn. Ak `ns prnmuitns hdy mns ma hfmrùcakn y ukn ma nxìcakn, `n qua fkmfid q
`d `ay ma `d inksarvdifùk ma `d ldsd kn sa astä iulp`fakmn, yd qua `d idktfmdm nxìcakns kn as fcud`.
Ak asta idsn, sa raqufara djustdr d aiudifùk, fktrnmuifakmn kúlarns aktarns paquôns, pdrd fcud`dr `d idktfmdm ma ätnlns. Inln a` qua astä ak mæbfift as a` nxìcama `ns prnmuitns sa fkfifd a` djusta pnr dhì.
Ak `ns raditfvns aktrdk mns ätnlns ma nxìcakn, pnr `n qua maearìdk sd`fr mns ak
prnmuitns7 d` hdear sù`n ukn, sa djustd `d aiudifùk in`nidkmn uk vd`nr kulærfd` brakta ma `d ln`æiu`d ma` dcud, qua parlftd d`idkzdr `d fcud`mdm. Ak asta idsnkúlarn as a` 5.
Dhnrd, raiuarma qua a` kúlarn lu`tfp`fid d tnmd `d ln`æiu`d7 ak inksaiuakifdkn hdy mns ätnlns ma hfmrùcakn ak `ns prnmuitns, sfkn =, `n qua ne`fcd d djuskuavdlakta `d aiudifùk, parn dhnrd ak `ns raditfvns. D` fcud` qua a` idsn dktarfsa eusid uk kúlarn qua d` lu`tfp`fidr`n fcud`a `d mfbarakifd. Kuavdlakta sa tfaqua a` vd`nr as 5. Dhnrd `d aiudifùk quamd:
5 H 5 + N 5 5H5N
= ätnlns ma H y 5 ma N = ätnlns ma H y 5 ma N
Dhnrd sì `d aiudifùk iulp`a ink `d `ay, yd qua `d idktfmdm ma ätnlns fkfifd`as
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Ed`dkian pnr ùxfmn-ramuiifùk (Uamnx): ak ns prniasns quìlfins kn sù`n hdy idlefnak `d mfstrfeuifùk ma `ns ätnlns, sfkn qua puama hdear idlefns ak `ns astdmns mnxfmdifùk, maefmn justdlakta d astns ranrmakdlfaktns. Asta bakùlakn sa prasaktyd qua ak `ns kuavns inlpuastns, pnr abaitns ma a`aitrnkacdtfvfmdm, `ns kuavnätnlns buarzdk d fktaridlefns ma a`aitrnkas mfbaraktas, vdrfdkmn `d idktfmdm ma`aitrnkas inlpdrtfmns, iamfmns n idptdmns.
Iudkmn uk ätnln pfarma a`aitrnkas sa mfia qua sa hd nxfmdmn7 ak a` idsn inktrdrfsa ramuia:
K+1 pdsd d K+5 cdkd 9 a`aitrnkasY-5 pdsd d Y? pfarma 5 a`aitrnkas
_drd a` ed`dkian sa maeak sacufr `ns sfcufaktas pdsns:
d. Astde`aiar `ns astdmns ma nxfmdifùk ma tnmns `ns ätnlns ak `d aiudifùk:
HKN9+ H5 Y KN+Y+H5 N
H4+ K1+ N95-+ H5
4+ Y5- K5+ N5-+Y?+H54+ N5-
e. Fmaktfbfidr `ns a`alaktns qua idlefdrnk sus astdmns ma nxfmdifùk y matalfkdr iuä` sa nxfmù y iuä` sa ramujn:
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K1+ K5+
Y 5- YN
i. Matarlfkdr `d idktfmdm ma a`aitrnkas cdkdmns y parmfmns:
K 1 + K5+ cdkù 9a- 7sa ramujn
Y 5- YN parmfù 5a[- 7sa nxfmù
m. Fcud`dr `d idktfmdm ma a`aitrnkas, inkvfrtfakmn d `ns a`aitrnkas cdkdmy parmfmns ak bditnras, qua lu`tfp`fidräk `ds aiudifnkas. _drd a``n `ns vd`nras
fktaridlefdk:
(K1++ 9a- K5+) X 5
(Y5- - 5a- YN ) X 9
a. Lu`tfp`fidr y rasn`var `d aiudifùk, a`flfkdkmn `ns a`aitrnkas:
5K1+ + 2a- 5K5+
9Y5- - 2a- 9Y?
^^^^^^^^^^^^^^^^^^^
5K1+ +9Y5- 5K5++ 9Y?
b. Dsfckdr `ns bditnras netakfmns inln inabfifaktas astaqufnlætrfins ak ln`æiu`ds raspaitfvds ma `d aiudifùk fkfifd`:
5HKN9+ 9H5Y 5KN+9Y+H5N
c. ]arlfkdr ma ed`dkiadr `d aiudifùk, pnr lamfn ma` lætnmn ma` tdktan:
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Ak inki`usfùk:
4. Ed`dkiaa `ds sfcufaktas aiudifnkas pnr tdktan:
IdI`5 + KdNH Id (NH)5 + KdI`
I2H45 N2 + N5 IN5 + H5N
5. Ed`dkiaa `ds sfcufaktas aiudifnkas quìlfid pnr a` lætnmn Uamnx:
HKN9 + GF + HI` F5 + K5 +GI` +H5N
I + H - 5YN= IN5 + YN5 + H5N
GLkN = + HI F +H5Y GIF + LkI`5 + Y + H5N
• Qk a`alaktn sa nxfmd sf dulaktd su kúlarn ma nxfmdifùk.
• Qk a`alaktn sa ramuia sf mfslfkuya su kúlarn ma nxfmdifùk.
• @ns prniasns sa rad`fzdk sflu`täkadlakta, yd qua ns a`aitrnkas quapfarma a` zfki, `ns cdkd a` inera.
• A` zfki (mnkdmnr ma a`aitrnkas), as a` dcakta ramuitnr, lfaktrds qua a`inera (quftd a`aitrnkas), as dcakta nxfmdkta7 pnr tdktn, a` a`alaktn
qua sa nxfmd ditúd inln dcakta ramuitnr y a` qua sa ramuia as dcaktanxfmdkta.
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RA@NIFMDM MA @DY UADIIFNKAY TQÌLFIDY
@ds radiifnkas pnsaak va`nifmdm.
As a` tfalpn alp`admn pnr `ns raditdktas ak d`idkzdr `ns prnmuitns. @d va`nifmma radiifùk fkvn`uird ukd mfslfkuifùk ak `d inkiaktrdifùk ma `ns raditdktas iuk dulaktn ak `d inkiaktrdifùk ma `ns prnmuitns. @d va`nifmdm ma radiifùk `d pmalns axprasdr ak ra`difùk ink `ns raditdktas y prnmuitns dsì:
Uaditdktas n raditfvns:
Ra`nifmdm ma mfslfkuifùk Rdrfdifùk ak `d inkiaktrdifùk ma `ns raditfvns
ak `d inkiaktrdifùk < ma `ns raditfvns Fktarvd`n ma tfalpn
@d dktarfnr aiudifùk kns luastrd ukd mfslfkuifùk ak d inkiaktrdifùk ma raditfvak uk tfalpn mdmn.
_rnmuitns:
Ra`nifmdm ma dpdrfifùk Rdrfdifùk ak `d inkiaktrdifùk ma `ns prnmuitns ak `d inkiaktrdifùk <
ma `ns raditfvns Fktarvd`n ma tfalpn
Bditnras qua dbaitdk `d va`nifmdm ma radiifùk
]alpardturd: ma diuarmn ink a` tfpn ma radiifùk, idusd uk dulaktn n mfslfkuiak `d va`nifmdm ma radiifùk. Cakard`lakta, uk fkiralaktn ak `d talpardturd nsfnkd uk dulaktn ak `d va`nifmdm ma radiifùk
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• _urazd ma ns raditfvns: d ldynr purazd ma ns raditfvns, ldynr va`nifmdm mdmqufsfifùk ma `ns prnmuitns.
• Idtd`fzdmnras: snk inlpuastns qua dia`ardk `d va`nifmdm ma radiifùk, pntdktn, sa d`idkzd räpfmdlakta `ns prnmuitns. _drd a``n mfslfkuyak `d akarc
ma ditfvdifùk, mfslfkuyak `d akarcìd ma ditfvdifùk, quæ as `d akarcìd kaiasrfd pdrd qua a` lnvflfaktn ma `ds pdrtìiu`ds cakarak in`fsfnkas abaitfvds, qu`ncrak rnlpar ak`dias y ma asta lnmn sa mak `ds radiifnkas quìlfids.
• Astdmn bìsfin ma ns raditfvns: a` tdldôn y suparbfifa ma inktditn ma `ns raditvns dbaitd d va`nifmdm ma radiifùk. Qkd ifktd ma ldckasfn ink HI` radiifnkläs `aktdlakta qua a` ldckasfn ak pn`vn.
• Inkiaktrdifùk ma raditfvns: d` dulaktdr `d inkiaktrdifùk ma raditfvns, s
Uadiifùk sfk `d
prasakifd ma`
idtd`fzdmnr.
Uadiifùk
ink idtd`fzdmnr
(kùtasa qua mfslfkuya
`d akarcìd ma ditfvdifùk).
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Ldsd ma uk ln` ma a`alaktns
@d ldsd ln`dr ma uk a`alaktn as ukd idktfmdm ak crdlns fcud` d su ldsd dtùlfy inktfaka uk kúlarn ma Dvncdmrn ma ätnlns ma` a`alaktn. _nr ajalp`n, `d lma uk ätnln ma id`ifn as =? u, pnrqua su ldsd ln`dr, as maifr, `d ldsd ma uk lma ätnlns ma id`ifn as =? c. Ldsd ma uk ln` ma ln`æiu`ds.
@d ldsd ma uk ln` ma ln`æiu`ds as fcud` d `d suld ma `ds ldsds ak crdlns ma a`alaktns qua `d inlpnkak.
Ätnln crdln
_drd lamfr ldsds rad`as ma ns a`alaktns quìlfins sa utf`fzd ukd ukfmdm ma lam``dldmd ätnln-crdln, qua sa mabfka inln `d idktfmdm ma uk a`alaktn iuyd ldas fcud` d `d ldsd dtùlfid axprasdmd ak crdlns.
Kúlarn ma Dvncdmrn
Kúlarn inkstdkta ma ätnlns y ln`æiu`ds pdrd uk inlpuastn n a`alaktn mtarlfkdmn.
Kúlarn ma Dvncdmrn < 2,?59 x 4?59
Ajalp`n:
Id`iu`dr a` kúlarn ma ätnlns axfstaktas ak 8 crdlns ma äifmn i`nrhìmrfin (HI`).
_drd masdrrn``dr a` dktarfnr ajarififn, id`iu`dlns a` pasn ma` inlpuastn.
H < 4 crI` < 91,1 cr_asn ln`aiu`dr < 4 + 91,1 < 92,1 cr
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AY]ATQFNLA]UÌD
Inln sa lakifnkù ak `d axp`fidifùk ma` ed`dkian ma `ds aiudifnkas quìlfids, djusta ma `ds aiudifnkas dtfakma d `d @ay ma `d inksarvdifùk ma `d ldsd. Qkd vaastde`aifmns `ns inabfifaktas astaqufnlætrfins, æstns sa ldktakmräk inkstdktas d `drcn ma `d radiifùk, pnr `n qua as pnsfe`a astde`aiar ra`difnkas ma ldsd aktra `didktfmdmas ma `ns raditfvns qua fktacrdk a` sfstald y `ns inabfifaktas.
D` astumfn ma astds aqufvd`akifds ldtalätfids ak `ds radiifnkas quìlfids sa `inknia inln astaqufnlatrìd y parlftak pramaifr `d idktfmdm ma prnmuitn qurasu`tdrä iudkmn `d radiifùk bfkd`fia.
_drd pnmar rad`fzdr ns iä`iu`ns ldtalätfins sa maeak takar ak iuaktd ds sfcufaktaukfmdmas ma lamfmd:
_asn n ldsd ln`aiu`dr: as `d ldsd tntd` ma ukd ln`æiu`d y sa netfaka d`suldr `ds ldsds ma tnmns `ns ätnlns inkstftuyaktas ma` inlpuastn.
Ln`: `d ldsd ln`dr (uk ln`) ma uk a`alaktn n inlpuastn as fcud` d `d ldsd dtùlfid ma` a`alaktn n `d ldsd ln`aiu`dr ma uk inlpuastn.
4. IDK]FMDM MA _UNMQI]NY V UADI]FRNY
Dktas ma `avdr d iden iud`qufar radiifùk quìlfid sfalpra sa maea takar i`drn iuäkma` prnmuitn sa qufara netakar. _drd a``n tdlefæk as flprasifkmfe`a inkniar `didktfmdmas ma raditfvns qua sa maeak alp`adr.
_drd inkniar astds idktfmdmas sa raiurra d `ns iä`iu`ns astaqufnlætrfins, quvfakak mdmns ak prfkifpfn pnr `ds aiudifnkas ed`dkiadmds, iuyns inabfifaktaastaqufnlætrfins sa ldktfakak inkstdktas ak tnmn a` prniasn, parlftfakmastde`aiar ra`difnkas ma ldsd aktra `ds idktfmdmas ma raditfvns usdmds y mprnmuitns netakfmns.
_drd asta iä`iu`n sa alp`adk tras lætnmns:
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Lætnmn crdln d crdln: sf sa inkniak `ds idktfmdmas ma ldsd ak crdlns maraditfvns ak `d aiudifùk quìlfid, as pnsfe`a hd``dr `ns crdlns ma prnmuitn quanetakmrä ak `d radiifùk. Dquì sa usdk `ds ldsds ln`aiu`dras:
Ajalp`n:
5H5 + N5 5H5 N
¾Iuäktns crdlns ma dcud sa prnmuiak ink 36 c. ma hfmrùcakn>
_drd pnmar raspnkmar d pracuktd sa maea ak prflar ucdr varfbfidr qua d aiudiastæ ed`dkiadmd inrraitdlakta.
D inktfkudifùk sa id`iu`dk `ds ldsds ln`aiu`dras ma ds sustdkifds fkvn`uirdmds`d pracuktd, dsì:
Idmd ätnln ma hfmrùcakn tfaka ukd ldsd dtùlfid ma 4c, yd qua idmdln`æiu`d ma hfmrùcakn tfaka mns ätnlns y a` inabfifakta la fkmfid qua
hdy mns ln`æiu`ds7 ak inksaiuakifd, ak tntd` hdy = ätnlns ma hfmrùcakn
iuyd ldsd inrraspnkma d = crdlns:
5X(4cX5)<=c
@d ln`æiu`d ma` dcud pnr su pdrta pasd 48c, puastn qua `ns mns ätnlnsma hfmrùcakn pasdk 5c y a` ma nxìcakn 42c qua d` suldr`ns md 48,parn d` fcud` qua ak a` idsn dktarfnr, hdy mns ln`æiu`ds, pnr `n qua `dldsd tntd` ma` dcud as 92c.
5X((4cX5)+42c)<92
@ns iä`iu`ns vd`nras dktarfnras sfckfbfidk qua =c ma hfmrùcakn prnmuiak92c ma dcud. Æstd ra`difùk ma ldsd astaqufnlætrfid sa inknia inlnbditnr ukftdrfn.
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Dhnrd sa ra`difnkdk `ds idktfmdmas ma ldsd qua radiifnkdk ak `d rad`fmdm, ink `nbditnras ukftdrfns.
92cH5 N
=cH5
Lætnmn ln` d ln`: ak astns iä`iu`ns `d ldsd sa id`iu`d úkfidlakta ak tærlfknln`dras. Yfcufakmn ink a` lfsln ajalp`n:
@ns inabfifaktas astaqufnlætrfins snk aqufvd`aktas d kúlarn ma ln`as ma idmdsustdkifd7 dsì, mns ln`as ma hfmrùcakn radiifnkdk ink ukd ln` ma nxìcakn, pdrd
prnmuifr mns ln`as ma dcud. Ak asta idsn a` bditnr ukftdrfn sa astde`aia aktra `dsln`as ma hfmrùcakn y `ds ma dcud:
Mns ln`as ma H prnmuiakta 5 ln`as ma H5N
Inln `ns iä`iu`ns sa hdiak ak tærlfkns ln`dras, maea inkvartfrsa `d ldsd ma raditfvn d ln`as, dsì:
4ln`H5
5cH5
Bfkd`lakta sa ra`difnkdk `ds ln`as qua radiifnkdk ink a` bditnr ukftdrfn:
96.1ln`H5 *
Lætnmn ln`/crdln: inln sa vfn ak `ns idsns dktarfnras, as pnsfe`a matarlfkdr a
< 334cH5 N
<96.1ln`H5
36cH5 *
36cH5 *
5ln`H5 N
5ln`H5
<96.1ln`H5 N
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inabfifaktas astqufnlætrfins. Ak inksaiuakifd, as pnsfe`a hdiar ra`difnkas crdlln` n ln`/crdln.
_nr ajalp`n: 5 ln`as ma H, prnmuiak 92c ma dcud, dsì:
96.1ln`H5*
5. UADI]FRN @ÌLF]A
¾@a hd pdsdmn d`cukd vaz qua d` prapdrdr uk D`gd-sa`tzar ak nidsfnkas raqufara difnkdr ldynr idktfmdm ma dcud, pnrqua kn tnmn a` lamfidlaktn sa lazi`d y radiifnkd ink a` dcud> Fki`usn, ak ntrns idsns sa raqufara in`nidr ntrd pdstf``d ak dcud, pnrqua a` lamfidlaktn as fksubfifakta pdrd `d idktfmdm ma dcud.
@ns ajalp`ns dktarfnras sa maeak d` raditfvn `ìlfta. Ak tnmn prniasn sfalpra hde uk raditfvn qua astæ ak laknr idktfmdm (prnpnrifùk) ink raspaitn d`(ns) ntrn(s
D astd sustdkifd sa a inknia inln raditfvn ìlfta y sa idrditarfzd pnrqua sa inkla pnr inlp`atn, lntfvn pnr a` iud`, d` dcntdrsa brakd `d radiifùk, `flftdkmn `didktfmdm ma prnmuitn bnrldmn.
Ajalp`n:
5H5 + N5 5H5 N
41c ma H radiifnkdk ink 8 ln`as ma N7 ¾iuäktds ln`as ma dcud sa netfakak>
Hdstd a` lnlaktn as inlp`atdlakta masinknifmn iuä` ma `ns mns raditfvns as `ìlfta7 pnr a``n sa id`iu`d d ldsd ma dcud prnmuifmd, ink idmd ukn ma ns raditfvy a` rasu`tdmn qua mæ laknr idktfmdm as a` inrraitn y a` raditfvn ink a` qua sa h
↕
92cH5N
5ln` H5
<344cH5N
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prnmuiifùk ma dcud7 pnr a``n `d idktfmdm ma H5N bnrldmd as pnid.
Ak iudktn d` nxìcakn, æ` as a` raditfvn ak axiasn, n qua qufara maifr qua d` bfkd`fzd`d radiifùk hderä d`cn ma nxìcakn sfk radiifnkdr.
5ln`H5N
=cH5
5ln` H5N
4ln` N5
9. _QUAZD
_drtfakmn ma `d edsa ma qua kn tnmds `ds sustdkifds ink qua sa rad`fzdk radiifnkaquìlfids snk tntd`lakta purds, as flpnrtdkta takar ak iuaktd a` crdmn ma purazdma ns raditfvns ak ns iä`iu`ns astaqufnlætrfins, yd qua kn tnmd d ldsd ma raditfvalp`admd inrraspnkma d æ`.
Ajalp`n:
5H5 + N5 5H5N
¾Iuäktns crdlns ma dcud sa prnmuiak d pdrtfr ma 51c ma H d` 61% ma purazd>
Dktas ma id`iu`dr a` dcud prnmuifmd sa maea astde`aiar `d idktfmdm rad` ma hfmrùcakn qua radiifnkù, yd qua a` pnriaktdja fkmfid qua a` 61% ma` raditfvn usdmn in-
<3.1ln`H5N41cH5*
8ln` N5* <42ln` H5N
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51c
4??%
@d idktfmdm ma hfmrùcakn qua radiifnkd as 59,8c y kn 51. Dhnrd sì as pnsfe`a iiu`dr `d ldsd ma dcud bnrldmd
59.8cH5*
92cH5N
<54=.5c H5N
=. UAKMFLFAK]N MA UADIIFÙK N _NUIAK]DJA MA _UNMQIIFÙK
Ak `d rad`fmdm luihns bditnras inln `d talpardturd, id`fmdm y purazd ma `nsraditfvns, dbaitdk `d idktfmdm ma prnmuitn bnrldmn y luihns prniasns kn sa ajiutdk d` 4??%.
Ajalp`n:
¾Iuä` as a` pnriaktdja ma rakmflfaktn ma `d radiifùk sf sa prnmuiak 5?? crdlnma dcud, d pdrtfr ma 51c ma H>
5H5 + N5 5H5N
_drd pnmar matarlfkdr a` pnriaktdja ma rakmflfaktn as flpnrtdkta hd``dr a` raklfaktn taùrfin, qua inrraspnkma d` vd`nr ma dcud prnmuifmd sf d radiifùk sa `avdriden d` 4??%. Asta iä`iu`n as a` lfsln ma `d idktfmdm ma prnmuitns y raditfvns:
↕
<59.31 <59.8cH561%*
=cH5
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51cH5*92cH5 N
=cH5
5??cH5N*4??%
551cH5N
_rapdrdifùk ma cd``atds ma ldktaquf``d:
4. _asa uk raifpfakta ma p`ästfin `flpfn.
5. In`nqua ak a` raifpfakta 5??c ma ldktaquf``d d talpardturd dlefakta, in21c ma dzúidr. Lazi`a hdstd qua kn sa dpraifak crulns ma dzúidr. _rabarfe`lakta usa dzúidr pdrd aspn`vnradr.
9. Dcracua pnin d pnin 2?c ma bæiu`d ma ldìz, lazi`dkmn inktfkudlakta.
=. Dôdmd 4=?c ma hdrfkd ak mns tdkmds ma 3?c idmd ukd, lazi`dkmn inkstdktlakta, hdstd netakar ukd ldsd `fsd y sfk crulns.
1. In`nqua 5?c ma d`lakmrds pfidmds y 5 iuihdrdmds ma ihfps ma ihnin`dta (aspdsn as npifnkd`).
2. _asa tnmn a` inktakfmn ma` raifpfakta y pnr mfbarakifd astde`azid `d idktfmd
<551cH5N<4??% Uakmflfaktn ]aùrfin
<88.88 < 88.6% Uakmflfaktn ma radiifùk
5
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3. Iuerd ukd edkmajd latä`fid ink pdpa` id`idkta n pdrdbfkdmn iuefartn ldktaquf``d. Ink dyumd ma ukd iuihdrd in`nqua ldsd snera `d edkmajd, m
jdkmn aspdifns prumaktas aktra `ds cd``atds, puastn qua æstds vdk d iraiar i`d iniifùk.
8. Inifka ak uk hnrkn praid`aktdmn d 41?¿I, murdkta 41 lfkutns n hdstd q`ds cd``atds astæk `avalakta mnrdmds.
6. Maja rapnsdr `ds cd``atds ak uk `ucdr sain y brasin. Qkd vaz brìds, pæsa`dastde`azid a` pnriaktdja ma rakmflfaktn.
4?. Uaspnkmd `ds sfcufaktas pracuktds: ¾pnr quæ idlefd `d inksfstakifd ma d lds
¾a` idlefn qua niurra as uk idlefn bìsfin, quìlfin n `ns mns>
44. @d lajnr pdrta: ¡inlpdrtd `ds cd``atds ink sus bdlf`fdras y/n inlpdôarns i`dsa!
4. A` d`ulfkfn radiifnkd ink a` äifmn su`búrfin y prnmuia su`bdtn ma d`ulfkfn l
hfmrùcakn cdsansn. Yf 5? crdlns ma d`ulfkfn sa dmfifnkdk d ukd sn`uifùk q
inktakcd 441 c ma äifmn, rasua`vd:
d. Asirfed `d aiudifùk quìlfid ed`dkiadmd d pdrtfr ma `d fkbnrldifùk m
prne`ald.
e. ¾Iuä` as a` raditfvn `ìlfta>
i. ¾Iuäktds ln`as ma hfmrùcakn sa bnrldräk>
m. ¾Iuäktns crdlns ma su`bdtn ma d`ulfkfn sa bnrldräk>
3
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a. ¾Iuäktns crdlns snerdräk ma` raditfvn ak axiasn>
9. A` i`nrurn ma tftdkfn (FR) radiifnkd ink dcud pdrd prnmuifr mfùxfmn ma tftdk
y äifmn i`nrhìmrfin.
d. Asirfed `d aiudifùk quìlfid ed`dkiadmd ma` prniasn quìlfin.
e. Yf inlfakzd ink 4= l` ma i`nrurn ma tftdkfn (FR) (m < 4,= Gc/@) ¾Tuæ ld
ma dcud, ak crdlns, sa raqufara pdrd ukd radiifùk tntd`>
i. ¾Tuæ idktfmdm ma prnmuitn sa netakmrä, sf dhnrd sa pdrta ma 9? l` m
i`nrurn ma tftdkfn (FR) y ?.?9 Gc ma dcud7 sf a` rakmflfaktn ma `d radiifù
bua ma` 68% y `d purazd00 ma `ns raditfvns snk ma` 8? y 31% raspa
tfvdlakta>
5. Ed`dkiaa ds sfcufaktas aiudifnkas pnr ùxfmn-ramuiifùk y i`dsfbfqua ds sfcufaktradiifnkas quìlfids:
d. IdI`5 + KdNH Id(NH)5 + KdI`
e. KN + N5 KN5
i. HcN Hc + N5
m. I2H45N2 + N5 IN5 + H5N
a. Kd + H5N Kd(NH) + H5
9. @d barlaktdifùk as uk prniasn quìlfin qua sa alp`ad ak `d a`denrdifùk m
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eaefmds d`inhù`fids, inln a` vfkn y `d iarvazd.
I2H45N2 5I5H1NH + 5IN5
C`uinsd Atdkn`
=. Yf sa alp`adk 1??,=c ma c`uinsd ¾iuäktn atdkn` sa netakmrä pnr lamfn
asta prniasn>
@d mfslfkuifùk ma `d idpd ma nznkn as uk tald luy praniupdkta aktra `dinlukfmdm ifaktìbfid y ak cakard` pdrd tnmns, puastn qua su mastruiifùkparlfta a` fkcrasn ma `ns rdyns u`trdvfn`atd (QR) ma` sn`, qua kn sù`n cakard
prne`alds ak `d pfa`, sfkn qua dmaläs idusdk a` marratflfaktn ma `ns pn`nYa iraa qua a` nznkn radiifnkd ink a` KN axpu`sdmn pnr `ns dvfnkas maprnpu`sfùk. @d radiifùk as:
N9 + KN N5+KN5
Yf ?.3=?c ma N9 radiifnkdk ink ?.23?c ma KN, ¾iuäktns crdlns
KN5 saprnmuifräk>, ¾iuä` inlpuastn as a` raditfvn ìlfta> Id`iu`a a` kúlarn ma lnma` raditfvn ak axiasn qua snerdräk ak a` prniasn.
4. @d radiifùk aktra a` snmfn y a` dcud prnmuia `d edsa ma` latd`, juktn ink a`
masprakmflfaktn ma hfmrùcakn ak bnrld cdsansd, inln sa luastrd d inktfkudifù
Kd(Y)+H5N(`) KdNH(di) + H5(c)
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↕
↕
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5. Ink edsa ak astd fkbnrldifùk raspnkmd `ds sfcufaktas pracuktds:
@d aiudifùk inrraitdlakta ed`dkiadmd as:
d. K d ( Y ) + H5N(`) KdNH(di) + H5(c)
e. 5 K d ( Y ) +H5N(`) 5KdNH(di) +H5(c)
i. 5 K d ( Y ) +5H5N(`) 5KdNH(di) +H5(c)
m. K d( Y )
+5H5N
(`) KdNH
(di) +5H
5(c)
9. @d idktfmdm rad` ma snmfn qua radiifnkd as:
d. 51c e. 59.8c i. 55.6c m. 5?.1c
=. A` raditfvn `ìlfta ak asta prniasn as:
d. H5N e. KdNH i. H5 m. Kd
1. @d idktfmdm ak ln`as ma KdNH bnrldmns inrraspnkma d:
d. ?,65ln` e. 4,1=ln` i. 5,?4ln` m. 4,?9ln`
↕
↕
↕
↕
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2. @d idktfmdm ak crdlns ma hfmrùcakn bnrldmn as:
d. ?,81c e. 4,?9c i. 4,6?c m. 5,54c
3. Yf ak `d rad`fmdm sa bnrldk 91c ma KdNH, a` rakmflfaktn ma `d radiifùk
inrraspnkma d`:
d. 4??%
e. 61% i. 6?% m. 81%
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]ùlasa ukns lfkutns pdrd paksdr ma bnrld fkmfvfmud` snera `ds sfcufaktaspracuktds:
¾_nr quæ rdzùk ukd pfpatd ma cds kn astd``d>
¾Yf sa nprfla a` sprdy ma ukd enta``d ma parbula ak ukd asqufkd ma` sd`ùk, a`n`nr ma` parbula sa saktfrìd ak `d asqufkd npuastd> ¾_nr quæ>
¾Tuæ bnrld tfaka uk cds> ¾As if`ìkmrfin inln `d pfpatd ma cds> ¾V sf `d pfpatdbuard trfdkcu`dr n iudmrdmd>
¾Tuæ vn`ulak tfaka uk cds>
A` cds as uk astdmn ma `d ldtarfd qua sa idrditarfzd pnr `d pnid fktardiifùk y dtrd-iifùk aktra `ds ln`æiu`ds, hdifakmn qua æstds astæk luy sapdrdmds aktra sì.A` inlpnrtdlfaktn ma `ns cdsas sa axp`fid masma `d ]anrìd Ifkætfid Ln`aiu`dr:
Qk cds astä inlpuastn pnr ln`æiu`ds luy sapdrdmds ukds ma ntrds, ink mfstdkifdqua snerapdsdk `ds mflaksfnkas ma `ds pdrtìiu`ds inln td`.
@ds pdrtìiu`ds inkstftuyaktas ma ns cdsas sa luavak inkstdktalakta ak mfraiifnka
CdsasQkfmdm 3. Cdsas Yasfùk
8
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`fsfnkak aktra sì ak ihnqua a`ästfins, puastn qua ds pdrtìiu`ds maspuæs ma d in`fsraentdk, lntfvn pnr a` qua kn hdy radiifùk aktra a``ds.
@ds ln`æiu`ds ak uk cds kn tfakak buarzds ma dtrdiifùk n rapu`sfùk aktra a``ds.
@d akarcìd ifkætfid ma uk cds mapakma ma `d talpardturd d `d qua sa akiuaktra.
A` vn`ulak ma uk cds kn as mabfkfmn, yd qua `ds pdrtìiu`ds niupdk tnmn a` aspdimfspnkfe`a ma` raifpfakta qua `ds inktfaka, sfk qua a``n flp`fqua radiifùk quìld`cukd.
@ns cdsas snk inlprasfe`as. Astd prnpfamdm inksfsta ak mfslfkufr a` aspdifn vdi
qua hdy aktra `ds ln`æiu`ds.
@ns cdsas dmnptdk `d bnrld ma` raifpfakta qua `ns inktakcd.
Maefmn d su edjd maksfmdm, a` prniasn ma mfbusfùk as läs räpfmn qua ak `ns ntrnastdmns.
_rasfùk ma `ns cdsas
Inln sa vfn ink `d ]anrìd Ifkætfid Ln`aiu`dr, `ds pdrtìiu`ds ma uk cds kukid astqufatds7 d` inktrdrfn, a``ds sa luavak inkstdktalakta ihnidkmn ink pdrtìiu`ds cds y ma` raifpfakta ak a` qua a` cds sa akiuaktrd, ajarifakmn buarzds.
Inln mfihds buarzds (B) sa cakardk snera ukd suparbfifa (ärad), astds buarzds sa tmuiak inln prasfùk:
_ <
B
D
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Qk ajalp`n ma `d prasfùk `n akinktrdlns d` vfdjdr. @ns nìmns snk `ns ùrcdkns maaquf`ferfn ma` iuarpn y snk luy saksfe`as d `ns idlefns ma prasfùk7 pnr a``n, uprflar sìktnld qua kns fkmfid qua `d prasfùk hd idlefdmn as dqua` maknlfkdmninln nìmn tdpdmn.
Ntrn ajalp`n as `d prasfùk dtlnsbærfid, quaas `d pras fùk qua ajaria `d dtlùsbard
snera `ns iuarpns y vdrìd sacúk a` sftfn ma `dtfarrd. @d ldynr prasfùk dtlnsbærfidsa akiuaktrd d kfva` ma` ldr y mfslfkuya ink `dd`turd, pdrd lamfr`d utf`fzdlns a` edrùlatrnfkvaktdmn ak 422= pnr Avdkca`fstd ]nrrfia`f, bìsfinftd`fdkn.
D kfva` ma` ldr, `d prasfùk lamfmd ak a` edrùlatrn sa `a maknlfkd, ukd dtlùsbard ma prasfùk (4 dtl), y aqufvd`a d:
4 dtl < 32 il Hc < 32? ll Hc < 32? tnrr. 4 dtl < 32? tnrr.
@d prasfùk ak `ns cdsas
as prnmuifmd pnr a` ihnqua
ma `ds ln`æiu`ds
ma` cds aktra sì y inktrd `ds pdram
ma` raifpfakta.
@ds ln`æiu`ds ma uk cds ihnidk aktra sì ink `ds
pdramas ma` raifpfakta iradkmn `d prasfùk.
Astd enta``d p`ästfid bua sa``dmd dd`turd ma =523 l., `uacn edjdmd dd`turd ma 53=9, y bfkd`lakta d ukd rd ma 9?1 l. _uama nesarvdrsa iùlidlefn ak `d prasfùk ma` dfra `d dp`d
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Yf prasfùk as buarzd pnr ukfmdm ma ärad. Aktnkias:
_ < B/D < Mfkds/ il5 , Kawtnk/ l5 < _dsid`
A` _dsid` as ukd ukfmdm ma lamfmd ak a` Yfstald Fktarkdifnkd`
4 dtl < 4,?49x4?9 _dsid`as (_d)
Ajalp`n:
¾D iuäktns lf`ìlatrns ma lariurfn aqufvd`ak: 9 dtlùsbards y 4 _dsid`>
@AVAY TQA UFCAK A@ INL_NU]DLFAK]NMA @NY CDYAY
@ay ma Eny`a
Ak a` sfc`n XRFF a` Tuìlfin y Bf`ùsnbn erftäkfin Uneart Eny`a astumfù a` inlpnrtdlfatn ma `ns cdsas, ra`difnkdkmn a` idlefn ma `d prasfùk brakta d` vn`ulak, iudk`d idktfmdm ma pdrtìiu`ds y `d talpardturd ak `d qua sa hd``dk snk inkstdkt
Ak sus astumfns, Eny`a ncrù matarlfkdr qua d prasfùk ma uk cds as fkvarsdlakta prnpifnkd` d su vn`ulak7 as maifr, qua lfaktrds ukd dulaktd, `d ntrd maea mfslfku
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_nr ajalp`n: ustam inca ukd jarfkcd, `a quftd `d dcujd y suiifnkd dfra. Dhnrd, sf in`nid su mamn snera `d enid ma `d jarfkcd, nestruyakmn `d aktrdmd n sd`fmd ma` dfy alpfazd d edjdr a` ælen`n, sfk majdr sd`fr a` cds, varä qua a` vn`ulak vd mflfkuyakmn, parn idmd vaz tfaka qua dp`fidr ldynr buarzd7 as maifr, ldynr prasfùk snera a` ælen`n pdrd sacufr inlprflfakmn a` cds. Yf quftd a` mamn räpmdlakta, a` sfstald raiupard su vn`ulak fkfifd` y `d prasfùk mfslfkuy
]d` bakùlakn sfalpra as fcud` ak tnmns ns cdsas, ma dhì qua sa mfcd qua astd ra`difùk prsfùk/vn`ulak sad inkstdkta. _nr a``n, pnmalns trdksbnrldr d aiudifùk dktarfnr ds
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@ay ma Ihdr`as
A` bìsfin brdkiæs Jdiquas D`axdkmra Iasdr Ihdr`as eusiù d ra`difùk ma` vn`ulak intalpardturd, iudkmn `d prasfùk y `d idktfmdm ma ldsd parldkaiak inkstdk
Ink edsa ak sus astumfns astde`aifù qua `d ra`difùk R Rs ] as mfraitdlakta prnifnkd`, astn sfckfbfid qua sf ukd ma `ds mns vdrfde`as dulaktd `d ntrd tdlefækhdia, n pnr a` inktrdrfn, sf ukd mfslfkuya, d ntrd tdlefæk n hdrä, yd qua d ra`disfalpra as inkstdkta.
Maspajdkmn, sa netfaka `d aiudifùk ma Ihdr`as:
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Asta inlpnrtdlfaktn sa ra`difnkd ink `d akarcìd ifkætfid, yd qua d` dulaktdr talpardturd, sa fkiralaktd a` lnvflfaktn ma `ds pdrtìiu`ds y ink æ` a` aspdifn quniupdk `ds pdrtìiu`ds.
@ay ma Cdy-@ussdi
Jnsaph @ufs Cdy-@ussdi ard uk bdkätfin ma ns c`nens darnstätfins y sa fktarasù pnr
astumfn ma `ns cdsas, iudkmn `d prasfùk y `d talpardturd vdrìdk, ldktakfakmn a`vn`ulak y `d ldsd inkstdktas.
Æsta quìlfin y bìsfin brdkiæs akinktrù qua, d` dulaktdr d talpardturd, sa fkiralak`d prasfùk7 pnr a` inktrdrfn, sf mfslfkuya `d talpardturd, `d prasfùk tdlefæk maidaak ukd ra`difùk mfraitdlakta prnpnrifnkd`:
@ns c`nens darnstätfins sa fkb`dk id`aktdkmn a` dfra
inktakfmn ak `d en`sd.
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Maspajdkmn:
@ay ma Dvncdmrn
Ak 4844 a` ftd`fdkn Dldman Dvncdmrn pue`fiù uk astumfn ak a` qua axp`fid `d ra
ifùk fkharakta aktra a` vn`ulak y `d idktfmdm ma pdrtìiu`ds, iudkmn `d ] y `d _ sinkstdktas. Ak a` astumfn di`drd qua `d ra`difùk aktra a` vn`ulak y `ds pdrtìiu`dsmfraitdlakta prnpnrifnkd`:
A` bukifnkdlfaktn ma `ds n``ds d prasfùk sa
axp`fid ak pdrta ink astd `ay. Yf efak dquì hdypærmfmd ma ldtarfd ak bnrld ma cds, `ns d`f-
laktns sa inifkdk maefmn d` fkiralaktn ma `d
prasfùk, pnr abaitns ma `d talpardturd.
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@ay ma Ihdr`as-Eny`a n inlefkdmd
Inln yd sa hd astde`aifmn, `d prasfùk puama ra`difnkdrsa mfraitdlakta ink a` vn`ulak y æsta d su vaz ink `d talpardturd. Uapdsdkmn, sa sdea qua a` vn`ulak asfkvarsdlakta prnpnrifnkd` d `d prasfùk y mfraitdlakta prnpnrifnkd` d `d talpardturd, dsì:
Mfihd ra`difùk as ukd inkstdkta, aktnkias:
@ay ma `ns cdsas fmad`as
Uasulfakmn `ds `ayas dktarfnras, takalns `n sfcufakta:
Inln puama varsa, `ds tras `ayas tfakak ak inlúk d` vn`ulak7 ak inksaiuakifdastds aiudifnkas puamak ra`difnkdrsa dsì:
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D` fcud` qua ak `ds maläs `ayas, astds ra`difnkas snk inkstdktas:
Mnkma U as `d inkstdkta ma `ns cdsas fmad`as.
Inln sa trdtd ma cdsas fmad`as, ns vd`nras pdrd rasn`var d aiudifùk y hd``dr a` vdma `d inkstdkta snk:
_rasfùk: 4dtl
Rn`ulak: 55.=@
Ln`as (k): 4ln`
]alpardturd: 539G. A` ga`vfk as ntrd ukfmdm ma lamfmd pdrd `d talpardturd y said`iu`d ink `d sfcufakta aiudifùk:
Maspajdkmn ink `ns vd`nras kulærfins `d aiudifùk ma cdsas fmad`as sa tfaka:
Uaiuarma qua `d ra`difùk ma astns bditnras as inkstdkta7 ma dhì `d rdzùk pnr `d isa id`iu`ù a` vd`nr ma U.
Inki`uyakmn, `d aiudifùk ma `ns cdsas fmad`as as fcud` d:
4dtl * 55.=@
4ln` * 539G<?.?89 dtl.@
ln`.G
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Astd aiudifùk sa alp`ad iudkmn tnmns `ns bditnras astäk ra`difnkdmns aktra sì.
_drd kn n`vfmdr a` nrmak ma `d aiudifùk, puama utf`fzdr astd dyumd:
_ R < k U ] _dtns Rn`dkmn fcud` d` Kúlarn ma Udtnkas ]rntdkmn
- Iä`iu`ns ma maksfmdm: maspajdkmn d aiudifùk ma ns cdsas fmad`as as pnsfe
matarlfkdr `d ldsd, a` pasn ln`aiu`dr y maksfmdm ma ukd sustdkifd:
Mnkma l as `d ldsd n idktfmdm ma cds qua fktarvfaka ak a` prniasn y L su ldsdln`aiu`dr:
Uainrmdkmn qua:
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Mnkma m as `d maksfmdm ma `d sustdkifd, dsì `d aiudifùk quamd:
@ay ma Md`tnk ma `d _rasfnkas _drifd`as
A` dfra, pnr ajalp`n as a` rasu`tdmn ma ukd lazi`d ma sustdkifds cdsansds inln nxìcakn, lnkùxfmn y mfùxfmn ma idrenkn, ùxfmns ma kftrùcakn y dzubra, vdpnr mdcud, latdkn, kftrùcakn y luihns läs. Ak inksaiuakifd, d prasfùk dtlnsbærfid as raspnksdef`fmdm ma ukd sn`d ma ds sustdkifds inkstftuyaktas ma` dfra, sfkn ma tnmd` lfsln tfalpn, yd qua idmd inlpuastn ajaria su prnpfd prasfùk.
Dsì, `d @ay ma Md`tnk kns mfia qua `d _rasfùk tntd` ma uk sfstald as d suldtnrfd
`ds prasfnkas pdrifd`as qua idmd cds ajaria snera æ`.
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A` pasn ma `ds ln`æiu`ds y `ds nesarvdifnkas ma Crdhdl ]hnlds
Crdhdl ak 4858 nesarvdkmn `ds ln`æiu`ds ma `ns cdsas kntù qua:• @ns cdsas ink ln`æiu`ds pasdmds sa mfbukmak `aktdlakta.
• @ns cdsas ink ln`æiu`ds `fvfdkds sa mfbukmak räpfmdlakta.
Crdhdl tnldkmn inln edsa astns pnstu`dmns y ntrds nesarvdifnkas inki`uyù:
‐@d va`nifmdm ma mfbusfùk ma `ns cdsas as fkvarsdlakta prnpnrifnkd` d `d rdìz iumrdmd ma sus ldsds n maksfmdmas“.
Bùrlu`d ma `d `ay
Ak `d bùrlu`d dktarfnr nesarvdlns `ds va`nifmdmas (4-5) y `ds maksfmdmas (4-5) m
mns cdsas mfbaraktas:
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Ak `d cräbfid dktarfnr, `ds ln`æiu`ds ma` sfstald ukn sa mfbukmak läs räpfmn qua ma` sfstald mns, yd qua prasaktdk ukd laknr maksfmdm.
4. @denrdtnrfn
A` abaitn ma `d prasfùk dtlnsbærfid.
Ldtarfd`as:
• @dtd ma cdsansd vdiìd • _fkzds qua puamdk snstakar `d `dtd. • Laiharn n astubd
• Uaifpfakta latä`fin, p`ästfin n ma pnria`dkd.
_rniamflfaktn:
d. In`nqua ak d dtd ukd idktfmdm ma dcud qua kn supara ns 1il. ma d`tu dp`fidkmn `ns prfkifpfns ma `ns cdsas.
e. Yf d präitfid sa rad`fzd ak a` denrdtnrfn, utf`fia a` trìpnma y d ld``d ma dseapdrd id`aktdr. Ak su mabaitn usa `d astubd.
i. _rapdra a` raifpfakta latä`fin. Asta maea takar dcud subfifakta pdrd tdp`d `dtd läs n lakns hdstd uk iudrtn.
m. Iudkmn a` dcud astæ hfrvfakmn, tnla `d pfkzd y ink luihd praiduifvn`taa räpfmdlakta `d `dtd ak a` raifpfakta.
4
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Dkä`fsfs:
d. ¾_nr quæ suiamfù asta bakùlakn>
e. Qsdkmn `d tanrìd ma `ns cdsas, ¾iùln axp`fid `n suiamfmn>
i. Uad`fia uk cräbfin ma `n qua prnede`alakta a niurrfù d `d `dtd.
m. Yf kn sa rad`fzd räpfmdlakta a` prniamflfaktn ma vn`tadr `d `dtd,¾suiama a` lfsln abaitn>
5. Uasua`vd:
4. Qk tdkqua ma 4? ftrns ma ha`fn sa `akd d ukd prasfùk ma 41? dtlùsbards. ¾Iuäktc`nens ma jucuata ma 4.1? ftrns puamak sar fkb`dmns d ukd prasfùk ma 4 dtlùsbaink a` ha`fn ma` tdkqua> Yupnkcd qua kn hderä idlefn ma talpardturd ak tdkqua.
4. Qk tdkqua ma 4? `ftrns ma ha`fn sa ``akd d ukd prasfùk ma 41? dtlùsbard¾Iuäktns c`nens ma jucuata ma 4.1? `ftrns puamak sar fkb`dmns d ukd prasfùma 4 dtlùsbard ink a` ha`fn ma` tdkqua> Yupnkcd qua kn hderä idlefn mtalpardturd ak a` tdkqua.
5. A` vn`ulak ma ukd luastrd ma cds d 5?¿I as 5,1 `ftrns. Yupnkcd qua `d pr
sfùk sa ldktfaka inkstdkta. d) ¾Iuä` as a` vn`ulak ma` cds d 5??¿I> e) ¾D qutalpardturd (ak ¿I) sarä a` vn`ulak ma 9 `ftrns> i) ¾D qua talpardturd (ak ¿Isarä a` vn`ulak ma 4 `ftrn>
9. Qk cds tfaka ukd maksfmdm ma ?,135 c/`ftrn d 6?¿I y ukd prasfùk ma ?,1 dtl¾Iuä` as a` pasn ln`aiu`dr ma` cds>
=. Qkd luastrd ma ?,9?? c ma uk `ìqufmn bua vdpnrfzdmd d 41?¿I. A` vdpnr niup
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48? l` edjn ukd prasfùk ma ?,668 dtl. ¾Iuä` as a` pasn ln`aiu`dr ma` `ìqufmn
1. A` ifdkurn ma hfmrùcakn, uk inlpuastn d`tdlakta vakaknsn, sa prapdrd ilarifd`lakta lamfdkta `d sfcufakta radiifùk rad`fzdmd d d`td talpardturd `d prasakifd ma uk idtd`fzdmnr.
IH= (c) + N5 (c) + KH9 (c) HIK (c) + H5N (c)
2. Ak a` euian rairadtfvn sa alp`ad dfra inlprflfmn hdstd prnbukmfmdmas iaridkd 2? pfas. Iudkmn sa alp`ad ukd lazi`d ma cdsas ``dldmd Kftrnx (qua inktfahdstd 92% ma N5) `ns euzns puamak parldkaiar d prnbukmfmdmas ma asta tfpnr uk parfnmn ldynr. Yfk aledrcn, pdrd masiakmar duk läs, maeak alp`alazi`ds aspaifd`as ma cdsas inln a` ]rflfx. Æstd as ukd lazi`d raspfrdtnqua inktfaka nxìcakn, ha`fn y kftrùcakn. Axp`fqua utf`fzdkmn `ns prfkifpfns `ns cdsas `ds fkbnrldifnkas dktarfnrlakta lakifnkdmds.
3. Qstam tfaka uk c`nen tntd`lakta a`ästfin ink uk vn`ulak ma 1 ftrns. Axp`fqtras bnrlds mfbaraktas ak ds iud`as pnmrìd dulaktdr a` vn`ulak ma mfihn c`ndp`fidkmn `ns prfkifpfns ma `ns cdsas.
Qkd bdlf`fd vfdjù ma Idrtdcakd d Encntä. D` ``acdr `ns kaulätfins ma` dutnlùvfsa astd``drnk sfk axp`fidifùk dpdrakta, pnr a``n hfifarnk `d sfcufakta `fstd ma pnsef`fmdmas pdrd axp`fidr `n niurrfmn
D. Qkd tdihua`d ak a` idlfkn, qua pfkihù ukd ma `ds ``dktds
E. Fkb`drnk `ds ``dktds d` läxfln ak Idrtdcakd
I. Qk huain
M. A` euak i`fld d` ``acdr d Encntä
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4. @d axp`fidifùk dmaiudmd as:
d. D
e. E
i. I
m. M
5. A` bakùlakn sa axp`fid pnr `d @ay ma:
d. Eny`a
e. Ihdr`as
i. Cdy @ussdi
m. Cdsas fmad`as
9. @ds vdrfde`as qua fkb`uyarnk ak `d axp`nsfùk ma `ds ``dktds buarnk:
d. Rn`ulak y talpardturd
e. Rn`ulak y idktfmdm ma ldtarfd
i. Rn`ulak y prasfùk
m. _rasfùk y talpardturd
=. Inlakta ink sus inlpdôarns iùln fkb`uyarnk ds vdrfde`as pdrd qua ds `dktaxp`ntdrdk.
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]ùlasa ukns lfkutns pdrd paksdr ma bnrlfkmfvfmud` snera `ds sfcufaktas pracuktds:
¾_nr quæ ds eaefmds cdsansds pfarmak a` cds ink läs rdpfmaz ak i`flds id`fakta
¾_nr quæ as pnsfe`a sd`dr ukd snpd sfk dmfifnkdr läs sd`, sù`n avdpnrdkmn a` dcuma `d lfsld>
¾_nr quæ sa mfia qua ak a` ldr Luartn tnmn b`ntd>
¾_nr quæ iudkmn sa inla uk d`flaktn luy sd`dmn ukn sfakta sam>
¾_nr quæ sumdlns>
@ds sn`uifnkas sa i`dsfbfidk inln lazi`ds hnlncækads, inlpuastds ma mnsn läs sustdkifds, qua kn puamak fmaktfbfidrsa d sflp`a vfstd y qua kn radi-ifnkdk aktra sì
_rnpfamdmas in`fcdtfvds ma `ds mfsn`uifnkas
Yn`uifnkasQkfmdm 8. Yn`uifnkas Yasfùk
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Qkd mfsn`uifùk n sn`uifùk as ukd lazi`d hnlncækad ma mns n läs sustdkifds7 aa``ds kn puamak mfstfkcufrsa sus inlpnkaktas. @ds sn`uifnkas snk edstdkta inlukasd mfdrfn takalns inktditn ink a``ds. A` dfra qua raspfrdlns, a` dcud ma ldr, a` dtùa` ernkia y a` nrn inkstftuyak ajalp`ns ma æstds. @ds sn`uifnkas astäk inlpuastpnr mns sustdkifds: a` sn`utn y a` mfsn`vakta.
• A` sn`utn as d sustdkifd qua sa mfsua`va. _nr n cakard`, astä prasakta ak lakidktfmdm qua a` mfsn`vakta.
• A` mfsn`vakta as a` lamfn ma mfsparsfùk ma` sn`utn.
A]D_DY MA @D BNULDIFÙK MA QKD MFYN@QIFÙK
@ds mfsn`uifnkas sa i`dsfbfidk sacúk a` kúlarn ma inlpnkaktas ak:
• Efkdrfds, bnrldmds pnr mns inlpnkaktas.• ]arkdrfds, bnrldmds pnr tras inlpnkaktas.• Iudtarkdrfds, bnrldmds pnr iudtrn inlpnkaktas.
@ds mfsn`uifnkas prasaktdk idrditarìstfids aspaiìbfids inln ds sfcufaktas:
• Yu dspaitn as ukfbnrla, as maifr, qua sus inlpnkaktas kn sa puamak mfstfkcud sflp`a vfstd.
• @ds pdrtìiu`ds kn sa praifpftdk ink a` trdksiurrfr ma` tfalpn iudkmn a` sn`usa hd mfsua`tn tntd`lakta
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• A` sn`utn ma ukd mfsn`uifùk puama astdr prasakta ak mfbaraktas prnpnrifnk
• @ds mfsn`uifnkas, pnr `n cakard`, snk trdkspdraktas.
• @ns inlpnkaktas ma `ds mfsn`uifnkas kn idlefdk su inlpnsfifùk quìlfid
• A` sn`utn ma ukd mfsn`uifùk puama pdsdr d trdvæs ma iud`qufar bf`trn, pnr n tdtn, kn sa puama sapdrdr pnr bf`trdifùk7 astn sa maea d` tdldôn ma `ds pdrtìiuqua `d inlpnkak.
@ds dktarfnras idrditarìstfids mfstfkcuak d `ds sn`uifnkas ma `ds lazi`ds hatarnckads, iuyd inlpnsfifùk kn as `d lfsld ak tnmns `ns puktns, y sus inlpnkaktaspuamak mfstfkcufr ink bdif`fmdm.
D` inksfmardr `d idktfmdm ma sn`utn prasakta ak `d mfsn`uifùk, sa puamak mfstfkcvdrfns tfpns ma sn`uifnkas sacúk su inkiaktrdifùk: fksdturdmds, inkiaktrdmds, sdrdmds y snera sdturdmds.
]fpns ma sn`uifùk
Qkd sn`uifùk mf`ufmd as dqua``d ak d iud` d ink-
iaktrdifùk (idktfmdm) ma sn`utn as ra`dtfvdlakta
edjd ak ra`difùk ink `d idktfmdm ma mfsn`vakta.
Yn`uifùk inkiaktrdmd, as d qua inktfaka ldynr
idktfmdm ma sn`utn qua ukd mf`ufmd.
Yn`uifùk sdturdmd, as dqua``d ak `d iud` `d
idktfmdm ma sn`utn qua sa puama mfsn`var d ukd
talpardturd mdmd ``acd d` läxfln vd`nr.
Yn`uifùk snerasdturdmd, as dqua``d qua inktfaka
ldynr idktfmdm ma sn`utn ma n qua knrld`lakta
puama inktakar d ukd matarlfkdmd talpardturd.
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_UN_FAMDMAY A@AI]UN@Ì]FIDY MA @DY YN@QIFNKAY
@ns sn`utns sa puamak i`dsfbfidr ak mns crupns: dqua``ns qua d` mfsn`varsa snk idpdiama inkmuifr d a`aitrfifmdm, `dldmns a`aitrn`ftns y dqua``ns qua kn, kn a`aitrn`ftns
D su vaz, `ns a`aitrn`ftns puamak sar buartas n mæef`as y mapakma ma `d idpdifmdqua tfakak æstns pdrd mfsn`varsa, yd qua `ns prflarns, d` aktrdr ak inktditn ink asn`vakta, sa mfsnifdk pnr inlp`atn ak sus fnkas, lfaktrds qua ns sacukmns, sf efasa mfsua`vak, kn sa mfsnifdk d` 4??% .
Dhnrd as pnsfe`a axp`fidr lajnr `ns rasu`tdmns netakfmns ak a` `denrdtnrfn ma `sasfùk 1:
I`dsfbfidifùk ma `ds sustdkifds ak mfsn`uifùk diunsd
Mfsn`uifnkas sù`fmds:
Qkd sn`uifùk kn sa inlpnka sù`n ma `ìqufmns mfsua`tns ak dcud. @ds sn`uifnkapuamak sar ma vdrfns tfpns:
A`aitrn`ftn buarta A`aitrn`ftn mæef` Kn a`aitrn`ftn
HI` IH9INN (KH
5 )
5IN úrad
HKN9 HB IH
9NH Latdkn`
IH`N= HKN5 I5H1NH Atdkn` H5YN
= KH
9I
2H
45N
2 C`uinsd
KdNH H5N I
45H
55N
44 Ydidrnsd
Ed (NH)5
KdI` y inlpuastns
fùkfins
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Inlpnkakta 4 Inlpnkakta 5 Astdmn bfkd` ma `d sn`uifùk Ajalp`ns
Cds Cds Cds Dfra Cds @ìqufmn @ìqufmn Cdsansds Cds Yù`fmn Yù`fmn Hfa`n
@ìqufmn @ìqufmn @ìqufmn Iarvazd Yù`fmn @ìqufmn @ìqufmn Dcud Yd`dmd Yù`fmn Yù`fmn Yù`fmn Hfarrn
Dukqua `ds mfsn`uifnkas ak su ldynrìd snk `ìqufmds, axfstak sn`uifnkas qua sa aiuaktrdk ak astdmn sù`fmn7 æstds sa maknlfkdk d`adifnkas, ak `ds iud`as uk sù`fsa akiuaktrd mfsua`tn ink ntrn, n, dld`cdlds qua snk d`adifnkas ma latd`as inl`d p`dtd n a` astdôn ink a` lariurfn. ]nmds `ds lazi`ds ma sù`fmns, `ìqufmns n cds
mfsua`tns ak uk sù`fmn sa maknlfkdk mfsn`uifnkas sù`fmds.
Ldtarfd`as inln a` ernkia (inera y astdôn), a` diarn (hfarrn, idrenkn, ldkcdkakìqua`, vdkdmfn), a` `dtùk (inera y zfki), snk ajalp`ns ma mfsn`uifnkas sù`fmds.
Mfsn`uifnkas ìqufmds
@ds mfsn`uifnkas `ìqufmds snk `ds läs inknifmds y alp`admds, sa bnrldk d` lazi
ukd sustdkifd sù`fmd, `ìqufmd n cdsansd ak uk `ìqufmn.
Yn`utn
Cds
@ìqufmn
Yù`fmn
Mfsn`vakta
@ìqufmn
@ìqufmn
@ìqufmn
Ajalp`n
Eaefmds cdsansds (mfùxfmn ma idrenkn ak dcud).
A` vfkdcra (äifmn diætfin ak dcud).
Yd` ak dcud.
Mfsn`uifnkas cdsansds
Iudkmn sa mf`uya ak uk lamfn cdsansn iud`qufar sustdkifd sù`fmd, ìqufmd n cdsansa bnrldk `ds sn`uifnkas cdsansds. Ya puamak knlerdr inln ajalp`ns ma asta tfma sn`uifnkas, a` dfra y a` cds qua sa usd ak `ds astubds.
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Yn`utn Mfsn`vakta Ajalp`n
Cds Cds A` dfra.
@ìqufmn Cds I`nrnbnrln avdpnrdmn ak kftrùcakn.
Yù`fmn Cds Hfa`n sain sue`fldmn ak kftrùcakn.
BDI]NUAY TQA DBAI]DK @D YN@QEF@FMDM
Inln `d sn`uef`fmdm hdia rabarakifd d `d idktfmdm ma sn`utn qua sa mfsua`va ak usn`vakta d ukd talpardturd aspaiìbfid, as pnsfe`a d`tardr`d idlefdkmn `ds inkmfifnkas ak `ds qua sa prapdrdk `ds sn`uifnkas. Hdy mns bditnras qua fktarvfakak ak sn`uef`fmdm: `d talpardturd y `d prasfùk.
- ]alpardturd:
Iudkmn sa dulaktd d talpardturd ma uk sfstald, sa fkiralaktd d akarcìd ifkætfima` lfsln, maefmn d qua `ds pdrtìiu`ds sa luavak läs y ink ldynras va`nifmdmaAstn flp`fid qua as läs bäif` mfsn`var ukd sustdkifd sf `d talpardturd as a`avdmd7 aidlefn, `ds insds sa inlp`fidk d edjds talpardturds.
_nr `d lfsld rdzùk qua, d ldynr talpardturd, hdy ldynr lnvflfaktn ma `ds pdrtiu`ds, a` idsn dktarfnr kn dp`fid d ns cdsas. Uaiuærmasa qua æstns snk lakns maksnqua `ns `ìqufmns y sf `d talpardturd sa fkiralaktd, a` lnvflfaktn ma `ds pdrtìiu`cdsansds tdlefæk n hdrä, ma dhì qua a``ds sa asidpak ma d sn`uifùk d talpardturläs d`tds.
- _rasfùk:
@n qua sì bdvnraia `d sn`uef`fmdm ma uk cds as `d prasfùk. D ldynr prasfùk, ldyn
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IN y IN5 dlefaktd`as, yd qua astns cdsas snk d`ldiakdmns pnr `ns niædkns y updrta ma a``ns ncrd radiifnkdr quìlfidlakta, bnrldkmn äifmn idreùkfin, d`tardk`ds inkmfifnkas kdturd`as ma` ainsfstald ldrfkn.
_UN_FAMDMAY IN@FCD]FRDY N IN@AI]FRDYYnk prnpfamdmas axtaksfvds, puastn qua mapakmak ma `d idktfmdm ma pdrtìiu`ds sn`utn (kn ma su kdturd`azd), prasaktas ak `d mfsn`uifùk y snk prnpfds ma sn`uifnkfksdturdmds (mf`ufmds).
- Mfslfkuifùk ma `d prasfùk ma vdpnr:
]akcd ak iuaktd qua `ds pdrtìiu`ds qua inkbnrldk `d ldtarfd kukid astäk qufatak pdrtfiu`dr sf sa trdtd ma uk `ìqufmn n cds.
Ak a` idsn pdrtfiu`dr ma `ns `ìqufmns, sus pdrtìiu`ds sa luavak ak tnmds `ds mfraiikas y d`cukds ma `ds qua astäk ak `d suparbfifa `ncrdk asidpdr ma` sfstald ak bnrlma cds, lfaktrds qua `ds qua astäk ak astdmn cdsansn, pnr abaitns ma `d dmhasfùvua`vak d` astdmn `ìqufmn. Dsì, iudkmn `d va`nifmdm ma avdpnrdifùk as fcud` d `d inkmaksdifùk, sa tfaka `d prasfùk ma vdpnr ma uk `ìqufmn.
Iudkmn uk sn`utn as kn vn`ätf`, dbaitd mfraitdlakta d prasfùk ma` mfsn`vakta, puaqua `a mfbfiu`td `d `feardifùk ma pdrtìiu`ds ak bnrld cdsansd, d` hdear ldynr dmhsfùk, mfslfkuyakmn `d prasfùk ma vdpnr ma` sfstald.
- A`avdifùk ma` puktn ma aeu``fifùk:
A` puktn ma aeu``fifùk as uk bakùlakn ak a` qua `d prasfùk ma vdpnr ma uk `ìqufas fcud` d `d prasfùk axtarkd. Ink `d dmfifùk ma uk sn`utn kn vn`ätf` `d prasfùk vdpnr mfslfkuya. Ak inksaiuakifd, as läs mfbìif` `ncrdr fcud`dr astd prasfùk inkma `ns d`ramamnras, lntfvn pnr a` qua a` puktn ma aeu``fifùk sa fkiralaktd.
- Mfslfkuifùk ma` puktn ma inkca`difùk:
Ak `ns pdìsas mnkma kfavd, as usud` racdr `d kfava ink sd`, yd qua æstd sa marr
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A` dcud y luihns ntrns ìqufmns sa akiuaktrdk luy astde`as ak asta astdmn ma dcracdifùk, inln inksaiuakifd ma `ns puaktas ma hfmrùcakn. Æstns snk fktardiifnkaa`æitrfids qua sa prasaktdk aktra `ds ln`æiu`ds, inln inksaiuakifd ma `ds idrcdqua sa cakardk pnr abaitns ma `d dtrdiifùk ma `ns a`aitrnkas ak uk ak`dia (a`aitrnkacdtfvfmdm). @ns puaktas ma hfmrùcakn snk läs buartas d talpardturds dlefaktalaknras7 pnr asn, pdrd avdpnrdr a` dcud as kaiasdrfn id`aktdr`d.
Iudkmn sa dmfifnkd uk sn`utn, ak pdrtfiu`dr ukd sd`, ds ln`æiu`ds ma` ìqufmn hfmrtdk `d sd`, as maifr, `ds pdrtìiu`ds ma` `ìqufmn rnmadk `ns fnkas pnsftfvns y kacdtfvnma `d sd`, mfslfkuyakmn `d idktfmdm ma puaktas ma hfmrùcakn, hdifakmn läs mfbìisn`fmfbfidr a` `ìqufmn.
- _rasfùk nslùtfid:
@d ùslnsfs as uk bakùlakn prnpfn ma `ds lalerdkds ia`u`dras, qua inksfsta ak pdsn sù`n ma dcud hdifd a` fktarfnr n axtarfnr ma `d iæ`u`d y sa ditfvd mapakmfakmma `d inkiaktrdifùk (idktfmdm) ma sustdkifds mfsua`tds ak a` iftnp`dsld ia`u`dr.
Iudkmn `d iæ`u`d tfaka axiasn ma a`aitrn`ftns ak a` iftnp`dsld, parlfta a` pdsn m
dcud d su fktarfnr, ink a` nejatfvn ma mfsn`var `ns fnkas y dsì mfslfkufr su inkiaktrdifùk, ``aväkmn`d d kfva`as knrld`as. _nr asta lntfvn as qua saktflns sam iudkmfkcarflns d`flaktns luy sd`dmns.
Ak a` idsn inktrdrfn, iudkmn hdy mabfifakifd ma fnkas ak a` iftnp`dsld, d iæ`u`d masd`fr dcud pdrd inkiaktrdr ns a`aitrn`ftns. Asta bakùlakn as prnpfn ma d sumnrdifùIudkmn sumdlns, `d iæ`u`d kaiasftd parmar a`aitrn`ftns pdrd qua æstns dyumak ak trdkslfsfùk ma ns flpu`sns karvfnsns, ak d inkvarsfùk ma ns kutrfaktas ak akarcy pdrd qua `ns lúsiu`ns puamdk lnvarsa. D` parmar a`aitrn`ftns, `d iæ`u`d raqufafcud`dr d inkiaktrdifùk fkfifd` pdrd qua bukifnka inrraitdlakta, aktnkias ditfvd sd`fmd ma dcud, ak bnrld ma sumnr, pnr asn asta kn sù`n inktfaka dcud, sfkn dmaläsd`7 ma dhì su sdenr idrditarìstfin.
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@NY IN@NFMAY
@ns in`nfmas snk lazi`ds fktarlamfds aktra `ds mfsn`uifnkas y `ds suspaksfnkas. Ak umfsn`uifùk, `ds pdrtìiu`ds ma sn`utn astäk mfsparsds ma ldkard hnlncækad y kn subrsamflaktdifùk d` quamdr ak rapnsn, maefmn d qua æstds sa akiuaktrdk pdrifd`laukfmds d `ds ln`æiu`ds ma` sn`vakta. Ak `ds suspaksfnkas sì sa prasaktd samflaktdifùmaefmn d qua `ds pdrtìiu`ds snk ra`dtfvdlakta crdkmas.
@ds pdrtìiu`ds ma `ns in`nfmas snk läs crdkmas qua `ds ln`æiu`ds qua bnrldk mfsn`uifnkas7 sfk aledrcn, kn sa prasaktd samflaktdifùk d` majdr`ns ak rapnsn.
@ns in`nfmas sa akiuaktrdk bnrldmns pnr mns pdrtas:
Bdsa mfsparsd: aqufvd`a d` sn`utn ak ds mfsn`uifnkas7 astä inkstftufmd pnr ln`æiu`ds sak``ds n ln`æiu`ds cfcdktas inln a` d`lfmùk. _uama ditudr inln uk inkjuktn ma pdrtìiufkmapakmfaktas n qua sa dcrupdk pdrd bnrldr astruiturds ldynras y efak nrcdkfzdm
Bdsa ma mfsparsdkta: as d sustdkifd ak d iud` ds pdrtìiu`ds in`nfmd`as astäk mfstrfeufm
Yacúk a` astdmn bìsfin ak a` qua sa akiuaktrak d bdsa mfsparsd y a` lamfn mfsparsdk`ns in`nfmas puamak sar:
Alu`sfùk (diafta y dcud)
@fnbùefins n `fùbnens, iudkmn `ds pdrtìiu`ds mfsparsds tfakak pnid dbfkfmdmink a` lamfn mfsparsdkta. Astns in`nfmas snk pnin astde`as, ajalp`n ma a``nsnk `ds alu`sfnkas, inln `d bnrldmd d` dcftdr ukd lazi`d ma dcud y diafta.
@fnbì`fins, iudkmn `ds pdrtìiu`ds mfsparsds tfakak ukd buarta dbfkfmdm ink a`
lamfn ma suspaksfùk, pnr ajalp`n, jdeùk mfsua`tn ak dcud.
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I`dsas ma in`nfmas
FL_NU]DKIFD MA @NY IN@NFMAY
Luihns ma ns d`flaktns qua inksulflns inln a` quasn, d ldktaquf``d y d jd`adsnk in`nfmas.
@ds alu`sfnkas inkstftuyak lamfidlaktns, inln pnr ajalp`n `d Alu`sfùk ma Yintt.
Ak d fkmustrfd sa utf`fzdk pdrd d bderfidifùk ma iarälfids, p`ästfins, taxtf`as, pdpapa`ìiu`ds bntncräbfids, tfktds, ialaktns, cnlds, iuarns, `uerfidktas, jdenkas, fksaitfifmds dcrìin`ds y matarcaktas, aktra ntrns.
I`dsa ma in`nfma Bdsa mfsparsd Bdsa mfsparsdkta Ajalp`ns
Aspuld Cds @ìqufmn Irald edtfmd
Aspuld sù`fmd Cds Yù`fmn _famrd pùlaz
Darnsn` @ìqufmn Cds Kueas
Alu`sfùk @ìqufmn @ìqufmn Ldynkasd, `aiha, prntnp`dsld ia`u`dr
Alu`sfùk sù`fmd @ìqufmn Yù`fmn Tuasn, ldktaquf``d
Huln Yù`fmn Cds Huln, pn`vn ma` dfra
Yn` Yù`fmn @ìqufmn Akcrumn, jd`ads
Yn` sù`fmn Yù`fmn Yù`fmn Ifartds d`adifnkas
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_UN_FAMDMAY MA @NY IN@NFMAY
• Abaitn ]ykmd``: sa prasaktd iudkmn d trdvæs ma uk in`nfma sapuama var `d trdyaitnrfd ma uk rdyn ma `uz, maefmn d qua `dspdrtìiu`ds suspakmfmds `d rab`ajdk.
• Lnvflfaktn Ernwkfdkn: masirfea a` lnvflfaktn inktfkunma `ds pdrtìiu`ds ma uk in`nfma.
• Dmsnrifùk: d` pnsaar ukd crdk ärad suparbfifd`, `ds pdrtìiu`ds
ma `ns in`nfmas dtrdak y ratfakak sustdkifds ak su suparbfifa.
• Mfä`fsfs: prniasn ma sapdrdifùk ma fnkas y ln`æiu`ds ma pdr-tìiu`ds in`nfmd`as d trdvæs ma lalerdkds salfparlade`as.
Mfsn`uifnkas diunsds y su inkiaktrdifùk
Iudkmn ak ukd sn`uifùk a` mfsn`vakta as a` dcud, sa bnrld `ds mfsn`uifnkas diuns_nr `n cakard`, ak asta tfpn ma sn`uifnkas a` sn`utn sa akiuaktrd prasakta ak lakprnpnrifùk qua a` sn`vakta.
D`cukns ajalp`ns ma sn`uifnkas diunsds qua sa utf`fzdk d mfdrfn snk: `d `aiha, rabrasins, a` idbæ fkstdktäkan ak dcud, a` vfkdcra, ns matarcaktas ìqufmns, ns ìqufm
pdrd `flpfdr vfmrfns, `d lfa`, ati.
Yn`uef`fmdm
@d sn`uef`fmdm as `d prnpfamdm qua tfaka ukd sustdkifd ma mfsn`varsa n mf`ufrsa ntrd. Masirfea `d idktfmdm ma sn`utn qua as mfsua`td ak ukd idktfmdm ma sn`vak_drd lamfr `d sn`uef`fmdm ma ukd sustdkifd, sa id`iu`d `d idktfmdm ak crdlns ma sn`utn kaiasdrfn pdrd sdturdr ifak crdlns ma uk sn`vakta matarlfkdmn, d ukd ta
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Ajalp`n:
88 crdlns ma kftrdtn ma snmfn sa mfsua`vak ak 4?? crdlns ma dcud d 5?ºI, pinksfcufakta, `d sn`ue`fmdm ma astd sd` as ma 88 c ma kftrdtn/4?? c ma dcud.
QKFMDMAY MA INKIAK]UDIFÙK
Iudktdtfvdlakta, d inkiaktrdifùk ma ds mfsn`uifnkas sa axprasd dtakmfakmn d` tfpma ra`difùk qua axfsta aktra `ds idktfmdmas axditds ma sn`utn y mfsn`vakta.
_nriaktdja: as `d ra`difùk ma ldsd n vn`ulak aktra a` sn`utn y a` sn`vakta atærlfkns ma pnriaktdja:
Ajalp`n:
Yf 91c ma KdI` sa mfsua`vak ak 4?1c ma dcud, ¾iuä` as a` pnriaktdja ma KdI` ak sn`uifùk>
Yn`uifùk:
@ns mdtns sulfkfstrdmns pdrd a` ajarififn snk:
• Yn`utn: KdI`
• Idktfmdm ma sn`utn: 91 c
• Mfsn`vakta: Dcud
• Idktfmdm ma mfsn`vakta: 4?1 c
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• % ma KdI` ak `d sn`uifùk < >
_nr `n tdktn, `d mfsn`uifùk prapdrdmd inktfaka ukd inkiaktrdifùk ma` 51% (ldldsd) ma KdI`. Asta vd`nr sfckfbfid qua ak `d sn`uifùk hdy 51c ma KdI` pnr id4??c ma sn`uifùk.
A` pnriaktdja vn`ulak d vn`ulak, sa alp`ad pdrd axprasdr `ds inkiaktrdifnk
ma `ìqufmns. Ya mabfka inln a` vn`ulak ma sn`utn ak uk vn`ulak ma 4?? l` sn`uifùk. Dsì, ukd sn`uifùk d` 41% ak vn`ulak ma d`inhn` ak dcud, inktfaka l@ ma d`inhn` pnr idmd 4??l@ ma sn`uifùk (a`flfkdr 31l@ ma dcud). A` pnriaktvn`ulak d vn`ulak sa id`iu`d utf`fzdkmn `d sfcufakta axprasfùk ldtalätfid:
Ajalp`n:
¾Iuä` as a` pnriaktdja vn`ulak d vn`ulak ma ukd mfsn`uifùk qua inktfaka 1 lma d`inhn` ak 51 l` ma dcud>
Yn`uifùk:
Mdtns ma` ajarififn.
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• Yn`vakta: 51 l` (dcud)
Rn`ulak tntd` ma `d mfsn`uifùk:
51% l` ma dcud + 1 l` ma d`inhn` < 9? l` ma sn`uifùk.
_nr `n tdktn, a` pnriaktdja ak vn`ulak ma d`inhn` ma ukd mfsn`uifùk qua inktfak1 l` ma d`inhn` ak 51 l` ma dcud as 42,22%.
- Brdiifùk ln`dr (X): raprasaktd `d ra`difùk ma mns idktfmdmas salajdktas. Yaxprasd inln XD y sa id`iu`d dsì:
D` bfkd`, `d suldtnrfd ma `ns pnriaktdjas ma idmd sustdkifd qua bnrld `d sn`uifùmaea sar fcud` d` 4??%
- Ln`drfmdm (L): hdia rabarakifd d `d idktfmdm ma ln`as ma sn`utn prasaktaak uk `ftrn ma sn`uifùk:
- Ln`d`fmdm (l): as `d idktfmdm ma ln`as ma sn`utn pnr idmd gf`ncrdln ma snvakta:
1 l` ma d`inhn`
9? l` ma sn`uifùk% ak Rn`ulak < x 4?? < 42,22
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- Knrld`fmdm (K): idktfmdm ma aqufvd`aktas-crdln (Aq-c) ma sn`utn ak uk fma sn`uifùk:
@ns aqufvd`aktas snk mfbaraktas, mapakmfakmn ma `d sustdkifd, dsì:
• Aqufvd`akta-crdln pdrd äifmns:
_nr ajalp`n, id`iu`a `ns aqufvd`aktas crdln ma 36c ma H5YN=:
• Aqufvd`akta-crdln pdrd hfmrùxfmns:
• Aqufvd`akta-crdln pdrd hfmrùxfmns:
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• Aqufvd`akta-crdln pdrd sd`as u ùxfmns:
@denrdtnrfn ma sn`uifnkas:
d. Ùslnsfs
4. In`nqua 9?l@ ma ukd sn`uifùk ma d`lfmùk d` 1% ak uk Ar`aklayar m4??l@. Iuerd d enid ma` Ar`aklayar ink pdpa` ia`nbäk ma bnrld ukfbnrlama lnmn td` qua d` vn`tadr`n kn sa marrdla a` d`lfmùk (puama dldrrdr a
ia`nbäk ink dyumd ma uk iduihn).
5. Uapftd a` lfsln prniamflfaktn ak ntrn Ar`aklayar ma` 4??l@, parn avaz ma dmfifnkdr d`lfmùk, in`nqua 9?l@ ma Fsnmfka n iud`qufar dktfsæptfid edsa ma ynmn. _uama usdrsa @ucn` sf hdy ak a` `denrdtnrfn.
9. ]nla mns vdsns ma praifpftdmns ma 51?l@ y in`nqua ak a` prflar4??l@ ma `d sn`uifùk ma d`lfmùk d` 1%. D` sacukmn dmfifùka`a 4??l@ mFsnmfka.
=. Fktrnmuzid ma bnrld fkvartfmd a` Ar`aklayar ink a` d`lfmùk ak a` vdsqua inktfaka Fsnmfka.
1. Uapftd a` prniamflfaktn dktarfnr, parn astd vaz in`nqua a` Ar`aklayaink Fsnmfka snera a` vdsn ink d`lfmùk.
4
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2. In`nqua ak uk tuen ma aksdyn 4?l@ ma sn`uifùk ma d`lfmùk y maja idsnera æstd uk ihnrrftn ma Fsnmfka. ]akcd prasakta d in`nrdifùk qua tnldsn`uifùk pdrd qua puamd dkd`fzdr `n qua niurrfrä ink a` axparflaktn.
3. Fkfifa `d sfcufakta präitfid (prapdrdkmn sn`uifnkas) y iudkmn tarlfink a``d nesarva `ns idlefns qua sa prasaktdrnk ak `ns Ar`aklayars n `ns vdsns ma praifpftdmns.
8. Inlakta ink sus inlpdôarns ak p`akdrfd.
e. _rapdrdkmn sn`uifnkas:
6. Ldrqua 4? vdsns ma p`ästfin ink kúlarns.
4?. Dcracua d idmd ukn 5??l@ ma dcud.
44. Dmfifnka d idmd vdsn `ds sfcufaktas idktfmdmas ma rabrasin ak pn`vink dyumd ma ukd iuihdrftd:
Rdsn Idktfmdm ma rabrasin
4 @n qua injd ink `d puktd ma ukd iuihdrftd 5 Lamfd iuihdrdmftd 9 Qkd iuihdrdmftd = Qkd iuihdrdmftd y ukd pfzid läs
1 Iuihdrdmftd y lamfd 2 Mns iuihdrdmftds 3 Mns iuihdrdmftds y lamfd 8 9 iuihdrdmftds 6 = iuihdrdmftds4? 3 iuihdrdmftds
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45. Lazi`a `ds sn`uifnkas hdstd `d läxfld mfsn`uifùk7 kn fksfstd ink `dqua kn sa mfsua`vak.
49. _ruaea idmd ukd ma `ds lazi`ds y ink edsa ak a` sdenr matarlfka qu
tfpn ma sn`uifùk as. Dknta sus nesarvdifnkas ak `d sfcufakta tde`d:
Rdsn
45
9=1238
64?
Ydenr ]fpn ma sn`uifùk
Hd``a `ds sfcufaktas ukfmdmas ma inkiaktrdifùk:
4. Ya prapdrd ukd sn`uifùk qua inktfaka 51c ma KdI` ink 5??c ma dcudId`iu`a d) `d brdiifùk ln`dr ma `ns inlpnkaktas y e) `d ln`d`fmdm ma `d sn`uifùk.
5 Id`iu`a a` pnriaktdja ma idmd ukd ma `ds sfcufaktas sn`uifnkas: d) 81
6
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ma dzúidr ak 5??l@ ma sn`uifùk, e) 38c ma inera ink 4??c ma sn`uifùk,9? l@ ma atdkn` ak 51?l@ ma sn`uifùk.
9. Id`iu`a a` vn`ulak ma sn`uifùk qua maea lamfrsa pdrd prapdrdr u
sn`uifùk ma dzúidr ma lasd (sdidrnsd I45H55N44) 5L, d pdrtfr ma 5?ma` dzúidr.
=. Id`iu`a a` pnriaktdja, `d L y `d K ma ukd sn`uifùk ma 98c ma KdI` 41?l@ ma sn`uifùk.
1. Id`iu`a a` pnriaktdja, `d L y `d K ma ukd sn`uifùk ma 65c ma H9_N= 51?l@ ma sn`uifùk.
Qk astumfdkta rad`fzd uk axparflaktn ak a` qua tnld tras vdsns mapraifpftdmns ink 4?? c ma dcud d 5?¿I y sfcua a` prniamflfaktn qua samasirfea d inktfkudifùk:
D` vdsn 4 a dcracd 41 c ma GI` y dcftd. @uacn, dcracd uk irfstd` dmfifnkdma GI` qua sa mfsua`va. D` vdsn 5 `a dcracd 91 c ma GI` y dcftd. D` idenma uk tfalpn, dcracd uk irfstd` dmfifnkd` ma GI` qua ida d` bnkmn. Dvdsn 9 `a dcracd 1? c ma GI`, id`faktd hdstd 3?¿I y `n majd rapnsdr pdrd
mfslfkufr d talpardturd aktdlakta. Maspuæs ma uk tfalpn, dcracd ukirfstd` dmfifnkd` ma GI`, a` iud` alpfazd d iraiar dc`nlardkmn d idktfmdmma sn`utn qua astä ak axiasn.
@d tde`d qua lajnr raprasaktd `d inki`usfùk ma` astumfdkta snera a` tfpnma sn`uifùk qua sa netfaka ak idmd ukn ma `ns vdsns as:
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Rdsn Inki`usfùk
4 @d sn`uifùk sa akinktrded sdturdmd pnrqua kn
mfsua`va läs sd`.
5 @d sn`uifùk as snerasdturdmd pnrqua kn mfsua`va läs
sd` y parlfta bnrldr irfstd`as.
9 @d sn`uifùk as kn sdturdmd pnrqua dúk puama mfsn`var
läs sd`.
Rdsn Inki`usfùk
4 @d sn`uifùk as snerasdturdmd pnrqua kn mfsua`va läs
sd` y parlfta bnrldr irfstd`as.
5 @d sn`uifùk as kn sdturdmd pnrqua dúk puama mfsn`var
läs sd`.
9 @d sn`uifùk sa akinktrded sdturdmd pnrqua kn mfsua`
va läs sd`.
d.
e.
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Rdsn Inki`usfùk
4 @d sn`uifùk as kn sdturdmd pnrqua dúk puama mfsn`var
läs sd`.
5 @d sn`uifùk sa akinktrded sdturdmd pnrqua kn
mfsua`va läs sd`.
9 @d sn`uifùk as snerasdturdmd pnrqua kn mfsua`va läs
sd` y parlfta bnrldr irfstd`as.
Rdsn Inki`usfùk
4 @d sn`uifùk as snerasdturdmd pnrqua kn mfsua`va lässd` y parlfta bnrldr irfstd`as.
5 @d sn`uifùk sa akinktrded sdturdmd pnrqua kn
mfsua`va läs sd`.
9 @d sn`uifùk as kn sdturdmd pnrqua dúk puama mfsn`var
läs sd`.
i.
m.
Astumfdktas ]rdksbnrlalns,ink a` Yfstald Fktarditfvn.
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]ùlasa ukns lfkutns pdrd paksdr ma bnrldfkmfvfmud` snera `ds sfcufaktas pracuktds:
¾Tuæ as `d cdstrftfs>, ¾quæ lamfidlaktns sua`as usdrsa pdrd trdtdr astd akbarla-mdm>, ¾iùln bukifnkdk quìlfidlakta asns bärldins>
¾_nr quæ `d Inid-In`d quftd a` ùxfmn ma `ns latd`as>
D`cukns ma ns prniasns quìlfins ma` iuarpn y d fkmustrfd sa `avdk d iden pnr lamma radiifnkas äifmn-edsa, inknifmds tdlefæk inln radiifnkas ma kautrd`fzdifùk
Inln vflns ak `d sasfùk 2, `ns äifmns snk sustdkifds inkbnrldmds pnr `d ukfùk m
uk hfmrncakfùk (H+) ink uk a`alaktn kn latä`fin, qua d vaias puama astdr dinlpdôdmn pnr nxìcakn.
Axfsta ntrd mabfkfifùk pdrd äifmns, inln dqua``ns qua d` aktrdr ak inktditn ink dcud sa fnkfzdk, `feardkmn prntnkas (H+) d` lamfn. Asta inkiaptn bua prnpuastpnr Drrhakfus, qufæk dmaläs pnstu`ù qua ukd sustdkifd eäsfid as idpdz ma fnkfzdrsak dcud, `feardkmn fnkas hfmrnxf`ns (NH)-4.
Äifmns, edsas y sd`as
pH y aquf ferfn quìlfinQkfmdm 8. Yn`uifnkas Yasfùk
4?
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• Buartas: sa mfsnifdk ak uk 4??% ak dcud.
• Mæef`as: sa mfsnifdk pdrifd`lakta.
Aquf`ferfn äifmn-edsa
_drd `d quìlfid, `ns aquf`ferfns sa mdk iudkmn `ds va`nifmdmas ma `ns prniasns sfcud`as. Ak a` idsn ma ukd radiifùk quìlfid, a` aquf`ferfn sa `ncrd iudkmn `d va
ifmdm ma `d radiifùk ma `ns raditfvns pdrd bnrldr prnmuitns as fcud` d `d va`nifmma radiifùk ma `ns prnmuitns pdrd bnrldr d `ns raditfvns. D asta tfpn ma radiifnktdlefæk sa `as ``dld radiifnkas ravarsfe`as, yd qua kn vdk ak uk sn`n saktfmn, sfqua puamak mavn`varsa ma `ns prnmuitns d `ns raditfvns7 sa raprasaktdk ink b`aihd ma mne`a saktfmn n ink mns b`aihds ak saktfmn inktrdrfn.
Qk ajalp`n ma asta tfpn ma radiifùk as `d qua sa md aktra `ns äifmns y `ds edsas
@d b`aihd kns fkmfid qua a` sfstald astä ak aquf`ferfn y pnmalns raiurrfr d `ds ltalätfids pdrd hd``dr ukd inkstdkta ak `d qua asta bakùlakn sa md. D mfihn vdsa `a inknia inln `d inkstdkta ma aquf`ferfn (G) y sa id`iu`d dsì:
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pH inln lamfmd ma `d difmaz
A` tærlfkn pH makntd ukd ukfmdm ma lamfmd ma `d inkiaktrdifùk ma `ns prntnkaak ukd sn`uifùk. Ink a` pH as pnsfe`a matarlfkdr iuäkmn `ds sustdkifds snk äifmdeäsfids n kautrds7 pdrd a``n as flpnrtdkta astumfdr ak prflar `ucdr ukd sustdki
qua inktfaka tdktn prntnkas inln hfmrnxf`ns y qua as a` ldrin ma rabarakifd ma nvd`nras ma pH. Asta inlpuastn as a` dcud.
D pasdr ma sar uk a`aitrn`ftn mæef`, a` dcud axparflaktd ukd paquaôd fnkfzdifùk ds
Ink edsa ak asta sfstald, `d inkstdkta ma aquf`ferfn ma dutnfnkfzdifùk ma` dcud a
Maefmn d qua sù`n ukd paquaôd idktfmdm ma` dcud sa fnkfzd, idsf qua `d inkiaktrifùk ma` dcud kn idlefd7 aktnkias:
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Ak inksaiuakifd, iudkmn:
Crdifds d astds ra`difnkas ldtalätfids as qua sa hd `ncrdmn astde`aiar d` pH inlukfmdm ma lamfmd ma `d difmaz ma `ds sustdkifds y sa id`iu`d dsì:
Ink edsa ak `n dktarfnr sa tfaka qua:
Ma fcud` bnrld qua ink a` pH, tdlefæk as pnsfe`a hdiar d lfsld ra`difùk ldtaltfid ink `ns hfmrnxf`ns, aktnkias:
Dhnrd, sf sa dp`fid a` `ncdrftln kacdtfvn d` vd`nr ma `d Gw ma` dcud sa netfaka:
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Dhnrd:
Lu`tfp`fqua pnr -4 d `ns mns `dmns ma `d fcud`mdm:
Asta vd`nr parlftfù astde`aiar ukd asid`d kulærfid ma pH, qua vd masma a` 4 hds4=, mnkma a` 3 as kautrn, dktas ma asa vd`nr as äifmn y maspuæs ma 3 as eäsfin:
Asid`d ma pH
pH äifmnpH kautrn
pH eäsfin
4 5 9 = 1 2 3 8 6 4? 44 45 49 4=
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Kautrd`fzdifùk
@ds rdiifnkas ma kautrd`fzdifùk sa rad`fzdk aktra äifmn y eäsas. Ynk aspaifas radiifnkas ma sustftuifùk. A` äifmn i`nrhìmfin (HIF) radiifnkd ink a` hfmrùxfmn
snmfn (KdNH) pdrd prnmuifr i`nrurn ma snmfn (sd` kautrd):
Astds radiifnkas raifeak td` knlera, maefmn d qua `ns prnmuitns ma `d radiiftfakak pH kautrn, td` inln sa puama var ak a` ajalp`n, mnkma a` i`nrurn ma snm
y a` dcud snk sustdkifds kautrds.
Ak a` dkä`fsfs quìlfin sa sdea qua sa hd `ncrdmn kautrd`fzdr uk äifmn ink ukd ediudkmn a` fkmfidmnr ma pH (dmfifnkdmn d` äifmn dktas ma mdr fkfifn d `d radiifùidlefd ma in`nr.
@ns fkmfidmnras snk sustdkifds luy saksfe`as d `ns idlefns ma pH, puastn qua sidpdias ma ukfrsa d `ns prntnkas y `ns hfmrnxf`ns y mapakmfakmn d qufæk astæk u
mns, takmräk in`nrdifnkas luy aspaiìbfids7 pnr a``n snk fmad`as ak `ds vd`nrdifnkäifmn-edsa.
Fkmfidmnras
Aktra `ns fkmfidmnras äifmn - edsa läs usud`as takalns:
d. A` pdpa` tnrkdsn` dzu` y rnjn. e. A` pdpa` fkmfidmnr ukfvarsd`.
@ns fkmfidmnras snk sustdkifds quìlfids qua sa usdk pdrdinkniar d difmaz n edsfifmdm ma ukd sn`uifùk, a` lnlaktn
iudkmn sa rad`fzd ukd radiifùk ma kautrd`fzdifùk n puktnbfkd` ma ukd tftu`difùk.
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m. A` dkdrdkjdmn ma latf`n. a. Dzu` ma erlntfln`. b. Rarma ma ernlnirasn`.
D`cukns fkmfidmnras sa puamak prapdrdr ak a` denrdtnrfn d pdrtfr ma vacatd`as inl`d in` lnrdmd, `d iaen``d rnjd n `d b`nr ma jdldfid harvfmds ak dcud.
@d pnsfef`fmdm ma lamfr a` pH kn sù`n tfaka vd`nr quìlfin. @d inkstdkifd ma` pH a`ns sfstalds efn`ùcfins as i`dva pdrd su bukifnkdlfaktn.
A` pH ma `d sdkcra as dprnxfldmdlakta 3,9 edjn matarlfkdmds inkmfifnkas, pnajalp`n, ink a` ld` bukifnkdlfaktn ma uk ùrcdkn, a` pH knrld` ma d sdkcra puam
varsa dbaitdmn. Yf a` pH as laknr qua 3,9 sa prnmuia `d difmnsfs latdeù`fid, ukakbarlamdm qua puama dbaitdr a` sfstald karvfnsn iaktrd` y inkmuifr d uk astdmma inld.
B n t n t n l d m d m a w f g f p a m f d
Ak `d ditud`fmdm axfstak `d-enrdtnrfns d`tdlakta aspa-ifd`fzdmns pdrd a` dkä`fsfs masdkcra
Yf pnr a` inktrdrfn, a` pH ma d sdkcra duklaktd, efak sad pnr pærmfmd ma jucn cästrfiak vùlftns raiurraktas, pnr `d fkcastfùk ma bärldins dktfäifmns n pnr dbaiifnkas
rfônk, puama prnmuifrsa d`id`nsfs latdeù`fid, dbaiifùk qua idusd `d mfslfkuifùma` rftln raspfrdtnrfn, aspdslns lusiu`dras y inkvu`sfnkas.
Astds mns d`tarkdtfvds ma pH iudkmn snk savards, puamak idusdr `d luarta.
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Fkmfidmnras ma pH kdturd`as:
4. In`nidr 9?l@ ma atdkn` ak 9 vdsns ma praifpftdmns.
5. Dmfifnka ak a` vdsn ukn uk puôdmn inksfmarde`a ma pætd`ns ma rnsds rnjds, a` vdsn mns irfsdktalns y ak a` vdsn tras ldrcdrftds.
9. Id`fakta d buacn edjn pnr 1 lfkutns idmd vdsn, hdstd qua a` d`inhn` sa in`nr
ink `ns pætd`ns ma `ds b`nras.
=. Enta `ns pætd`ns y cudrma `ns `ìqufmns. Kn n`vfma ldridr `ns vdsns pdrd qua sa inkbukmd ma fkmfidmnr.
1. ]nla 4? tuens ma aksdyn y dcracua:
D` tuen 4: 5?l@ ma jucn ma `flùk. D` tuen 5: 5?l@ ma vfkdcra. D` tuen 9: 5?l@ ma dcud. D` tuen =: 5?l@ ma matarcakta ak pn`vn mf`ufmn. D` tuen 1: 5?l@ ma sn`uifùk sd`fkd. D` tuen 2: 5?l@ ma `aiha. D` tuen 3: 5?l@ ma `aiha ma ldckasfd. D` tuen 8: 5?l@ ma ihdlpú mf`ufmn.
D` tuen 6: 5?l@ ma dzúidr mfsua`td ak dcud. D` tuen 4?: 5?l@ ma Inid-In`d.
2. D idmd tuen dmfifnka 4l@ ma` fkmfidmnr netakfmn ink ns pætd`ns ma `ds rns
3. Uapftd a` pdsn 1 y 2 ink a` fkmfidmnr ma `ns irfsdktalns y `uacn ink a` ma ldrcdrftds. @`aka `d tde`d.
4?
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Yustdkifd In`nrnrfcfkd`
Fkmfidmnr rnsds
Fkmfidmnrirfsdktalns
Fkmfidmnrtu`fpdkas
Jucn ma `flùk
Rfkdcra
Dcud
Matarcakta
Yd`
@aiha
@aiha ma ldckasfd
Ihdlpú
Dzuidr
Inid-In`d
8. Axp`fqua ink edsa ak `ns in`nras iùln ditúdk `ns tras fkmfidmnras.
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4. Nesarva `d sfcufakta cräbfid ma `d asid`d ma pH y `ns raspaitfvns vd`nras md`cukds sustdkifds ma usn idsarn.
Asinjd ifkin sn`uifnkas ma usn inlúk,inln d`flaktns, `flpfdmnras, jdenkas,ati. Qeìqua`ds maktrn ma astd asid`d ma
pH y ra`difnka d`cukds ma sus prnpfamd-mas bìsids, inln in`nr sdenr, n vn`dtfmdmink su pH.
5. A` asquald luastrd a` pH ma d`cukds sustdkifds ma usn braiuakta inkn ihdlpú, dsì inln d`ckns b`ufmns efn`ùcfins inln `d sdkcra, fkmfidkmn pdrd idm
ukn, `d inkiaktrdifùk ma hfmrncakfnkas (WH+\).
Ink edsa ak `d bfcurd fkmfqua:
d. ¾Iuä` as `d sustdkifd läs äifmd> ¾Iuä` as su pH>
e. ¾Iuä` sustdkifd prasaktd uk pH kautrn>, ¾pnr quæ>
4?
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i. ¾Tuæ pdsd ink `d inkiak- trdifùk ma hfmrncakfnkas d
lamfmd qua dulaktd a` pH>
m. ¾Iuä` as `d sustdkifd maldynr edsfifmdm>, ¾iuä` as supH>
9. Inlp`ata `d sfcufakta tde`d:
Yustdkifd Inkiaktrdifùk (L) pH pNH WH+\ WNH-\
HKN9 ?.?4
Lc(NH) 4?
HIF ?.51
KdNH 9
H5
YN=
4X4?-9
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Uaspnkmd `ds pracuktds ink edsa ak `d sfcufakta fkbnrldifùk:
Murdkta a` latden`fsln ia`u`dr sa bnrld IN5 qua as `feardmn d `d sdkcra y atrdkspnrtdmn pnr `ds vakds. D` sar uk ùxfmn äifmn, radiifnkd ink a` dcud pdrbnrldr äifmn idreùkfin, a` iud` fktarvfaka ak a` aquf`ferfn äifmn edsa sdkcuìkadpnr lamfn ma `ds sfcufaktas radiifnkas:
@d sfcufakta tde`d luastrd d`cukds mabfkfifnkas ma äifmns y edsas:
4. Ma diuarmn ink `d fkbnrldifùk dktarfnr, a` fnk efidrenkdtn, HIN9-4, ditú
ak `d aiudifùk:
d. 5, inln ukd edsa pnrqua tfaka ätnlns ma H ak su astruiturd.e. 9, inln ukd edsa pnrqua mnkd d` lamfn uk pdr ma a`aitrnkas `feras.
Ernkstamy @nwry
Äifmn: sustdkifd idpdz ma mnkdr prntnkas (H+4)Edsa: sustdkifd idptdmnrd ma prntnkas
Äifmn: sustdkifd qua diaptd pdras ma a`aitrnkas `ferasEdsa: sustdkifds mnkdmnrd ma pdras ma a`aitrnkas `feras
@awfs
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i. 9, inln uk äifmn pnrqua `feard d` lamfn prntnkas (fnkas H+).m. 5, inln uk äifmn pnrqua puama diaptdr prntnkas (fnkas H+) ma` lamfn.
5. A` pH as ukd lamfmd fkmfraitd ma `d inkiaktrdifùk ma prntnkas, fnkas H+, aukd sn`uifùk. Aktra ldynr as `d idktfmdm ma prntnkas, laknr as a` pH. Madiuarmn ink `ds aiudifnkas dktarfnras, a` fkiralaktn ma IN5 ak `d sdkcra:
d. Fkiralaktd `d inkiaktrdifùk ma prntnkas (fnkas H+) y mfslfkuya a` pH:e. Masp`dzd a` aquf`ferfn hdifd `d fzqufarmd a fkiralaktd `d inkiaktrdifùk ma
prntnkas.i. Fkiralaktd d inkiaktrdifùk ma prntnkas (fnkas H+) sfk lnmfbfidr a` aquf`ferfm. Mfslfkuya `d inkiaktrdifùk ma prntnkas (fnkas H+) y masp`dzd a` aquf`ferfn
hdifd `d maraihd.
9. Qk trdtdlfaktn utf`fzdmn knrld`lakta pdrd mfslfkufr d difmalfd latdeù`fin difmaz ma` p`dsld as a` sulfkfstrn ma` fnk efidrenkdtn HIN9
-4. Ma diuarmink ds aiudifnkas 4 y 5, a` trdtdlfaktn ma d difmalfd latdeù`fid inksfsta adulaktdr `d inkiaktrdifùk ma HIN9
-4ak a` aquf`ferfn pdrd:
d. Mfslfkufr `d inkiaktrdifùk ma IN5 y dulaktdr a` pH.
e. Masp`dzdr d `d fzqufarmd a` aquf`ferfn y dulaktdr a` pH.i. Kautrd`fzdr `d inkiaktrdifùk ma H+ y mfslfkufr a` pH.m. Dulaktdr `d inkiaktrdifùk ma H5N y mfslfkufr a` pH.
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Efe`fncrdbìd
• Drfds _äaz, Harkdkmn. 463=. Cuìd mfmäitfid pdrd a``denrdtnrfn ma quìlfid fknrcäkfid. Qkfvarsfmdm Kdifnkd` maIn`nlefd. Mapdrtdlaktn ma Tuìlfid. Encntä
• Edenr, Jnsaph D`eart. 4689. Tuìlfid cakard` lnmarkd: ukdfktrnmuiifùk d `d Tuìlfid bìsfid y d `d Tuìlfid masirfptfvdsuparfnr (Fknrcäkfid, Nrcäkfid y Efnquìlfid) trdmuifmd,dmdptdmd y dlp`fdmd pnr J. Fedrz. Amftnrfd` Ldrìk. Encntä.
• Earkdrm, Ldurfia. 4661. Iursn ma quìlfid fknrcäkfid7 trd-muiifùk Vn`dkmd Brdkifs C. Amftnrfd` Inktfkaktd`, Læxfin.
• Idstrn Kdrväaz, Ydkmrd _dtrfifd. 5??1. _räitfids ma `denrd-tnrfn: quìlfid fknrcäkfid F. Qkfvarsfmdm Ydktfdcn ma Id`f,QYI. Id`f.
• Ihdkc Udylnkm (5??5). Tuìlfid. Am 3¿. Læxfin: LiCrdwHf``
• Lfkfstarfn ma Amuidifùk Kdifnkd` (5?45). Ydear 44¿ 5?45.Iudmarkf``n ma pracuktds sdear 44¿. In`nlefd: FIBAY. _p.=1 ’ 15.
• (5??=). Astäkmdras eäsfins ma inlpatakifds ak ifakifds kd-tur`as. Bnrldr ak ifakifds: ¡A` masdbìn! @n qua kaiasftdlnssdear y sdear hdiar. In`nlefd: Idrcrdphfis. _p. 55-59
• Nsnrfn U. y Cùlaz D (5??=). Axparflaktns mfvartfmns maquìlfid pdrd jùvakas. Lama``ìk: Qkfvarsfmdm ma Dktfnqufd.
• ]rfdkd Cderfa` (5??4). Tuæ bäif` as `d quìlfid. _räitfids ma`denrdtnrfn. Encntä: Bnkmn ma _ue`fidifnkas ma` CflkdsfnLnmarkn.
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Lùmu`n fktacrdmn pdrd ifi`n 1
]rdksbnrlalns Amuidkmn
Ärad Bìsfid 4?
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A s t ä k m d r a s e ä s f i n s
m a i n l p a t a k i f d s a k
B ì s f i d
A k t n r k n b ì s f i n
I f a k i f d
, t a i k n ` n c ì d
y s n i f a m d m
_ r n i a s n s q u ì l f i n s
•
A x p ` f i n ` d a s t r u i t u r d m a ` n s ä t n l
n s d
p d r t f r m a m f b a r a k t a s t a n r ì d s .
•
R a r f b f i n a ` a b a i t n m a p r a s f ù k y
t a l -
p a r d t u r d a k ` n s i d l e f n s q u ì l f
i n s .
•
U a d ` f z n i ä ` i u ` n s i u d k t f t d t f v n
s a k
i d l e f n s q u ì l f i n s .
•
A x p ` f i n ` n s i d l e f n s q u ì l f i n s m
a s m a
m f b a r a k t a s l n m a ` n s .
•
Q s n ` d t d e ` d p a r f ù m f i d p d r d m a t a
r l f -
k d r p r n p f a m d m a s b ì s f i d s y q u ì l f i d s m a
` n s a ` a l a k t n s .
•
I d r d i t a r f z n i d l e f n s q u ì l f i n
s a k
i n k m f i f n k a s m a a q u f ` f e r f n .
•
A x p ` f i n ` d n e t a k i f ù k m a a k a r c ì d
k u i ` a d r d p d r t f r m a ` d d ` t a r d i f ù k m a
` d a s t r u i t u r d m a ` ä t n l n
_ r n i a s n s b ì s f i n s
•
A s t d e ` a z i n r a ` d i f n k a s a k t r a ` d s m f b a r a k t a s
b u a r z d s q u a d i t ú d k s
n e r a ` n s i u a r p n s
a k r a p n s n n a k l n v f l f a k t n r a i t f ` ì k a n
u k f b n r l a y a s t d e ` a z i n
i n k m f i f n k a s p d r d
i n k s a r v d r ` d a k a r c ì d l
a i ä k f i d .
•
L n m a ` n l d t a l ä t f i d l a
k t a a ` l n v f l f a k t n
m a n e j a t n s i n t f m f d k n s d p d r t f r m a ` d s b u a r -
z d s q u a d i t ú d k s n e r a a
` ` n s .
•
A s t d e ` a z i n r a ` d i f n k a s a k t r a a s t d e f ` f m d m y
i a k t r n m a l d s d m a u k
n e j a t n .
•
A s t d e ` a z i n r a ` d i f n k a s a k t r a
` d i n k s a r v d -
i f ù k m a ` l n l a k t n ` f k a
d ` y a ` f l p u ` s n a k
s f s t a l d s m a n e j a t n s .
•
A s t d e ` a z i n r a ` d i f n k a s a
k t r a a ` l n m a ` n m a `
i d l p n c r d v f t d i f n k d ` y ` d ` a y m a ` d c r d v f t d -
i f ù k u k f v a r s d ` .
•
U a ` d i f n k n l d s d , m f s t d k i f d y b u a r z d m a
d t r d i i f ù k c r d v f t d i f n k d ` a k t r a n e j a t n s .
•
A x p ` f i n ` d t r d k s b n r l d i f ù k m a a k a r c ì d l a -
i ä k f i d a k a k a r c ì d t æ r l
f i d
U a ` d i f n k n ` d a s t r u i t u r d m a
` d s l n ` æ i u ` d s n r c ä k f i d s a
f k n r c ä k f i d s i n k s u s p r n -
p f a m d m a s b ì s f i d s y q u ì l f i d s
y s u i d p d i f m d m m a i d l e f n
q u ì l f i n .
A x p ` f i n ` d s b u a r z d s a k t r a
n e j a t n s i n l n f k t a r d i i f n k a s
m a e f m d s d ` d i d r c d a ` æ i t r f i d
y d ` d l d s d .
Q t f ` f z n l n m a ` n s e f n ` ù c f i n s ,
b ì s f i n s y q u ì l f i n s
p d r d
a x p ` f i d r ` d t r d k s b n r l d i f ù k y
B d i t n r a s m a n r c d k f z d
i f ù k
¾ I ù l n m a l u a s t r n ` n d p
r a k m f m n >
I n l p a t a k i f d s
¾ D q u æ
q u a r a l n s
` ` a c d r >
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A s t ä k
m d r a s e ä s f i n s m a i n l
p a t a k i f d s a k B ì s f i d ( i n k t f k u d i f ù k )
•
N e s a r v n y b n r l u ` n p r a c u k t d s a s p a i f b f i d s s n e r a d p ` f i d i f n k a s m a t a n
r ì d s i f a k t ì b f i d s
•
B n r l u ` n h f p ù t a s f s i n k e d s a a k
a ` i n k n i f l f a k t n i n t f m f d k n , t a n r ì d s y l n m a ` n s i f a k t ì b f i n s
•
F m a k t f b f i n v d r f d e ` a s q u a f k b ` u y a
k a k ` n s r a s u ` t d m n s m a u k a x p a r f l a k t n
•
_ r n p n k c n l n m a ` n s p d r d p r a m a
i f r ` n s r a s u ` t d m n s m a u k a x p a r f l a k t n
•
U a d ` f z n l a m f i f n k a s i n k f k s t r u l a k t n s y a q u f p n s d m a i u d m n s
•
U a c f s t r n l f s n e s a r v d i f n k a s y r a s u ` t d m n s u t f ` f z d k m n a s q u a l d s , c r ä b f i n s y t d e ` d s
•
U a c f s t r n l f s r a s u ` t d m n s a k b n r l
d n r c d k f z d m d y s f k
d ` t a r d i f ù k d ` c u k
d
•
A s t d e ` a z i n m f b a r a k i f d s a k t r a m a
s i r f p i f ù k , a x p ` f i d i f ù k , y a v f m a k i f d
•
A s t d e ` a z i n m f b a r a k i f d s a k t r a l
n m a ` n s , t a n r ì d s , ` a y a s a h f p ù t a s f s
•
U a i n k n z i n ` n s d p n r t a s m a i n k n i f l f a k t n s m f b a r a k t a s d ` i f a k t ì b f i n
•
U a i n k n z i n q u a ` n s l n m a ` n s m a ` d i f a k i f d i d l e f d k i n k a ` t f a l p n y q u a v d r f n s p u a m a k s a r v ä ` f m n s s f l u ` t ä k a d l a k t a .
•
I u f m n , r a s p a t n , y a x f j n r a s p a t n
p n r l f i u a r p n y p n r a ` m a ` d s m a l ä s p a r s n k d s
•
] n l n m a i f s f n k a s r a s p n k s d e ` a s
y i n l p d r t f m d s s n e r a l f s a x u d ` f m d m
•
D k d ` f z n i r ì t f i d l a k t a ` n s p d p a ` a s t r d m f i f n k d ` a s m a c æ k a r n a k k u a s t r d i u ` t u r d i n k r a s p a i t n d ` d s a x u d ` f m d m y ` d r a p r n -
m u i i f ù k
•
] n l n m a i f s f n k a s s n e r a d ` f l a k t d i f ù k y p r ä i t f i d m a a j a r i f i f n q u a b d v n r a z i d k l f s d ` u m
•
A x p ` f i n d p ` f i d i f n k a s t a i k n ` ù c f i d s m a ` l n m a ` n
m a l a i ä k f i d m a b ` u f m n s
•
D k d ` f z n a ` p n t a k i f d ` m a ` n s r a i u r s n s k d t u r d ` a s a k
` d n e t a k i f ù k m a a k a r c ì d p d r d
m f b a r a k t a s u s n s .
•
A s t d e ` a z i n r a ` d i f n k a s a k t r a a ` m a p n r t a y ` d s d ` u m
b ì s f i d y l a k t d ` .
•
A x p ` f i n i d l e f n s q u ì l f i n s
a k ` d i n i f k d , ` d
f k m u s t r f d y a ` d l e f a k t a
•
D r c u l a k t n ` d f l p n r t d k i f d m a ` d s l a m f m d s m a
p r a v a k i f ù k m a ` a l e d r d z n y m
a ` d s a k b a r l a m d -
m a s m a t r d k s l f s f ù k s a x u d ` a k a
` l d k t a k f l f a k t n
m a ` d s d ` u m f k m f v f m u d ` y i n ` a i
t f v d .
A k t n r k n b ì s f i n
I f a k i f d ,
t a i k n ` n c
ì d
y s n i f a m d m
_ r n i a s n s q u ì l f i n s
_ r n i a s n s b ì s f i n s
F m a k t f b f i n d p ` f i d i f n k a s m a
m f b a r a k t a s l n m a ` n s e f n ` ù -
c f i n s , q u ì l f i n s y b ì s f i n s a k
p r n i a s n s f k m u s t r f d ` a s y a k
a ` m a s d r r n ` ` n t a i k n ` ù c f i n 7
d k d ` f z n
i r ì t f i d l a k t a ` d s
f l p ` f i d i f n k a s m a s u s u s n s .
B d i t n r a s m a n r c d k f z d
i f ù k
¾ I ù l n m a l u a s t r n ` n d p
r a k m f m n >
I n l p a t a k i f d s
¾ D q u æ
q u a r a l n s
` ` a c d r >
L a d p r n x f l n d ` i n -
k n i f l f a k t n i n l n
f a k t ì b f i n ( d ) k d t u r d `
M a s d r r n ` ` n
n l p r n l f s n s
p a r s n k d ` a s y s n i f d ` a s
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Ì k m f i a
Qkfmdm 4. Ifkalätfid 96?
Yasfùk 4. Iudktfbfidifùk ma` lukmn bìsfin 96? Yasfùk 5. Lnvflfaktn F =41 Yasfùk 9. Lnvflfaktn ak a` p`dkn =95
Qkfmdm 5. Mfkälfid. A` lnvflfaktn y sus idusds ==3
Yasfùk =. Buarzd ==3
Qkfmdm 9. Astätfid =39
Yasfùk 1. Aquf`ferfn ma `ns iuarpns =39
Qkfmdm =. Akarcìd =88
Yasfùk 2. ]rdedjn, pntakifd y akarcìd
Qkfmdm 1. Hfmrnlaiäkfid 1?3
Yasfùk 3. Laiäkfid ma b`ufmns 1?3 Yasfùk 8. _räitfid ma hfmrnlaiäkfid 152
Qkfmdm 2. ]arlnmfkälfid 195
Yasfùk 6. Id`nr y talpardturd 195Yasfùk 4? _räitfid ma id`nr y talpardturd 1=3
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Iudktfidifùk ma` lukmn bìsfin
Qkfmdm 4. Ifkalätfid Yasfùk
4
Ldcfd y lftn
A` sur ma Brdkifd as ukd tfarrd id`fzd suridmd pnr vfajns rìns y hnrd-mdmd pnr fkkularde`as iuavds. Hdia 5?? sfc`ns kuastrns dktapd-sdmns, ns hnleras ma Irnldôùk, hfifarnk ldcfd ak asds crdkmasiuavds. @ns `ucdras sairatns ma` rftud` astäk ``akns ma ldckìbfinslurd`as pn`firnlns ma hnleras y dkfld`as. _fktdmns d `d `uz ma`ds älpdrds ma pfamrd d`flaktdmds ink crdsd, astds fläcakas snk`ns rastns ma `ns rftns läcfins ma idzd ma `d amdm ma pfamrd.
Jdlas Brdzar, ak `d rdld mnrdmd, hde`d ma `d ``dldmd `ay ma `d sflf`ftum.‐Qk abaitn sa pdraia d su idusd“. Iudkmn a` erujn ma Irnldôùk drrnjdedsu `dkzd snera ukd fldcak pfktdmd ak `d pdram, sdeìd qua sf `d ldcfd ma`lnlaktn kn `a bd``ded, a` dkfld` inkjurdmn sarìd idzdmn ink tnmd sacu-rfmdm. As ukd ldcfd sflpätfid qua prasupnka qua `ds insds ditúdk ukdssnera ntrds d mfstdkifd, d trdvæs ma ukd dbfkfmdm sairatd trdkslftfækmnsa`ns flpu`sns ma ukd d ntrd. _draia qua axfsta tdlefæk ntrd i`dsa ma ldcfdsflpätfid, ra`difnkdmd ink `d `ay ma` inktditn, ‐`ds insds qua hdk astdmn
ak inktditn d`cukd vaz, inktfkúdk ditudkmn aktra sì. Qk ldknjn ma pa`nn uk pamdiftn ma uôd as tnmn `n qua kaiasftd a` erujn pdrd astde`aiar `dinktfkufmdm y, d pdrtfr ma æstd, a` inktrn`.
A` masan ma fkb`ufr ak `d kdturd`azd idprfihnsd, yd sad vakifakmn a` nsn ma`ds idvarkds n inksfcufakmn uk eakabfifn mfbìif`, pdraia edstdkta huldkn.‐Euakd suarta“, ‐Iruzd ns mamns“, ma iud`qufar bnrld d ldcfd akvn`vfù d`lukmn praifvf`fzdmn flprackù tnmds `ds iu`turds hfstùrfids y sa ldktfaka
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Qkd vaz rad`fzdmd `d `aiturd, raspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds¾D`cukd vaz hd haihn ldcfd > ¾Tuætfpn ma ldcfd>Masirfed pdsn d pdsn iùln hfzn`d ldcfd.¾Iraa qua asd ldcfd astä ra`difnk-dmd ink d ifakifd> ¾Ma quæ bnrld>¾Tuæ axparflaktns inknia qua sa
puamak ra`difnkdr ink `d ldcfd>Axprasa ink sus pd`derds `n quaaktfakma iudkmn a` dutnr dbfrld:‐@d ifakifd y `d ldcfd snk aspìrftusma `d lfsld bdlf`fd“.
Fktrnmuiifùk d `d bìsfid
Masma hdia luihn tfalpn ds parsnkds hdk trdtdmn ma aktakmar a` pnr quæ ma d kdtu-
rd`azd y ns bakùlakns qua ak a``d sa nesarvdk: a` pdsn ma ds astdifnkas, ns bakùlakns
i`flätfins, a` lnvflfaktn ma ns iuarpns y ma ns dstrns, ati. @d huldkfmdm sfalpra sahd pracuktdmn snera `d bnrld ma fktardiifùk ma `ds pdrtìiu`ds, y snk luihds `ds axp`f-
idifnkas qua masma `d ifakifd y `d bf`nsnbìd sa akiuaktrdk d` raspaitn. Dsì, `ns bf`ùsnbns
crfacns astde`aiìdk dkd`ncìds aktra a` iuarpn huldkn, sus ra`difnkas y `ns bakùlakns
kdturd`as, `n iud` `as parlftìd hdiar pramfiifnkas. _nr ajalp`n, a` ldckatfsln pnmìd
masirfefr `d ldkard inln `ds parsnkds sfaktak dtrdiifùk aktra a``ds y qua kn as fcud
pdrd tnmds. @ns inkiaptns ma dtrdiifùk y rapu`sfùk ardk iaktrd`as ak d ifakifd pra- dr
Bukmdlaktn taùrfin
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B n t n
t n l d m d m a S f g f l a m f d
Drfstùta`as bukmdlaktù d bìsfid ak iudtrn prfkifpfns eäsfins: d kacdifùk ma` vdiìn
`d axfstakifd ma ukd idusd abfifakta ak tnmn idlefn, a` prfkifpfn ma `d diifùk
pnr inktditn, y `d axfstakifd ma uk prflar dcakta fklùvf`. ]dlefæk i`dsfbfiù alnvflfaktn kdturd` y vfn`aktn, mdkmn axp`fidifùk d `n qua sa pnmìd nesarvd
ak asa tfalpn, y dbfrlded qua a` lnvflfaktn surcìd ma d kdturd`azd ma` nejatn
sf `d kdturd`azd ma æsta ard astdr qufatn, parldkaiìd qufatn, n ak idsn ma `ns
nejatns ia`astas, astdr ak lnvflfaktn. A` lnvflfaktn vfn`aktn ard cakardmn pn
ukd buarzd qua sa flpnkìd d uk nejatn pdrd qua æsta sa lnvfard.
Ak d ditud`fmdm, tnmdvìd as flpnrtdkta a` lnvflfaktn ma d ldtarfd y a` sdeaa` pnr quæ sa inlpnrtd ma matarlfkdmds ldkards. _nr asn, pdrd inlprak
mar `d bìsfid y a` inlpnrtdlfaktn ma `ds insds qua nesarvdlns y ink `ds qua
fktarditudlns mìd d mìd, as euakn inlprakmar a` lnvflfaktn ma uk nejatn
y iùln sa masirfea. Iudkmn sa nesarvd uk nejatn idlefdr ma ukd pnsfifùk
d ntrd, n cfrdr ak uk tfalpn matarlfkdmn, sa mfia qua astä ak lnvflfaktn
Yf ak asa tfalpn sa inksarvd ak su pnsfifùk, maiflns qua astä ak rapnsn7
sf sa luava ink va`nifmdm inkstdkta (pnr ajalp`n, `ns iuarpns ia`astas), sa
maea sar iufmdmnsn pdrd mabfkfr sf uk nejatn astä ak rapnsn n ak lnvflfaktn
_drd astumfdr a` lnvflfaktn ma
`ns iuarpns, `ad a` sfcufakta idsn
y nesarva a` vfman:
Fldcfka qua astä ak ukd mfsinta-
id7 tnmds `ds vaktdkds astäk iarrd-
mds y pfktdmds ma kacrn7 `d puartd
tdlefæk astä iarrdmd, pnr n qua d
úkfid buakta ma uz as uk strnvar n
`uz rnentfzdmd uefidmd ak ukd ma
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Knlera: ]d``ar 4: Lnvflfaktn y prne`alätfid.Murdifùk 4:5= lfkutns
Ma diuarmn d `n qua nesarvù, raspnkmd `ds sfcufaktas pracuktds
@d bìsfid as d ifakifd qua sa akidrcd ma` astumfn ma d ldtarfd, d akarcìd
ma` ukfvarsn y `d fktardiifùk aktra `ds lfslds7 astumfd `ds prnpfamdmas
ma `d ldtarfd, `d akarcìd, a` tfalpn, a` aspdifn y sus fktardiifnkas. @d
bìsfid astumfd pnr n tdktn uk dlp`fn rdkcn ma idlpns y bakùlakns kdtu-
rd`as, masma `ds pdrtìiu`ds suedtùlfids hdstd `d bnrldifùk y avn`uifùkma` ukfvarsn, dsì inln `d lu`tftum ma bakùlakns kdturd`as intfmfdkns,
y ukn ma sus nejatfvns as masirfefr `ds rac`ds qua rfcak kuastrn ukfvarsn.
@d bìsfid as `d läs eäsfid y bukmdlaktd` ma tnmds `ds ifakifds. Astumfd
`d kdturd`azd ma dspaitns tdk a`alaktd`as inln a` lnvflfaktn, `ds
buarzds, `d ldtarfd, `d akarcìd, a` snkfmn, `d `uz y `d inlpnsfifùk ma `ns
ätnlns y sus dp`fidifnkas, ns iud`as hdk ajarifmn ukd crdk fkb`uakifdak a` prncrasn ma `d snifamdm. Yfrva ma edsa d ntrds ifakifds läs aspa-
ifd`fzdmds inln `d quìlfid, `d efn`ncìd, d dstrnknlìd, `d taikn`ncìd, `d
fkcakfarìd, ati. @d quìlfid alp`ad `ds `ayas ma `d bìsfid pdrd astumfdr `d
bnrldifùk ma `ds ln`æiu`ds y `ds bnrlds präitfids ma trdksbnrldr ukds
d. ¾Iraa qua `d pa`ntd ak `d mfsintaid sa luava d` dzdr, n tfaka uk
pdtrùk ma lnvflfaktn>
e. ¾Tuæ hdrìd ustam pdrd sdear d qufæk `a pacdrä `d pa`ntd ak `d
mfsintaid>
i. Yf tuvfard qua racfstrdr a` idlfkn qua sfcua d pa`ntd ma uk ucdr
d ntrn, ¾iùln `n hdrìd>
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sustdkifds ak ntrds, ak `ds radiifnkas quìlfids. @d efn`ncìd, d su vaz,
mapakma ak euakd pdrta ma `d bìsfid pdrd pnmar axp`fidr luihns ma`ns prniasns qua niurrak ak `ns saras vfvns. @d dstrnknlìd raqufara
ma `ds `ayas ma `d bìsfid pdrd axp`fidr a` lnvflfaktn ma `ns p`dkatds y
ntrns iuarpns ia`astas y `ns bakùlakns qua niurrak ak a``ns. @d dp`f-
idifùk ma `ns prfkifpfns ma `d bìsfid d `d sn`uifùk ma `ns prne`alds
taikn`ùcfins, td`as inln `d inkstruiifùk ma amfbfifns, ldqufkdrfds,
vahìiu`ns, prniasns fkmustrfd`as, ati., hd mdmn `ucdr d `ds mfbaraktas
rdlds ma `d fkcakfarìd.
@d bìsfid as flpnrtdkta kn sù`n pnrqua kns dyumd d inlprakmar ns prn-
iasns qua niurrak ak `d kdturd`azd, sfkn tdlefæk pnrqua hd parlftfmn
masdrrn``dr tæikfids y lætnmns axparflaktd`as qua sa dp`fidk ak ukd
crdk vdrfamdm ma ditfvfmdmas huldkds. Edstd ink vfsftdr uk hnspftd`, uk
nesarvdtnrfn dstrnkùlfin, uk denrdtnrfn canbìsfin n latanrn`ùcfin, ukdfkmustrfd, ati., pdrd mdrsa iuaktd ma ns kularnsns aqufpns edsdmns ak
prfkifpfns bìsfins qua sa utf`fzdk ak mfihns `ucdras.
@d bìsfid rasu`td asakifd` y sfrva ma dpnyn d ntrds ifakifds7 pnr a``n,
pnmalns aktakmar lajnr ntrds ifakifds sf dktas aktakmalns `d bìsfid.
_nr ntrd pdrta, ns inkiaptns bìsfins y sus ra`difnkas inkstftuyak d edsa
ma crdk pdrta ma` masdrrn``n taikn`ùcfin qua idrditarfzd d snifamdm. Qkdmaiudmn dprakmfzdja ma d ldtarfd parlftfrä inlprakmar astns bukmd-
laktns, dsì inln d`cukds inksaiuakifds ma asta masdrrn``n, bdvnraifakmn
ukd rab`axfùk irìtfid y bukmdlaktdmd snera d fkifmakifd ma` masdrrn``n
taikn`ùcfin ak a` lamfn kdturd`, snifd` y dlefaktd`.
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Yf ukn ma `ns nejatfvns bukmdlaktd`as as masiuerfr `ds rac`ds qua rfcak
kuastrn ukfvarsn, maealns alpazdr pnr fkvastfcdr n qua suiama d kuastrn
d`ramamnr7 astn as, pnkarkns ak inktditn ink a` lukmn axtarfnr, y astn `n
hdialns d trdvæs ma kuastrns saktfmns.
_drd a``n utf`fzdlns `ns inkiaptns ma lamfmd, yd qua astns kns parlftak
astde`aiar ra`difnkas iudktftdtfvds pdrd `d masirfpifùk ma` sfstald bìsfin.
Aktra `ds ldckftumas bfsids takalns:
_drd axprasdr ds mfbaraktas lamfifnkas rad`fzdmds, d bìsfid utf`fzd a` Yfstald
Fktarkdifnkd` ma Lamfmds.
A` Yfstald Fktarkdifnkd` ma Lamfmd
Masma `ds æpnids prflftfvds, a` sar huldkn tuvn `d kaiasfmdm ma lamfr: lamfr `nkcftumas, lamfr ldsd, lamfr tfalpn, ati. V `d prflard harrdlfaktd n fkstrulaktnma lamfifùk bua su iuarpn, `d `nkcftum ma su pfa, ma su erdzn, ma sus ldkns n atdldôn ma sus mamns, qua `a parlftìd ``avdr inksfcn su prnpfn pdtrùk ma lamfmd@ns idlefns ma `ukd, `d lfcrdifùk ma `ds dvas y `ns idlefns i`flätfins `a prnpnr-ifnkdedk ukd fmad ma `d vdrfdifùk ma `ns mìds (lamfmd ma tfalpn)7 sa inlpdrdrnk`ds idktfmdmas ma pfamrds, rnids, rdlds, inkihds, ati., ink ntrns a`alaktns pdrdmatarlfkdr `d ldsd.
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Ink a` pdsn ma` tfalpn, sa hfzn kaiasdrfn ukfbfidr sfstalds ma lamfmd qua parl
ardk `d inlarifd`fzdifùk ma prnmuitns aktra `ns puae`ns, `d matarlfkdifùk ma ä
ma tarrakns pdrd maldridr tarrftnrfns, `d murdifùk ma uk vfdja aktra mns ifumd
ati. Astds aktra ntrds, buarnk ds idusds prflnrmfd`as qua mfarnk pfa d d iradifù
uk sfstald fktarkdifnkd` ma lamfmd.
• @nkcftum: as `d ldckftum bukmdlaktd` pdrdlamfr mfstdkifds n mflaksfnkas ak a` aspdifn.
• Ldsd: sa utf`fzd pdrd masirfefr `d idktfmdm ma
ldtarfd qua pnsaa uk iuarpn.
• ]falpn: as uk inkiaptn mfbìif` ma mabfkfr7sa inksfmard inln ukd sarfa ma suiasns quaniurrak ak bnrld akidmakdmd sfalpra hdifddma`dkta. D`cukns n inksfmardk inln d axp`f-idifùk d d axfstakifd ma ukd iudrtd mflaksfùk._drd su lamfifùk, axfstak fkstrulaktns idmdvaz läs snbfstfidmns y ma ldynr praifsfùk, parn
kn snk `d harrdlfaktd pdrd mabfkfr`n (fktaktamabfkfr`n).
A` sfstald ics qua tfaka inln ukfmdm pdtrùk ma d nkcftum, a` iaktìlatrn7ma `d ldsd, a` crdln7 y ma` tfalpn, a` sacukmn.
A` sfstald fkc`æs qua tfaka inln ukfmdm pdtrùk ma `d `nkcftum, a` pfa7 ma`d ldsd, a` s`uc7 y ma` tfalpn, a` sacukmn.
A` sfstald LGY qua tfaka inln ukfmdm pdtrùk ma d `nkcftum, a` latrn7 ma`d ldsd, a` Gf`ncrdln7 y ma` tfalpn, a` sacukmn. Ya `a maknlfkd YfstaldFktarkdifnkd` ma Lamfmd (YF).
Ak `d ditud`fmdm, axfstak vdrfns sfstalds ma lamfmds:
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Ya puama rad`fzdr inkvarsfùk ma lamfmds aktra `ns mfbaraktas sfstalds, takfakmn akiuaktd `ds ra`difnkas qua axfstak y sa luastrdk ak `d sfcufakta tde`d:
Ak cakard`, a` Yfstald Fktarkdifnkd` ma Lamfmd inksfmard sfata ukf-mdmas eäsfids qua inrraspnkmak dsfata idktfmdmas qua snk: @nkcftum
- latrn (l)7 Ldsd - Gf`ncrdln (Gc)]falpn - sacukmn (s)7 Inrrfaktaa`æitrfid - Dlparas (D)7 ]alpardturd - Crdmns Ga`vfk (ºG)7 idktfmdm masustdkifd - ln`as (ln`)7 fktaksfmdm`ulfknsd - Idkma`ds (im).
Latrn(l)
Iaktìlatrn(il)
_fa(bt)
(l) 4 4?? 9.58
(il) ?.?4 4 ?.?958
(bt) ?.9?1 9?.1 4
Yacukmn(s)
Lfkutn(l)
Hnrd(h)
(s) 4 4/2? 4/92??
(l) 2? 4 4/2?
(h) 92?? 2? 4
Gf`ncrdln(gc)
Crdln(c)
Y`uc(Yc)
(gc) 4 4.??? ?.?28
(c) ?.??4 4 2.81x4?-1
(Yc) 4=.18 4=18= 4
Ajalp`n:Inkvartfr `d va`nifmdm ma 512 Gl/h d l/s.
Yn`uifùk: pdrd sn`uifnkdr asta ajarififn sa takmräk ak iuaktd `ns sfcufaktas
puktns:
4. Ya maea takar ak iuaktd `ds tde`ds ma inkvarsfùk (ak asta ajarififn sa ak-iuaktrdk mns ukfmdmas ma inkvarsfùk, ukd ma `nkcftum y ntrd ma tfalpn)
5. Ya maeak idlefdr `ns gf`ùlatrns d latrns y `ds hnrds d sacukmns (pdrd astn
as kaiasdrfn takar ak iuaktd `ns bditnras ma inkvarsfùk ):
4Gl < 4???l 4h < 92??s
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@d kntdifùk ifaktìbfid
Ya utf`fzd pdrd axprasdr idktfmdmas ldynras n laknras qua 4, lamfdkta d pnta(pnsftfvd n kacdtfvd), ma mfaz inrraspnkmfakta.
Yf `d idktfmdm as ldynr qua 4,
sa utf`fzdk ds pntakifds pnsftfvdsma 4?, ak `ds iud`as a` axpn-kakta inrraspnkmarä d` vd`nrpnsfifnkd` ma `d idktfmdm, dsì:
Yf `d idktfmdm as laknr qua 4,
sa utf`fzdk `ds pntakifds kacdtf-vds ma 4?, ak `ds iud`as a` ax-pnkakta inrraspnkmarä d` vd`nrpnsfifnkd` ma `d idktfmdm dsì:
_nmalns rad`fzdr npardifnkas ma suld, rastd, lu`tfp`fidifùk y mfvfsfùk ink kúl
?,4 < 4?-4 7 ?,?4 < 4?-5 7 ?,??4 < 4?-
?,???4 < 4?-= 7 ?,????4 < 4?-1
4 < 4?? 7 4? < 4?4 7 4?? < 4?5 74??? < 4?9 7 4?.??? < 4?=
9. Ya asirfea `d idktfmdm qua sa vd d inkvartfr y sa asincak `ns bditnras minkvarsfùk qua idkia`dk `ds ukfmdmas
Yf qufara prditfidr astns ajarififns, nesarva a` vfman:
Knlera: Inkvarsfùk ma ukfmdmas. Murdifùk: 1:5=
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Ak `d lu`tfp`fidifùk, sa rad`fzd a` prnmuitn aktra `ds pdrtas maifld`as7 `uacn sa lutfp`fidk `ds pntakifds ma 4?, takfakmn ak iuaktd `d prnpfamdm ma `d pntakifdifùpdrd edsas fcud`as y axpnkaktas mfbaraktas (iudkmn sa lu`tfp`fidk pntakifds ma edsfcud`as y axpnkaktas mfbaraktas, sa majd `d lfsld edsa y sa suldk `ns axpnkaktas
Ak `d mfvfsfùk, sa mfvfmak prflarn `ds pdrtas maifld`as y `uacn `ds pntakifds ma 4?
takfakmn ak iuaktd `d prnpfamdm pdrd edsas fcud`as y axpnkaktas mfbaraktas ak inifakta (iudkmn sa mfvfmak mns pntakifds ma edsas fcud`as y axpnkaktas mfbaraktasa majd `d lfsld edsa y sa rastdk `ns axpnkaktas).
( 4,98 x 4? 9 ) x ( 9,25 x 4?-6 ) < =,6612 x 4?-2
2,18 x 4?= / 5,5= x 4?-6 < 5,693 x 4?49
Ak a` idsn ma `d suld y `d rastd,sa maea asirfefr fkfifd`lakta `dspdrtas maifld`as inln bditnrasma `d lfsld pntakifd ma 4?.@uacn, sa dp`fid `d prnpfamdmmfstrfeutfvd ma` prnmuitn raspai-tn ma `d dmfifùk n sustrdiifùk.
9,51 x 4?= + 5,54 x 4?= <( 9,51 + 5,54 ) x 4?= < 1,=2 x 4?=
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_rnpnrifnkd`fmdm
Ak d vfmd intfmfdkd sa utf`fzd a` tærlfkn ma prnpnrifùk ink mfbaraktas sfckfbfidmn
• Iudkmn maiflns qua d`cn astä efak prnpnrifnkdmn mdlns d asta
tærlfkn uk saktfmn ma drlnkìd y astætfid: ‐Asta kfôn hd iraifmn
luihn, parn astä efak prnpnrifnkdmn“.
• Yf inlaktdlns qua a` æxftn ma ukd parsnkd as prnpnrifnkd` (n
astä ak prnpnrifùk) d su trdedjn, quaralns maifr qua hdy ukd
inrra`difùk aktra astds mns vdrfde`as: æxftn y trdedjn.
Ak d bìsfid y d ldtalätfid astd pd`derd tfaka uk sfckfbfidmn läs rastrfkcfmn, pua
qua ra`difnkd ldckftumas lamfe`as7 dsì, iudkmn ukd rdzùk sa fcud`d d ntrd, sa m
@ds ifbrds sfckfbfidtfvds
@ds ifbrds sfckfbfidtfvds ma ukd lamfmd inrraspnkmak d` kúlarn ma mìcftns sacrns läs a` mìcftn mumnsn. _nr ajalp`n: sf `d `nkcftum ma ukd edrrd ma d`ulfk
as ma 1,=2 il, astn kns cdrdktfzd qua `ns mns prflarns kúlarns (1 y =) sn
sacurns, parn puama axfstfr uk arrnr ak a` ú`tfln, a` 2 qua pnmrìd sar 1 n 37 p
`n tdktn, takalns tras ifbrds sfckfbfidtfvds. Astn mapakma luihn ma` fkstrulak
ma lamfifùk utf`fzdmn7 sf `d lamfmd buard 1,=2?, `d fkiartfmulera astdrìd ak
kúlarn ?, parn takmrìdlns iudtrn ifbrds sfckfbfidtfvds qua inrraspnkmak d u
lamfmd läs praifsd.
Ak `d inkvarsfùk ma ukfmdmas, as flpnrtdkta utf`fzdr `d kntdifùk ifaktìbfid ink
äkfln ma avftdr inkbusfnkas d` asirfefr `ns rasu`tdmns ma uk mdtn axparflaktd`, y
rasu`tdmn takmrä a` lfsln kúlarn ma maifld`as qua a` kúlarn ma laknr praifsfù
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Qk dutnlùvf` dvdkzd =?gl hdifd a` knrta ak ukd hnrd.d. Matarlfka `d rdzùk aktra idmd mfstdkifd y su raspaitfvn tfalpn ak 2
hnrds.
e. ¾Tuæ tfpn ma prnpnrifnkd`fmdm tfakak astds vdrfde`as>
]falpn (h) 4 5 9 = 1 2
Mfstdkifd (gl) =? 8? 45? 42? 5?? 5=?
Ra`nifmdm (l/s) =? =? =? =? =? =?
Ajalp`n:
d. @d rdzùk aktra idmd mfstdkifd y su raspaitfvn tfalpn sa id`iu`d dsì:
Yn`uifùk:
e. @ds ldckftumas snk mfraitdlakta prnpnrifnkd`as, pnrqua d rdzùk aktra
sus raspaitfvns vd`nras as inkstdkta a fcud` d =?l/s.
Ak `d cräbfid pnmalns nesarvdr qua sa astäk ra`difnkdkmn `ds mns vdrfde`as:mfstdkifd (gl) y tfalpn (t)
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• Mfraitd
Mns ldckftumas tfakak prnpnrifnkd-`fmdm mfraitd, sf d` dulaktdr a` vd`nrma ukd, dulaktd tdlefæk a` vd`nr ma`d ntrd. Dmaläs, snk mfraitdlaktaprnpnrifnkd`as, sf su cräbfid inrras-pnkma d ukd ìkad raitd qua pdsd pnra` nrfcak.
• Mfraitd d` iudmrdmn
Ya prasaktd iudkmn su cräbfid inrras-pnkma d ukd iurvd ma nrfcak pdrd-eù`fin y `d ra`difùk sa inkvfarta ak`fkad` iudkmn `d sacukmd ldckftum saaxprasd d` iudmrdmn.
• Fkvarsd
Mns ldckftumas tfakak prnpnrifnkd`f-mdm fkvarsd, sf d lamfmd qua dulaktda` vd`nr ma `d prflard, mfslfkuya a`vd`nr ma `d sacukmd. _uama sar `fkad`n iudmrätfid.
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Id`ferdmnr
Latrn
@nkcftum
Ldsd
Irnkùlatrn
]falpn
Buarzd
Mfkälnlatrn
Lfirùlatrn
Ed`dkzd mainlpdrdifùk
Crdlard
Ed`dkzd matras erdzns
_räitfid ma `denrdtnrfn: dktas ma fkfifdr a` trdedjn ma `denrdtnrfn, as flpnrtdkrainkniar d`cukns fkstrulaktns ma lamfmd pdrd `nkcftum, ldsd, tfalpn y buarzd
4
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Ldtarfd`as
Iuarmd n pftd ma 4,5 l, 2 ldsds paquaôds mfbaraktas, id`ferdmnmfmäitfin (sa inkstruya), irnkùlatrn, ed`dkzd (sa inkstruya)snpnrta y asiudmrd.
]de`d 4.9
@nkcftum # ma nsi. _arìnmn Braiuakifd @nkcftum # ma nsi. _arìnmn Braiuakifd
4? 2?
5? 3?
9? 8?
=? 6?
1? 4??
_rniamflfaktn
4. Nrcdkfzdr a` aqufpn ma trdedjn.
5. Yujatdr ukd ldsd paquaôd d`axtraln ma d pftd y d inktfkud-ifùk, hdiar ldridifnkas snera`d iuarmd, idmd 4? il d pdrtfrma` puktn mnkma sa sujatù `dldsd y hdstd ``acdr d 4?? il, inlakzdkmn ak `d `nkcftum ma 4? il.Masp`dzdr `d ldsd d uk `dmn ma` puktn bfjn hdstd qua `d iuarmd quama
inlp`atdlakta hnrfznktd`7 sn`tdr `d ldsd y matarlfkdr a` kúlarn mansif`difnkas (lnvflfaktn ma fmd y vua`td ma `d ldsd), murdkta 9? s.Uapatfr `d axparfakifd pdrd `nkcftumas ma 5?, 9?, =?, 1?, 2?, 3?, 8?,6? y 4?? il. @`avdr `ns mdtns d `d tde`d 4.9.
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]atrdamrn
_arìnmn (]): tfalpn kaiasdrfn pdrd rad`fzdr ukd 3?ª nsif`difùkinlp`atd (9? s/kúlarn ma nsif`difnkas).
Braiuakifd (b): kúlarn ma nsif`difnkas ak `d ukfmdm ma tfalpn(kúlarn ma nsif`difnkas /9? s).
d. A`denrdr d cräbfid ma nkcftum inktrd parìnmn (]) y matarlfkdra` tfpn ma prnpnrifnkd`fmdm.
e. A`denrdr `d cräbfid ma `nkcftum inktrd braiuakifd (b) y matar-lfkdr a` tfpn ma prnpnrifnkd`fmdm. 9. Matarlfkdr a` parìlatrn y a` ärad ma mns pn`famrns racu`dras, a`
tatrdamrn y a` axdamrn (uk pn`famrn as uk sù`fmn `flftdmn pnr pn-`ìcnkns racu`dras qua d su vaz, snk bfcurds p`dkds ma `dmns fcud`asinln trfäkcu`n, iudmrdmn, paktäcnkn, ati.).
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Axdamrn
]atrdamrn
Axdamrn
=. Inkstrufr `ns sù`fmns prnpuastns y matarlfkdr a` vn`ulak ma idmdukn.
1. Inlp`atdr `d tde`d 4.=.
Rn`ulak_n`famrn
Latrn
Maiìlatrn
_fa
Latrn
Maiìlatrn
_fa
_arìlatrnYfstald
ma lamfmd Ärad
]de`d 4.=
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]de`d 4.1
Gf`ncrdlns Crdlns Y`ucLdsd
DônsAvaktnssa`aiifnkdmns Yacukmns Lfkutns Hnrds Mìds
]de`d 4.2
2. Ma sar kaiasdrfn, inkstrufr ukd ed`dkzd ma d ldynr axditftum pnsf-e`a, y pnr inlpdrdifùk ink ukd n vdrfds ldsds inknifmds, matarlfkdra` vd`nr ma ntrds ldsds (pnr `n lakns =). Axprasdr a` rasu`tdmn ak
Gc, c y s`uc (tde`d 4.1).
3. Ya`aiifnkdr tras avaktns mfbaraktas ma inrtd n lamfdkd murdifùk,matarlfkdr a` tfalpn ma idmd ukn y axprasdr`n ak sacukmns, lf-kutns, hnrds, mìds y dôns, utf`fzdkmn `d kntdifùk ifaktìbfid ak `dtde`d 4.2.
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4
Yn`uifùk:
_rne`alds ma dp`fidifùk
4. Ya inksfmard qua d mfstdkifd lamfd ma d ]farrd d` Yn` as ma 4=6.163.83? @ds lamfifnkas inktalpnräkads sa hdiak ink tæikfids `äsar n ma rdmdr, ukd praifsfùk ma ukn n mns gf`ùlatrns. Axprasdr ak kntdifùk ifaktìbfid mfstdkifd ak latrns, ak iaktìlatrns y ak pfas.
A` bditnr ma inkvarsfùk ma Gl d l as 4.??? pnrqua uk Gl aqufvd`a d4.??? l. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr prnpuastn, pnr lf`pdrd axprasdr `d raspuastd ak latrns.
4=6.163.83? Gl X 4.??? < 4=6.163.83?.??? l < 4,=616383? X 4?44l
A` bditnr ma inkvarsfùk ma l d il as 4?? pnrqua uk l aqufvd`a d 4??il. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr ak latrns pnr ifak pdrdnetakar `d raspuastd ak iaktìlatrns.
4,=616383? X 4?44latrns X 4?? < 4,=616383? X 4?49 il
A` bditnr ma inkvarsfùk ma l d pfas as 9,58 pnrqua 4 l aqufvd`a d 9,58bt. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr ak latrns pnr 9,58 pdrdnetakar `d raspuastd ak pfas (bt).
4,=616383? X 4?44 latrns X 9,58 < =,6?284?492 X 4?44bt.
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Yn`uifùk:
_drd inkvartfr ukfmdmas ldynras d laknras salu`tfp`fid7 y ma laknras d ldynras sa mfvfma
pnr a` bditnr ma inkvarsfùk.
5. Inln `d va`nifmdm ma `d `uz as ma 9??.??? Gl/s, ¾iuäktds hnrds, iuäktnslfkutns y iuäktns sacukmns tdrmdrä `d `uz ma` Yn` pdrd ``acdr d `d suparbfifama `d ]farrd>
Inln `d `uz rainrra 9??.??? Gl ak uk sacukmn y `d mfstdkifd ma` Yn` d
`d ]farrd as ma 4=6.163.83? Gl, a` tfalpn kaiasdrfn as:
ts <
tlfk <
th <
]akar ak iuaktd qua a` bditnr ma inkvarsfùk ma hnrds d lfkutns y ma lf-kutns d sacukmns as 2?. _nr `n tdktn, pdrd axprasdr hnrds ak sacukmns, samaea lu`tfp`fidr pnr 9.2??.
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l(lc) ? ?,1 4,? 4,1 5,? 5,1 9,?
](sac) ? 9? 2? 6? 45? 41? 48?
h(il) ?
t(sac) ? 9? 2? 6? 45? 41? 4
Yn`uifùk:
9. Ya inksfmard qua `d ldsd ma `d @ukd as dprnxfldmdlakta 3,9=6 Ó 4?55
Axprasdr asta vd`nr ak crdlns y s`uc.
A` bditnr ma inkvarsfùk ma Gc d c as 4.???, pnrqua uk Gc aqufvd`a d 4.???c. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr prnpuastn ak Gc pnr 4.???pdrd netakar `d raspuastd ak crdlns.
3,9=6 X 4?55 Gc X 4.??? < 3.9=6 X 4?51 c
A` bditnr ma inkvarsfùk ma Gc d s`uc as ?,?28, pnrqua uk Gc aqufvd`a d?,?28 s`uc. _nr `n tdktn, maealns lu`tfp`fidr a` vd`nr prnpuastn ak Gcpnr ?,?28 pdrd netakar `d raspuastd ak s`uc.
3,9=6 X 4?55 Gc X ?,?28 < =6,6395 X 4?5? s`uc
=. Ak ukd präitfid ma denrdtnrfn, sa dcracù d uk raifpfakta iùkfin, ukd sustd`ìqufmd ma 4? il9 idmd 9? sacukmns murdkta tras lfkutns. Ak idmd idsnmatarlfkù `d ldsd y `d d`turd d`idkzdmds pnr a` `ìqufmn y sa astde`aifarnksfcufaktas tde`ds ma mdtns.
]de`d 4.4 ]de`d 4.5
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D pdrtfr ma `d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns, matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn sa`aiifnkdmn.
Dkä`fsfs ma rasu`tdmns
4. _rnpnrifnkd`fmdm 5. Ärads y parìlatrns 9. Rn`úlakas =. Inlpdrdifùk ma ldsds 1. Dkä`fsfs ma tfalpn
t(sac)
t(sac)
A`denrdr `d cräbfid inrraspnkmfakta pdrd idmd tde`d y matarlfkdr quæ tfpn ma prnpnrifnkd`fmdm sa prasaktd ak idmd idsn.
Cräbfid 4 Cräbfid 5
Ldsd y tfalpn snk mfraitdlaktaprnpnrifnkd`as.
Udmfn y tfalpn tfakak prnpnr-ifnkd`fmdm mfraitd d` iudmrdmn.
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D inktfkudifùk, ukd sarfa ma ajarififns ma dp`fidifùk qua dyumdräk d ukd lajninlpraksfùk y dprnpfdifùk ma` tald trdtdmn. Ak `n pnsfe`a, hdiar `d sn`uifùk
ak bnrld fkmfvfmud`.
4. ]akfakmn ak iuaktd ns prniamflfaktns dmaiudmds pdrd d inkvarsfùkma ukfmdmas ma lamfmd ma `nkcftum, ldsd y tfalpn, inlp`atdr `dssfcufaktas tde`ds, justfbfidkmn idmd raspuastd (prniamflfaktn).
Asirfed `ns prniasns ak su iudmarkn.
Uad`fialns ntrns ajarififns
45
Hnrds Lfkutns Yacukmns
45
45
45Latrns Iaktìlatrns _fas
45
45
45Gf`ncrdlns Crdlns Y`uc
45
45
5. Qtf`fzdkmn uk rasnrta n edkmd a`ästfid, uk snpnrta y ldsds mfbarak-tas, prnpnkar y dp`fidr uk prniasn bìsfin qua `a parlftd astde`aiar `dprnpnrifnkd`fmdm mfraitd a fkvarsd, y hdiar d malnstrdifùk lamfdkta
`d utf`fzdifùk ma cräbfids axp`fidtfvds.
9. Uad`fzdr `ds sfcufaktas npardifnkas:
d. =,=1 x 4?9 + 8,=9 x 4?= <
e. 8,?2 x 4?1 X ?,21 x 4?-9 <
i. 9,=86 x 4?-5 / 2,842 x 4?= <
m (9 x 4?5 X 6 5 x 4?-9) / = ?3 x 4?2 <
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Inki`usfnkas
Dutnavd`udifùk
Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdrd
sn`uifnkdr sftudifnkas bìsfids rad`as.
_drd fr inksn`fmdkmn a` prniasn ma dprakmfzdja, sa prnpnka astd ditfvfmdmiuyd bfkd`fmdm as raidpf`utdr n trdedjdmn hdstd asta puktn. Dsì sa prnluavak`ns prniasns ma latdinckftfvns qua a dyumdräk d praifsdr difartns y mfbfiu`-
tdmas ak a` dprakmfzdja, `ns iud`as maea dkd`fzdr y dyumdr d sn`vaktdr pnrlamfn ma ntrn tfpn ma ditfvfmdmas. @d fmad as qua trdedja fkmfvfmud`lakta,parn sf `n inksfmard, puama snifd`fzdr ink sus inlpdôarns. D inktfkudifùkhdy ukd sarfa ma pracuktds7 `n fkvftdlns d raspnkmar`ds: • ¾Inksfmard qua `ns inkniflfaktns y `d prasaktdifùk ma fkbnrldifùk
buarnk `ns dmaiudmns>Yf ^^^^ Kn ^^^^ ¾_nr quæ>
• Asirfed mns kuavns inkniflfaktns qua hdyd netakfmn: d. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ e. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
• ¾Tuæ mfbfiu`tdmas tuvn d` rad`fzdr `ds ditfvfmdmas p`dktadmds ak astdukfmdm>
• ¾_drtfifpù ditfvdlakta ma tnmds `ds ditfvfmdmas n `a bd`tn pnkar läsfktaræs ak d`cukd atdpd ma` prniasn>
Uacrasa d `ds pracuktds ink qua fkfifdlns astd ukfmdm, ravfsa susraspuastds y inktasta `ds sfcufaktas pracuktds:
• ¾Iuä` ma `ns inkiaptns d``ì p`dktadmns `a bd`td dúk pnr ravfsdr>, ¾tfaka
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Lnvflfaktn F
DQ]NY / HNUDY MA ENCN]Ä _A]UNEUDY-LN]NU
Kn sa ‘dcuù‖ `d bfastd ak ]nidkifpä
@NY _F@N]NY tuvfarnk qua snrtadr `d ``uvfd y `d kfae`d qua inefjù a` dutù-mrnln ak `d tdrma y `d kniha ma` säedmn.
Barkdkmn Drfzd-A@ ]FAL_N.
Yf ldkajdr uk dutnlùvf` aksus `ìlftas murdkta safs hnrds asyd uk ratn baknlakd`, hdiar`n
edjn ukd ``uvfd tnrrakifd`, snera`älfkds ma crdkfzn, pdrihas makfae`d y murdkta ukd euakd pdrtaak d kniha, ds 2 Hnrds _atrnerdsLN]NU bua `d idrrard läs murd,mfbìif`, prnedtnrfd y dzdrnsd quasa hd inrrfmn ak `d hfstnrfd ma`Dutùmrnln ma ]nidkifpä.
_arn asd inktfkcakifd kn `araedjù uk äpfia d` aktusfdsln inka` iud` ukd kutrfmd inkiurrakifddinlpdôù `d idrrard. A` rapartnrfn ma trnlpns, mas-`fzdmds, sd`fmds ma pfstd, dutnsfkukmdmns, diifmaktas buartasdukqua sfk inksaiuakifds mfba-raktas d `ns mdôns laiäkfins,ak lamfn ma `ns iud`as `d hd-
ef`fmdm, td`aktn y rfascn ma `ns pdrtfifpdktas qua sneravfvfarnkma ns 34 qua fkfifdrnk d pruaed
edjn uk sn` rdmfdkta, buarnk ukdtaksd inkstdkta d `n `drcn ma `d
dcntdmnrd jnrkdmd. Bfkd`lakta, d `ds 8:?? p.l., ak puktn, asidlpù, justn pdrd sd`umdrd `ns cdkdmnras ma `d mrdlätfididrrard. Yaedstfäk y Ju`fäk Ldr-tìkaz, ak uk prntntfpn Udmfid` ma`d idtacnrìd fera, buarnk qufakasläs vua`tds `ncrdrnk hdiar aktratnmns, ink uk dutn astupakmn parnmasiuefartn, sfk prntaiifùk inktrd
`d `uvfd, n iud` hfzn läs vd`fnsnsu rftln ma pruaed. _nr su pdrta ]nläs Ytauar,D`ajdkmrn @fkia y Jnrca Inrtæssa flpusfarnk ak a` crupn ma asta
tfpn ma dutns ink lntnras hdstd5??? i.i. Ma pdsn, Inrtæs dkntùsu vfitnrfd 4= ak `ds 2 Hnrds. A` lajnr ma `ns turfslns hdstd5??? i.i. bua a` I`ìn ma Ydktfdcny Mfacn Barkdkmn Lajìd qua vak-ifù d` _aucant ma ns aiudtnrfdkns@drrad, Lnyd y Inrrad, qufakas`ncrdrnk hdstd a` lnlaktn a`lajnr rasu`tdmn ma uk aqufpn
axtrdkjarn. A` Ywfbt ma `d bdlf-`fd _uyn ma Lama``ìk hfzn ukdflpaide`a prasaktdifùk y bua a`lajnr i`dsfbidmn ma `ns turfslns
y ma d idtacnrìd hdstd 4=?? i.i.,
lfaktrds qua _arafrd cdkù lara-ifmdlakta a` crupn ma dutns inklntnras ma sn`n 8 vä`vu`ds inkJudk Idlf`n y Jhnk D`axdkmarUfvard. Bfkd`lakta, `d sarfa ma`]I 5.??? `d cdkù a` Hyukmdf maUnkd`m Qrrad, Dkmræs Ufdôn yJdfla Cdriìd.
JNYÆ I@N_D]NBYGV
Qkfmdm 4. Ifkalätfid Yasfùk
5
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Bukmdlaktn taùrfin
D pdrtfr ma `d `aiturd dktarfnr, raspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds¾Iùln iraa qua sa bukifnkd a`
lnvflfaktn ma `ns idrrns>¾Iraa ustam qua dbaitd ak d`cn a`
lnvflfaktn iudkmn hdy `uvfd, crdkfzn
n kfae`d> ¾_nr quæ>
_ärasa brakta d ukidlfkn, id` `a n
dvakfmd y matarlfka
`d va`nifmdm ma:
Qk idrrn /Qkd efifi`atdQkd parsnkd
Qk dkfld`
Masirfed a` prniasn qua rad`fzù pdrd
id`iu`dr idmd ukn ma `ns lnvflfaktns
Lnvflfaktn
As a` idlefn ma pnsfifùk ma uk iuarpn ink raspaitn ma uk puktn n ldrinma rabarakifd7 astn kns fkmfid qua a` lnvflfaktn as ra`dtfvn, mapakmama` puktn ma rabarakifd qua tnla a` nesarvdmnr. Astn qufara maifr, quapdrd ukd parsnkd, uk nejatn puama astdr ak lnvflfaktn, lfaktrds quapdrd ntrd, uefidmd ak ntrn puktn ma rabarakifd, a` lfsln nejatn puamapdraiar ak rapnsn.
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A`alaktns ma` lnvflfaktn
Idktfmdmas asid`dras: snk ds idktfmdmas qua sù`n raqufarak ma uk vd`nr (ldc
kftum), pdrd sar inlp`atdlakta axp`fidmds. _nr ajalp`n: a` tfalpn, `d ldsy `d talpardturd.
_drd a` idsn ma` lnvflfaktn, sa inksfmardk asid`dras:
• ]rdyaitnrfd: as a` idlfkn rainrrfmn y rasu`td ma d ukfùk ink saclaktnma raitd ma tnmns y idmd ukn ma `ns puktns pnr mnkma hdyd pdsdmn a
iuarpn.
• Udpfmaz: as `d rdzùk aktra `d `nkcftum n aspdifn rainrrfmn y a` tfalpnutf`fzdmn pdrd rainrrar`n.
• Udpfmaz lamfd: as `d rdzùk aktra a` idlfkn tntd` rainrrfmn y a` tfalptntd` qua tnlù rainrrar asd mfstdkifd ∂t.
v < < m m
∂ t t 5 - t
4
rdpfmaz lamfd < mfstdkifd rainrrfmd
tfalpn tntd`
• Mfstdkifd: as d nkcftum tntd` ma` idlfkn rainrrfmn, iudkmn uk nejatnsa masp`dzd ma uk `ucdr (puktn ma pdrtfmd), d ntrn (puktn ma ``acdmd)
• Idktfmdmas vaitnrfd`as: snk ds idktfmdmas qua raqufarak ma d ldcktum y mfraiifùk pdrd sar axp`fidmds. _nr ajalp`n: buarzd y dia`ardifùk
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_drd a` idsn ma` lnvflfaktn, sa inksfmardk vaitnrfd`as:
• Ra`nifmdm: as a` aspdifn rainrrfmn ak `d ukfmdm ma tfalpn. Yf sainksfmard ak uk fktarvd`n ma tfalpn qua tfakma d iarn, sa inksfmardfkstdktäkad y pdrd fktarvd`ns ma tfalpn ldynr, sa inksfmard inlnva`nifmdm lamfd.
• _nsfifùk: sa ra`difnkd ink a` ldrin ma rabarakifd utf`fzdmn y `dsinnrmakdmds (x, y), ak mnkma sa akiuaktrd ink raspaitn ma` nrfcak
(vaitnr pnsfifùk).
• Masp`dzdlfaktn: as `d mfstdkifd ak `ìkad raitd, aktra a` puktn mapdrtfmd y a` puktn ma ``acdmd ma` nejatn (vaitnr masp`dzdlfaktn).
v < < x
5 - x
4 ∂ x
t 5 - t
4 ∂ t
Ra`nifmdm lamfd <masp`dzdlfaktn (latrns)
tfalpn (sacukmns)
Masp`dzdlfaktn
]rdyaitnrfd
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Lnvflfaktn ukfbnrla
Ya prasaktd iudkmn a` iuarpn rainrra aspdifns fcud`as ak tfalpns fcud`as. Yf `dyaitnrfd as `fkad`, a` lnvflfaktn sa maknlfkd Uaitf`ìkan Qkfbnrla. @d cräbfid
aspdifn inktrd tfalpn as ukd raitd ink ifartn crdmn ma fki`fkdifùk, y `d cräbfidva`nifmdm inktrd tfalpn as ukd raitd pdrd`a`d d` aja hnrfznktd`.
Y (l)
t (s)
t (s)
R (l/s)
v <s
5 - s
4
t 5 - t
4
Aspdifn vs. tfalpn
Ak `d cräbfid ma aspdifn inktrdtfalpn, `d pakmfakta ma `d raitdinrraspnkma d `d ldckftum ma `dva`nifmdm.
Ra`nifmdm vs. tfalpn
Ak `d cräbfid ma va`nifmdm inktrdtfalpn, a` ärad edjn d raitd aquf-vd`a d` aspdifn tntd` rainrrfmn.
s < v . t
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Lnvflfaktn vdrfdmn
Niurra iudkmn a` iuarpn rainrra aspdifns mfbaraktas ak idmd ukfmdm ma tfalpn, yhdy vdrfdifùk ak `d va`nifmdm (dia`ardifùk). Yf `d va`nifmdm vdrìd idktfmdmas fcud-`as ak fktarvd`ns ma tfalpn fcud`as, aktnkias sa maknlfkd Lnvflfaktn QkfbnrlaRdrfdmn. @d cräbfid ma aspdifn inktrd tfalpn as ukd salfpdräen`d, `d ma va`nifmdminktrd tfalpn as ukd raitd ink ifartn crdmn ma fki`fkdifùk, y d ma dia`ardifùk inktrd
Ajalp`n:
Qk dt`atd qua aktrakd mfdrfdlakta, rainrra ukd mfstdkifd ma 51?gl ak 5hnrds. ¾Tuæ va`nifmdm ak l/s rainrra a` dt`atd pnr mìd>
Yn`uifùk: pdrd sn`uifnkdr asta tfpn ma prne`alds sa maeak sacufr astns pdsns:
d) ]nldr `ns mdtns mdmns pnr a` ajarififn.
e) Yn`uifnkdr `d aiudifùk.
i) Yf a` ajarififn `n pfma, hdiar `d inkvarsfùk ma ukfmdmas.
MD]NY:
Y(l)<51?gl
t(s)< 5h
Aiudifùk
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Y (l)
t (
R (l/s)
t (
t (s)
d (l/s5
)
Aspdifn vs. tfalpn
Ra`nifmdm vs. tfalpn
Dia`ardifùk vs. tfalpn
@d pakmfakta ma `d raitd tdkcakta d `diurvd ak uk puktn ‐p“, aqufvd`a d `d
ldckftum ma d va`nifmdm ak mfihn puktn.
A` ärad edjn `d iurvd aqufvd`a d` aspdifntntd` rainrrfmn.
@d cräbfid ma dia`ardifùk inktrd tfalpn,raprasaktd ukd dia`ardifùk inkstdkta
v5 < vn
5 + 5 d.x
@d pakmfakta ma `d raitd ak `d cräbfid mava`nifmdm inktrd tfalpn, inrraspnkma d`d ldckftum ma `d dia`ardifùk.
Nesarva `ns sfcufaktas ajalp`ns.
Qkd parsnkd D rainrra 6 gl ak 49? lfkutns7 `d parsnkd E rainrra 41?? l
ak 6?? s7 y `d parsnkd I ``avd ukd va`nifmdm ma 1 gl/h. ¾Iuä` ma `ds tras
parsnkds as `d läs räpfmd>
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Yf `d parsnkd D rainrra 6 gl ak 49? lfkutns, `d E 41??l ak 6?? s, y `d I ukdva`nifmdm ma 1Gl/h, `n inkvakfakta as pdsdr ns vd`nras ma mfstdkifd y tfalpn d `dlfsld ukfmdm ma lamfmd.
Ajalp`n:
Qk trak qua vfdjd fkfifd`lakta d 5?l/s dia`ard d rdzùk ma 1l/s5 ak `d lfsldmfraiifùk. ¾Tuæ tdk `ajns vfdjdrä ak =? s> ¾Iuä` sarä su va`nifmdm bfkd`>
Yn`uifùk: d takar ak iuaktd:
m) ]nldr `ns mdtns mdmns pnr a` ajarififn. a) A`acfr `d aiudifùk dmaiudmd y sn`uifnkdr`d. MD]NY:vn < 5?l/sd < 1l/s5t < =?ss <>
vb < >
Aiudifùk_drd sdear quæ tdk `ajns vfdjd a` trak ak =?s sa utf`fzd `d aiudifùk:
@d va`nifmdm bfkd` sa hd``d d pdrtfr ma `d aiudifùk:
6gl< 6???l
1Gl< 1???l
49? lfkutns< 38?? s
4 hnrd< 92?? s
Dhnrd sa puama inlpdrdr:@d parsnkd D takmrìd ukd va`nifmdm ma 6???/38??(l/s)< 4.41 (l/s)@d parsnkd E takmrìd ukd va`nifmdm ma 41??/6??(l/s)< 4.23 (l/s)@d parsnkd I takmrìd ukd va`nifmdm ma 1???/92??(l/s)< 4.96 (l/s)
D` inlpdrdr ns vd`nras dktarfnras, sa puama astde`aiaqua d parsnkd läs räpfmd as d E, pnrqua su va`nifmdmas ldynr.
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Lnvflfaktn ma idìmd `fera
Yacúk Drfstùta`as, `d va`nifmdm ma `ns iuarpns d` idar, sa ra`difnkd ink su pa
as maifr, aktra läs pasdmn sad a` nejatn, läs räpfmn ida. Cd`f`an inksfmarqua `d rasfstakifd ma` dfra pnmìd ratdrmdr `d idìmd ma d`cukns iuarpns `fcarnscrdk suparbfifa, parn bfkd`lakta Kawtnk rasn`vfù a` prne`ald, maspraifdkmbrfiifùk ink a` dfra, y inki`uyù qua tnmns `ns iuarpns idak ink `d lfsld dia`ifùk, sfk flpnrtdr su bnrld, ldsd, in`nr, ati. Id`iu`ù dmaläs, `d dia`ardifùk axparflaktd uk iuarpn edjn `d diifùk ma `d buarzd ma crdvamdm qua aqufvd`aprnlamfn d 6.8 l/s5.
•
Aiudifnkas ma` lnvflfaktn ukfbnrlalakta dia`ardmn:
d.t 5x < vf.t +
5
vb < vf + d.t
d < vb vf t
x: mfstdkifdvf: va`nifmdm fkfifd`t: tfalpnd: dia`ardifùk
• Ak `ds aiudifnkas ma` lnvflfaktn maidìmd `fera, `d dia`ardifùk as inkstdktay aqufvd`a d c < 6,8 l/s5 y a` aspdifnrainrrfmn x as `d d`turd h. @d va`nifmdmfkfifd` kn sa tfaka ak iuaktd pnrqua as ?.
h: d`turdc: crdvamdm
c.t 5
h <
5
vb < c.t
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Ajalp`n:
Qk nejatn sa majd idar masma ukd d`turd ma 8l ak uk tfalpn ma 5s. Ma-
tarlfka su va`nifmdm.
Yn`uifùk:
MD]NY:
vn < ?l/s
d < c < 6.8l/s5
h < 8l
t < 5s
vb < >
Aiudifùk: pdrd matarlfkdr `d va`nifmdm ma idìmd utf`fzdlns `d sfcufakta
aiudifùk:
Uavfsa a` sfcufakta `denrdtnrfn vfrtud`:http://www.xtai.idt/~nidsa``d/dpp`ats/idfcumd/dpp`atsn`5.htl,
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_räitfid ma `denrdtnrfn
Ldtarfd`as
Irnkùlatrns, maiälatrn, asiudmrd y pdpa` iudmrfiu`dmn n lf-`flatrdmn.
_rniamflfaktn
4. Nrcdkfzdr a` aqufpn ma trdedjn y sa`aiifnkdr ma inlúkdiuarmn, d` lajnr mapnrtfstd.
5. Ynera uk aspdifn dmaiudmn, matarlfkdr ukd mfstdkifd ak
`ìkad raitd ma 1? l, fkmfidkmn uk saclaktn ma 4? l ma`nkcftum.
9. Ak idmd ukn ma `nspuktns saôd`dmns,uefidr uk irnknla-trfstd pdrd qua ra-cfstra `ns tfalpns maidmd inlpatfmnr d`lnlaktn ma pdsdrbrakta d æ`.
5
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=. Inksaiutfvdlakta a` raprasaktdkta ma idmd aqufpn (mapnrtfstd), maeatnldr d pdrtfmd, ldktakfakmn ukd rdpfmaz inkstdkta murdkta tnmn a`rainrrfmn (kn as kaiasdrfn inrrar).
1. Ak a` sacukmn fktaktn edjn `ds lfslds inkmfifnkas, maea dulaktdrprncrasfvdlakta su va`nifmdm hdstd qua d` bfkd`, masdrrn``a d läxfld.
2. @d inlpatakifd qua sa prasaktd inksfsta ak netakar d pdrtfr ma` masp`d- zdlfaktn ma` inrramnr ak idmd idsn, d lajnr cräbfid inrraspnkmfaktad uk lnvflfaktn raitf`ìkan y d uk lnvflfaktn ukfbnrla dia`ardmn.
3. @ns mdtns netakfmns ak `ns crupns, sa maeak inksfckdr ak d tde`d 5.4.
8. A`denrdr `ds cräbfids inrraspnkmfaktas d aspdifn vs. tfalpn, va`nifmdmvs. tfalpn, dia`ardifùk vs. tfalpn, y matarlfkdr iuä` bua a` aqufpncdkdmnr (`d cräbfid läs dprnxfldmd d` lnvflfaktn fmad`).
]de`d 5.4
Dkä`fsfs ma rasu`tdmns
D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasns
]1]4 ]5 ]9Knlera ]=
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Dutnavd`udifùk
_drd fr inksn`fmdkmn a` prniasn ma dprakmfzdja, sa prnpnka astd ditfvf-mdm iuyd bfkd`fmdm as qua raidpftu`a `n trdedjdmn hdstd asta puktn. Dssa prnluavak `ns prniasns ma latdinckftfvns qua `a dyumdräk d praifsdrdifartns y mfbfiu`tdmas ak a` dprakmfzdja, `ns iud`as maea dkd`fzdr y dyumdrd sn`vaktdr pnr lamfn ma ntrn tfpn ma ditfvfmdmas. @d fmad as qua trdedjafkmfvfmud`lakta, parn sf `n inksfmard, puamak snifd`fzdr ink sus inlpdôa-
rns. D inktfkudifùk hdy ukd sarfa ma pracuktds7 n fkvftdlns d raspnkmar`ds:
Rd`nra sus dprakmfzdjas. _drd a``n, ldrqua ink ukd X a` pnriaktdja quaastfla dmaiudmn:
Idtacnrìd _racuktd ?% 5?% =?% 2?% 8?% 4??%
Iulp`flfaktn y
raspnksdef`fmdm
¾Iulp`fù ink ds aiturds
dsfckdmds, ds ditfvfmdmasmasdrrn``dmds ak i`dsa
y `d aktracd ma tdrads y
trdedjns fkmfvfmud`as>
Iradtfvfmdm y
id`fmdm
¾Dpnrtù fmads y æstds
buarnk sfckfbfidtfvds>
¾Uad`fzù sfk arrnr d`cukn`ds tdrads y/n `ns trdedjns
dsfckdmns>
Dprakmfzdja ydpnrtdifùk ma
inkniflfaktns
¾Tuæ tdktn dprakmfù y
quæ tdktns inkniflfak-tns dpnrtù ak `ds i`dsas,
ak `ds tdrads y/n `ns trd-
edjns rad`fzdmns>
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s < v . t < 5 l/s . 51 s < 1? l
v < < < ?,?41 l/ss ?,53 l
t 48 s
s < 53 il < < ?,53 l53 il
4??
v < < 5 l/s3,5 Gl/h
9,2
_rne`alds ma dp`fidifùk
Lnvflfaktn Uaitf`ìkan Qkfbnrla
4. Axprasdr ak l/s, `d va`nifmdm ma uk lùvf` qua rainrra 53 il ak 48 s:
Yn`uifùk: `d va`nifmdm sa ma-bfka inln a` inifakta aktra a`aspdifn rainrrfmn y a` tfalpnutf`fzdmn, d mfstdkifd rainrrfmd
`d axprasdlns ak latrns:
5. Axprasdr ak l, d mfstdkifd rainrrfmd pnr uk lùvf` murdkta 51 s, sf su va`nifmdmas ma 3,5 Gl/h.
Yn`uifùk: a` aspdifn rainrrfmninrraspnkma d` prnmuitn ma`d va`nifmdm pnr a` tfalpn7axprasdlns `d va`nifmdm maGl/h d l/s, mfvfmfakmn aktra9,2 (bditnr ma inkvarsfùk).
5
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9. Matarlfkdr a` tfalpn kaiasdrfn pdrd qua uk vahìiu`n rainrrd 9 gf`ùlatrnsu va`nifmdm as ma 45 l/s.
Yn`uifùk: a` tfalpn tntd` aquf-vd`a d` inifakta aktra a` aspd-ifn rainrrfmn y `d va`nifmdm,axprasdlns d mfstdkifd ak l:
=. Ynera ukd idrratard raitd, mfstdktas 5?? Gl, astäk uefidmns mns vahìi D y E ink va`nifmdmas ma 91 l/s y 1= Gl/h raspaitfvdlakta. Matarlfkdmfstdkifd qua rainrra idmd ukn dktas ma iruzdrsa.
s < 9 Gl . 4.??? < 9.??? l
t < < 51? s9.??? l
45 l/s
v < < 41 l/s1= Gl/h
9,2
Yn`uifùk: tnmns `ns vd`nras maeak astdr ak a` lfsln sfstald ma lamfmd.
Axprasalns fkfifd`lakta `dva`nifmdm ak l/s:
5?? Gl
D v < 91 l/s Ev < 1= Gl/h
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t < < < =.??? s s 5??.??? l
v U
1? l/s
@d mfstdkifd ak latrns: s < 5?? Gl . 4.??? < 5??.??? l
@d va`nifmdm rasu`tdkta aktra`ns mns vahìiu`ns iudkmn samfrfcak ukn hdifd a` ntrn,aqufvd`a d d suld ma ds va`n-ifmdmas ma idmd ukn ma a``ns.
v U < v
D + v
E <
91 l/s + 41 l/s < 1? l/s
A` tfalpn qua raqufara uk lùvf` ink astd va`nifmdm pdrd rainrrar `d mfs-tdkifd fkmfidmd as:
A` vahìiu`n D ak asa tfalpnrainrra:
s D < v
D . t <
91 l/s . =.??? s < 4=?.??? l
A` vahìiu`n E ak asa tfalpnrainrra:
s E
< v E . t <
41 l/s . =.??? s < 2?.??? l
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h < vf . t +
c . t 5
5
t < < < < 4?? s5 < 4? s5 . h 5 x =6? l 68? l
c 6,8 l/s5 6,8 l/s5
Lnvflfaktn Qkfbnrla Dia`ardmn:
1. Matarlfkdr a` tfalpn qua tdrmd uk nejatn ak idar masma ukd d`turd ma l. ¾Ink quæ va`nifmdm ``acd>
Yn`uifùk: d pdrtfr ma `daxprasfùk:
Inksfmardkmn qua `d va`nifmdm fkfifd` vf < ?, maspajdlns t pdrd netakar:
_drd matarlfkdr `d va`nifmdm qua tfaka d` ``acdr d` pfsn, utf`fzdlns ukdaxprasfùk qua kns parlftd ra`difnkdr va`nifmdm, dia`ardifùk y tfalpn:
v b < v
f + c . t < ? + 6,8 l/s5 x 4? s < 68 l/s
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Uac`dlaktn
Ya `dkzd masma uk pd-sf``n ma ukd dkihurdma = latrns, didedmnak uk drin ma 8 latrns
ma rdmfn. A` saitnr ma idìmd astdrä ldr-idmn ink mns ìkads e`dkids ma 1 il madkihurd, ma td` lnmn qua sf `ns enrmas
fktarkns ma `ds `ìkads sa prn`nkcdsakmaearìdk pdsdr pnr `ds mns fktarsaiifn-kas ma `ns enrmas fktarfnras ma` driny `ds `ìkads pdrd`a`ds qua ma`flftdk a`pdsf``n ma flpu`sn y qua sa iruzdk aka` puktn iaktrd` ma` iìriu`n, ma` iud` a`drin bnrld pdrta. A` saitnr takmrä dsì 56º dprnxfldmdlakta.
_drd rad`fzdr idmd fktaktn, a` dt`atd tfakauk lfkutn. Knrld`lakta, idmd dt`atdrad`fzd tras fktaktns.
@d jded`fkd maea incarsa pnr `d akinr-mdmurd (d` lakns `d ldkn ma` dt`atdmaea tnidr`d), y `dkzdrsa pnr akifld
ma` hnlern n ma` erdzn ma dkzdr7 kn saparlfta dkzdr`d ak rntdifùk kf puama a
dt`atd mdr `d aspd`md d` saitnr ma idìmddktas ma sn`tdr `d jded`fkd7 `ns astf`nskn i`äsfins kn astäk dutnrfzdmns. Yf `d
jded`fkd sa rnlpa ak a` fktaktn n ak adfra kn sa inktdrä inln ku`n7 tdlpninsf `d rnturd hdia parmar a` aquf`ferfn ddt`atd y prnvnid qua tnqua buard madrin7 ak asta idsn sa a parlftfrä vn`var d
inlakzdr. Ak d idìmd, d puktd latä`fidmaea tnidr a` sua`n dktas qua iud`qufantrd pdrta ma `d jded`fkd.
A` idlpaùk n`ìlpfin, Arfg @allfkc, ak `d pruaedma jded`fkd ma `ns Juacns N`ìlpfins ma 46?8.A` `dkzdlfaktn ma jded`fkd as ukd pruaed
ma` dt`atfsln ditud` ak qua sa `dkzd ukd jded`fkd
@dkzdlfaktn ma jded`fkd9
B n t n t n l d m d m a S f g f p a m f d
Lnvflfaktn ak a` p`dkn
Qkfmdm 4. Ifkalätfid Yasfùk
9
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Idrditarìstfids ma `d jded`fkd
@d jded`fkd as uk vakde`n d`drcdmn ink`d puktd latä`fid. @d `nkcftum ma `d jd-
ed`fkd as ma 52?-53? il ak idtacnrìdldsiu`fkd y 55?-59? il ak idtacnrìdbalakfkd, y uk pasn läxfln ma 8?? cpdrd `ns hnleras y 2?? c pdrd `ds lu-
jaras. ]faka uk dsfmarn, bderfidmn inkinrma`, ma ukns 41 il ma `drcn, quasa akiuaktrd dprnxfldmdlakta ak a`iaktrn ma crdvamdm ma `d jded`fkd.
D `n `drcn ma `d hfstnrfd sa hd vakfmndiaridkmn d `d puktd a` iaktrn ma crd-vamdm ma `ds jded`fkds, pdrd hdiar quaidfcdk dktas, yd qua sa inlakzdedk drad`fzdr ldrids qua axiamìdk a` drcn ma`ns idlpns ma idìmd, ink a` inksfcufakta
pa`fcrn.
]æikfids ma `dkzdlfaktn
A` nejatfvn ma abaitudr uk euak `dlfaktn tæikfin as a` ma qua `d jded
takcd `d ldynr va`nifmdm pnsfe`aa` lnlaktn ma sar `dkzdmd, duktdlefæk fkb`uyak ntrns dspaitns puamak sar inktrn`dmns, inln a` äkma sd`fmd n a` d`fkadlfaktn ma d jdedink `ns hnlerns.Masma a` fkfifn ma`dkzdlfaktns ak `d ard lnmarkd, axfstfmn vdrfds tæikfids ma dkzdlfa
axfstfakmn fki`usn murdkta d`cúk tfpn ukd tæikfid rntdtnrfd marfvdmd`dkzdlfaktn ma edrrd, qua sa prdiak a` _dìs Rdsin. Astd tæikfid ard lpa`fcrnsd sf kn sa mnlfkded parbalakta, puastn qua axfstìd d pnsfef`ma qua d jded`fkd sd`fard hdifd ntrn qua kn buard `d znkd ma `d idìmd in
inksfcufakta pa`fcrn.
n l d m d m a S f g f p a m f d
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D pdrtfr ma `d `aiturd dktarfnr, raspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds
¾Tuæ tfpn ma lnvflfaktn rad`fzd d jded`fkd ak a` `dkzdlfaktn>
¾Tuæ vdrfde`as iraa ustam qua maeatakar uk mapnrtfstd ma dkzdlfaktnma jded`fkd pdrd netakar uk euaktfrn>
¾Ink qua ntrn mapnrta ra`difnkd a``dkzdlfaktn ma jded`fkd>
Rdyd d ukd idkihd ma edsquaten`.Masma a` iaktrn ma` drin, `dkia `dpa`ntd hdifd d iastd. Yf kn tfaka di-iasn d ukd idkihd ma edsquaten`,trdta ma akiastdr ukd en`d ma pdpa`n ukd pa`ntd ak ukd idkaid, n akuk nejatn sflf`dr. Axp`fqua quæ tfpnma lnvflfaktn rad`fzù (tnla `ds
lamfmds qua sadk kaiasdrfds pdrddrculaktdr su hfpùtasfs).
Lnvflfaktns inln `ns masirftns ak `d `ai-
turd sa puama prasakifdr y axparflaktdr ak
mfbaraktas tfpns ma avaktns n sftudifnkas._nr ajalp`n, dktas sa utf`fzdedk drlds ma
inledta qua sa ``dldedk idtdpu`tds, `ds
iud`as drrnjdedk rnids cfcdktas pdrd mar-
rfedr d` akalfcn7 su rainrrfmn raprasaktd
uk lnvflfaktn pdrdeù`fin.
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¾Tuæ tfakak ak inlúk `ns `dkzdlfaktns qua sa hdiak ink `d ldkn, ink uk id
y ink ukd hnkmd>
Nesarva a` sfcufakta vfman, ak a` iud` sa prasaktd ukd sftudifù
sflf`dr d` `dkzdlfaktn ma prnyaitf`as:
Knlera: ]d``ar 5. @dkzdlfaktn ma tnrtdsMurdifùk: 4:58 lfkutns
Ma diuarmn d `n qua nesarvù ak a` vfman, raspnkmd `ds sfcufaktas pracuktds
¾Tuæ idlfkns sacufrìd a` pdsta` sf n dkzd d ifartd mfstdkifd d ukn ma sus dlfcn
¾Iraa qua pdrd qua sa luavd a` pdsta` tfaka qua parldkaiar ukd buarzd qu
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Bukmdlaktn taùrfin
Lnvflfaktn pdrdeù`fin
Ya maknlfkd lnvflfaktn pdrdeù`fin d` qua rad`fzd uk nejatn iuyd trdyaitnrfd mas-irfea ukd pdräen`d. Inrraspnkma d d trdyaitnrfd fmad` ma uk prnyaitf` qua sa luavaak uk lamfn qua kn nbraia rasfstakifd d` dvdkia y qua astä sujatn d uk idlpn crdvftdtnrfn ukfbnrla. ]dlefæk as pnsfe`a malnstrdr qua puama sar dkd`fzdmn inln `dinlpnsfifùk ma mns lnvflfaktns, uk lnvflfaktn raitf`ìkan ukfbnrla (hnrfznktd`)y uk lnvflfaktn ma idìmd `fera (vartfid`).
• A` lnvflfaktn ma lamfdpdräen`d n salfpdrdeù fin(`dkzdlfaktn hnrfznktd`):sa puama inksfmardr inln
`d inlpnsfifùk ma uk dvdk-ia hnrfznktd` raitf`ìkanukfbnrla y `d idìmd `fera.
• A` lnvflfaktn pdrdeù`f-in inlp`atn: sa puamainksfmardr inln `d inl-pnsfifùk ma uk dvdkiahnrfznktd` raitf`ìkan ukf-bnrla y uk `dkzdlfaktnvartfid` hdifd drrfed, qua asuk lnvflfaktn raitf`ìkanukfbnrlalakta dia`ardmnhdifd dedjn (LUQD), pnr`d diifùk ma `d crdvamdm.
Rx
Rf
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Ak inkmfifnkas fmad`as ma rasfstakifd ku`dd` dvdkia y idlpn crdvftdtnrfn ukfbnrla,`n dktarfnr flp`fid qua:
4. Qk iuarpn qua sa majd idar feralak-ta y ntrn qua as `dkzdmn hnrfznktd`-lakta masma `d lfsld d`turd, tdrmdka` lfsln tfalpn pdrd ``acdr d` sua`n.
5. @d fkmapakmakifd ma `d ldsd ak `didìmd `fera y a` `dkzdlfaktn vartfid`
as fcud` ma vä`fmd ak ns lnvflfaktnspdrdeù`fins.
9. Qk iuarpn `dkzdmn vartfid`laktahdifd drrfed y ntrn pdrdeù`fidlaktainlp`atn qua d`idkia d lfsld d`turdtdrmd a` lfsln tfalpn ak idar.
Astds aiudifnkas sa puamak netakar d pdrtfr ma` prfkifpfn ma fkmapakmakifd ma vflfaktns, tdktn ak a` saktfmn hnrfznktd` (aja x), inln ak a` saktfmn vartfid` (aja
Ak a` saktfmn hnrfznktd`, sa hdia prasakta a` lnvflfaktn raitf`ìkan ukfbnrla yparlfta akinktrdr a` d`idkia hnrfznktd`.
x < v
b . t
Ak a` saktfmn vartfid`, sa inksfmard a` lnvflfaktn ma idìmd `fera, y kns parmatarlfkdr a` tfalpn ma idìmd (t ), `d va`nifmdm d` ``acdr d` pfsn v
b y `d d`turd ma
mnkma bua sn`tdmn a` nejatn (h)7 sa inksfmard qua vf < ?.
c t5 5 h
Aiudifnkas ma` lnvflfaktn salfpdrdeù`fin (lsp)
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Ajalp`n:
Ya majd idar ukd pa`ntd ink ukd va`nifmdm fkfifd` ma 2l/s, masma `d suparbfifa
ma ukd lasd p`dkd qua tfaka ukd d`turd ma 4.1l. Matarlfka: d) `d pnsfifùk ma
`d pa`ntd d ns ?.9 sacukmns maspuæs ma` dkzdlfaktn, e) d pnsfifùk ma d pa`ntdd` ihnidr ink a` pfsn y i) `d va`nifmdm ma `d pa`ntd dktas ma tnidr ink a` pfsn.
Yn`uifùk:
MD]NY:
vn < 2l/s
d < c < 6.8l/s5h < 4.1l
t < ?.9s
vb < >
Aiudifùk: pdrd matarlfkdr d va`nifmdm ma idìmd utf`fzdlns d sfcufakta aiudifùk:
d.
e. pdrd matarlfkdr `d pnsfifùk d` ihnidr a`
pfsn maealns matarlfkdr a` tfalpn d`
ihnidr a` pfsn prflarn
i. pdrd hd``dr `d va`nifmdm ak a` aja x as fcud` y ak a` aja y takalns:
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Aiudifnkas ma lnvflfaktn pdrdeù`fin
]dlefæk ``dldmn lnvflfaktn ma prnyaitf`as, pnrqua tnmn nejatn `dkzdmn va`nifmdm fkfifd` y ink ifartn crdmn ma fki`fkdifùk raspaitn ma` d`idkia hnrfzn
masirfea ukd trdyaitnrfd ma idrditarìstfids sflf`dras. Dmaläs, `n lfsln qua alnvflfaktn lsp, axfsta fkmapakmakifd ma lnvflfaktn y pnr `n tdktn, pnmasfktatfzdr su astumfn, matarlfkdkmn ds inlpnkaktas raitdkcu`dras ma d va`niv
x , v
y `d d`turd läxfld H
l, a` tfalpn ma vua`n t, y a` d`idkia hnrfznktd` x.
_rne`alds ma dp`fidifùk
4. Masma n d`tn ma uk didktf`dmn ma 1? l, as mfspd-rdmn uk prnyaitf` ink va`nifmdm hnrfznktd` ma 41l/s. Matarlfkdr a` tfalpn ma vua`n, a` d`idkia
hnrfznktd` y `d va`nifmdm d` ``acdr d` dcud.
Yn`uifùk: inknifakmn `d d`turd, as pnsfe`amatarlfkdr a` tfalpn ma idìmd:
As flpnrtdkta rainrmdr qua ak `d d`turd läxfld, `d v y as iarn.
A` tfalpn qua tdrmd a` nejatn ak suefr, as a` lfsln qua fkvfarta ak edjdr hdstlfsld d`turd ma mnkma sa `dkzù.
t < < < < 4? 5?= s5 < 9 46= s5 . h 5 x 1? l 4?? l
vn
5 . sak5δ 5vnsakδ v
n
5 . sak5δ
5.c c cv
x
< v . insδ 7 v y
< v . sakδ 7 H l < 7 t < 7 x <
9
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Inknifmn a` tfalpn y d va`nifmdm hnrfznktd`, pnmalns matarlfkdr a` d`idkia hnrfznktd`
_drd matarlfkdr a` vd`nr ma `d va`nifmdm bfkd`, sa raqufara matarlfkdr a` vd`nr ma `dva`nifmdm vartfid` d` lnlaktn ma hdiar inktditn ink a` dcud.
v y < c . t < 6,8 l/s5 . 9,46= s < 94,9?4 l/s
@d va`nifmdm bfkd` sarä aktnkias:
5. Matarlfkdr `ds inlpnkaktas raitdkcu`dras, `d d`turd läxfld, a` tfalpn mavua`n y a` d`idkia hnrfznktd` ma uk prnyaitf` qua hd sfmn mfspdrdmn d` kfvama` pfsn ink va`nifmdm fkfifd` ma 44? l/s y uk äkcu`n ma fki`fkdifùk ma 9?º.
x < v x . t < 41 l/s . 9,46= s < =3,64 l
v b < v
x
5 + v y
5 < (41 l/s)5 + (94,9?4l/s)5 < 45?=,315l/s < 9=,34 l/s
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vn
5 . sak5δ (44? l/s)5 . sak59? º 45.4?? x ?,51 9.?51
5.c 5 x 6,8 l/s5 46,2 46,2 H
l < < < < < 41=,99
5vn .sakδ 5(44? l/s) . sak9? º 55? . ?,1 l/s 44? l/s
c 6,8 l/s5 6,8 l/s5 6,8 l/s5
x < < < < < 4?26,5= v
n
5 . sak5δ (44? l/s)5 . sak5 x9? º 45.4?? xsak 2?º 4?.=38,2
c 6,8 l/s5 6,8 6,8
Yn`uifùk: inlpnkakta hnrfznktd`
v x
< v . insδ < 44? l/s . ins9? º < 44? l/s . ?,822 < 61,52 l/s
Inlpnkakta vartfid`
v y
< v . sakδ < 44? l/s . sak9? º < 44? l/s . ?,1 < 11 l/s
D`turd läxfld
]falpn ma vua`n
t < < < < < 44,5
D`idkia hnrfznktd`
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4. _rflarn, nrcdkfzdr crupns ma trd-edjn pdrd inkstrufr ukd idtdpu`-td. _ravfdlakta, fkvastfcdr quæ
as, su hfstnrfd= y `ns ldtarfd`askaiasdrfns pdrd inkstrufr`d.
5. Inlprnedr su bukifnkdlfaktn y axditftum pdrd ukd mfstdkifd ma 9 l.9. Ak `d präitfid, sa rad`fzdräk ifkin `dkzdlfaktns pdrd diartdr snera uk td-
e`arn ma tfrn d` e`dkin, in`nidmn pravfdlakta ak a` pfsn y d `d mfstdkifdprnpuastd.
=. A`denrdr ukd cräbfid masirfptfvd ma d trdyaitnrfd ma` prnyaitf` masma a` ln-laktn ma` dkzdlfaktn hdstd a` lnlaktn ma hdiar inktditn ink a` tde`arn.
Ldtarfd`as
Ifktd lætrfid, ed`fkas, idtdpu`td, tde`arn pdrd tfrn d` e`dkin(sa puama mfsaôdr ak uk p`facn ma idrtu`fkd, pdpa` parfùmfinn aspuld murd).
_räitfid ma `denrdtnrfn
_rniamflfaktn
Dkä`fsfs ma rasu`tdmns
=. www.as.wfgfpamfd.nrcwfgfIdtdpu`td59g,ma`dgrngatd.wnmprass.inl
=
Fldcak lnmfbfidmd ma www.ma`dgrngatd.wnrmprass.inl
Uavfsa a` sfcufakta `denrdtnrfn vfrtud`:http://www.xtai.idt/~nidsa``d/dpp`ats/lnvpdrde/dpp`atsn`5.htl
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Yn`uifnkdr ns sfcufaktas prne`alds, utf`fzdkmn ns inkiaptns, ds bùrlu`dsy `ns prniamflfaktns dmaiudmns pdrd idmd ukn.
• A`denrdr `d cräbfid ma aspdifn inktrd tfalpn (s vs t), dkd`fzdr yinki`ufr snera `d ra`difùk qua axfsta aktra s y t, `d pakmfaktama `d raitd y su saktfmn bìsfin.
• A`denrdr d cräbfid ma va`nifmdm inktrd tfalpn (v vs t), dkd`fzdry inki`ufr snera `d ra`difùk aktra v y t, a` ärad edjn `d raitd ysu saktfmn bìsfin.
4. @ns mdtns racfstrdmns d pdrtfr ma` lnvflfaktn ma uk vahìiu`n snera
ukd pfstd p`dkd y raitd drrnjdrnk `ns sfcufaktas rasu`tdmns:
5. Axprasdr ak Gl/h `d va`nifmdm ma uk lùvf` qua rainrra ?,?91 Gl ak 41 s.
9. Iuä` as a` aspdifn rainrrfmn (ak l), pnr uk lùvf` qua sa masp`dzd
ink ukd va`nifmdm ma 58,8 Gl/h murdkta 9 lfkutns.
=. Iuäktn tfalpn tdrmd ak rainrrar 3? gl, uk lùvf` qua vfdjd ink ukdva`nifmdm ma 3 l/s. Axprasdr `d raspuastd ak sacukmns.
=1s (l) ? 1 4? 41 5? 51 9? 91 =?
6t (s) ? 4 5 9 = 1 2 3 8
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@ns sfcufaktas ajarififns sa rasua`vak edjn a` sfcufakta akukifdmn: mns vahìiu-`ns mfstdkifdmns pnr 4?? Gl tfakak va`nifmdmas ma 5? l/s y =? Gl/h ras-paitfvdlakta. Matarlfkdr d mfstdkifd qua ns sapdrd d` iden ma 5 hnrds sf:
4. _drtak ma` lfsln `ucdr, d `d lfsld hnrd y ak `d lfsld mfraiifùky saktfmn.
5. _drtak ma` lfsln `ucdr, d `d lfsld hnrd y ak `d lfsld mfraiifùkparn ak saktfmn inktrdrfn.
9. _drtak ma sus raspaitfvds astdifnkas d` lfsln tfalpn, D hdifd E yE hdifd D.
=. _drtak ma sus raspaitfvds astdifnkas D hdifd E y E hdifd D, parn Dsd`a ukd hnrd maspuæs.
1. _drtak ma sus raspaitfvds astdifnkas d` lfsln tfalpn, D hdifd E y
E ak a` lfsln saktfmn ma D.
2. D puama d`idkzdr d E, sf pdrtak ma sus raspaitfvds astdifnkas d`lfsln tfalpn, D hdifd E y E ak a` lfsln saktfmn ma D. Yf as dsì,iuäktn tfalpn raqufara D pdrd d`idkzdr d E.
3. Matarlfkdr `d d`turd ma uk amfbfifn, sf masma su puktn läs d`tn sa
majd idar ukd asbard qua tdrmd 3,1 sacukmns ak ``acdr d` pfsn.
8. Ink quæ va`nifmdm ``acd `d asbard ma` ajarififn dktarfnr.
6. Masma ukd d`turd ma 5? l, sa `dkzd hdifd drrfed uk nejatn inkva`nifmdm ma 5? l/s. Matarlfkdr `d d`turd läxfld qua puamad`idkzdr, a` tfalpn qua tdrmd ak ``acdr d` pfsn y `d va`nifmdm ma``acdmd
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Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdrd
sn`uifnkdr sftudifnkas bìsfids rad`as ma `d vfmd mfdrfd.
Inki`usfnkas
Avd`udifùk
¾Tuæ dprakmfù ink `d ditfvfmdm>Rd`nrdr a` trdedjn rad`fzdmn, d prasaktdifùk y masdrrn``n ma d cuìd, d dp`fid-ef`fmdm ma d aiturd, y ma sar pnsfe`a, prnpnkar lnmfbfidifnkas pdrd lajnrd
Qtf`fzdr ds axprasfnkas vfstds y ns prniasns ldtalätfins dmaiudmns pdrdsn`uifnkdr `ns sfcufaktas prne`alds:
4. Qkd asbard latä`fid as `dkzdmd masma ukd d`turd ma 5 l ink va`n-ifmdm hnrfznktd` ma = l/s. Matarlfkdr:
d. A` tfalpn qua tdrmd ak idar.e. A` d`idkia hnrfznktd`.i. @d va`nifmdm vartfid` d` ``acdr d` pfsn.m. @d va`nifmdm bfkd`.
5. Qk dvfùk vfdjd ink va`nifmdm hnrfznktd` ma 45? l/s d ukd d`turd ma5 Gl7 ak asa fkstdkta, sua`td uk nejatn qua maea idar ak uk puktnsnera `d ]farrd d ukd mfstdkifd ma 5.=?? l. Edjn astds inkmfifnkas,¾sarä pnsfe`a iulp`fr a` nejatfvn>
9. _drd netakar d ldynr abfifakifd ak uk dkzdlfaktn ma mfsin, a` dt`atdmaea id`iu`dr a` lajnr äkcu`n pdrd su dkzdlfaktn. Yf supnkalns qua`d va`nifmdm ink `d iud` as `dkzdmn as ma 9? l/s, id`iu`dr a` d`idkia
hnrfznktd` pdrd 9?º, =?º, =1º, 1?º y 2?º, y matarlfkdr ink iuä` maastns äkcu`ns sa netfaka a` ldynr d`idkia. ¾Yuiamarä n lfsln ink`d d`turd läxfld> ¾Tuæ pdsd ink a` tfalpn>
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Dutnavd`udifùk
UAB@AXFNKN YNEUA LF _UNIAYN MA D_UAKMFZDJA
Ditfvfmdmas ma dprakmfzdja qua masdrrn``æ Dprakmfzdjas
DitfvfmdmLa
custùKn lacustù
Luymfbìif`
Mfbìif` Bäif` Dprakmì
d`cn KuavnAstn yd`n sdeìd
_drd fr inksn`fmdkmn a` prniasn ma dprakmfzdja, sa prnpnka astd ditfvf-mdm iuyd bfkd`fmdm as qua raidpftu`a `n trdedjdmn hdstd asta puktn. Dsìsa prnluavak `ns prniasns ma latdinckftfvns qua `a dyumdräk d praifsdrdifartns y mfbfiu`tdmas ak a` dprakmfzdja, `ns iud`as maea dkd`fzdr y dyumdrd sn`vaktdr pnr lamfn ma ntrn tfpn ma ditfvfmdmas. @d fmad as qua trdedjafkmfvfmud`lakta, parn sf `n inksfmard, puamak snifd`fzdr ink sus inlpdôa-
rns. D inktfkudifùk hdy ukd sarfa ma pracuktds7 n fkvftdlns d raspnkmar`ds:
_faksa ak `ds ditfvfmdmas qua rad`fzù ak astd ukfmdm y raspnkmd:
• ¾Iuä`as snk `ns dpnrtas läs vd`fnsns ma astd ukfmdm>
• ¾Ak quæ ifriukstdkifds puama dp`fidr d`cukns ma `ns inkiaptns dprak-mfmns ak astd ukfmdm> Mæ ajalp`ns.
• Masirfed ma quæ ldkard `ncrù inlprakmar lajnr `ns talds masdrrn`-`dmns ak astd ukfmdm. Qtf`fia `d sfcufakta rajf``d:
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Buarzd
Qkfmdm 5. Mfkälfid. A lnvflfaktn y sus idusds Yasfùk
=
Dtrdiifùk bdtd`
@d inlukfmdm ifaktìbfid inksfmard qua tnmd `d ldtarfd ma`ukfvarsn astä sujatd d iudtrn buarzds bukmdlaktd`as: `d crd-
vamdm, a` a`aitrnldckatfsln y `ds buarzds kui`adras buartasy mæef`as. @d fktardiifùk kui`adr buarta ldktfaka juktns `nsprntnkas y `ns kautrnkas ak a` kúi`an dtùlfin, d pasdr ma
`d rapu`sfùk aktra `ns prntnkas ma idrcd pnsftfvd qua ma ntrn lnmn `nshdrìd sapdrdrsa. @d buarzd kui`adr mæef` ’ukd mflfkutd pdrta (4?-59) ma`d fktardiifùk kui`adr buarta’ as d qua rnlpa ns kautrnkas, bnrldkmnuk prntùk y axpu`sdkmn uk a`aitrùk ak bnrld ma rdmfnditfvfmdm eatd.
@d inlprasfùk ma astds iudtrn buarzds eäsfids hd sfmn fkb`uakifdmd pnr`d tanrìd iuäktfid, sacúk `d iud` `d rdmfdifùk sa alfta n kn ak nkmdsinktfkuds, sfkn ak paquaôns pdquatas ma akarcìd maknlfkdmns iudktns.Astd fmad sa dp`fiù pnr prflard vaz d `ns idlpns a`aitrnldckætfins, y`d tanrìd iuäktfid ma d a`aitrnmfkälfid inksfmard tnmds ds rdmfdifnkasa`aitrnldckætfids ak tærlfkns ma iudktns ``dldmns bntnkas, qua snkdesnrefmds y alftfmds pnr `ns a`aitrnkas.
Idmd buarzd pdraia takar su prnpfd pdrtìiu`dlaksdjard inln a` bntùk. @d buarzd kui`adrmæef` as trdkspnrtdmd pnr `ds pdrtìiu`ds Sy Z7 `d fktardiifùk kui`adr buarta, pnr `nspfnkas. @d crdvamdm pnr `ns crdvftnkas, dúksfk mataitdr.
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Ink a` masiuerflfaktn ma `ns TQDUGY, `ds pdrtìiu`ds qua bnrldk `nsprntnkas y ns kautrnkas, sa masdrrn``n d tanrìd irnln mfkälfid iuäktfid(TIM), pdrd axp`fidr `ds buarzds qua ditúdk aktra a``ns.
Ak `d tanrìd iuäktfid a`aitrnmfkälfid sn`n axfsta uk tfpn ma pdrtìiu`dlaksdjard: a` bntùk, sfk aledrcn ak `d TIM axfstak kn lakns ma nihn``dldmns C@QNKAY qua trdkslftak `d buarzd y ‐pacdk“ d `ns qudrgs.
@d buarzd kui`adr mæef` as `d qua mfvfma `ns kautrn-
kas, idusdkmn `d rdmfnditfvfmdm eatd. Astd buarzd astrdkspnrtdmd pnr ds pdrtìiu`ds S y Z. Mdmn qua astdspdrtìiu`ds snk luy crdkmas, d buarzd kui`adr mæef` asabaitfvd sn`n ak mfstdkifds axtraldmdlakta inrtds.
Iudkmn ak uk kúi`an dtùlfin uk kautrùk sa masinlpn-ka ak uk prntùk y uk a`aitrùk (ukd pdrtìiu`d eatd), ukdpdrtìiu`d S pdsd akarcìd aktra ds pdrtìiu`ds. @d pdrtìiu`d
eatd sa alfta masma a` kúi`an ma` ätnln ak a` qua a`kautrùk astä idlefdkmn. Ma `d masinlpnsfifùk eatdsa masprakma tdlefæk uk dktfkautrfkn, ukd lfstarfnsdpdrtìiu`d sfk ldsd, dukqua pnrtdmnrd ma ukd akarcìdqua kn tfaka idrcd.
@d fktardiifùk kui`adr buarta ldktfaka ukfmn `ns prn-tnkas y kautrnkas ak a` kúi`an, d pasdr ma qua `ns
prntnkas ma idrcd pnsftfvd sa rapa`ak. Ak astd buarzd, dakarcìd, trdkslftfmd pnr pfnkas, ditfvd ds enleds kui`adras y ldktfakaakiakmfmds d `ds astra``ds. As abaitfvd snera ukd mfstdkifd inrtd, dsì quapuama dpratdr pnmarnsdlakta `ns kúi`ans läs paquaôns. @ns kúi`ansläs crdkmas kn astäk ukfmns tdk buartalakta, y snk fkastde`as maefmnd `d rapu`sfùk dmfifnkd` aktra crdkmas kúlarns ma prntnkas.
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trfifmdm, y sa akidrcd ma ldktakar d `ns a`aitrnkas sapdrdmns y ak ùreftdd`ramamnr ma` kúi`an. Ya trdkslfta pnr pdrtìiu`ds maknlfkdmds bntnkas
vfrtud`as. Dukqua ns idlpns a`aitrnldckætfins kn snk tdk crdkmas inln`ns ma `d crdvamdm, a` ma `d ]farrd sa axpdkma pnr lf`as ma gf`ùlatrnshdifd a` aspdifn axtarfnr.
@d crdvamdm as `d buarzd qua kns ldktfaka snera `d ]farrd, d `d @ukd akùreftd, d `ns p`dkatds cfrdkmn d`ramamnr ma` Yn` y d `ds cd`dxfds ukfmds. As`d lakns inlprakmfmd ma `ds iudtrn buarzds eäsfids, as prnede`a qua sa
trdkslftd pnr pdrtìiu`ds ``dldmds crdvftnkas, dukqua æstds kukid sadkmataitdmds, puas kn pdraiak takar abaitn snera ntrd ldtarfd. As `d läsmæef` ma `ds iudtrn buarzds1.
1 Dutnr Ifakifd axp`fidmd Encntä: Rn`uktdm
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Bukmdlaktn taùrfin
Inln saclaktn ma raitd mfrfcfmd, su raprasaktdifùk cräbfidas ukd b`aihd. A` puktn ma mnkma pdrta, matarlfkd a` puktnma dp`fidifùk y `d puktd fkmfid a` saktfmn.
Raitnr
Ak tærlfkns cakard`as, uk vaitnr as uk saclaktn ma raitd mfrfcfmn iuyd `nkcftum asa` vd`nr ma `d ldckftum vaitnrfd` qua raprasaktd, y iuyd nrfaktdifùk kns fkmfid `dmfraiifùk y a` saktfmn ma dquæ``d.
Qkd vaz rad`fzdmd `d `aiturd dktarfnr, raspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds¾Ya hd pracuktdmn quæ buarzdsditúdk snera `ns dvfnkas pdrd quasa ldktakcdk ak a` dfra>¾Iraa ustam qua uk iuarpn puamaparldkaiar ak lnvflfaktn sfkqua ditúa kfkcukd buarzd snera æ`>Axp`fqua.¾Iùln iraa qua ditúd `d buarzdma `d crdvamdm pdrd qua `d `ukd saldktakcd ak ùreftd y `ns p`dkatdscfrak d`ramamnr ma` sn`>Alpuja uk `dmrf``n ak ukd su-parbfifa p`dkd. ¾_nr quæ `d idjdmfslfkuya su va`nifmdm> Axp`fqua.
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Ak iudktn d d kntdifùk ldtalätfid ds idktfmdmas vaitnrfd`assa raprasaktdk ink b`aihd snera a` knlera ma` vaitnr. _nrajalp`n: a` vaitnr buarzd as:
Axfstak vaitnras qua tfakak a` lfsln puktn ma dp`fidifùk y samaknlfkdk inkiurraktas. V sf dmaläs, inlpdrtak ldckftum,mfraiifùk y saktfmn, snk aqufpn`aktas. Qk vaitnr npuastn dntrn as a` qua tfaka a` lfsln puktn ma dp`fidifùk, lùmu`ny mfraiifùk, parn saktfmn inktrdrfn. _nr ajalp`n: pdrd a`vaitnr su npuastn as - .
Npardifnkas ink vaitnras
Yuld ma vaitnras
Lætnmn ma` pdrd`a`ncrdln
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Ya puama suldr vaitnras pnr mns lætnmns cräbfins: a` ma` pdrd`a-`ncrdln qua inksfsta ak raprnmuifr ns mns vaitnras inkiurraktasinktrdrfns, bnrldkmn uk pdrd`a`ncrdln. A` rasu`tdmn sa netfakad` ukfr a` puktn ma inkiurrakifd y a` puktn iaktrd` hdifd mnkmasa juktdk ds raprnmuiifnkas ma ns mns vaitnras fkfifd`as. V a` ma`
pn`ìcnkn inksfsta ak uefidr idmd vaitnr ukn d inktfkudifùk ma`ntrn7 a` vaitnr rasu`tdkta sa netfaka d` ukfr a` fkfifn ma` prflarvaitnr ink a` bfkd` ma` ú`tfln.
Lætnmn ma` pn`ìcnkn
Uastd ma vaitnras
@d rastd ma mns vaitnras as `d suld ma` prflarn ink a` npuastnma` sacukmn. _drd hdiar `d mfbarakifd ma mns vaitnras, edstd ink
dp`fidr D - E < D + (-E), astn as, suldr a` vaitnr npuastn.
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_rnmuitn pnr uk asid`dr
Lu`tfp`fidr uk vaitnr pnr uk asid`dr as tnldr a` vaitnr tdktds vaias inln fkmfa` asid`dr, `n iud` as vä`fmn tdlefæk, ak `ns idsns iudkmn a` asid`dr as brdiifnk
n kacdtfvn.
Inlpnkaktas raitdkcu`dras ma uk vaitnr
Qk vaitnr sa puama masinlpnkar ak mns inlpnkaktas: `d inlpnkakta `d inlpnkakta y:
D x
< D . insδ 7 D y
< D . sakδ
Buarzd
As `d diifùk qua sa ajaria snera uk iuarpn pdrd idlefdr su astdmn ma lnvflfa
ma rapnsn n pdrd prnmuifr mabnrldifnkas ak a` lfsln. _nr ukd buarzd, pnma
pnkar ak lnvflfaktn uk iuarpn, idlefdr su mfraiifùk ma masp`dzdlfaktn n m
kar`n, `n lfsln qua dp`fidr ukd prasfùk pdrd mabnrldr`n.
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@d buarzd sa inksfmard ukd idktfmdm vaitnrfd` pnrqua pdrd inlprakmar su abaitnbìsfin, sa raqufara inkniar kn sù`n su ldckftum sfkn tdlefæk, su mfraiifùk y sak-tfmn. D` dp`fidr ukd buarzd snera uk e`nqua qua sa akiuaktrd snera ukd suparbfifahnrfznktd`, sf `d mfraiifùk ma `d buarzd infkifma ink `d suparbfifa y astä mfrfcfmdhdifd `d maraihd, a` nejatn sa lnvarä ak a` lfsln saktfmn. Yf idlefdlns a` sak-tfmn ma `d buarzd hdifd `d fzqufarmd, parn inksarvdkmn su mfraiifùk y ldckftuma` nejatn sa lnvarä hdifd `d fzqufarmd.
Iudkmn snera uk lfsln iuarpn ditúdk vdrfds buarzds, a` nejatn sa lnvarä ak a
saktfmn qua fkmfid a` vaitnr ma `d buarzd rasu`tdkta.
Ya dp`fidk mns buarzds: D y E.
@d buarzd rasu`tdkta sa netfaka d pdrtfr ma `d suld vaitnrfd` ma tnmds `ds buarzdsdp`fidmds.
A` nejatn sa luava ak a`saktfmn ma `d buarzd rasu`tdkta.
D E
Br
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Buarzds laiäkfids
_asn ( ): as `d buarzd qua ajaria `dcrdvamdm snera uk iuarpn7 sa mabfkainln a` prnmuitn ma `d ldsd pnr `dcrdvamdm. Astn sfckfbfid qua a` pasnpuama vdrfdr, sacúk a` vd`nr ma `dbuarzd ma `d crdvamdm.
]aksfùk (]): as d buarzd qua sa ajariapnr lamfn ma ukd iuarmd fkaxtaksfe`a,ma ldsd maspraifde`a ak ra`difùk ink`d ldsd ma` iuarpn `fcdmn d a``d.
Knrld` (K): as `d buarzd parpakmfiu-`dr d `d suparbfifa qua rasu`td inln
radiifùk d ukd buarzd dp`fidmd akasa lfsln puktn, pnr diifùk ma ukiuarpn dpnydmn snera a``d. Iudkmn dsuparbfifa as hnrfznktd`, tfaka `d lfs-ld ldckftum ma` pasn7 sf d suparbfifaas fki`fkdmd, d knrld` infkifma ink dinlpnkakta vartfid` ma` pasn.
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B n t n S f g f p a m f dUnzdlfaktn (Br): as `d buarzd qua axfsta
aktra mns suparbfifas ak inktditn. Axfstakmns i`dsas: a` rnzdlfaktn astätfin qua
sa prasaktd iudkmn ukd buarzd axtarkdtrdtd ma masp`dzdr `ds suparbfifas7 tfaka `dlfsld ldckftum qua `d buarzd axtarkd ysaktfmn inktrdrfn7 a` rnzdlfaktn ifkætfin saprasaktd iudkmn hdy lnvflfaktn ra`dtfvnaktra `ds mns suparbfifas ak inktditn.
Buarzd a`ästfid raiupardmnrd: as d buarzdajarifmd pnr uk rasnrta, lua``a n edkmda`ästfid qua as mabnrldmd (dulaktn nmfslfkuifùk ma su `nkcftum fkfifd`), astämfrfcfmd ak saktfmn inktrdrfn d d mabnrld-ifùk y su ldckftum mapakma ma d vdrfdifùk
ma d nkcftum y d inkstdkta ma a`dstfifmdmG. @d ra`difùk aktra `d buarzd dp`fidmd y `d`nkcftum ma `d mabnrldifùk astä mdmd pnr@d `ay ma Hnng.
Buarzd iaktrìpatd: inrraspnkma d `dinlpnkakta rdmfd` ma `d buarzd rasu`tdktaqua ditúd snera uk iuarpn qua masirfeaukd trdyaitnrfd ifriu`dr.
Buarzd iaktrìbucd: sa inksfmard inln ukdbuarzd ma radiifùk d `d buarzd iaktrìpatd,iudkmn æstd as prnmuifmd pnr `d pdrtìiu`dqua cfrd ink lnvflfaktn ifriu`dr snera a`dcakta qua nidsfnkd a` lnvflfaktn
B n t n S f g f p a m f d
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@ay ma `d fkarifd:
@ns trdedjns masdrrn``dmns pnr Cd`f`an a prnpnrifnkdrnk`d edsa pdrd d prflard ay ma Kawtnk. Cd`f`an majù idar`feralakta nejatns pdrd nesarvdr d diifùk ma d crdvamdm,y pdrd nesarvdr lajnr a` bakùlakn, majù rnmdr asbards pnruk p`dkn fki`fkdmn. @d asbard masiakmìd y uacn dsiakmìd pnr ntrnp`dkn ink mfstfktd fki`fkdifùk d` prflarn, `n iud` matarlfkù qua `d asbardd`idkzded sfalpra `d lfsld d`turd, parn rnmded hnrfznktd`lakta luihnläs `ajns iudkmn a` äkcu`n ma fki`fkdifùk ma` sacukmn p`dkn ard laknr.Inki`uya qua tnmns `ns nejatns tfakmak d ldktakar su astdmn fkfifd` malnvflfaktn. Kawtnk `ncrù ra`difnkdr a` inkiaptn ma fkarifd ink `d ldsd ydsì akukifd su prflard `ay ‐tnmn iuarpn tfakma d parldkaiar ak su astdmnma rapnsn n ma lnvflfaktn raitf`ìkan ukfbnrla ak a` qua sa akiuaktrahdstd iudkmn ukd buarzd axtarkd ditúa snera æ` pdrd idlefdr mfihn astdmn.
D` hde`dr ma fkarifd sa fkvn`uird a` inkiaptn ma psaumnbuarzd, inksfmardmdinln dqua``d buarzd ma `d iud` sa inknia su abaitn bìsfin parn kn su nrfcakkf puktn ma dp`fidifùk
@ayas ma Kawtnk
Fsddi Kawtnk kdifù ak a` dôn 42=5, a` lfsln dôn iudkmn luara Cd`f`an. Idsf tnsus dôns ma iradtfvfmdm `ns iulp`fù ak `d Qkfvarsfmdm ma Idlerfmca, Fkc`dta
_rflarn inln astumfdkta y maspuæs, inln prnbasnr d`tdlakta mfstfkcufmn. Kusa idsù, y su parsnkd`fmdm inktfkúd fktrfcdkmn d `ns astumfnsns hdstd kuastrns mrasarvdmn, d vaias irìptfin, akramdmn ak rfôds parsnkd`as ink `ns arumftns, inkmfù su dtakifùk kn sù`n d `d bìsfid y `ds ldtalätfids, sfkn tdlefæk d `d ra`fcfùk d`quflfd.
@n úkfin ak `n iud` tnmn a` lukmn astä ma diuarmn as ak su erf``dkta td`aktn. prne`alds fktrfcdedk d `ns ifaktìbfins ak `ns tfalpns ma Kawtnk: `ds `ayas ma` l
lfaktn, ds ayas ma ds ùreftds p`dkatdrfds y d ldtalätfid ma d vdrfdifùk inktfkuidktfmdmas, uk idlpn qua sa inknia ditud`lakta inln: iä`iu`n mfbarakifd` a fkta_uama dbfrldrsa ink justfifd, qua Kawtnk bua a` prflarn ak rasn`var ns tras prne`al
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_rfkifpfn bukmdlaktd` ma `d mfkälfid:
Kawtnk astde`aia d ra`difùk mfraitd aktra d buarzd dp`fidmd y d vdrfdifùkak d va`nifmdm (dia`ardifùk), qua axparflaktd ukd ldsd qua parldkaiainkstdkta.
_nr `d dktarfnr ra`difùk, pnmalns matarlfkdr `ds ukfmdmas ma buarzd dsì:
Ak a` sfstald LGY, `d ukfmdm ma buarzd as a` kawtnk (K) y ak a` sfstaldics, as `d mfkd. Ya inksfmard qua 4 K < 4??.??? mfkds.
¾Hd paksdmn d`cukd vaz quæ maea hdiar pdrd qua uk iuarpn inlfakia d lnvarsa>
¾Tuæ sa maea hdiar pdrd qua uk iuarpn maja ma lnvarsa>
A` sfcufakta vfman prasaktd `d flpnrtdkifd qua tfaka `d prflard @ay ma Kawtnk
pdrd d laiäkfid. Astd ay astde`aia `ns ldrins ma rabarakifd fkarifd`as y d bnrld
p`dkd ma` aspdifn7 dmaläs, d trdvæs ma a``d sa puama mabfkfr `d ldsd fkarifd`.
Ak a` sfcufakta ak`dia hdy uk vfman snera `d prflard `ay ma Kawtnk:
Knlera: ]d``ar 9 4rd @ay ma KawtnkMurdifùk: 4=:58 lfkutns
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@ay ma diifùk y radiifùk
Fkfifd`lakta, sa puama dbfrldr qua pdrd tnmd diifùk axfsta ukd radiifùk,y masma a` puktn ma vfstd ma` dkä`fsfs ma buarzd, Kawtnk inki`uyù qua sfsa dp`fid ukd buarzd snera ukd suparbfifa ak uk puktn _ (diifùk), fkla-mfdtdlakta dpdraia ukd buarzd ma `d lfsld ldckftum parn ma saktfmninktrdrfn (radiifùk), d d buarzd dp`fidmdak a` lfsln puktn ma `d suparbfifa. Dastds buarzds sa `as maknlfkd pdras mabuarzd. _nr ajalp`n: uk iuarpn in`nidmnsnera ukd suparbfifa hnrfznktd` ajariapnr diifùk ma su pasn, ukd buarzd snera`d suparbfifa, fklamfdtdlakta d suparbf-ifa ajaria ukd buarzd ma ldckftum fcud`y ak saktfmn npuastn d `d prflard ak a`lfsln puktn ma dp`fidifùk.
Uaspnkmd d `ds sfcufaktas pracuktds:
- ¾Ak a` aspdifn, `ajns ma iud`qufar buakta ma crdvftdifùk, uk
a`abdkta y uk rdtùk takmrìdk a` lfsln pasn> ¾_nr quæ>
Yf masma ukd kdva aspdifd` mfspdrd ukd ed`d ma idôùk hdifd a`
aspdifn sfk brfiifùk, ¾sdeas iuäktd buarzd hdy qua ajariar snera
`d ed`d pdrd qua sa ldktakcd ak lnvflfaktn>
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Flpu`sn:
Inrraspnkma d` prnmuitn ma `d buarzd dp`fidmd snera uk nejatn pnr uktfalpn matarlfkdmn. Ak a` sfstald LGY sa lfma ak K/s y ak a` sfstaldics, sa lfma ak mfkds/s. _nr sar a` prnmuitn ma uk vaitnr pnr uk asid`dr,a` rasu`tdmn as uk vaitnr.
Idktfmdm ma lnvflfaktn `fkad`:
]nmn iuarpn qua sa akiuaktrd ak lnvflfaktn pnsaa ukd idktfmdm malnvflfaktn qua aqufvd`a d` prnmuitn ma su ldsd pnr `d va`nifmdm.
@ds ukfmdmas ak a` sfstald LGY snk `ns kawtnks, y ak a` sfstald ics, `dsmfkds.
Yf quaralns matarlfkdr `d idktfmdm ma lnvflfaktn ma uk sfstaldma pdrtìiu`ds, maealns akinktrdr `d suld vaitnrfd` ma `d idktfmdm malnvflfaktn ma idmd pdrtìiu`d ak cakard`.
Knlera: ]d``ar 9: 5md @ay ma KawtnkMurdifùk: 48:=5 lfkutns
Asta vfman fktaktd raspnkmar d `d pracuktd: ¾quæ
inksaiuakifds tfaka d fktardiifùk ink ns nejatns
bìsfins>
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Lùmu`n ma laidkfzdmn edsdmn ak lntnras `fkad-`as masdrrn``dmn ak Fmagn, ink va`nifmdmas ma 4??
l/lfk y dia`ardifnkas ma 4? l/s5.
B n t n h t t p : / / w w w . f k t a r a l p r a s d s . k a t
Ma fcud` bnrld, `d buarzd qua ajaria a` ldrtf``n snera `d puktf``d, y `d qua
ajaria d puktf``d snera a` ldrtf``n, snk buarzds ma diifùk-radiifùk. Idmd ukd
ma astds buarzds ditúd snera mfbaraktas iuarpns: ukd snera d puktf``d y d ntrd
snera a` ldrtf``n7 iud`qufard ma æstds puama sar `d diifùk y ntrd `d radiifùk.
Uaspnkmd ds sfcufaktas sftudifnkas ma diuarmn d n qua nesarvd mfdrfdlakta:
• Axp`fqua n qua suiama iudkmn mns parsnkds lnktdmds snera pdtfkas
sa alpujdk `d ukd d `d ntrd.
• Yf astä snera ukd pfstd ma hfa`n y pratakma dkzdr uk nejatn, ¾quæ iraa
qua suiamarä>
Knlera: ]d``ar 9: 9ard @ay ma KawtnkMurdifùk: 8:=1 lfkutnsAk æsta vfman sa md raspuastd d `d pracuktd: ¾Iùln fktarditúdk
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_räitfid ma `denrdtnrfn
Ldtarfd`as
_dpa` pdrd p`acdmn, ifktd lætrfid,tfzd n ldridmnr, p`dkn, e`nquama ldmard, pdpa` `fjd, pn`ad bfjd,4,1 l ma pftd, ldsds ma 4?? c,1? c, 5? c y 4?c, cdkihns i`fpsldrfpnsd, cdkihns i`fps inrrfaktasy trdkspnrtdmnr.
_rniamflfaktn
4. Nrcdkfzd uk aqufpn ma trdedjn ink ifkin astumfdktas.
5. Idmd ukn, inkstrufr ukd rdkd ma pdpa` ak nrfcdlf.
9. Ya`aiifnkdr `d qua sd`ta lajnr.
=. Mfeujdr uk p`dkn idrtasfdkn snera a` pfsn.
1. Qefidr d rdkd ak a` nrfcak y mdr`a mfaz flpu`sns, inksarvdkmn sfal-pra `d mfraiifùk qua fkmfqua `d ideazd ma `d rdkd.
2. Uacfstrdr `ns puktns (pdrajds nrmakdmds), ma `d pnsfifùk pdrd idmd
flpu`sn.
3. A`denrdr ukd cräbfid d asid`d 4:1? ak pdpa` lf`flatrdmn, y matarlfkdr
`d `nkcftum ma idmd vaitnr.
8. Akinktrdr `d trdyaitnrfd (suld ma ldckftumas ma `ns vaitnras).
1
F l d c a k l n m f b f i d m d m a w w w . t d r f k
c d . k a t .
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6. Akinktrdr a` vaitnr masp`dzdlfaktn.4?. Mfspnkar a` p`dkn, a` trdkspnrtdmnr, `d pn`ad bfjd y `d iuarmd, ma td`
bnrld qua sa puamd vdrfdr a` äkcu`n ma fki`fkdifùk (bfcurd 4), ink
bdif`fmdm.
44. _acdr a` pdpa` `fjd ak ukn ma `ns `dmns ma` e`nqua ma ldmard.
45. Matarlfkdr `d ldsd ak gc y `d buarzd ak K, kaiasdrfds pdrd qua a`e`nqua sa mas`fia snera a` p`dkn hnrfznktd` (fkfifd`lakta pdrd ldmard-ldmard y `uacn pdrd `fjd-ldmard). Matarlfkdr ink dktarfnrfmdm `dldsd ma `ns mfbaraktas a`alaktns utf`fzdmns.
_`dkn fki`fkdmn ]rdkspnrtdmnr_n`ad
@fjd
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49. In`nidr a` e`nqua ma ldmard snera uk axtraln ma` p`dkn y `avdktdr`aktdlakta a` lfsln axtraln, hdstd ncrdr qua a` e`nqua inlfakia dmas`fzdrsa snera d suparbfifa. Matarlfkdr a` vd`nr ma` äkcu`n (prflarnldmard - ldmard y `uacn ldmard `fjd).
Dkä`fsfs ma rasu`tdmns
D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn astumfdmn
Matarlfkdr d inlpnkakta vartfid` ma` pasn, d inlpnkakta hnrfznktd` ma`pasn y d buarzd ma rnzdlfaktn astätfin, supnkfakmn qua a` inabfifakta marnzdlfaktn as ± < ?,9.
Buarzd marnzdlfaktn
Inlpnkaktavartfid` ma` pasn
Inlpnkaktahnrfznktd` ma` pasn Knrld` Äkcu`n
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=
Yn`uifùk:
Yn`uifùk:
Ajarififns ma dp`fidifùk
4. Matarlfkdr cräbfidlakta a` vaitnr rasu`tdkta d pdrtfr ma `ns sfcufavaitnras:
5. Qk vaitnr tfaka ukd ldckftum ma 8 il y prasaktd ukd fki`fkdifùk inkpaitn ma `d hnrfznktd` ma 9?º. Matarlfkdr `ds inlpnkaktas raitdkcu`d
D x
< D . insδ < 8 ins 9?N < 8 x ?,822 < 2,658
D y
< D . sakδ < 8 sak 9?N < 8 x ?,1 < =
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9. Ak a` sfcufakta sfstald, matarlfkdr sf `d ldsd l4 sa luava, y sf as dsì, ma-tarlfkdr `d dia`ardifùk: l4 < 1 Gc7 l5 < = Gc. ± < ?,9.
Ynera l4 ditúdk = buarzds: a` pasn,`d knrld`, `d taksfùk maefmn d` pasnma l5 y a` rnzdlfaktn d` fktarditudrink `d suparbfifa.
Yn`uifùk:
@d knrld` y a` pasn tfakak a` lfsln vd`nr pnrqua astäk d`fkadmds pnrakinktrdrsa l4 snera ukd suparbfifa hnrfznktd`. _nr `n tdktn, `d buarzd
rasu`tdkta aktra `ds mns as fcud` d iarn (?).
Matarlfkalns dhnrd, d buarzd rasu`tdkta aktra d taksfùk y a` rnzdlfaktn:l4 sù`n sa luava, sf `d prflard as ldynr qua `d sacukmd.
@d suldtnrfd ma `ds buarzds hnrfznktd`as as:
l4
l5
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Yn`uifùk:
D pdrtfr ma` prfkifpfn bukmdlaktd` ma d mfkälfid (sacukmd ay ma Kawtnk),pnmalns matarlfkdr a` vd`nr ma `d dia`ardifùk:
=. Qk ifi`fstd sa masp`dzd snera ukd idrratard raitd ink ukd va`nifmdm maGl/h. Yf su ldsd as ma 15 Gc y `d ma `d efifi`atd as ma 4? Gc, matarla` vd`nr ma `d idktfmdm ma lnvflfaktn.
`d ldsd tntd` ma` sfstald aqufvd`a d `d suld ma `d ldsd ma` ifi`fstd y `d ldsdma `d efifi`atd, y `d va`nifmdm `d axprasdlns ak l/s:
Dp`fidlns `d `ay ma Hnnga:
1. Matarlfkdr `d inkstdkta ma a`dstfifmdm ma uk rasnrta qua raqufara buarzd ma 9 K pdrd dulaktdr su `nkcftum ak ?,1 l.
Yn`uifùk:
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4. Ak `ds sfcufaktas cräbfids qua raprasaktdk sftudifnkas intfmfdkds,matarlfkdr ds buarzds qua ditúdk snera idmd iuarpn y raprasaktdr`dsink vaitnras snera idmd mfeujn.
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9. Matarlfkdr ds inlpnkaktas raitdkcu`dras ma ns sfcufaktas vaitnras
• Ldckftum fcud` d 9 il fki`fkdifùk ma 9?º.
• Ldckftum fcud` d 1 il fki`fkdifùk ma =1º.
• Ldckftum fcud` d 8 il fki`fkdifùk ma 2?º.
5. Matarlfkdr ak bnrld cräbfid y utf`fzdkmn a` lætnmn qua inksfmarainkvakfakta, a` vaitnr rasu`tdkta ak idmd idsn:
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=. Ak ns sfcufaktas sfstalds ma iuarpns fcdmns, matarlfkdr d buarzdrasu`tdkta snera d ldsd 4 y akinktrdr su dia`ardifùk ak idmd idsn:
l4 < 9 Gc7 l5 < 1 Gc7 l9 < 8 Gc7 ± < ?,9
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1. Qk rasnrta subra ukd vdrfdifùk ma = il ak su `nkcftum, d` dp`fidr`aukd buarzd ma ?,9 K. Matarlfkdr a` vd`nr ma `d inkstdkta ma a`ds-tfifmdm.
2. ¾Tuæ buarzd maea hdiarsa snera uk rasnrta pdrd vdrfdr su nkcftumak 1 il, sf su inkstdkta ma a`dstfifmdm as ma 26 K/l>
3. ¾Iuä` as d inkstdkta ma a`dstfifmdm rasu`tdkta d` in`nidr ns rasnrtasma `ns ajarififns 1 y 2 ak sarfa>
Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdrdsn`uifnkdr sftudifnkas bìsfids rad`as ma `d vfmd mfdrfd.
Inki`usfnkas
Avd`udifùk
¾Tuæ dprakmfù ink `d ditfvfmdm>
Rd`nrdr a` trdedjn rad`fzdmn, d prasaktdifùk y masdrrn``n ma d cuìd, d dp`fid-ef`fmdm ma d aiturd, y ma sar pnsfe`a, prnpnkar lnmfbfidifnkas pdrd lajnrd`d netakifùk ma `ns `ncrns prnpuastns.
@ns sfcufaktas ak`dias `a dyumdräk d rabnrzdr `d talätfid vfstd y d p`dktadr sakif``ds
axparfakifds ma `denrdtnrfn.
_UFLAUD @AV MA KAS]NK:
http://axparflaktnsidsarns.kat/5?4?/4?/axparflaktn-prflard-`ay-ma-kawtnk/
http://axparflaktnsidsarns.kat/5?4?/4?/fkarifd-y-`ayas-ma-kawtnk/
]AUIAUD @AV MA KAS]NK:
http://axparflaktnsidsarns kat/5?4?/4?/axparflaktns-tariard-`ay-ma-kawtnk/
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Dutnavd`udifùk
A` sfcufakta asquald ma avd`udifùk rab`ajd `ns dspaitns d vd`nrdr ma sutrdedjn y, snera tnmn, ma sus dprakmfzdjas murdkta astd ukfmd. @d id`fbfid-ifùk lìkfld sarä ma 1, y d läxfld ma 5? puktns, pnr n qua d puktudifùklamfd inksfmardmd kaiasdrfd pdrd dprnedr ds ditfvfmdmas sarä, ak asta idsnma 4? puktns.
Asidsn
dprakmfzdja4
Dprakmfzdja
lamfn5
Euak dprakmf-
zdja9
Axia`akifd ak
a` dprakmfzdja=
Kntdifùkkulærfid
Inlprak-sfùk ma `nsinktakfmns
B d ` t d m ainlprak -sfùk ma `nsinktakfmns.
Asidsd inlp-raksfùk ma `dsfkmfidifnkasmdmds pdrd `drad`fzdifùk.
I n l p r a k m aeäsfidlakta`ds fkmfidifnkasmdmds pdrd `drad`fzdifùk.
Euakd inlp-raksfùk ma `dsfkmfidifnkasmdmds pdrd `drad`fzdifùk.
Eúsquamdma `d fkbnr-ldi fùk yutf`fzdifùkma `ns ra-iursns akFktarkat
Kn hd utf-` fzdmn mabnrld sdt-f s b d i tn r f d`ns raiursnsr ai nl ak -mdmns.
Ak nidsfnkaskn hd utf`fzdmnma bnrld sdt-fsbditnrfd `nsraiursns rain-lakmdmns
Hd utf`fzdmn nsraiursns rain-lakmdmns mabnrld sdtfsbdi-tnrfd.
Hd utf`fzdmn nsraiursns rain-lakmdmns mabnrld sdtfsbdi-tnrfd.
Hd alp`admnntrns raiursnskn rainlak-mdmns ma bnrldfkjustfbfidmd
Hd alp`admnntrns raiursnskn rainlak-mdmns ma bnrldfkjustfbfidmd.
Ya hd `flftdmnd alp`adr `nsraiursns rain-lakmdmns pdrd`d rad`fzdifùkma `ds ditfvf-mdmas.
Dmaiudifùkma `ds tdradsd` prniasnraquarfmn
@ds tdradskn sa ra-d ` fzdk td `y inln saprnpnkak.
Ak pnids nid-sfnkas rad`fzdk`ds tdrads td` yinln sa prn-pnkak.
Idsf sfalpra`ds tdrads sadjustdk d` prn-iasn prnpuas-tn.
@d rad`fzdifùkma `ds tdradssa djustdk d `nprnpuastn.
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4Aquf`ferfn ma `ns iuarpns
Qkfmdm 9. Astätfid Yasfùk
1
Yua`n: murdkta uk ajarififn ma sua`n, tnmda` ärad ma` dpdrdtn maea sar iuefartd pnr a`cflkdstd. A` ajarififn inkstd prfkifpd`laktama tras d ifkin mfdcnkd`as (sarfas dirneätf-ids rad`fzdmds d `n `drcn ma ukd mfdcnkd`ma` sua`n), ``avdmds d iden ak mfbaraktasmfraiifnkas. @ns a`alaktns ma trdksfifùk(lnvflfaktns cflkästfins qua sa rad`fzdk
aktra `ds mfdcnkd`as), maeak sar ajaiutdmnsink a` rftln y d drlnkìd dprnpfdmns. A` äradma` dpdrdtn inlprakma 45 pnr 45 latrns.
Ided``n ink drins: a` cflkdstd maea iuerfrink su ajarififn `ds tras ärads ma` pntrn, a`lamfn y dlens axtralns, lfaktrds rad`fzdinktfkuns lnvflfaktns ifriu`dras fktarrul-pfmns sù`n pnr ds raquarfmds tfjards. @ds úkf-ids pdrtas ma` iuarpn qua puamak tnidr a`dpdrdtn snk `ds ldkns. A` ided``n ink drinslfma 441 il ma d`tn y a` ided``n ak sì, lfma91 il ma dkihn pnr 42? il ma `drcn. @dscrupds ma` ided``n maeak astdr sapdrdmds ma=? d =1 il.
Cflkdsfd2
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Dkf``ds: a` ajarififn ma dkf``ds maeafki`ufr d` lakns mns pdrdmds maldkns: ukd, ajaiutdmd pnr lamfnma `d buarzd y `d ntrd, d trdvæs ma`
ed`dkian. D` lakns uk a`alaktnma buarzd maea sar ``avdmn d idenmurdkta mns sacukmns. Ajalp`ns maastns a`alaktns ma buarzd snk a`Irfstn, d iruz fkvartfmd n d p`dkihd.
Yd`tn: idmd sd`tn astä i`dsfbfidmn aka` iùmfcn ma puktudifùk, qua ntnrcd
`d kntd sacúk a` a`alaktn qua sa``avd d iden murdkta a` ajarififn, asmaifr, d idmd tfpn ma sd`tn. A` cflkdstd tfaka qua supardr ukdd`turd y ukd mfstdkifd lìkflns akidmd sd`tn. A` dtarrfzdja maea sar
bfrla, sfk kfkcúk pdsn ma snerd yak `ìkad ink a` pntrn.
Edrrds pdrd`a`ds: uk ajarififn mapdrd`a`ds inksfsta eäsfidlakta aka`alaktns ma ed`dkian y vua`n.
Inlpnkaktas ma buarzd puamak saralp`admns ak `d rutfkd, dukqua knsnk kaiasdrfns.
Ya axfca qua a` cflkdstd ajaiuta mnsa`alaktns ma ed`dkian: ukn dpnyd-mn y a` ntrn in`cdkmn ma `ds edrrds.
@ds edrrds pdrd`a`ds sa sftúdk d 461il ma d`tn. Idmd edrrd lfma 41? ilma drcn y d sapdrdifùk aktra dledspuama sar djustdmd ma =5 d 15 il.
Edrrd bfjd: a` ajarififn ma edrrd bfjdinksfsta axi`usfvdlakta ma a`alak-tns ma ed`dkian sfk pdrdmds. Ya `aaxfca d` cflkdstd qua ajaiuta pnr`n lakns uk lnvflfaktn ak a` iud`sua`ta `d edrrd y `uacn sa vua`vd d
dcdrrdr d a``d (ukd ‘‖sua`td‖‖), y tdl-efæk maea `avdr d iden uk ed`dkian(swfkc), mnrsd` (ink `d aspd`md maidrd d `d edrrd). @d edrrd bfjd sa sftúdd 531 il ma d`tn. Lfma 5=? il ma`drcn y tfaka 5,8 il ma mfälatrn.
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Uaspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds¾Ya hd pracuktdmn iùln as qua puamaldktakarsa ma pfa> ¾V iùln as qua tn-mns ns iuarpns qua astäk d su d`ramamnrsa ldktfakak ak aquf`ferfn> ¾Iuä` as suaxp`fidifùk d astns bakùlakns>¾Tuæ tfpn ma aquf`ferfn utf`fzdk ns cfl-kdstds pdrd kn idarsa> ¾Iraa ustam quaasta mapnrta astä `fcdmn d `d bìsfid> ¾Maquæ ldkard>
_ùkcdsa ma pfa ink `ns erdzns defartnsy matarlfka mnkma astä su iaktrn maaquf`ferfn. Axp`fqua su raspuastd.
Qefqua a` iaktrn ma crdvamdm ma iudtrnnejatns qua ustam asinjd (pnr ajalp`n:ukd brutd, uk `fern, uk zdpdtn, ati.).
Uavfsa a` sfcufakta `denrdtnrfn vfrtud`:
http://www.xtai.idt/~nidsa``d/dpp`ats/p`dfki`/dpp`atsn`5.htl,
Bukmdlaktn taùrfin
Aquf`ferfn ma `ns iuarpns
Qk iuarpn sa akiuaktrd ak aquf`ferfn, iudkmn `d suldtnrfd vaitnrfd` ma tnmdbuarzds qua ditúdk snera æ`, as fcud` d iarn, as maifr, `d buarzd rasu`tdkta as fcuiarn. _drd qua astn sa iulp`d maeak axfstfr mns inkmfifnkas: `d prflard, qua ak aquf`ferfn trds`difnkd`7 y d sacukmd, qua astæ ak aquf`ferfn rntdifnkd`. Qk iuapuama astdr ak aquf`ferfn trds`difnkd` sfk takar uk aquf`ferfn rntdifnkd` y vfiava
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Aquf`ferfn trds`difnkd`: uk iuarpn astä ak aquf`ferfn trds`difnkd` iudkmn d suldtnrfdma tnmds ds buarzds inkiurraktas (buarzds qua ditúdk snera uk lfsln puktn), sneraæ`, as fcud` d iarn.
Aquf`ferfn rntdifnkd`: uk iuarpn astä ak aquf`ferfn rntdifnkd` iudkmn `d suld ma`ns tnrquas n lnlaktns ma tnrsfùk qua ditúdk snera æ`, as fcud` d iarn, as maifr,iudkmn mns n läs buarzds pdrd`a`ds (kn inkiurraktas), aktra sì, ditúdk snera ukiuarpn y puamak hdiar qua a` iuarpn cfra n rnta snera uk aja y prnmuzid uk tnrquan lnlaktn ma tnrsfùk snera a` lfsln.
Ya inksfmard qua a` tnrqua n lnlaktn ma tnrsfùk ma ukd buarzd, as a` prnmuitn ma`d fktaksfmdm ma `d buarzd pnr `d mfstdkifd parpakmfiu`dr masma a` puktn n aja marntdifùk hdstd su `ìkad ma diifùk.
@d suld vaitnrfd` ma ds buarzds sa ncrd, akinktrdkmn fkfifd`lakta ds inlpnkaktasraitdkcu`dras ‐x“ y ‐y“ pdrd `uacn, rad`fzdr `d suldtnrfd inrraspnkmfakta y d` bfkd`,hd``dr a` vaitnr rasu`tdkta.
(tanrald ma _ftäcnrds )
As rainlakmde`a a`denrdr `d cräbfid ma `ns vaitnras ditudktas, ink a` äkfln mainlprakmar ink ldynr bdif`fmdm a` sfstald.
I`dsas ma aquf`ferfn
Ak iudktn d` aquf`ferfn trds`difnkd`, axfstak tras i`dsas ma aquf`ferfn qua sa inksf-mardk pdrd mns inkmfifnkas mfbaraktas ak `ds iud`as sa puama akinktrdr uk iuarpn
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Iuarpn suspakmfmn: `d inkmfifùk pdrd qua uk iuarpn suspakmfmn astæaquf`ferfn as qua `d vartfid` qua pdsd pnr a` puktn ma suspaksfùk maea pdsdr pniaktrn ma crdvamdm ma` iuarpn.
Iaktrn macrdvamdm _uktn ma
suspaksfùk
Iaktrn macrdvamdm
_uktn masuspaksfùk
_uktn masuspaksfùk
Iaktrnma crdvamdm
• Aquf`ferfn astde`a: sa prasak
a` puktn ma suspaksfùk astä akifld ma` iaktrn ma crdvamYa idrditarfzd pnrqua a` ned` sar sapdrdmn ma su pnsfifùkaquf`ferfn, d` majdr ma ditudbuarzd, vua`va d su pnsfifùk fkf
• Aquf`ferfn fkastde`a: sa prasa
sf a` puktn ma suspaksfùk astämaedjn ma` iaktrn ma crdvamdmidrditarfzd pnrqua a` nejatn dsapdrdmn ma su pnsfifùk ma a`ferfn, d` majdr ma ditudr d buakn vua`va d su pnsfifùk fkfifd
•
Aquf`ferfn Fkmfbarakta: sa prastd sf a` puktn ma suspaksfùk iifma ink a` iaktrn ma crdvamdmidrditarfzd pnrqua a` nejatn dsapdrdmn ma su pnsfifùk ma a`ferfn, d` majdr ma ditudr d buadmnptd ukd pnsfifùk sflf`dr dpnsfifùk fkfifd`.
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Iuarpns dpnydmns: `d inkmfifùk pdrd qua uk iuarpn dpnydmn astæ ak aquf`ferfnas qua `d vartfid` qua pdsd pnr su iaktrn ma crdvamdm idfcd maktrn ma `d edsa masustaktdifùk n sad `d pdrta snera `d iud` masidksd a` iuarpn.
Iaktrn ma crdvamdm ma uk iuarpn
As a` puktn mnkma sa supnka qua ditúd `d buarzd ma crdvamdm. Ak uk nejatn rìcfmna` iaktrn ma crdvamdm as uk puktn bfjn ink raspaitn ma` nejatn, dukqua kn astækaiasdrfdlakta `nid`fzdmn ak a` lfsln nejatn.
Läqufkds sflp`as
Ynk dqua``ds läqufkds qua bdif`ftdk `d rad`fzdifùk ma uk trdedjn pnrqua parlftak
• Aquf`ferfn astde`a: iudkmn d` sapdrdra` iuarpn ma su pnsfifùk ma aquf`ferfn,vua`va d raiupardr`d pnr sì lfsln.
• Aquf`ferfn fkastde`a: iudkmn d` sapdrdra` iuarpn ma su pnsfifùk ma aquf`ferfn, `dpfarma mabfkftfvdlakta.
• Aquf`ferfn fkmfbarakta: iudkmn d` sapdrdr
a` iuarpn ma su pnsfifùk ma aquf`ferfn,dmqufara iud`qufar pnsfifùk y sfcua ink-sarvdkmn `d qua takìd dktas.
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_d`dkid: as ukd edrrd bfjd rasfstakta, qua puama cfrdr d`ramamnr ma uk puktn ]faka tras a`alaktns: d pntakifd (_), d rasfstakifd (U), y a` bu`irn n puktn ma dp( ). Yacúk `d uefidifùk ma` bu`irn, `ds pd`dkids sa puamak i`dsfbfidr ak tras cæka
• _d`dkid ma prflarcækarn: sa idrdi-tarfzd pnrqua a`bu`irn sa akiuaktrdaktra `d pntakifdy `d rasfstakifd.
Ajalp`n: `ds tfja-rds, `ns d`fidtas, `dspfkzds, ati.
• _d`dkid ma sacukmncækarn: sa idrditarfzdpnrqua `d rasfstakifdastä aktra a` puktn madpnyn y `d pntakifd.Ajalp`n: `d idrratf``d,a` mastdpdmnr.
• _d`dkid ma tariar cækarn: sa idrditarfzd pnrqua `dpntakifd astä aktra d rasfs-takifd y a` puktn ma dpnyn.Ajalp`n: a` mapf`dmnr, `dspfkzds pdrd a` pdk n pdrda` hfa`n.
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_n`ads: inkstdk ma ukd ruamd didkd`dmd qua puama cfrdr snera su aja, mfslfku-yakmn d` läxfln a` rnzdlfaktn, y idlefdkmn `d mfraiifùk ma `d buarzd (taksfùk),qua sa dp`fid snera d iuarmd qua pdsd pnr su idkd`. Axfstak `ds sfcufaktas i`dsas:
• _n`ad bfjd: sa idrditarfzd pnrqua suaja sa akiuaktrd bfjn d `d edrrd qua `duka d` snpnrta pdrd ldktakar`d sus-pakmfmd. Yu bukifùk as sflp`alaktaidlefdr d mfraiifùk y kn d ldckftumma `d buarzd.
Ajalp`n: sf hdy ukd pn`ad bfjd y k lùvf`as, `d cdkdkifd laiäkfid qua sa netfakaastä mdmd pnr 7 sf hdy vdrfds bfjds y vdrfds lùvf`as `d cdkdkifd laiäkfid as
• _n`ad lùvf`: su aja sfrva inln snpnrtapdrd `d rasfstakifd y sa snstfaka snera`d iuarmd snera `d iud` sa dp`fid `dbuarzd, `n iud` hdia qua `d buarzd sad`d lftdm ma `d rasfstakifd aqufvd`aktad ukd cdkdkifd laiäkfid.
• _n`fpdstns: as uk sfstald ma pn`adslùvf`as ink ukd n vdrfds pn`ads bfjds
Yacúk `d inkbfcurdifùk qua sa `a mæsa netfaka ldynr n laknr cdkdkifdlaiäkfid.
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_rniamflfaktn
4. Nrcdkfzdr a` aqufpn ma trdedjn y inkstrufr ak idrtu`fkd ds bfcurds prnpuastds.
5. Matarlfkdr a` iaktrn ma crdvamdm y a` iaktrn ma ldsd ma idmd bfcurd
Inksu`tdr snera a` lætnmn dprnpfdmn pdrd `ncrdr`n.
9. Qefidr tras puktns mfbaraktas ak idmd bfcurd, akifld, snera y maedjnma` iaktrn ma crdvamdm.
=. Yuspakmar ink a` hf`n y `d dcujd, `ds bfcurds ak bnrld inksaiutfvd maidmd ukn ma `ns puktns saôd`dmns, y matarlfkdr `d i`dsa ma aquf`ferfnak idmd idsn.
_räitfid ma `denrdtnrfn
Ldtarfd`as
]rfäkcu`n fsùsia`as, trfäkcu`n asid`akn, iudmrdmn, raitäkcu`npaktäcnkn racu`dr, paktäcnkn frracu`dr, haxäcnkn racu`drhaxäcnkn frracu`dr, iìriu`n, dcujd, hf`n, inkn mfkdlùlatrnldsds mfvarsds, 5 l ma pftd (iuarmd), trdkspnrtdmnr, 9 pn`adsbfjds y 9 pn`ads lùvf`as.
2
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1. Inkstrufr uk inkn ak idrtu`fkd y in`nidr`n ak `ds tras pnsfifnkas pnsf-e`as pdrd matarlfkdr `ds tras i`dsas ma aquf`ferfn. Ya puama prnpnkary inkstrufr ntrd bfcurd pdrd inksacufr a` lfsln abaitn dktarfnr.
2. Ak a` iuarpn huldkn, sa akiuaktrdk `ds tras i`dsas ma pd`dkids, ¾akmùkma sa akiuaktrd idmd ukd> Uad`fzdr a` mfeujn inrraspnkmfakta afkmfidr ak idmd idsn, `d uefidifùk ma `ns tras a`alaktns inkstftutfvns:rasfstakifd, pntakifd y puktn ma dpnyn.
3. Ink a` aqufpn ma trdedjn, raukfr `d ldynr idktfmdm ma nejatns quatakcdk dp`fidifùk ma pd`dkids.
8. I`dsfbfidr`ns ma diuarmn ink su cækarn (4º, 5º, 9º).
6. Ak ukd idrta`ard, rad`fzdr `ns mfeujns inrraspnkmfaktas, fkmfidkmn `duefidifùk ma `d pntakifd, `d rasfstakifd y a` puktn ma dpnyn ak idmdidsn.
4?. Hdiar ukd axp`fidifùk d` rastn ma` iursn ink malnstrdifùk präitfid.
44. Qtf`fzdkmn mfbaraktas lnktdjas a fkfifdkmn ink d pn`ad bfjd, matarlfkdrak bnrld präitfid, `d vaktdjd laiäkfid ma idmd ukn. A`denrdr cräbfidsy malnstrdr`d ak bnrld kulærfid.
45. A`denrdr `ds cräbfids ma idmd lnktdja.
Dkä`fsfs ma rasu`tdmns
D pdrtfr ma `d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y `nsprniasns rad`fzdmns, matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktnnesarvdmn
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1
=1º?2?º
y
B4
B5
x
_rne`alds ma dp`fidifùk
4. Ya raqufara ldktakar suspakmfmd ukd ldsd ma 1? gc pnr lamfn ma mns imds qua bnrldk ink `d hnrfznktd`, äkcu`ns ma 2?º y =1º. ¾Iuä` as a` vd`n`d buarzd qua sa maea ajariar ak a` axtraln ma idmd iuarmd>
Yn`uifùk: snera a` p`dkn idrtasfdkn sa raprasaktd a` sfstald ma buarzds,mnkma ? inrraspnkma d` puktn (?,?)
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_drd qua a` iuarpn astæ ak aquf`ferfn, `d suldtnrfd ma `ds buarzdsmaea sar ?. ]akfakmn ak iuaktd `ds inlpnkaktas raitdkcu`dras y `dnrfaktdifùk ma idmd ukd, pnmalns p`dktadr mns aiudifnkas:
Ya maspajd ak `d prflard aiudifùk y sa raalp`dzd ak `d sacukmd:
Uasn`vfakmn d aiudifùk pdrd sa matarlfkd qua < 918,34 K . Inkasta vd`nr, pnmalns matarlfkdr : < 512,554 K
Yn`uifùk: pdrd `avdktdr`d idrratf``d y pnkar`dak lnvflfaktn, a` sfs-tald maea quamdr akaquf`ferfn. _nr `n tdktn,`d suld ma `ns tnrquasmaea sar fcud` d iarn.
_
U
5. Iuä` as `d buarzd kaiasdrfd pdrd pnmar trdkspnrtdr snera ukd idrratf``d, ukpasn ma 68 K. @d mfstdkifd ma` aja ma `d ruamd (bu`irn), d `d buarzd ma` pasn asma 1? il7 y ma` bu`irn d` puktn ma dp`fidifùk ma `d pntakifd, as ma 4,9 l.
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Fcud`dkmn `ns mns tnrquas y maspajdkmn _, sa puama matarlfkdr suvd`nr:
9. _drd suefr hdstd ifartd d`turd, ukd ldsd ma 91 Gc, sa utf`fzd uk pn`fpdstnmns pn`ads lùvf`as y ukd bfjd. ¾Iuä` sarä d buarzd kaiasdrfd pdrd suefr d l
Yn`uifùk: maefmn d `d ldsd ma 91 Gc, `d rasfstakifd aqufvd`a d su pasn:
U < 91Gc . 6,8 l/ sac 5 < 9=9 Kaw.
Ink mns pn`ads lùvf`as y ukd bfjd, d vaktdjd laiäkfid qua sa netfaka as:
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4. Ynera uk iuarpn, sa dp`fidk trasbuarzds ma fcud` ldckftum B4 <B5 < B9 < 5 K, inln sa fkmfidak `d bfcurd. Matarlfkdr cräbfidy kulærfidlakta, a` vd`nr ma `dbuarzd rasu`tdkta y sf as mfbarakta
ma iarn, astde`aiar d dia`ardifùkqua axparflaktd a` iuarpn.
5. Matarlfkdr d buarzd kaiasdrfd pdrd ldktakar a` sfstald ak aquf`ferfn,sf `d ldsd as ma 5? Gc.
B2?º
9. _drd avdktdr uk pasn ma 48 K, sa iuaktd ink ukd edrrd ma hfarrn ma 4,1
l ma nkcftum dpnydmd snera ukd pfamrd. Yf d mfstdkifd aktra a` nejatn
y `d pfamrd as ma 1? il, ¾Iuä` sarä `d buarzd kaiasdrfd pdrd lnvar`n.
=. Qk mastdpdmnr ma akvdsa tfaka ukd `nkcftum ma 45 il7 `d tdpd ma
`d cdsansd tfaka uk rdmfn ma 4,5 il y npnka ukd rasfstakifd ma ?,9
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1. Iuä` as d buarzd kaiasdrfd pdrd suefr ukd ldsd ma =1 Gc, qua utf`fzd:
Uaprasaktdr ak bnrld cräbfid, a` lnktdja ak idmd ukn ma ns idsns dktarfnr
• Qkd pn`ad bfjd
• Qkd pn`ad lùvf`
• Qkd pn`ad bfjd y ukd lùvf`as
• Qkd pn`ad bfjd y mns lùvf`as
• Qkd pn`ad bfjd y tras lùvf`as
Dutnavd`udifùk
Inlp`ata `d sfcufakta tde`d pdrd vd`nrdr `ds ditfvfmdmas prnpuastds y rad`fzdmds hdstd a` lnlaktn. _drd a``n, ldrqua ink ukd X a` pnriaktdja quastfla dmaiudmn.
Idtacnrìd _racuktd ?% 5?% =?% 2?% 8?% 4??%
Iulp`flfaktn y
raspnksdef`fmdm
¾Iulp`fù ink ds aiturds
dsfckdmds, ds ditfvfmdmas
prnpuastds ak astd ukf-
mdm y `ns trdedjns fkmf-
vfmud`as n pnr aqufpn>
Iradtfvfmdm yid`fmdm
¾Dpnrtù fmads> ¾Astdsbuarnk sfckfbfidtfvds>
¾Uad`fzù sfk arrnr d`cukn`ds tdrads y/n `ns trdedjnsdsfckdmns>
Dprakmfzdja ydpnrtdifùk mainkniflfaktns
¾Tuæ tdktn dprakmfù yquæ tdktns inkniflfak-tns dpnrtù ak `ds i`dsas,ak `ds tdrads y/n `ns trd-edjns rad`fzdmns>
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Akarcìd kui`adr3
Akarcìd kui`adr: as dqua``dqua sa `feard inln rasu`td-mn ma ukd radiifùk kui`adr. Ya puamanetakar pnr a` prniasn ma Bfsfùk Kui`adr(mfvfsfùk ma kúi`ans dtùlfins pasdmns) nefak pnr Busfùk Kui`adr (ukfùk ma kúi`ansdtùlfins luy `fvfdkns). Ak `ds radiifnkaskui`adras sa `feard ukd crdk idktfmdm ma
akarcìd maefmn d qua pdrta ma `d ldsd ma`ds pdrtìiu`ds fkvn`uirdmds ak a` prniasn,sa trdksbnrld mfraitdlakta ak akarcìd. @ndktarfnr sa puama axp`fidr edsäkmnsa ak`d ra`difùk Ldsd-Akarcìd prnmuitn ma `dcakfd`fmdm ma` crdk bìsfin D`eart Afkstafk.
Ink ra`difùk d d feardifùk ma akarcìd, ukd radiifùk kui`adr as uk lf``dr mavaias läs akarcætfid qua ukd radiifùk quìlfid. _nr ajalp`n: `d cakardmdpnr `d inleustfùk ma` inleustfe`a bùsf` ma` latdkn.
Bfsfùk kui`adr: as ukd radiifùk kui`adr qua tfaka `ucdr pnr `d rnturd ma ukkúi`an pasdmn d` sar enledrmadmn pnr kautrnkas ma ifartd va`nifmdm. Drdìz ma astd mfvfsfùk a` kúi`an sa sapdrd ak mns brdclaktns dinlpdôdmn maukd alfsfùk ma rdmfdifùk, `feardifùk ma 5 ù 9 kuavns kautrnkas y ma ukdcrdk idktfmdm ma akarcìd (5?? LaR) qua sa trdksbnrld bfkd`lakta ak id`nr.
D`eart Afkstafk,bdlnsn ifaktìbfin d`aläk.
B n t n S f g f p a
m f d
4]rdedjn, pntakifd y akarcìd
Qkfmdm =. Akarcìd Yasfùk
2
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Qsns pdiìbfins ma `d akarcìd kui`adr
Crdifds d` usn ma raditnras kui`adras hny ak mìd as pnsfe`a netakar flpnr-tdktas idktfmdmas ma ldtarfd` rdmfditfvn d edjn instn. As dsì inln masmabfkd`as ma `ns dôns =?, sa prnmuia ukd axpdksfùk ak a` alp`an pdiìbfinma mfvarsns tfpns ma Fsùtnpns Udmfditfvns ak mfvarsds ärads ma` quahdiarifaktìbfin y prnmuitfvn ma` hnlera.
Dcrfiu`turd y d`flaktdifùk: inktrn` ma p`dcds: ink `d taikn`ncìd kui`adras pnsfe`a dp`fidr `d ``dldmd ‐]æikfid ma `ns Fksaitns Astærf`as (]FA)“, quainksfsta ak sulfkfstrdr d`tds alfsfnkas ma rdmfdifùk fnkfzdkta d uk ifartncrupn ma fksaitns ldihns ldktakfmns ak `denrdtnrfn. @uacn `ns ldihnsastærf`as sa majdk ak feartdm pdrd bdif`ftdr su dpdradlfaktn ink ns fksaitnshalerd. Kn sa prnmuia, pnr akma, `d kaiasdrfd masiakmakifd. Ma astalnmn, `uacn ma suiasfvds y rfcurnsds rapatfifnkas ma` prniasn, as pnsfe`a
inktrn`dr y mfslfkufr su pne`difùk ak ukd matarlfkdmd racfùk cancräbfid.
Lutdifnkas: `d frrdmfdifùk dp`fidmd d salf``ds, maspuæs ma flpnrtdktasy rfcurnsns astumfns, parlfta idlefdr `d fkbnrldifùk cakætfid ma ifar-tds vdrfamdmas ma p`dktds y vacatd`as ma inksuln huldkn. A` nejatfvnma `d tæikfid, as `d netakifùk ma kuavds vdrfamdmas ma aspaifas inkidrditarìstfids pdrtfiu`dras qua parlftdk a` dulaktn ma su rasfstakifd yprnmuitfvfmdm
A` prniasn ma `d bfsfùk parlfta a` bukifnkdlfaktn ma `ns Uaditnras Ku-i`adras qua ditud`lakta npardk ak a` lukmn.
Busfùk kui`adr: `d busfùk kui`adr niurra iudkmn mns kúi`ans dtùlfinsluy `fvfdkns sa ukak, bnrldkmn uk kúi`an dtùlfin läs pasdmn ink ld-ynr astdef`fmdm. Astds radiifnkas `feardk akarcìds tdk a`avdmds qua ak `dditud`fmdm sa astumfdk bnrlds dmaiudmds pdrd ldktakar `d astdef`fmdm yinkbfkdlfaktn ma `ds radiifnkas.
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Inksarvdifùk ma d`flaktns: `ds rdmfdifnkas snk utf-`fzdmds ak luihns pdìsas pdrd dulaktdr a` parìnmnma inksarvdifùk ma luihns d`flaktns. As flpnrtdkta
saôd`dr, qua d tæikfid ma frrdmfdifùk kn cakard abaitnssaiukmdrfns ak `d sd`um huldkd, sfakmn idpdz ma ra-muifr ak bnrld inksfmarde`a a` kúlarn ma nrcdkfslnsy lfirnnrcdkfslns pdtùcakns prasaktas ak vdrfdmnsd`flaktns ma inksuln ldsfvn.
Hfmrn`ncìd: crdifds d` usn ma `ds tæikfids kui`adras aspnsfe`a masdrrn``dr mfvarsns astumfns ra`difnkdmns inkraiursns hìmrfins. Ak astumfns ma dcuds suparbfifd`asas pnsfe`a idrditarfzdr y lamfr `ds inrrfaktas ma dcuds``uvfds y ma kfava7 idumd`as ma rìns, bucds ak aled`sas,`dcns y idkd`as y `d mfkälfid ma `dcns y mapùsftns. Akastumfns ma dcuds suetarräkads as pnsfe`a lamfr `nsidumd`as ma ds kdpds, fmaktfbfidr a` nrfcak ma ds dcudssuetarräkads, su amdm, va`nifmdm, mfraiifùk, b`ujn, ra`d-
ifùk ink dcuds suparbfifd`as, inkaxfnkas aktra diuìbarns,pnrnsfmdm y mfsparsfùk ma diuìbarns.
Rdiukds: sa hdk a`denrdmn rdmfn vdiukds pdrd inledtfrakbarlamdmas pdrdsftdrfds ma` cdkdmn y qua dbaitdk `dprnmuiifùk paiudrfd ak cakard`. @ns dkfld`as snla-tfmns d` trdtdlfaktn snpnrtdk murdkta uk parìnmn läsprn`nkcdmn a` pa`fcrn ma ra fkbaiifùk sfalpra `dtakta
ak su lamfn kdturd`.
Lamfifkd kui`adr: sa hd axtakmfmn ink crdk rdpfmaza` usn ma rdmfdifnkas y ma rdmfnfsùtnpns ak lamfifkdinln dcaktas tardpæutfins y ma mfdckùstfin. Ak a` mfdc-kùstfin sa utf`fzdk rdmfnbärldins pdrd mfvarsns astumfnsma: tfrnfmas, hìcdmn, rfôùk, latden`fsln, ifriu`difùk
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Ak tardpfd læmfid: ink `ds tæikfids kui`adras sa puama inledtfr ifartnstfpns ma iäkiar. Ink braiuakifd sa utf`fzdk trdtdlfaktns ak edsa d frrdmfd-ifnkas ink rdyns cdlld prnvakfaktas ma buaktas ma Ined`tn-2?, dsì inln
tdlefæk, asbards fktarkds rdmfditfvds, dcujds a hf`ns ma Ined`tn rdmfditfvn.Inlefkdkmn a` trdtdlfaktn ink ukd dmaiudmd y praldturd mataiifùk ma`iäkiar, sa netfakak tardpfds ink axftnsns rasu`tdmns.
Lamfn dlefakta: ak astd ärad sa utf`fzdk tæikfids kui`adras pdrd `d matai-ifùk y dkä`fsfs ma mfvarsns inktdlfkdktas ma` lamfn dlefakta. @d tæikfidläs inknifmd raifea a` knlera ma Dkä`fsfs pnr Ditfvdifùk Kautrùkfid,edsdmn ak `ns trdedjns masdrrn``dmns ak 4692 pnr a` ifaktìbfin húkcdrn J.C.Havasy, _ralfn Knea` ma Tuìlfid ak 46==. @d tæikfid inksfsta ak frrdmfdrukd luastrd, ma td` bnrld, ma netakar d pnstarfnrf `ns aspaitrns cdlldqua a``d alfta, pdrd bfkd`lakta prniasdr `d fkbnrldifùk ink dyumd inl-putdifnkd`. @d fkbnrldifùk aspaitrd` fmaktfbfid `ns a`alaktns prasaktas ak`d luastrd y `ds inkiaktrdifnkas ma `ns lfslns.
Fkmustrfd a fkvastfcdifùk
]rdzdmnras: sa a`denrdk sustdkifds rdmfditfvds qua snk fktrnmuifmds ak uk
matarlfkdmn prniasn. @uacn sa mataitd d trdyaitnrfd ma `d sustdkifd crdifdsd su alfsfùk rdmfditfvd, n qua parlfta fkvastfcdr mfvarsds vdrfde`as prnpfdsma` prniasn. Aktra ntrds vdrfde`as, sa puama matarlfkdr idumd`as ma b`ufmns,bf`trdifnkas, va`nifmdmas ak tuearìds, mfkälfid ma` trdkspnrta ma ldtarfd`as,idlefns ma bdsa ma `ìqufmn d cds, va`nifmdm ma mascdsta ma ldtarfd`as, ati.
Fläcakas: as pnsfe`a netakar fläcakas ma pfazds ink su astruiturd fktarkdutf`fzdkmn rdmfncrdbìds ak edsa d rdyns cdlld n efak ink uk b`ujn ma kau-
trnkas. Astds fläcakas raifeak a` knlera ma Cdlldcrdbìd y Kautrncrdbìdraspaitfvdlakta, y snk ma crdk utf`fmdm ak `d fkmustrfd inln lætnmn knmastruitfvn ma inktrn` ma id`fmdm. Ink astns lætnmns sa puama inlprnedr did`fmdm ak sn`mdmurds astruiturd`as, ak pfazds latä`fids bukmfmds, ak pfazdsiarälfids, pdrd dkä`fsfs ma hulamdm ak ldtarfd`as ma inkstruiifùk, ati.
Ak a` äleftn ma `d efn`ncìd, `d fktrnmuiifùk ma inlpuastns rdmfditfvnsldridmns hd parlftfmn nesarvdr ds ditfvfmdmas efn`ùcfids hdstd ak sus läs
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@d akarcìd d trdvæs ma `d hfstnrfd
A` sar huldkn, masma sus prflarns pdsns ak `d ]farrd y d trdvæs ma `d
hfstnrfd, sfalpra hd eusidmn bnrlds ma utf`fzdr `d akarcìd pdrd netakar
ukd lajnr id`fmdm ma vfmd. _drd a``n, hd haihn usn ma mfvarsds bnrlds
ma akarcìd: buacn (akarcìd quìlfid), va`ds y ln`fkns (akarcìd ma` vfaktn
n aù`fid), ruamds hfmräu`fids (akarcìd ma` dcud n hfmräu`fid), idreùk (ak-
arcìd quìlfid), patrù`an (akarcìd quìlfid), kui`adr (akarcìd kui`adr), ati.
- 91?.??? d. I.: a` sar huldkn masiuera
a` buacn. Astn a parlftfù id`aktdrsa, in-
ifkdr ns d`flaktns y d`ajdr d ds eastfds.
- 6.??? d. I.: a` sar huldkn mnlastfid
dkfld`as pdrd pnmar inlar y pdrd utf-
`fzdr`ns inln dyumd ak a` trdedjn.
- 9.1?? d. I.: a` sar huldkn fkvaktd `d
ruamd, ntrd bnrld ma alp`adr d akarcìd
ak eakabfifn prnpfn.
- 5.??? d. I.: a` sar huldkn fkvaktd `d
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va`d, ukd bnrld ma dprnvaihdr d akarcìdaù`fid pdrd kdvacdr.
- 1? d. I.: a` sar huldkn fkvaktd `d
ruamd hfmräu`fid y a` ln`fkn ma vfaktn,
`n qua supnka ukd bnrld ma dprnvaihdr
`d akarcìd hfmräu`fid ma` dcud y d aù`fid
ma` vfaktn.
- 4.345: sa fkvaktd d läqufkd ma vdpnr.
Astn supnka uk aknrla dvdkia ak `d fkmustrfd y ak a` trdkspnrta.
- 4.6??-4.639: aktra 46?? y 4643, a` inksuln ma akarcìd dulaktd aknr-
lalakta, sfakmn a` idreùk `d prfkifpd` buakta ma akarcìd. Aktra 4643 y4639 mfslfkuya a` inksuln ma idreùk y dulaktd kntde`alakta a` ma
patrù`an. A` patrù`an, dmaläs, ard buakta ma luihds ntrds sustdkifds.
- 4.639-4.681: buarta irfsfs akarcætfid: a` patrù`an inlfakzd d dcntdrsa
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Uaspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds
Inksu`ta: ¾pnr quæ as tdk flpnr-tdkta ak kuastrds vfmds `d akarcìd
kui`adr>¾Iraa qua as pnsfe`a trdksbnrldr
akarcìd laiäkfid ak ntrn tfpn ma
akarcìd> Axp`fqua su raspuastd.Knlera ifkin nejatns ma su idsd
mnkma sa trdksbnrla `d akarcìd aktrdedjn. Axp`fqua.¾Tuæ tfpn ma akarcìd iraa ustam as
`d qua prnmuia a` buacn>Iudkmn `ns idrrns astäk ak lnv-
flfaktn astäk prnmuifakmn uk tfpn
ma akarcìd. ¾Tuæ tfpn ma akarcìd as>
y sa inlfakzdk d usdr ntrds akarcìds:
kui`adr, hfmrna`æitrfid, aù`fid, sn`dr, ati.
2. ]nldmn ma: http://raiursnstfi.amuidifnk.as/saiukmdrfd/amdm/=asnbfsfidquflfid/flprasns/qufkiakd2.pmb
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]rdedjn
As uk prniasn ma trdksbarakifd ma akarcìd lamfdkta a` iud` sa prnmuia uk idlma pnsfifùk ma ukn n vdrfns iuarpns, as maifr, rad`fzdr uk trdedjn flp`fid dp`fidrbuarzd y uk masp`dzdlfaktn ‐mfbarakta ma iarn“.
4J < 4?3 a
4 ju`fn aqufvd`a d 4 Kawtnk
pnr latrn,
4 arcfn aqufvd`a d 4 mfkd pnr
iaktìlatrn,
Bukmdlaktn taùrfin
A` trdedjn (S) sa mabfka aktnkias, inlna` prnmuitn aktra `d buarzd rasu`tdktadp`fidmd y a` masp`dzdlfaktn ma` iuar-pn snera a` iud` sa dp`fid mfihd buarzd.
A` trdedjn as ukd idktfmdm asid`dr qua
sa axprasd ak a` sfstald LGY ak K/l7astd ukfmdm sa maknlfkd ju`fn (J).
Ak a` sfstald ics, a` trdedjn as `d buarzdrasu`tdkta aqufvd`akta d ukd mfkd qua
ditúd snera uk iuarpn pdrd masp`dzdr`nuk iaktìlatrn y sa `a maknlfkd arcfn.
Axfsta ukd aqufvd`akifd aktra `ds mnsukfmdmas:
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_ntakifd
D pdrtfr ma `d aiudifùk, pnmalns akinktrdr qua d ukfmdm ma
pntakifd ak a` sfstald LGY as Ju`fn / sacukmns qua aqufvd`ad` vdtfn (S), n pntakifd ma `d läqufkd qua `avdktd uk pasnma 4 K d ukd d`turd ma uk l ak uk sacukmn.
Ntrd ukfmdm ma pntakifd as a` ided``n ma buarzd (H_), quaaqufvd`a d 3=2 S, a` gf`nvdtfn hnrd qua as a` trdedjn qua rad`fzdukd läqufkd iuyd pntakifd as ma uk gf`nvdtfn murdkta ukdhnrd ma bukifnkdlfaktn.
Axfsta ra`difùk aktra d pntakifd y d va`nifmdm pdrd fktarvd`ns matfalpn lìkflns (‐t“ tfakma d iarn), qua sa puama axprasdr inln:
_ < B . v . ins δ
Aqufvd`a d` trdedjn (S) rad`fzdmn pnr ukfmdm ma tfalpn (t). Akcakard`, ukd läqufkd takmrä läs pntakifd ak d lamfmd inlnrad`fzd uk trdedjn ak a` laknr tfalpn pnsfe`a.
Qk kfôn drrdstrd ukd idrratd ink ukd buarzd ma 2?K, ak ukd mfstdkifd ma =?lbnrldkmn uk äkcu`n ma 9?º ink `d hnrfznktd`.¾Tua trdedjn rad`fzd asta>
Yn`uifùk:
Mdtns:
B < 2?K
x < =?l
θ < 9?º
Ajalp`n:
w< B(ins?).x :
w< 2?K (ins9?º).(=?l) < 5?38.=2K.l
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Akarcìd
@d akarcìd dsnifdmd d` lnvflfaktn sa maknlfkd akarcìd laiäkfid y inrraspnd `d suld ma `d akarcìd ifkætfid y `d akarcìd pntakifd`.
@d akarcìd ifkætfid d pnsaak tnmns`ns iuarpns ak vfrtum ma` lnvflfak-tn, y iudkmn `d trdksbfarak d ntrniuarpn ak rapnsn, sa mfia qua sarad`fzù uk trdedjn. _nr `n tdktn, a`trdedjn rad`fzdmn aqufvd`a d d mfba-
rakifd aktra d akarcìd ifkætfid bfkd`y `d akarcìd ifkætfid fkfifd`.
Bntn Sfgfpamfd
@d akarcìd pntakifd` crdvftdifnkd` `d pnsaa ukiuarpn ak vfrtum ma `d d`turd mnkma sa akiuaktrdink raspaitn ma` kfva` ma` pfsn.
Ap < l . c . h
Mnkma l as `d ldsd, c `d dia`ardifùk maefmd d `dcrdvamdm y h d d`turd mnkma sa akiuaktrd d ldsd
@d akarcìd pntakifd` a`ästfid `d pnsaak `ns rasnrtas y `dsedkmds a`ästfids.
G as `d inkstdkta ma a`dstfifmdm ma` rasnrta n edkmd a`ästfid, x inrraspnkma`d vdrfdifùk ma d nkcftum qua axparflaktd a` rasnrta n edkmd a`ästfid iudkmsa `as dp`fid ukd buarzd B .
@d akarcìd d` fcud` qua a` trdedjn, sa axprasd ak ju`fns (J) pdrd a` sfstald LG
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@ns idrrns ma ukd lnktdôd rusd d`idkzdk suläxfld akarcìd ifkætfid iudkmn astäk ak a`
bnkmn ma su trdyaitnrfd.
B n t n w f g f p a m f d
B n t n w f g f p a m f d
@ay ma inksarvdifùk ma `d akarcìd
@d akarcìd kn sa irad kf sa mastruya, sfknqua sa trdksbnrld. Ak a` idsn ma `d akar-
cìd laiäkfid, pnmalns dbfrldr qua akuk sfstald ma buarzds inksarvdtfvds, `dakarcìd parldkaia inkstdkta, as maifr,`d akarcìd laiäkfid fkfifd` as fcud` d `dakarcìd laiäkfid bfkd`.
Qk iuarpn qua sa akiuaktrd d ifartd d`tu-rd (h) pnsaa akarcìd pntakifd` crdvftdifn-kd`, as maifr, d` sar `feardmn, inlfakzd didar pnr diifùk ma `d buarzd ma crdvamdmy `d akarcìd pntakifd` crdvftdifnkd` satrdksbnrld prncrasfvdlakta ak akarcìdifkætfid. As ma kntdr qua ak asta idsn, sasupnka uk sfstald fmad` iuyn rnzdlfaktninktrd a` dfra as ku`n.
Qk sfstald inksarvdtfvn fkvn`uird buarzdsqua mdk nrfcak d `d akarcìd pntakifd` crd-vftdifnkd` n d `d akarcìd pntakifd` a`ästfid,inln ukd bukifùk qua mapakma axi`usf-vdlakta ma `d pnsfifùk fkfifd` y bfkd` ma`iuarpn y kn ma `d trdyaitnrfd sacufmd pnra` lfsln.
Idsf tnmd d akarcìd utf`fzdmd pnr d huldkfmdm sa hd nrfcfkdmn d pdrtfr ma d rdmfdifùksn`dr ``acdmd d `d ]farrd. Qk 62% ma `ds kaiasfmdmas akarcætfids quamdk sdtfsbaihdspnr `d inleustfùk ma idreurdktas bùsf`as inln idreùk, patrù`an y cds kdturd`, quaraprasaktdk `d akarcìd quìlfid d`ldiakdmd ak `d ]farrd. Iudkmn astds buaktas sahdydk dcntdmn, sa maearä eusidr idmd vaz ink ldynr mamfidifùk `ns idreurdktaskui`adras (busfùk kui`adr y bfsfùk kui`adr), `d akarcìd ma crdvftdifùk ak `ds ldrads y
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3
Ldtarfd`as
Eäsiu`d, ifktd lætrfid y irnkùlatrn.
_rniamflfaktn
4. Inkbnrldr a` aqufpn ma trdedjn.
5. Qtf`fzdr `d ifktd lætrfid pdrd matarlfkdr ukd mfstdkifd ma 5? l.
9. Ma inlúk diuarmn, sa`aiifnkdr d uk inlpdôarn pdrd rad`fzdr`d präitfid.
=. Qefidr mns fktacrdktas ma` aqufpn ak a` puktn fkfifd` y mns ak a`
puktn bfkd`. A` qufktn maea ldkajdr a` irnkùlatrn.
1. @d tdrad ma` astumfdkta sa`aiifnkdmn as trds`dmdr d sus inlpdôarnsd` `ucdr npuastn ma mnkma sa akiuaktrdk fkfifd`lakta, ma uknak ukn y ak a` laknr tfalpn pnsfe`a.
2. A` irnknlatrfstd maea matarlfkdr ns tfalpns pdrifd`as pdrd idmdrainrrfmn.
_räitfid ma `denrdtnrfn
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3. @ns mdtns sa racfstrdk ak `d tde`d 4 lnma`n (sa raqufara inkniar `dldsd ma idmd ukn).
8. ]akfakmn ak iuaktd a` trdedjn rad`fzdmn, `d pntakifd y `d akarcìdraquarfmds ak a` ajarififn, matarlfkdr a` kúlarn ma id`nrìds yinksu`tdr snera `ns pnsfe`as d`flaktns qua `as parlftfrìdk raiupa-rdr asds id`nrìds. A`denrdr uk `fstdmn ma pnr `n lakns, tras lakúsmfbaraktas, ak ukd tde`d inln `d lnma`n.
]de`d 4
MfstdkifdAkarcìdifkætfid
]rdedjn _ntakifd]falpn
Dkä`fsfs ma rasu`tdmns
D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn astumfdmn
Lakú 4 Lakú =Lakú 5 Lakú 9
]de`d 5
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2
Ajarififns ma dp`fidifùk
4. Qk e`nqua ma ldmard ma 5 Gc sa akiuaktrd snera ukd suparbfifa hnrfztd`, a` inabfifakta ma rnzdlfaktn as ma ?,9 y sa dp`fid ukd buarzd ma 4pdrd`a`d d `d suparbfifa d trdvæs ma ukd iuarmd. Yf a` e`nqua ma ldmarmasp`dzd d ukd mfstdkifd ma 1? il, matarlfkdr a` trdedjn rad`fzdmn.
Yn`uifùk: fkfifd`lakta sa maea matarlfkdr a` vd`nr ma d buarzd rasu`tdkta:
A` trdedjn rad`fzdmn as:
< 6,45 K x ?,1 l < =,12 J
5. ]akfakmn ak iuaktd a` ajarififn dktarfnr, sf `d buarzd kn as hnrfznktd`
qua prasaktd ukd fki`fkdifùk ma 2?º ink raspaitn ma `d hnrfznktd`, malfkdr a` trdedjn rad`fzdmn.
Yn`uifùk:
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Dsiaksnr
Inktrdpasn
_n`ad
9. Matarlfkdr d pntakifd, axprasdmd ak ided``ns ma buarzd, ma` lntnr pdrd ukdsiaksnr ma ldsd fcud` d 1?? Gc, qua pnsaa uk inktrdpasn ma 5?? Gc, ukdidpdifmdm pdrd suefr ukd idrcd ma =8? Gc (8 parsnkds ink uk prnlamfn ma2? Gc idmd ukd), y suefr ma` pfsn 4 d 4? ak 51 s. @d d`turd ma idmd pfsn ama 5,8 l.
Yn`uifùk: sa matarlfkd fkfifd`lakta `d ldsd tntd`:
@d buarzd qua maea rad`fzdr a` lntnr maea sar prnpnrifnkd` d` pasn ma `dldsd tntd`:
A` trdedjn tntd` rad`fzdmn as: (pdrd ``acdr ma` 4º d` 4?º pfsn a` dsiaksnr ra-inrra 6 pfsns).
< 32== K x 51,5 l < 465.258,8 J
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@d pntakifd ak vdtfns (S) as:
@ns vdtfns sa axprasdk ak ided``ns ma buarzd (H_)
=. Ak a` axtraln suparfnr ma uk p`dkn fki`fkdmn ma 4 l ma `nkcftum y fki`fkdifùk ma =1º, sa sua`td uk e`nqua ma ldmard ma 1 Gc ma ldsd. Ymas`fzd snera `d suparbfifa sfk rnzdlfaktn, ink quæ va`nifmdm ``acd d` bma` p`dkn.
Yn`uifùk: Fkfifd`lakta sa matarlfkd d d`turd
mnkma sa akiuaktrd a` nejatn.
h < 4 l . sak =1n < 4 l . ?,3? < ?,3? l
Dhnrd sa puama matarlfkdr d akarcìd pntakifd`.
A p < l . c . h < 1 Gc . 6,8 l/s5 x ?,3? < 9=,9 J
_nr a` prfkifpfn ma inksarvdifùk ma `d akarcìd y inksfmardkmn qua kn hdyrnzdlfaktn, `d akarcìd pntakifd` sa hd inkvartfmn ak akarcìd ifkætfid d```acdr d` bfkd` ma` p`dkn. Yf maspajdlns `d va`nifmdm, pnmalns sn`uifnkdra` prne`ald:
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4. Matarlfkdr a` trdedjn rad`fzdmn ak `ns sfcufaktas idsns:
• Ynera ukd suparbfifa hnrfznktd`, ukd buarzd tdlefæk hnrfznktd`ma 4? K drrdstrd ukd ldsd ma ?,1 Gc y a` inabfifakta marnzdlfaktn as ma ?,51.
• @d lfsld buarzd ma` ajarififn dktarfnr sa dp`fid ink uk äkcu`nma 9?º.
• Ya dp`fid ukd buarzd ma 8 K pdrd hdiar suefr ukd ldsd ma ?,1Gc snera uk p`dkn fki`fkdmn 9?º, ink ukd `nkcftum fcud` d 4l sfk rnzdlfaktn.
5. Mns trdedjdmnras tfakak d lfsfùk ma `avdr idmd ukn hdstd a` tariarpfsn ma ukd inkstruiifùk, 4? eu`tns ma pacdkta pdrd ed`mnsd ma`akihdpa ma `d inifkd. Idmd eu`tn tfaka ukd ldsd ma 51 Gc y `dmfstdkifd prnlamfn as ma 9 l pnr pfsn. A` prflarn suea ma eu`tnak eu`tn, lfaktrds qua a` sacukmn suea ak `ns tras prflarns vfdjasma d tras eu`tns y ak a` ú`tfln suea tdlefæk a` ú`tfln eu`tn. ¾Tufækrad`fzù läs trdedjn>
9. Qkd pd`d laiäkfid `avdktd ukd rnid ma 5=? Gc ma ldsd hdstd ma-pnsftdr`d snera a` p`dtùk ma ukd vn`quatd qua astä d 9 l ma d`turd,y tdrmd ak a` ajarififn ?,59 s. Matarlfkdr a` vd`nr ma `d pntakifd ma`d läqufkd.
=. Ak a` ajarififn 5, a` prflar trdedjdmnr sa malnrù 41 lfkutns y a`sacukmn 49 lfkutns. ¾Iuä` as `d pntakifd masdrrn``dmd pnr idmdukn>
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1. Masma ukd d`turd ma 51 l, sa majd idar uk nejatn ma ldsd fcud`4? Gc. Matarlfkdr `d akarcìd ifkætfid y `d va`nifmdm d` lnlaktnma hdiar inktditn ink a` pfsn.
2. Masma a` axtraln suparfnr ma uk p`dkn fki`fkdmn =1º y ma 4,5 l,sa mas`fzd ukd ldsd ma 41 Gc sfk rnzdlfaktn. D` ``acdr d` bfkd` ma`p`dkn sa mas`fzd snera ukd suparbfifa hnrfznktd` iuyn inabfifaktama rnzdlfaktn as ma ?,9 qua as `d va`nifmdm d` ``acdr d` bfkd` ma`p`dkn. ¾Tuæ mfstdkifd d`idkzù d rainrrar dktas ma matakarsa>
< =1º
L 4
h
Avd`udifùk
¾Tuæ dprakmfù ink `d ditfvfmdm>Rd`nrdr a` trdedjn rad`fzdmn, d prasaktdifùk y masdrrn``n ma d cuìd, d dp`fid-ef`fmdm ma d aiturd, y ma sar pnsfe`a, prnpnkar lnmfbfidifnkas pdrd lajnrdr
Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdrd
sn`uifnkdr sftudifnkas bìsfids rad`as ma `d vfmd mfdrfd.
Inki`usfnkas
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Dutnavd`udifùk
D` tarlfkdr astd ukfmdm as flpnrtdkta rad`fzdr `d avd`udifùk ma tus dprak-mfzdjas. _drd a``n, asirfed ak a` mfeujn ma` iuarpn huldkn ak a` `ucdrfkmfidmn `ds raspuastds d `ns sfcufaktas fktarrncdktas:
d. Ak `d ideazd: ¾quæ dprakmfù ak astd ukfmdm>e. Ak a` iua``n: ¾pdrd quæ a sfrva d talätfid denrmdmd ak astd ukfmdm>i. Ak ukn ma `ns erdzns: ¾ak quæ ifriukstdkifds puama dp`fidr d`cukns
ma `ns inkiaptns dprakmfmns ak astd ukfmdm>m. Ak a` ntrn erdzn: ¾quæ pdrta ma `d talätfid sa `a mfbfiu`tù>
a. Ak a` astùldcn: ¾quæ nestdiu`fzù su dprakmfzdja>b. Ak a` paihn: ¾quæ tdktn `a custù `n qua dprakmfù>c. Ak `ns pfas: ¾quæ inksajn sa mdrìd d sì lfsln pdrd sar a` lajnr astu-
mfdkta ma astd i`dsa>
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4Yasfùk
Kuavds taikn`ncìds
ak `d fkmustrfd d`flaktdrfd8
A` masdrrn``n ma kuavds taikn`ncìdsak `d Fkmustrfd D`flaktdrfd ink `dbfkd`fmdm ma netakar d`flaktnslìkfldlakta prniasdmns d `d vazqua sacurns y qua inksarvak sus
iud`fmdmas kutrfifnkd`as y nrcdkn-`æptfids, astä parlftfakmn d`drcdr dvfmd útf` ma luihns prnmuitns y sd-tfsbdiar `ns custns ma` inksulfmnr.
@d dpdrfifùk ma prnmuitns lìkfldlakta prniasdmns astä dsnifdmd d idlefn`ns häeftns ma inksuln. Ynk prnmuitns qua prasaktdk uk vd`nr dôdmfmn y ukdid`fmdm kutrftfvd y saksnrfd`, qua cakard`lakta sa inksulak irumns n ink uk tr
lfaktn tærlfin sudva. _nr asta lntfvn, rasu`td flprasifkmfe`a inkniar a` abaitn`ds mfstfktds taikn`ncìds ma inksarvdifùk ak su id`fmdm.
@ns ldynras dvdkias ak asta idlpn sa hdk inksacufmn ink a` masdrrn``n ma slds bìsfins, qua dbaitdk `d vfdef`fmdm ma `ns lfirnnrcdkfslns, sfk uk fkirala
8 HAUUAUN D L y UNLAUN MA ÄRF@D L M Kuavds taikn`ncìds ak `d fkmustrfd d`flaktdrfd Qkfva
Laiäkfid ma ufmnsQkfmdm 1. Hfmrnlaiäkfid Yasfùk
3
A`denrdifùk ma id
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sustdkifd` ma d talpardturd ma` d`flaktn. Astns lætnmns‐kn tærlfins“ kn dbaitdk, n n hdiak lìkfldlakta d `dsidrditarìstfids kutrftfvds y saksnrfd`as ma `ns d`flaktns.
D`tds prasfnkas
Ditud`lakta, axfstak mns prniamflfaktns: `d prasfùk mf-kälfid, tnmdvìd kn utf`fzdmn d kfva` fkmustrfd` y d prasfùkastätfid, qua as `d qua hny tfaka dp`fidifùk präitfid.
Ak `d d`td prasfùk mfkälfid a` fkiralaktn ma prasfùk sanrfcfkd ak uk tfalpn luy inrtn (lf`æsflds ma sacukmn)inln inksaiuakifd ma ukd axp`nsfùk qua cakard ukdnkmd ma ihnqua, maknlfkdmd nkmd ma ihnqua hfmrn-mfkälfid. Astd taikn`ncìd inksfcua `d fkditfvdifùk malfirnnrcdkfslns y a` de`dkmdlfaktn ma ifartns tajfmns,inln idrka, pnr rupturd ma d astruiturd ia`u`dr. Asta prn-iamflfaktn sa akiuaktrd ak bdsa ma astumfn y masdrrn``n.
@d dp`fidifùk ma d`td prasfùk astätfid sa edsd ak snlatard uk prnmuitn d a`avdmns kfva`as ma prasfùk hfmrnstätfid(4??-4??? L_d) ma bnrld inktfkud murdkta uk ifartntfalpn (vdrfns lfkutns). D asta tfpn ma taikn`ncìd sa `dmaknlfkd inlúklakta d`tds prasfnkas hfmrnstätfids(Hfch _rassura _rniassfkc, H_). @d utf`fzdifùk ma d`tdsprasfnkas hfmrnstätfids sa rfca, bukmdlaktd`lakta pnr
mns prfkifpfns: d) @a Ihdta`far, akukifd qua iud`qufarbakùlakn (radiifnkas quìlfids, idlefns ln`aiu`dras,ati.), qua vd dinlpdôdmn ma mfslfkuifùk ma vn`ulaksubra uk fkiralaktn d` dulaktdr d prasfùk, y vfiavarsdy e) `d `ay ma _dsid`, sacúk `d iud` ukd prasfùk axtarkddp`fidmd d uk b`ufmn inkbfkdmn sa trdkslfta ma bnrldukfbnrla a fkstdktäkad ak tnmds `ds mfraiifnkas. Madiuarmn ink asta ú`tfln prfkifpfn astd taikn`ncìd puama
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prnmuitn akvdsdmn sularcfmns ak uk b`ufmnma prasurfzdifùk (ma edjd inlprasfef`fmdm).@d prasfùk dp`fidmd d` sfstald parlftfrìd uktrdtdlfaktn fsnstätfin y ukfbnrla fkmapak-mfaktalakta ma` tdldôn, bnrld y vn`ulak
ma` ldtarfd` prniasdmn.
Ak a` laridmn puamak akinktrdsa prnmuitnsprasurfzdmns inln larla`dmds zulns, jd-`ads, inkiaktrdmns y puræs ma brutds, pnstrasprnmuitns `äitans marfvdmns iärkfins iurdmns y inifmns `nkihadmns y prapdrd`fstns pdrd su inksuln Ink bfkas mfstfktns d `d inksarvdifùk, `d dp`fidifùk ma
prasfnkas hfmrnstätfids parlfta netakar mfstfktns tfpns ma ca`as ma pasidmn, idhuavn y `aiha. Dsì lfsln, astd taikn`ncìd dia`ard `d mfbusfùk ma sn`utns ak mfvad`flaktns, `d sn`uef`fzdifùk ma cdsas y `ns prniasns.
Q`trdsnkfmns
@ns u`trdsnkfmns puamak mabfkfrsa inln nkmds diústfids fkdumfe`as ma ukd brai
ifd suparfnr d 5? gHz. _drd `d inksarvdifùk ma `ns d`flaktns, snk läs abfidiankmds u`trdsùkfids ma edjd braiuakifd (48-4?? gHz7 < 4=1 ll) y d`td fktaks(4?-4??? S/il5). A` abaitn inksarvdmnr ma `ns u`trdsnkfmns astä dsnifdmn d `nkùlakns inlp`ajns ma idvftdifùk cdsansd, qua axp`fidk `d cakardifùk y avn`uma lfirn eureujds ak uk lamfn `ìqufmn. Kn nestdkta, a` abaitn ma `ns u`trdsnksnera ns dcaktas d`tardktas ma ns d`flaktns as flftdmn y mapakmfakta ma lú`tbditnras pnr a``n, su dp`fidifùk sa hd akidlfkdmn hdifd d inlefkdifùk, sflu`tdn d`tarkd, ink ntrds fkknvdifnkas ak a` prniasn ma d`flaktns.
Frrdmfdifùk
Ak `d Fkmustrfd D`flaktdrfd, a` tærlfkn ma ‐frrdmfdifùk“ sa utf`fzd pdrd rabad trdtdlfaktns ak `ns qua `ns d`flaktns sa axpnkak d `d diifùk ma rdmfdifnfnkfzdktas murdkta uk ifartn tfalpn. Ak a` sfstald fktarkdifnkd`, `d mnsfs de
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Ak mfvarsds fkvastfcdifnkas sa hd puastn ak avfmakifd qua iudkmn `d mnsfs desnr-efmd as m“ d 4? gCy `d bnrldifùk ma inlpuastns rdmfn `ìtfins kn supnka rfascnpdrd `d sd`um.
Idlpns a`æitrfins ma d`td fktaksfmdm
A` abaitn snera `ns lfirnnrcdkfslns sa edsd ak `d d`tardifùk n mastruiifùk ma `d pd-
ram ia`u`dr iudkmn sa dp`fid ukd fktaksfmdm ma idlpn a`æitrfin qua md `ucdr d ukdmfbarakifd ma pntakifd` aktra dlens `dmns ma `d lalerdkd (pntakifd` trdkslal-erdkd). Iudkmn astd mfbarakifd ma pntakifd` d`idkzd uk vd`nr irìtfin matarlfkdmn,qua vdrìd ak bukifùk ma` tfpn ma lfirnnrcdkfsln, nrfcfkd `d bnrldifùk ma pnrnsfrravarsfe`a ak d lalerdkd ia`u`dr (a`aitrnpnrdifùk) y ak inksaiuakifd d pærmfmdma su fktacrfmdm, fkiralaktn ma `d parladef`fmdm y bfkd`lakta mastruiifùk ma `diæ`u`d dbaitdmd. As ukd ma ds lajnras d`tarkdtfvds d ns lætnmns inkvakifnkd`as mapdstaurfzdifùk, `n qua hfzn qua sa maknlfkdrd pdstarfzdifùk brìd.
Yu usn astä flftdmn d prnmuitns enleade`as, idpdias ma inkmuifr d a`aitrfifmdm yaxaktns ma lfirnnrcdkfslns aspnru`dmns. Yfk aledrcn, kn prnmuia kfkcúk abaitnsnera akzflds. @ns d`flaktns läs fmùkans pdrd asta trdtdlfaktn snk: `aiha, huavn`ìqufmn, zulns ma brutds y inkiaktrdmns, snpds y axtrditns ma idrka.
Idlpns ldckætfins nsif`dktas
@d talpardturd murdkta a` prniasdmnsa ldktfaka aktra ?ºI y 1?ºI. A` abaitninksarvdmnr sa maea, bukmdlaktd`lakta,d mns bakùlakns: (d) d `d rupturd ma `dln`æiu`d ma DMK y ma ifartds prntaìkds,y (e) d `d rnturd ma ak`dias invd`akta ak
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@ns d`flaktns läs fmùkans pdrd snlatarsa d astaprniasn ma inksarvdifùk snk: zulns, larla`dmds,brutns trnpfid`as ak sn`uifnkas dzuidrdmds, marfvdmnsiärkfins, prnmuitns inifmns, akvdsdmns y `fstns pdrdsu inksuln.
@uz e`dkid ma d`td fktaksfmdm
@d dp`fidifùk ma pu`sns ma `uz e`dkid ma d`td fktaksf-mdm as uk trdtdlfaktn `flftdmn d `d suparbfifa ma `nsprnmuitns, qua puama utf`fzdrsa pdrd d pdstaurfzdifùkma `ìqufmns trdkspdraktas y d`flaktns akvdsdmns akldtarfd`as trdkspdraktas. ]dlefæk puama dp`fidrsapdrd `d astarf`fzdifùk ma suparbfifas ma ldtarfd`as yaqufpns. @d murdifùk ma idmd pu`sn as ma 5??-9?? ls
y `d braiuakifd as ma 4 d 5? s-4 (447 45).
Asta trdtdlfaktn prnmuia idlefns bntnquìlfins y bn-tntærlfins. @ns prflarns nrfcfkdk lnmfbfidifnkas aka` DMK, ak ds lalerdkds ia`u`dras y ak ns sfstaldsma rapdrdifùk y akzflätfins. @ns sacukmns prnmuiakuk fkiralaktn ma d talpardturd lnlaktäkan ak dsuparbfifa trdtdmd qua, pnr d inrtd murdifùk ma` pu`-sn, kn dbaitd d `d talpardturd c`ned` ma` prnmuitn.@ns aqufpns utf`fzdmns prasaktdk iäldrds ak `ds quamasta``dk, ink `d braiuakifd raquarfmd, `älpdrds macdsas (xakùk n grfptùk) ma d`td fktaksfmdm y abfidifd._rnmuitns trdtdmns, ink rasu`tdmns edstdkta sdtfsbdi-tnrfns, snk bf`atas y pnrifnkas ma idrka y pasidmn,cdleds, idrka ma pn``n y sd`ihfihds.
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D pdrtfr ma `d `aiturd qua rad`fzù, raspnkmd `ds sfcufaktas pracuktds:
_racuktds Uaspuastds¾Tuæ d`flaktns ink akvdsas
prasurfzdmns inknia> Lakifnka
ifkin.Yacúk `d `aiturd, ¾ink quæ bfk sa
utf`fzdk `ns akvdsas prasurfzdmns>¾Tuæ tfaka qua var d hfmrnlaiäkf-
id ink `ns akvdsas prasurfzdmns>¾_nr quæ iudkmn uk euzn astä
maktrn ma` dcud kn sa hukma kf
b`ntd>¾Tuæ pdsd iudkmn ukd parsnkd
fkcrasd d` dcud sfk kfkcúk aqufpnaspaifd`fzdmn pdrd euiadr>
Dvdkias ak akvdsdmn ma d`flaktns
A` akvdsa tfaka uk pdpa` bukmdlaktd` ak d inksarvdifùk ma ns d`flaktns
y ak `ds ú`tflds mæidmds sa hdk rad`fzdmn inksfmarde`as fkknvdifnkas, akldtarfd`as y sfstalds ma akvdsdmn, ink fkmumde`a ra`avdkifd ak d inlar-
ifd`fzdifùk ma d`flaktns läs sacurns, sd`umde`as y dpataife`as.
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Bukmdlaktn taùrfin
Yustdkifd Maksfmdm ak Gc/l9 Maksfmdm ak c/il9
Diafta 65? ?,65
Diarn 3.8?? 3,8
Dcud 4.??? 4
D`inhn` 84? ?,84
D`ulfkfn 5.3?? 5,3
Inera 8.6?? 8,6
C`fiarfkd 4,52 45,2?
Hfarrn 3.8?? 3,8
Ldmard 6?? ?,6
Lariurfn 49.2?? 49,2
Nrn 46.9?? 46,9
Hfmrnstätfid
As a` astumfn ma `ns b`ufmns ak rapnsn. @ns b`ufmns snk `ds sustdkifds qua tfakaprnpfamdm ma b`ufr ma uk raifpfakta d ntrn, dmnptdkmn `d bnrld tntd` n pdrifd`kuavn raifpfakta, `n iud` sa maea d qua `ds buarzds ln`aiu`dras aktra `ns mfbarainkstftuyaktas snk mæef`as. Ya inksfmardk b`ufmns `ns `ìqufmns y `ns cdsas.
Maksfmdm: ldckftum bìsfid (τ) qua sa mabfka inln a` inifakta aktra `d ldsdma uk iuarpn y su vn`ulak (v). Ak a` sfstald fktarkdifnkd` (YF) sa lfma ak Gc/l
Ak `d sfcufakta tde`d, sa puama dpraifdr `d maksfmdm ak c/il9 y ak Gc/l9 d talrdturd ma 5?º iaktìcrdmns:
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_rasfùk: aqufvd`a d `d buarzd parpakmf-iu`dr (B) dp`fidmd pnr ukfmdm ma ärad (D).
Ak a` YF, sa axprasd ak K/l5
, ukfmdm quasa maknlfkd pdsid` (_d), qua ak bnrlddprnxfldmd aqufvd`a d `d prasfùk quaajaria snera a` sua`n ukd `älfkd ma 4?5 c ma ldsd ak 4 l5 ma suparbfifa.
_rasfùk ak ns ìqufmns: tdlefæk sa a ma-knlfkd prasfùk hfmrnstätfid. As `d buarzd
ajarifmd pnr uk ìqufmn ak aquf`ferfn par-pakmfiu`dr d `d suparbfifa ma` raifpfaktaqua `n inktfaka n d `d suparbfifa ma uksù`fmn sularcfmn ak æ`.
Aiudifùk bukmdlaktd` ma `d hfmrnstätfid
Luastrd qua `d prasfùk ak uk puktn kn mapakma ma` vn`ulak ma` `ìqufmn quahdy pnr akifld ma mfihn puktn y as prnpnrifnkd` d `d maksfmdm (τ) ma` `ìqufmn, `ddia`ardifùk ma `d crdvamdm (c) ma` sftfn y `d prnbukmfmdm (h) d `d iud` sa akiuaktrdmfihn puktn. As maifr, mns puktns sftudmns d `d lfsld prnbukmfmdm ak a` fktarfnma uk `ìqufmn, astäk snlatfmns d `d lfsld prasfùk.
_ < τ . c . h
Kfva` ma` `ìqufmn_rnbukmfmdm
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Mns raifpfaktas ma mfbaraktas bnrlds snk ``akdmns ink cdsn`fkd
hdstd qua a` kfva` ma` b`ufmn as ma 9?il pnr akifld ma `d idsa maidmd ukn. @ds ärads ma ds edsas ma ns raifpfaktas snk ma 5?il9 y
4?il raspaitfvdlakta. Inlpdrd `d prasfùk y `d buarzd tntd` snera
`d edsa ma idmd raifpfakta.
Yn`uifùk: _drd sn`uifnkdr asta ajarififn maealns takar ak iuaktd
`d maksfmdm ma `d cdsn`fkd
Mdtns:
p < 28?gc/l9
c < 6,8l/s5
h < 9?il ?.9l
D4 < 5?il5 5x4?-9l5.
D5 < 4?il5 4x4?-9l5
Ajalp`n:
r4 r5
_ < pch < (28?gc/l9)(6.8l/s5)(?.9l) < 4666.5_D
B < _D4 < (4666.5 _d)(5x4?-9l5)<9.66K
B < _D5 < (4666.5 _d)(4x4?-9l5)<4.66K
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_rfkifpfn ma Drquìlamas
]nmn iuarpn sularcfmn ak uk ìqufmn, axparflaktd uk alpuja vartfid` hdifd drrfed,fcud` d` pasn ma` vn`ulak ma` `ìqufmn masp`dzdmn. Asta prfkifpfn tfaka dp`fidifnkas
ak `d darnstätfid y ak `d fkmustrfd `aihard ink a` maksìlatrn pdrd matarlfkdr `dpurazd ma `d `aiha, ati.
Yf a` iuarpn sa akiuaktrd inlp`atdlakta sularcfmn y a` alpuja qua axparflaktdas ldynr qua su pasn, mabfkftfvdlakta suefrä d `d suparbfifa y a` alpuja snera `dpdrta sularcfmd ma vn`ulak vs sarä fcud` d` pasn ma` iuarpn.
_rfkifpfn ma _dsid`
@ns ìqufmns trdkslftak ak tnmds mfraiifnkasy ink `d lfsld fktaksfmdm, `ds prasfnkas
qua sa ajariak ak matarlfkdmd racfùk maa``ns. Dp`fidifnkas ma asta prfkifpfn snk: `dpraksd hfmräu`fid, `ns sfstalds ma brakns madutnlùvf`as, ati.
Ak a` idsn ma `d praksd hfmräu`fid, sadprnvaihd `d mfbarakifd aktra a` mfälatrnma` ælen`n mnkma sa dp`fid `d buarzd y a`mfälatrn ma` ælen`n mnkma sa ajaria `d prasfùk7 snera a` pfstùk ma` ärad D4 sadp`fid `d buarzd B4, @d prasfùk ajarifmd aqufvd`a d B4 /D47 astd prasfùk sa trdkslfta dtnmns `ns puktns ma` `ìqufmn y ma fcud` bnrld d uk pfstùk ma` ärad D 5. _drd netakarukd buarzd B5, `d ra`difùk ma ärads as D4 0 D5. _nr `n tdktn, inln _4 < _5 aktnkias:
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@d prasfùk dtlnsbærfid as `d prasfù
ajarifmd pnr a` dfra ak iud`qufar pukt
ma d dtlùsbard. Knrld`lakta sa raar
d d prasfùk dtlnsbærfid tarrastra, par
a` tærlfkn as axtaksfe`a d d dtlùsbar
A` fkstrulaktn qua sa utf`fzd pdrd lamfr `d prasfùk ma uk `ìqufmn as a` Ldkùlqua inksfsta ak uk tuen ak bnrld ma Q qua inktfaka `ìqufmn ma maksfmdm () bukifnkdlfaktn sa md, sf ukn ma sus axtralns sa inkaitd ink a` raifpfakta iprasfùk sa masad dvarfcudr.
_N < p + τ . c . h
_rasfùk dtlnsbærfid
A` pasn ma` dfra ajaria prasfùk snera`d suparbfifa tarrastra. D mfbarakifd ma`ns ìqufmns, ns cdsas snk inlprasfe`as
y inln su maksfmdm puama vdrfdr, `dsidpds suparfnras ma d in`ulkd ma dfrainlprflak d `ds läs edjds. _nr astdrdzùk, a` dfra d kfva` ma` ldr as läsmaksn y d lamfmd qua dsiakmalns savd akrdraifakmn hdstd qua sa masvdka-ia d ukd d`turd dprnxfldmd ma =? Gl.
@d idpd edjd trnpnsbard ma 44 Glinktfaka a` 8?% ma` dfra tntd` ma `ddtlnsbard y prasaktd `ds inkmfifnkaskaiasdrfds pdrd `d vfmd. @d prasfùkdtlnsbærfid bua matarlfkdmd pnr a`ifaktìbfin ftd`fdkn Avdkca`fstd ]nrrfia``fak 42=9. Qkd dtlùsbard aqufvd`a d 32?
Ak a` sfcufakta ak`dia akinktrdrä uk `denrdtnrfn vfrtud` ma` prfkifpfn ma
quìlamas:
http://www.ldthsnk`fka.in.ug/knklalears/cdlasrnnl/sfls/drihf/drihf=.ht
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Hfmrnmfkälfid
Aiudifùk ma inktfkufmdm
As a` astumfn ma `ns b`ufmns ak lnvflfaktn. Astalnvflfaktn nrfcfkd uk b`ujn qua as tureu`aktniudkmn `ds pdrtìiu`ds qua inkbnrldk a` b`ufmn,
masirfeak trdyaitnrfds qua sa iruzdk aktra sì ymdk nrfcak d raln`fkns7 y a` b`ujn `dlfkdr iuydspdrtìiu`ds ma` lamfn sa masp`dzdk ink trdyaitnrfdspdrd`a`ds.
_drd a` astumfn ma` lnvflfaktn ma `ns b`ufmns,sa inksfmardk ifartds idrditarìstfids pdrtfiu`dras:d. Yar dlfkdr pdrd qua tnmds ds pdrtìiu`ds ma ukb`ufmn takcdk d lfsld va`nifmdm d` pdsdr pnr ukpuktn matarlfkdmn7 e. Kn vfsinsn pdrd maspra-ifdr a` rnzdlfaktn ink ds pdramas ma` tuen qua ntrdkspnrtd n aktra `ds idpds ma b`ufmns y kn hdydpærmfmd ma akarcìd laiäkfid7 i. Fkinlprasfe`apdrd cdrdktfzdr qua d maksfmdm ma` b`ufmn sa ldk-takcd inkstdkta. _nr astn as flpnrtdkta sapdrdr
a` astumfn ma ns `ìqufmns (qua snk präitfidlaktafkinlprasfe`as), y ma `ns cdsas qua sì sa puamakinlprflfr n axpdkmfr (kaulätfid).
Iudkmn pnr a` fktarfnr ma uk tuen sa luava uk b`ufmn fkinlprasfe`a, `d va`nifmdmas ldynr ak `d lamfmd inln a` mfälatrn ma` tuen sad laknr, y mfslfkufrä ak `dlamfmd inln dulakta su mfälatrn. As maifr, `d ra`difùk aktra `d va`nifmdm mab`ufmn y a` ärad ma `d saiifùk trdksvarsd` ma` tuen snk fkvarsdlakta prnpnrifnkd`as
D4
. v4
< D5
. v5
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@d dp`fidifùk ma `d aiudifùk ma inktfkufmdm sa dpraifd bäif`lakta iudkmn d` zdr ukd ldkcuard y masadlns qua a` ihnrrn takcd uk ldynr d`idkia, nestrupdrifd`lakta `d sd`fmd ma` dcud (mfslfkuflns a` ärad ma `d saiifùk trdksvarsd` mldkcuard), pdrd `ncrdr`n.
]anrald ma Earknu``f
Uaprasaktd `d `ay ma inksarvdifùk ma `d akarcìd laiäkfid ak uk b`ufmn ak llfaktn. A` trdedjn katn aqufvd`a d `d suld ma `d vdrfdifùk ma `d akarcìd ifkæt`d vdrfdifùk ma `d akarcìd pntakifd`.
A` trdedjn as buarzd pnr mfstdkifd, . Ak tærlfkns ma prasfùk aqufvd`a d
Qkd dp`fidifùk ma` tanrald ma Earknu``f as a` dtnlfzdmnr qua pnr mfbarakifdprasfnkas aktra `d pdrta suparfnr ma` tuen y `d suparbfifa ma` `ìqufmn qua inktfaæsta suea y `d inrrfakta ma dfra `n mfsparsd @n lfsln a` tuen n inktdmnr ma Rak
p . D .∂ x < p . ∂R
Astn kns parlfta axprasdr d prasfùk ak tærlfkns ma trdedjn y vdrfdifùk ma vn`u
, inln `d netakalns ma dquì sa netfaka `d bncakard` ma `d aiudifùk ma Earknu``f:
Skatn < ∂ Ai+ ∂ A p
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Yustaktdifùk ma dvfnkas. Maefmn d `d bnrld, hdy vdrfdifùk ak `d va`nif-mdm ma` dfra drrfed y maedjn ma `ds d`ds ma ns dvfnkas, n iud` cakard ukdmfbarakifd ma prasfùk qua nrfcfkd d maknlfkdmd buarzd ma sustaktdifùk.
Yfk aledrcn, a` prfkifpfn ma Earknu``f kn sa dp`fid d astd sftudifùk, ma-efmn d qua ak æ` sa inksfmard a` b`ujn ma b`ufmns fmad`as y inksarvdifùkma d akarcìd maktrn ma` sfstald, `n iud` kn sa iulp`a ak ds inkmfifnkasma vua`n.
@ay ma Hdcak-_nfsauf``a. _drd ukd vfsinsfmdm inkstdkta ak uk b`ujn dlf-kdr fkinlprasfe`a, d tdsd prnlamfn ma b`ujn as fkvarsdlakta prnpnrifnkd`d `d vfsinsfmdm y d `d `nkcftum ma` tuen qua `n trdkspnrtd, y mfraitdlaktaprnpnrifnkd` d `d vdrfdifùk ma prasfùk aktra mns puktns mfbaraktas ma`tuen inkmuitnr y a` rdmfn ma `d saiifùk trdksvarsd` ma` lfsln.
Mnkma mv/mt as `d vdrfdifùk ma vn`ulak ma `ìqufmn qua ifriu`d ak `d ukf-mdm ma tfalpn, v
lamfd as `d va`nifmdm lamfd ma` b`ufmn, r as a` rdmfn ma
`d saiifùk trdksvarsd` fktarkd ma` tuen inkmuitnr, mp as `d vdrfdifùk maprasfùk aktra mns puktns axtralns ma` tuen, γ as d vfsinsfmdm ma` ìqufmny @ `d `nkcftum ma` tuen.
Qkd dp`fidifùk ma `d `ay ma Hdcak-_nfsauf``a as `d halnmfkälfid qua
as `d pdrta ma `d idrmfn`ncìd qua sa akidrcd ma` astumfn dkdtùlfin y buk-ifnkd` ma` inrdzùk, fktrnmuifakmn idtætaras bfkns d trdvæs ma `ds drtarfdsma `d fkc`a n ma` erdzn.
Kaulätfid. As a` astumfn ma` inlpnrtdlfaktn ma ns cdsas, masma a` puktnma vfstd ma `d hfmrnstätfid y ma `d hfmrnmfkälfid.
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Ak suecrupns, rad`fiak ds sfcufaktas axparfakifds. _drd a``n, maeak aar dtaktdla
`ds fkmfidifnkas, inksacufr ns ldtarfd`as y nesarvdr dtaktdlakta n qua niurra,
dsì mdr raspuastd d `ds pracuktds p`dktadmds.
4. Inksfcdk ukd enta``d p`ästfid ink tdpd.
5. Dhnrd, parbnrak `d enta``d hdifækmn`a uk paquaôn huain uk pnin l
dedjn ma `d lftdm.
9. @`akak `d enta``d ink dcud.
=. Nesarvak y masirfedk `n qua niurra.
Iudkmn d enta``d astä tdpdmd: Iudkmn mastdpdk d enta``d:
Ink `d enta``d tdpdmd, hdcdk huaquftns ink uk d`bf`ar.
Masirfedk `n qua nesarvdk:
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3
Ajarififns ma dp`fidifùk
4. ¾Iuä` as a` vn`ulak ma ukd asbard ma hfarrn iuyd ldsd as ma 1 Gc>
Yn`uifùk: pnr d ra`difùk aktra ldsd maksfmdm y vn`ulak, sa puamamatarlfkdr a` vn`ulak ma `d asbard ak iuastfùk.
Inksfcdk uk c`nen (enled), uk vdsn,
ukd va`d y uk p`dtn ink dcud.
Yfcdk asta prniasn:
Masirfedk `n qua niurra:
_rakmdk d va`d 7 d ukd mfstdkifd ma ukns
3 i.l. dprnxfldmdlakta, in`nquak a`vdsn inln sa luastrd ak `d fldcak.
Maspuæs ma ukns 9? sacukmns, vn`taak
a` vdsn y täpak`n ink a` c`nen fkb`dmn,
ajarifækmn`a prasfùk hdifd dedjn. @uacn,
fktrnmuzidk a` c`nen ak a` p`dtn ink dcud. Dhnrd, tnlak uk c`nen y ``ækak`n ma
dcud. @uacn, ìkb`ak`n y diærquak`n d `dva`d akiakmfmd.
Masirfedk `n qua niurra:
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5. ¾Tuæ prasfùk ajaria snera a` pfsn, uk mapnrtfstd ma 11 Gc ma ldsd, iudkmdpnyd snera uk sn`n pfa, sf a` ärad ma `d sua`d ma su zdpdtn as ma 48? il
Yn`uifùk: a` ärad sa axprasd ak l57 48? il5 < ?,?48? l5. Ink `dldsd, matarlfkdlns a` pasn:
φ < l . c < 11 Gc . 6,8 l/s5 < 196 K
9. ¾Iuä` as d prasfùk qua axparflaktd uk mapnrtfstd, d` sularcfrsa ak ukd pfsd ukd prnbukmfmdm ma 9 l>
Yn`uifùk: sa dp`fid a` prfkifpfn ma prasfùk hfmrnstätfid:
_ < τ. c . h < 4.??? Gc/l9 x 6,8 l/s5 x 9l < 56=?? _d
=. Ak ukd praksd hfmräu`fid, a` pfstùk paquaôn tfaka uk rdmfn ma 4,1 il y a`tùk ldynr uk rdmfn ma 55 il. Ya raqufara `avdktdr uk pasn ma =.6?? K, ¾buarzd sa maea ajariar ak a` pfstùk laknr>
Yn`uifùk: pnr d ra`difùk aktra a` tdldôn ma ns pfstnkas, sa puamamatarlfkdr `d buarzd kaiasdrfd pdrd `avdktdr a` pasn ak lakifùk:
D4 < Ϗ . r
4
5 < Ϗ. (?,?41l)5 < Ϗ x 5,51x4?-= l5 < 3 x 4?-= l5
D5 < Ϗ . r
5
5 < Ϗ. (?,55l)5 < Ϗ x =,8=x4?-5 l5 < ?,415 l5
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1. Qkd asbard ma ldmard ma 9? il9 b`ntd ak a` dcud, sf `d maksfmdm as ma ?,6 cil9. Matarlfkdr `d pnrifùk ma vn`ulak qua parldkaia sularcfmn.
Yn`uifùk: sf `d asbard astä b`ntdkmn, sa akiuaktrd ak aquf`ferfny pnr `n tdktn, `d suldtnrfd ma `ds buarzds qua ditúdk as fcud` diarn. As maifr, a` alpuja y a` pasn snk ma fcud` ldckftum, parnma saktfmn inktrdrfn.
Astäk sularcfmns 6/4? ma su vn`ulak tntd`.
2. Ya masad idkd`fzdr uk rìn iuyn idumd` as ma 1 l/s7 aktrd ak uk tuen ink ukrdmfn ma 9 l y d` bfkd` sd`a pnr uk tuen ink uk rdmfn ma ?,8 l. Matarlfkdr `dva`nifmdm ma sd`fmd ma` dcud.
Yn`uifùk:
Dp`fidlns `d aiudifùk ma inktfkufmdm dsì:
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Dutnavd`udifùk
Ak `d sfcufakta tde`d, asirfed `ds ditfvfmdmas quæ läs `a custdrnk d`rad`fzdr`ds, d`cukds sftudifnkas ma dp`fidifùk y ns raiursns kaiasdrfns
pdrd su dp`fidifùk.
Ditfvfmdmas qua `a
custdrnk
Yftudifnkas madp`fidifùk
Uaiursnskaiasdrfns
4.
5.
9.
]dlefæk raspnkmd:
d. ¾Tuæ bua `n läs sfckfbfidtfvn qua dprakmfù ak a` ärad>
e. ¾Tuæ ditfvfmdm bua `d läs masdbfdkta d` masdrrn``dr ukfmdm>
i. Yf tuvfard qua mdr`a d inkniar d su inlukfmdm uk dprakmfzdja
dmqufrfmn ak astd ärad, ¾iuä` asincarìd> ¾_nr quæ>
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_räitfid ma `denrdtnrfn
_rniamflfaktn
4. Matarlfkdr a` kúlarn ma cdkihns i`fps qua sa raqufarak pdrd aquf-`ferdr `d ed`dkzd pdrd idmd ukd ma `ds ldsd qua sa utf`fiak (ukds =).
5. _nkar dcud ak a` vdsn, hdstd ifartn kfva` ma bnrld qua d prflardldsd suspakmfmd dúk ma `d ed`dkzd, sa sularjd inlp`atdlakta.Matarlfkdr ntrd vaz, a` kúlarn ma cdkihns i`fps qua sa raqufarak
Ldtarfd`as
Ed`dkzd (sa puama inkstrufr), vdsn, dcud, d`inhn`, diafta,c`fiarfkd, ldsds ma d`ulfkfn, hfarrn, ldmard y edqua`ftd(puama raalp`dzdrsa `ds ldsds pnr ``dvas inlukas ymfbaraktas), cdkihns i`fp (`d ldsd ma uk cdkihn i`fp asiarid ma ?.?9 c).
3
_räitfid ma hfmrnlaiäkfid
Qkfmdm 1. Hfmrnlaiäkfid Yasfùk
8
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9. Uapatfr a` axparflaktn pdrd `ds ldsds sfcufaktas.
=. Fkfifdr kuavdlakta a` prniasn ink `d ldsd 4, parn idlefdkmn a`dcud pnr d`inhn`, `uacn pnr c`fiarfkd y pnr ú`tfln pnr diafta.
1. Uacfstrdr `ns mdtns ak `d tde`d 4.
2. Yuspakmar mns enleds ma td` bnrld qua quamak d `d lfsld d`turdy sapdrdmds pnr ukd mfstdkifd ma ukns 2 il. Ynp`dr pnr a` aspdifnqua hdy aktra `ds enleds, nesarvdr y inki`ufr.
3. Uapatfr `d axparfakifd dktarfnr, raalp`dzdkmn `ds enleds pnr mnshnjds ma pdpa`.
8. Lamfr ak ukd jarfkcd (sfk dcujd), 1 il9 ma dcud, e`nquadr `d sd`f-md y ajariar prasfùk snera a` ælen`n. Matarlfkdr `d vdrfdifùk mavn`ulak y rapftd a` prniamflfaktn, utf`fzdkmn dfra7 y pnr ú`tfln,``avdr a` ælen`n ma `d jarfkcd d` bnkmn, e`nquadr `d sd`fmd ma` dfray `uacn, fktaktdr masp`dzdr`n hdifd drrfed. Masirfefr quæ niurrfù.
Di aft al Dfra Dcud
4
=
9
5
D` in hn ` C`f iar fk d
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A` dcud kns dyumd ak `d iradifùk ma akarcìd
@ad dtaktdlakta a` sfcufakta taxtn y raspnkmd `ds pracuktds:
A` dcud hd sfmn sfalpra a` raiursn läs flpnrtdkta pdrd `d huldkfmdm,
dmaläs ma sar uk a`alaktn vftd` pdrd a` hnlera, parn ¾iùln `ns rìns y
`dcns sa inkvfartak ak ukd buakta ma akarcìd> A` ifi`n ma` dcud iulp`a
uk pdpa` flpnrtdkta ak d netakifùk ma akarcìd hfmräu`fid: a` sn` avdpnrd
a` dcud y astd sa praifpftd bnrldkmn rìns y dcns pdrd pnmar sar `avdmds d
raprasds mnkma sa cakard akarcìd. Ak `d Aurnpd
dktfcud, mnkma sa utf`fzdedk `ns rìns pdrd hdiar
lnvar `ns ln`fkns, lamfdkta ukd ruamd ink
idkd`as ak su parìlatrn in`nidmd ak a` iduia
ma` dcud pdrd cakardr akarcìd hfmräu`fid y hdiar
lnvar a` ln`fkn, pdrd dsì avftdr utf`fzdr buarzd ma
trdedjn huldkd n dkfld`, asta raiursn ard läsabaitfvn, yd qua sa pnmìd cakardr ukd buarzd
läs crdkma, dmaläs ma qua kn sa pdcded pnr
utf`fzdr`d.
Ditud`lakta sa puamak dprnvaihdr `ns iduias
ma `ns rìns pdrd trdksbnrldr `d akarcìd hfmräu`fid
ak a`æitrfid7 ¾iùln as pnsfe`a astn> @ns rìns snk``avdmns d uk raprasdlfaktn mnkma sa diulu`d
ukd crdk idktfmdm ma dcud7 asta raprasdlfaktn
tfaka uk masdcða qua `avd a` ìqufmn d ukd turefkd cfcdkta. _nr d rdpfmaz
ma` dcud, astd turefkd cfrd7 d` rad`fzdr asta lnvflfaktn ifriu`dr, d turefkd
cakard flpu`sns a`aitrnldckætfins qua snk trdkspnrtdmns d uk trdksbnr-
ldmnr qua racu`d `d akarcìd a`æitrfid
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@d rdzùk ma d utf`fzdifùk ma` dcud as qua cakard ukd buarzd inkstdkta7
as inksfmardmd ukd buakta ma akarcìd raknvde`a läs ainkùlfid y läs
sacurd ma ldkajdr, y dmaläs kn cakard kfkcúk tfpn ma inktdlfkdifùkd` dfra y d` lamfn dlefakta. Dmaläs, sa puama inktrn`dr a` b`ujn ma
a`aitrfifmdm.
D pdrtfr ma `d `aiturd dktarfnr, raspnkmd `ds sfcufaktas pracuktds:
Uad`fia ukd `fstdakulardkmn a`nrmak ma` ifi`nma` dcud y iùlnastd as trdksbnr-ldmd ak akarcìda`æitrfid.
¾_nr quæ a`dcud as `d la- jnr buakta mairadifùk maakarcìd>
¾Tuæ sa raq-ufara pdrd hdiarukd buakta hf-mrna`æitrfid>
¾_nr quæ In-`nlefd as ukpdìs ink `dslajnras ink-mfifnkas pdrd`ds buaktas hf-mrna`æitrfids>
¾ T u æ e a kabfifns tfakukd buakta hmrna`æitrfid>
Nesarva dtaktdlakta `d sfcufakta
fldcak. Yaôd`a y masirfed a` bukifnk-
dlfaktn ma ukd p`dktd hfmrna`æitrfid.
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4. ¾Tuæ mfbarakifd ma prasfùk axparflaktd uk euzn d` masiakmar aka` dcud ma uk `dcn, ma 4 l d 1 l ma prnbukmfmdm>
5. Matarlfkdr a` vn`ulak ma uk iuen ma d`ulfkfn iuyd ldsd as ma 9Gc.
9. ¾Ma quæ ldtarfd` astä inkstrufmn uk iuen, sf su ldsd qua as ma=.68= c niupd uk vn`ulak ma 12? il9>
=. @d bnrld ma ukd puktf``d, ukd tdihua`d, ukd dcujd n uk tnrkf``n knas idprfihnsd7 pnr a` inktrdrfn, iulp`a uk prfkifpfn bìsfin. ¾Iuä`as> Axp`fidr.
1. Ak ukd praksd hfmräu`fid, a` pfstùk y a` ldynr astäk ak prnpnrifùk
4 d 5?, y sa raqufara `avdktdr uk pasn ma 1.??? K, ¾quæ buarzd samaea ajariar ak a` pfstùk laknr>
2. Ma quæ bditnras bìsfins mapakma a` haihn ma qua uk e`nqua maldmard ma 41 c ma ldsd b`nta ak a` dcud, lfaktrds qua uk e`nquama hfarrn ma `d lfsld ldsd sa sularca ak a``d. Axp`fidr.
3. ¾Iuä` as `d maksfmdm ma uk iuen ma ldmard, sf d` sularcfrsa ak uk
raifpfakta qua inktfaka dcud y diafta, `d lftdm sa sularca ak a`dcud y `d ntrd lftdm as iuefartd pnr a` diafta>
Diafta
Dcud
Ldmard
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8. @d saiifùk trdksvarsd` ma uk tuen tfaka uk rdmfn ma 4? il y d` bfkd`sa rdlfbfid ak mns tuens iuyds saiifnkas trdksvarsd`as snk ma 5 y9 il ma rdmfn. ¾Iuä` as `d va`nifmdm ink `d iud` sd`a a` dcud pnr
idmd rdlfbfidifùk>
6. D trdvæs ma uk tuen ma 5? il ma rdmfn, ifriu`d dcud ink ukd va`n-ifmdm ma 1 l/s. ¾Iuä` maea sar a` mfälatrn ma sd`fmd ma` tuen pdrdnetakar ukd va`nifmdm ma` dcud ma 8 l/s>
4?. Qk tdkqua if`ìkmrfin sfk tdpd, ma 5 l ma d`turd, inktfaka 1 l9 madcud. D ukd prnbukmfmdm ma 4,1 l sa hdia uk nrfbfifn pdrd quasd`cd a` dcud. ¾Ink quæ va`nifmdm sd`a>
R5
R9
R4
_rnbukmfmdm
Rn`ulak ma dcud
Dutnavd`udifùk
Uaspnkmd:
d. ¾Iuä`as snk ns dpnrtas läs vd`fnsns ma d prasakta ukfmdm> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
e. ¾Ak quæ ifriukstdkifds puama dp`fidr d`cukns ma `ns ink-iaptns dprakmfmns ak astd ukfmdm> Mæ ajalp`ns.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Idlfkdtds pa`fcrnsds6
D `ns dstrnkdutds `as dcrdmdk `ds idlfkdtdsaspdifd`as. B`ntdkmn sfk pasn d ifaktns ma
gf`ùlatrns snera d ]farrd, ink d supar-bfifa maedjn cfrdkmn d 53.??? gph,kfkcúk vfdjarn aspdifd` qufara qua satarlfka. _arn sù`n sa kaiasftdk mnspd`derds pdrd ldkmdr d ukn ma asns
vd`faktas axp`nrdmnras ma vua`td d sukdva: ‐Arupifnkas sn`dras“.
‐@ds arupifnkas sn`dras snk ds ldyn-ras axp`nsfnkas ma` sfstald sn`dr“, mfia
Uneart @fk ma` @denrdtnrfn ma IfakifdAspdifd` ma `d Qkfvarsfmdm ma Id`fbrnkfd
ak Earga`ay (QI Earga`ay‖s Ypdia Yifakia
@de). ‐Arupifnkdk iarid ma `ds ldkihds sn`drasink `d buarzd ma ifaktns ma lf``nkas ma enleds ma hfmrùcakn“. @ns
dstrnkdutds qua snk snrprakmfmns murdkta ukd idlfkdtd aspdifd` pnr ukd arupifùksn`dr n ukd ma sus prflds, ukd ayaiifùk ma ldsd inrnkd`, puamak desnrear ukdmnsfs ma rdmfdifùk aqufvd`akta d 4?? rdmfncrdbìds ma rdyns X ak a` paihn, rdzùksubfifakta pdrd rabucfdrsa räpfmdlakta.
Id`nr y talpardturd
Qkfmdm 2. ]arlnmfkälfid Yasfùk
6
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@ds arupifnkas sn`dras kn raprasaktdk uk pa`fcrn ld-ynr pdrd ns hdeftdktas ma d ]farrd, yd qua d dtlùsbardma` p`dkatd kns prntaca ma astds lnrtd`as rdmfdifnkas._arn axp`nsfnkas sn`dras flpravfstds sì dbaitdk kuastrds
vfmds. _uamak fkutf`fzdr sdtæ`ftas, mfbfiu`tdr `d kdvacd-ifùk dærad, a fktarrulpfr ds inlukfidifnkas ma rdmfnma d`td braiuakifd murdkta hnrds.
¾Tuæ as n qua masakidmakd ds arupifnkas sn`dras>¾Iùln `feardk tdktd akarcìd tdk räpfmdlakta> ¾V,as pnsfe`a pramaifr iuäkmn niurrfräk>
]d`as pracuktds hdk masinkiartdmn d `ns dstrùknlnsmasma 4816 iudkmn @nrm Idrrfkctnk nesarvù ukdarupifùk sn`dr pnr prflard vaz. ‐Astded Winktdkmnldkihds sn`dras snera ukd fldcak prnyaitdmd ma`Yn`\“, raiuarmd, iudkmn ma rapakta ‐dpdraifarnk mnsldkihds ma uz e`dkid luy fktaksd“ iarid ma uk crupnma ldkihds sn`dras kntde`alakta crdkmas. ‐Ynerasd`-tdmn pnr `d snrprasd“, Idrrfkctnk majù su ta`asinpfn
y sd`fù inrrfakmn d eusidr uk tastfcn7 parn d` vn`varlfkutns läs tdrma `d axp`nsfùk hdeìd masdpdraifmn.
Idrrfkctnk sdeìd qua hdeìd nesarvdmn d`cn aknrla-lakta pnmarnsn, parn `n qua æ` vfn ard sù`n `d puktdma` fiaearc. _drtìiu`ds ma d`td va`nifmdm qua alarcakma `ds arupifnkas alftak prfkifpd`lakta rdyns X y
rdyns cdld ma d`td akarcìd. @d `uz vfsfe`a, ma laknrakarcìd, kn as tdk flpnrtdkta.
V astd as `d rdzùk pnr `d iud` `ds arupifnkas sn`dras hdkpnmfmn cudrmdr sus sairatns pnr tdktn tfalpn. @ds ax-p`nsfnkas snk läs pnmarnsds d `nkcftumas ma nkmd qua`ns nesarvdmnras tarrastras kn puamak var ink sus njns.@ns ta`asinpfns tdlpnin snk idpdias ma var`ds pnrqua
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Dhnrd, uk kuavn sdtæ`fta ma d KDYD pratakmasupardr asta prne`ald. A` Crdbfidmnr Aspai-trnsiùpfin Yn`dr ma D`td Akarcìd, n HAYYFpnr sus sfc`ds ak fkc`æs (Hfch Akarcy Yn`drYpaitrnsinpfi Fldcar), `dkzdmn ak baerarn 1,5??5, astä nreftdkmn `d ]farrd d idsf 2?? glpnr akifld ma d npdid dtlùsbard ma kuastrnp`dkatd, mnkma puama mataitdr alfsfnkas mardyns X y rdyns cdld prnmuifmds pnr ds arup-ifnkas sn`dras. HAYYF kn as `d prflard kdvaaspdifd` idpdz ma mataitdr td` rdmfdifùk. _arn sarä `d prflard ak idpturdr fläcakaskìtfmds ma rdyns X y rdyns cdld prnvakfaktas ma `ds vfn`aktds axp`nsfnkas.
_drd takar ukd lajnr fmad ma astds idktfmdmas, inksfmara `n sfcufakta: Iudkmn ukdarupifùk sn`dr alarca, id`faktd ukd racfùk ma `d dtlùsbard ma` Yn` ma uk tdldônaqufvd`akta d vdrfds vaias a` mfälatrn ma `d ]farrd, astn as snrprakmakta pnrqua`ns rdyns X y cdld ma d`td akarcìd kn puamak sar akbnidmns7 dtrdvfasdk `ds `aktasinkvakifnkd`as inln sf buardk vfmrfns inlukas. Yfk aledrcn, HAYYF inlpnka `dsfläcakas nesarvdkmn d` Yn` d trdvæs ma tde`f``ds bfkdlakta aspdifdmds ’inln sf buardukd parsfdkd vakaifdkd lfirnsiùpfid’ qua prnmuia snlerds snera mataitnras ma
rdmfdifùk d enrmn ma `d kdva. ‐Untdralns `d kdva idmd = sacukmns pdrd iradr ukpdtrùk ma lnmu`difùk d pdrtfr ma `ds snlerds qua pnmalns dkd`fzdr pdrd netakarukd fldcak ma` Yn`“, axp`fid @fk. A` prniasn as sflf`dr d ukd rdmfncrdbìd ma rdyns Xaxiaptn qua `ns ifaktìbfins astäk fktarasdmns ak `d buakta ma `ns rdyns (a` Yn`), y knak a` ldtarfd` qua `ns e`nquad (`ds tde`f``ds).
@ns masiuerflfaktns ma HAYYF pnmräk tdlefæk asi`draiar d`cukns dinktaiflfaktns
lfstarfnsns qua niurrak luy `ajns ma kuastrn sfstald sn`dr. ‐@n qua sad qua nrf-cfkd `ds arupifnkas sn`dras, pnmrìd sar a` lfsln laidkfsln qua drrnjd ihnrrns mapdrtìiu`ds masma `ns mfsins ma diraifùk ldckatfzdmns ma dcujarns kacrns y astra``dsma kautrnkas“, mfia Makkfs. ‐A` Yn` astä ra`dtfvdlakta iarid, pnr n qua as uk euak`denrdtnrfn pdrd astumfdr astns axùtfins prniasns“. Lfaktrds tdktn, `d ldynrìd ma`ns dstrnkdutds astdräk sdtfsbaihns ink `d talprdkd pramfiifùk ma `ds arupifnkassn`dras inlukas y inrrfaktas7 uk eakabfifn fkmfraitn ma `d lfsfùk HAYYF. Yf `d kdvaaspdifd` puama iulp`fr sù`n asta nejatfvn, a` aspdifn sa inkvartfrä ak uk `ucdr läs
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Id`nr: as ukd bnrld ma akarcìd qua sa trdks-bfara ma ukns iuarpns d ntrns. ]faka qua varink `d akarcìd ifkætfid ma `ds ln`æiu`ds quainkbnrldk ukd sustdkifd.
Lamfmd ma` id`nr: ak a` YF (LGY) as a` Ju`fn.Kn nestdkta, axfsta ntrd ukfmdm ma id`nr utf-`fzdmd braiuaktalakta qua sa ``dld id`nrìd y
as `d idktfmdm ma id`nr kaiasdrfd qua sa maeatrdksbarfr d uk crdln ma dcud pdrd qua dulaktasu talpardturd ak uk crdmn iaktìcrdmn.
4 id`nrìd aqufvd`a d =,482 J.
Astd idktfmdm as luy fkinkvakfakta pnr `n paquaôd pdrd qufakas sa pra-niupdk pnr su pasn, y aktnkias sa usd a` tærlfkn gf`nid`nrìd (4.??? id-`nrìds). Qkd hdleurcuasd pnr ajalp`n: inktfaka ak prnlamfn 99? Gid`y dinlpdôdmd ma ukd iarvazd (43? Gid`), prnpnrifnkddprnxfldmdlakta mns lf``nkas ma ju`fns.
Id`nr aspaiìbfin: as `d idktfmdm ma id`nr kaiasdrfd pdrdqua uk crdln ma ukd sustdkifd dulakta su talpardturdak uk crdmn iaktìcrdmn.
Id`nr
@ds knifnkas ma id`fakta y brìn astäk luy `fcdmds d kuastrd pariapifùk saksn Dsì, `ns tærlfkns ma id`nr y talpardturd hdiak pdrta ma` `akcudja utf`fzdmn fktarpratdr a` inlpnrtdlfaktn ma sfstalds tdk mfvarsns inln d dtlùsbard, ns svfvns y `ds astra``ds.
Bukmdlaktn taùrfin
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Rfmrfn
_`nln
D`ulfkfn
Inera
Hfarrn
Ldmard (vd`nr prnlamfn)
Iuarpn Huldkn (vd`nr prnlamfn)
Hfa`n
Dcud
Lariurfn
?,5
?,?94
?,5?
?,4?
?,4?
?,=?4
N,8=
?,1?
4
?,?99
YustdkifdId`nr aspaiìbfin
Id`/c.ºI
]alpardturd
As d lamfmd ma `d akarcìd ifkætfid lamfd, ma ds ln`æiu`ds qua inkstftuyak uk iuarpn
Lamfmd ma `d talpardturd: sa utf`fzdk tras asid`ds mfbaraktas:
• Asid`d Iaktìcrdmd: matarlfkd `ns vd`nras ma iarn y ifak crdmnspdrd ns puktns ma busfùk y aeu``fifùk ma` dcud, raspaitfvdlakta.
• Asid`d Bdhrakhaft: matarlfkd inln 95 y 545, `ns vd`nras pdrd`ns puktns ma busfùk y aeu``fifùk ma` dcud, raspaitfvdlakta.
• Asid`d Ga`vfk: ak a``d sa bfjd a` vd`nr iarn inrraspnkmfakta d `dtalpardturd läs edjd (iarn desn`utn), ma` astdmn ak a` iud` `dsln`æiu`ds qua inkbnrldk uk iuarpn sa akiuaktrdk ak rapnsndesn`utn y aqufvd`a d -539 cdmns iaktìcrdmns.
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Ua`difùk aktra asid`dsma talpardturd:
ºI ºB ºG
4?? 545 939
? 95 539
-43,38 ? 511,55
-539 -=16,= ?
Inkvarsfùk ma Ia`sfus d Bdhrakhaft:
Inkvarsfùk ma Bdhrakhaft d Ia`sfus:
Inkvarsfùk ma Ia`sfus d Ga`vfk: ] G < ]
I + 539
Inkvarsfùk ma Ga`vfk d Ia`sfus: ] I < ]
G - 539
Mf`dtdifùk tærlfid
Iudkmn uk iuarpn n ukd sustdkifd subrak ukd a`avdifùk ak su talpardturd,parflaktdk ukd vdrfdifùk ak su `nkcftum, ärad y vn`ulak, pnr `n iud` as kaiasmfbarakifdr`ds.
Mf`dtdifùk `fkad`: inrraspnkma d `d vdrfdifùk ak `d `nkcftum qua axparflaktd vdrf``d n ukd edrrd d` dulaktdr su talpardturd:
` < `f x (4 + δ x ∂])
` as `d `nkcftum kd`, ` f as `d `nkcftum fkfifd`, δ as a` inaifakta ma
mf`dtdifщk fkad`, ∂] as `d vdrfdifщk ma talpardturd.
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Inabfifakta ma mf`dtdifùk `fkad` δ (ºI)’4
5= x 4?-2
45 x 4?-2
4= x 4?-2
?,= x 4?-2
56 x 4?-2
5? x 4?-2
= x 4?-2
52 x 4?-2
6 x 4?-2
9,5 x 4?-2
Yustdkifd
D`ulfkfn
Diarn
Inera
Iudrzn
_`nln
@dtùk
]ukcstakn
Ifki
Rfmrfn inlúk
Rfmrfn _yrax
Mf`dtdifùk suparbfifd`: as d vdrfdifùk ak a` ärad dtard` qua axparflaktd uk iuarpny qua sa va rab`ajdmd ak a` dulaktn ma `d `nkcftum ma sus drfstds.
Mf`dtdifùk vn`ulætrfid: d` vdrfdr d nkcftum, uk iuarpn axparflaktd ukd vdrfdifùkak su vn`ulak bfkd`:
R < R f x (4 + ε x ∂])
R as a` vn`ulak kd`, R f as a` vn`ulak fkfifd`, ε as a` inaifakta ma
mf`dtdifщk vn`ulжtrfid.
D < Df x (4 + 5δ x ∂])
D as a`vd`nr ma` дrad kd`, Df as a` vd`nr ma` дrad fkfifd`,
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_nr `n cakard`, `d ldtarfd puama axfstfr ak astdmn n bdsa sù`fmd, `ìqufmd n cdsaYfk aledrcn, sa inksfmardk ntrds bdsas inln a` p`dsld y `ns suparinkmuitnras
Idmd idlefn ma astdmn n ma bdsa, raifea uk knlera pdrtfiu`dr dsì:
• Yù`fmn d `ìqufmn: busfùk• @ìqufmn d cds: vdpnrfzdifùk• Cds d sù`fmn: sue`fldifùk• Yù`fmn d cds: sue`fldifùk ravarsdmd• Cds d `ìqufmn: `fiuabdiifùk• @ìqufmn d sù`fmn: sn`fmfbfidifùk
Idlefns ma astdmn
@ns idlefns ma astdmn ak `d ldtarfd, vdk dinlpdôdmns ma desnrifùmasprakmflfaktn ma id`nr sfk qua axfstd vdrfdifùk ak `d talpardturd, pnrqua qua `ds ln`æiu`ds sa sapdrak n sa d`ajak ukds ma ntrds, sa raqufara rad`fzdrtrdedjn ak inktrd ma `ds buarzds ma dtrdiifùk y ak inksaiuakifd, `d akarcìd qu`a sulfkfstrd pnr diifùk ma` id`nr sa fkvfarta ak mfihn trdedjn.
4,85 x 4?-=Lariurfn
Inabifakta ma mf`dtdifùk vn`ulætrfid (ºI)’4Yustdkifd
C`fiarfkd =,81 x 4?-=
D`inhn` atì`fin
Cdsn`fkd Dcud
3,=1 x 4?-=
6,1 x 4?-=
5,4 x 4?-=
Iudkmn uk iuarpn idlefd ma bdsa, sa raqufarasulfkfstrdr`a ukd ifartd idktfmdm ma id`nr pnr
ukfmdm ma ldsd, `d iud` as pdrtfiu`dr pdrd idmdsustdkifd y sa maknlfkd id`nr `dtakta.
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]arlnmfkälfid
As a` astumfn matd``dmn ma `d trdksbarakifd ma id`nr, as maifr, astumfd `ds ra`difnkasaktra `ds mfbaraktas prnpfamdmas ma `d ldtarfd fkharaktas d `ns idlefns ma `d tal-
pardturd. _drd su lajnr inlpraksfùk, sa raqufara inkniar ntrns inkiaptns:
Yfstald: flp`fid ìlftas rad`as n fldcfkdrfns ma mnkma astä inktakfmd ukdidktfmdm mabfkfmd ma ldtarfd. _nr ajalp`n: `d idktfmdm ma dfra inktakfmnak ukd jarfkcd, tfaka `ìlftas rad`as parn d` hde`dr ma 5 il9 ma dfra ak ukaspdifn defartn, sus brnktards snk fldcfkdrfds. Yf a` sfstald kn fktaridlefd
akarcìd ink a` axtarfnr, sa `a ``dld sfstald dfs`dmn.
Astdmn ma uk sfstald: aqufvd`a d` aquf`ferfn tarlnmfkälfin ma` sfstald,matarlfkdmn pnr vd`nras ma vn`ulak, prasfùk, talpardturd y idktfmdmma ldtarfd (vdrfde`as ma` sfstald). _nr ajalp`n: iudkmn sa akiuaktrd akaquf`ferfn laiäkfin, tærlfin y quìlfin. _drd matarlfkdr a` aqufvd`akta
laiäkfin ma` id`nr, Jdlas Jnu`a utf`fzù uk sfstald ma pd`atds (qua cfrdedkpnr diifùk ma d`cukds pasds suspakmfmds), sularcfmds ak ukd ldsd inknifmdma dcud, maktrn ma uk raifpfakta dfs`dmn tærlfidlakta. D` idar `ds pasds,pfarmak akarcìd pntakifd` qua sa trdksbnrld ak id`nr, maefmn d` lnvflfaktnma `ds pd`atds maktrn ma` dcud, nrfcfkdmd pnr `d buarzd ma brfiifùk. Ak astdbnrld, malnstrù axparflaktd`lakta d aqufvd`akifd aktra id`nrìds y ju`fns.
4 id`nrмd < =,482 J
_rniasns: puamak sar ravarsfe`as (cdsas fmad`as), n frravarsfe`as (prniasnstarlnmfkälfins rad`as), y inrraspnkmak d trdksbnrldifnkas n idlefns maastdmn. _nr inksfcufakta, hdy vdrfdifùk ak `ns vd`nras ma `ds vdrfde`as qua`n matarlfkdk.
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_
_5
R4 R5 R
_
_5
_4
R4 R
_rflard ay ma d tarlnmfkälfid: masirfea d ra`difùk aktra a` trdedjn,id`nr y `d akarcìd fktarkd ma uk sfstald y axprasd qua ‐a` id`nr desnrefmpnr uk sfstald as fcud` d` trdedjn rad`fzdmn pnr a` sfstald läs a` dulak
ma `d akarcìd fktarkd“:
T < S + ∂Q
Mnkma T as a` id`nr desnrefmn, S a` trdedjn rad`fzdmn y ∂Q as d vdrfdifùma `d akarcìd fktarkd ma` sfstald.
D`cukns prniasns sa dp`fidk bukifnkd`lakta d `d prflard `ay (cdsfmad`as):
• _rniasn fsneärfin: sa rad-`fzd d prasfùk inkstdkta y a`trdedjn rad`fzdmn as mfbarak-ta ma iarn.
T < _(R b - R
f ) + ∂Q
• _rniasn fsùinrn n fsnvn-`ulætrfin: sa inksfmard a`vn`ulak inkstdkta, a` trded-
jn rad`fzdmn as fcud` d iarny a` id`nr qua sa sulfkfstrdd` sfstald as utf`fzdmn pdrddulaktdr su akarcìd fktarkd.
S < ? 7 Q 5 - Q
4< ∂Q< T
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• _rniasn fsntærlfin: sa rad-`fzd d talpardturd inkstdktay kn hdy vdrfdifùk ma akarcìd
fktarkd.
T < S
Asta prniasn tfaka ukd axiap-ifùk iudkmn sa inksfmard ukcds fmad`.
• _rniasn dmfdeätfin: sa pra-saktd iudkmn kn hdy fktaridl-efn ma id`nr aktra a` sfstald ya` lamfn, a` sfstald kn cdkd kfpfarma id`nr y ak inksaiuak-ifd, a` trdedjn rad`fzdmn snera
a` sfstald inrraspnkma d `dvdrfdifùk ma d akarcìd fktarkdma` lfsln.
Q 5 - Q
4< ∂Q < - S
Yacukmd ay ma d tarlnmfkälfid. Ak prflar ucdr, sa puama dbfrldr quaa` id`nr b`uya aspnktäkadlakta ma uk bnin läs id`fakta d ntrn laknsid`fakta y kn d` inktrdrfn. _nr ajalp`n: iudkmn latalns ak a` inkca`dmnruk vdsn ma jucn pdrd inkvartfr`n ak ha`dmn, æsta kn desnrea id`nr sfknqua pnr a` inktrdrfn, `n iama d` dfra lakns id`fakta qua astä maktrn ma`inkca`dmnr hdstd d`idkzdr a` maknlfkdmn aquf`ferfn tærlfin. As maifr,mns sustdkifds d`idkzdk `d talpardturd ma aquf`ferfn tærlfin iudkmn `d
_
_
R
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läs id`fakta iamfù tdktn id`nr d `d lakns id`fakta qua dhnrd, `ds mns saakiuaktrdk d `d lfsld talpardturd. @n dktarfnr mapakma ma `d idktfmdmma ldsd, a` id`nr aspaiìbfin y `d vdrfdifùk ma talpardturd ma idmd ukd.
Id`nr desnrefmn (T) < Id`nr iamfmn (-T)
l4 x a
4(t
4b-t
4f ) < - l
5 x a
5(t
5b-t
5f )
Astd trdksbarakifd ma id`nr sa puama mdr pnr inkmuiifùk ak ldtarfd`assù`fmns. _nr ajalp`n: d` id`aktdrsa ukd edrrd ma hfarrn, a` id`nr sa vdtrdkslftfakmn prncrasfvdlakta d trdvæs ma tnmd su `nkcftum, sfk trdks-pnrtdr ldtarfd. _nr astd rdzùk, uk axtraln puama astdr id`fakta y a` ntrnd laknr talpardturd. _nr inkvaiifùk iudkmn a` id`nr sa prnpdcd ma uk`ucdr d ntrn d` trdkspnrtdrsa `d ldsd id`fakta. _nr ajalp`n: d` id`aktdrsa,a` dfra suea y a` dfra lakns id`fakta edjd y mdk nrfcak d `d bnrldifùk ma
inrrfaktas ma dfra (`ns vfaktns). V pnr rdmfdifùk iudkmn kn hdy inktditnaktra ds sustdkifds, parn sa md pnr d alfsfùk ma id`nr ak bnrld ma nkmdsa`aitrnldckætfids. _nr ajalp`n: a` id`nr qua raifeflns ma `d `uz ma` Yn`.
Ak sacukmn `ucdr, sa dbfrld qua: ‐Ak uk prniasn iìi`fin, (ifi`n tærlfin)iuyn úkfin rasu`tdmn sad `d desnrifùk ma id`nr ma uk bnin, `d akarcìdid`nrìbfid kn puama trdksbnrldrsa tntd`lakta ak trdedjn laiäkfin“ (Ga`-vfk-_`dkig). _nr ajalp`n: ak `ns vahìiu`ns hdy id`aktdlfaktn ma` lntnr
pnr diifùk ma `d inleustfùk ma `d cdsn`fkd. D` hdiar qua `ns pfstnkas samasp`diak pdrd netakar uk rakmflfaktn n bukifnkd`fmdm ma` 4??%, a`id`nr iamfmn maearä sar fcud` d iarn, parn astn as rad`lakta flpnsfe`a.
Ak tariar ucdr, sa dbfrld qua as flpnsfe`a inkstrufr ukd ldqufkd bukifn-kd` ma lnvflfaktn parpatun, pnrqua `d bukifnkd`fmdm ma ukd läqufkdkukid puama sar ùptfld, d` 4??%.
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Aktrnpìd
Ya inksfmard inln a` crdmn ma masnrmak ma uk sfstald. En`tzldkk dbfrld qua asak rad`fmdm ukd lamfmd ma` masnrmak ma` Qkfvarsn. _nr ajalp`n: ukd iarf``d tfaka
ifartn nrmak (n masnrmak), ln`aiu`dr, y d` drmar idlefd a` nrmak (dulaktd a` masnr-mak). _nr `n tdktn, `d aktrnpìd dulaktd y `d akarcìd inkiaktrdmd sa mfsalfkd dhnrdink ukfbnrlfmdm. Ak inksaiuakifd, ‐ak tnmn sfstald qua sa inksfmard nrmakdmnsfalpra axfstfrä uk crdmn ma masnrmak“. Ak d vfmd präitfid, pnmalns kntdr qua idmdukn ma knsntrns utf`fzd uk ifartn nrmak pdrd tnldr kuastrns dpuktas, pdrd nrcdkfzdrkuastrns `ferns, kuastrd rnpd7 parn sf d`cufak `n nesarvd, puama dbfrldr qua pdrd æhdy masnrmak, as maifr, as uk inkiaptn ra`dtfvn.
]ariard ay ma d tarlnmfkälfid: as flpnsfe`a d`idkzdr axparflaktd`lak-ta a` iarn desn`utn, as maifr, kfkcukd sustdkifd, edjn kfkcukd inkmfifùk,puama ``acdr d takar ukd talpardturd inrraspnkmfakta d` iarn desn`utn,pnrqua astn flp`fidrìd qua d akarcìd ifkætfid ma sus ln`æiu`ds buard iarn.Yfalpra axfstfrä lnvflfaktn ln`aiu`dr, pnr lìkfln qua sad.
(aktrnpìd)
]
]4
]5
Y4 Y5 Y
Läqufkd ma Idrknt: a` fkcakfa-rn brdkiæs Ydmf Idrknt, astumfùa` `ìlfta ma abfifakifd ma ukdläqufkd ma id`nr iìi`fid y mas-iuerfù qua `d läqufkd desnreaid`nr ma uk mapùsftn ma d`td tal-pardturd y maspfma id`nr hdifd
uk mapùsftn ma edjd talpardtu-rd. _nr asta lntfvn, ns inksfmarùprniasns tærlfins ravarsfe`as ya` ifi`n `n inlp`atd uk prniasndmfdeätfin ravarsfe`a:
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6
Ajarififns ma dp`fidifùk
4. A` puktn ma busfùk ma` hfarrn as ma 4.192ºI. Axprasdr `d talpardturd akºG.
Yn`uifùk: pnr `d ra`difùk aktra asid`ds, pnmalns inkvartfr ºI d ºB, y ºId ºG.
] G < ]
I + 539 < 4192 nI + 539 < 48?6 G
5. ¾Tuæ idktfmdm ma id`nr sa `a maea dcracdr d 4 `ftrn ma dcud qua sa akiuafkfifd`lakta d 5?ºI pdrd qua `acua d` puktn ma aeu``fifùk (4??ºI), sf d praas ma 4 dtlùsbard>
Yn`uifùk: 4 `ftrn ma dcud aqufvd`a d 4.??? il9 y inrraspnkma d ukdldsd ma 4.??? c:
T < ld xδ
d x∂] < 4.???c x4id`/cnI(4.???nI - 5?nI) <
4.??? x4 x8? < 8?.??? < 99=88? J
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9. Yf a` prniasn bìsfin dktarfnr sa rad`fzd ak uk raifpfakta iarrdmn, ¾iuä` sarä `dprasfùk bfkd`>
Yn`uifùk:
_nr `d `ay ma `ns cdsas fmad`as, sa puama matarlfkdr `d prasfùk bfkd`:
=. Ya lazi`dk 9? c ma dcud d 1?ºI ink 1? c ma d`inhn` d 8?ºI. Matarlfkdr avd`nr ma `d talpardturd pdrd `ncrdr a` aquf`ferfn tærlfin.
Yn`uifùk:
l4 x a
4(]
b-]
4f) < - l
5 x a
5(]
b-]
5f)
9?c x 4 id`/c nI (]
b-1?nI) < - 1?c x ?,1?1 id`/c nI
(]
b-8?nI)
] b
< 29,34nI
Dutnavd`udifùk
Asirfed `d ldkard inln `ncrù inlprakmar `ns talds masdrrn``dmns ak `dprasakta ukfmdm. Qtf`fia `d sfcufakta tde`d:
Lf prniasn ma dprakmfzdja
Ditfvfmdmas ma dprakmfzdja qua masdrrn``æ Dprakmfzdjas
DitfvfmdmLa
custùKn lacustù
Luymfbìif`
Mfbìif` Bäif` Dprakmì
d`cn kuavnAstn yd `n
sdeìd
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8
_räitfid ma id`nr y talpardturd
Qkfmdm 2. ]arlnmfkälfid Yasfùk
4?
_rniamflfaktn
Ldtarfd`as
Laiharn, vdsn ma praifpftdmn, dcud, tfkturd, edrrdma hfarrn ma 45 il, raifpfakta ma finpnr ink tdpd,tarlùlatrn, ed`ùk ma 1?? il9, tdpùk, tuen ma vfmrfny ed`dkzd.
_räitfid ma `denrdtnrfn
4. Inkstrufr ukd idjd ma pdpa`, dcracdr`a dcud y axpnkar`d d` buacn.Nesarvdr, axp`fidr y inki`ufr.
5. ]nldr uk idea``n y axpnkar`n d` buacn. ]nldr ntrn idea``n,akrn``dr`n snera uk trnzn ma latd` y axpnkar`n tdlefæk d` buacn.
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@ds sfcufaktas pdrdmnjds buarnk tnldmds ma` `fern _drdmnjds ma
Ä`vdrn Derf`, mfraitnr ma` aqufpn ma fkvastfcdifùk ma `d ‐tfakmd
taikn`ùcfid“. As rainlakmde`a qua a` ajarififn sad malnstrdtfvn
(rad`fzdmn pnr a` prnbasnr ink dyumd ma d`cukns astumfdktas).
9. Ak a` vdsn ma praifpftdmn, matarlfkdr d talpardturddlefakta ma 5?? il9 ma dcud.
=. Dmfifnkdr hfa`n y lamfr kuavdlakta d talpardturd
1. _nkar d` buacn y matarlfkdr ns vd`nras ma talpardturd idmd ^^^^ sacukmns hdstd ``acdr d` puktn ma aeu``fifùk ^^^^^^^
2. Id`aktdr murdkta 1 lfkutns, ukn ma `ns axtralns ma `d edrrd mahfarrn. ]rdksiurrfmn a` tfalpn, ¾`d talpardturd ma ns mns axtralns
as fcud`> Axp`fidr.
3. Matarlfkdr `d talpardturd ma 4?? il9 ma dcud ak inkmfifnkas
knrld`as. Fktrnmuifr `d edrrd ma hfarrn, lamfr `d talpardturd ak
asa fkstdkta y `uacn ma 4 lfkutn, inki`ufr y axp`fidr.
8. Ak a` raifpfakta ma finpnr, pnkar 1? il9 ma dcud d talpardturd
dlefakta y 8? il9 ma dcud d 31ºI. ]dpdr a` raifpfakta, dcftdr`n
sudvalakta y d inktfkudifùk, lamfr `d talpardturd bfkd` ma `d
lazi`d. Rn`var d tdpdr a` raifpfakta, majdr`n ak rapnsn pnr 1 lfkutns
y vn`var d lamfr `d talpardturd. Inki`ufr y axp`fidr `n nesarvdmn.
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6. Ak uk ed`ùk ma 1?? l` pnkard harvfr 5?? l` ma dcud.Iudkmn ``acua d` puktn ma
aeu``fifùk, ratfrdr ma` buacny räpfmdlakta tdpdr a` ed`ùkink uk tdpùk ma iduihn,ma td` bnrld qua a` vdpnrkn puamd asidpdr. Fkvartfra` ed`ùk, in`nidr`n snera a`drn, dmfifnkdr dcud id`fakta
snera a` ed`ùk7 `uacn dcudd talpardturd dlefakta ypnr ú`tfln, dcud ink hfa`n.Nesarvdr `n niurrfmn ak `nstras idsns, axp`fidr y inki`ufr.
Dkä`fsfs ma rasu`tdmns
D pdrtfr ma d nesarvdifùk matd``dmd, a` dkä`fsfs ma inktakfmns y ns prniasnsrad`fzdmns, matarlfkdr `d axp`fidifùk bìsfid pdrd idmd avaktn astumfdmn.
4?. _rapdrdr ukd iueatd ink subfifakta idktfmdm ma dcud d talpardturddlefakta, dcracdr`a `d tfkturd y majdr`d ak a` pfsn. D uk tdpùkma iduihn ink nrfbfifn iaktrd`, in`nidr`a a` tuen ma vfmrfn madprnxfldmdlakta 4 l ma nkcftum. D inktfkudifùk, pnkar d harvfrak a` ed`ùk kuavdlakta, 5?? l` ma dcud7 iudkmn ``acua d` puktnma aeu``fifùk, tdpdr`n ink a` tdpùk ma iduihn7 tdpdr a` axtraln`fera ma` tuen, fkvartfr a` ed`ùk ma td` bnrld qua a` axtraln ma`tuen quama maktrn ma` dcud ink tfkturd. Nesarvdr `n qua niurray axp`fidr.
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@ < 51 il
4. Qkd `älfkd iudmrdmd ma diarntfaka 51 il ma `dmn, su talpard-turd fkfifd` as ma 5?ºI y sa id`faktdhdstd ukd talpardturd ma 6?ºI,¾iuä` bua `d vdrfdifùk ak su ärad>
5. Fkfifd`lakta, d 1? il9 ma c`fiarfkd d 5?ºI sa a dmfifnkd id`nr hdstd
d`idkzdr ns 3?ºI, ¾axfstfrä vdrfdifùk ak su vn`ulak> Yf as dsì, ¾iuä`as su vn`ulak bfkd`>
9. Inlp`ata `d sfcufakta tde`d:
ºI
4?
ºG
4?
ºI
45?
ºB
4?
ºB
45?
ºG
45?
Kn.
4
5
9
Kn.
=
1
2
=. Matarlfkdr `d talpardturd pdrd a` aquf`ferfn tærlfin, iudkmn sa
lazi`dk 2? l` ma dcud d 5?ºI ink =1 c ma hfarrn d 81ºI.
1. Yf sa pnkak ak inktditn mns edrrds ma latd`as ma diarn y inera, a`prflarn ink ukd ldsd ma 31 c d =8ºI y a` sacukmn, ink ukd ldsd
ma 6? c y talpardturd ma 62ºI, ¾iuä` as a` vd`nr ma d talpardturd
bfkd` (aquf`ferfn tærlfin)>
2. @ds atfquatds ma d`cukns d`flaktns trdak `d tde`d kutrfifnkd` y a`
vd`nr akarcætfin ak id`nrìds Ya`aiifnkdr pnr `n lakns iudtrn
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3. Yf uk pamdzn ma ldmard y ukd puktf``d astäk d 41ºI, d` tnidr`ns a` lapdraia läs brìn, parn sf sa id`faktdk hdstd d`idkzdr ukd talpardturd m1?ºI, aktnkias a` latd` pdraiarä läs id`fakta, ¾pnr quæ>
8. Yf quaralns inksarvdr kuastrd eaefmd id`fakta murdkta uk euak dps
`n lajnr as utf`fzdr uk tarln pnrqua ak uk raifpfakta ma vfmrfn n mp`ästfin y dúk ma finpnr, sa akbrìd räpfmdlakta. ¾Iuä` as a` prfkifpma bukifnkdlfaktn ma` tarln>
Avd`udifùk
¾Tuæ dprakmfù ink `d ditfvfmdm>Rd`nrdr a` trdedjn rad`fzdmn, `d prasaktdifùk y masdrrn``n ma `d cuìd, `d dp`fid`fmdm ma `d `aiturd, y ma sar pnsfe`a, prnpnkar lnmfbfidifnkas pdrd lajnrdrnetakifùk ma `ns `ncrns prnpuastns.
Axp`fidr `d flpnrtdkifd y dp`fidifnkas ma `ns talds trdtdmns ak `d cuìd, pdsn`uifnkdr sftudifnkas bìsfids rad`as ma `d vfmd mfdrfd.
Inki`usfnkas
Dutnavd`udifùk
Rd`nra sus dprakmfzdjas. _drd a``n, ldrqua ink ukd X a` pnriaktdja qua astfldmaiudmn:
Idtacnrìd _racuktd ?% 5?% =?% 2?% 8?% 4??%
Iulp`flfaktn y
raspnksdef`fmdm
¾Iulp`fù ink `ds `aiturdsdsfckdmds, `ds ditfvfmdmasmasdrrn``dmds ak i`dsa y `d
aktracd ma tdrads y trdedjnsfkmfvfmud`as n pnr aqufpn>
Iradtfvfmdm yid`fmdm
¾Dpnrtù fmads> ¾Astds buarnksfckfbfidtfvds>
¾Uad fzù sfk arrnr d`cukn ds tdr-ads y/n ns trdedjns dsfckdmns>
Dprakmfzdja ydpnrtdifùk ma
¾Tuæ tdktn dprakmfù y quætdktns inkniflfaktns dpnrtùak `ds i`dsas, ak `ds tdrads y/n
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Efe`fncrdbìd
DEUF@, Ä`vdrn. _drdmnjds. Ydktdbæ ma Encntä: ]fakmd taikn`ùcfid, 4666.
DYFLNR, Fsddi. Lnlaktns asta`dras ma `d ifakifd. Edria`nkd: Yd`vdt,468=.
EDUKA]], Udylnkm y QUFEA, Ju`fn. Ä`caerd y canlatrìd 5. Ydktdbæ maEncntä: Li Crdw Hf``, 4662.
EDQ]FY]D, Ldurfifn, CDUIÌD, Amwfk y IDUUF@@N, Astaedk. Bìsfid F.Encntä: Ydktf``dkd, 5??4.
SF@YNK, Jarry, EQBBD, Dkthnky y EN, @nu. Bìsfid. 2 am. Kduid`pdkma Juäraz: _adrsnk, _raktfia Hd``, 5??3.
HAIH], Aucaka. Bìsfid ak parspaitfvd. Læxfin: Dmmfsnk Sas`ay@nkcldk, 4661.
HASF]], _du`. Bìsfid inkiaptud`. 4? am. Læxfin: _adrsnk DmmfsnkSas`ay, 5??3.
RD@AUN, Lfiha`. Bìsfid Bukmdlaktd` 4. Ydktdbæ ma Encntä: Knrld,4666.
RF@@ACDY, Ldurfifn. Cd`dxfd bìsfid 4?. Ydktdbæ ma Encntä: Rn`uktdm,4666.
RF@@ACDY, Ldurfifn. Cd`dxfd bìsfid 44. Ydktdbæ ma Encntä: Rn`uktdm,4666.
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Lùmu`n fktacrdmn pdrd ifi`n 1
]rdksbnrlalns Amuidkmn
Ldtalätfids 4?
Huasftn, Cudfkìd
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Astäkmdras eäsfins ma inlpatakifds ak Ldtalätfids
Aja drtfiu`dmnr prfkifpd`
_aksdlfaktn vdrfdifnkd`
y sfstalds d`caerdfins ydkd`ìtfins
Inharakifd hnrfznktd` ma paksdlfaktns
y sfstalds ldtalätfins
Dpnyd d` paksdlfaktn vdrfdifnkd` ak…
@d fmaktfbfidifùk ak bnrld vfsud`, cräbfid y d`caerdfid ras-paitn d `ds prnpfamdmas ma `ds iurvds qua sa nesarvdk ak `nsenrmas netakfmns pnr `ns inrtas `nkcftumfkd`as, mfdcnkd`asy trdksvarsd`as ak uk if`fkmrn y ak uk inkn7 `d `nid`fzdifùkma `ns nejatns canlætrfins iurvns y iùkfins ak sfstalds maraprasaktdifùk (idrtasfdkd, pn`dras, if`ìkmrfins, asbærfins), `aparlfta d` astumfdkta rasn`var prne`alds ak `ns qua sa usdktrdksbnrldifnkas ma raprasaktdifnkas d`caerdfids, usdkmndrculaktns y lnma`ns canlætrfins.
Dpnyd a` paksdlfaktn vdrfdifnkd` ak…
A` mfsaôn ma astrdtacfds pdrd denrmdr sftudifnkas ma lamfifùkqua raqufardk praifsfùk aspaiìbfid inln ak `d rasn`uifùk maprne`alds qua fkvn`uirdk ldckftumas iuyns vd`nras lamfnssa mabfkdk inln rdznkas, pnr ajalp`n `d va`nifmdm, `d dia-`ardifùk y `d maksfmdm lamfd, dsì, a` astumfdkta bnrlu`drä y
justfbfidrä `ns rasu`tdmns netakfmns lamfdkta prniasns madprnxfldifùk suiasfvd, rdkcns ma vdrfdifùk y `ìlftas ak sf-tudifnkas ma lamfifùk.
Dpnyd a` paksdlfaktn vdrfdifnkd` ak…
@d fktarpratdifùk y inlpdrdifùk ma rasu`tdmns pdrd astumfnsink fkbnrldifùk astdmìstfid prnvakfaktas ma lamfns mainlukfidifùk axtarkns n ma` äleftn asin`dr, justfbfidkmn nrabutdkmn fkbarakifds edsdmds ak rdznkdlfaktns astdmìstfins,mfsaôdkmn axparflaktns d`adtnrfns ak bìsfid, kdturd`as n sn-ifd`as pdrd astumfdr ukd pracuktd n prne`ald, masirfefakmntakmakifds qua sa nesarvdk ak inkjuktns ma vdrfde`as ra`d-ifnkdmds ink a` ldkajn ma fkbnrldifùk, usdkmn lamfmds maiaktrd`fzdifùk, `nid`fzdifùk, mfsparsfùk y inrra`difùk.
Dpnyd a` paksdlfaktn vdrfdifnkd` ak…A` dkä`fsfs ma raprasaktdifnkas maifld`as ma `ns kúlarnsrad`as parlftak mfbarakifdr aktra rdifnkd`as a frrdifnkd`as,rainknifakmn `d maksfmdm a fkinlp`atftum ma `ns lfslnsd trdvæs ma lætnmns kulærfins, canlætrfins y d`caerdfins,inlpdrdkmn y inktrdstdkmn `ds prnpfamdmas ma `ns kúlarns(kdturd`as, aktarns, rdifnkd`as y rad`as) y ds ma sus ra`difnkas ynpardifnkas `n qua `a parlfta d` astumfdkta inkstrufr, ldkajdry utf`fzdr dprnpfdmdlakta `ns mfstfktns sfstalds kulærfins
_aksdlfaktnaspdifd` y sfs-talds canlæ-trfins.
_aksdlfaktnlætrfin y sfs-talds ma la-mfmds.
_aksdlfaktnd`adtnrfn ysfstalds mamdtns.
_aksdlfaktnkulærfin ysfstalds ku-lærfins.
Murdkta tnmn a` Ifi`n 1,a` astumfdkta utf`fzdrä tæi-kfids ma dprnxfldifùkak prniasns fkbfkftns ku-lærfins, fktarpratdkmn `dknifùk ma marfvdmd inlnrdzùk ma idlefn y inlnvd`nr ma `d pakmfakta ma`d tdkcakta d ukd iurvd,masdrrn``dkmn lætnmnspdrd hd``dr ds marfvdmds ma
d`cukds bukifnkas eäsfidsak inktaxtns ldtalätfinsy kn ldtalätfins, `n qua`a parlftfrä dkd`fzdr ra`d-ifnkas y prnpfamdmas aktraaxprasfnkas d`caerdfidsraspaitn d `ds cräbfids mabukifnkas pn`fkùlfidsy rdifnkd`as ma sus ma-rfvdmds, lnma`dkmn dsìsftudifnkas ma vdrfdifùkparfùmfid ink bukifnkastrfcnknlætrfids y sus ras-paitfvds marfvdmds.
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Qkfmdm 4. Inkiaptns eäsfins 113
Yasfùk 4. Mabfkfifùk ma inkiaptns canlætrfins 113 Yasfùk 5. Yfstald ma lamfifùk ma äkcu`ns saxdcasfld` 12? Yasfùk 9. Kúlarn Ϗ (pf) 12=
Yasfùk =. A` rdmfäk 122 Yasfùk 1. @nkcftum ma drin ma `d ifriukbarakifd 135 Yasfùk 2. Ärad ma uk saitnr ifriu`dr 13=
Yasfùk 3. ]anrald ma _ftäcnrds 133
Qkfmdm 5. Ua`difnkas y bukifnkas 184
Yasfùk 4. _rnmuitn idrtasfdkn 184 Yasfùk 5. Ua`difùk 185 Yasfùk 9. Bukifùk 189
Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n 168
Yasfùk 4. Bukifnkas trfcnknlætrfids 168 Yasfùk 5. _rne`alds dp`fidmns ak `d rasn`uifùk
ma trfäkcu`ns raitäkcu`ns 2?? Yasfùk 9. D`cukds fmaktfmdmas eäsfids 2?1
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns rad`as 2?6
Yasfùk 4. Bukifnkas sakn y insakn 2?6 Yasfùk 5. Cräbfids ma `d bukifùk sakn 25? Yasfùk 9. Cräbfid ma `d bukifùk insakn 251 Yasfùk =. @d bukifùk tdkcakta 256 Yasfùk 1. D`cukds fmaktfmdmas trfcnknlætrfids 295
Yasfùk 2. Cräbfid ma `d bukifùk intdkcakta 291
Ì km f i a
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Yasfùk 8. @d bukifùk insaidkta 2=4 Yasfùk 6. Rarfbfidifùk ma fmaktfmdmas trfcnknlætrfids 2==
Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd 21?
Yasfùk 4. Ajalp`ns f`ustrdtfvns 21? Yasfùk 5. @ay ma sakns 213 Yasfùk 9. ]anrald ma` insakn 22= Yasfùk =. Aiudifnkas trfcnknlætrfids 23= Yasfùk 1. Bùrlu`ds ma dmfifùk pdrd `ds bukifnkas 284
Yasfùk 2. Bùrlu`d ma Harnk 28=
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn 286
Yasfùk 4. Uaitds ak a` p`dkn 286 Yasfùk 5. Mfstdkifd aktra mns puktns 264 Yasfùk 9. Innrmakdmds ma` puktn lamfn 26= Yasfùk =. _akmfakta ma ukd raitd 262 Yasfùk 1. Aiudifnkas ma `d raitd ak a` p`dkn 266
Yasfùk 2. Uaitds pdrd`a`ds y raitds parpakmfiu`dras 344
Qkfmdm 3. Iurvds ak a` p`dkn 346
Yasfùk 4. @d ifriukbarakifd 346Yasfùk 5. @d a`fpsa 353 Yasfùk 9. @d hfpæren`d 398 Yasfùk =. @d pdräen`d 3=2
Qkfmdm 8. _rnedef`fmdm y astdmìstfid 313
Yasfùk 4. Inkiaptns eäsfins ma prnedef`fmdm 313 Yasfùk 5. Knifnkas snera inkjuktns 324 Yasfùk 9. Axparflaktn ak astdmìstfid 321
Yasfùk =. _rnedef`fmdm ma avaktns 33?
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Cräbfid 5
Fkfifdralns a` astumfn ma `d ]rfcnknlatrìd, ink `d mabfkfifùk d`cukns inkiaptns canlætrfins qua kns parlftak hdiar uprasaktdifùk i`drd y praifsd ma `ns talds qua vdlns d masdrrn`
Yf mas`fzdlns a` `äpfz masma uk puktn D hdifd ntrn puktn Eutf`fzdlns pdrd a``n a` bf`n ma `d rac`d, netakalns ukd salfrrama nrfcak D, ak mfraiifùk d` puktn E.
Yalfrraitd
Cräbfid 4
UaitdMns puktns ak a` p`dkn matarlfkdk ukd raitd. _drd mfeujdr `d raiin`nidlns `d rac`d ma td` ldkard qua su enrma infkifmd ink `ns puk
D y E, y `uacn mas`fzdlns a` `äpfz, pdsdkmn pnr asns mns puktns.
Makfifùk ma inkiaptns canlætrfinsQkfmdm 4. Inkiaptns eäsfins Yasfùk
4
Dprakmfakmn ink a` prnba Ju`fn
Ärads ma bfcurds p`dkds. Murdifùk: 48:?2
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Cräbfid 9
Äkcu`n
@d ukfùk ma mns salfrraitds ink nrfcak inlúk ak a` p`dkn, bnrld uk äkcu
inln sa f`ustrd ak d cräbfid 9. Idmd salfrraitd as uk dmn ma` äkcu`n y puktn inlúk ma `ds salfrraitds sa maknlfkd værtfia ma` äkcu`n.
Ak d cräbfid, d salfrraitd DE y d salfrraitd DI snk ns dmns ma` äkcu`ny a` puktn D as a` værtfia ma` äkcu`n.
Asta äkcu`n `n pnmalns ``dldr: Dkcu`n EDI ù äkcu`n IDE.
D` trdedjdr ink äkcu`ns, sfalpra tnldlns ukn ma sus `dmns inln `dmfkfifd` y a` ntrn inln dmn tarlfkd`. @d lamfmd ma uk äkcu`n as uk kúlarqua lfma a` cfrn n masp`dzdlfaktn ma` `dmn fkfifd` hdstd infkifmfr insu `dmn tarlfkd`.
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Cräbfid
Yf a` cfrn sa hdia ak saktfmn inktrdrfn d ds ldkaif``ds ma` ra`nj, a` äkctfaka ukd lamfmd pnsftfvd. Yf a` cfrn sa hdia ak a` lfsln saktfmn maldkaif``ds ma` ra`nj, `d lamfmd ma` äkcu`n as kacdtfvd.
]nmn sfstald ma lamfifùk raqufara ma ukfmdmas7 pdrd lamfr `ns äkcuaxfstak vdrfns sfstalds ma ukfmdmas qua masirfefralns läs dma`dkta
Äkcu`n iaktrd`
Iudkmn uk äkcu`n tfaka su værtfia ak a` iaktrn ma uk iìriu`n y sus dminrtdk d` iìriu`n ak mns puktns, asta äkcu`n sa ``dld äkcu`n iaktA` drin DE ma` iìriu`n inlprakmfmn aktra sus `dmns sa ``dld a` dsuetakmfmn pnr a` äkcu`n.
Ak trfcnknlatrìd, uk äkcu`n as matarlfkdmn pnr d bnrld inln sa nrfcfMaealns inkniar a` `dmn fkfifd` a` `dmn tarlfkd` y a` tfpn ma rntdi
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A` sfstald saxdcasfld` as uk sfs-tald ma kulardifùk pnsfifnkd`iuyd edsa as 2?. Bua fmadmn pnr`ns edef`nkfns y sa sfcua usdkmn ak`d ditud`fmdm. Ak asta sfstald, a`
iìriu`n as ukd ifriukbarakifd qua sa mfvfmaak 92? pdrtas fcud`as. A` äkcu`n iaktrd` iuyndrin suetfakma ukd ma astds pdrtas, tfaka ukdlamfmd ma uk crdmn, ma td` ldkard qua sfd` `dmn fkfifd` `n rntdlns ukd vua`td inlp`atd, hderä cfrdmn 92? crdmns.@ns edef`nkfns mfvfmìdk idmd crdmn ak 2? lfkutns y idmd lfkutn ak 2?sacukmns, pdrd netakar dsì uk sfstald ma lamfifùk luy rabfkdmn. Ak a`
trdkspnrtdmnr, pnmalns lamfr uk äkcu`n ink crdk praifsfùk, usdlns ma-ifld`as. Ajalp`n: uk äkcu`n ma =8.1 d` lu`tfp`fidr su pdrta maifld` pnr2?, md inln rasu`tdmn =8 crdmns 9? lfkutns.
@d id`iu`dmnrd ifaktìbfid inkvfarta ukd lamfmd maifld` ak saxdcasfld`,in`niäkmn`d ak crdmns, lfkutns y sacukmns, y vfiavarsd.
Ajalp`n:_drd pdsdr 51¿,45½,=?“ ma` sfstald saxdcasfld` d` sfstald maifld`, as kaiasdrfn sacastns pdsns:
4. Asirfed `d ifbrd 51 y nprfld `d tai`d cls. Dpdraiarä 51¿7 `uacn, fktrnmuzid `d i45 y nprfld `d tai`d cls7 dpdraiarä 45¿7 rapftd `d npardifùk ink `d ifbrd =?, y akpdktd``d ma `d id`iu`dmnrd pdraiarä `d ifbrd inlp`atd 51¿ 45¿ =?¿.
5. Ink astd ifbrd, nprfld `d tai`d fcud` (<), sacufmd ma `d tai`d cls y dpdraiarä ak
Yfstald ma lamfifùk ma äkcu`ns saxdcasfld`
Qkfmdm 4. Inkiaptns eäsfins Yasfùk
5
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4. @d lamfmd ma uk äkcu`n as 5=¿. Hd``dr su lamfmd ak lfkutns y sacukm
Yn`uifùk
_drd axprasdr `d lamfmd ak lfkutns, lu`tfp`fidlns pnr 2? puastn qidmd crdmn tfaka 2? lfkutns, dsì:
5= x 2? < 4.==? lfkutns
_drd inkvartfr ns lfkutns ak sacukmns, lu`tfp`fidlns 4.==? pnr 2?, pqua idmd lfkutn tfaka 2? sacukmns dsì: 4.==? x 2? < 82.=?? sacukmAstn sfckfbfid qua 5=¿ aqufvd`ak d 4.==? lfkutns n 82.=?? sacukmns
5. Qk äkcu`n lfma 31.=92 sacukmns. Axprasdr su lamfmd ak crdmns, lkutns y sacukmns.
Yn`uifùk
Yf mfvfmflns 31.=92 sacukmns aktra 2?, sa netfaka 4.513,522223 qas `n lfsln qua 4.513 lfkutns 42 sacukmns. Dhnrd, mfvfmflns 4.5lfkutns aktra 2? pdrd pdsdr`ns d crdmns y sa netfaka 5?.61¿ qua as
lfsln qua 5?¿ 13‖.
@uacn, 31.=92‖‖ aqufvd`ak d 5?¿ 13‖ 42‖‖.
@d kntdifùk läs usdmd pdrd asta sfstald ma ukfmdmas, as:crdmns (¿), lfkutns (‖), sacukmns (‖‖).
4
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Axprasdr idmd maifld` ak crdmns, lfkutns y sacukmns.
Nesarvdifùk
@d lamfmd ma uk äkcu`n mdmd ak crdmns, lfkutns y sacukmns
sa maea axprasdr ma td` ldkard qua `d úkfid in`ulkd quapuama supardr d 2? as `d ma crdmns (`ds ukfmdmas läscrdkmas), pnrqua sf ak d in`ulkd ma sacukmns n ma lfkutns,a` vd`nr as ldynr ma 2?, sa inkvfarta ak lfkutns n akcrdmns7 idmd 2? sacukmns as uk lfkutn y idmd 2? lfkutnsas uk crdmn.
`d id`iu`dmnrd
d. 59¿ 26‖ 81“
e. =6¿ 34‖ 64“
i. 29¿ 88‖ 2?“
m. 41¿ 63‖ 4?4“
a. 91¿ 52‖ 38“
b. 19¿ 41‖ 62“
5
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Ajalp`n
@d lamfmd 43¿ 25‖ 31‖‖ maea asirfefrsa: 43¿ 29‖ 41‖ 48¿ 9‖ 41‖‖
A` rasu`tdmn ma `d suld as 12¿ 2‖ 48‖‖
Ak mnkma a` ú`tfln rakc`ùk, as `d bnrld inrraitd ma asirfefr astd lamfmd ak crdmlfkutns y sacukmns.
@d lamfmd ma` äkcu`n D < 51º 93‖ =1‖‖ y `d lamfmd ma` äkcu`n E < 9?º 58‖ 99‖‖. Hd``dr `d suld ma `ds lamfmds ma `ns äkcu`ns
D y E.
Yn`uifùk
Ajarififns rasua`tns
51¿ 93‖ =1‖‖ 9?¿ 58‖ 99‖‖
11¿ 21‖ 38‖‖ 11¿ 22‖ 48‖‖ 12¿ 2‖ 48‖‖
+
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Qkfmdm 4. Inkiaptns eäsfins Yasfùk
9
D` lamfr `d `nkcftum ma `d ifriukbarakifd y mfvfmfr`daktra a` vd`nr ma d nkcftum ma` mfälatrn ak uk iìriu`n,`ns crfacns akinktrdrnk qua pdrd mfbaraktas tdldônsma` iìriu`n, astd ra`difùk mded a` lfsln rasu`tdmn
qua sa inknia inln a` kúlarn Ϗ < 9.4=416521...7pnstarfnrlakta, sa akinktrù qua asta kúlarn tfakafkbfkftds ifbrds maifld`as y qua su axprasfùk maifld`as dparfùmfid. Astns kúlarns sa ``dldk kúlarns frrd-ifnkd`as pnrqua kn snk a` rasu`tdmn ma` inifakta mamns aktarns.
I <Ϗ
M
A` kúlarn Ϗ (pf)
_arn inln M < 5r , raalp`dzdlns M7 ak `d aiudifùk dktarfnr takalns: , mmnkma sa netfaka qua I < 5Ϗr , `n iud` sfckfbfid qua `d `nkcftum ma `d ifriukbarakiinktfaka 5Ϗ vaias `d `nkcftum ma` rdmfn.
5Ϗ < 2,58948194...
I < @nkcftum ma `d ifriukbarakifdϏ< Kularn pf 9.4=416521…M< Mfälatrn ma `d ifriukbarakifd
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Ajarififns rasua`tns
_rne`ald 4
@d ifriukbarakifd iaktrd` ma ukd idkihd ma búten` tfakauk mfälatrn ma 2 latrns. ¾Iuäktn lfma `d `nkcftum ma `difriukbarakifd>
Yn`uifùk
Inln a` rdmfn as `d lftdm ma` mfälatrn, r < 9 l, `uacnI < 5Ϗr . D` raalp`dzdr a` vd`nr ma r , takalns I < 5.Ϗ.9 <
48.8=611165, vd`nr qua pnmalns dprnxfldr d 48.81 l.
_rne`ald 5
Qk trnzn ma d`dlera ma =.8 latrns ma `nkcftum sa mne`d pdrdbnrldr uk iìriu`n. Hd``dr `d `nkcftum ma` rdmfn.
Yn`uifùk
Ydealns qua I < 5Ϗr , `uacn maealns maspajdr r, dsìr < I /5Ϗ.
=.8As maifr r < < ?,3296=9352 l
5.Ϗ
n sad qua `d `nkcftum ma` rdmfn as dprnxfldmdlakta 32 il.
Hdstd dquì, halns usdmn a` sfstald saxdcasfld` ma crdmns, lfkutns
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Ntrd bnr-ld pdrdlamfr `ns
ä k c u ` n sas utf`fzdr a` rdmfäk, quaas `d lamfmd ma uk äkcu`niaktrd` iuyn drin pnsaa ukd`nkcftum fcud` d` rdmfn.
Astn sfckfbfid qua ak ukdifriukbarakifd ma rdmfn r ,
ideak 5Ϗ rdmfdkas n sad uk cfrn inlp`atn aqufvd`a d 5Ϗ rdmfdkas, astn maefmn qua `d `nkcftum ma` rdmfn astä 5Ϗ vaias ak `d `nkcftum ma `d ifriukbarakifd.
Inkvarsfùk ma crdmns d rdmfdkas y vfiavarsd
_nmalns axprasdr `d lamfmd ma uk äkcu`n ak rdmfdkas n ak crdmns, hdifakmn raspaitfvd inkvarsfùk. Radlns `ns sfcufaktas ajalp`ns:
Cräbfid 3
Äkcu`n ma uk rdmfäk
D E < r
92? 5Ϗ
48? Ϗ
6? Ϗ /5
=1 Ϗ /=
Crdmns (º) Udmfdkas
A` rdmfäkQkfmdm 4. Inkiaptns eäsfins Yasfùk
=
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_nmalns hdiar `d inkvarsfùk ma iud`qufarlamfmd ak a` sfstald saxdcasfld` d rdmfdkas yvfiavarsd. Radlns:
Iudkmn mdlns `d lamfmd ma uk äkcu`n ak rdmfdkas, a` rasu`tdmn dpdraia pnrcakard`, ak bukifùk ma Ϗ inln ak a` idsn dktarfnr. Qsdkmn d id`iu`dmnrd ifaktìbfpnmalns hd``dr asta rasu`tdmn ak bnrld maifld` ink ukd axia`akta dprnxfldifùAk a` ajalp`n dktarfnr valns qua 31¿ aqufvd`ak dprnxfldmdlakta d 4 9 rdmfdk
Ajalp`n 4
Yf uk äkcu`n lfma 31¿, hd``dr su lamfmd akrdmfdkas.
Yn`uifùk
_nmalns rasn`var asta prne`ald lamfdkta a`usn ma ukd rac`d ma tras sflp`a mfraitd, dsì:
Ϗ rdmfdkas 48?¿
x 31¿
31Ϗ x < < 1Ϗ/45 4,9?6 48?
Uasn`vfakmn pdrd x takalns:
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Ajalp`n 5
@d lamfmd ma uk äkcu`n as uk rdmfäk. Hd``dr su lamfmd ak
a` sfstald saxdcasfld`.
Yn`uifùk
48?¿ Ϗ rdmfdkas
x 4
48?º Uasn`vfakmn pdrd x takalns x < < 13,56133614¿
Ϗ
asta rasu`tdmn `n inkvartflns d crdmns, lfkutns y sacuk-mns, y takalns x < 13¿ 43‖ ==,84‖‖. Astn sfckfbfid quauk äkcu`n qua lfmd uk rdmfäk, lfma uk pnin läs ma 13¿.
4. Mdmds `ds sfcufaktas lamfmds ma uk äkcu`n ak rdmfdkas, asirfefr ak idmd idsnsu aqufvd`akta ak crdmns, lfkutns y sacukmns:
Qsalns
`d id`iu`dmnrd
c. 9Ϗ /5
h. 3Ϗ /=
f. 1Ϗ /=
j. 9Ϗ /8
g. 1Ϗ
` 9Ϗ/5
d. 9Ϗ /=
e. Ϗ /=
i. Ϗ /9
m. Ϗ /2
a. Ϗ /1
b 44Ϗ/=
4
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5. Mdmds `ds sfcufaktas lamfmds ma uk äkcu`n ak crdmns, hd``dr su aqufvd`aktardmfdkas y asirfefr `d raspuastd ak bnrld maifld`.
Ak uk vfdja ma Encntä d ]ukjd, `d ruamd ma ukd lntnifi`atd hfzn 4?6.?64 cfinlp`atns7 sf a` mfälatrn ma `d ruamd as 91.12 il.
d. ¾Iuä` as d mfstdkifd qua hdy akEncntä y ]ukjd>
e. @ns 4?6.?64 cfrns qua mfn d rua¾d iuäktns rdmfdkas y d iuäkcrdmns aqufvd`ak>
`d id`iu`dmnr
d. 8?¿ < =Ϗ /6 < 4,962529=?5 rdmfdkas
e. 551¿ <i. 941¿ <m. 491¿ <a. 45?¿ <b. -41?¿ <c. -=1¿ <
h. 5=?¿ <f. 86¿ < j. 451¿ <g. 35?¿ <`. -4==?¿ <
5
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Qk äkcu`n astä ak pnsfifùk astäkmdr ak uk sfstald ma innrmakdmds idr-tasfdkds raitdkcu`dr, sf su værtfia as a` puktn ma nrfcak ma innrmakdmds ysu `dmn fkfifd` astä snera a` `dmn pnsftfvn ma` aja hnrfznktd` n aja x.
A` `dmn tarlfkd` ma uk äkcu`n ak pnsfifùkastäkmdr puama astdr ak iud`qufard ma `ns
iudmrdktas ma` sfstald ma innrmakdmds.
Yf a` dmn tarlfkd` ma uk äkcu`n ak pnsfifùkastäkmdr infkifma ink `d mfraiifùk ma `nsajas ma innrmakdmds, a` äkcu`n sa ``dld
iudmrdktd`.
Cräbfid 8
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Ajalp`ns
@ns äkcu`ns ak pnsfifùk astäkmdr qua lfmak 6?¿, 48?¿, 53?¿, 92?¿, =1?¿, -6-53?¿, snk äkcu`ns iudmrdktd`as.
@ns äkcu`ns intarlfkd`as snk `ns qua astäk ak pnsfifùk astäkmdry tfakak a` lfsln `dmn tarlfkd`.
Ajalp`n
Yf takalns a` äkcu`n ma 9?¿ ak pnsfifùk astäkmdr y cfrdlns su `dmn tarlf92?¿ ak mfraiifùk pnsftfvd, vua`va d niupdr d pnsfifùk ak mnkma astded n squa ns äkcu`ns ma 9?º y a` äkcu`n ma 9?¿ + 92?¿ < 96?¿, tfakak a` lfsln dtarlfkd`, `n iud` sfckfbfid qua `ns äkcu`ns ma 9?¿ y 96?¿ ak pnsfifùk astäkm
Cräbfid
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Yf r as a` rdmfn ma ukd ifriukbarakifd y t `d lamfmd ma ukäkcu`n iaktrd` ak rdmfdkas qua fktariaptd ak `d ifriukba-rakifd, uk drin ma `nkcftum s, aktnkias:
s < r.t
Cräbfid 4?
@nkcftum ma drin ma `d ifriukbarakifdQkfmdm 4. Inkiaptns eäsfins Yasfùk
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Ajarififns rasua`tns
_rne`ald 4
Yf a` lfkutarn ma uk ra`nj lfma 2 iaktìlatrns ¾quæ mfstdkifdrainrrarä ak 48 lfkutns>
@d `nkcftum ma` drin ma ifriukbarakifd inlprakmfmn aktra`ns `dmns ma` äkcu`n iaktrd` as a` prnmuitn ma` rdmfn pnr `dlamfmd ma` äkcu`n ak rdmfdkas.
Ya maknlfkd saitnr ifriu`dr d `d pdrta fktarfnr ma` iìriu`nqua as `flftdmd pnr mns rdmfns y a` drin fktariaptdmn pnra``ns.
_rne`ald 5
¾Iuä` as d mfstdkifd rainrrfmd pnr ukd pdrtìiu`d d n drcn ma
ukd ifriukbarakifd ma 9 l ma rdmfn, sf d pdrtìiu`d sa masp`dzduk äkcu`n ma 2 rdmfdkas>
Yn`uifùk
Ya maknlfkd saitnr ifriu`dr d d pdrta fktarfnr ma` iìriu`n qua as flftdmdpnr mns rdmfns y a` drin fktariaptdmn pnr a``ns:
s < r δ aktnkias: 9 l 2 rdm
Cräbfid 44
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Ma ns inkiaptns ma d canlatrìd a`alaktd`, sa sdea qua`d rdzùk ma` ärad ma` saitnr y a` ärad ma` iìriu`n (Ϗ.r 5),as fcud` d `d rdzùk ma `d `nkcftum ma` drin fktariaptdmny `d `nkcftum ma `d ifriukbarakifd (5Ϗ.r )7 d` trdksirfefrastns inkiaptns ak ukd aiudifùk, takalns:
55
D Y
r r p p< , sf maspajdlns D takalns: .
5
r Y D < ,
parn inln Y < r. t takalns qua D <
As maifr, a` ärad ma` saitnr sa netfaka a`avdkmn a` rdmfn d`iudmrdmn, lu`tfp`fidkmn asta rasu`tdmn pnr `d lamfmd masu äkcu`n iaktrd` ak rdmfdkas y mfvfmfakmn asta rasu`tdmnaktra mns.
r 5.t
5
Ärad ma uk saitnr ifriu`drQkfmdm 4. Inkiaptns eäsfins Yasfùk
2
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Qkd `älfkd ma inera ak bnrld ma saitnr
ifriu`dr tfaka 2 il ma rdmfn y su äkcu`niaktrd` lfma 4??¿, hd``dr:
d. @nkcftum ma` drin.
e. Ärad ma` saitnr ifriu`dr.
Yn`uifùk
d. Axprasdlns `d lamfmd ma` äkcu`n ak rdmfdkas
48?º Ϗ rdmfdkas
4??º x
@uacn
1
6 x
p<
Aktnkias, `d `nkcftum ma drin Y < r.δ, `uacn Y < (2 il).(1
6
p) < 4?,=3 il
e. raalp`dzdkmn takalns il
Ajalp`n
D <r 5.t
5
D < . (2 il)5. ( )4
5
1Ϗ
6
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4. Udmfn 6 il, lamfmd ma` äkcu`n iaktrd` 45?¿
5. A` rdmfn lfma 8 il y a` äkcu`n iaktrd` =1¿
9. A` rdmfn lfma 42 il y a` äkcu`n iaktrd` 491¿
=. A` rdmfn lfma 45 il y a` äkcu`n iaktrd` 5Ϗ /9
1. A` rdmfn lfma 41 il y a` äkcu`n iaktrd` 5,14 rdmfdkas
2. Qk kaulätfin tfaka uk mfälatrn ma 92 pu`cdmds7 ¾iuäktds ravn`uifnkaabaitudrä `d ruamd iudkmn a` dutnlùvf` rainrrd ukd lf``d (1.58? pfas
Kntd: uk pfa aqufvd`a d 45 pu`cdmds.
3. A` lfkutarn ma uk ra`nj lfma = pu`cdmds. ¾Tuæ mfstdkifd rainrrarä saxtraln ak ukd hnrd y 5? lfkutns>
8. A` rdmfn ma ukd ifriukbarakifd lfma 4? il, hd``dr `d `nkcftum ma` driiuyn äkcu`n iaktrd` lfma uk crdmn.
6. ¾Iuäktns rdmfdkas tfaka uk äkcu`n ma uk crdmn>
4?. A` axtraln ma uk pækmu`n ma =? il ma `nkcftum rainrra uk drin ma il inkbnrla nsif`d, masirfefakmn uk äkcu`n D. Matarlfkdr `d lamfm
Ak ns ajarififns ma` 4 d` 1, akinktrdr d nkcftum ma` drin y a` ärad ma` saitnr ifriu`dinknifakmn a` rdmfn ma` iìriu`n y `d lamfmd ma` äkcu`n iaktrd`:
4
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Uainrmalns qua a` tanrald ma_ftäcnrds sa rabfara d `ns trfäkcu`nsraitäkcu`ns qua snk dqua``ns quapnsaak uk äkcu`n raitn y mns äkcu-`ns dcumns7 `ns `dmns qua bnrldk a`äkcu`n raitn sa maknlfkdk idtatnsy a` `dmn ldynr sa ``dld hfpntakusd,as flpnrtdkta rainrmdr`n pnrqua kns
parlfta trdtdr ink ldynr inlnmfmdm,d`cukns talds ma `d trfcnknlatrìd.
Inln `d suld ma `ns äkcu`ns fk-tarfnras ma uk trfäkcu`n as fcud` d48?¿, ak a` trfäkcu`n raitäkcu`nhdy uk äkcu`n raitn qua lfma 6?¿y ns rastdktas 6?¿ sa rapdrtak aktra`ns ntrns mns äkcu`ns dcumns. Idmdäkcu`n dcumn tfaka inln `dmns `d
Cräbfid 45
Yacúk a` tanrald ma _ftäcnrds, `d hfpntakusd a`avdmd d` iudmrdmn as fcud`d `d suld ma `ns iudmrdmns ma `ns mns idtatns.
i5 < d5 + e5
]anrald ma _ftäcnrdsQkfmdm 4. Inkiaptns eäsfins Yasfùk
3
]anrald ma _ftäcnrds
Murdifùk: 4?:19 lfk.
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Ajalp`n
Qk trfäkcu`n tfaka ukn ma sus værtfiasak a` puktn (?,?), a` ntrn ak a` puktn(9,?) y a` ntrn ak a` puktn (9,=). Mfeu-
jdr a` trfäkcu`n, hd` dr `d `nkcftum ma`ns idtatns y ma `d hfpntakusd. _drdidmd äkcu`n dcumn, matarlfkdr a`idtatn npuastn y a` idtatn dmydiakta.
Ak idmd idsn, mfeujdr a` trfäkcu`n, hd``dr `d `nkcftum ma sus idtatns y su hfpntakusy matarlfkdr a` idtatn npuastn y a` dmydiakta pdrd idmd äkcu`n dcumn.
4. @ns værtfias ma` trfäkcu`n astäk ak `ns puktns (?,?), (2,?) y (2,=)5. A` trfäkcu`n tfaka sus værtfias ak (?,?), (1,?) y (1,1)9. @ns værtfias ma` trfäkcu`n snk `ns puktns (?,?), (9,?) y (9,1)= @ns værtfias ma` trfäkcu`n snk `ns puktns (? ?) (2 5) y (2 ?)
i5 < d5 + e5, `uacn 5 5i d e< + , raalp`dzdkmn takalns 5 59 =i < +
ma mnkma i < 1.
Ink ra`difùk d` äkcu`n δ, a` idtatn npuastn lfma = y a` idtatn dmydiaktalfma 9.
Ink ra`difùk d` äkcu`n θ, su idtatn dmydiakta lfma = y su idtatn npuastnlfma 9.
Cräbfid 4=
4
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_racuktds ma sa`aiifùk lú`tfp`a ink úkfid raspuastd - (tfpn F)@ds pracuktds ma asta tfpn inkstdk ma uk akukifdmn y ma iudtrn pnsfef`fmdmasma raspuastd, aktra ds iud`as ustam maea asincar d qua inksfmara inrraitd.
4. Yf `d lamfmd ma uk äkcu`n as 558¿. @d npifùk qua lajnr sa djustdd su lamfmd ak lfkutns y sacukmns as.
d. 45.=1? lfkutns: 39?.=12 sacukmns
e. 49.28? lfkutns: 85?.8?? sacukmns i. 44.938 lfkutns: 21?.95= sacukmns m. 49.551 lfkutns: 84?.5?? sacukmns
5. D` inksfmardr uk äkcu`n iuyd lamfmd as =1.986 sacukmns. @d lamfd
asprasdmd ak crdmns, lfkutns y sacukmns as:
d. 45¿92½56“ e. 44¿5?½4?“ i. 4?¿41½45“ m. 6¿ 45½ 9=“
9. Axprasdr idmd maifld` ak crdmns, lfkutns y sacukmns.
d. 59¿, =9 e. ==¿, 68 i. 13¿, ?6
=. @d lamfmd ma` äkcu`n D < 15¿ 93‖ =?‖‖ y `d lamfmd ma` äkcu`nE < =?¿ 48‖ ?9‖‖. Hd``dr d suld ma ds lamfmds ma ns äkcu`ns D y E.
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1. @d ifriukbarakifd ma ukd idkdstd ma edsquaten` tfakak uk mfälatrn
ma = latrns. @d `nkcftum ma `d ifriukbarakifd as:
d. 5 latrns
e. 2.58 latrns
i. 45,1229 latrns
m. 49,55=9 latrns
2. Qk trnzn ma iuarmd ma 48.= latrns ma nkcftum sa mne`d pdrd bnrldr
uk ifriu`n. @d `nkcftum ma` rdmfn as.
d. 9,69 latrns
e. 5,6581 latrns
i. 9.4=41 latrns
m. 3.59 latrns
3. D` inkvartfr =1¿ d rdmfdkas a` rasu`tdmn sa axprasd:
d. ?.3819 rdmfdkas e. ?.13?3 rdmfdkas
i. 4,64 rdmfdkas m. ?.8=19 rdmfdkas
8. Id`iu`dr ak rdmfdkas:
d. 6?¿ e. 9?¿ i. 44?¿
6. Inkvartfr d crdmns:
d. Ϗ /9 e. Ϗ /2 i. 9Ϗ /=
m. Ϗ /45 a. 5
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A` prnmuitn idrtasfdkn ma mns inkjuktns D y E kn vdiìns,as a` inkjuktn ma tnmds `ds pdrajds nrmakdmds ( x,y), matd` ldkard qua a` prflar a`alaktn ma `d pdrajd as uka`alaktn ma D y a` sacukmn a`alaktn ma `d pdrajd asuk a`alaktn ma E.
{( , ) | D E x y x D y E <
4. Yf
Aktnkias D x E < {(4 ,d), (4 ,e), (5 ,d), (5 ,e), (9 ,d), (9 ,e)}
5. D < {9, 1, 2} aktnkias
Ajalp`n
D < {4, 5, 9}
E < {d, e}
_rnmuitn idrtasfdknQkfmdm 5. Ua`difnkas y bukifnkas Yasfùk
4
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4. {(9,9),(9,1),(9,2)
4 U <
5. {(9,9),(9,1),(9,2),(1,9),(1,2)5 U <
9. {(9,9),(1,1),(2,2),(2,9)
9 U <
Ajalp`n
Ink raspaitn ma` idsn dktarfnr, `ds sfcufaktas snk ra`difnkas ma D ak E:
Nesarvdifùk
@ns a`alaktns ma ukd ra`difùksnk pdrajds nrmakdmds.
Qk sueinkjuktn ma` prnmuitn idrtasfdkn D x E sa ``dld ukdra`difùk ma` inkjuktn D ak a` inkjuktn E.
Ua`difùkQkfmdm 5. Ua`difnkas y bukifnkas Yasfùk
5
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Ma d mabfkfifùk ma bukifùk, valns qua ak a``d kn puama hdear mns pdrajds qua tacdk fcud` a` prflar a`alaktn ma `d pdrajd, `n iud` dsacurd qua a` sacukmn a`alakma `d pdrajd as úkfin pdrd uk vd`nr aspaiìbfin ma` prflar a`alaktn.
Mnlfkfn ma b < {4, 5, 9, =, 1}U m b { e }
Qkd ra`difùk ma` inkjuktn D ak a` inkjuktn E, qua d idmd a`alaktn ma D `adsfckd uk úkfin a`alaktn ak E, sa ``dld ukd bukifùk ma` inkjuktn D ak a`inkjuktn E.
: b D E®
Inkiaptn ma bukifùk
BukifùkQkfmdm 5. Ua`difnkas y bukifnkas Yasfùk
9
Dprakmfakmn ink a` prnba Ju`fnAiudifùk iudmrätfid ak uk prne`ald ma canlatrìdMurdifùk: 4?:46 lfk.
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Ak ldtalätfids, as luy usud` mdr bukifnkas, utf`fzdkmn bùrlu`ds.
Rfsfta astd päcfkd y akiuaktra d`cukds dp`fidifnkas ma `ds bukifnkas d `dvfmd intfmfdkd
http://www.knvdsur.i`/knvdsur/dmlfkfstrdtnr/up5/up`ndms/[email protected]
Bukifnkas `fkad`as, pn`fkùlfids y rdifnkd`as
@ns prflarns a`alaktns ma `ds pdrajds ma ukd bukifùk bnrldk a` inkjuktn mnlfkfn ma `d bukifùk7 y a` inkjuktn bnrldmn pnr `ns sacukmns a`alaktns ma `pdrajds sa maknlfkd a` rdkcn ma `d bukifùk. Ak `d cräbfid valns qua a` mnlfkma `d bukifùk as:
Mnlfkfn ma b < {4, 5, 9, =,1} Udkcn ma b < {d, e, i}
A`alaktns ma ukd bukifùk
Bukifùk `fkad`
Ak asta idsn d bukifùk tnld iud`qufarvd`nr x, suläkmn`a 5. D inktfkud-ifùk asirfeflns d`cukds pdrajds ma `d
bukifùk.
b < {(?,5), (4,9), (5,=), (9,1), (=,2)...}
D` raprasaktdr ns puktns y ukfr`ns aka` p`dkn idrtasfdkn, netakalns ukd`ìkad raitd7 b ( x) as ukd bukifùk fkad`.
4. Bukifùk `fkad`
b ( x ) < x + 5
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Cräbfid 43
5. Bukifùk inkstdkta
c ( x ) < 9
D` raprasaktdr ak a` p`dkn idrtasfdkn `ns puktns ma c y ukfr`ns lamfdkta uk trdnetakalns ukd `ìkad raitd pdrd`a`d d` aja x7 kn nestdkta, pnmalns fkmfidr qua c
as ukd bukifùk inkstdkta.
c < {(-5,9), (-4,9),(?,9), (4,9), (5,9),(9,9)...}
D` raprasaktdr ak a` p`dknidrtasfdkn ns puktns ma yukfr`ns lamfdkta uk trdzn,netakalns ukd ìkad raitdpdrd`a`d d` aja x, c ( x), asukd bukifùk inkstdkta. A`inkjuktn rdkcn ma tfakasn`dlakta a` a`alaktn 9.
Bukifùk inkstdkta
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D` raprasaktdr ns puktns y ukfr`ns lamfdkta uk trdzn ak a` p`dkn idrtasfdkn,sa netfaka ukd raitd qua pdsd pnr a` nrfcak ma ds innrmakdmds y mfvfma d nsiudmrdktas F y FFF ak pdrtas fcud`as. Astd bukifùk sa ``dld `d bukifùk fmæktfid.Yu rdkcn y su mnlfkfn snk a` lfsln inkjuktn.
_drd raprasaktdr bukifnkas ink sìlen`ns ldtalätfins, pnr `n cakard`usdlns `atrds, sdefakmn a` sfckfbfidmn ma `n qua a``ds raprasaktdk. Yf ta-kalns b ( x) < x5 sfckfbfid qua d bukifùk b tnld iud`qufar vd`nr y `n a`avd a`
iudmrdmn dsì, b (2) < 25
< 92.
9. Bukifùk fmæktfid
H(x) < x
Ak asta idsn, `d bukifùk tnld uk vd`nr x y `n majd fcud`. D`cukds pdrajds ma H, sfkmfidk d inktfkudifùk.
H < {(-5,-5), (-4,-4), (?,?), (4/9,4/9), (9/8,9/8)...}
b as ukn d ukn
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Ajalp`ns
=. Bukifnkas pn`fkùlfids
Ynk sulds ma tærlfkns n lnknlfns. @ns inabfifaktas ma d vdrfde`a astäk raprasa
tdmns ak idmd tærlfkn ink d atrd d ink sueìkmfias. @ns axpnkaktas ma d vdrfde`asnk kúlarns aktarns pnsftfvns. A` crdmn ma d bukifùk as a` axpnkakta ma ldynr vdqua bfcura ak a` pn`fknlfn. @ds bukifnkas pn`fkùlfids axfstak pdrd tnmn vd`nr ma
Qkd bukifùk pn`fkùlfid as ma `d bnrld:
4. = 9 5( ) 1 9 8 3 2 b x x x x x< + +
Asta as ukd bukifùk pn`fkùlfid ma crdmn iudtrn. @ns inabfifaktas masus tærlfkns snk `ns kúlarns 1, -9, 8, 37 -2 sa ``dld a` tærlfkn fkma-pakmfakta n tærlfkn inkstdkta.
5. 9 5( ) ?.6 5 6 p x x x x< +
Astd bukifùk as ma crdmn tras. @ns inabfifaktas ma ns tærlfkns snk ?.6,
-5, 6. Ak asta ajalp`n, a` tærlfkn fkmapakmfakta tfaka a` vd`nr iarn.
9. ( ) 9 3h x x< +
Astd as ukd bukifùk pn`fkùlfid ma crdmn ukn qua tdlefæk d `dldlnsbukifùk `fkad`. ]faka uk tærlfkn ak x ink inabfifakta 9, y su tærlfknfkmapakmfakta as 3. D` crdbfidr astd bukifùk ak a` p`dkn idrtasfdkn,kns md ukd `ìkad raitd.
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1. Bukifnkas rdifnkd`as
Ynk `ds bukifnkas qua rasu`tdk ma` inifakta ma mns bukifnkas pn`fkùlfids.
Mnkma _( x) y T( x) snk pn`fknlfns.
Qkd bukifùk rdifnkd` axfsta n astä mabfkfmd, sfalpra qua sumaknlfkdmnr sad mfbarakta ma iarn, ma td` ldkard qua ma` mn-lfkfn ma ukd bukifùk rdifnkd` maealns masidrtdr tnmns dqua``nsvd`nras qua hdcdk iarn d su maknlfkdmnr.
Ajalp`n
Ajalp`n
4. 5
9( )
3
x b x
x x
+<
+5.
5
5( )
4
xc x
x<
+
@d bukifùk rdifnkd`9
( )5
c x x
<+
kn astä mabfkfmd pdrd x < -5, pnrqua d`
raalp`dzdr asta vd`nr ak `d bukifùk, takalns
9 9( 5)
5 5 ?c < <
+
b ( x) <_ ( x)
T ( x)
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5. Bukifùk snera
Qkd bukifùk as snera, sf tnmn a`alaktn ma` rdkcn as fldcak ma d`cúk a`alak
_drd idmd ukd ma ds sfcufaktas bukifnkas rdifnkd`as, hdiar su raprasaktdifùk cräbak a` p`dkn idrtasfdkn a fmaktfbfidr a` mnlfkfn y a` rdkcn ma `d bukifùk.
@ds bukifnkas puamak i`dsfbfidrsa ma luihds ldkards, parn mastdidralns ds sfcufakt
Qkd bukifùk b ( x) as ukn d ukn, sf pdrd mns a`alaktns mfstfktns ak su mnlfkdsfckd vd`nras mfbaraktas ak a` rdkcn ma `d bukifùk, as maifr, sf
4 5 x x , aktnki b ( x
4) ≯ b ( x
5).
I`dsas ma bukifnkas
4. Bukifùk ukn d ukn
4.
5.
9.
=.
1.
44
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Cräbfid 46
c as snera
9. Bukifùk efyaitfvd
Qkd bukifùk c ma uk inkjuktn D ak uk inkjuktn E as efyaitfvd iudkmn as uknsnera d `d vaz.
=. Bukifùk pdr a flpdr
d. Bukifùk pdr
Qkd bukifùk b as pdr, sf pdrd tnmn x, ak a` mnlfkfn ma `d bukifùk sa tfaka qu
b (-x) < b ( x)
Ajalp`n
@d bukifùk b ( x) < x5 as ukd bukifùk pdr.
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Cräbfid 5?Bukifùk pdr
Cräbfid 5
e. Bukifùk flpdr
Qkd bukifùk c as flpdr sf pdrd idmd x ak a` mnlfkfn ma `d bukifùk sa tfaka q
c (-x) < -c ( x).
@d cräbfid ma ukd buk-ifùk flpdr as sflæ-trfid ink raspaitn d`puktn ma nrfcak (?,?).
Ajalp`n b ( x) < x9
as ukd bukifùkflpdr.
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1. Bukifùk parfùmfid
Qkd bukifùk b as parfùmfid, sf axfsta uk kúlarn rad` pnsftfvn p, td` qua pdrd iudqufar x ma` mnlfkfn ma b , sa tfaka qua x + p partakaia tdlefæk d` mnlfkfn m b y b (x + p) < b (x).
A` vd`nr p läs paquaôn sa maknlfkd a` parìnmn ma `d bukifùk. _nstarfnrlakta, atumfdralns ak matd``a d`cukds bukifnkas parfùmfids.
Ajalp`ns
4. Mdmd b ( x) < 9 x -4 inkstrufr `d cräbfid, fmaktfbfidr su mnlfkfn, su rdkcn y matarlfkdr sf as bukifùk.
Hd``dr d`cukns puktns ma `d cräbfid, inkstruyakmn ukd tde`d ma vd`nras.
x -4 -5 -9 ? 4 5 9
b
( x
) -= -3 -4? -4 5 1 8
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@d cräbfid as ukd raitd ak a` p`dkn idrtasfdkn. Yu mnlfkfn snk tnmns `ns klarns rad`as y su rdkcn tdlefæk snk tnmns `ns kúlarns rad`as. Astd cräbinrraspnkma d ukd bukifùk pnrqua pdrd mns a`alaktns mfbaraktas ma mnlfkfn, `d bukifùk dsfckd vd`nras mfbaraktas d su rdkcn.
Yf d` trdzdr iud`qufar raitd parpakmfiu`dr d` aja x, æstd inrtd ukd cräbfid uk úkfin puktn, `d cräbfid inrraspnkma d ukd bukifùk, qua as ukd bnrlfktuftfvd y bäif` ma matarlfkdr, sf ukd cräbfid mdmd as `d raprasaktdifùk ukd bukifùk.
x ? 4 5 9 = 6
b ( x) ? 4 4.=4 4.39 5 9
5. Yf ( ) b x x< , hdiar `d cräbfid ma b ( x), hd``dr su mnlfkfn, su rdkcn y as
e`aiar sf as bukifùk.
Inkstruydlns `d cräbfid, hdifakmn ukd tde`d ma vd`nras.
Ak `d cräbfid, pnmlns nesarvdr quainrraspnkma d ubukifùk. Yu mnlkfn snk ns kúla
rad`as kn kacdtfvas maifr, a` fktarv`n (?, + ∛), puaqua d rdìz iudmrdmaea inrraspnkmd uk kúlarn kn kcdtfvn, a` rdkcn mabukifùk tdlefækCräbfid 59
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@d cräid ma d bukifùk kn inrtd d d raitd x < -9, dukqua sa diaridd a``d tdktn pnr `d fzqufarmd inln pnr `d maraihd. Maiflns qua `draitd x < -9 as ukd dsìktntd vartfid` ma `d cräid ma `d bukifùk.
9. Yf5
( )9
b x x
<+ , matarlfkdr sf inrraspnkma d ukd bukifùk, akinktrdr s
mnlfkfn y a` rdkcn.
@d cräbfid inrraspnkma d ukd bukifùk, su mnlfkfn snk `ns kúlarns rad`as axiaptn a` a`alaktn -9 pnrqua b (-9) kn axfsta. A` rdkcn ma `d bukifùk snk tnmn`ns kúlarns rad`as, axiaptn a` vd`nr ? puastn qua `d cräbfid kn inrtd a` aja
Nesarvdifùk
x -1 -= -5 -4 ? 4 5 9 b ( x) -4 -5 5 4 ?.22 ?.1 ?.= ?.9
Cräbfid 5=
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=. @d bukifùk?
( )?
W x sf x b x x
x sf x< <
0
Fmaktfbfidr a` mnlfkfn, a` rdkcn y matarlfkdr sf `d cräbfid inrraspnkma d u
bukifùk.
Yn`uifùk
Ralns qua pdrd ? ù vd`nras pnsftfvns, `d bukifùk dsfckd a` lfsln vdlfaktrds qua pdrd vd`nras kacdtfvns ma su mnlfkfn, as dsfckd a` vd`nr npuas
D`cukds pdrajds ma puktns `ds mdlns ak `d sfcufakta tde`d.
@d cräbfid inrraspnkma d ukd bukifùk. Yu mnlfkfn snk tnmns `ns kúlarad`as y su rdkcn snk `ns kúlarns rad`as kn kacdtfvns as maifr a` fktarvd
x -1 -= -5 -4 ? 4 5 9
x 1 = 5 4 ? 4 5 9
Cräbfid 51
b ( x) < | x|
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Ak idmd ukn ma `ns ajarififns sfcufaktas, trdzdr `d cräbfid, matarlfkdr
sf as bukifùk y maifr, sf as ukn d ukn7 fmaktfbfidr a` mnlfkfn y a` rdkcn.4. @d bukifùk b(x)< 1 d qua crdbfid inrraspnkma
5. b ( x) < -9 x + 4
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9. @d crdbfid qua inrraspnkma d `d bukifùk b(x)< 5x5 - 4
=.
1.
2.
3.
8.
6.
4?.
b ( x) < x9 + 4
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Ak uk trfäkcu`n raitäkcu`n, sdealns qua hdy mnsäkcu`ns fktarkns dcumns δ y θ. Yf ``dldlns i d `d
hfpntakusd, y d, e d `ns idtatns, pnmalns astde`aiar `dssfcufaktas ra`difnkas:
d idtatn npuastnsakn
i hfpntakusdd < <
e idtatn dmydiaktainsakni hfpntakusd
d < <
tdk d idtatn npuastn
caktae idtatn dmydiakta
d < <
_nmalns astde`aiar ra`difnkas raiìprnids inrraspnkmfaktas d idmd ukd ma `ds ra`
Cräbfid 52
Bukifnkas trfcnknlætrfidsQkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n
Yasfùk
4
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Dsì lfsln, pnmalns mabfkfr astds safs ra`difnkas pdrd a` ntrn äkcu`n dcumn θ trfäkcu`n raitäkcu`n:
]akfakmn ak iuaktd qua pdrd asta äkcu`n θ, a` idtatn npuastn as d y a` idtatn dm
iakta as e, lfaktrds qua `d hfpntakusd i kn subra d`cukd vdrfdifùk.
Inln pnmalns var, idmd ukd ma astds vdrfdifnkas kn as läs qua a` inifakta ma`nkcftumas ma uk saclaktn.
Dsì, pdrd hd``dr sakn δ, mfvfmflns `d `nkcftum ma` idtatn npuastn aktra `d `nkcftum`d hfpntakusd7 y pdrd hd``dr tdkcakta ma δ, mfvfmflns `d `nkcftum ma` idtatn npuaaktra `d `nkcftum ma` idtatn dmydiakta y sa prniama ma ldkard sflf`dr pdrd `ds
läs ra`difnkas.
]dkcakta θ < tdk θ
Insaidkta θ < insi θ
Yaidkta θ < sai θIntdkcakta θ < intdk θ
Dmaläs, ma `ds ra`difnkas dktarfnras pnmalns astde`aiar qua:
insi θ < 4/ sak θ n sak θ < 4/insi θ
sai θ <4/ins θ n ins θ < 4 /sai θ
intdk θ < 4/tdk θ n tdk θ < 4/intdk θ
Astds fcud`mdmas snk vä`fmds, sfalpra y iudkmn `ns maknlfkdmnras takcdk vd`n
K θ < tdkθ7 insaidkta θ < insi θ7 saidkta θ <sai θ7 intdkcakta θ < intdk θ
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4. Ak ukd hnjd ak e`dkin, mfeujdr uk trfäkcu`n raitäkcu`n, lamfr `d `nkcftum midmd ukn ma sus `dmns y pdrd idmd äkcu`n dcumn (äkcu`ns laknras ma 6?¿hd``dr `ns vd`nras ma sak, ins, tdk, intdk, sai y insi.
5. Mdmn a` sfcufakta trfäkcu`n raitäkcu`n, hd``dr `ns vd`nras ma sak δ, ins δ, tdδ, sai δ, insi δ, intdk δ, sak θ, ins θ, tdk θ, sai θ, insi θ, intdk θ.
Uasn`var uk trfäkcu`n, inksfsta ak hd``dr ds nkcftumas ma sustras `dmns y `ds lamfmds ma sus tras äkcu`ns fktarfnras.
Cräbfid 53
_rne`alds dp`fidmns ak `d
rasn`uifùk ma trfäkcu`ns raitäkcu`ns
Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n Yasfùk
5
4
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Cräbfid 56
5. Uasn`var a` trfäkcu`n raitäkcu-`n pdrd a` iud`d < 95,=2
e < 51,38y a` äkcu`n dcumn θ < 98.=2¿.
Yn`uifùk
Yacúk `ns mdtns akukifdmns ak a` prne`ald, inknialns `ns vd`nras ma mns idtatns, ma` äkcu`n dcumn θ y masma `uacn, a` äkcu`n raitn. _drd hd``däkcu`n dcumn θ, `a rastdlns a` vd`nr ma θ d 6?¿ y netakalns:
Cräbfid 58
Ajalp`ns
4. Ak `d cräbfid, a` trfäkcu`n rai-
täkcu`n astä rasua`tn, pnrquasa inkniak `ds lamfmds ma sustras dmns y ma sus tras äkcu`ns.
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_drd hd``dr a` vd`nr ma `d hfpntakusd i, hdialns:
d / i < sak δ, ma mnkma i < d /sak δ.
Uaalp`dzdkmn `ns vd`nras takalns:
i < 95.=2/sak 14.1= < =4.=1
Halns hd``dmn `ns safs vd`nras inrraspnkmfaktas d `ds `nkcftumas ma sus tra`dmns y d `ds lamfmds ma sus tras äkcu`ns, `uacn takalns rasua`tn a` trfäkcuraitäkcu`n.
Mabfkfifùk
A` saclaktn ma raitd masma uk puktn ma nesarvdifùk N d uk puktnnesarvdmn _, sa ``dld `d vfsud` ma _. A` äkcu`n ink værtfia ak a` puktn manesarvdifùk N, iuyns `dmns snk `d vfsud` y ukd salfrraitd hnrfznktd`, sa``dld äkcu`n ma a`avdifùk ma _, iudkmn _ sa akiuaktrd pnr drrfed ma N7
y sa ``dld äkcu`n ma maprasfùk iudkmn _ sa akiuaktrd pnr maedjn ma N.
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Cräbfid 94
Ma `d cräbfid, valns qua:
4,6? / x < tdk =5¿
ma mnkma sa netfaka
x < 4.6? / tdk =5¿ < 5,44 l
@uacn `d snlerd prnyaitdmd pnr a` hnlera tfaka ukd `nkcftum
Ajalp`n
Yf d matarlfkdmd hnrd ma` mìd, a` äkcu`n
ma a`avdifùk ma` Yn` as ma =5¿, ¾iuä` as `d
`nkcftum ma `d snlerd qua prnyaitd ak a`
sua`n, uk hnlera ma 4,6? l>
Yn`uifùk
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Cräbfid 9
4. Ak idmd cräbfid akinktrdr a` vd`nr ma x.
5. Iudkmn a` äkcu`n ma a`avdifùk d` puktn läs d`tn ma d tnrra Afbba` ak _drìs, ama 58.=¿, `d snlerd prnyaitdmd as ma 4.855 pfas ma drcn. ¾Iuä` as `d d`tur
ma `d tnrra>
9. Qkd asid`ard ma 5? pfas ma drcn sa dpnyd ak ukd pdram, bnrldkmn uk äkcu`ma 32¿ ink a` sua`n. ¾D quæ d`turd astä a` axtraln suparfnr ma `d asid`ard
=. Masma d pdrta suparfnr ma uk amfbfifn ma 2? pfas ma d`turd, a` äkcu`n ma a`avdifùk d uk pnsta as ma 4=¿. Ak `d edsa ma` amfbfifn, a` äkcu`n ma a`avdifùd `d puktd ma` pnsta as ma 58¿ akinktrdr `d d`turd ma` pnsta y `d d`turd ma
d.
m.
i.e.
a. b.
5
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Dprakmfakmn ink a` prnba Ju`fnAiudifùk iudmrätfid ak uk prne`ald ma canlatrìdMurdifùk: 3:91 lfk.
dsak
i
d <
ins e
id <
tdk d
ed <
e
Ma` trfäkcu`n raitäkcu`n ma`d cräbfid 95, takalns qua:
Cräbfid 99
Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n Yasfùk
9D`cukds fmaktfmdmas eäsfids
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Yf hdialns `ns inifaktas:
tdkins
dsak di
e ei
d
dd < < < y
ins
intdk
eei
dsak di
d
dd < < <
@uacn valns qua:ins
tdk intins
sak y dk
sak
d dd d
d d< <
Ma mnkma valns qua tnmds `ds rdznkas trfcnknlætrfids sa puamak mdr ak tærlfknma sakn y insakn.
Ajalp`n
Yf sak δ < ?,1 y ins δ < ?,822 pnmalns hd``dr tdk δ dsì:
?,1tdk ?,133
?,822d < <
?,8222intdk 4,395
?,1
d < <
Dmaläs,
4sai 4,41=
?.822d < <
4insai 5
?.1d < <
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`d id`iu`dmnr
Qsn ma `d id`iu`dmnrd
Qsdkmn ukd id`iu`dmnrd ifaktìbfid, sa puama hd``dr akbnrld räpfmd y praifsd, `ns vd`nras ma sakn, insakn,tdkcakta, intdkcakta, saidkta y insaidkta ma äkcu`nsdcumns y ak cakard` ma iud`qufar äkcu`n. As kaiasdrfn
ajariftdrsa ak a` ldkajn ma d id`iu`dmnrd puastn qua asukd harrdlfaktd vd`fnsd ak a` astumfn ma d trfcnknlatrìd.
D` lnlaktn ma utf`fzdr `d id`iu`dmnrd ifaktìbfid, as buk-mdlaktd` `aar luy efak `ds fkstruiifnkas ma `d lfsld,yd qua mapakmfakmn ma` lnma`n, murdkta `d ajaiuifùkma d`cukds bukifnkas puamak vdrfdr `ns rasu`tdmns.
Inlp`atdr `d sfcufakta tde`d:
4?
41
5?,8
9?
=1
2?
31,2
38
D (¿) Yak δ Ins δ ]dk δ Intdk δ Yai δ Insi δ
4
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4. Masma `d pdrta suparfnr ma ukdidktf`dmn ma 452 l ma d`turd,a` äkcu`n ma maprasfùk ma ukedrin as 5?.53¿ `d mfstdkifd d`d iud` sa akiuaktrd a` edrin ma`d edsa ma` didktf`dmn as:
d. ==1,238 l e. 459,832 l i. 991,543 l m. 952,682 l Cräb
5. Ink dyumd ma `d id`iu`dmnrd, inlp`atdr `d sfcufakta tde`d:
9. A` äkcu`n ma a`avdifùk ma `d dzntad ma uk amfbfifn, lamfmn masma ukpuktn D sftudmn d 4??l ma `d edsa, as ma 2?¿, `d d`turd ma` amfbfin as:
d. 439,5?1 l e. 434,=12 l i. 435,234 l m. 43?,5=1 l
D (¿) Yak δ Ins δ ]dk δ Intdk δ Yai δ Insi δ
5?8¿451¿1¿=8¿93¿416¿9?1¿438¿
86¿
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Vd vflns qua ukd ifriukbarakifd i ma rdmfn r tfaka ukd`nkcftum ma 5Ϗr .
Qk cfrn inlp`atn ma` puktn axtraln ma uk rdmfn snera
`d ifriukbarakifd, masirfea uk äkcu`n ma 5Ϗr rdmfdkas.
Yf inksfmardlns inln ukfmdm ma nkcftum, d nkcftum ma` rdmfn, as maifr,r < 4, trdedjdralns ink ukd ifriukbarakifd ma rdmfn 4, qua ``dldralnsifriukbarakifd ukftdrfd. Ak a``d, uk cfrn inlp`atn ma su rdmfn ak mfraiifùkpnsftfvd, edrra uk äkcu`n ma 5Ϗ rdmfdkas7 lamfn cfrn edrra uk äkcu`n maϏ rdmfdkas7 uk iudrtn ma cfrn edrra uk äkcu`n ma Ϗ /5 rdmfdkas.
Yf hdialns a` cfrn ma` rdmfn ak saktfmn kacdtfvn, lamfd vua`td inrraspnk-ma d uk äkcu`n ma ’ Ϗ rdmfdkas, 9/= ma cfrn aqufvd`a d - 9Ϗ / 5 rdmfdkas.
D` inksfmardr uk äkcu`n iaktrd` ak su pnsfifùk astäkmdr ak ukd ifriuk-barakifd ma rdmfn 4, `d `nkcftum ma su drin s < r.t , mnkma t as `d lamfmdma` äkcu`n iaktrd` ak rdmfdkas, parn inln r < 4 sa tfaka qua s < t , matd` ldkard qua `d `nkcftum ma` drin suetakmfmn pnr a` äkcu`n, as fcud`
d `d lamfmd ma` äkcu`n iaktrd` ak rdmfdkas.
Inln `d lamfmd ma` äkcu`n as uk vd`nr kulærfin (iud`qufar kúlarnrad`), aktnkias `d `nkcftum ma` drin t pdrd uk äkcu`n iaktrd` ak ukd ifr-iukbarakifd ukftdrfd, sa inksfmard masma a` puktn fkfifd` (4,?) hdstd a`puktn _ ma innrmakdmds (x, y), mnkma a` `dmn bfkd` ma` äkcu`n inrtd `difriukbarakifd ukftdrfd y astd `nkcftum as iud`qufar kúlarn rad` t .
Bukifnkas sakn y insakn
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`asYasfùk
4
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@ds innrmakdmds idrtasfdkds ma` puktn bfkd` ma` drin snera d ifriukbarakifd ukftdrsnk bukifnkas ma` drin ma `nkcftum t . D astds bukifnkas `ds ``dldlns insakn y sak
mat
, dsì: x < ins t
y < sak t
As maifr, qua `ds innrmakdmds ma` puktn bfkd` _ astäk mdmds pnr:
_ < (x, y) < (ins t, sak t).
Inln iud`qufar puktn _ ma innrmakdmds (x, y) snera `d ifriukbarakifd ukftdrsdtfsbdia `d aiudifùk:
5 54 x y+ <
Uaalp`dzdkmn x pnr ins t, y pnr sak t, takalns:
5 5
Cräbfid 91
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Tua inrraspnkma d ukd fmaktfmdm trfcnknlætrfid bukmdlaktd` y qua usud`lak`d asirfeflns dsì:
_rflard fmaktfmdm bukmdlaktd` 5 5ins 4sak t t + <
Inln t as iud`qufar kúlarn rad`, a` mnlfkfn ma `d bukifùk sakn y ma `d bukifinsakn as a` inkjuktn ma `ns kúlarns rad`as. Nesarvdlns tdlefæk qua `ns vd`nma x y ma y vdrìdk aktra -4 y 4, `n iud` sfckfbfid qua a` rdkcn ma `d bukifùk saknma `d bukifùk insakn as a` fktarvd`nW4,4 .
Inln ins t y sak t snk ds innrmakdmds ma` puktn _ snera d ifriukbarakifd ukftdr
`ds bukifnkas sakn y insakn sa ``dldk bukifnkas ifriu`dras. ]dlefæk sa `as ``dlbukifnkas trfcnknlætrfids mabfkfmds snera `ns kúlarns rad`as.
_drd vd`nras ma t , ldynras ma 5Ϗ, pnmalns mabfkfr `ds bukifnkas trfcnknlætrfiak d lfsld bnrld, usdkmn d ifriukbarakifd ukftdrfd, puastn qua sf t as uk äkcuiaktrd` ak pnsfifùk racu`dr iuyn dmn tarlfkd` inrtd `d ifriukbarakifd ukftdrfd akpuktn _(x, y), y d nkcftum t ma su drin as laknr ma 5Ϗ, aktnkias a` dmn tarlfkd` asta äkcu`n infkifma ink iud`qufar dmn tarlfkd` ma uk äkcu`n iaktrd` ak pnsfif
racu`dr, iuyd lamf-md sad t + 5g Ϗ, mnk-ma g as uk kúlarnaktarn.
Astn sfckfbfid quasf tnldlns inln`dmn fkfifd`, a` `dmn
bfkd` ma` äkcu`n t y `a dmfifnkdlnsuk cfrn, mns cfrns,tras cfrns, a` `dmnbfkd` ma asns äkcu`nsinfkifma ink a` dmnbfkd` ma` äkcu`n t .
t t + 5Ϗ
t ’ 5Ϗ
]fakak a` lfsln`dmn bfkd`
Cräbfid 92
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Ma fcud` ldkard, `ds innrmakdmds ( x, y) ma` puktn bfkd` t snk `ds lfslds, ma mnkmtakalns qua:
sak t < sak (t+5g Ϗ)
ins t < ins (t + 5g Ϗ)
@n dktarfnr fkmfid qua `ds bukifnkas sakn y insakn snk parfùmfids, sfakmn:
Ϗ < 5Ϗ qua as su parìnmn.
Ajalp`ns
Qsdkmn `d id`iu`dmnrd, pnmalns inlprnedr a f`ustrdr ink d`cukns ajalp`n`d parfnmfifmdm ma astds bukifnkas.
4. sak (5) < sak (5 + 5Ϗ) < ?,6?6563=52
5. ins (5) < ins (5 + 5Ϗ) < -?,=424=2892
9. sak (5) < sak(5 - 5Ϗ) < ?,6?6563=52
=. ins (5) < ins (5 - 5Ϗ) < -?,=424=2892
1. sak (5,8) < sak(5,8 + 5Ϗ) < ?,99=68841
2. ins (5,8) < ins (5,8 - 5Ϗ) < -?,6=55559=
Ajalp`n:
Hd``dr a` vd`nr ma `ds bukifnkas trfcnknlætrfids pdrd a` äkcu`n ma Ϗ /=, sfk us
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Yn`uifùk
D` in`nidr a` äkcu`n ak su pnsfifùk racu`dr, a` `dmn bfkd` fktariaptd `d ifriuk
rakifd ukftdrfd ak a` puktn _ ma innrmakdmds x, y. Dmaläs, inln a` `dmn bfma asta äkcu`n mfvfma a` prflar iudmrdkta ak mns pdrtas fcud`as, takalns q x < y. Yf dp`fidlns a` tanrald ma _ftäcnrds pdrd a` trfäkcu`n raitäkcu`n ITvar cräbfid, takalns qua:
5 54 x y+ < . Inln x as fcud` d y takalns 5 5
4 x x+ < .
5
5 4 x < , ma mnkma
5 4
5
x <
`uacn rasn`vfakmn pdrd x
takalns
5
5
x <
, haltnldmn sn`dlakta a` vd`nr pnsftfvn ak d sn`uifùk, maefmn d qua x ak a` prfl
iudmrdkta as pnsftfvn. Inln x < y, aktnkias y < 5
5, ma td` ldkard qua:
Ins Ϗ /= <
Yak Ϗ /= <
Cräbfid 93
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Ak bnrld sflf`dr, pnmalns hd``dr`ns vd`nras ma `ds bukifnkas trfcn-knlætrfids pdrd a` äkcu`n ma Ϗ /9< 2?¿, dsì:
9sak
p<
4sfk
2 5
p<
9ins
2 5
p<
45
95
4 9tdk
2 99
p< < <
9int 9
2 4dk
p< <
5 5 9sai 2 9 9
p
< <
5insi 5
2 4
p< <
Hd``dr `ns vd`nras ma tdkcakta, intdkcakta, saidkta y insaidkta pdrd a` äkcuma Ϗ /=.
Ajalp`n
Hd``dr `ns vd`nras ma `ds bukifnkas trfcnknlætrfids ma `ns äkcu`ns Ϗ / 9 < 2?
Ϗ / 2 < 9?¿.
Yn`uifùk
Inkstruflns uk trfäkcu`n aquf`ätarnN_T ma `dmn 57 pnr supuastn,
idmd ukn ma sus äkcu`ns fktarfnraslfma 2?¿. Yf U as a` puktn lamfn ma
_T, a` trfäkcu`n N_T as raitäkcu-`n, `d `nkcftum ma `d hfpntakusd N_ as 5, a` idtatn NU tfaka nkcftum 9 y a` idtatn _U, tfaka `nkcftum 4, matd` ldkard qua:
4ins
p<
44
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Yf in`nidlns a` äkcu`n maϏ /2 ak pnsfifùk astäkmdr ak`d ifriukbarakifd ukftdrfd, a`puktn _ takmrä inln innr-
makdmds:
(9
5 ,4
5 )
Hd``dr tdkϏ /9, intdk Ϗ /9, sai Ϗ /9 y insi Ϗ /9.
Cräbfid 98
Cräbfid 96
5
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A` puktn T, sflætrfin ma _ ink raspaitn ma` aja y, uefid-mn snera a` `dmn bfkd` ma` äkcu`n ma 1Ϗ /2 < 41?¿, takmräinln innrmakdmds:
44 4
2 5sak
p< y
1 4
2 5sak
p<
Ma fcud` bnrld, a` puktn U sflætrfin ma _ ink raspaitnma` nrfcak iuyn `dmn bfkd` inrraspnkma d uk äkcu`n ma3Ϗ /2 < 54?¿ tfaka inln innrmakdmd:
9 4( , )
5 5
_nr `n tdktn, ins 3Ϗ /2 < 9
5 y sak 3p /2 <
Dkä`ncdlakta, pdrd a` puktn Y, sflætrfin ma _ ink ras-
paitn ma` aja x qua astä snera a` `dmn bfkd` ma` äkcu`n
ma 44Ϗ /2, tfaka inln innrmakdmds ma td` bnrld
qua:
y
Inknifakmn `ns vd`nras ma sakn y insakn pdrd uk vd`nriud`qufard ``dldmn ot½, pnmalns hd``dr `ns vd`nras ma `dsmaläs bukifnkas trfcnknlætrfids pdrd asa vd`nr t.
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Cräbfid =?
Inln `d cräbfid ma `d ifriukbarakifd ukftdrfd ink iaktrn ak a` nrfcak as sflætrink raspaitn ma` aja x, raspaitn ma` aja y, raspaitn ma` nrfcak, sa tfaka qua:
A` puktn T sflætrfin ma _, ink raspaitn ma` aja y tfaka inln innrmakdmds (- x,A` puktn Y, sflætrfin ma _ ink raspaitn ma` aja x, tfaka inln innrmakdmds ( x, y a` puktn U sflætrfin ma _ ink raspaitn ma` nrfcak tfaka inln innrmakdm(- x, - y).
Astn sfckfbfid qua:
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Ma bnrld sflf`dr, a` puktn U sflætrfin ma _ ink raspaitn ma`nrfcak tfaka inln innrmakdmds (- x,- y). Inln a` puktn U astä
ak a` `dmn bfkd` ma` äkcu`n ma 1Ϗ /=, aktnkias takalns qua:
Ins 1Ϗ /= < -5
5
y sak 1Ϗ /= < -
5
5
]dlefæk pdrd a` puktn U, sflætrfin ma _ ink raspaitn ma` aja x, takalns qua sus innrmakdmds snk ( x,- y), inln a` puktn Y astä ak a` `dmn bfkd` ma 3Ϗ /=, aktnkias:
ins 3Ϗ /= <5
5
y sak 3Ϗ /= < -5
5
Yf inknialns ns vd`nras ma insakn y ma sakn pdrd uk äkcu`nt , iuyn dmn bfkd` inrtd d d ifriukbarakifd ukftdrfd ak a` puktn_, pnmalns hd``dr tdlefæk ns vd`nras ma sakn y insakn pdrd`ns äkcu`ns iuyn `dmn bfkd` inrtdk d `d ifriukbarakifd ukftdrfdak ns puktns sflætrfins ma _, ink raspaitn ma` nrfcak y d nsajas innrmakdmns y pnr akma, pnmalns hd``dr a` vd`nr ma `dsmaläs bukifnkas trfcnknlætrfids pdrd mfihns äkcu`ns.
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Yf dkd`fzdlns a` vd`nr ma ds bukifnkas trfcnknlætrfids pdrd ns äkcu`ns iudmrdktdiuyds innrmakdmds ma su puktn bfkd` d` inrtdr `d ifriukbarakifd ukftdrfd snk (4(?,4), (-4,?), (?,-4) takalns qua:
Ins ? < 4 sak t < ?
Ins Ϗ /5 < ? sak Ϗ /5 < 4
Ins 9Ϗ /5 < ? sak 9 Ϗ /5 < -4
Cräbfid =4
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_drd mfeujdr `d cräbfid ma `d bukifùk sakn ak a` p`dkn idrtasfdknvdlns d id`iu`dr sak t pdrd t aktra ? y 5Ϗ rdmfdkas, `n iud` supnkqua astfrdlns d ifriukbarakifd ukftdrfd, hdifækmn`d infkifmfr ink mfraiifùk pnsftfvd ma` aja x. Rdlns d inkstrufr ukd tde`d ma vd`nra
Cräbfid =5
θ¿ ? 9? =1 2? 6? 45? 491 41? 48? 54? 551 5=? 53? 9?? 941 99? 9
Udm ? Ϗ /2 Ϗ /= Ϗ /9 Ϗ /5 5Ϗ /9 9Ϗ /= 1Ϗ /2 Ϗ 3Ϗ /2 1Ϗ /= =Ϗ /9 9Ϗ /5 1Ϗ /9 3Ϗ /= 44Ϗ /2 5
Yak θ ? ?,1 ?,3 ?,82 4 ?,82 ?,3 ?,1 ? -?,1 -?,3 -?,82 -4 -?,82 -?,3 -?,1
Cräids ma `d bukifùk sakn
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`as
Yasfùk
5
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Yf sacuflns tnldkmn vd`nras ldynras ma 5Ϗ hdstd =Ϗ, netakmralns `d rapaifùk ma `d cräbfid, as maifr, pnmalns var qua `d cräbfid ma sakn t , sa rapfta fktarvd`ns ma `nkcftum 5Ϗ, pnrqua `d bukifùk sakn as parfùmfid7 rainrmalns qsak (t + 5Ϗ) < sak t .
Ma `d cräbfid pnmalns nesarvdr qua sak t tnld vd`nras masma -4 hdstd +4,maifr, qua a` rdkcn ma `d bukifùk as fcud` d` fktarvd`n W-4,4\. Dmaläs, pnmalns qua aktra ? y Ϗ, `ns vd`nras ma` sakn snk pnsftfvns y aktra Ϗ y 5Ϗ, `ns vd`nras sakn snk kacdtfvns, `n iud` sfckfbfid qua ak `ns iudmrdktas F y FF, sak t as pnsftfvnak `ns iudmrdktas FFF y FR sak t as kacdtfvn. Nevfdlakta, `d cräbfid ma sak t , inrrpnkma d `d cräbfid ma ukd bukifùk, parn kn d ukd bukifùk ukn d ukn, pnr ajalpsak Ϗ /= < sak 9Ϗ /= < ?,3.
Ak cakard`, pdrd hd``dr `ns vd`nras ma `ds bukifnkas trfcnknlæ-trfids sa utf`fzd `d id`iu`dmnrd ifaktìbfid ink `d iud` netakalnsak bnrld räpfmd, vd`nras läs axditns hdstd ink 4? ù läs ifbrdsmaifld`as.
@d id`iu`dmnrd prasaktd vdrfns sfstalds ma ukfmdmas pdrd `dslamfmds ma ns äkcu`ns inln crdmns y rdmfdkas, as kaiasdrfn ma-tarlfkdr ak quæ ukfmdmas trdedjdlns pdrd kn fkiurrfr ak arrnras.
Ink d id`iu`dmnrd, tdlefæk pnmalns hdiar a` iä`iu`n pdrd sak t ,`n iud` cakard uk vd`nr aktra -4 y +4 ù mdmn a` vd`nr ma sak t ,hd``dr uk vd`nr ma t qua cakarù asa vd`nr, `n iud` hdialns la-mfdkta `d tai`d sfk-4, ``dldmd sakn fkvarsn.
Ajalp`n
Yak 9?¿ < ?,1 ù sfk-4 ?,1 < 9?¿.
D`cukds cräbfids aspaifd`as ma `d bukifùk sak-4θ.
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Ajalp`n
Crdbfidr b(t) < 5.sak t
Nesarvdlns qua idmd vd`nr ma sak t quamd lu`tfp`fidmn pnr 5. Inln sak
vdrìd aktra -4 y +4, sa tfaka qua 5.sak t vdrìd aktra -5 y +5.
_nmalns nesarvdr ak bnrld sflu`täkad, `ds cräbfids ma sak t y 5.sakt ak a` fktarvdiarrdmn (?,5Ϗ), `ds iud`as tfakak a` lfsln parìnmn, parn mfbarakta dlp`ftum7
Cräbfid =9
t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ
5.Yak t 4.=4 5 4.=4 ? -4.=4 -5 -4.=4 ?
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4. Inlp`atdr `ns vd`nras ak `d tde`d y hdiar `d cräbfid ma 9.sak t 7 matarlfkdrdlp`ftum.
_drd hdiar `ds cräbfids ma b(t) < sak et d pdrtfr ma:
()5 5
( ) ( 5 )
( )e e
b t sak et sak et
sak e t b t p p
p< < +
< + < +
@n dktarfnr luastrd qua d bukifùk b(t) < sak et as parfùmfid, ink parìnmn 5ep . Yf e
kacdtfvn, tnldlns a` vd`nr desn`utn ma e, pdrd qua a` parìnmn sad pnsftfvn. Dsparìnmn as 5
e
p
Ajalp`n
Hdiar `d cräbfid ma b(t) < sak et
5. Inlp`atdr `ns vd`nras ak `d tde`d y hdiar `d cräbfid ma 4/5.sak t 7 matarlfkdrdlp`ftum.
t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ
9.Yak t
t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ
4/5.Yak t
4
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`d id`iu`dmnrd
Ma `d cräbfipnmalns vaqua a` parìnmn ma sak
as 5Ϗ /5 < Ϗ
`d dlp`ftuas `d lfslqua d cräbfima sak t .
t Ϗ /= Ϗ /5 9Ϗ /= Ϗ
Yak 5t 4 ? -4 ?
4. ( ) =. b t sak t <
5. 4( ) .
= b t sak t <
9. 4( ) b t sak t <
Qsa `d id`iu`dmnrd pdrd trdzdr `ds sfcufaktas cräbfids y ak idmd idsn, hd``dr su dlp`ftum y su parìnmn.
=. ( ) = b t sak t <
1. b (t ) < 9.sak 9t
Cräbfid ==
5
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θ
Ma `d cräbfid pnmalns var qua ins t vdrìd aktra -4 y +4, as
maifr, a` rdkcn ma `d bukifùk as a` fktarvd`n (-4,4).
Yf sa sfcuak mdkmn vd`nras pdrd t ldynras ma 5Ϗ, `d cräbfidsa rapfta ak a` fktarvd`n (5Ϗ,=Ϗ) y dkä`ncdlakta, `d cräbfid sarapfta ak `ns fktarvd`ns (=Ϗ,2Ϗ), (2Ϗ,8Ϗ), (-5Ϗ,?) maefmn d qua`d bukifùk ins t as ukd bukifùk parfùmfid ink parìnmn 5Ϗ.
Ntrds cräbfids qua fkvn`uirdk ins t : c(t) < d ³ ins t
Cräbfid =1
¿ ? 9? =1 2? 6? 45? 491 41? 48? 54? 551 5=? 53? 9?? 941 99?
Udm ? Ϗ /2 Ϗ /= Ϗ /9 Ϗ /5 5Ϗ /9 9Ϗ /= 1Ϗ /2 Ϗ 3Ϗ /2 1Ϗ /= =Ϗ /9 9Ϗ /5 1Ϗ /9 3Ϗ /= 44Ϗ /2
ins t 4 ?,82 ?,3 ?,1 ? -?,1 -?,3 -?,82 ? -?,82 -?,3 -?,1 ? ?,1 ?,3 ?,82
Cräid ma `d bukifùk insakn
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`asYasfùk
9
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Ajalp`n
Hdiar `d cräbfid ma c(t) < 9 ³ ins t
c(t) < ins et
c(t) < ins (et+5Ϗ), pnr `d parfnmfifmdm ma `d bukifùk ins t
@uacn:
Ma `d cräbfid, nesarvdlns qua 9.ins t tfaka ukd dlp`ftum tras vaias ldynr qua ma ins t , parn su parìnmn as a` lfsln pdrd `ds mns.
Cräbfid =2
t Ins t 9.ins t
? 4 9 Ϗ /= ?,3 5,45 Ϗ /5 ? ?
9 Ϗ /= -?,3 -5,45 Ϗ -4 -9 1 Ϗ /= -?,3 -5,45 9 Ϗ /5 ? ? 3 Ϗ /= ?,3 5,45 5 Ϗ 4 9
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@n iud` luastrd qua c(t) < ins et as ukd bukifùk parfùmfid ink parìnmn 5ep
Yf e as kacdtfvn, tnldlns inln parìnmn a` vd`nr pnsftfvn ma Ϗ snera a` vd`nr desn`ma e dsì: 5
e
p
Mdmds `ds sfcufaktas bukifnkas, ak idmd idsn, matarlfkdr su dlp`ftum y su parìnm
Ajalp`n
Hdiar `d cräbfid ma `d bukifùk c(t) < ins 4/5t.
Cräbf
=. ( ) 1ins 2c t t <
1. ( ) ?, =ins 1c t t <
4. ( ) 1ins 9c t t <
5. ( ) ins =c t t <
9. 4
( ) ins5
c t t <
4
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Ak idmd idsn, hd``dr `d dlp`ftum y a` parìnmn, y trdzdr `d cräbfid ma `d bukifùk
mdmd.
@d dlp`ftum ma `d cräbfid as y a` parìnmn as =Ϗ. Ak d cräbfisa luastrdk d `d vaz, a` ins t
a` ins 4/5t
t Ins t Ins 4/5t
? 4 4
Ϗ /= ?,3 ?,65
Ϗ /5 ? ?,3 9 Ϗ /= -?,3 ?,98
Ϗ -4 ?
1 Ϗ /= -?,3 -?,98
9 Ϗ /5 ? -?,3
3 Ϗ /= ?,3 -?,65
5 Ϗ 4 -4
@ds bukifnkas sakn y insakn snk `ds läs flpnrtdktas7 su inlpraksfùkbdif`ftd a` astumfn ma `ds ntrds bukifnkas ifriu`dras, `d tdkcakta, `dintdkcakta, `d saidkta y `d insaidkta. Dmaläs, inln a` mnlfkfn ma `dbukifùk sakn y insakn as a` inkjuktn ma `ns kúlarns rad`as, sfckfbfidqua sak t y ins t axfstak iud`qufard sad a` vd`nr t
=. 4=
( ) 5insc t t <
1. 49
( ) 9insc t t <
4. ( ) =insc t t <
5. ( ) 9insc t t <
9. 4=
( ) insc t t <
5
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Mabfkflns tdk sak t
t ins t
< pdrd ?ins t .
Ma `d mabfkfifùk, valns qua tdk t kn tfaka uk vd`nr mabfkfmn iudkmn ins
t < ?, astn niurra iudkmn t< Ϗ /5, 9 Ϗ /5, 1 Ϗ /5, 3 Ϗ /5, - Ϗ /5, - 9Ϗ /5, - 1Ϗ /5,
ak cakard`, sf t as ma `d bnrld (5 4)5
g p
+ , mnkma g as iud`qufar aktarn.
Astns vd`nras sa axi`uyak ma` mnlfkfn ma `d bukifùk tdk t .
Ajalp`n
Yf t sa dprnxfld d` vd`nr Ϗ /5 < 6?¿, sak t sa dprnxfld d 4 y ins t sa dprnxfld d ?, y
bukifùk tdk t as crdkma. Radlns `ns sfcufaktas vd`nras:
θ(¿) 86 86,6 86,66 86,666
tdk t 13,586 135,613 1356,133 13.561,336
@ns vd`nras ma tdk θ vdk iraifakmn d lamfmd qua θ sa diarid d Ϗ/5 < 6?¿. Dqtnmns `ns vd`nras ma tdkcakta snk pnsftfvns maefmn d qua tnldlns vd`nras aktry Ϗ/5 ak `ns iud`as tdktn sak θ inln ins θ snk pnsftfvns θ snk pnsftfvns
_drd dkd`fzdr a` rdkcn ma `d bukifùk tdkcakta ma t , rainrmalns qua sak t y in
vdrìdk ak a` fktarvd`n 4,4 `uacn `d bukifùk tdkcakta puama tnldr vd`nras tcrdkmas inln sa masaak, sf a` maknlfkdmnr ins t sa dprnxfld d iarn.
@d bukifùk tdkcakta
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`asYasfùk
=
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Nesarvalns `d sfcufakta tde`d:
Ak asta idsn, tdk θ tnld vd`nras kacdtfvns luy crdkmas iudkmn θ sa dprnxfld Ϗ /5, maefmn qua `ns vd`nras ma θ astäk aktra Ϗ /5 y Ϗ (sacukmn iudmrdkta), ak mnkmsakθ as pnsftfvn y insakn θ as kacdtfvn.
Ma `n dktarfnr, pnmalns var qua a` rdkcn ma `d bukifùktdk
θ
as a` inkjuktn ma `nkúlarns rad`as.
Yf fktaktdlns hd``dr ink ukd id`iu`dmnrd tdk Ϗ /5 < tdk 6?¿, `d raspuastd as arrnmaefmn d qua `d bukifùk tdkcakta kn astä mabfkfmd pdrd asa vd`nr, as maifr, Ϗ /5 kpartakaia d` mnlfkfn ma `d bukifùk tdkcakta.
Ma d mabfkfifùk ma d bukifùk tdkcakta, pnmalns var qua tdk θ as pnsftfvd ak a` pr
larn y tariar iudmrdkta, y tnld vd`nras kacdtfvns ak a` sacukmn y iudrtn iudmrdkt
θ(¿) 6?,4 6?,?4 6?,??4 6?,???4
tdk θ -135,613 -1.356,133 -13.561,336 -135.613,361
θ
Ak `d cräbfid pnmalns nesarvdr qua `d bfcurd sa rapfta ak fktarvd`ns ma `nkcftum Ϗ
as maifr, takalns `d lfsld cräbfid ak `ns fktarvd`ns
, ,
9 9, , ,
5 5 5 5 5 5
p p p p p p
¿ ? =1 2? 6? 45? 491 48? 551 53? 941 92?
Udm ? Ϗ /= Ϗ /9 Ϗ /5 5Ϗ /9 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ
tdk θ -- ? 4 9 KN - 9 -4 ? 4 KN -4 ?
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Cräbfid =
`n iud` sfckfbfid qua `d bukifùk tdkcakta as parfùmfid ink parìnmn Ϗ n sad q()tdk tdkt t p+ <
@ds raitds vartfid`as qua pdsdk pnr `ns puktns9 9
, , ,5 5 5 5
p p p p snk dsìktn
vartfid`as ma tdkcakta t. @d cräbfid ma d bukifùk tdkcakta sa diarid d astd raitd pakukid `d inrtd.
Ajalp`n
Hd``dr `ns vd`nras ma:
4. Id`iu`dr
5. Hd``dr tdk 9??º tdk 9??º < tdk (45?º + 48?º) < tdk 45?º < -4
4. tdk 46?º 5. 9. tdk 5=?º =. tdk 9=1º 1.
4
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Ajalp`n
Ydealns qua tdkinssakqq
q<
@uacn, sf raalp`dzdlns ak `d fcud`mdm mdmd, takalns:5
5
54 4
ins
sak sak
ins
q q
q q
+ < + ó
5 5
5 5ins 4
ins inssakq q
q q
+< <
5
54sai
insq
q
< < ó
@n qua luastrd qua 5 54 tdk saiq q+ < as vä`fmd pdrd tnmns `ns vd`nras ma q , a
Qkd fcud`mdm qua as varmdmard pdrd tnmns `ns vd`nrasma `ds vdrfde`as fkvn`uirdmds ak a``d, sa ``dld fmaktfmdm.
D`cukds fmaktfmdmas trfcnknlætrfids
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`asYasfùk
1
Dprakmfakmn ink a` prnba Ju`fnInlprnedifùk ma ukd Fmaktfmdm ]rfcnknlætrfidMurdifùk: 1:=6 lfk.
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@d bukifùk b (t ) < tdk et , tfaka inln parìnmn4=
=p
p<
Crdifds d qua e as aqufvd`akta d °, y sf e as kacdtfvn, tnldlns su vd`nr desn`u
pnrqua a` parìnmn maea sar pnsftfvn.
Ajalp`ns
4. Yf b (t ) < tdk 1t, a` parìnmn as: Ϗ /1
5. Yf 4( ) tdk
=
b t t < , aktnkias a` parìnmn as 4
=
=p
p<
4. b (t ) < tdk 5t
5. b (t ) < tdk (-9t )
9.
Mdmds `ds sfcufaktas bukifnkas, akinktrdr a` parìnmn:
Ajalp`n
4
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Ak asta idsn, valns qua `ds dsìktntds vartfid`as ma `d cräbfid snk `ds raitds qupdsdk pnr ’Ϗ /2, Ϗ /2, Ϗ /5, 1Ϗ /2.
@d cräbfid tfaka bnrld pdraifmd d `d bukifùk tdkcakta, parn su parìnmn sa ramuia d Ϗ /9.
@d bukifùk intdkcakta
Mabfkflns `d bukifùk pdrd vd`nras ma 7 sf a` vd`nr m
maknlfkdmnr sakt as iarn, `d bukifùk intdkcakta kn astä mabfkfmd7 inln sakt a
iarn ak Ϗ, 5Ϗ, 9Ϗ, -Ϗ, -5Ϗ, - 9Ϗ, as maifr, ak tnmns `ns vd`nras ma t < g .Ϗ, ak `n
iud`as g as uk kúlarn aktarn. Aktnkias, astns vd`nras kn partakaiak d` mnlfkfn m
Cräbfid =6
Hd``dr `d cräbfid ma 49( ) tdk b t t <
5
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Yf t sa diarid d uk lú`tfp`n ma Ϗ, ins t sa diarid d iarn y a`vd`nr ma intdkcakta sa hdia luy crdkma, ink vd`nr pnsftfvnn kacdtfvn.
Dkd`fialns a` inlpnrtdlfaktn ma `d cräbfid ak a` fktarvd`n (?, Ϗ):
Ak a` puktn lamfn ma` fktarvd`n, takalns qua int ?5
dkp
< 7 dhnrd, sftnldlns vd`nras luy iaridkns d Ϗ, aktnkias a` vd`nr ma intdkcaktatnld vd`nras luy crdkmas kacdtfvns. Radlns d`cukns idsns:
Intdk 436¿ < -13,58
Intdk 436,6 < -135,61 Intdk 436,66 < -1.356,13
Inln valns, `d bukifùk vd mairaifakmn luy räpfmn d lamfmd qua t sa diarid d` vd`nr Ϗ < 48?¿.
Yf `a mdlns vd`nras d t prùxflns d iarn, netakalns vd`nras pnsftfvns
luy crdkmas pdrd intdkcakta mat
. Radlns d`cukns idsns: Intdk ?,4 < 135,65
Intdk ?,?4<1.356,13
Intdk ?,??4<13.561,33
Ak asta idsn, d bukifùk iraia, tnldkmn vd`nras luy crdkmas d lamfmd
Cräid ma `d bukifùk intdkcakta
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`asYasfùk
2
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D` trdzdr d cräbfid ma intdkcakta ma t , ak ns fktarvd`ns (-Ϗ, ?) y (Ϗ, 5Ϗ) netakalns ukcräbfid sflf`dr d d netakfmd ak a` fktarvd`n (?, Ϗ), n iud` kns fkmfid qua d cräbfid mintdk t sa rapfta parfùmfidlakta, y dsì d bukifùk intdk t as parfùmfid ink parìnmn Ϗ
As maifr, intdk (t + Ϗ) < intdk t
Inln `ds bukifnkas tdk t y intdk t sa puamak mdr ak tærlfkns ma sak t y ins t , astkns parlfta var d`cukds ma sus prnpfamdmas flpnrtdktas.
Ajalp`n
@ds bukifnkas tdk t y intdk t snk bukifnkas flpdras, vadlns:
d.
( )tdk( )ins( )
tdkins ins
sak t t t
sakt sakt t
t t
<
< < <
@uacn, tdk(-t) < -tdk t qua kns mfia qua `d bukifùk tdk t as ukd bukifùk flpd
t ( t) t t
Cräbfid 1?
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Ntrd fmaktfmdm trfcnknlætrfid:
_rnedr `d fmaktfmdm 4 + intdk5 θ < ins i5 θ.
Yn`uifùk
5
5
5
5 55
5 5
ins4 int 4
ins 4ins
dksak
saki
sak sak
q
q qq
q q
+ < +
+< < <
Ma `ds mabfkfifnkas 9 9 1... , , , , ...5 5 5 5 5p p p p p takalns qua `ds bukifnkas tdkcakt
intdkcakta snk raiìprnids. As maifr, 4
inttdk
dkqq
< , sf tdk ?q .
Yf takalns ( ) int b t dk et < , pnmalns lnstrdr qua su parìnmn ase
p.
pnr `d parfnmfifmdm ma int dk t . Aktnkias:
Ak a` maknlfkdmnr, tnldlns pdrd qua a` parìnmn sad pnsftfvn.
Ajalp`n
Hd``dr a` parìnmn y hdiar `d cräbfid ma `d bukifùk b (t ) < intdk 5t .
Yn`uifùk
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Matarlfkdr a` parìnmn ma `ds sfcufaktas bukifnkas:
4. ( ) int 9 b t dk t <
5. ( ) int 2 b t dk t <
9. ( ) int ?,1 b t dk t <
=. ( ) int ?, 51 b t dk t <
1. ( ) 5int 5b t dk t<
Cräbfid 14
4
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4sai
inst
t < , sf ins ?t 7 iudkmn ins ?t < , `d bukifùk
saidkta kn astä mabfkfmd7 astn niurra iudkmn 5 (5 4)t g p< + ,
as maifr, `ds raitds vartfid`as qua pdsdk pnr `ns puktns
snk dsìktntds ma `d cräbfid.
Ma d cräbfid nesarvdlns qua d bukifùk sai t kn tnld vd`nras ak a` fktarvd`n defa(47-4). Yu rdkcn ma vd`nras as a` inkjuktn ma `ns kúlarns rad`as ldynras n fcudd ukn, ukfmn ink a` inkjuktn ma `ns kúlarns rad`as laknras n fcud`as qua ukn,iud` pnmalns asirfefr dsì:
Halns prasaktdmn d` lfsln tfalpn `ds cräbfids ma ins t y sait pdrd nesarvdr la
Cräbfid 15
Bukifùk saidkta
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`asYasfùk
3
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Nesarvdifùk
@d bukifùk saidkta as parfùmfid y su parìnmn as 5Ϗ, `n iud` pnmalns varfbfidr bäif`lakta.
4 4sai sai( 5 )
ins ins( 5 )t t
t t p
p< < < +
+
Astd parfnmfifmdm tdlefæk `d pnmalns var ak `d cräbfid, ak mnkma sa rapfta ak lfsld bnrld ink fktarvd`ns ma `nkcftum 5Ϗ.
Ajalp`n
4.4
sai 9?º 2, =8
ins9?º
< <
5. 4
sai 31º 4,?8ins31º
< <
Ink `d id`iu`dmnrd, rad`fzdr `ns sfcufaktas iä`iu`ns:
4. sai =1¿5 sai 45?¿
=. int 41¿1 int 4?8¿
@ds bukifnkas intdkcakta, saidkta y insaidkta kn dpdraiak ak `nstai`dmns ma `ds id`iu`dmnrds ifaktìids, parn pdrd hdiar iä`iu`ns inkastds bukifnkas, pnmalns usdr sus raiìprnins dsì:
9. 4
int 81º 1,16
tdk 81º
dk < <
4
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Mabfkflns4
insi t sak t
< , sf ?sak t , iudkmn ?sak t <
`d bukifùk insaidkta kn astä mabfkfmd, `n iud` niurra iudkm
.t g p< , y g as iud`qufar kúlarn aktarn.
Ajalp`n
Ak ... -9Ϗ, -5Ϗ, -Ϗ, ?, Ϗ, 5Ϗ, 9Ϗ..., `d bukifùk insaidkta t kn astä mabfkfmd, `ds raivartfid`as qua pdsdk pnr astns puktns snk dsìktntds ma insi t .
@d bukifùk insaidkta as parfùmfid ink parìnmn 5Ϗ, inln sa luastrd d inktfkudif
Asta haihntdlefæk `npnmalnsnesarvdr,d` hdiar `dcräbfid mainsi t .
@d bukifùk insaidkta
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`as
Yasfùk
8
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@d bukifùk ma insi t kn tnld vd`nras ak a` fktarvd`n defartn ma lakns ukn d uk(-4,+4) , ma mnkma valns qua a` rdkcn ma `d bukifùk insaidkta as a` inkjuktn m`ns kúlarns rad`as laknras n fcud`as qua lakns ukn, ukfmn ink a` inkjuktn ma nkúlarns rad`as ldynras n fcud`as ma ukn.
ins ( , 4\ W4, ) Udkcn ma i t < +
Yf quaralns id`iu`dr `d insaidkta ma uk vd`nr t ink `d id`iu`dmnrd, maealns usd
a` raiìprnin ma insaidkta qua as sakn, pnrqua `d tai`d insaidkta t kn bfcurd ak atai`dmn ma `d id`iu`dmnrd.
Ajalp`n
Hd``dr:
Ya puama malnstrdr qua `ds bukifnkas ( ) sai ( ) ins b t et y c t i et < < sn
d. 4ins 2?º 4,41=
2?i
sak< <
e. 4ins 2?º 4,41=
2?i
sak< <
i. 4ins ( 1?º ) 4,9?1
( 1?)i
sak < <
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Ajalp`n
4 4
( ) ins( 5 )
c t i et sak et sak et p
< < <+
maefmn d `d parfnmfifmdm ma `d bukifùk sakn,
`uacn sai ins .tdksakq q q q < .
]nldlns vd`nr desn`utn ma e ak a` maknlfkdmnr ma` parìnmn pdrd dsacurdr qsad pnsftfvn.
4. ( ) sai 1 b t t <
5. ( ) ins ( 9 ) b t i t <
9. 4( ) sai ( )9
b t t <
=. ( ) 5 ins (?, 2 ) b t i t <
1. ( ) ins ( ?,4 ) b t i t <
Ak `ns sfcufaktas kulard`as, matarlfkdr a` parìnmn ma `d bukifùk:
4
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_nmalns varfbfidr d`cukds fmaktfmdmas trfcnknlætrfids, dpnyäk-
mnkns ak ds fmaktfmdmas eäsfids masdrrn``dmds hdstd dhnrd, y aka` inkniflfaktn ma `ds bukifnkas trfcnknlætrfids.
Ajalp`n
Ma `d fmaktfmdm bukmdlaktd` 5 5ins 4sak t t + < , netakalns:
5 5
4 inssak t t <
y
5 5
ins 4t sak t <
.Ajalp`ns
Rarfbfidr `d sfcufakta fmaktfmdm:
4. sai ins tdk .sakq q q q <
Yn`uifùk
Masdrrn``dkmn a` prflar `dmn ma `d fcud`mdm, takalns:
5 5
4sai ins ins
ins
4 ins. tdk .
ins ins ins
sak saksak sak
q q qq
q q qq q q
q q q
<
< < < <
Rarfidifùk ma fmaktfmdmastrfcnknlætrfids
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns
rad`as Yasfùk
6
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_drd varfbfidr ukd fmaktfmdm trfcnknlætrfid, sa puama tnldr `d axprasma` prflar `dmn ma `d fcud`mdm y trdksbnrldr`d ak a` sacukmn `dmn n tnl`d axprasfùk qua bfcurd ak a` sacukmn `dmn, y trdksbnrldr`d ak `d axprasma` prflar `dmn.
D vaias, as kaiasdrfn trdedjdr `ds axprasfnkas ak dlens `dmns ma `dfcud`mdm hdstd ``avdr`ds d uk puktn ak mnkma rasu`tak fcud`as.
5. Rarfbfidr `d fmaktfmdmis 4 4
i sai t
i
tc c
q
q q q
+<
Yn`uifùk
]rdedjalns a` prflar `dmn:
( )( )ins 4 sai t ii c tcq q q q+ <
Aktnkias, asirfeflns ma ntrd bnrld a` prflar lfalern ma `d aiudifùk:
]akalns qua:
Halns netakfmn a` sacukmn `dmn ma `d fcud`mdm nrfcfkd` quamdkmn varfbfid
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9. Rarfbfidr `d fmaktfmdm ins int4 ins
saki dk
qq q
q< +
Yn`uifùk
_nmalns alpazdr, trdedjdkmn a` sacukmn `dmn ma `d fcud`mdm dsì:
5 5 5(tdk sai ) tdk 5 tdk sai saiq q q q q q < +
5
5 5 5
5 4
ins ins ins
sak sakq q
q q q< +
5
5
( 4)
ins
sakq
q<
(4 ins )(4 ins )
(4 ins )sak
q q
q q
+ <
Halns lu`tfp`fidmn a` kulardmnr y a` maknlfkdmnr pnr (4 ins )q
Yflp`fbfidlns pnr sakθ y netakalns:
Dsì, halns ``acdmn d` prflar `dmn ma `d fcud`mdm nrfcfkd`, `uacn quamvarfbfidmd `d fmaktfmdm.
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=. Rarfbfidr `d fmaktfmdm
5 4(tdk sai )
4
sak
sak
qq q
q <
+
Yn`uifùk
Rarfbfidlns astd fmaktfmdm, lnstrdkmn qua idmd `dmn ma `d fcud`mdmsa puama trdksbnrldr ak `d lfsld axprasfùk. _rflarn trdedjalns a``dmn fzqufarmn y masdrrn``dlns a` iudmrdmn:
5
int .saidk q q
5
5
( 4)
ins
sakq
q<
Hdstd dquì, masdrrn``dlns `d axprasfùk inrraspnkmfakta d` `dmn fz-qufarmn ma `d fcud`mdm.
Dhnrd, tnlalns `d axprasfùk ma` `dmn maraihn y lu`tfp`fidlns a`kulardmnr y a` maknlfkdmnr pnr a` inkjucdmn ma` maknlfkdmnr dsì:
5
5
5
5
4 (4 ) (4 ).
4 (4 ) (4 )
4 5
4
5 4
ins
sak sak sak
sak sak sak
sak sak
sak
sak sak
q q q
q q q
q q
q
q q
q
<
+ +
+<
+<
5
5
( 4)
ins
sakq
q<
Astd as `d lfsld axprasfùk qua netuvfliudkmn trdedjdlns a` prflar `dmn. @uaquamd varfbfidmd `d fmaktfmdm.
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@ds sfcufaktas nihn fmaktfmdmas snk eäsfids pdrd varfbfidr fmaktfmdmas läs inlp`ajds.
4. 4
.ins 4 inssak i n isak
q q qq
< <
5. 4
ins .sai 4 saiins
nq q qq
< <
9. 4
tdk .int 4 inttdk
dk n dkq q qq
< <
=. tdkins
sakqq
q<
1. insintdksak
qqq
<
2. 5 5ins 4sak q q+ < , ma mnkma 5 5 5 54 ins ins 4sak y sakq q q q< <
3. 5 5 5 5tdk 4 sai tdk sai 4nq q q q+ < <
8. 5 5 5 54 int ins int ins 4dk i n dk iq q q q+ < <
Uainrmdkmn astds fmaktfmdmas y `ds mabfkfifnkas ma `ds bukifnkas
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4. D` varfbfidr `d sfcufakta fmaktfmdm sakθ + insθ .intdkθ < insiθ , a`rasu`tdmn as:
d. Dlefcun e. Masfcud` i. Fmaktfmdm m. Iarn
5. D` varfbfidr d sfcufakta fmaktfmdm tdkθ +5insθ.insiθ < saiθ.insiθ+intdkθ ,a` rasu`tmn as:
d. Dlefcun e. Masfcud` i. Fmaktfmdm m. Iarn
Rarfbfidr `ds sfcufaktas fmaktfmdmas trfcnknlætrfids:
9.
=.
1.
2. Axprasdr ak tærlfkns ma sakθ, `d axprasfùk
3. Axprasdr ak tærlfkns ma insθ, `d axprasfùk
8. Axprasdr ak tærlfkns ma insθ, `d axprasfùk intdk5θ . saiθ.
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Qkd ma `ds dp`fidifnkas läs braiuaktas ma `d trfcnknlatrìd sa md ak `d rasn-`uifùk ma trfäkcu`ns.
Uasn`var uk trfäkcu`n inksfsta ak hd``dr `ds `nkcftumas ma sus tras `dmns y `dslamfmds ma sus tras äkcu`ns fktarfnras. Cakard`lakta, sa inkniak d`cukns maastns safs a`alaktns ma` trfäkcu`n y sa pfma akinktrdr `ns rastdktas.
Iudkmn a` trfäkcu`n as raitäkcu`n, raiurrflns d` usn ma `ds rdznkas trfcnkn-lætrfids netakfmds ma `ds ra`difnkas aktra sus `dmns.
Iudkmn a` trfdkcu`n kn as raitäkcu`n, raiurrfralns d` usn ma mns `ayas buk-mdlaktd`asak trfcnknlatrìd qua snk:
@d `ay ma sakns@d `ay ma insakn
Qtf`fzdkmn astds harrdlfaktds, pnmalns rasn`var iud`qufar trfäkcu`n.
Ajalp`ns f`ustrdtfvns
Qkfmdm 1. Dp fidifnkas ma `d trfcnknlatrìd Yasfùk
4
Dprakmfakmn ink a` prnba Ju`fn_rne`ald ink @ay ma Yakns Murdifùk: 6:94 lfk._rne`ald ink @ay ma Insakns Murdifùk: 5:11 lfk.
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Alpazdralns `ds dp`fidifnkas, rasn`vfakmn prne`alds qua tfakak qua var inktrfcnknlatrìd ma` trfäkcu`n raitäkcu`n.
D` rasn`var prne`alds ma trfcnknlatrìd, kns akinktrdralns ink axprasfnkas inl
?,1sak q < ù 4ins q < , ma mnkma takalns qua maspajdr a` vd`nr maAk a` prflar idsn, valns qua `d bukifùk sakn tnld uk vd`nr ma θ y `a dsfc?,17 `d bukifùk sakn fkvarsn qua sa kntd inln 4sfk mavua`va a` vd`nr ?,1
2
pq < ,
_arn a` vd`nr 2
p
, kn as úkfin puastn qua tdlefæk pnr `d parfnmfifmdm mabukifùk sakn, takalns qua:
Astn sfckfbfid qua d` mavn`var ?,1 pnr lamfn ma `d bukifùk sakn fkvarsn,puama netakar lú`tfp`as vd`nras pdrd θ7 pnr `n tdktn, ma `ds inkmfifnkas y
Cräbfid 11
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Ajalp`ns
Hd``dr a` vd`nr ma θ aktra ? y 5Ϗ iudkmn sak θ < ?,8.
Yn`uifùk
Uasn`vfakmn, takalns qua sak-4 ?,8 < 19¿ ?3‖ =8‖‖
Asta äkcu`n tfaka su dmn bfkd` ak a` puktn _ (prflar iudmrdkta). A` äkcu`n iuy`dmn bfkd` pdsd pnr a` puktn T sflætrfin ma _, ink raspaitn ma` aja, y iuylamfmd as 48? ’ (19¿ ?3‖ =8‖‖) < 452¿ 15‖ 44‖‖ tdlefæk as sn`uifùk, pnrqu
a` vd`nr ma` sakn pdrd `ns mns äkcu`ns as a` lfsln ?,8.
@uacn `ds sn`uifnkas snk θ < 19¿ ?3‖ =8‖‖ y θ < 452¿ 15‖ 44‖‖, y `ds malsn`uifnkas snk vd`nras qua astäk buard ma` fktarvd`n (?, 5Ϗ).
Cräbfid 12
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Ajalp`ns
Yn`uifùk
Inknialns qua pdrd tnmn trfäkcu`n a` ärad as:
5
edsa d turd D
<
Ma d bfcurd takalns5
e h D
< , parn h
d sak d< uacn maspajdkmn h, takal
qua .h d sak d< y raalp`dzdkmn ak `d prflard bùrlu`d, netakalns:
.5
d esak D d< .
Astd as ukd bùrlu`d útf` pnrqua kns parlfta hd``dr a` ärad ma uk trfäkcu
4. Mdmn uk trfäkcu`n inln a` ma `d cräbfid 13, pdrd a` iud` sa inkniak`nkcftum ma mns `dmns d, e y a` äkcu`n δ inlprakmfmn aktra a``ns, hd``dr u
bùrlu`d pdrd a` ärad ma` trfäkcu`n.
Cräbfid 13
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Yn`uifùk
Ak `d cräbfid, valns qua δ < 54¿, `uacn 451tdk x
d < 7 sf maspajdlns takalns qua:
5. @ns dmns ma uk trfäkcu`n lfmak 9?,1 y =8 l, y a` äkcu`n inlprakmfmn akta``ns, as ma =4¿. ¾Iuä` as a` ärad ma` trfäkcu`n>
Yn`uifùk
Dp`fidkmn a` rasu`tdmn ma` prne`ald dktarfnr, takalns qua:
9. Masma `d ifld ma uk didktf`dmn ma 451 l ma d`turd, a` äkcu`n ma maprasfù
ma ukd dkihd as 54¿. ¾D quæ mfstdkifd sa akiuaktrd d dkihd ma` didktf`dmn
Cräbfid 18
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Cräbfid 16
5. Qk inkstruitnr masad hdiar ukd rdlpd ma 8,1 l ma drcn qua sa `avdktd d ud`turd ma 4,81 l ma` sua`n. Id`iu`dr a` äkcu`n ma `d rdlpd ink `d hnrfznkt
9. Qkd asid`ard qua lfma 5? pfas, sa dpnyd ak uk amfbfifn y a` äkcu`n aktra dleas ma 55¿. Id`iu`dr:
d. @d mfstdkifd ma` pfa ma `d asid`ard d` amfbfifn.
e. Yf `d mfstdkifd ma` pfa ma `d asid`ard dulaktd 9 pfas, ¾iuäktn edjdräpuktd suparfnr ma `d asid`ard>
=. Masma uk puktn D qua astä d 8,5 l snera a` kfva` ma` sua`n, a` äkcu`n ma avdifùk ma `d pdrta d`td ma uk fkluae`a as 94¿ 5?‖ y a` äkcu`n ma maprasfùk
4. Id`iu`dr a` äkcu`n ma a`avdifùk ma` Yn`, sf ukd parsnkd qua lfma 1 pfas astdturd, prnyaitd ukd snlerd ma = pfas ma `drcn d kfva` ma` sua`n.
4
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1. Akinktrdr `ns vd`nras axditns ma x, y inrraspnkmfakta d `d cräbfid 13.
x
6
y
2?n
x
3y
=1n
x
448
2. Ak a` trfäkcu`n DEI :
d < 5=,2 e < 29,5 Id`iu`dr `ds lamfmds ma `ns ntrns
a`alaktns ma` trfäkcu`n.
3. Masma uk puktn d` kfva` ma` sua`n y d 491 pfas ma `d edsa ma ukd tnrra, a` äkcu`n ma a`avdifùk d `d pdrta läs d`td ma `d tnrra as 13¿. Id`iu`dr `d d`turd m`d tnrra.
@ns äkcu`ns fktarfnras ma` trfäkcu`n sapuamak fmaktfbfidr, usdkmn d lfsld`atrd ma` værtfia inrraspnkmfakta nsa sua`ak usdr tdlefæk, `atrds ma`d`bdeatn crfacn inln δ, ε y θ.
D` rasn`var trfäkcu`ns, kaiasftdlns astde`aiar d`cukds kntdifnkas pdrd matar-lfkdr sus pdrtas y bdif`ftdrkns a` ldkajn ma `ns rasu`tdmns. _drd matarlfkdruk trfäkcu`n, `a dsfckdlns ukd `atrd ldyúsiu`d ak idmd ukn ma sus værtfias
y d lfsld atrd parn lfkúsiu`d, pdrd fkmfidr a` dmn npuastn d idmd værtfia.
Cräbfid 2?
Cräbfid 24
Cräbfid 25
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Cräbfid 29
_nmalns hdiar ukd malnstrdifùk pdrifd`:
Yf in`nidlns a` trfäkcu`n ma td` bnrld qua a` værtfia D infkifmd ink uk sfstald innrmakdmds idrtasfdkn y su äkcu`n δ astæ ak pnsfifùk racu`dr, as maifr, a` `dmn ma` trfäkcu`n infkifmfakmn ink `d mfraiifùk pnsftfvd ma` aja x y a` `dmn DI as
Yf δ, ε y θ snk ns äkcu`ns fktarfnras ma uk trfäkcu`n iud`qufard, y d, e y i snk`ds `nkcftumas raspaitfvds ma `ns `dmns npuastns d astns äkcu`ns, aktnkias:
d e i
sak sak sakd e q< <
@d ay ma sakns astde`aia ds ra`difnkas aktra d nkcftum ma uk dmn y a` saknma su äkcu`n npuastn y as vä`fmd pdrd iud`qufar trfäkcu`n.
@ay ma sakns
Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd Yasfùk
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Cräbfid 2=
Ak d cräbfid 2=d pnmalns trdzdr a` saclaktn IM parpakmfiu`dr d` aja x, y `dlalnh su `nkcftum. Inln `ns trfäkcu`ns DMI y a` trfäkcu`n EMI snk raitäkcu`ntakalns:
hsak
ed< , ma mnkma h e sakd<
]dlefækh
sakd
e< , ma mnkma h d sak e< 7 fcud`dkmn ns vd`nras ma h takalnqua:
d.
e.
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_drd dp`fidifnkas präitfids, as kaiasdrfn var qua hdy tras fcud`mdmas qua snk
sak sak
d e
d e<
sak sak
d i
d q<
sak sak
e i
e q<
Asta rasu`tdmn as inknifmn inln `d `ay ma sakns.
Ak `d cräbfid 2=e in`nidkmn a` værtfia I ak a` nrfcak y a` äkcu`n θ ak pnsfiracu`dr, kns quamd inln `dmn fkfifd` ID y inln `dmn bfkd` IE7 masma E trdzdla` saclaktn EM, parpakmfiu`dr d` aja x, y dsì takalns `ns trfäkcu`ns raitäkcu
IME y DME, ma mnkma:
h
sakd
q< dsì h d sak q<
]dlefækh
saki
d< `uacn h i sak d<
Fcud`dkmn `ns vd`nras ma h, takalns qua:
d sak i sakq d< ma mnkma sak sak sak
d e i
d e q< < ,
Halns lnstrdmn qua:
sak sak
d e
d e< y
sak sak
d i
d q< ,
`uacn inki`uflns qua:
sak sak sak
d e i
d e q< <
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Yn`uifùk
Ya trdtd ma akinktrdr ds nkcftumas ma ns dmns e y i, y `ds lamfmds ma` äkcu`n
Inln inknialns `ds lamfmds ma mns äkcu`ns, pnmalns hd``dr θ dsì:
θ < 48?¿ ’ (=1¿ + 2?¿) < 31¿
_drd id`iu`dr `ds `nkcftumas ma `ns `dmns e y i, dp`fidlns `d `ay ma sakns.
2?º =1º
=,2
sak sak
e< `uacn
=,2 2?º1,29
=1º
sake
sak< <
Dmaläs,31º =1º
=,2
sak sak
i< `uacn
=,2 31º=,2
=1º
saki
sak< <
Ajalp`n
4. Uasn`var a` sfcufakta trfäkcu`n, sf d < =,27 δ < =1¿7 ε < 2?¿.
Cräbfid 21
5. Uasn`var a` trfäkcu`n, sf sdealns qua: d < 8,97 δ < 25¿, θ < 11¿
Yn`uifùk
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Hd``dr dhnrd, `ds `nkcftumas ma `ns `dmns:
11º 25º
8,9
sak sak
i< `uacn
8,9 11º3,3
25º
saki
sak< <
_nr ntrd pdrta,29º 25º
8,9
sak sak
e< `uacn
8,9 29º8,93
25º
sake
sak< <
9. Mns nesarvdmnras in`nidmns d 44? l ma mfstdkifd ak `ns puktns D yak `d nrf``d ma uk rìn, astäk lfrdkmn uk ären` ak `d nrf``d npuastd ak
puktn I. Lfmfarnk `ns äkcu`ns IDE y IED, y sus lamfmds buarnk =9¿ y raspaitfvdlakta. ¾D quæ mfstdkifd astä idmd nesarvdmnr ma` ären` ak a` `dnpuastn ma` rìn>
Yn`uifùk
Ma `d bfcurd takalns: θ < 48?¿ ’ (=9¿ + 13¿) < 8?¿
=9º 8?º
44?
sak sak
IE< `uacn
44? =9º32,43
8?º
sakIE
sak< <
13º 8?ºsak sak 44? 13ºsak
Cräbfid 22
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As maifr qua `ns nesarvdmnras astäk sftudmns d 32,43 y 69,23 l ma` ären` uefidmak `d nrf``d npuastd ma` rìn.
Yf ak uk trfäkcu`n sa inkniak úkfidlakta `ds `nkcftumas ma sus tras `dmns n `d
`nkcftumas ma mns ma sus `dmns y a` äkcu`n inlprakmfmn aktra a``ns, ak astns mnidsns kn pnmalns dp`fidr `d `ay ma sakns pdrd rasn`var `ns trfäkcu`n y takmralnqua diumfr d ntrn rasu`tdmn flpnrtdkta qua sa ``dld a` tanrald ma` insakn.
Iudkmn sa inkniak `dmns ma uk trfäkcu`n y uk äkcu`n npuastn d ukn ma a``ns, sdp`fid `d `ay ma sakns, parn pnmalns akinktrdr vdrfds sftudifnkas:
Yupnkcdlns qua d y e snk `ds `nkcftumas ma mns `dmns ma` trfäkcu`n DEI y qua u
äkcu`n δ as npuastn d` dmn d (δ as dcumn), y inksfmardlns d δ ak su pnsfifùk racu`ink a` saclaktn DI ma `nkcftum e inln `dmn bfkd` ma δ7 a` værtfia E maea astdr ad`cúk puktn ma` aja x, ak mfraiifùk pnsftfvd. Inln kns mdk a` `dmn d npuastn værtfia D, pnmalns nid`fzdr a` puktn E, trdzdkmn ink a` inlpäs uk drin ma nkcftud, ink iaktrn ak I7 `n iud` kns puama inkmuifr d iudtrn pnsfe`as rasu`tdmns:
Cräbfid 23
4. A` drin kn tnid d` aja x, y kn sa bnrld trfäkcu`n7 ak asta idsn, d`fktaktdr rasn`var a` prne`ald, kns akinktrdlns ink ukd axprasfùkma `d bnrld sak ε ; 4 y ak asta idsn, kn axfsta trfäkcu`n.
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Cräbfid 28
Cräbfid 26
Cräbfid 3?
=. A` drin inrtd d ds pdrtaspnsftfvds y kacdtfvdsma` aja x y sa bnrld ukúkfin trfäkcu`n.
9. A` drin inrtd d` aja x pnsftfvn ak mns puktnsmfstfktns y sa bnrldkmns trfäkcu`ns.
5. A` drin tnid tdkcakifd`-lakta d` aja x7 ak asta
idsn, sa bnrld uk úkfintrfäkcu`n raitäkcu`n,ink ε < 6?¿.
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_drd iud`qufar trfäkcu`n, a` iudmrdmn ma ukn ma sus `dmns asfcud` d `d suld ma `ns iudmrdmns ma `ns ntrns mns `dmns, la-kns mns vaias a` prnmuitn ma asns mns dmns pnr a` insakn ma`äkcu`n inlprakmfmn aktra a``ns.
Ak sìlen`ns, takalns:
Cräbfid 34
d5 < e5 + i5 ’ 5ei ins δ
e5 < d5 + i5 ’ 5di ins ε
i5 < d5 + e5 ’ 5de ins θ
d5 < e5 + i5 ’ 5ei ins δ
]anrald ma` insakn
Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd Yasfùk
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Ajalp`ns
4. Mns `dmns ma uk trfäkcu`n lfmak 3 y 1 l raspaitfvdlakta, y a` äkcinlprakmfmn aktra a``ns as =5¿. Hd``dr a` tariar `dmn.
Yn`uifùk
Inln maealns hd``dr a` tariar dmn ma` trfäkcu`n, dp`fidlns a` tanrald insakn:
5 5 53 1 5.(3).(1).ins =1º x < +
5 54,636 x < , ma mnkma 54,636 =.28 x l< <
@d `nkcftum ma` tariar `dmn as ma =.28 l.
5. Qk jdrmìk trfdkcu`dr tfaka `dmns qua lfmak =5, 1? y 29 l. Akinktrdlamfmd ma` äkcu`n laknr.
Yn`uifùk
Ak asta idsn, inknialns `ds `nkcftumas ma `ns tras `dmns ma` trfäkcu`maealns hd``dr pnr `n lakns, mns ma sus äkcu`ns7 a` tariarn rasu`tdräsuldr astns mns äkcu`ns y rastdr`ns ma 48?¿.
Dp`fidkmn a` tanrald ma` insakn, takalns:
5 5 529 =5 1? 5.(=5).(1?).ins d< +
Maspajdkmn ins δ takalns:5 5 5=5 1? 29
ins5.(=5).(1?)
d +
<
561ins d < as maifr qua ins ? ?3?598?61d
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Dp`fidkmn insakn fkvarsn ma δ, netakalns:
4ins (?,?3?598?61)d <
81º,63599353d < ù 81º,18o5?ood < .
_drd hd``dr ntrn äkcu`n, dp`fidlns kuavdlakta a` tanrald ma` insakn dsì
5 5 5=5 29 1? 5.(29).(1?).ins e< +
Ma mnkma5 5 5
29 1? =5ins5.(29).(1?)
e + <
=3?1
ins ?,3=385196329??
e < < , as maifr, qua
4ins (?,3=2851963)e <
X =4º,28983584e < n5 5 5
ins5
e i d
eid
+ <
Inln yd inknialns mns äkcu`ns ma` trfäkcu`n, a` tariarn `n akinktrdlnrastäkmn`a `d suld ma `ns mns d 48?¿, dsì:
48?º ( )q d e< +
5 5 5
4ins ( )5
e i d
eid +
<
@uacn a` äkcu`n laknr as =4º,=4o5ooe <
A` tariar äkcu`n tdlefæk n pnmralns hd``dr, dp`fidkmn a` tanrald ma` insak
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Cräbfid 35
Yupnkcdlns qua δ as uk äkcu`n dcumn. Yf trdzdlns `d parpakmfiu`dr mma a` værtfia I d` `dmn DE, netakalns mns trfäkcu`ns raitäkcu`ns, trfäkc
DMI y trfäkcu`n EMI 7 maknlfkalns `ds `nkcftumas:
IM h<
DM x<
ME i x<
Inksfmardkmn `ns mns trfäkcu`ns raitäkcu`ns y dp`fidkmn a` tanrald _ftäcnrds, takalns:
5 5 5
h e x< y5 5 5( )h d i x<
Fcud`dkmn `ds axprasfnkas ma h5, takalns:
5 5 5 5( )d i x e x < , `uacn:
5 5 5 5( )d e x i x< +
5 5 5 5 55d e x i ix x< + +
5 5 5 5d e i ix< +
Hdralns ukd malnstrdifùk pdrifd` ma` tanrald ma` insakn, edsäkmnkak a` trfäkcu`n ma `d bfcurd qua inrraspnkma d` trfäkcu`n DEI .
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Ak a` trfäkcu`n DMI , takalns:
Ma mnkma .ins x e d< , raalp`dzdkmn a` vd`nr ma x ak `d fcud`mdm
5 5 5 5d e i ix< + , takalns:
5 5 5 5 insd e i ie d< +
Iudkmn kaiasftdlns hd``dr `d lamfmd ma uk äkcu`n, maspajdlns
5 5 5
ins
5
e i d
ei
d +
<
y `uacn dp`fidlns insakn fkvarsn pdrd hd``dr δ
5 5 5
4ins ( )5
e i d
eid +
<
Ak d`cukns prne`alds, as kaiasdrfn inlefkdr astns mns rasu`tdmns,`d `ay ma sakns y a` tanrald ma` insakn pdrd rasn`var`ns.Yù`n `d präitfid kns mdrä a` mnlfkfn kaiasdrfn, pdrd ldkajdrdprnpfdmdlakta astns rasu`tdmns.
Ajalp`ns
4. @ds nkcftumas ma ns dmns ma uk trfäkcu`n snk 9=, 59 y =5 il. Matarlfkd
d. @d lamfmd ma` äkcu`n laknr.
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Yn`uifùk
Qsdkmn a` tanrald ma` insakn, takalns qua:
19,6= 19º 12½11.99½½d < <
5 5 559 =5 9=ins
5.(59).(=5)d
+ <
ins δ < ?,1887 δ < ins -4 (?,188), ma mnkma
19,6= 19º 12½11.99½½d < <
Maealns hd``dr `d lamfmd ma ntrn äkcu`n, pdrd `n iud` pnmalns dp`fid`ay ma` sakn, dsì:
. .
5
d e sak
D
e
< `uacn,
(59) 19º 12½11.99½½
9=
saksak e <
@uacn, ?,1=26sak e < , ma mnkma 4sfk (?,1=26)e <
99.4116 99º 6½54.=8½½e < <
_drd netakar a` tariar dkcu`n θ hdialns
θ < 48?¿ ’ (19¿ 12‖ 11,99‖‖ + 99¿ 6‖ 54,=8‖‖) < 65,8615 < 65¿ 16‖ =9,
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_drd sn`uifnkdr `d pdrta e, usdlns `d bùrlu`d:
yd vfstd y takalns:
59.=5. 19º 12½11.99½½
5
sak D <
596?,1? D il<
_drd netakar a` ärad, sa puama varfbfidr, usdkmn iud`qufard ma ds nkcftuma
ma mns `dmns y a` äkcu`n inlprakmfmn aktra a``ns.
5. Ink `d fkbnrldifùk mdmd, rasn`var a` trfäkcu`n:
d. d < 2,=, e < =,3 y δ<=5¿
=5º
=,3 2, =
sak sake<
Aktnkias:
=,3 =5
2,=
saksak e <
4
?,=649
sfk (?, =649)
56º 51½11.8½½
sak e
e
e
<
<
<
Cräbfid 39
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_drd hd``dr `d lamfmd ma` tariar äkcu`n, hdialns:
θ < 48? ’ (=5¿ + 56¿ 51‖11.8‖‖) < 4?8¿ 9=‖ =.5‖v
Kns bd`td hd``dr `d `nkcftum ma` `dmn i, pdrd `n iud` dp`fidlns a` trald ma sakn:
2,= 4?8º9=½=.5½½2,=
=5º
saki
sak<
6,?2i <
Tuamd dsì, rasua`tn a` trfäkcu`n.
e. d < =,1, e < 2,9 y θ < 2?¿
Yn`uifùk
Inln inknialns mns `dmns ma` trfäkcu`n y a` äkcu`n inlprakmaktra a``ns, pnmalns dp`fidr a` tanrald ma` insakn pdrd hd``d`nkcftum ma` `dmn i dsì:
5 94,16i < , ma mnkma:
94, 16 1, 25i < <
_drd hd``dr a` vd`nr ma ntrn äkcu`n, pnmalns dp`fidr fkmfstfktdla`d `ay ma sakns n a` tanrald ma` insakn.
Dp`fidkmn `d `ay ma sakns, takalns:
1,25 =,1
2?ºsak sak d<
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4. Ak idmd idsn rasn`var a` trfäkcu`n:
Ajarififns pdrd rairadr `d lakta
?,269=sak d <
as maifr, qua =9º 1=½4?½½d <
_drd hd``dr a` ntrn äkcu`n, hdialns
ε < 48? ’ (2?¿ + =9¿ 1=½ 4?½½) < 32¿ 1½ 1?‖‖,
y quamd dsì rasua`tn a` trfäkcu`n:
9=º, 34º , 5=dd e< < <
d.
e. =,1 2,9, 2?ºd e q< < < i. 9,= 5,8, 85ºe i d< < < m. =9 95, 16ºd i e< < < a. 8,= 5,3, 3,9d e i du< < < b. =?8 512, 589d e i< < <
4
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Cräbfid 3=
3. Masma uk ifartn puktn ma` tarrakn, sa lfrd d `n d`tn ma ukd lnktdôd y`d vfsud` bnrld uk äkcu`n ma 1?¿ ink a` sua`n. D` d`ajdrsa 5?? l ma `dlnktdôd, `d vfsud` bnrld uk äkcu`n ma 91¿ ink a` sua`n. Hd``dr `d d`turd,h ma `d lnktdôd
5. Qk pamdzn ma d`dlera ma 2? il as mne`dmn ak bnrld trfdkcu`dr. Akink-trdr `ns äkcu`ns ma` trfäkcu`n, sf mns ma sus `dmns lfmak 5= y 5? il.
9. Mns nesarvdmnras in`nidmns ak ns puktns D y E d ukd mfstdkifd ma 44? lak d nrf``d ma uk rìn, astäk lfrdkmn ukd tnrra sftudmd ak d nrf``d npuastdak uk puktn I. Lfmfarnk `ns äkcu`ns IDE y IED iuyds lamfmds buarnk=9¿ y 13¿ raspaitfvdlakta. ¾D quæ mfstdkifd astä idmd nesarvdmnr ma `dtnrra>
=. Qk pnsta vartfid` ma 9 l prnyaitd ukd snlerd ma 5 l7 ¾quæ d`turd tfakauk ären` qua d `d lfsld hnrd, prnyaitd ukd snlerd ma =,1 l>
1. Masirfed d ay ma ns sakns y a` tanrald ma` insakn, usdkmn úkfidlaktapd`derds.
2. Masma uk puktn D ma` sua`n sa nesarvd ukd tnrra, _T, y sa `d va edjn ukäkcu`n ma 94¿. Ya dvdkzd =? l ak mfraiifùk d d tnrra, sa lfrd y sa d va,dhnrd, edjn uk äkcu`n ma 18¿. Hd``dr `d d`turd h ma `d tnrra y `d mfstdkifd
ma D d` pfa, T, ma `d tnrra.
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Yn`uifùk
Maspajdlns:
4
5sak q <
4 4sfk
5q
< ó
p
Ajalp`n
4. Uasn`var `d aiudifùk 5 9ins
=t <
Vd halns vfstn qua `ds fmaktfmdmas trfcnknlætrfids snk aiudifnkasqua sa sdtfsbdiak pdrd tnmns `ns kúlarns rad`as n vd`nras ma `nsäkcu`ns ak `ns iud`as idmd lfalern ma `d aiudifùk astä mabfkfmn.
Dhnrd, astumfdralns aiudifnkas trfcnknlætrfids qua sa sdtfsbdiakúkfidlakta pdrd d`cukns vd`nras pdrtfiu`dras ma `d vdrfde`a. @nslætnmns alp`admns pdrd d sn`uifùk ma astds aiudifnkas trfcnknlæ-trfids snk sflf`dras d `ns alp`admns ak `d rasn`uifùk ma aiudifnkasd`caerdfids. Ak d`cukns idsns, sa usdk ds fmaktfmdmas trfcnknlætrfidspdrd netakar aiudifnkas aqufvd`aktas.
Aiudifnkas trfcnknlætrfids
Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd Yasfùk
=Aiudifùk trfcnknlætrfid _drta4. Murdifùk: 2:5= lfk.
Aiudifùk trfcnknlætrfid _drta5. Murdifùk: 1:16 lfk.
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Astd as ukd sn`uifùk ma `d aiudifùk dktarfnr. _arn sf hdy ukd sn`uifùkukd aiudifùk trfcnknlætrfid, aktnkias hdy fkbfkftds sn`uifnkas. Ak aidsn, pnr `d parfnmfifmdm ma `d bukifùk sakn, `d bnrld pdrd netakar tn
`ds sn`uifnkas, as:
5 ,2
g mnkma g as uk aktarnp
q p< + ,
parn d sn`uifùk netakfmd drrfed, as `d úkfid qua sa akiuaktrd ak a` fktarv
.
5. Uasn`var `d aiudifùk 5 9ins ? 5
=t pdrd t p<
Yn`uifùk
Id`iu`dlns `ds rdìias iudmrdmds, netakfakmn9 9
ins= 5
t < ´ <
rasn`vfakmn takalns qua 4 9ins5
t < ó ó
ma mnkma 442 2
t y t p p
< <
y dmaläs,9
ins5
t < ma mnkma sa netfaka 4 9ins
5t
< ó ó
ma mnkma1 3
2 2t y t
p p< < .
@uacn hdy iudtrn sn`uifnkas pdrd d aiudifùk ak a` fktarvd`n ? 5t p , iuvd`nras snk:
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9. Uasn`var `d aiudifùk 5 5sai 4 tdk ? 5 pdrdq q q p< + .
Yn`uifùk
Qtf`fzdlns `d fmaktfmdm 5 5sai 4 tdkq q< + y `d aiudifùk kns quamd:
54 tdk tdk 4q q+ < 7 idkia`dkmn ukn ak dlens `dmns takalns:
5tdk tdk ?q q < , sf bditnrfzdlns tdk θ, sa netfaka:
( )tdk tdk 4 ?q q < , ma mnkma netakalns `ds aiudifnkas:
tdk ? tdk 4 ? yq q< < .
Uasn`valns tdk ?q < y netakalns ?,q q p< <
Yf rasn`valns tdk 4q < netakalns `ns vd`nras 1,
= =
p pq q< < ,
`uacn `ds sn`uifnkas ma `d aiudifùk ak a` fktarvd`n ? 5q p sn
=. Hd``dr tnmds `ds sn`uifnkas ma `d aiudifùk .
Yn`uifùk
, as maifr, qua ma mnkma
Inln kn hdy fktarvd`n ma rastrfiifùk pdrd a` äkcu`n θ, pnmalns hd``dr tnm`ds sn`uifnkas ma `d aiudifùk7 ak vfrtum ma `d parfnmfifmdm ma` sakn, `dsn`uifnkas sa netfakak dsì:
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3 5 85 5
9 9 9 9
49 5 4== =9 9 9 9
46 5 5?2 2
9 9 9 9
p p p pp p
p p p pp p
p p p pp p
+ < + <
+ < + <
+ < + <
Mdkmn vd`nras d g , netakalns fkbfkftds sn`uifnkas inln pnr ajalp`n:
Halns hd``dmn safs sn`uifnkas läs, mäkmn`a vd`nras d g < 4, 5, 9
1. Hd``dr `ds sn`uifnkas ma `d aiudifùk 5 9 ? ? 5ins pdrdq q p+ <
Yn`uifùk
9
5ins q
<
4 9 1 3ins
5 2 2n
p pq q
ó< < < ó
_nmalns var qua `ds sn`uifnkas sa akiuaktrdk ak a` sacukmn y ak a` tariudmrdkta, puas ma `d aiudifùk valns qua a` ins θ as kacdtfvn.
2. Uasn`var `d aiudifùk 5 ? ? 5sak sak pdrdq q q p+ <
Yn`uifùk
Bditnrfzdkmn, takalns ( 4) ?sak sakq q + < , ma mnkma:
? 4sak n sakq q< <
Uasn`vfakmn ?sakq < , takalns ? 5 yq q p q p< < <
Uasn`vfakmn 4sak q < takalns9
5
pq < 7 `uacn `ds sn`uifnkas ma
aiudifùk ak a` fktarvd`n mdmn snk:
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Ya puama varfbfidr qua `d aiudifùk sa sdtfsbdia ink astns vd`nras,utf`fzdkmn `d id`iu`dmnrd.
3. 55 4 ins ? 5sak pdrdq q q p< +
Yn`uifùk
Dcrupalns tnmns `ns tærlfkns ak a` prflar `dmn y quamd:
55 ins 4 ?sak q q <
_nmalns axprasdr tnmn ak tærlfkns ma ins θ, pdrd n iud` usdlns d fmaktfmdbukmdlaktd` 5 54 inssak q q< y `d aiudifùk kns quamd:
55 ( 4 ) ins 4 ?ins q q <
Abaitudkmn `ds npardifnkas kns quamd: 55 ins 4 ?ins q q+ <
Maealns rasn`var astd aiudifùk iudmrätfid7 dp`fidkmn `d bùrlu`d cakard`tnldkmn inln fkiùckftd ins θ netakalns:
(5 ins 4)(5 5) ?sakq q+ < . Uaalp`dzdkmn `ns vd`nras ma `d aiudifùtakalns:
54 4 =(5)( 4)ins
5(5)q
< . Ma mnkma sa netfaka
4ins ins 45
nq q< <
Uasn`vfakmn 4ins
5q < takalns 1
9 9n
p pq q< <
Uasn`vfakmn ins 4q < takalns q p<
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Uasn`var `ds sfcufaktas aiudifnkas trfcnknlætrfids pdrd ? 5q p .
4. ins 4q <
5. 5tdk 4q <
9. (5 ins 4)(5 5) ?sakq q+ <
=. 5tdk 9 tdkq q<
1. 5sai 4 tdkq q< +
2. 5= 9 ?sak q <
3. 55 ins ins ?q q <
8. 5sak q <
6. 5 ins 4 ?q + <
4?. tdk sai 4q q+ <
4
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Qtf`fia `d id`iu`dmnrd pdrd hd``dr `ns sfcufaktas rasu`tdmns:
4. 4sfk (?, =885)
5. 4sfk (?, 532=)
9. 4ins (?, =885)
=. 4ins (?, 532=)
1. 4tdk (?, =9=2)
2. 4tdk (5, 399)
3. 4sai (5, ?89)
8. 4ins (4, 512)i
6. 4sai ( 4, 512)
_drd bfkd`fzdr astd saiifùk, prasaktdlns d`cukns rasu`tdmnsy bùrlu`ds útf`as pdrd masdrrn``dr prne`alds dp`fidmns.Astns talds puamak sar inksu`tdmns y dlp`fdmns madiuarmn ink `ds kaiasfmdmas ma idmd inktaxtn.
5
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Bùrlu`ds ma dmfifùk pdrd `d bukifùk sakn
4. ( ) .ins ins .sak D E sakD E D sakE+ < +
5. ( ) .ins ins .sak D E sakD E D sakE <
Bùrlu`ds ma dmfifùk pdrd `d bukifùk insakn
4. ins( ) ins .ins . D E D E sakD sakE+ <
5. ins( ) ins .ins . D E D E sakD sakE < +
Bùrlu`ds ma dmfifùk pdrd `d bukifùk tdkcakta
4. tdk tdk
tdk( )4 tdk . tdk
D E D E
D E
++ <
5. tdk tdk
tdk( )4 tdk . tdk
D E D E
D E <
+
Bùrlu`ds ma dmfifùk pdrd `ds bukifnkas
Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd Yasfùk
1
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Ajalp`ns
4. Masdrrn``dr sak (5 x) ak tærlfkns ma sak x y ins x.
Yn`uifùk
Dp`fidkmn `d bukifùk ma dmfifùk pdrd a` sakn, takalns:
5 ( )
.ins ins .
5 .ins
sak x sak x x
sakx x x sakx
sakx x
< +
< +
<
@uacn 5 5 .inssak x sakx x<
5. Id`iu`dr: 2? (5 9?) (9? 9?)sak sak sak< < +
Yn`uifùk
2? (5 9?) (9? 9?)
4 9 95. 9?.ins 9? 5( )( )
5 5 5
sak sak sak
sak
< < +
< < <
9. Masdrrn``dr ak tærlfkns ma ins x `d axprasfùk ins 5 x
Yn`uifùk
Dp`fidkmn `d bùrlu`d ma dmfifùk pdrd a` insakn, takalns:
5 5 5 5
5
ins 5 ins( )
ins .ins .
ins ins (4 ins )
5 ins 4
x x x
x x sakx sakx
x sak x x x
x
< +
<
< <
<
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@uacn
5 5
tdk 45? tdk (5 2? )
5 tdk 2? 5 9 5 9 954 tdk 2? 4 ( 9)
<
< < < <
=. Asirfefr tdk 5 x ak tærlfkns ma tdk x.
Yn`uifùk
Qsdkmn `d bùrlu`d ma dmfifùk pdrd tdkcakta, takalns:
5
tdk tdk 5 tdktdk 5 tdk ( )
4 tdk tdk 4 tdk
x x x x x x
x x x
+< + < <
@uacn
5
5tdktdk 5
4 tdk
x x
x
<
1. Id`iu`dr tdk 45?¿
Yn`uifùk
5 5
tdk 45? tdk (5 2? )
5 tdk 2? 5 9 5 99
54 tdk 2? 4 ( 9)
<
< < < <
Ntrn rasu`tdmn ma crdk utf`fmdm iudkmn sa trdtd ma hd``dra` ärad ma uk trfäkcu`n, as `d bùrlu`d ma Harùk.
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Ajalp`n
@ns `dmns ma uk trfäkcu`n lfmak 8, 4? y 45 l raspaitfvdlakta. Hd``dr a` ärama` trfäkcu`n.
Yn`uifùk
_rflarn id`iu`dlns a` salfparìlatrn5
d e is
+ +< raalp`dzdkmn p
`ds `nkcftumas ma `ns `dmns, takalns:
8 4? 45 9?41
5 5s
+ +< < <
Dp`fidkmn `d bùrlu`d ma Harùk pdrd a` ärad, takalns:
41(41 8)(41 4?)(41 45) D <
Yf `ds `nkcftumas ma `ns `dmns ma uk trfäkcu`n snk d, e, i,
raspaitfvdlakta.
A` salfparìlatrn ma` trfäkcu`n vfaka mdmn pnr5
d e is
+ +< y a` ärad
ma` trfäkcu`n astä mdmd pnr `d axprasfùk:
( )( )( ) D s s d s e s i<
Astd bùrlu`d parlfta hd``dr a` ärad ma iud`qufar trfäkcu`n, inknifakmn `ds`nkcftumas ma sus `dmns.
Bùrlu`d ma Harnk
Qkfmdm 1. Dp fidifnkas ma `d trfcnknlatrìd Yasfùk
2
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5. Qk jdrmìk trfdkcu`dr tfaka `dmns qua lfmak =5, 1? y 29 l. Akinktrdrärad ma` jdrmìk.
4. Ak `ns sfcufaktas ajarififns, sa mdk `ds `nkcftumas ma `ns `dmns ma uk trfäkcu Dp`fqua `d bùrlu`d ma Harnk pdrd hd``dr a` ärad ma` trfäkcu`n.
d. d < 48,3 e < 45,2 i < 43,6
e. d < 951 e < 592 i < =44
i. d < 1,6 e < 2,3 i < 4?,9
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4. Qkd tnrra ma 491 pfas ma d`turd sa `nid`fzdak `d nrf``d ma uk `dcn. Masma `d puktd ma `dtnrra, a` äkcu`n ma maprasfùk ma uk nejatnak `d nrf``d ma` `dmn npuastn ma` `dcn as ma92¿. @d mfstdkifd d trdvæs ma` `dcn as:
d. 423 pfas e. 481,84 pfas i. 95,123 pfas m. 459,9= pfas
5. Masma uk puktn d 41 l snera a` kfva` ma` sua`n, uk tnpùcrdbnnetfaka ukd lamfmd ma28¿ pdrd a` äkcu`n ma maprasfùk ma uknejatn snera a` sua`n.
@d mfstdkifd ma` nejatn d` puktn snera a` sua`n qua astämfraitdlakta maedjn ma` tnpùcrdbn.
d. 3.83 l e. 6.=9 l i. 2.?2 l m. =.32 l
9. Qk ide`a astä sujatn ak `n d`tn ma ukd dktakd ma rdmfn y d ukpuktn ak a` sua`n hnrfznktd`, qua astä d =? l ma `d edsa ma `ddktakd. Yf a` ide`a bnrld uk äkcu`n ma 18¿ snera a` sua`n, `d`nkcftum ma` ide`a as.
d. 31,=8 l e. 21,68 l i. 83,1= l
m 1= 59 l
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=. Lfaktrds vua`d d ukd d`turd ma 4??? l, uk pf`ntn nesarvd qua a`äkcu`n ma maprasfùk hdstd a` darnpuartn as ma 9?¿. @d mfstdkifdd` darnpuartn as.
d. 4123 l e. 42?6 l i. 4395,1 l m. 481?.5 l
1. Matarlfka `d mfstdkifd aktra uk c`nen y uk edrin, sf a` äkcu`n
ma maprasfùk masma a` c`nen hdstd a` edrin as ma 9?¿ y a` c`nenastä d ukd mfstdkifd vartfid` ma ma 1?? l ma` edrin.
d. 4681 l e. 4321 l i. 4??? l m. 481? l
2. Mdmn uk trfäkcu`n y `d ifriukbarakifd fksirftd ma rdmfn r , axprasdrr ak tærlfkns ma `ns `dmns d, e, i ma` trfäkcu`n.
3. Ink `d fkbnrldifùk mdmd ak idmd idsn, rasn`var a` trfäkcu`n:
d. 9=º , 34º , 5=dd e< < <
e. 59, =1º , 9?ºe e q< < <
i. 52,1º , 95.3º , 483ed e< < <
m. 6,1, 491º , 9?ºd d e< < <
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8. Qk idlpn ma bnrld trfdkcu`dr tfaka `dmns qua lfmak 545,511 y 428
l. a` ärad ma` idlpn as.
d. 4686? l e. 48321 l i. 4?=12 l m. 43264 l
6. @ns dmns ma uk tarrakn trfdkcu`dr lfmak 5=?, 42? y 48= l. Yf a` instn
pnr latrn iudmrdmn ma tarrakn as $=?.???. A` instn ma` tarrakn as.
d. $ 188½1?3.2?? e. $ 288½1?3.2?? i. $ 118½1?3.2?? m. $ 128½1?3.2??
4?. @ns axtralns ma `ns erdzns ma uk inlpäs mfstdk 2 il y idmd erdzn
lfma4= il. A` äkcu`n qua bnrldk `ns mns erdzns.
d. =1¿ e. 48,9¿ i. 4?=¿ m. 5=.3¿
44. Ak ukd ifriukbarakifd ma 2 l ma rdmfn, sa
ukak mns ma sus puktns ink ukd iuarmdma = l. `d lamfmd ma` äkcu`n iaktrd`
inrraspnkmfakta iftdmd iuarmd.
d. =1¿ e. 98,6=¿ i. 4?=¿
m 83¿
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Qk puktn _ ma` p`dkn sa matarlfkd lamfdkta susinnrmakdmds qua inksfstak ak ukd pdrajd nrmakdmd ( x, y),ma` p`dkn7 `d prflard inlpnkakta sa ``dld `d desifsd y `d
sacukmd inlpnkakta sa ``dld `d nrmakdmd. Ak `ns iursnsdktarfnras, halns dprakmfmn d nid`fzdr puktns ma` p`dkn,`n iud` kns bdif`ftdrä a` trdzdmn y a` astumfn ma `ds cräbfids.
Ajalp`n
Ak `d cräbfid, nesarvdlns iudtrn puktns ma` p`dkn, iuyds innrmakdmds snk:
Cräbfid 31
Uaitds ak a` p`dkn
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk
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Yf dkd`fzdlns a` puktn (1/5,-9), valns qua su desifsd n prflard inlpnkakta as 1/`n iud` qufara maifr qua a` puktn sa hd``d d ukd mfstdkifd ma 1/5 ak mfraiifùk hnr
znktd` hdifd `d maraihd. ]dlefæk valns qua su nrmakdmd n sacukmd inlpnkakas -9, `n iud` sfckfbfid qua a` puktn sa akiuaktrd d ukd mfstdkifd ma 9 ukfmdmas a
mfraiifùk hdifd dedjn, inln sa va ak `d cräbfid.
@ns puktns iuyd desifsd as iarn, sa akiuaktrdk snera a` aja vartfid` n aja y, pajalp`n: `ns puktns (?,?), (?,2), (?,-1), astäk `nid`fzdmns snera a` aja vartfid`.
@ns puktns iuyd nrmakdmd as iarn, sa akiuaktrdk snera a` hnrfznktd` n aja x, pajalp`n: `ns puktns (?,?), (=,?), (-3/5,?), astäk uefidmns snera a` aja hnrfznktd`.
]rdzdr ak idmd idsn, `d raitd qua pdsd pnr idmd pdr ma puktns:
4. (-5,4) y (9,1)
5. (-9,=) y (=,=)
9. (-4,1) y (2,-5)
=. (-5,4) y (-5, 1)
1. (?,?) y (1,1)
2. (?,2) y (3,?)
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Yf takalns mns puktns _ y T, ak a` p`dkn ink innrmakdmds
5 5 55 4 5 4( ) ( )m x x y y< +
@d mfstdkifd aktra _ y T astä mdmd pnr:
5 55 4 5 4( ) ( )m x x y y< +
Ak `d cräbfid 3? valns qua a` trfäkcu`n _TU as raitäkcu`n, ink5 _U x <
TU y y
Cräbfid 32
Mfstdkifd aktra mns puktns
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk
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Ajalp`ns
Yf axtrdalns `d rdìz iudmrdmd ak dlens `dmns ma astd fcud`mdm, sa netfaka:
5 55 4 5 4( ) ( )m x x y y< +
qua as `d bùrlu`d qua sa utf`fzd pdrd hd``dr `d mfstdkifd aktra mns puktns ma` p`dkn
4. Hd``dr `d mfstdkifd aktra `ns puktns (4,5) y (9.3):
Yn`uifùk
5 5(9 4) (3 5)m < +
56 1,98142=8?3...m <
@d mfstdkifd aktra _ y T as uk kúlarn frrdifnkd`. Astns kúlarns dpdraiak inbraiuakifd, iudkmn id`iu`dlns mfstdkifds aktra mns puktns ma` p`dkn.
5. Hd``dr `d mfstdkifd aktra `ns mns puktns (-=, -4) y (9, 8):
Yn`uifùk
() (5 5
3 6m < +
() (5 5
3 6m < +
49? 44, =?431=51...m <
9. Hd``dr `d mfstdkifd aktra `ns mns puktns (?,3) y (=, ?):
Yn`uifùk
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42 =6 21 8, ?255133=8...m < + <
=. Hd``dr `d mfstdkifd aktra `ns mns puktns (-5,9) y (=,-=):
Yn`uifùk
( )5
5= ( 5) ( = 9)m < +
92 =6 81 6, 5461===13...m < + <
1. Hd``dr a` parìlatrn ma` trfäkcu`n iuyns værtfias astäk ak `ns puktns (?,-4), (?y (=,-4):
Yn`uifùk
A` parìlatrn as `d suld ma `ds `nkcftumas ma `ns `dmns ma` trfäkcu`n, `uacn mealns hd``dr `d `nkcftum ma idmd `dmn ma` trfäkcu`n y hdiar `d suld.
5 54 (? ?) ( 4 5)m < +
4 ? 6 6 9m < + < <
5 5
5 (= ?) (( 4 ( 4))m < +
5 42 ? =m < + <
5 5
9 (= ?) ( 4 5)m < +
_nr n tdktn, a` parìlatrn as:
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4. Akinktrdr `ds innrmakdmds ma` puktn lamfn ma` saclaktn iuyns axtralnsnk (5,=) y (8,=), y hdiar a` cräbfin.
Yn`uifùk: a` puktn lamfn vfaka mdmn pnr:
(4 5 4 5 5 8 = =1 =
x x y y_
+ + + +
Ajalp`ns
Yf inknialns ns axtralns ma uk saclaktn raitn, pnmalns hd``dr innrmakdmds ma su puktn lamfn. Yf ns puktns axtralns ma` saclaksnk ( x4, y4) y ( x5, y5) aktnkias `ds innrmakdmds ma` puktn lamfn:
4 5 4 5,
5 5l
x x y y_
+ +< ó
ó
Cräbfid 33
Innrmakdmds ma` puktn lamfn
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk
9
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( )( )5 5
5 ? ( =) 4 ( 5) 1m < + <
5 54 (= ?) (= 4) 1m < + <
Hd``dr a` puktn lamfn ma `ns saclaktns iuyns axtralns snk `ns puktns mdmns`uacn varfbfidr `d mfstdkifd ma` puktn lamfn d idmd axtraln ma` saclaktn. Hdi`d cräbfid inrraspnkmfakta.
4. (-9, =) y (1, 5)
5. (-8, 5) y (-5,4)
_nmalns varfbfidr, hd``dkmn `d mfstdkifd ma` puktn lamfn d idmd axtrama` saclaktn dsì:
5 54 (1 5) (= =) 9m < + <
Hd``dkmn `d mfstdkifd ma` puktn lamfn d` ntrn axtraln, takalns:
5 55 (8 1) (= =) 9m < + <
5. Hd``dr a` puktn lamfn ma` saclaktn iuyns axtralns snk (-=, -5) y (=,=):
Yn`uifùk: (4 5 4 5 = = = 5, , ?,4
5 5 5 5l
x x y y_
+ + < < < ó ó
ó ó
_nmalns varfbfidr, hd``dkmn `d mfstdkifd ma` puktn lamfn d idmd axtrama` saclaktn dsì:
=. (-9,-=) y (-5, 2)
1. (-=, -1) y (-=, 1)
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Ydealns qua ak a` p`dkn, mns puktns matarlfkdk ukd raitd, iudkmninknialns `ds innrmakdmds ( x4, y4) y ( x5, y5) y as pnsfe`a trdzdr `d raitd @qua pdsd pnr asns puktns.
]dlefæk pnmalns hd``dr ukd lamfmd pdrd `d fki`fkdifùk ma `d raitd @,sf inknialns `ds innrmakdmds ma mns ma sus puktns7 astd fki`fkdifùk `d``dldlns pakmfakta ma `d raitd.
Yf @ as ukd raitd qua pdsd pnr `ns puktns ( x4, y4) y ( x5, y5) `d pakmfakta ma
astd raitd @ astä mdmd pnr:5 4
5 4
y yl
x x<
Ralns qua `d pakmfakta as a` inifakta ma` dvdkia vartfi y
5 ’
y
4 snera a` dvdkia hrfznktd` x5 ’ x4 aktra astnmns puktns ma `d raitd.
A` vd`nr ma `d pakmfakpuama sar pnsftfvn, kcdtfvn n iarn. Hdy raitiuyd pakmfakta kn as
_akmfakta ma ukd raitd
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk
= Dprakmfakmn ink a` prnba Ju`fnAiudifùk ink `d pakmfakta ma ukd raitdMurdifùk: =:18 lfk.
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Ajalp`n
Hd``dr `d pakmfakta ma `d raitd qua pdsd pnr `ns puktns:
4. (-4, -4) y (9, 1)
Yn`uifùk
5 4
5 4
1 ( 4) 2 9
9 ( 4) = 5
y yl
x x
< < < <
Ma` vd`nr ma d pakmfakta, pnmalns var qua sf uk puktn snera d raitd dvd zd mns ukfmdmas ak mfraiifùk hnrfznktd` pnsftfvd, a` dvdkia vartfid` as tukfmdmas hdifd drrfed.
A` vd`nr ma `d pakmfakta ak asta idsn, kns mfn uk vd`nr pnsftfvn7 d` trdzdcräbfid, æstd prasaktd ukd mfraiifùk dsiakmakta ma fzqufarmd d maraihd.
5. (-5, 9) y (=, -4)
Yn`uifùk
5 4
5 4
4 9 = 5
= ( 5) 2 9
y y
l x x
< < < <
Ak asta idsn, `d pakmfakta as kacdtfvd y ma su vd`nr, pnmalns var qsf uk puktn snera `d raitd sa masp`dzd tras ukfmdmas hdifd `d maraihsu masp`dzdlfaktn vartfid` sarä ma mns ukfmdmas hdifd dedjn. Iudkmnpakmfakta as kacdtfvd `d cräbfid ma astd raitd as masiakmakta ma fzqufa
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9. (-9, 5) y (=, 5)
Yn`uifùk
5 4
5 4
5 5 ??
= ( 9) 3
y yl
x x< < < <
Ak asta idsn, `d pakmfakta vd`a iarn y `d cräbfid kns luastrd ukd raitd pdr`a`d d` aja x. Yf uk puktn sa masp`dzd snera d raitd, kn axparflaktd dsiakskf masiaksn.
Iudkmn ukd raitd as pdrd`a`d d` aja y (raitd vartfid`), su pakmfakta asfkmatarlfkdmd y pnr asn maiflns qua su pakmfakta as fkmabfkfmd.
]akalns ukd raitd qua pdsd pnr `ns puktns (9,=) y (9, -5), d` fktaktdrid`iu`dr su pakmfakta, netakalns:
5 4
5 4
5 = 2
9 9 ?
y yl
x x
< < <
Inln kn sa puama mfvfmfr aktra iarn, kn axfsta uk vd`nr pdrd d pakmfaktal y pnr asn maiflns qua as fkmatarlfkdmd.
]nmd raitd pdrd`a`d d` aja y su pakmfaktasnk fkmatarlfkdmds.
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@d aiudifùk ma ukd cräbfid as dqua``d sdtfsbaihd sn`dlakta pnr innrmakdmds ma `ns puktns qua astäk ak `d cräbfid. Ma `n dktarftakalns:
Ajalp`n
Yf takalns `d aiudifùk 9 x + 5 y < 2, a` puktn _(5,?) astä snera `d cräbfid pusdtfsbdia `d aiudifùk pnrqua d` raalp`dzdr, takalns 9(5) + 5(?) < 2.
Ak idlefn, a` puktn (9,=) kn sa akiuaktrd snera d cräbfid, pnrqua d` raalp`dzsus innrmakdmds ak `d aiudifùk, takalns:
9(9) + 5(=) < 43, a` vd`nr netakfmn kn sdtfsbdia `d aiudifùk.
4. Yf uk puktn _( x, y) astä snera `d cräbfid, aktnkias `ds innrmakdmds sd-tfsbdiak su aiudifùk.
5. Yf uk puktn _( x, y) kn sa akiuaktrd snera `d cräbfid, aktnkias sus innr-makdmds kn sdtfsbdiak `d aiudifùk.
_drd netakar `d aiudifùk ma ukd raitd, sa utf`fzd a` haihn ma qua a` puktn( x4, y4) y a` vd`nr ma `d pakmfakta l, matarlfkdk ukd úkfid raitd.
Yad ( x, y) uk puktn iud`qufard ma d raitd mfbarakta ma` puktn ( x4, y4) aktnkias`d pakmfakta ma `d raitd as 4
4
y yl
x x< . Lu`tfp`fidkmn astd aiudifùk pnr
Aiudifnkas ma `d raitd ak a` p`dkn
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk
1
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4. Hd``dr `d aiudifùk ma `d raitd qua pdsd pnr a` puktn (5,9) y su pakmfakta l < =
Yn`uifùk
Dp`fidkmn mfraitdlakta `d aiudifùk puktn pakmfakta, takalns:
(9 = 5 y x <
5. Qkd raitd pdsd pnr `ns puktns (-5,-=) y (4,9), hd``dr su aiudifùk puktpakmfakta:
Yn`uifùk
Ak asta idsn, inknialns mns puktns ma `d raitd y pnr `n tdktn, pnmalnhd``dr su pakmfakta
9 ( =) 3
4 ( 5) 9l
< <
Inln inknialns mns puktns ma `d raitd, a`acflns iud`qufard ma a``ns pdasirfefr `d aiudifùk puktn pakmfakta ma `d raitd, dsì:
3( = ( 5)
4 4( ) y y l x x <
Astd aiudifùk sa ``dld `d aiudifùk puktn pakmfakta ma `d raitd y puamaasirfefrsa ak astd bnrld, sf sa inknia uk puktn pnr mnkma pdsd `d raitd ya` vd`nr ma su pakmfakta.
Ajalp`ns
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n usdkmn a` ntrn puktn, netakalns `d aiudifùk:
inln ajarififn, sa puama inlprnedr qua d` trdspnkar tærlfkns ak
aiudifnkas dktarfnras, sa ``acd d ukd úkfid aiudifùk 3 9 5 x y <
9. Qkd raitd @ inrtd d` aja y ak a` puktn (?,=) y su pakmfakta l<-4/9. Hd``d aiudifùk ma `d raitd:
Yn`uifùk
Yf dp`fidlns `d aiudifùk puktn pakmfakta, takalns:
n maspajdkmn y sa tfaka
Ak a` ajalp`n dktarfnr, dpdraia maspajdmd `d vdrfde`a y ak `d aiudifùk ma `d rai
astn kns ``avd d ntrd aiudifùk astäkmdr ma `d raitd ``dldmd `d aiudifùk pakmfakfktariaptn. Ak cakard`, sf ukd raitd @ inrtd d` aja y ak a` puktn (?,e) y su pakmfaas l, dp`fidkmn `d aiudifùk puktn pakmfakta takalns:
V maspajdkmn `d y, netakalns `d aiudifùk:
Ak astd aiudifùk ma `d raitd, pnmalns `aar a` vd`nr ma `d pakmfakta l quaa` inabfifakta ma x, y `d nrmakdmd ak a` nrfcak, qua as `d mfstdkifd masma a` nrfchdstd a` puktn ma inrta ma `d raitd ink a` aja y, sf e as pnsftfvn, `d raitd inrtd d` y ak a` puktn (?,e) drrfed ma` nrfcak, sf e as iarn, `d raitd pdsd pnr a` nrfcak, sf e
kacdtfvn `d raitd pdsd pnr a` puktn (? e) pnr maedjn ma` nrfcak
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Ajalp`n
?e el < <
4. @d raitd iuyd aiudifùk as y < 1 x ’ 5, tfaka pakmfakta 1 y inrtd d` aja y ak
puktn (?,-5).
5. Mdmd `d raitd iuyd aiudifùk as y ’ 4 < -9( x + =), hd``dr `d pakmfakta ma raitd y a` puktn ma inrta ink a` aja y.
Yn`uifùk
Ak asta idsn, `d aiudifùk astä mdmd ak `d bnrld puktn pakmfakta, y ak a`pnmalns `aar a` vd`nr ma `d pakmfakta l < -9. _drd hd``dr a` puktn ma inrink a` aja vartfid`, maspajdlns `d vdrfde`a y pdrd netakar `d aiudifùk ma raitd ak su bnrld pakmfakta fktariaptn, dsì:
y ’ 4 < -9( x + =)
y ’ 4 < -9 x ’ 45
y < -9 x ’ 44
Ma `d ú`tfld aiudifùk, pnmalns `aar a` puktn ma inrta ma `d raitd ink a` avartfid` qua as a` puktn (?, -44)7 tdlefæk pnmalns `aar `d pakmfakta l <-
9. Qkd raitd @ pdsd pnr `ns puktns (d,?) y (?,e). Hd``dr ukd aiudifùk pdrd asraitd:
Yn`uifùk
Ak asta idsn, kns mdk a` puktn ma inrta ma `d raitd ink a` aja x qua as (d,y a` puktn ma inrta ink a` aja y qua as (?,e). @uacn pnmalns hd``dr d pamfakta
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dp`fidkmn d aiudifùk puktn pakmfakta y usdkmn a` puktn (?,e), netakaln
( ?)e
y e xd
<
e y e x
d <
e x y e
d+ <
mfvfmfakmn pnr e ak dlens lfalerns ma `d aiudifùk, takalns:
4ex y
de e+ <
Ma mnkma:
4 x y
d e+ <
Ajalp`n 4
Astd ú`tfld as ukd aiudifùk flpnrtdkta ma `d raitd pnrqua maedjn maidmd vdrfde`a dpdraia a` vd`nr mnkma `d raitd inrtd d idmd ukn ma `ns ajasinnrmakdmns.
Yf takalns `d aiudifùk 41 9
x y+ < , astd raitd pdsd pnr `ns puktns (1,?
(?,9)7 astn kns parlfta trdzdr d raitd, hd``dr su pakmfakta, as maifr, fmaktfbfid
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Ajalp`n 5
Asta as uk ajalp`n ma `d aiudifùk `fkad` cakard`:
Ak astd aiudifùk, D, E, I snk kúlarns (inkstdktas), dmaläs D y E kn snkiarn d` lfsln tfalpn
Hd``dr `d aiudifùk ma `d raitd qua pdsd pnr `ns puktns (-9,?) y ( ?,3):
Yn`uifùk
Inln inknialns `ns puktns ma inrta ma `d raitd ink idmd ukn ma `ns ajinnrmakdmns, pnmalns asirfefr fklamfdtdlakta `d aiudifùk ma `d raitd aastd bnrld:
Astd lfsld aiudifùk tdlefæk sa puama asirfefr ak ntrd ma `ds bnrlds yinknifmds, inln d bnrld puktn pakmfakta n d bnrld pakmfakta fktariapt
Qkd aiudifùk ma d bnrld , sa puama asirfefr ak ukd bnrld aqufv`akta ak pdrtfiu`dr, sf lu`tfp`fidlns astd aiudifùk pnr = y tnmns ns tærlfknsa pdsdk d` prflar `dmn. Aktnkias sa tfaka:
@uacn:
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Ma `d aiudifùk `fkad` cakard`, sa puama maspajdr y pdrd netakar 19
5 y x< +
Astd aiudifùk as `d aiudifùk ma `d lfsld raitd ak su bnrld pakmfakta fktariapt
Uasulfakmn `d bnrld ma `ds aiudifnkas ma `d raitd, takalns:
4. Aiudifùk puktn pakmfakta:
4 4( )l x y y x <
5. Aiudifùk pakmfakta fktariaptn:
y lx e< +
9. Aiudifùk ma `ns inrtas ink idmd ukn ma `ns ajasinnrmakdmns:
4 x y
d e+ <
=. Aiudifùk `fkad` cakard`:
? Dx Ey I + <+
Astds iudtrn aiudifnkas kns parlftak matarlfkdr `ds idrditarìstfids maiud`qufar raitd, y sa puama inkvartfr ukd aiudifùk ma ukd bnrld d `d ntrd,sacúk `d fkbnrldifùk qua sa raqufard.
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Akinktrdr `d pakmfakta y a` puktn ma inrta ink a` aja y ma `d raitd iuyaiudifùk as 12 5 ? x y <+ .
Yn`uifùk
@d aiudifùk astä mdmd inln ukd aiudifùk fkad` cakard`: Dx Ey I + <+
Yf maspajdlns `d vdrfde`a y takalns:
Astd ú`tfld as `d aiudifùk pakmfakta fktariaptn, ink l < 9, e < 1/5, amaifr, `d raitd tfaka pakmfakta 9 y a` puktn ma inrta ink a` aja y as (?, 1/5
Ajalp`n
Akinktrdr `d aiudifùk ma `d raitd qua pdsd pnr `ns puktns (5,-9) y (9,-4)asirìed`d ak sus iudtrn bnrlds.
Yn`uifùk
Ajalp`n
4. Rdlns d hd``dr `d aiudifùk puktn pakmfakta:
4 ( 9)
59 5l
< <
Yf tnldlns a` puktn (5,-9), d aiudifùk kns quamd: qua as d aiudifùma `d raitd ak su bnrld puktn pakmfakta.
5. _drd asirfefr d aiudifùk ak d bnrld pakmfakta fktariaptn, maspajdln`d vdrfde`a y, ink `n iud` netakalns: y < 5x ’ 3 qua as `d aiudifù
y < ’I + Dx
E
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d. (9,=) l< 5
e. (5,9) l < 4
i. (4,-5) l < ?
m. (-5,9) l < =
a. (5,4) l < 4/5
b. (?,?) l < 1
9. _drd netakar `d aiudifùk `fkad` cakard`, pdsdlns tnmns `ns tærlfkns `d aiudifùk dktarfnr d` prflar `dmn y quamdk -5 x + y < -37 ak mnk D < -5, E < 4 y I < 3.
=. _drd hd``dr `d aiudifùk ma `ns inrtas ink idmd ukn ma `ns ajas innrmkdmns, tnldlns `d aiudifùk dktarfnr -5 x + y + 3 < ? y pdsdlns a` tlfkn 3 d` sacukmn dmn. Mfvfmfakmn dlens `dmns ma d aiudifùk pnr takalns:
54
3 3
x y < qua as `n lfsln qua
35
43
x y < , qua as
aiudifùk pamfmd. Ak a``d, valns qua a` puktn ma inrta ink a` aja x(3/5, ?) y a` puktn ma inrta ink a` aja y as (?, -3).
4. Asirfefr ak `d bnrld puktn pakmfakta, `d aiudifùk ma `d raitd qua pdsd pa` puktn mdmn ink `d pakmfakta fkmfidmd:
5. Akinktrdr d pakmfakta ma d raitd matarlfkdmd pnr ns puktns D(-9,1) E(4
4
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9. Asirfefr idmd aiudifùk ak `d bnrld pakmfakta fktariaptn a fkmfqua, a` vd`nma `d pakmfakta y a` puktn ma inrta ma `d raitd ink a` aja y.
d. 9 x + y < =
e. 2 x ’ 9 y < 4
i. = x ’ 9 y ’ 3< ?
m. 1 x ’ 5 y + 4?< ?
a. x < 1 y + 9
=. Asirfefr d aiudifùk ma d raitd qua pdsd pnr ns mns puktns mdmns ak d bnrl Dx + Ey + I < ?
d. (-4, 5) y (5, -4)
e. (5, 9) y (9,5)
i. (4, 4) y (-4, -4)
m. (9, -=) y (?, ?)
a. (9, ?) y (?, -9)
1. Mdmds `ds sfcufaktas aiudifnkas ma raitds pdrd idmd ukd ma a``ds, asirfefr aiudifùk ma `ns inrtas a fkmfidr `ds innrmakdmds ma `ns puktns ma inrta inidmd ukn ma `ns ajas.
d. 5 x + 9 y < 2
e. -= x + 1 y < 5?
i. 49 x - 52 y < 15
m. x + 8 y < 5=
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Aiudifnkas ma `ds raitds pdrd`a`ds d
`ns ajas innrmakdmns:
Cräbfid 36
Ak cakard`, iud`qufar raitd pdrd`a`d d` aja x tfaka inln aiudifùk y < g ,mnkma g as ukd inkstdkta qua puama tnldr vd`nr pnsftfvn, kacdtfvn niarn. @d aiudifùk ma` aja x pnr ajalp`n: as y < ?.
]nmd raitd pdrd`a`d d` aja x tfaka pakmfakta iarn.
Yf ukd raitd pdsd pnr a` puktn (4,=) y as pdrd`a`d d` aja x inln sa f`ustrdak d cräbfid 35, tnmn puktn qua sa masp`dia snera asd raitd, astä d iudtrnukfmdmas ma` aja x n sad qua su mfstdkifd vartfid` ak a` p`dkn sfalpra as=, ma td` ldkard qua su aiudifùk as y < =.
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Qkd raitd @ quapdsd pnr a` puktn(1, ?) pdrd`a`d d`
aja y tfaka inlnaiudifùk x < 1,pnrqua iud`qufarpuktn qua sa mas-p`dia snera asd raitdtfaka inln prflarinlpnkakta x < 1.
Ak cakard`, ukd raitdpdrd`a`d d` aja y tfa-ka inln aiudifùk x < g , mnkma g as ukvd`nr inkstdkta.
@d raitd x < -9 aspdrd`a`d d` aja y.
Ak asa idsn, uk puk-tn qua sa masp`diasnera `d raitd, sfal-
pra sa akiuaktrd dtras ukfmdmas ma`aja, y yd sdealnsqua pdrd astd raitd,su pakmfakta as fk-matarlfkdmd.
Cräbfid 8?
Cräbfid 84
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D` hde`dr ma pdrd`a`fsln y par-
pakmfiu`drfmdm ma raitds ak a`p`dkn, n hdralns pdrd raitds qua kn takcdk`d lfsld mfraiifùk ma ns ajas innrmakdmns.
Iudkmn mns raitds mfbaraktas ak a` p`dkntfakak `d lfsld mfraiifùk, astds raitds knsa inrtdk y pnr asn maiflns qua snk pdrd-`a`ds. _drd hde`dr ma lnmn läs bnrld` maraitds pdrd`a`ds, utf`fzdralns a` inkiaptnma pakmfakta pnrqua æstd matarlfkd `dmfraiifùk ma `d raitd.
Ajalp`n
4. @ds raitds iuyds aiudifnkas snk:
y < 5 x + 9 y < 5 x + 5 y < 5 x + 4
Mns raitds @4 y @5 ink pakmfaktas l4 y l5 raspaitfvdlakta, snk pdrd`a`ds sfl4 < l5, as maifr, a` vd`nr ma sus pakmfaktas as a` lfsln.
Uaitds pdrd`a`ds y raitds
parpakmfiu`dras
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn Yasfùk
2
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Yn`uifùk
@ds raitds snk pdrd`a`ds pnrqua tfakak `d lfsld pakmfakta.
Nesarva iuä` cräbfid ma `d raitd y ’ 5 < 9( x + =) astä pnr akifld ma ds malälfaktrds qua d cräbfid ma d raitd y < 5 x ’ 5 astä pnr maedjn ma tnmds, d cräbfima y < 5 x pdsd pnr a` puktn (?,?).
5. @d aiudifùk ma `d raitd raitd @4 as y ’ 5 < 9( x + =) y `d aiudifùk ma `d raitd @
as -9 x + y < 8. Matarlfkdr sf `ds mns raitds snk pdrd`a`ds.
Yn`uifùk
@d aiudifùk ma @4 astä mdmd ak `d bnrld puktn pakmfakta, y valns qua vd`nr ma su pakmfakta as l < 9. @5 tfaka `d bnrld ma `d aiudifùk `fkad` cakrd`7 sf maspajdlns y netakalns y < 9 x + 8 qua as ukd aiudifùk ma `d bnrlpakmfakta fktariaptn, valns qua `d pakmfakta l < 9. D` sar fcud` a` vd`nr m
Cräbfid 85
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_drd trdtdr a` inkiaptn ma parpakmfiu`drfmdm aktra raitds, tdlefæk alp`adlnspakmfakta.
Ajalp`n
Nesarvdr qua `ds raitds iuyds aiudifnkas snk y < x y @4 y @5 inrraspnkmak d raiparpakmfiu`dras.
@ns vd`nras ma sus pakmfaktas snk 4 y -4 raspaitfvdlakta. D` lu`tfp`fidr `ns vd`n
Cräbfid 89
Uaitds parpakmfiu`dras
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Ak cakard`, takalns qua mns raitds @4 y @5 ink pakmfaktas:
y < l4 x y < l5 x
raspaitfvdlakta snk parpakmfiu`dras, sf l4 x l5 < -4.
Ma `d fcud`mdm l4 x l5 < -4, pnmalns maspajdr 4 5
5 4
4 4l y l
l l
< < aktnkia
pnmalns maifr qua mns raitds snk parpakmfiu`dras, iudkmn d pakmfakta ma ukd ma``ds as a` raiìprnin kacdtfvn ma `d pakmfakta ma `d ntrd.
Ajalp`ns
= ( 4)9
? 4l
< <
4. @ds raitds iuyds aiudifnkas snk 41 8 5
1 y x y x< < + snk rait
parpakmfiu`dras7 pnmalns var qua a` prnmuitn ma sus pakmfaktas md laknukn.
1(-4/1) < -4
5. Matarlfkdr sf ns puktns D(?, -=), E(4, -4), I (5, 5) astäk uefidmns ak d lfslraitd (snk in`fkad`as):
Yn`uifùk
_rflarn, hd``alns `d pakmfakta ma `d raitd qua pdsd pnr `ns puktns D(?, -y E(4, -4):
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`uacn, hd``alns `d pakmfakta ma `d raitd qua pdsd pnr `ns puktns E(4, -4I (5, 5).
4 59
4 5l
< <
inln `ds pakmfaktas snk fcud`as, pnmalns inki`ufr qua `ns puktns astäk `d lfsld raitd, as maifr, snk in`fkad`as.
9. Qkd raitd @ pdsd pnr `ns puktns (-9, 5) y (=, 1)7 hd``dr:
d. @d aiudifùk ma ukd raitd pdrd`a`d d @ qua pdsa pnr a` puktn (4,5).
e. @d aiudifùk ma ukd raitd parpakmfiu`dr d @ qua pdsa pnr a` puk(-5,-9).
Yn`uifùk
d. _rflarn maealns hd``dr `d pakmfakta ma @, puastn qua inknialns m
puktns ma `d raitd:
1 5 9
= ( 9) 3l
< <
@uacn, tnmd raitd qua sad pdrd`a`d d @ maea takar inln pakmfakta 9
Aktnkias, `d aiudifùk pamfmd as (
9
5 43 y x <
.
e. ]nmd raitd parpakmfiu`dr d @ maea takar inln pakmfakta, a` raiìprnkacdtfvn ma 9/3 ù sad -3/97 inln pdsd pnr a` puktn (-5, -9), `d aiudipamfmd as:
(3
( 9) ( 5) y x < n 5 4l y e< <
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4. A` mairaiflfaktn ma `d ainknlìd ak a` ú`tfln dôn sa matarlfkdlamfdkta ukd bukifùk fkad` qua pdsd pnr ns puktns (9,=) y (5, -1).@d bùrlu`d pdrd mfihd bukifùk `fkad` as:
d. B(x)< 9x-5
e. B(x)<-6x + 59
i. B(x)< 5x+ =1
m. B(x)<-x+9
5. @d bukifùk qua pdsd pnr a` puktn (5,9) y iuyd pakmfakta as = as:
d. B(x)< =x-1 e. B(x)<-5x+=
i. B(x)<=x+5
m. B(x)<x+4
9. Rarfbfidr, sf `d raitd qua pdsd pnr `ns puktns D(2,-1) y E(8, -8) aspdrd`a`d d `d raitd qua pdsd pnr `ns puktns I (-9, 45) y M(4, 2).
=. Qkd raitd @ pdsd pnr `ns puktns (-=, 1) y (8, -5):
d. ]rdzdr `d raitd qua pdsd pnr (?,?) y as parpakmfiu`dr d @.
e. ¾Iuä` as `d pakmfakta ma ukd raitd parpakmfiu`dr d @>
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1. Ak idmd idsn, asirfefr `d aiudifùk ma `d raitd ak su bnrld pakmfaktafktariaptn, sf
d. l < 5 y e < 5
e. l < -4/5 y e < ?
i. 5 4 y e< <
m. l < 3 y e < -2
a. l < -9 y e < -4
2. Asirfefr d aiudifùk ma d raitd qua pdsd pnr a` puktn mdmn y qua tfakapakmfakta l.
d. (5, 2) y l < -9
e. (-4, =) y l < 4/5
i. (1, -5/9) y l < 4
m. (4, -4) y l< -5
a. (-9,-1) y l < ?
3. Asirfefr idmd aiudifùk mdmd ak `d bnrld pakmfakta fktariaptn:
d. 9 x + y < =
e. 5 x ’ y < 1
i. 2 x ’ 9 y < 4
m. = x + 5 y < 4?
a =x 9y < ?
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8. Asirfefr `d aiudifùk ma `d raitd qua pdsd pnr `ns puktns mdmns ak `dbnrld Dx + Ey + I < ?
d. (-4, 5) (5, -4) e. (5, 9) (9,5)
i. (4, 4) (-4, -4)
m. (9,-=) (?,?)
a. (-4, -49) (-8,-4)
6. Akinktrdr ukd aiudifùk ma `d raitd qua sdtfsbdcd `ds inkmfifnkas:
d. @d pakmfakta as -5/9 y pdsd pnr a` puktn (?,4)
e. _dsd pnr a` puktn (-1,5) y as pdrd`a`d d` aja x
i. _dsd pnr a` puktn (-9,-=) y as pdrd`a`d d` aja y
m. A` puktn ma inrta ink a` aja x as (-9,?) y ink a` aja y (?,=)
a. _dsd pnr a` puktn (-5,9) y as pdrd`a`d d `d raitd iuyd aiudifùk as5 x ’ y ’5 < ?
b. _dsd pnr a` puktn (5,=) y as parpakmfiu`dr d d raitd iuyd aiudifùkas x ’ 1 y + 4? < ?
4?. Qsdkmn d pakmfakta, matarlfkdr sf ns tras puktns mdmns snk in`fkad`as:
d. (5, 9) (-=, -3) (1, 8)
e. (5, -4) (4,4) (9, =)
i. (=, 2) (4,5) (-1, -=)
m. (-9, 2) (9,5) (6,5)
a (-9 2) (9 5) (6 -5)
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Qkd ifriukbarakifd as a` inkjuktn ma tnmns `ns puktns_ ma uk p`dkn qua aqufmfstdk ma uk puktn bfjn I . D`puktn bfjn sa `a ``dld a` iaktrn, y d `d mfstdkifd aktra _ y I sa `a ``dld a` rdmfn.
_drd netakar `d aiudifùk ma `d ifriukbarakifd ink iaktrn ak a` puktn (h,g ) y rdr , pnmalns utf`fzdr `d bùrlu`d ma `d mfstdkifd aktra mns puktns.
Yf _( x, x) sa akiuaktrd ak `d ifriukbarakifd, aktnkias `d mfstdkifd aktra _ y a` puiaktrn (h,g ) as r , as maifr:
Cräbfid 8=
@d ifriukbarakifd
Qkfmdm 3. Iurvds ak a` p`dkn Yasfùk
4
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Cräbfid 81
Yf a` iaktrn ma `d ifriukbarakifd as a` nrfcak (?,?), aktnkias `d aiudifùk quamd a`d sfcufakta bnrld:
x5 + y5 < r 5
Yf a` rdmfn ma d ifriukbarakifd as 4, d `dldlns ifriukbarakifd ukftdrfd. Yf sa inkiak a` iaktrn y a` rdmfn ma `d ifriukbarakifd, quamd inlp`atdlakta matarlfkdmdpuama mfeujdrsa, usdkmn a` inlpäs.
Ma d aiudifùk x5 + y5 < r 5 pnmalns maspajdr y netakalns 5 5 y r x< ´ ù sa
5 5 y r x< 5 5y r x<
Yf sa a`avd d` iudmrdmn dlens `dmns ma `d aiudifùk, takalns: ( x ’ h)5 + ( y ’ g )5 <æstd as `d aiudifùk ma `d ifriukbarakifd ink iaktrn ak (h,g ) y rdmfn r .
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Idmd ukd ma astdsaiudifnkas matar-lfkd ukd salfifr-iukbarakifd inlnsa va ak `d bfcurd82.
Yn`uifùk
5
42 y x< 7 `dprflard ma astdsaiudifnkas masirfea`d ifriukbarakifd su-parfnr y `d sacukmd,`d fkbarfnr.
Ajalp`ns
4. @d aiudifùk x5 + y5 < 42 inrraspnkma d ukd ifriukbarakifd ink iaktrn
(?,?) y rdmfn =, qua pnmalns masinlpnkar inln
Cräbfid 82
Cräbfid 83
y < r5 ’ x5
y < 42 ’ x5
y < - r5 ’ x5
y < - 42 ’ x5
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5. Hd``dr d aiudifùk ma d ifriukbarakifd qua tfaka su iaktrn ak a` puktn lamma` saclaktn iuyns axtralns snk `ns puktns (-5,9) y (=,1).
Yn`uifùk
_rflarn, maealns hd``dr a` iaktrn ma `d ifriukbarakifd:
4 5 4 5,5 5
x x y yI
+ + < ó
(
9 15 =
, 4, =5 5I
+ +
< < ó
Inln yd takalns `ds innrmakdmds ma` iaktrn ma `d ifriukbarakifd, dhnid`iu`dlns a` rdmfn, dp`fidkmn d bùrlu`d ma mfstdkifd masma a` puktn iaktd iud`qufard ma `ns axtralns ma` saclaktn, pnr ajalp`n: d` puktn (=,1).
(
55 5
( 4) ( =) 4? x y + <
Dhnrd, pnmalns asirfefr `d aiudifùk ma `d ifriukbarakifd:
(5
5 5( 4) ( =) 4? x y + < n 5 5 ? x y Mx Ay B + + + + <
9. @d aiudifùk ma `d ifriukbarakifd ink iaktrn ak a` puktn (9,5) y rdmfn 1 a
Yn`uifùk
5 5 5( ) ( ) x h y g r + <
Yf masdrrn``dlns `ns iudmrdmns y pdsdlns tnmns `ns tærlfkns d` prflar dmtakalns:
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Astd aiudifùk astä mdmd ak `d bnrld:
5 5 ? x y Mx Ay B + + + + <
Tua sa ``dld aiudifùk cakard` ma `d ifriukbarakifd.
Ak a` ajalp`n dktarfnr, M < -2, A < -=, B < -45
Iudkmn kns mdk `d aiudifùk cakard` ma `d bnrld 5 5 5( ) ( ) x h y g r + <
Maealns trdksbnrldr`d d `d bnrld:5 5 5
( ) ( ) x h y g r + <
Ak astd ú`tfld aiudifùk, pnmalns var iuä` as a` iaktrn y iuä` as a` rdmfn ma `d iiukbarakifd.
_drd hdiar astd trdksbnrldifùk7 maealns hdiar a` prniasn pdrd inlp`atdr iudmrdm
Qkd axprasfùk ma d bnrld ( x + d)5 sa `dld iudmrdmn parbaitn, iudkmn d` masdrrn
asta iudmrdmn, netakalns tras tærlfkns: ( x + 1)5.
Ajalp`n
4. Hd``dr a` iaktrn y a` rdmfn ma `d ifriukbarakifd iuyd aiudifùk as x5 + y5
5 x + 4? y + 48 < ?.
Yn`uifùk
Inlp`atdlns iudmrdmns pdrd x, y dsì:
( )( )5 55 4 4? 51 48 4 51 x x y y+ + + + + < + +
@uacn, takalns:
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Qkd ma `ds prnpfamdmasma `d ifriukbarakifd ink-sfsta ak qua `d raitd tdk-cakta d `d ifriukbarakifdak iud`qufard ma sus puk-tns, as parpakmfiu`dr inka` rdmfn ma d ifriukbarak-ifd qua vd masma a` iaktrnd` puktn ma tdkcakifd.
Astd aiudifùk inrraspnkma d ukd ifriukbarakifd ink iaktrn ak a` puk(-4,-1) y rdmfn 8 .
Ak d`cukns idsns, d aiudifùk 5 5 ? x y Mx Ay B + + + + < sa sdtfsbdia pd
uk úkfin puktn n pdrd kfkcúk puktn.
5. Ak `d aiudifùk x5 + y5 + 5 x ’ = y + 1 < ?
Yn`uifùk
D` inlp`atdr iudmrdmns, takalns:
( )( )5 55 4 = = 1 4 = x x y y+ + + + < + + ù sad ()( )5 54 5 ? x y+ + <
astd aiudifùk sa sdtfsbdia pdrd uk úkfin puktn (-4,5)
9. Mdmd `d aiudifùk x5 + y5 ’ 4? x + 2 y + 92 < ? qua tfaka `d bnrld ma aiudifùk cakard` ma `d ifriukbarakifd d` inlp`atdr iudmrdmns, takaln( x5 ’ 4? x + 51) + ( y5 + 2 y + 6) < -92 + 51 + 6 ù sad ( x ’ 1)5 + ( y + 9)5 < -5
Astd ú`tfld aiudifùk kn sa sdtfsbdia pdrd kfkcúk puktn pnrqua `d suld mmns iudmrdmns kn puama sar kacdtfvd.
Cräbfid 88
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4. Akiuaktra d aiudifùk ma d raitd tdkcakta d d ifriukbarakifd iuyd aiudias x5 + y5 ’ 2 x ’ 5 y ’ 41 < ? ak a` puktn (2,1).
Yn`uifùk
D` inlp`atdr `ns iudmrdmns, takalns: ( )( )55 2 6 5 4 41 6 4 x x y y + + + < + +
Aktnkias kns quamd: (9
1 2=
y x <
Astd aiudifùk inrraspnkma d ukd ifriukbarakifd ink iaktrn ak a` puktn (9y rdmfn 1. ]dlefæk pnmalns var qua a` puktn (2,1) sdtfsbdia `d aiudifùpnr `n tdktn, as uk puktn ma a``d.
5. Hd``dr `d pakmfakta ma `d raitd qua pdsd pnr a` puktn (2,1) y pnr a` iak(9,4)
Yn`uifùk
1 4 =
2 9 9l
< <
Astd raitd inktfaka a` rdmfn qua vd masma a` iaktrn d` puktn (2,1) y quaparpakmfiu`dr d `d raitd tdkcakta ak asta puktn7 pnr `n tdktn, `d pakmfakma `d raitd tdkcakta ak a` puktn (2,1) as:
9
=l <
V pnr `n tdktn, `d aiudifùk ma `d raitd tdkcakta as:
9
Ajalp`n
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4. ]rdzdr `d cräbfid inrraspnkmfakta d idmd aiudifùk:
d. 5 5 92 x y+ <
e. 5 5 42 x y+ <
i. ( )( )5 55 9 4?? x y+ + <
m. 5 5 5 4? 51 ? x y x y+ + + <
a. 5 5 45 91 ? x y x+ + <
5. Matarlfkdr sf idmd aiudifùk as ukd ifriukbarakifd (sa md su rdmfn y su iatrn)7 sf as uk puktn (sa mdk sus innrmakdmds)7 n sf as uk inkjuktn vdiìn.
d. 5 5 = 2 49 ? x y x y+ + + <
e. 5 5 4? 2 92 ? x y x y+ + + <
i. 5 5 2 4 ? x y x+ + <
m. 5 5 8 2 9? ? x y x y+ + + <
a. 5 52 6 8 42 =6 x x y y+ + + + <
4
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Qkd a`fpsa as a` inkjuktn ma tnmns `ns puktns _ ma` p`dkn,td`as qua `d suld ma `ds mfstdkifds ma idmd ukn ma a``ns d mnspuktns bfjns ``dldmns bnins, as ukd inkstdkta.
Ak `d cräbfid, valns ukd a`fpsa iuyn iaktrn as a` puktn (?,?). @ns puktns läs d`ajdmma` nrfcak ak a` aja hnrfznktd` snk D (-d,?) y D‖ (d,?), astns puktns sa ``dldk `ns vtfias ma `d a`fpsa. @ns puktns läs `ajdkns ma` iaktrn ak a` aja vartfid` snk E(?,y E‖(?,e). @ns saclaktns ½ ½ DD y EE snk `ns ajas ma `d a`fpsa y sus `nkcftumas s5d y 5e raspaitfvdlakta @ns puktns ( ?) ( ?)B B snk `ns bnins ma `d a`fpsa q
Cräbfid 86
@d a`fpsa
Qkfmdm 3. Iurvds ak a` p`dkn Yasfùk
5
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Qkd bnrld bäif` ma trdzdr ukd a`fpsa, as tnldr uk hf`n y bfjdr sus axtralns ak mnpuktns n astdids snera uk p`dkn, majdkmn qua a` hf`n quama luy b`njn7 `uacn stnld uk `äpfz pdrd taksdr a` hf`n, bnrldkmn ukd aspaifa ma trfäkcu`n. D` rntdr `äpfz, ldktakfakmn a` hf`n taksn, a` `äpfz vd masirfefakmn `d a`fpsa.
Ma `d cräbfid ma `d a`fpsa, pnmalns var ink bdif`fmdm qua ak a``d sa iulp`a `d ra`ifùk 5 5 5d e i+ < , qua as flpnrtdkta pdrd mamuifr ukd bùrlu`d ma `d aiudifùk m`d a`fpsa.
Ma `ds inkmfifnkas ma `d mabfkfifùk ma `d a`fpsa, pnmalns hd``dr su aiudifùk.
Inln `d suld ma `ds mfstdkifds4 5
5_B _B d+ < (inkstdkta).
Yf _( x,y) as iud`qufar puktn ma `d a`fpsa, d` usdr `d bùrlu`d ma `d mfstdkifdtakalns:
@uacn inln:
D` raalp`dzdr, kns quamd:
Maspajdkmn uk rdmfid`, netakalns:
V a`avdkmn dlens `dmns d` iudmrdmn, kns quamd:
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( )( ) ( )( ) ( )(5 5 5 5 5 55? = = . ? ? x i y d d x i y x i y+ + < + + +
Maspuæs ma ramuifr tærlfkns, takalns:
( )5 5 5. .d x i y d i x + <
Kuavdlakta a`avdlns dlens `dmns d` iudmrdmn y sflp`fbfidlns:
( ) (5 5 5 5 5 5 5 5d i x d y d d i + <
Inln: 5 5 5e d i<
Uaalp`dzdkmn ak `d aiudifùk dktarfnr takalns: 5 5 5 5 5 5e x d y d e+ <
Mfvfmfakmn astd ú`tfld aiudifùk aktra 5 5d e quamd:
5 5 5 5 5 5
5 5 5 5 5 5
e x d y d e
d e d e d e+ <
V netakalns5 5
5 5 4
x y
d e+ <
Yf d ; e, `d a`fpsa as d`drcdmd hnrfznktd`lakta y `ns bnins sa akiuaktrdksnera a` aja hnrfznktd` ak `ns puktns (-i,?) y (i,?).
Yf e ; d, d a`fpsa as d`drcdmd vartfid`lakta y ns bnins sa akiuaktrdk sneraa` aja vartfid`, ak `ns puktns (?,i) y (?,-i).
Ya ``dld axiaktrfifmdm ma `d a`fpsa a` inifakta 5?
?,3=2
i
d< .
Astd as `d aiudifùk cakard` ma `d a`fpsa ink iaktrn ak a` puktn (?,?).
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Asta kúlarn fkbnrld snera `d bnrld ma `d a`fpsa: iudkmn i sa dprnxf-ld d 4, `d a`fpsa as luy d`drcdmd y `ns bnins astäk luy dpdrtdmns ma`iaktrn7 iudkmn `d axiaktrfifmdm
i
d
astä iarid ma iarn, `ns bnins saakiuaktrdk iarid ma` iaktrn y d a`fpsa sa pdraia d ukd ifriukbarakifd,nevfdlakta ? 4
i
d0 0 .
4. Qkd a`fpsa tfaka inln aiudifùk 5 5
492 42
x y+ < . Hd``dr `ns værtfias, `ns bnin
`d axiaktrfifmdm, y mfeujdr `d a`fpsa.
Yn`uifùk
Ma `d aiudifùk, takalns qua: 5 92d < . @uacn, 2d < .
Dsì, `ns værtfias ak a` aja hnrfznktd` snk `ns puktns (-2,?) y (2,?).
]dlefæk: e5 < 42. @uacn, e < =.
V `ns puktns läs `ajdkns ma` iaktrn ak a` aja vartfid` snk (?,-=) y (?,=).
Ma `d fcud`mdm d5 < e5 + i5, pnmalns maspajdr a` vd`nr ma i y sa netfaka
@uacn `ns bnins astäk ak `ns puktns
@d axiaktrfifmdm as fcud` d
Ajalp`ns
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5. @d aiudifùk ma ukd a`fpsa as 5 5
44 51
x y+ < . Hd``dr sus værtfias, sus bnins,
axiaktrfifmdm, y mfeujdr `d iurvd.
Yn`uifùk
Ak asta idsn, d5 < 4
@uacn, d < 4
Dmaläs: e5 < 51
Aktnkias: e < 1
d e
Cräbfid 6?
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@ns værtfias ma `d a`fpsa snk `ns puktns (?,1) y (?,-1), `ns iud`as astäk ak a` avartfid`7 `ns puktns (-4,?) y (4,?) snk `ns puktns läs mfstdktas ma` iaktrn ak aja hnrfznktd`.
_drd hd``dr i hdialns: 51 4 5= =,86i < <
@uacn `ns bnins snk `ns puktns: (?, 5= ) (?, 5=) y
A` vd`nr ma `d axiaktrfifmdm as: 5=?,63
1
A` vd`nr ma d axiaktrfifmdm sa diarid d 4, y d cräbfid ma d a`fpsa as luy d`drcdm
Cräbfid 64
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d. Rærtfias ak ns puktns (-8,?) y (8,?)7 Bnins ak ns puktns (?,3)y (-3).
e. Rærtfias ak `ns puktns (?,6) y (?,-6), y `d `nkcftum ma` ajalaknr ma `d a`fpsa as 45.
i. Iaktrn ak (?,?) Bnins ak `ns puktns (-1,?) y (1,?) y `ns bninsak `ns puktns (9,?)y (-9,?).
m. Rærtfias ak `ns puktns (?,2) y (?,-2) y `ns bnins ak `ns puktns(?,=) y (?,-=).
a. Rærtfias ak ns puktns (?,1) y (?,-1) y ns puktns läs mfstdktasma` nrfcak ak `d mfraiifùk hnrfznktd` snk (-4,?) y (4,?).
4. Akiuaktra `ds innrmakdmds ma `ns værtfias y ma `ns bnins, a` vd`nr ma `d axiatrfifmdm, y mfeuja `d iurvd iuyd aiudifùk as:
d. 5 5
46 =
x y+ <
e. 5 5
4
42 84
x y+ <
i.
5 5
4=6 51
x y+ <
5. Asirfed `d aiudifùk ma `d a`fpsa qua tfaka `ds inkmfifnkas mdmds:
4
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@d a`fpsa ink iaktrn ak a` puktn (h,g)
D` masp`dzdr a` iaktrn ma d a`fpsa ma` puktn (?,?) d uk puktn (h,g ) ma` p`dkn,su aiudifùk sa trdksbnrld ak:
( ) ( )5 5
5 5 4
x h y g
d e
+ <
@ns værtfias ma `d a`fpsa quamdk ak `ns puktns (h ’ d, g ) y (h + d, g ).
@ns puktns läs mfstdktas ma` nrfcak ak `d mfraiifùk vartfid` snk (h, g + e)y (h, g ’ e).
x(h,-d)
G+e
G
G-e
h
ed
(h,+d)
(h,g)
@ns bnins astdräk ak `ns puktns (h + i, g ) y (h ’ i, g ), sf a` aja ldynr ma `da`fpsa as hnrfznktd`.
Cräbfid 65
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Ajalp`n
@d a`fpsa iuyd aiudifùk as ( ) ( )5 5
5 94
51 42
x y ++ <
tfaka su iaktrn ak a` puktn (5, -9), d < 1 y e < =7 51 42 9i < <
@uacn `ns bnins ma `d a`fpsa astäk ak `ns puktns (-4, -9) y (1, -9). @ns værtfima `d a`fpsa snk `ns puktns (-9,-9) y (3, -9). @ns puktns läs mfstdktas ma` iatrn ak mfraiifùk vartfid` snk (5,4) f (5,-3), y a` vd`nr ma `d axiaktrfifmdm maa`fpsa as i/d < 9/1.
Yn`uifùk
Iudkmn d < e `d aiudifùk `d a`fpsa quamd: ( ) ( )5 5
5 5 4
x h y g
d d
+ <
Yf lu`tfp`fidlns pnr d5, netakalns `d aiudifùk:
42 6 3 5, 2=i < <
Tua inrraspnkma d d aiudifùk ma ukd ifriukbarakifd ink iaktrn ak a` puk(h,g ) y rdmfn d. Astn kns mfia qua `d ifriukbarakifd as uk idsn pdrtfiu`dr ma
Cräbfid 69
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Ajalp`n
@d aiudifùk ma ukd a`fpsa as() ( )
5 5
54
42 6
x y+ < . Hd``dr a` iaktrn, sus værtfia
`ns bnins, su axiaktrfifmdm, y mfeujdr `d iurvd.
Yn`uifùk
@ds innrmakdmds ma` iaktrnsnk (?,5), d < =, e < 9,
42 6 3 5, 2=i < <
@ns værtfias snk `ns puktns(-=,5) y (=,5). @ns bnins
a s täk ak `n s puk tns()(3 , 5 3 , 5 y 7 `n spuktns läs mfstdktas ma`iaktrn ak `d mfraiifùkvartfid` snk (?,1) y (?,-4).
4. Hdiar `d cräbfid ma idmd aiudifùk:
d.5 5
4= 4
x y+ <
e.5 5
44 =
x y+ <
i.5 5
442 51
x y+ <
Ajarififns pdrd prnbukmfzdr
Cräbfid 6=
5
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m.5 5
44?? =6
x y+ <
a. 5 551 92 ? x y+ <
b. 5 551 = 4?? x y+ <
c. ( ) ( )5 5
9 =4
42 51
x y + <
h. ()5
544
51 4
x y+ <
f. ( ) ( )5 5
= 94
6 51
x y ++ <
5. Matarlfkdr ak idmd idsn, `d aiudifùk ma `d a`fpsa qua tfaka `ns iudtrn pukmdmns inln axtralns ma `ns ajas ldynr y laknr, y mfeuja `d cräbfid.
d. (9, ?), (-9,?), (?,1), (?,-1)
e. (5, ?), (-5,?), (?,9), (?,-9)
i. (3, ?), (-3,?), (?,=), (?,-=)
m. (4, ?), (-4,?), (?,2), (?,-2)
9. Inksu`tdr iuä` as `d lamfmd ma` ärad akiarrdmd pnr `d a`fpsa.
=. ¾Iuäktns puktns tfaka `d cräbfid ma `d aiudifùk 51 x5 + 92 y5 < ?>
1. Inlp`atdr `ns iudmrdmns y asirfefr `d aiudifùk sfcufakta inln `d aiudi
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Ak `d cräbfid `d mfbarakifd tdkB _ _B inks ta<
Qkd hfpæren`d as a` inkjuktn ma ns puktns _ ak uk p`dkn,td`as qua `d mfbarakifd ma sus mfstdkifds d mns puktns bfjns``dldmns bnins as inkstdkta.
Cräbfid 61
@d hfpæren`d
Qkfmdm 3. Iurvds ak a` p`dkn Yasfùk
9
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Qkd hfpæren`d tfaka mns værtfias7 a` puktn lamfn ma` saclaktn qua ukasus værtfias as a` iaktrn ma `d hfpæren`d7 `d raitd qua pdsd pnr `ns værtfiassa ``dld aja trdksvarsd`.
Iudkmn ukd hfpæren`d tfaka a` iaktrn ak a` nrfcak (?,?), ns puktns værtfiassa inrtdk ink ukn ma `ns ajas innrmakdmns, y `d aiudifùk ma `d hfpæren`dastä mdmd pnr:
55
5 5 4
y x
d e <
Mnkma d as d mfstdkifd ma` værtfia ma d hfpæren`d d su iaktrn, y e as d nk-cftum ma` saclaktn parpakmfiu`dr d` aja trdksvarsd` qua pdsd pnr a` værtfiay inrtd `d raitd e
y xd
< ak a` puktn (d,e).
Cräbfid 62
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_drd crdbfidr d hfpæren`d ink iaktrn ak a` nrfcak, pnmalns mfeujdr a` raitäkcu`n mmflaksfnkas 5d pnr 5e7 ak sacufmd, trdzdr ds dsìktntds, y uacn mfeujdr d hfpæren`
Ajalp`n
@ds dsìktntds snk `ds raitds ink aiudifnkas:
e y x
d< y e
y xd
< .
Astds raitds pdsdk pnr a` iaktrn ma `d hfpæren`d y pnr `ns puktns (d,e), (-d, -e), (-d,y (d, -e), qua snk `ns værtfias ma` raitäkcu`n ma mflaksfnkas 5d x 5e. @ds dsìktntsnk luy flpnrtdktas pdrd pnmar trdzdr `d cräbfid ma `d hfpæren`d.
Ma d cräbfid pnmalns var qua ak d hfpæren`d sa tfaka d ra`difùk: 5 5 i d e< +
Ma mnkma: 5 5i d e< +
V i as `d mfstdkifd masma a` iaktrn d iud`qufard ma `ns værtfias.
A` kúlarn i/d sa ``dld `d axiaktrfifmdm ma `d hfpæren`d,
i/d as ldynr ma ukn.
Hdiar `d cräbfid ma `d hfpæren`d iuyd aiudifùk as55
451 6
y x <
Yn`uifùk
Ak `d aiudifùk, takalns qua d < 1 y e < 9. Ak asta idsn, a` raitäkcu`n 5d x 5tfaka sus værtfias ak `ns puktns (1, 9), (1, -9), (-1, 9) y (-1, -9).
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_nmalns hd``dr a` vd`nr ma i, dsì: 5 59 1 9= 1, 89i < + < 7
@uacn, `ns bnins ma `d hfpæren`d snk `ns puktns: ( ) (9= , ? 9= , ? y
Hdstd dquì halns vfstn ukd hfpæren`d iuyds hnjds sa derak d maraihd y dfzqufarmd.
Axfsta tdlefæk ukd hfpæren`d ink a` lfsln iaktrn y `ds lfslds dsìktntds,iuyds hnjds sa derak hdifd drrfed y hdifd dedjn.
Yus værtfias snk `ns puktns (?,e) y (?,-e) y sus bnins snk `ns puktns (?, i) y(?, -i). Astd hfpæren`d sa ``dld `d hfpæren`d inkjucdmd y su aiudifùk as:
5 5
5 5 4
y x
d e <
Iudkmn ak `d aiudifùk ma `d hfpæren`d takalns qua d < e, `d hfpæren`dsa ``dld aquf`ätard.
Cräbfid 63
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Ajalp`n
Yf5
5
442 =
x y <
Yaôd`dr `ds innrmakdmds ma` iaktrn ma `ns værtfias y ma `ns bnins. Matarlfkd`ds aiudifnkas ma `ds dsìktntds y mfeujdr `d iurvd.
Yn`uifùk
Ak `d aiudifùk valns qua d < =, e < 5 y i < 42 =+ n 5? =, =3i < .
@uacn:
Iaktrn < (?,?)7
Rærtfias ak `ns puktns:
(-=,?) y (=,?)7
Bnins ak `ns puktns:
()5? ,? ( 5?,?) y
@ds aiudifnkas ma `ds dsìktntds snk:
4
5V x< 7 4
5V x<
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Iudkmn d hfpæren`d tfaka su iaktrn ak uk puktn (h,g), mfbarakta ma` puktn(?,?), su aiudifùk astäkmdr as:
( ) ( )5 5
5 5 4
x h y g
d e
<
@ds aiudifnkas ma `ds dsìktntds snk:
( ) (e e
y g x h y y g x hd d
< <
@d hfpæren`d inkjucdmd tfaka inln aiudifùk:
( )( )5 5
5 5 4
y g x h
d e
<
Cräbfid 68
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Ajalp`n
@d aiudifùk ma ukd hfpæren`d as ()( )5 5
4 54
= 6
x y + < . Hdiar `d cräbfid ma as
hfpæren`d y ma su inkjucdmd.
Yn`uifùk
Iaktrn < (h, g ) < (4, -5)7 d < 57 e < 9
@ds aiudifnkas ma `ds dsìktntds snk:
() (9 9
5 4 5 45 5
y x y y x+ < + <
Cräbfid 66
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4. Mdmd `d aiudifùk ma `d hfpæren`d, mfeujdr `d cräbfid y asirfefr `dsaiudifnkas ma `ds dsìktntds.
d. 5 5
442 6 y x <
e. 5 56 = 92 x y <
i. 5 551 = 4?? y x <
5. Hd``dr `d aiudifùk ma `d a`fpsa qua iulp`a `ds inkmfifnkas mdmds yhdiar su cräbfid.
d. Bnins ak (?,1) y (?, -1)7 værtfias ak (?,=) y (?, -=)
e. Rærtfias ak (-5,?) y (5, ?), e < 9
i. @d aiudifùk ma ukd hfpæren`d astä mdmd pnr ( )( )5 5
9 94
= 4
x y+ <
4
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@d pdräen`d astä matarlfkdmd pnr a` inkjuktn _ ma`p`dkn iuyd mfstdkifd d uk puktn bfjn ``dldmn bnin, asfcud` d `d mfstdkifd (parpakmfiu`dr), d ukd raitd ``dldmdmfraitrfz.
Cräbfid 4??
@d pdräen`d
Qkfmdm 3. Iurvds ak a` p`dkn Yasfùk
=
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Yf inksfmardlns d pdräen`d ink værtfia ak (?, ?), bnin ak a` puktn (?, i), d mfraittfaka inln aiudifùk y < -i.
Ma `d mabfkfifùk ma `d pdräen`d sa tfaka qua:
m 4 < m
5
Yf dp`fidlns `d bùrlu`d ma `d mfstdkifd, takalns:
Cräbfid 4?4
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A`avdkmn d` iudmrdmn, takalns:
( ) ( ) ( ) ((
( ) ( ) ( ) ( )
5 55 5 5 5
5 5 5 5
?
?
x y i x x y i
x y i x x y i
+ < + + ó
+ < + +
D` masdrrn``dr `ds npardifnkas, sa tfaka:
5 5 5 5 55 5 x y iy i y iy i+ + < + +
@uacn,
5 = x iy<
Tua as `d aiudifùk astäkmdr ma `d pdräen`d ink værtfia ak a` puktn (?, ?).
’ Yf i as pnsftfvn, `d pdräen`d sa dera hdifd drrfed inln ak `d cräbfid.
’ Yf i as kacdtfvn, `d pdräen`d sa dera hdifd dedjn.
’ @d raitd qua pdsd pnr a` bnin y a` værtfia, sa `dld aja ma `d pdräen`d.
’ A` saclaktn qua uka mns puktns ma `d pdräen`d, pdsdkmn pnr a` bniny pdrd`a`n d `d mfraitrfz sa ``dld a` `dmn raitn.
Ya puama var qua sus puktns axtralns snera `d pdräen`d tfakak innrmakdmds
(5i, i) y (-5i, i)
@uacn, `d `nkcftum ma` `dmn raitn as a` vd`nr pnsftfvn ma =i.
Astns puktns snk flpnrtdktas d` trdzdr `d pdräen`d pnrqua kns nrfaktdk ak iuäk
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_drd hd``dr `ds innrmakdmds ma `ns puktns axtralns, valns qua `d aiudifùk maraitd snera `d iud` astä a` `dmn raitn as: y < i
Dhnrd, inln `d aiudifùk ma `d pdräen`d as: 5 = x iy<
Uaalp`dzdlns y pnr i y takalns: 5 5= x i<
Ma mnkma: 5 x i< ´
Ma fcud` ldkard, sf `d pdräen`d sa dera hdifd `d maraihd n hdifd `d fzqufarmd yværtfia astä ak a` nrfcak, takalns qua:
m 4
< m 5
V d` dp`fidr `d bùrlu`d ma mfstdkifd quamd:
Ma mnkma netakalns:
Cräbfid 4?5
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Masdrrn``dkmn y sflp`fbfidkmn, takalns:
5 45 y x<
Ya netfaka dsì, `d aiudifùk ma `d pdräen`d qua sa dera hdifd `d mara-ihd iudkmn i as pnsftfvn inln sa va ak `d cräbfid y sa dera hdifd
`d fzqufarmd iudkmn i as kacdtfvn.
4. Mdmd `d aiudifùk ma `d pdräen`d x5 < 8 y, hd``dr a` værtfia, a` bnin, `d aiuifùk ma d mfraitrfz, d nkcftum ma` dmn raitn y ns puktns axtralns ma` dmraitn, y mfeujdr `d pdräen`d.
Yn`uifùk
Ma d aiudifùk x5 < 8 y
pnmalns `aar qua=i < 8 ma mnkmai < 5, `uacn `d pd-räen`d sa dera hdifddrrfed, su værtfia astdak (?,?) y su bnin aka` puktn (?,5), d aiud-ifùk ma `d mfraitrfz as
y < -5, ns puktns axtra-lns ma` dmn raitn snk(-5i, i) < (-=,5) y(5i, i) < (=,5), `d `nk-cftum ma` `dmn raitn as8 inln sa f`ustrd ak dcräbfid 61.
Ajalp`n
Cräbfid 4?9
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Ma ds sftudifnkas dktarfnras, pnmalns var qua iudkmn a` tærlfkn iudmrätma d aiudifùk ma d pdräen`d astä ak d vdrfde`a x, d pdräen`d sa dera hddrrfed, sf i as pnsftfvn n hdifd dedjn, sf i as kacdtfvn.
Iudkmn a` tærlfkn iudmrätfin ma `d aiudifùk ma `d pdräen`d astä ak `d rfde`a y, `d pdräen`d sa dera snera hdifd `d maraihd sf i as pnsftfvn n hd`d fzqufarmd sf i as kacdtfvn.
5. Mdmd `d aiudifùk ma `d pdräen`d y5 < -45 x, hd``d a` værtfia, a` bnin, `d aiuifùk ma d mfraitrfz, d nkcftum ma` dmn raitn y ns puktns axtralns ma` `draitn, mfeujdr `d pdräen`d.
Yn`uifùk
Ma d aiudifùk y5 < -45 x pnmalns aar qua =i < -45 ma mnkma i < -9, ua`d pdräen`d sa dera hdifd d fzqufarmd, su værtfia astä ak (?,?) y su bnin akpuktn (-9,?)7 d aiudifùk ma d mfraitrfz as d raitd x <9, ns puktns axtralma` `dmn raitn snk (-9,2) y (-9,-2), `d `nkcftum ma` `dmn raitn as 45 inlnf`ustrd ak `d cräbfid 62.
Cräbfid 4?=
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Ak `ns sfcufaktas ajarififns pdrd `d pdräen`d iuyd aiudifùk sa md, hd``dr a` værtfia` bnin, `d aiudifùk ma `d mfraitrfz, `ns puktns axtralns ma` `dmn raitn, y mfeujdr pdräen`d.
d. 5 = x y<
e. 5 42 x y<
i. ( )5
= ( ) y g i x h <
m. 5 2 y x<
a. 5 y x<
Ajalp`n
Iudkmn `d pdräen`d tfaka su værtfia ak uk puktn (h,g ) ma` p`dkn, y sa deravartfid`lakta, `d aiudifùk astäkmdr quamd:
( ) (5
= x h i y g <
Yf `d pdräen`d sa dera hdifd `d maraihd n hdifd `d fzqufarmd, su aiudifùk as:
( )5
= ( ) y g i x h <
4 Qkd pdräen`d tfaka su værtfia ak a` puktn (9 5) y su bnin ak a` puktn (9
4
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Yn`uifùk
Ralns qua `d mfstdkifd aktra a` værtfia y a` bnin as 9, `uacn i < 97 ininknialns qua a` iaktrn as a` puktn (9, 5), `d aiudifùk ma `d pdräen`d as
( )5
9 =(9)( 5) x y <
N sad qua:
( )5
9 45( 5) x y <
5. Qkd pdräen`d tfaka su værtfia ak a` puktn (?, 5) y su bnin ak a` puktn (-5,
asirfed `d aiudifùk ma `d pdräen`d y hdcd `d cräbfid.
Yn`uifùk
A` bnin astä d `d fzqufarmd ma` værtfia `uacn `d pdräen`d sa dera hdifd `d qufarmd, i < -5, su aiudifùk as ( )
55 =( 5)( ?) y x < n sad ( )
55 8 y <
Cräbfid 4?1
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4. Qkd pdräen`d tfaka su værtfia ak a` puktn (4, -5) y su mfraitrfz as`d raitd x < -4. Hd``dr `d aiudifùk ma `d pdräen`d, a` bnin y `nspuktns axtralns ma` `dmn raitn, y hdiar `d cräbfid.
5. Qkd pdräen`d tfaka su bnin ak a` puktn (5,?) y su mfraitrfz as `draitd x < -5. Hd``dr a` værtfia, ns puktns axtralns ma` dmn raitn,y mfeujdr `d pdräen`d.
9. Qkd pdräen`d tfaka su værtfia ak a` puktn (-5, -5), su bnin ak a`puktn (-5,?)7 hd``dr d aiudifùk ma d mfraitrfz, ns puktns axtralnsma` `dmn raitn, y hdiar `d cräbfid.
=. ]rdzdr `d pdräen`d iuyd aiudifùk as5
= 9 ? y x+ <
5
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@d ifriukbarakifd, `d a`fpsa, `d hfpæren`d y `d pdräen`d snk iurvds quapartakaiak d d bdlf`fd ma `ds iurvds iùkfids, pnrqua puamak netakarsad` inrtdr uk inkn ma mns hnjds pnr uk p`dkn ak mfbaraktas mfraiifnkas,inln sa fkmfid ak `ds sfcufaktas cräbfids:
C äbf
a
<6?
6?
<
@d ifriukbarakifd, `d a`fpsa, `d hfpæren`d y `d pdräen`d snk iurvds quapartakaiak d d bdlf`fd ma `ds iurvds iùkfids, pnrqua puamak netakarsad` inrtdr uk inkn ma mns hnjds pnr uk p`dkn ak mfbaraktas mfraiifnkas,inln sa fkmfid ak `ds sfcufaktas cräbfids:
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4. @d aiudifùk x5+y5<51, inrraspnkma d:
d. Qkd ifriukbarakifd ma iaktrn (?,?) y qua pdsd pnr a` puktn (5,?) e. Qkd ifriukbarakifd ma iaktrn (?,?) y qua pdsd pnr a` puktn (?,1)
i. Qkd a`fpsa ma iaktrn (h.g) qua pdsd pnr a` puktn (?,1) m. Qkd a`fpsa ma iaktrn (?,?) qua pdsd pnr a` puktn (?,1)
5. Akiuaktra `ds innrmakdmds ma `ns værtfias y ma `ns bnins, a` vd`nr ma`d axiaktrfifmdm, y mfeuja `d iurvd iuyd aiudifùk as:
d.
5 5
44?? 2=
x y+ < e. 5 542 4 x y+ <
9. Mdmd `d aiudifùk ma `d hfpæren`d, mfeujdr `d cräbfid y asirfefr `dsaiudifnkas ma `ds dsìktntds.
d. 55
42= 92
y x < e.
55
4= =
y x < i. 5 5
451 4==
y x <
=. @d aiudifùk y5<42x, inrraspnkma d:
d. Qkd a`fpsa ma bnin (?,=) y mfraitrfz y <-= e. Qkd a`fpsa ma bnin (=,?) y mfraitrfz y <= i. Qkd a`fpsa ma bnin (?,?) y mfraitrfz y <4 m. Qkd a`fpsa ma bnin (?,4) y mfraitrfz y<=
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A` nejatfvn ma d astdmìstfid as hdiar fkbarakifds ink raspaitn ma ukd pne`d-
ifùk, d pdrtfr ma `d fkbnrldifùk qua inktfaka ukd luastrd. @d astdmìstfidldkajd `d tanrìd ma `d fkbnrldifùk pdrd prasaktdr `ns hd``dzcns ak bnrldiudktfbfidmd y utf`fzdr`ns ak `d tnld ma maifsfnkas.
Yfalpra qua sa hdiak astumfns astdmìstfins, dpdraia a` inkiaptn ma prn-edef`fmdm qua pdrd d ldynrìd ma d cakta, as uk tærlfkn vdcn qua fkmfid`d pnsfef`fmdm ma niurrakifd ma uk avaktn ak a` buturn. A` inkiaptn maprnedef`fmdm as útf` iudkmn sa trdedjd ink prniasns bìsfins, efn`ùcfins,snifd`as, prnkùstfins ma` i`fld, inlpnrtdlfaktn ma `d en`sd, ati., quacakardk nesarvdifnkas y rasu`tdmns qua snk flpnsfe`as ma pramaifr inkaxditftum. Ajalp`ns: `d prasfùk drtarfd` ma ukd parsnkd ak uk lnlaktnmdmn, a` prnkùstfin ma` tfalpn pdrd uk mìd saôd`dmn, a` praifn ma `dsdiifnkas ak d en`sd ma vd`nras, a` inlpnrtdlfaktn ma d ainknlìd, ati.,pnrqua tnmns astns bakùlaknspuamak subrfr d`tardifnkas fk-
aspardmds y dbaitdrsa pnr ntrnshaihns n ifriukstdkifds qua samaknlfkdk bakùlakns d`adtn-rfns n prnedef`ìstfins. Ak ifartdldkard, tnmn n qua niurra akkuastrd intfmfdkfmdm, tfaka ukifartn crdmn ma d`adtnrfamdm.
Inkiaptns eäsfins ma prnedef`fmdm
Qkfmdm 8. _rnedef fmdm y astdmìstfid Yasfùk
4
Inkiaptns eäsfins ma prnedef`fmdm _drta 4. Murdifùk: 4:=5 l
Inkiaptns eäsfins ma prnedef`fmdm _drta 5. Murdifùk: 6:1= l
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@d braiuakifd ink `d iud` sa prasaktdk astns avaktns ak ukd crdk sarfama nesarvdifnkas, as d lakumn astde`a y pnr `n tdktn, kns prnpnrifn-kd ukd lamfmd fktuftfvd ma `d pnsfef`fmdm ma niurrakifd ma uk avaktn
d`adtnrfn ak uk buturn asiakdrfn.
Ajalp`n
Yf ak `ns ú`tflns 5? dôns, ak a` lasma nituera hd hdefmn ``uvfds deuk-mdktas, astd fkbnrldifùk `a sarvfrä d`
dcrfiu`tnr pdrd p`dkfbfidr sus sfalerdsy rain`aitdr sus insaihds, dukqua aka` prùxfln dôn, a` las ma nituerapuama idraiar ma `uvfds deukmdktas.
Ak ukd bnrld läs sakif``d, iudkmn`dkzdlns ukd lnkamd, kn pnma-lns astdr sacurns ma qua d` idarkns luastra `d idrd. _arn sf usdlnsukd lnkamd parbaitd, maspuæs ma5? `dkzdlfaktns pnmalns prama-ifr qua `d lftdm ma `dkzdlfaktnsluastrd idrds y `d ntrd lftdm sa``ns7ak asta idsn, pnmalns maifr qua ma5? `dkzdlfaktns, a` 1?% ma a``ns
luastrak idrd y a` 1?% luastraksa``n. Astd braiuakifd ra`dtfvd, knsnrfaktd pdrd paksdr qua d` hdiaruk sn`n `dkzdlfaktn ma `d lnkamd,hdy uk 1?% ma pnsfef`fmdm ma qualuastra `d idrd.
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Yf `d lnkamd as flparbaitd y ak uk kúlarn ma `dkzdlfaktns matar-lfkdmns, a` 8?% ma a``ns luastrd idrd, sa puama paksdr qua pdrd ukdpnstdmnr ak uk sn`n `dkzdlfaktn ma `d lnkamd, as bdvnrde`a qua
dpuasta d `d idrd, y sfk aledrcn, uk euak dpnstdmnr kukid `n hdrìd. @dprnedef`fmdm qua as a` inkiaptn qua dkd`fzdralns aksacufmd, as ukdharrdlfaktd luy útf` pdrd hdiar fkbarakifds.
Inksfmaralns a` idsn ma ukdpnstdmnr qua masad hdiarukd fkbarakifd ink raspaitnma `d parbaiifùk ma uk mdmn,as maifr, qufara sdear sf d``dkzdr a` mdmn, hdy `d lfsldprnedef`fmdm ma qua ak `didrd suparfnr luastra uk kú-larn ma ukn d` safs7 aktnkias,`d pne`difùk astumfdmd as a`inkjuktn ma kúlarns qua
rasu`tdrìd d` `dkzdr a` mdmnrapatfmdlakta. Yf a` mdmnbuard parbaitn, `d saxtd pdrtama ns dkzdlfaktns lnstrdrìdukn, `d saxtd pdrta lnstrdrìdmns, `d saxtd pdrta lnstrdrìd
tras, `d saxtd pdrta lnstrdrìd iudtrn, `d saxtd pdrta lnstrdrìd ifkin y `dsaxtd pdrta lnstrdrìd safs, as maifr, idmd idrd ma` mdmn tfaka `d lfsld
pnsfef`fmdm ma dpdrfifùk. _drd varfbfidr su hfpùtasfs, a` dpnstdmnr hdia5? `dkzdlfaktns y nesarvd qua ak 48 ma a``ns dpdraifù mns, `n iud` `acakard ifartd masinkbfdkzd snera su hfpùtasfs ma qua a` mdmn as parbaitny pnr supuastn, tfaka qua raihdzdr`d. A` rdznkdlfaktn ma` dpnstdmnr akasta idsn, rainknia `d bukifùk ma `d prnedef`fmdm d` hdiar fkbarakifds afktuya qua d dpdrfifùk ma 48 vaias a` mns, maluastrd qua as luy pninprnede`a qua sa trdta ma uk mdmn inrraitn.
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Maspuæs ma fmaktfbfidr`d pne`difùk lntfvn maastumfn, mabfkfr idmd
ukfmdm ma nesarvdifùkak `d pne`difùk, sa`ai-ifnkdr ukd luastrd ma`d pne`difùk y lamfr`ds idrditarìstfids ma `dsukfmdmas ma `d luastrd,vfaka `d atdpd läs fl-pnrtdkta ma `d fkvastfcd-ifùk n sad, `d fkbarakifdastdmìstfid qua as a`prniasn qua dtrfeuyan dsfckd d `d pne`difùkaktard, ds idrditarìstfidsnesarvdmds n lamfmdsak `d luastrd.
@d inkbfdef`fmdm ma `ns rasu`tdmns ma ukd fkvastfcdifùkastdmìstfid mapakma ak crdk pdrta, ma d a`aiifùk inrrai-td ma `d luastrd. Æstd maea sar raprasaktdtfvd, as maifr,inksarvdr `ds lfslds idrditarìstfids ma `d pne`difùk,
dukqua su tdldôn sad laknr, ink a` nejatn ma `ncrdruk inrraitn ldkajn ma `d fkbnrldifùk.
Axfstak vdrfds tæikfids ma luastran pdrd sa`aiifnkdrdprnpfdmdlakta `ds luastrds.
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D` rad`fzdr uk axparflaktn astdmìstfin, sa netfaka ukinkjuktn ma nesarvdifnkas n rasu`tdmns. As kaiasdrfninksfmardr d`cukds knifnkas flpnrtdktas snera `d tan-rìd ma inkjuktns pdrd qua pnmdlns aktakmar lajnr, a`
astumfn ma `d prnedef`fmdm. Qtf`fzdralns `atrds ldyús-iu`ds pdrd fkmfidr `ns inkjuktns y `atrds lfkúsiu`ds pdrd raprasaktdr `nsa`alaktns ma uk inkjuktn. @`dldlns inkjuktn ukfvarsd` d` inkjuktn quainktfaka tnmns `ns a`alaktns inksfmardmns, as maifr, qua `ns a`alaktnsma iud`qufar ntrn inkjuktn astäk ak a` ukfvarsd`.
Qk inkjuktn D as uk sueinkjuktn ma E, sf tnmn a`alaktn ma D astä ak E.
Asirfeflns D ⊅ E y `aalns D astä inktakfmn ak E.
Cräbfid 4?3
D ⊅ E
Qkfvarsd`
D
E
Knifnkas snera inkjuktns
Qkfmdm 8. _rnedef fmdm y astdmìstfid Yasfùk
5
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Yf inksfmardlns mns ink- juktns iud`qufard D y E,`d ukfùk ma D y E, asirftd
inln D∪E, as a` inkjuktnma tnmns `ns a`alaktnsma D, ma E n ma dlens,as maifr, pdrd astdr ak `dukfùk, uk a`alaktn maeaastdr ak pnr `n lakns,ukn ma `ns inkjuktns.
Yf D as uk sueinkjuktnma Y, aktnkias a` inl-p`alaktn ma D, asirftn
D‖ as a` inkjuktn maa`alaktns ma Y qua knastäk ak D.
@d fktarsaiifùk ma mnsinkjuktns D y E, asirftd
D∦E n efak DE, as a`inkjuktn ma puktns nma a`alaktns qua astäktdktn ak D inln ak E.
Cräbfid 4?8
D ∪ E
Y
D E
Cräbfid 4?6D ∦ E
Y
D E
Cräbfid 44?
D
D‖Y
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Ya mfia qua mnsinkjuktns D y E snkmfsjuktns n lutud-lakta axi`uyaktas, sf
D ∦ E < ς. As maifr,`ns inkjuktns lutud-lakta axi`uyaktaskn tfakak a`alaktnsinlukas.
Ajalp`ns
4. Yupnkar qua sa asirfeak `ns lasas ma` dôn ak 45 pdpa`ftns y sa in`nimaktrn ma ukd urkd. @uacn sa sdidk `ns pdpa`ftns ukn pnr ukn. A` inkjukma tnmns `ns rasu`tdmns pnsfe`as as:
Y<{akarn, baerarn, ldrzn, derf`, ldyn, jukfn, ju`fn, dcnstn, saptfalenituera, knvfalera, mfifalera}.
Yn`uifùk
Yf tnldlns:
D < {akarn, baerarn, ldrzn, derf`, ldyn, jukfn}
E < {akarn, ldrzn, ldyn, ju`fn, saptfalera, knvfalera}
D y E snk sueinkjuktns ma Y.
D ∪ E < {akarn, baerarn, ldrzn, derf`, ldyn, jukfn, ju`fn, saptfalera, n
Cräbfid 444
D ∦ E < ∁
Y
D E
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]dlefæk takalns D ∦ E <{akarn, ldrzn, ldyn}
A` inlp`alaktn ma D as:
D‖ < {ju`fn, dcnstn, saptfalera, nituera, knvfalera, mfifalera}. Æsta as
`fstdmn ma tnmns `ns lasas qua kn astäk ak D, y a` inlp`alaktn mE as:
E‖ < {baerarn, derf`, jukfn, dcnstn, nituera, mfifalera}, as maifr, æsta as `fstdmn ma `ns a`alaktns qua kn astäk ak E.
Ya tfaka qua D ∦ D‖< ς, as maifr, iud`qufar inkjuktn y su inlp`alaktn snmfsjuktns n lutudlakta axi`uyaktas.
5. Ya `dkzdk tras lnkamds inrraitds. A` inkjuktn ma tnmns `ns pnsfe`as rasutdmns as:
Y< {iii, iis, isi, iss, sii, sis, ssi, sss}, mnkma i < idrd7 s< sa``n.
Yn`uifùk
Yf mabfkflns D: dpdraiak axditdlakta mns idrds, aktnkias
D < {iis, isi, sii}. I`drdlakta, D ⊅ Y
Yf mabfkflns E: dpdraiak tras idrds, aktnkias
E < {iii}. ]dlefæk E ⊅ Y
]akalns D ∪ E < {iis, isi, sii, iii}
]dlefæk D ∦ E < ς. @uacn inki`uflns qua D y E snk lutudlakta axi`yaktas, pnrqua kn tfakak a`alaktns inlukas.
]dlefæk valns qua a` E‖ < {iis, isi, iss, sii, sis, ssi, sss}
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Ajalp`ns
4. Axparflaktn: `dkzdr ukd lnkamd
Aspdifn luastrd`: I, Y
5. Axparflaktn: `dkzdr uk mdmn
Aspdifn luastrd` {4, 5, 9, =, 1, 2Y <
Ya ``dld avaktn sflp`a d uk a`alaktn nlfalern ma` aspdifn luastrd`. Qk avaktninlpuastn n sflp`alakta uk avaktn, astäbnrldmn pnr ukn n läs avaktns sflp`as.
D`cukns avaktns dsnifdmns ink a` axparf-laktn ma `dkzdr uk mdmn snk:
Qk axparflaktn d`adtnrfn as a` prniasn pnr lamfn ma` iud`,sa netfaka ukd nesarvdifùk n rasu`tdmn.
Ya `dld aspdifn luastrd` Y ma` axparflaktn, d ra`difùk ma tnmds ds pnsfe`as
nesarvdifnkas n rasu`tdmns ma` axparflaktn.
Axparflaktn ak astdmìstfid
Qkfmdm 8. _rnedef fmdm y astdmìstfid Yasfùk
9
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D: Ya nesarvd uk kúlarn flpdr
E: Ya nesarvd uk kúlarn laknr qua ifkin
I: Ya nesarvd uk tras n uk iudtrn
M4: Ya nesarvd uk ukn
M5: Ya nesarvd uk mns
M9: Ya nesarvd uk tras
M=: Ya nesarvd uk iudtrn
M1: Ya nesarvd uk ifkin
M2: Ya nesarvd uk 2
Dquì valns qua `ns ú`tflns safs avaktns ma` `fstdmn snk avaktns sflp`as
pnrqua idmd ukn ma a``ns as uk a`alaktn ma` aspdifn luastrd`. Qk avaktnsflp`a as dqua` qua sù`n puama niurrfr ma ukd bnrld.
@ns tras prflarns ajalp`ns D,E,I snk avaktns inlpuastns.
A` avaktn D as uk avaktn inlpuastn pnrqua sa puama masinlpnkar ak`ns avaktns M4, M9 y M1.
A` avaktn E sa puama masinlpnkar ak `ns avaktns M4, M5, M9 y M=.
A` avaktn I sa puama masinlpnkar ak `ns avaktns M9 y M=.
D` rad`fzdr uk axparflaktn d`adtnrfn y matarlfkdr su aspdifn luastrd`,fmaktfbfidlns `ns avaktns sflp`as ma` axparflaktn qua snk idmd ukn ma
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`ns a`alaktns ma` aspdifn luastrd`. _nmalns dsfckdr uk kúlarn aktraiarn y ukn d idmd avaktn sflp`a7 asta kúlarn sa ``dld `d prnedef`fmdmma` avaktn. Yf suldlns `ds prnedef`fmdmas ma tnmns `ns avaktns sflp`as
ma uk aspdifn luastrd`, su suld maear sar fcud` d ukn. Ak ntrds pd`derds,sf knsntrns saôd`dlns `ns avaktns sflp`as ma` aspdifn luastrd` inln a4, a5, a9, ak y asirfeflns `d prnedef`fmdm ma idmd avaktn sflp`a inln: _(a4),_(a5), _(a9)... _(ak).
Aktnkias:
4. ? ≭ _(af) ≭ 4 pdrd f < 4, 5, 9, ... k
5. _(a4) + _(a5) + _(a9) + ... + _(ak) < 4
Yf `d prnedef`fmdm ma niurrakifd ma idmd avaktn sflp`a as `d lfsld, satfaka qua prnedef`fmdm ma _(af) < 4/k.
@d prnedef`fmdm ma niurrakifd ma uk avaktn as uk kúlarn aktra iarn yukn7 sf a` vd`nr ma `d prnedef`fmdm astä iarid ma ukn, hdy läs pnsfef`fmdmas
ma qua a` avaktn niurrd. _nr ajalp`n: sf a` aqufpn idlpaùk hd cdkdmn a`6?% ma `ns i`äsfins, aktnkias hdy ukd d`td prnedef`fmdm ma qua a` aqufpnidlpaùk cdka a` i`äsfin, pnrqua `d prnedef`fmdm ma cdkdr as fcud` d ?,6.
Ma ns astumfdktas qua saprasaktdk pdrd fkcrasdrak `d ukfvarsfmdm nbfifd`sù`n a` 1%, as dmlftfmn.@uacn, `d prnedef`fmdmma qua uk astumfdktaiud`qufard pdsa ak `dukfvarsfmdm nbfifd` asluy edjd pnrqua d prn-edef`fmdm as fcud` d ?,?1.
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_rnedef`fmdm ma uk avaktn inlpuastn D, makntdmd pnr _(D) as fcud` d `dsuld ma tnmds `ds prnedef`fmdmas ma `ns avaktns sflp`as qua partakaiakd D. @n pnmalns axprasdr dsì:
_(D) < ∔ _(af) pdrd tnmn af ak D, mnkma a` sìlen`n ∔, sfckfbfid`d suld ma `ds prnedef`fmdmas ma `ns avaktns sflp`as ma D.
Yf uk avaktn D astä inlpuastn pnr avaktns sflp`as ink fcud`prnedef`fmdm ma niurrakifd ak uk aspdifn luastrd`, aktnkias
`d prnedef`fmdm ma` avaktn D as fcud` d` kúlarn ma avaktnssflp`as ma D, mfvfmfmn aktra a` kúlarn ma avaktns sflp`as ma`avaktn luastrd`.
Ajalp`ns
4. Ak a` axparflaktn ma dkzdr mns mdmns inrraitns n justns y nesar-vdr ns puktns qua dpdraiak ak sus idrds suparfnras, netakalnsa` sfcufakta aspdifn luastrd`:
Y < {(4,4), (4,5), (4,9), (4,=), (4,1), (4,2), (5,4), (5,5), (5,9), (5,=),
(5,1), (5,2), (9,4), (9,5), (9,9), (9,=), (9,1), (9,2), (=,4), (=,5),
(=,9), (=,=), (=,1), (=,2), (1,4), (1,5), (1,9), (1,=), (1,1), (1,2),
(2,4), (2,5), (2,9), (2,=), (2,1), (2,2)}
Ralns qua a` aspdifn luastrd` tfaka 92 a`alaktns n avaktnssflp`as. Yf mabfkflns:
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D: @d suld ma `ds idrds lnstrdmds md mfaz.
E: @d suld ma `ds idrds as laknr ma sfata.
D < {(=,2), (1,1) (2,=)}.
@uacn, _(D) < 9/92 < 4/45 < ?,?89
E < {(4,4), (4,5), (4,9), (4,=), (4,1), (5,4), (5,5), (5,9), (5,=), (9,4),
(9,5), (9,9), (=,4), (=,5) (1,4)}
@uacn _(E) < 41/92 < 1/45 < ?,=42
5. Axparflaktn d`adtnrfn. Ya `dkzdk mns lnkamds inrraitds d` dfra.A` aspdifn luastrd` ma` axparflaktn as:
Y < {(idrd, sa``n), (sa``n, idrd), (sa``n, sa``n), (idrd, idrd)} A` aspdifn luastrd` tfaka iudtrn avaktns sflp`as.
Yf D: dpdraia läs ma ukd idrd, aktnkias D <{(idrd, idrd)}
@uacn _(D) < ° < ?,51
Yf E: dpdraia pnr `n lakns ukd idrd, aktnkias
E<{(idrd, sa``n),(sa``n, idrd),(idrd, idrd)} `uacn _(E) < 9/= < ?,31
Ak asta idsn, sa inki`uya qua a` avaktn E tfaka läs prnedef`fmdmma niurrakifd.
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_rnedef`fmdm ma` inlp`alaktn
y ma `d ukfùk
D` rad`fzdr uk axparflaktn, a` aspdifn luastrd` Y as a` inkjuktn matnmns `ns rasu`tdmns u nesarvdifnkas pnsfe`as ma` axparflaktn, asmaifr, as a` inkjuktn ukfvarsd` ma rabarakifd ink raspaitn ma `ns ma-läs avaktns.
Inln Y inktfaka tnmns ns rasu`tdmns pnsfe`as: _(Y) < 4, æsta sa `dlda` avaktn sacurn. Iudkmn sa tnld `d prnedef`fmdm ma uk avaktn qua
kn astä ak a` aspdifn luastrd` ma` axparflaktn, su prnedef`fmdm asiarn y aktnkias, sa ``dld uk avaktn flpnsfe`a.
Ajalp`n
Ak a` axparflaktn ma dkzdr uk mdmny nesarvdr a` kúlarn lnstrdmn aksu idrd suparfnr, a` avaktn D: a`
rasu`tdmn as uk kúlarn aktra 4 y 2._(D)<4, pnrqua ak iud`qufar idsn,a` mdmn lnstrdrä uk kúlarn aktraukn y safs, D as uk avaktn sacurn.
D` inktrdrfn, a` avaktn E: dpdraia uk3, as uk avaktn flpnsfe`a, _(E) < ?pnrqua a` mdmn kukid lnstrdrä ukdidrd ink sfata puktns.
_rnedef`fmdm ma avaktns
Qkfmdm 8. _rnedef fmdm y astdmìstfid Yasfùk
=
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Yf `ns avaktns D y E snk lutudlakta axi`uyaktas, `d prnedef`fmdm ma`d ukfùk ma D y E as fcud` d `d prnedef`fmdm ma D läs `d prnedef`fmdm
ma E. Astd as `d rac`d ma `d dmfifùk qua sa axprasd dsì:_(D ∪ E) < _(D) + _(E)
Nesarvdifùk
Iudkmn D, E, I y M snk avaktns lutudlakta axi`uyaktas,aktnkias sa tfaka qua:
_(D ∪ E ∪ I ∪ M ∪ A) < _(D) + _(E) + _(I)+ _(M) + _(A)
Yf D y E kn snk avaktns lutudlakta axi`uyaktas, aktnkias `d prned-ef`fmdm ma `d ukfùk as fcud` d `d suld ma `ds prnedef`fmdmas ma D y E,lakns `d prnedef`fmdm ma su fktarsaiifùk, as maifr:
_(D ∪ E) < _(D) + _(E) ’ _(D ∦ E)
Cräbfid 445_(D ∪ E) < _(D) + _(E)
Y
D E
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Ajalp`n
Id`iu`dr `d prnedef`fmdm ma netakar uk ukn n uk mns d` tfrdr uk mdmn.
Yn`uifùk
Mabfkflns a` avaktn:
D: Dpdraia ukn y E: Dpdraia mns
Astns mns avaktns snk lutudlakta axi`uyaktas pnrqua sn`n sa puama lnstrukd idrd. A` avaktn dpdraia uk ukn n uk mns as D∪E, `uacn:
Cräbfid 449
Y
D
D‖]dlefæk takalns qua_(Y) < 4, `uacn, _(D ∪ D‖)
< _(D) + _(D‖) < 4`uacn ma astd ú`tfldfcud`mdm, takalns qua_(D‖) < 4- _(D) y tdlefæk_(D) < 4 - _(D‖)
Inksfmaralns a` avaktn D y su inlp`alaktn D‖. Vd sdealnsqua astns avaktns snk lutudlakta axi`uyaktas y tdlefæk
takalns qua D ∪ D‖ < Y inln `n pnmalns var ak a` mfdcrdldma `d cräid 449.
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@d prnedef`fmdm ma uk avaktn vdrfdrä mapakmfakmn ma`d niurrakifd n `d kn niurrakifd ma ukn n läs avaktnsra`difnkdmns.
@d prnedef`fmdm ma qua uk avaktn D, niurrd ukd vaz qua hdyd niurrfmnuk avaktn E, sa ``dld `d prnedef`fmdm inkmfifnkd` ma D mdmn E y `d as-irfeflns dsì:
_(D|E), mnkma `d rdyd vartfid`, hdia a` pdpa` ma `d pd`derd mdmn, astdprnedef`fmdm `d mabfkflns dsì:
_(D|E) < ( ) ( ) ?( )
_ D E sf _ E_ E
@d prnedef`fmdm ma D mdmn E, as fcud` d d prnedef`fmdm ma d fktarsaiifùkma D y E mfvfmfmn aktra `d prnedef`fmdm ma E.
Yupnkcdlns qua D y E snk avaktns lutud`lakta axi`uyaktas inln sava ak `d cräbfid 44=.
Cräbfid 44=
Y
D E
_rnedef`fmdm inkmfifnkd` a
fkmapakmakifd ma avaktn
Qkfmdm 8. _rnedef fmdm y astdmìstfid Yasfùk
1
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Yf a` avaktn E niurra iudkmn uk axparflaktn mdmn sa rad`fzd, aktnkias asflpnsfe`a qua a` avaktn D niurrd sflu`täkadlakta y pnr d tdktn, pnmalnsasirfefr qua `d _(D|E) < ?, sf D y E snk lutudlakta axi`uyaktas.
Dhnrd, sf supnkalns qua D y E snk a` lfsln avaktn, aktnkias sf E niurra,niurra dutnlätfidlakta D y pnr `n tdktn, `d _(D|E) <4.
Astn kns sucfara qua `d _(D|E) astä ra`difnkdmd ink `d rdzùk ( )
( )
_ D E
_ E
Ajalp`n
Qtf`fzdkmn `d mabfkfifùk ma prnedef`fmdm inkmfifnkd`, akinktrdr `d prnede`fmdm ma `d dpdrfifùk ma uk ukn ak `d idrd suparfnr ma uk mdmn, sf sdealnqua dpdraifù uk kúlarn flpdr ak uk sn`n `dkzdlfaktn.
Yn`uifùk
_nmalns mabfkfr `ns avaktns:
D: Ya nesarvd uk ukn.
E: Ya nesarvd uk kúlarn flpdr.
@uacn sa eusid d prnedef`fmdm ma D, mdmn qua yd niurrfù a` avaktn E. @d predef`fmdm ma d niurrakifd ma D y E d` lfsln tfalpn, sfckfbfid d nesarvdifùma uk ukn y ma uk kúlarn flpdr, aktnkias: 4
( )2
_ D E < dmaläs takalnqua `d _(E) < 4/5, `uacn
( )
4( ) 42|
4( ) 9
5
_ D E_ D E
_ E< < <
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Yf d niurrakifd ma uk avaktn D kn sa dbaitd pnr d niurrakifd n kn niurrakma uk avaktn E, pnmalns dbfrldr qua `ns avaktns D y E snk fkmapakmfaky sa mabfka dsì:
Mns avaktns D y E snk fkmapakmfaktas sf _(D ∦ E) < _(D) _(E). Yf astd acakifd kn sa sdtfsbdia, `ns avaktns snk mapakmfaktas. Ma `d mabfkfifùk fkmapakmakifd ma avaktns sa puama var qua:
( ) ( ) ( ) ( )
| ( )( ) ( )
_ D E _ D _ E_ D E _ D
_ E _ E< < <
Ajalp`n
Inksfmaralns `ns avaktns sfcufaktas qua tfakak qua var ink a` `dkzdlfakma uk mdmn:
D: Ya nesarvd uk kúlarn flpdrE: Ya nesarvd uk kúlarn pdr
I: Ya nesarvd 4 ù 5 d. ¾Ynk fkmapakmfaktas `ns avaktns D y E> e. ¾Ynk fkmapakmfaktas `ns avaktns D y I>
Yn`uifùk
Maealns var, sf sdtfsbdia _(D|E) ≯ _(D)
d. @d prnedef`fmdm ma nesarvdr uk kúlarn flpdr iudkmn hd niurrfmn kúlarn pdr as fcud` d iarn, as maifr, _(D|E)<? parn _(D) < 4/5 pnrtdktn, D y E kn snk fkmapakmfaktas pnrqua
_(D|E)≯ _(D)
e. Kntdlns qua _(D|I) < 4/57 dmaläs, _(D) < 4/5, pnr `n tdktn, _(D
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D`cukns ajalp`ns ma prnedef`fmdm
4. Yf sa `dkzdk tras lnkamds
d. ¾Iuä` as `d prnedef`fmdm ma netakar mns n läs idrds>
e. ¾Iuä` as `d prnedef`fmdm ma netakar axditdlakta mns idrds>
Yn`uifùk
A` aspdifn luastrd` Y<{iii, iis, isi, sii, iss, sis, iss, sss}
d. _ < =/8 < 4/5 < ?,1
e. _ < 9/8 < ?,931
5. Yf sa `dkzdk ifkin lnkamds
d. ¾Iuä` as `d prnedef`fmdm ma netakar iudtrn n läs idrds>
e. ¾Iuä` as `d prnedef`fmdm ma netakar axditdlakta iudtrn idrds>
Yn`uifùk
d. A` aspdifn luastrd` tfaka 95 a`alaktns. A` avaktn iudtrn n läs idrds tfakinln a`alaktns:
Iiiii Iiiis Iiisi Iiisii Isiii Yiiii
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e. A` avaktn axditdlakta iudtrn idrds tfaka 1 a`alaktns, `uacn _ < 1/95?,412551
9. ¾Iuä` as `d prnedef`fmdm ma `ns sfcufaktas avaktns>
d. Ya dkzdk mns mdmns y d suld ma ds mns idrds suparfnras as fcud` d ifk
e. Netakar uk kúlarn pdr iudkmn sa `dkzd uk mdmn.
Yn`uifùk
d. A` aspdifn luastrd` tfaka 92 a`alaktns. A` avaktn mdmn tfaka iudtrn a
laktns ma` aspdifn luastrd`7 `uacn _ < =/92 < ?,4444
e. A` aspdifn luastrd` tfaka safs rasu`tdmns. A` avaktn ak iuastfùk tfaka ta`alaktns ma` aspdifn luastrd`, `uacn _ < 9/2 < 4/5
=. Yupnkcd qua _(D) < ?,=7 _(E) < ?,2 y _(D|E) < ?,9
d. ¾Ynk fkmapakmfaktas `ns avaktns D y E>
e. ¾Iuä` as _(D ∦ E)>
i. ¾Iuä` as _(D ∪ E)>
Yn`uifùk
d. Yf D y E snk fkmapakmfaktas, maea niurrfr qua _(D|E) < _(D), pa_(D|E) < ?,9 y _(D) < ?,=, uacn ns avaktns D y E kn snk fkmapakmfakt
e. Inln ( ) ( )
|( )
_ D E_ D E
_ E<
takalns qua
( ) ( ). ( | ) ?, 2 ?, 9 ?,48_ D E _ E _ D E< < <
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1. Ma uk `nta ma 4?? drtìiu`ns, 6? snk euakns y 4? snk mabaitunsns7 sa vdksa`aiifnkdr mns, ukn maspuæs ma ntrn. ¾Iuä` as `d prnedef`fmdm ma sa`aiifnkukd pfazd euakd sacufmd pnr ntrd tdlefæk euakd>
Yn`uifùk
@d sa`aiifùk ma` prflar drtìiu`n as a` avaktn D, `uacn: `d prnedef`fmdm mqua a` prflarn sad euakn as:
_(D)<6?/4?? < ?,6.
@d sa`aiifùk ma` sacukmn drtìiu`n as a` avaktn E7 sf sa inksfmard qua a` s
cukmn drtìiu`n tdlefæk as euakn, astn as: _(E|D)<86/66 < ?,868, pnrqua maspuæs ma sdidr a` prflar drtìiu
euakn, quamd uk tntd` ma 66, ma `ns iud`as 86 snk euakns.
@d prnedef`fmdm pamfmd as:
_(D|E) < _(D)_(E|D)<(6?/4??)(86/66) < ?,8?64.
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_rnedef`fmdm: lfma `d braiuakifd ink `d qua sa netfakauk rasu`tdmn (n inkjuktn ma rasu`tdmns) d` `avdr d idenuk axparflaktn d`adtnrfn, ma` qua sa inkniak tnmns `nsrasu`tdmns pnsfe`as, edjn inkmfifnkas suifaktalaktaastde`as.
Astdmìstfid: as ukd ifakifd ink edsa ldtalätfid raba-rakta d d rain`aiifùk, dkä`fsfs a fktarpratdifùk ma mdtns,qua eusid axp`fidr inkmfifnkas racu`dras ak bakùlaknsma tfpn d`adtnrfn.
Fkbarakifd: as ukd avd`udifùk qua rad`fzd d lakta aktrainkiaptns qua, d` fktarditudr, luastrdk sus prnpfamdmasma bnrld mfsiratd, kaiasftdkmn utf`fzdr `d destrdiifùk
pdrd ncrdr aktakmar ds ukfmdmas qua inlpnkak a` prn-e`ald, iradkmn uk puktn dxfnlätfin n ifriukstdkifd`, quakns parlftfrä trdzdr ukd `ìkad `ùcfid ma idusd-abaitn,aktra `ns mfbaraktas puktns fkbarfmns ak `d rasn`uifùkma` prne`ald.
_rnkùstfin: Akukifdmn snera `n qua as prnede`a quaniurrd ak a` buturn, edsäkmnsa ak dkä`fsfs y ak inksf-mardifnkas ma jufifn.
Inkbdef`fmdm: as usdmn cakard`lakta pdrd axprasdruk ifartn crdmn ma sacurfmdm ma qua uk mfspnsftfvn nsfstald npard axftnsdlakta ak uk dlefakta aspaiìinmurdkta uk ifartn parfnmn ma tfalpn.
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UAY_QAY]DY
Yasfùk 5. Yfstalds ma lamfifùk ma äkcu`n. Yaxdcasfld`
Ajarififn 5 (p. 125)
d. 5=¿ 4?‖ 51“
e. 1?¿ 45‖ 94“
i. 2=¿ 56‖
m. 42¿ 98‖ =4“a. 91¿ 53‖ 48“
b. 19¿ 42‖ 92“
Yasfùk =. A` Udmfäk
Ajarififn 4 (p. 128)
4. d. 491¿
e. =1¿
i. 2?¿
m. 9?¿
a. 92¿
b. =61¿
c. 53?¿
h. 941¿
f. 551¿
j. 23¿ 9?‖
g. 6??¿
`. -53?¿
5. d. =Ϗ /6 < 4.92529=?5 rdmfdkas.
e 1Ϗ/= < 9 65266?843 rdmfdkas
Qkfmdm 4. Inkiaptns eäsfins
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i. 3Ϗ /= < 1.=633834== rdmfdkas.
m. 9Ϗ /= < 5.91246==6 rdmfdkas.
a. 5Ϗ /9 < 5.?6=9614?5 rdmfdkas.
b. - 1Ϗ /2 < -5.243669838 rdmfdkas.
c. - Ϗ /= < ?.381968429 rdmfdkas.
h. =Ϗ /9 < =.48836?5?1 rdmfdkas.
f. 86Ϗ /48? < 4.1199=9?9= rdmfdkas.
j. 51Ϗ /92 < 5.484224121 rdmfdkas.
g. =Ϗ < 45.12293?24 rdmfdkas.
`. - 8Ϗ < -51.4953=459 rdmfdkas.
Ajarififn 5 (p. 126)
d. 454834?=.82 il ma mfstdkifd aktra Encntä y ]ukjd ù 454.834 gl.
e. 9653532?¿ ù 548485Ϗ < 281=98.6289 rdmfdkas.
Yasfùk 2. Ärad ma uk saitnr ifriu`dr
Ajarififn 4 (p. 132)
4. 48.8=62 il y 8=.859 il5
5. 2.5894 il y 51.499 il5
9. 93.2664 il y 9?4.169 il5
=. 51.4953 il y 41?.362 il5
1. 93.41 il y 538.251 il5
2. A` dutn vd d =2.281 ravn`uifnkas
3. A` lfkutarn rainrra ukd mfstdkifd ma 99.14 pu`cdmds
8. @d `nkcftum ma drin as ma ?.43 il
6. Qk äkcu`n ma 4¿ tfaka ?.?43=19565 rdmfdkas
4?. 3¿ 6‖ =9.4“ ù ?.451 rdmfdkas
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Yasfùk 3. ]anrald ma _ftäcnrds
Ajarififn 4 (p. 138)
4. Idtatns: = y 2 Hfpntakusd: 3.54
5. Idtatns: 1 y 1 Hfpntakusd: 3.?3
9. Idtatns: 9 y 1 Hfpntakusd: 1.89
=. Idtatns: 5 y 2 Hfpntakusd: 2.99
1. Idtatns: 4 y 3 Hfpntakusd: 3.?3
Ldkns d `d nerd (p. 136)
4. E. 49.28? lfkutns: 85?.8?? sacukmns
5. d. 45¿92½56“
9. d. 59¿ 51‖ =8“
e. =8¿ 18‖ =8“
i. 13¿ 1‖ 5=“
=. 65¿ 11‖ =?.9“
1. i. 45,1229 latrns
2. e. 5,6581 latrns
3. d. ?.3819 rdmfdkas
8. d. Ϗ /5 < 4.13?362953 rdmfdkas
e. Ϗ /2 < ?.159168331 rdmfdkas
i. 44Ϗ /48 < 4.646825433 rdmfdkas
6. d. 2?¿
e. 9?¿
i. 491¿
m. 41¿
a. 44=¿ 91‖ 56.2“
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Yasfùk 9. Bukifùk
Ajarififn 4 (p. 186)
Qkfmdm 5. Ua`difnkas y bukifnkas
4. Mnlfkfn: U - W?\
Udkcn (?, ∛)
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5. Mnlfkfn: U - W-4\
Udkcn (-∛,?) Q (?, ∛)
9. Mnlfkfn: U - W-4.5166\
Udkcn (-∛, ∛)
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=. Mnlfkfn: U - W?\
Udkcn (-∛,?) Q (?, ∛)
1. Mnlfkfn: U - W-9\, W4\ Udkcn (-∛,?) Q (?, ∛)
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Ldkns d `d nerd (p. 162)
4.
=. Mnlfkfn: U,Udkcn: U,
as bukifùk,
sf as ukn d ukn
9.
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1. Mnlfkfn: U-W9\,
Udkcn: (-∛, ?) Q (?,∛)
as bukifùk, as ukn d ukn
2. Mnlfkfn: U-W?\,Udkcn: U+,
as bukifùk,
kn as ukn d ukn
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3. Mnlfkfn: U-W-9\,
Udkcn: (-∛, 4) Q (4, ∛),
as bukifùk, as ukn d ukn
8. Mnlfkfn: U,Udkcn: U+,
as bukifùk,
kn as ukn d ukn
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6. Mnlfkfn:
U, Udkcn: U+,
as bukifùk,
kn as ukn d ukn
4?. Mnlfkfn: W9,∛),
Udkcn: U+,
as bukifùk,
as ukn d ukn
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Yasfùk 5. _rne`alds dp`fidmns ak `d rasn`uifùk ma trfäkcu`ns raitäkcu`ns
Ajarififn 4 (p. 2??)
5. Yak δ < ?.2
Ins δ < ?.8
]dk δ < ?.31
Intdk δ < 4.99
Yai δ < 4.51 Insai δ < 4.23.
Yak θ < ?.8
Ins θ < ?.2
]dk θ < 4.99
Intdk θ < ?.31
Yai θ < 4.23
Insai θ < 4.51.
Ajarififn 5 (p. 2?=)
4. d. x < 42.628
e. x < =9.884
i. x < =4.992
m. x < 94.99? a. x < 93.6=?
b. x < 22.2?1
5. @d d`turd ma `d tnrra Afbba` as ma 681.415 pfas.
9. A` axtraln suparfnr ma `d asid`ard astä d 46.=?2 pfas ma d`turd.
=. A` pnsta lfma 445.68 pfas ma d`turd.
Qkfmdm 9. ]rfcnknlatrìd ak uk trfäkcu`n raitäkcu`n
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D (¿) Yak δ Ins δ ]dk δ Intdk δ Yai δ Insi δ
Ldkns d `d nerd (p. 2?8)
4. i. 991,543 l
5.
5?8 -?,=26 -?,889 ?,195 4,884 -4,499 -5,49?
451 ?,846 -?,13= -4,=58 -?,3?? -4,3=9 4,554
1 ?,?83 ?,662 ?,?83 44,=9? 4,??= 44,=3=
=8 ?,3=9 ?,226 4,444 ?,6?? 4,=6= 4,9=2
93 ?,2?5 ?,366 ?,31= 4,953 4,515 4,225
416 ?,918 -?,69= -?,98= -5,2?1 -4,?34 5,36?
9?1 -?,846 ?,13= -4,=58 -?,3?? 4,3=9 -4,554
438 ?,?91 -?,666 -?,?91 -58,2=5 -4,??4 58,22?
86 4,??? ?,?43 13,9?5 ?,?43 13,944 4,???
9. d. 439,5?1 l
Yasfùk 5. D`cukds fmaktfmdmas eäsfids
Ajarififn 4 (p. 2?3)
D (¿) Yak δ Ins δ ]dk δ Intdk δ Yai δ Insi δ
4? ?,43= ?,681 ?,432 1,234 4,?41 1,316
41 ?,516 ?,622 ?,528 9,395 4,?91 9,82=
5?,8 ?,911 ?,691 ?,98? 5,299 4,?3? 5,842
9? ?,1?? ?,822 ?,133 4,395 4,411 5,???
=1 ?,3?3 ?,3?3 4,??? 4,??? 4,=4= 4,=4=
2? ?,822 ?,1?? 4,395 ?,133 5,??? 4,411
31,2 ?,626 ?,5=6 9,861 ?,513 =,?54 4,?9538 ?,638 ?,5?8 =,3?1 ?,549 =,84? 4,?55
8? ?,681 ?,43= 1,234 ?,432 1,316 4,?41
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Yasfùk 4. Bukifnkas sakn y insakn
Ajarififn 4 (p. 24=)
d. tdk < 4
e. intdk < 4
i. sai < 5
m. insai < 5
Ajarififn 5 (p. 241)
d. tdk < 5
e. intdk <
i. sai < 5
m. insai <
Yasfùk 5. Cräbfids ma d bukifùk sakn
Ajarififn 4 (p. 259)
4. Dlp`ftum: W9,-9\
Qkfmdm =. Bukifnkas trfcnknlætrfids ma kúlarns rad`as
Ϗ=
Ϗ=
Ϗ=
Ϗ=
Ϗ9
Ϗ9
99
Ϗ9
5 99
Ϗ9
t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ
9.Yak t 5,45 9,?? 5,45 ?,?? -5,45 -9,?? -5,45 ?,??
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Ajarififn 5 (p. 25=)
t Ϗ /= Ϗ /5 9Ϗ /= Ϗ 1Ϗ /= 9Ϗ /5 3Ϗ /= 5Ϗ
4/5.Yak t ?,91 ?,1? ?,91 ?,?? -?,91 -?,1? -?,91 ?,??
5. Dlp`ftum: W?.1,-?.1\
5. Dlp`ftum: W?.51,-?.51\
_arìnmn: 5Ϗ
4. Dlp`ftum: W=,-=\
_arìnmn: 5Ϗ
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9. Dlp`ftum: W4,-4\
_arìnmn: 8Ϗ
5
9
45
=. Dlp`ftum: W4,-4\
_arìnmn: Ϗ
1. Dlp`ftum: W9,-9\
_arìnmn: Ϗ
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Yasfùk 9. Cräbfid ma d bukifùk insakn
Ajarififn 4 (p. 253)
4. Dlp`ftum: W1,-1\
_arìnmn: Ϗ
5. Dlp`ftum: W4,-4\
_arìnmn: Ϗ
9. Dlp`ftum: W?.1,-?.1\ _arìnmn: 5Ϗ
=. Dlp`ftum: W1,-1\
_arìnmn: Ϗ
1. Dlp`ftum: W?.=,-?.=\
_arìnmn: Ϗ
Ajarififn 5 (p. 258)
49
45
59
5
1
4. Dlp`ftum: W=,-=\
_arìnmn: 5Ϗ
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5. Dlp`ftum: W9,-9\
_arìnmn: 5Ϗ
9. Dlp`ftum: W?.51,-?.51\
_arìnmn: 5Ϗ
=. Dlp`ftum: W5,-5\
_arìnmn: 8Ϗ
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1. Dlp`ftum: W9,-9\
_arìnmn: 2Ϗ
Yasfùk =. @d bukifùk tdkcakta
Ajarififn 4 (p. 294)
4. ?.485. -4
9. 4.39
=. -?.53
1. -?.18
Yasfùk 1. D`cukds fmaktfmdmas trfcnknlætrfids
Ajarififn 4 (p. 299)
4.
5.
9 2Ϗ
Ϗ5
Ϗ5
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Ajarififn 5 (p. 29=)
4.
Yasfùk 2. Cräbfid ma d bukifùk intdkcakta
Ajarififn 4 (p. 298)
4.
5.
9. 5Ϗ
=. =Ϗ
1.
Ϗ9
Ϗ2
Ϗ5
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Yasfùk 3. Bukifùk saidkta
Ajarififn 4 (p. 2=?)
4. 4.=55. -5
9. 13.9?
=. 9.39
1. -?.95
Yasfùk 8. @d bukifùk insaidkta
Ajarififn 4 (p. 2=9)4.
5.
9. 2Ϗ
=. 9.9Ϗ
1. 5?Ϗ
Yasfùk 6. Rarfbfidifùk ma fmaktfmdmas trfcnknlætrfids
Ldkns d `d nerd (p. 2=6)
5Ϗ9
5Ϗ1
@ns ajarififns ma` 9 d` 4?, snk malnstrdifnkas `ds iud`as `ds raspuastds snk `ds qua maeaksflp`fidr `ns astumfdktas maspuæs ma` fcud`.
4. i. Fmaktfmdm
5. m. Dlens lfalerns ma d fmaktfmdm snk fcud`as
9.
=.
1.
sak
4 ’ sak5
4
ins θ
ins
4 5
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Yasfùk 4. Ajalp`ns f`ustrdtfvns
Ajarififn 4 (p. 211)
4. A` äkcu`n ma a`avdifùk ma` sn` as ma 14¿ 5?‖ 5=.26‖‖.
5. A` äkcu`n ma `d rdlpd ink `d hnrfznktd` as ma 45¿ 9=‖ 41.4=‖‖.
9. d. @d mfstdkifd qua hdy d` amfbfifn as ma 3.1 pfas.e. @d asid`ard sa edjd 4.15 pfas.
=. A` amfbfifn lfma 9?.45 l ma d`turd.
1. i x < 4?.96 y < 1.5?
e. x < =.61 y < =.61
i. x < =2¿ 96‖ 56.23‖‖
2. x < 23.85 θ < 54¿ 42‖ =.64‖‖ δ < 28¿ =9‖ 11.46‖‖
3. @d ]nrra lfma 5?3.88 pfas ma d`turd.
Yasfùk 9. ]anrald ma` insakn
Ajarififn 4 (p. 235)
4. d. d < 5.55 i < ?,69 ε < 89¿
e. δ < =9.6¿ ε < 32.4¿ i < 1.25
i. d < 9.5 ε < 26.1¿ θ < 1?,1¿
m. e < 98.41 δ < 31¿ θ < =2¿
a. δ < 4?=.3¿ ε < 48.4¿ θ < 13.5¿
b δ < 68 9¿ ε < 98 =¿ θ < =9 =¿
Qkfmdm 1. Dp`fidifnkas ma `d trfcnknlatrìd
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5. @ns äkcu`ns snk: 85.8¿, 11.8¿ y =4.=¿, raspaitfvdlakta.
9. D astä d 69.28 l y E astä d 32.48 l ma mfstdkifd d `d tnrra.
=. A` ären` tfaka 2.31 latrns ma d`turd.
1. A` astumfdkta maea masirfefr ink sus pd`derds `ns inkiaptns sn`fiftdmns.2. @d tnrra lfma 98.=8 l y `d mfstdkifd DT lfma 2=.?1 l.
3. @d lnktdôd lfma 996.19l ma d`turd.
Yasfùk =. Aiudifnkas trfcnknlætrfids
Ajarififn 4 (p. 236)
4. θ < ? θ < 5Ϗ
5. θ <
9. θ < θ < θ <
=. θ < θ <
1. θ < ? θ < Ϗ θ < θ <
2. θ < θ < θ <
3. θ < θ < θ < θ <
8. Kn axfsta.
6. θ <
4?. θ < ? θ < Ϗ θ < θ <
Ajarififn 5 (p. 28?)
4. 56.5¿
5. 42.?=¿
9. 2?.28¿
=. 39.61¿
Ϗ=
5Ϗ9
Ϗ=
9Ϗ=
Ϗ=
=Ϗ9
Ϗ
=
1Ϗ
=Ϗ9
5Ϗ9
=Ϗ9
Ϗ5
9Ϗ5
Ϗ9
=Ϗ9
5Ϗ9
Ϗ5
9Ϗ5
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2. 26.6¿
3. 24.9¿
8. 15.8¿
6. 4=5.8¿
Yasfùk 2. Bùrlu`d ma Harnk
Ajarififn 4 (p. 281)
4. d. 4?8.?5=
e. 989?5.6?1
i. 48.294
5. A` ärad ma` jdrmìk as ma 4?=3.= l5
Ldkns d `d nerd (p. 282)
4. A` `dcn lfma 481.84 pfas ma `drcn.
5. Hdy 2.?2 latrns aktra a` puktn ma` sua`n ma` tnpùcrdbn y a` nejatn vfstn pnr a` lfsln.
9. A` ide`a lfma 31.=8l ma `nkcftum.
=. D 4395.1l astä a` darnpuartn.
1. A` c`nen sa akiuaktrd d 4.??? l ma` edrin.
2.
3. d. e < =?.18 i < =4.=2 θ < 31¿
e. d < 94.=5 i < 42.52 δ < 4?1¿
i. d < 41=.=1 i < 563.95 θ < 45?.8¿ m. e < 2.35 i < 9.=8 θ < 41¿
8. A` ärad ma` idlpn as ma 43264.52 l5.
6. A` tarrakn vd`a $188‖1?3.2??.
4?. A` äkcu`n qua bnrld `ns erdzns ma` inlpds as ma 5=.3¿.
44. Ak äkcu`n iaktrd` ma `ns rdmfns as ma 98.6=¿.
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Yasfùk 4. Uaitds ak a` p`dkn
Ajarififn 4 (p. 26?)
4.
Qkfmdm 2. Canlatrìd dkd`ìtfid ak a` p`dkn (pdc 211)
5.
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9.
=.
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1.
2.
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Yasfùk 9. Innrmakdmds ma` puktn lamfn
Ajarififn 4 (p. 261)
5. _uktn lamfn: (9, 9/5)
mfstdkifd d` puktn
lamfn:
4. _uktn lamfn: (4,9)
mfstdkifd d` puktn
lamfn: 43
4?45
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9. _uktn lamfn: (9/5, 3/5)
mfstdkifd d` puktn lamfn:
=. _uktn lamfn: (- 1/5, ?)mfstdkifd d` puktn lamfn:
185
4=15
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1. _uktn lamfn: (-=,?)
mfstdkifd d` puktn
lamfn: 1
2. _uktn lamfn: (?,?)mfstdkifd d` puktn lamfn:
52 *
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Yasfùk 1. Aiudifnkas ma `d raitd ak a` p`dkn
Ajarififn 4 (p. 3?3)
4. d. y ’ = < 5( x ’ 9)
e. y ’ 9 < x ’ 5
i. y + 5 < ?
m. y ’ 9 < =( x + 5)
a. y ’ 4 < ( x ’ 5)
b. y < 1 x
5. y < ’
9. d. y < -9 x + = l < -9 _uktn ma inrta aja y < (?,=)
e. y < 5 x ’ l < 5 _uktn ma inrta aja y < (?, - )
i. y < ’ l < _uktn ma inrta aja y < (?, - )
m. y < + 1 l < _uktn ma inrta aja y < (?,1)
a. y < ’ l < _uktn ma inrta aja y < (?, - )
=. d. x + y ’ 4 < ?
e. x + y ’ 1 < ?
i. x ’ y < ?
m. x + y < ?
a. x ’ y ’ 9 < ?
1. d. + < 4 _uktn ma inrta aja y < (?,5) _uktn ma inrta aja x < (9,?)
e. - + < 4 _uktn ma inrta aja y < (?,=) _uktn ma inrta aja x < (-1,?)
i. ’ < 4 _uktn ma inrta aja y < (?,-5) _uktn ma inrta aja x < (=,?)
m. + < 4 _uktn ma inrta aja y < (?,9) _uktn ma inrta aja x < (5=,?)
a. ’ < 4 _uktn ma inrta aja y < (?, - ) _uktn ma inrta aja x < ( ,?
45
x
535
49
49
= x9
39
=9
39
1 x5
15
x1 91 41 91
=9
x
9 y
5 x
1 y
= x
= y
5 x
5= y
99 x3
= y5
3=
39
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1. d. y < 5 x + 5
e. y < - x
i. y < 5 x + 4
m. y < 3 x ’ 2
a. y < -9 x ’ 4
2. d. 9 x + y ’ 45 < ?
e. ’ y + < ?
i. x ’ y ’ < ?
m. 5 x + y ’ 4 < ?
453
45
499
x
565
Yasfùk 2. Uaitds pdrd`a`ds y raitds parpakmfiu`dras
Ldkns d `d nerd (p. 342)
4. e. B(x)<-6x + 59
5. d. B(x)< =x-1
9. Ynk pdrd`a`ds
=. e. l <
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3. d. y < -9 x + =
e. y < 5 x ’ 1
i. y < 5 x ’
m. y < -5 x + 1
a. y < x
8. d. x + y ’ 4 < ?
e. x + y ’ 1 < ?
i. x ’ y < ?
m. x + y < ?
a. x + y + < ?
6. d. x + y ’ 4 < ?
e. y ’ 5 < ?
i. x + 9 < ?
m. = x ’ 9 y + 45 < ?
a. 5 x ’ y + 3 < ?
b. 1 x + y ’ 4= < ?
4?. d. Yf snk in`fkad`as.
e. Kn snk in`fkad`as.
i. Kn snk in`fkad`as.
m. Kn snk in`fkad`as.
a. Yf snk in`fkad`as.
49
49
=9
453
4?93
59
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Yasfùk 4. @d ifriukbarakifdAjarififn 4 (p. 352)
4. d.
e.
Qkfmdm 3. Iurvds ak a` p`dkn
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i.
m.
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a.
5. d. _uktn (5,-9).
e. Rdiìn.
i. Ifriukbarakifd: Iaktrn (-9,?) Udmfn 4?
m. Rdiìn.
a. Ifriukbarakifd: Iaktrn (-9,=) Udmfn 3.
Yasfùk 5. @d a`fpsa
Ajarififn 4 (p. 399)
4. d. Rærtfias: (-9,?), (9,?).
Bnins: (- 1, ?), ( 1, ?)
Axiaktrfifmdm: ?.31
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e. Rærtfias: (?,-6), (?,6)
Bnins: (?, ’ 21 ), (?, 21 )
Axiaktrfifmdm: ?.6?
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i. Rærtfias: (-3,?), (3,?)
Bnins: (-5 2, ? ), (5 2, ?)
Axiaktrfifmdm: ?.3?
x5
2= y5
41
x5
2
y5
2=
x5
42 y5
6
x5
5? y5
92
x5
4 y5
51
5. d. + < 4
e. + < 4
i. + < 4
m. + < 4
a. + < 4
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Ajarififn 5 (p. 392)
4. d.
e.
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i.
m.
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a. Kn sa puama crdbfidr
b.
c.
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h.
f.
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x5
6 y5
51
x5
= y5
6
5. d. + < 4
e. + < 4
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x5
4
y5
92
x5
=6 y5
42i. + < 4
m. + < 4
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9. Ärad ma `d a`fpsa: Ϗ * d * e
=. Yn`n tfaka uk puktn.
1. + < 4( x ’ =)5
4??( y ’ 4)5
51
Yasfùk 9. @d hfpæren`d
Ajarififn 4 (p. 3=1)
4. d. Dsìktntds: y < y < -9 x=
9 x=
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9 x5
9 x5
e. Dsìktntds: y < y < -
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1 x5
1 x5
x5
42
y5
6
i. Dsìktntds: y < y < -
5. d. + < 4
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x5
= y5
6
( x + 9)5
=
( y ’ 9)5
4
e. + < 4
i. + < 4
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Yasfùk =. @d pdräen`d
Ajarififn 4 (p. 315)
d. Rærtfia: (?,?) Aiudifùk mfraitrfz: y < -4Bnin: 4 _uktns axtralns: (-5,4),(5,4)
e. Rærtfia: (?,?) Aiudifùk mfraitrfz: y < = Bnin: -= _uktns axtralns: (8,-=),(-8,-=)
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i. Rærtfia: (h,g) Aiudifùk mfraitrfz: x < -i + h
Bnin: (h+i, g) _uktns axtralns: (g-i,-5i-h),( g-i,5i-h)
m. Rærtfia: (?,?) Aiudifùk mfraitrfz: x <
Bnin: - _uktns axtralns:95
95
95
(- , 9), (- , -9)95
a. Rærtfia: (?,?) Aiudifùk mfraitrfz: x < -
Bnin: _uktns axtralns:
4=
( , - ), ( , )4=
45
4=
45
4=
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Ajarififn 5 (p. 31=)
4. Aiudifùk: ( y + 5)5 < 8( x ’ 4) Bnin: (9,-5) _uktns axtralns: (9,5), (9,-2)
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9. Aiudifùk: ( y + 5)5 < 8( x + 5)
_uktns axtralns: (5,?), (-2,?)
5. Rærtfia: (?,?)
_uktns axtralns:
(5,=), (5,-=)
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=.
Ldkns d `d nerd (p. 312)
4. e. Qkd ifriukbarakifd ma iaktrn (?,?) y qua pdsd pnr a` puktn (?,1)
5. d. Rærtfias: (4?,?),(-4?,?)
Bnin: (2,?), (-2,?)
Axiaktrfifmdm < ?.2
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41=
41=
e. Rærtfias: (?,4),(?,-4)
Bnin: (?, - ), (?, )
Axiaktrfifmdm < ?.63
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9. d. y < x y < - x9=
9=