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# aplicatii rezolvate inginerie

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tL=30 K = 85 \= 17a --[ at4 cA rr- Brdc( Qcuotes At= o,ota f + o, lo soho, = 'o/tJ " 0,e ?5+ o,8lH - 0 I llta = o, {3 o t tall IE a 0 / 1216 dr = g tl2F d.1_= Q E l!! qts iltal = il[0,s3], = : N [o,tg) +*o ,t7 IN (o,s+) -N(o,N)J N [q l0 = 6 , ? 36T tdrL {'\$e) U.i to, S0 = 0,t 335 N td.r\ : 0f T3(+ 40,r? f o,L.ret^ 0t {3erJ = o'73f ? NlilD =r'rffilot) ? e) - ru[ o,?r)] = orot (o,vekr-0, F6 l0 = : N[o,T/) tr,tol lfJ(r,? h) LoSf) = a,J6 ll =- o,?6tl t N [o,Yf) = o,T6trl = O,]e ll Gx "Nt(L,)-kd)L ,\r = Ar -r6- o/ ,3L+ o, 33 rT o,?14
Transcript

tL=30K = 85

\= 17a

--[at4 cA rr-

Brdc( Qcuotes

At= o,ota f + o, lo soho, ='o/tJ " 0,e ?5+

o,8lH - 0I llta =

o, {3

o t tallIE

a0 / 1216

dr = g tl2Fd.1_= Q E l!!

qts

iltal = il[0,s3], =: N [o,tg) +*o ,t7 IN (o,s+) -N(o,N)J

N [q l0 = 6 , ? 36T tdrL {'\$e)

U.i to, S0 = 0,t 335

N td.r\ : 0f T3(+ 40,r? f o,L.ret^ 0t {3erJ = o'73f ?

NlilD =r'rffilot) ?

e) - ru[ o,?r)] =orot (o,vekr-0, F6 l0 =

: N[o,T/) tr,tol lfJ(r,?h) LoSf) = a,J6 ll =- o,?6tl tN [o,Yf) = o,T6trl = O,]e ll

Gx "Nt(L,)-kd)L

,\r = Ar -r6-

o/ ,3L+

o, 33 rT o,?14

Ct = go r

^-G- |w7- o,o f +tr

a-t

0 7s7f 95 C o'03 'arLr((e . a,,r(t ( =

= +ltfiJ' g5 , ;fu*r - 0,T6(r{:

o (q6zJ- = +1, YK - @,se s''r! or+( I / ::- 1,Vfi9

l{ onarl Biruorutr"

At = 7-t.

d=

ot-

rru do Nlu{/ u/!, =

_ l_qfg '[oJ6'Ci

t =J- -.l,oe\L &f-ob -d-

tt-d-

- 8eP33 * o,gt-os

= a,lo\ ;

f,o'4slrd = l,06Jt-

T-E-+

o/ ltl\$

{-p = 1* of (15 =

q ekoro.oj . 0, rcql

= L t

-Qsvog-I ,06 3Z - 0,0?0g

: A,SO|S

ot t3g f

lL =- Lr\E

tr)

-S(9-JS'r,s

\os>q7Io-l/rS&r{)

rOft'-J-

HSxs\o-:l--:{o

Hena

(t

Gtrr\al,\-J-

a\

(..f\co.a)*\$-O-

.6l.>-l.-,\_-.l oI o:r

-rl\t- !'g

.aa"-()o-la,

rl+J

Ft,d

d-*d

n^ia_l

-9Idi

T9- Q I{ rr \$r

:'

illil

.- rN+ 9Y f-o:J-

rsl:- J H g.-\ l\$ _= 5*w,rlu + gf

Iil ? qqn

.-*- at

i O KN-Y-I - ; H*rv | _ cl_ ;:Qi

2ll 8 +- LrS*1s'r- 1 \o o

>r = d 3sos

:3cc\;

l,\

Cllct\qJ

-!lt*n I

ooFI

l"c

t

t0-

sl

\

aoao(9

4{\e

/r

ta

*D& ,'5 fls

-J atz\-,ud

nd,drEovg

i>4oaJ.a€<)4

,6(5

-=--'*F

B5

ot/

-too

rF:S-(f,rr

.t\o\olstlg

\)

nrl.l

..i

I

I

l

ol\\.r\o(-l

f\lr+\Qil

3--'h

gorr--lt\.l(.)-

t",\

ec)4o

s\a(0\5.ll.r

(91\c't-] l'B\JFr\

(\

=r)

r}lsPlt^JT

.qoo

\r\\,a-1"

-t6

B\crt Iaa\ft\

6c)

\^\(l)l^l\'9\er't \

I

-It'at @

cq = C''' Ir r-

[ry, + ( t-P) ', crr]v387"57

= ll t+8a?

16,

+

crr : -tat Ip'ct-.-tLt -p) -CtrJ

= q ggoc Io, 5€5 - f * or?3ss . o) :

TCIT - i l t+b? t 0,+D, " 2(? sl)

€,v+6L + I ,z{ 3t) * Jr53 3e

Ct t = o-*ot tn a

=- o,Si06 f .,-z 0,3\$06 (

9 06 ( of66 ' t,78// + 6t+b8

s:oe [ (,5€(, )= l,eL61

+3r+ + 0t

r, l\$ Lg)i366 [r,396J:0I

-- 2(Y8ll

Cog =\$

cro = una6 [ p Q,J=

*or+35;' ll,w6q

.cgo.[,*) "

'=- 0/J506 C olrl5,L\,116+\$;trs

0/e306 (o,r ll"T,s13( + ot+3X5" 1,5!^95) :,( Lt,2eil f a,6f't3 ) z b,eil6 "'+,sv]:l= 4,t156

- o, TSs6 (tz ,6 b r 5, 03f () =

cr t ,1 r* n) " L,il--

5"0)-

cq = [,r4* fp"C.,+[r -p) -cor]

= 0,9t

.=CI/

t[r-d - crr]oruar [p. cr,Lznt\./ |

cro= "-rr-ac

tp 'cto+(

= 01 9366 t o(rgT -{

-=- 0,9 SoG L tq zar

I o, 330a ( b(Lll?

-P) " c- 1r] =

8, 3 t/J t 0,k58 t - +r tS 3e) =

r 3 }; .3+)/

= lb,+833

: o,si06 to, ,e 5 - t\, 7833 f o,Vb1r"?/ 8J 56)

-=- o,s30c ( 7, 5+ 12 + 2rt+€+) 2-

Z 3,CTL;

se- cdll\ e' "&- PA T al6n{ uDu ' ccrxo-J

Sr= {0 I <,d- tp aD*[ puru.q C /.(o{}rtK : {ot n[& gr-4c"(gcwL€s

.;I- =- Lz o/o r Lv giAffqh!- c,^ + lfi4&dLrL = 4l'rt L s€ & orttwaut- LLr^.,i,ftDn-Q-

T-L = 2\ L&o: * dq D\:lrdr/rz a!. ^t)rl*

o&Q/nn&^lduF A" Mdq;iln-

u^ e i",eb.bltr"fu'dL w%

st = t0l

K ={ozr - \ZYO

e) Pi_K ohr't) ,#6dr)*Strrr6d-{)

d-t =

Ti__L3 ffi_=*r=q&fr &t= o\.y- frl@lw Bur o ror * (o,tr+ffi)* _dt = q)3w

= kvro, ssot + (r,tt*w)t =-ut6+0'Mfl 90\$d=

o,1flT

=@-=*9hlQL -,o,ol6yo, as** qoir+

z- "o,oL€s -opsrr4 =tZ{giWA

N Gqc2e!)N [tQoz)+ a,(tLwFt,os] U(o,o:)] =

d, 5016 1 o,€E (qSlu- o,;olo) =qs0t0 t0i6S'qOok = QsoXo t o,00JF = Q 5107

N tq atbr\rr (q ol) t a,vs [il[oi as) - N (o, az)J=

o,r3{S + qt*s [o *51 - gs3lt) =0,s313 t Q +; o qffiV =otfiBtgCIot?= qffi*

N Eer) =

=4

=

N (;LD ==

=

I

, qW' la l ' 0,140+

'{ - I =asszl= [qoo6\$

- l,06\$ I '

-o,tl'*t0r LFt=

- 0 0063q_,

b) ^ o( 06f

^ ^o,LL.o, h5l o,0tgF=L' :[' =l,0lt1

:

I

i'" qoolr - oF{ @

ol a sr+t ''

i"

:1a<

_t

foo-rtlfrL=

\'.'

r,

P6 = (02 - orsi 3l " atW - M('0,5N =

2- 5+,W t+,589+ = 2t+84

,l -p = { at6J.J.6 = at+l++

= -L-J- =qs€82

-:

;-* i

z3@, = 0P62+?

,,-0,13.,IzreE?\L

= 0,3+fr

oll o opt57a- - 0,3{f+Z€

,f,0x3 I ^ %11+

01 5 2'J6

,/--\

.-j-lal-t\n

I (v)_vor

-.f*cr7e4

=-tr.-r llfF C--jJ-

-(-)- -(trfFfih;5+.-O' fF.€ ?a

..lI.^.1 .\

(.f\ .a)

ci-'-J

,le

Fl(',(O6tg

t

O

.-/6sCr2(}?

<td

c-la€tr-l6l(?

ll.na

a-

{(

(r(,(i?[-\q*co<):"-fa- O.-

G\$r{r \$

-

\Il\Os)'c(r.--Oi L-ol. )'F \Y

+(,-'t-L{tIav!.+

{.oer7,i -{\O: '!nn-

. ,\l_.-\ \-o*:lad-r- O -i-to t\()

-f c'.1o-N.V\

'a+1Oa

+cnl

e.j cYLto"c

, L,"-JL--/l cr I ='gr-.l d l-'t-

C ffi *-<nO1 Oo (=t

tlll

a-{l

ut-{3

.-tF6"€lCI-

d

rq **--/ ttJ ^{-.r xE

;- @ .,

tr d' il

A;.

-.1(.oA,A<-

cr?

t\G*-?r6

l-t/\) O-(

4/a\,

tr€=a-

c'la-{loJ]a-

)

\oE.Fo,O

c-loO.1'-,It

-i,.Vlv.1l

a

Oc4:lo_O5?.

c!JJ-

*€7

hL-+-F<t

t a,Y+l ' 3 /6s03 )

4fi60r)? 2,0053

?F- + of'6?),lp713 -: I,

:- 2 /+2]

5 )j - 4(al3)

o,5 613 tv 2- t+3 (6

orgl 8l [ ',(

0rJ\$82 \4/s 30,

o,hY? -a,4t€l)--

= o, L266

o l.5(El o

o,33Er (o,sls 'o +

= O/J381 . c/ Le-T

Pso =

: d,33x2 (0,52t- 0,+T6l

- s.3182 (0,)+3 t(

-: 0/\$382 " Lroo9t

a o,J(rl ( lr\$3ot

= d,33t2 " €t 5

(

7

}L

338

o,J3 gt

o 3{I

- d.-l

o, os82 ( o,lll0,3q82 (0, l/

P4o

13)

G, 3oa7

+ o, Ifi " [,3N)o 5r)

+1468

o,sL\' 2,a053

+,a+ afl

,l

LPo r

0,22\$ + 0/?TJ' !(0a5il =

0 13l

+ o,'tl I "

Pro

Poo

cr,\$ \$lr

Po, : 0/3s8)- lo,5LZ"J/ff03 *0,V7t'3tn')+( 38t

ff{.

(. tt(otrl + 3,0

. 4,85+l =

o s q- d\qX . /,.rr,t/rua 4 .q&[ cs'&q e^dilJh

[o!. a" fg,t.nfu-- c+LL - PUT

--_-\I

lLt +K a\h-t)= Ptrt)\ -

-:o'll'o'a63c{ = L(+94 ( t- t0{ lol &' 1-

o/313 (

=- r,HT( r {ct'l lalte\$62 -- '7fJ03

@ PDo-ast'6] =fnr &)-/

& -_ q ut"- TlCr-t) -,1e* f [A

LN (*) -_l= ot85 =) N Cx)= -1, 3l

x =-,({Je (d/^t t^W L

lr.) (".\= otSt+t

iN3

= 0,Jif

(o,rt -L:-

*2

r0 l"o("

ot,t

O90Ofz l,\$6 .

iL otll\t5L51 - 0tll, ,lo l, 4l tt

lo li 212 +/6,1^l 3 -= lol ,Ks2

{o\ ' o[o'lt -ry,a'l , g063 * t,36, o,Jl''l o,oB

(t''r1-+tlto(- L

, o os3 + 1,36 '0,L3W"3i

fo.=

St:K?r=TL=

trj{k?g-t %

tr%

T-t = oSDyo1tt 0ALL

BIJCI(

ct=

d.1 =

sC*Ors9

;;"; ^lia.o)

- K I'Lt-t) N (d,")

!,n * +h+S)ti=r)v''[a--

^ 16-3\tt\ lF

o'x[ \fm

o,l5E3

orT6kr orLt.m

'afv 0^ l,ok08 1 [qtt+ o,orr)t,et-

o,.L\ ' 1txLlf

9 h-r-r' - ot+€+L0{ 155 \$

0176 W- 0, 1539 = 0(60t{3

,Sl&1 --

&L=

L+=

N(e) = N (0,T6+t)

= Nto,%)r0z Ailq6+ t0,= A,7+6V + 0r

Ntd.\$\ = N to,6ov)=- s tc,6o) +

= 0't eST t

o, T)57

,+L f ,"1(0,v0 - N[r,T 6)] =

rA ( qT?\$k - o,?{6?) 2

00 tM = a,v T+ 66

o.q3 fr.,r [o,e l) - N Lo, C] =cr,tr3 " (o,Trgt - a,Tr 5+) E

+ 0r 001 +6 = A,W-T 16

-

I51 .. o,T+?66 l+F, q]or(t"o'50 o o,?r?{6

r53 + o,I+?ea - lfr . [0'0636 - o,+Jl16 =153 - CI,?+.7GG - lt+?. fu,0rtt[16 =tf,3 4 0r+?+66- ttp? " 0,q3U+ " 6i{eyfu =_tb} * o,1\$Tee - g9/+d6{3 ,=

W

A.= d"1 - C{T+

+ (o,tr

-.*.rt *tr-i*Nt= T-+. E trA- z 0. llr

"t-L 5-- v(ttlc

fL z. n*r INE

= d;ot'[o.F[ = g4t'0,ut05= n-u,o]15= 4p+ +i

& z -1- z l^ = Od\$3{0

lv {(0+rt-t (

P= *"ot -4 og,rl-" or((e _ qgal0

=: * | = Or 5?\$3

lL -d.t

{ -p -- t-

11o+tr{ - o,93lo

: 0, +f,o+or5+\$3

r {ol3 3

or lks t

I

cv.rr;&@#)9/*

(,/)

CFI

Jo

t

-F-J

kE>*

aa"isF=P?crl

P

LrtclrF

l-.,

*p+t().Jt-,-r

obt-9

14(s+\t7

--q

.-#G,J+t

a.5.-2

C)sO.

G-G-o*Pi(A a-o @4 '6VO eb Cf> VCI' O)f-fPPD .^. /- Fl

o-/opt,(I\r+{qr:-t-l&ro.)-t4 lgu)61xtd.'CJo"+J-L

-s .s I

_tJ -a- -+i C{, (4 [4 -lr, Lo !g ?-{sv{r6j+'A+ + Fi"_o _G E r_Jf,ETljAL./E 4 _tr,oe5Frr a9

_+{*C);^,* \-/ -c)S<, .r LOfirJ5-{olt=" -Q';APY

6--;_O tr +s "doGitt{^b(rrs\$ s i';trs?sr-s+t*--(i

-+l ;+J ,-=O 1." t-O ll-c- l-Os' 8,L oi

\$ilq(),) (Jrl (t.-o _ad {-oq; t'r! s =€l-_r {,\ B,

il^a(DBAJ

r)POA) {.},VP

t) ;r gl 1) ll

3

Lel =

e3o = q ,3X62 [ o,sf3 j, flgilf +at*a+ . 3ltfL"lf) =

= or\$tcr I s5,S++S t,l ]/}-63t) = 46,tsJ?

or 9861 [ o, r7\$i , 3l,fJ ? tr t a,+JN '9,9aW) =

: o,\$86t tt8,r-638 t k,{6ci) = rrr {Ul

4tr- = 0iSt6l I o,s+3] . grS0+gt o,ru0{,0) =-

= o, s86L " 5,73TY = {, 6526

Co3 :a \$

cro z.01gt6t- [0.5{q3 " hG,s 8\$+ t 0,+r0+.tq htfl=

c rl = 0r ste "r [o,5+si o 2Lr(r{( to/ht&F .{,e 586)o

: o,3t6r I tr , Sttr+ t 2, 380t) z l+,\$B 55

Cor = o,Sg6t ( o,s{S3" ,t ert|t A,+N+.0) =

Qo z o, gt6r_ [ o.;7g3 " 3s-,ff4r 1 0,krd { . l+tsars) =

= 0, tx6l ( ro 1 T3f? r G t 30k3) = t6 t(ll,63

= o,\$86r ( 1,68 {{ r 4, 3533) = 3, \$oah

Loo = 0.ttGt [0,5+53 * JGr 6663 +o,k)o+ " {,Sortt) =

._ Br3t( r. ( rr, r+klt + h 165€)= {gr3h33

,r

0,. Lt + K g-*ct*) -- po* st

Pt= C++ O n-t'k+)- st

c{

Pr= fuW + lr+T. ,Lo'lr'qu'*,rr=

+ rw , @r;0,r,

=.W+r.*T.qs3r8 -ls3=

= wulT,,ii, *(53=

P Co-t9L'-b7 ='nqJL r@- - [n-t';tr+)^ o f,rF+

st a- +o. [F-+

hr: g+ Lt'-\$5cror:m

3_Nb{-(=0, 1?6,

.ll-,

= i53 ,/L O,LW|+ =z fid".l,0otf - 6/dpl+ = 61,63+8

o. - 15 3 " l-'-''- 'L G,24a6

-=- tt3 o Lo' 0561"-o't3{tr = /53 ' L

&.= t5\ * .L' ' ,a'- - ,er - YAo -r^r t

= {s, :;,:Xi "oPt - t,Y ottuss =

b. / tiz " {P5th {o,r\$Ttr = lthl, \$35&

A ,{a - n [r, ,, - q) 0,58 * ti,re - o,u{s8 =

= !r3 - dEoe ? ls3,*r=lfb,q7sb(=lJo,\+ZZ

Gr= 153 " d,*6^r0'r\$+4 z lrl . fM'= ltrs. l,Jls=

= Ll8,,GLf

& " ffiI.: = st nn(r-t)

1*.rr^do) 2 tt /z_*) ,1v*a LerJ -.si ,f'n d [ {'Gt) ]

0 tl?- " o, sT

trLsTJ = 153 o 'L 2-

t=s^gElct

Eh.;:- a<

o=ctctAlflftil'ri F{GjrYEEtHI<

ETF\$fi.ct+dYS' -, dr.axfqdt

3\$\$vlillt ll8=-11 dId

fxE*H

ol()lolcllololatol6lolololklA.l+t.ul(l)lct5tol(t)l0l

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