Enas 194 Problem Set 5 Solutions

Enas 194 Problem Set 5 Solutions - vr t4"/C 5a/v'i s N...

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Unformatted text preview: vr/ t4/ / "/C #{ - 5a /v / 'i*' s . N' to- nas/t € /6--*-/ aue .a-., J=.,U-.,^e hl-f /,,/.. J I t c ta ak €-- J- g-<-"J..7t t?s c (a oa € wt " / /A-/o. -, h,/ r*, ; // b. nc*-Ld Po- lta l.<.ron J hn lP ./ ,rt- f>-o bk-r( ,"\ (u-=lt-"-1 /_9+f gl I t s { o l , s l r 1 ' , ' l = 3 a / * a l o b + ; / l o 6 + l TNZE?FN PFtvT b) w( coulLao LLr>l Z Zror"/f) il.,27) I I a ^|ros k)s,^G) Z cosri)st-G) I I a 4s,rzr*)-U ros"1.f) z.ac1t)-z s, _"Gl I : 3 l-L/ros/|sn//) z.-s/r) sr"/f) | I 4 gr^, /fl^ Q-rz1s1 z ros? /r) -zr,-qrrll = z //. | - r.E?)sr^ /+) ra c//*) sr^/*) f f ,,-r1r/- ef/t) ,or'r)'r':;';l = r r . l q _ < l I s - t / = z z / ' G " L t a b ) - o haa'"v'- *: (^o,?- .o t'/r) * 9/^,2/+\ = r : 3. {, +A'4/ rthT (o+raps,v7) .) /ca,-, { ^t (o,n f:/ L, /..o( lr,__ 4 f6a6, clt*_: I*t- , c oc /z/- ) _- "a s./il _ sr,_,z(/ ) / h / t {, . {, ^ {r1 (oresrubAtt) l,lo F z , 0 . f , = a (0r0sn AtVr\ b r ( . - | + t z , t l e I Z L # ' l e o z b + l o D o b I J ) u \ z) ,) Lw; l;u p-/ /r, 5tr-r'l*rft, b ) h p ( DsPsara € ^lj + 2+ ,r+l a e l ezt 3"q/ | 3a"* lr"'l' I I 6.4/ \,6 " f r= 31 " itl ra.tz zr 4A t Lz:Qz-Qt I e e I oz:sz-Ft I n 2 et+ 4o'/ | 4f" tbo4*l I o *' I el "" utlr| , 2, I u ;r e/+ l=,u' ' o l , ; b , 4 r l + ^q I 6';;t' I :n "',n c 'l :: lY'g', l: ^*"-i) :;l :,1 l:?,r'#q t tj'rut':"' | + l: j*:;:::"1 ' l" o zs ::l e ' 4t + , , :03 / ,: oPP -'l"rat7o,/at/! 'up(n CCl,c lo-" Lr-, a( rtzy'.tx fa /"roJ y r n u?rzorn rts /. ^e.,*.-\ "n ;* c'os /t) r , ^ "* - -l^ - sr.G) car( nr e- /' *casG) - st^ (f +- + o' - e gr -ft) -cas ( G,;rV")l-" -2' I lrt -7. I t \ wf -_ * arl \F4( ,t u 7) a ) , / " ' + C y " r / / y , / l v = o r 5 . l . 6 c L r / / r r 1 = e (r tl) f rz t sr /- c\ = o (. t ,) ( . *>) (r+3\ =d l v Y - y = o 4 - " r : / / o v u , ' ( , , S q r l . r l r l e +[v^, l^tll L/,'e t l c l ' e - = | Or, / Lu'' 5a s a 1 , 1 1 = l - l r l = l nt"u=/ vl^ )fl\r, : c a s C , \ t i , l r ' . f ^ J (a?(qd r t'sr^ (tla):l uc uerl- E," (4e)=o ad ?- 2 , - 3 e-3 r Z , '/) t | --+ -2+ / Y i C t a ' f C z a r c a t.-------- /t - ' / - r y " f t v / - l / v = o S r z f g r - - 4 : o \ 2 ,- t ) ( r ^ a _ t l r + 4 ) : _ a ) D ( c - z ) ' = o r = = - | / / \ 7 = - C t Z r ( Z e - ' + c s t e b ) y ' r 1 ( r /-- /- . ) =.1'Tl (^ v .*,i1,4c./) "/,^\* 1/, iv 3in1, : , , , e = - l , e - - ; t ) ,ot (qel= ) t' : 2 a'Tt /^v "Y' \ ' -d //,p v a/l I 9a tut ouaP lt_ ZnTf s{ O> )t +_> o.Tr ,/, tTt ; a ; ' a | ' c = ) e " l r ' S a e = l ) - , t * ' ) o-rl I r - r t . t - a r ) y ? c t e ' + c r o ' + C 3 ( a s ( l / r / 1 s r ' J ) y ' ' t z v ' t , * 2 . / ' - Y = o r q t ? ( z - ) r - - l = o ( r - ) ( r t t J r z t 3 r * l ) = o ( . * ) ( r r t \ 3 > o - - - - > r : l l- l - 1 , - I l l I T c uhzl .ao { \ Ll ) {ro-, 7ar/ 3 a bL h-o* ,/a- sa /u /r.- /- l-e, ; y - c, e-* * ,z .-* /(= ras //) / cq cr^ //) V' = c, " { - Cz .-/ -cb sro /*) / Cc1 co t //) v" = cr € f , czu4 - cz rag//) -.t/ sr-....
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This note was uploaded on 07/18/2008 for the course ENAS 194 taught by Professor Mitchellsmooke during the Spring '08 term at Yale.

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Enas 194 Problem Set 5 Solutions - vr t4"/C 5a/v'i s N...

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