Enas 194 Problem Set 11 Solutions

# Enas 194 Problem Set 11 Solutions - P ro\tetv, 94+ f tl r )...

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Unformatted text preview: P ro\tetv, 94+ f tl r ) ^ ) 7 " r y = o z b ) = o y / ( r O = 1 gaSl L sb/..,- : 1 = c, cae (x\ * C.sr.6.l Y 6 : c t = o 7 / ( n ) ' t'@ a ) V ' , , . - r : o . / ( o ) = 6 V l V ) = 3 a s ( q ) r Y = c , c o s f * \ + c . s r - / = \ . ) agar a. y = c 1 C a ' r ( r \ * c z s r . f x ) + . X y / = *4r S t,',(v) t- cz "-o15,. 1 z = | > c z = - l t '( = c, 'r'6'r =r I Y O -- > o y ^ _ t a a . a t ( > > * t z s r - G _ 1 1 fL) =o ^ ctrasG<\ + sr-6<) ClcaS {t) #sr^,(r) -> (k) ,.5 fx) * 5r- Cx) y / , . - c t s r - A ) | - t c z / cZ.os(,*) r , - - - 4 l \ ]o'r(t\ (r € cac(t)#a\ .os Cc\ 1O | ( ,o, (t1= o + 1"4 st\ (a)= | 1 ( ry. L^ (-t+ rl"-),.,) sa I L\: j l r,..ht"rn 1 o (o, € r^.,np.:=.b{<_) &' c ol(t-\ q a -:2 ', (*\ - {o,CL) (,.s,a_) l ce gCL) =o At e S- L cz Trcs n/ * s r- 4') J ) y " - l y = > ( y b ) = a v ( n \ : a Y =-Y ", + yp -- \rr.= Cl cez5(rc) ,r cz s r:6<)-le= ** (a-alJ--r,qJ cc.v.{4, eo97*tec/,"^!) s a ( - 1 , o b v r o . > 5 , C g t 1 a ) : C , : o 71n ) . C. st^ Ctr) + -fr =o -> Tr= a ? e) sqy rA'/ ro /c' /1o ^ : Y - 7/d):rt+ Jl: el V f t r ) : o o o * C , c o s h r ) r z t ? - + Z = o ( . - r ) z + I = o (-= lL ; e, Zo9 G)* c2s(;6.) + >< + cz I (, (rr) *T- l a 4 7 t e an Lr,/.o, y / L CZ s{\d.<) + >< Y (o ) --o y (17):6 Y = cr troa (x\ + c.eks, ^ f>.) Y b ) = o - > 6 - - c r y kl) : o 4 o = cr{>r-1-n\ =c> C2 | 9 ol*b r/.a*/ +y 'V f*> : cz.-rr -&) o \ t t , [ ' 7 - Z t ' 1 1 = o (- -t)a: a V '1o) =c, y fir) =-> y = c i c Y + r . x t y/= cr eK t*c.( keK+ j) = qf *crerc(*r rl- C , : - 1 , t h)=a - c,J (t*.r) r^= f , I CJr..'tr<- '*'t\ ,7'(o).o - o V : c r 6 j f t - x ) S a C r = O * r d € = = o-/-..........---. {crug ( V k) =o \1" *c,.- o *-t LY e,,/u l,o-l \=..-_-_____/ atstGLt ! Sac u Ito p fr't \ ) Y ' Y & t , t , f s " l- ).y' - , =o 1ft\=- a y / L ) = o { > l L s / L{ F- l<J. f) uct /rc,n ,u, , J'n.' ),,r = _t Ii 2 2- l l l \ = a = C - , + c . - > y(u|= Q: c, ( L- V L\ c, (x = /=) ft- - z.\) o ; ) gq.L.e so/olro- ,- y = C , * + c z l x y 0 \ . d , 9.tt^< ds tL.,> t r ' ( * r - - - c z - > Y ' l c ) - 3 1 > 1 y : c , ( v - Z t ) z ) Y{= a,(l *,/xr) , l L \ = B = c , ( l + r/r-.\ --> c, : S( / A tlrz)-l= -cz 4 ) 1 t ' * ) v = a y b ) = a 7 ' ( w ) = o CD urtr:'^ ))r, l"l )=-*+z (.r-t>o\ aad y"+-.<ry--o y = er ras(u5\ { czsr_&x\ y h ) = o = c I y'/n\ t a : ,,t-t cz caafu','\ *t2 a ail r._a_ c*,a4] czqL a lln u s lo s(,oc-fl) = a t utf = V/2, 3 T= / g=r/= 1e /n oc -t(-: 6 ^ t) /z 9 a...
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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 11 Solutions - P ro\tetv, 94+ f tl r )...

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