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hw3soln - $&0*1#2/34!1(56*1!22(5/5*7#3!45/8...

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!" $%&'!(!)*+(, -./( )./ *(&0) *1 2/34/!1*(56 *) *1 !22*(5 (/5!)*7/ 3.!45/ )+ )./ '/8) &'!)/ +8 9:6 ).01 (/5!)*7/ 3.!45/ ;!()1 )+ /13!&/ )./ 4*5.) &'!)/ +8 9:< =.*1 3!( +('> .!&&/( ).4+05. ?: @3044/() 8'+;1 *( +&&+1*)/ 2*4/3)*+( +8 (/5!)*7/ 3.!45/16 !(+2/ )+ 3!).+2/"< -./( )./ *(&0) 10&&'> *1 *(34/!1*(56 (/5!)*7/ 3.!45/ *1 4/A+7/2 84+A )./ '/8) &'!)/ +8 9:< =./4/8+4/6 (/5!)*7/ 3.!45/ ;!()1 )+ A+7/ )+ )./ 4*5.) &'!)/ +8 9:B ).*1 3!( +('> +3304 ).4+05. 2*+2/ ?C< D110A/ E/(/4 2*+2/ *( 4/7/41/ F*!1 3+(8*504!)*+( G//&1 +0)&0) !) HI @*5(+4*(5 3!&!3*)+4 !(2 2*+2/ 4/7/41/ '/!G!5/"6 !(2 01*(5 *2/!' 2*+2/ A+2/'< J)!4) !) )K):< =./ *(&0) *1 *(34/!1*(56 1+ 2*+2/ ?C ;*'' F/ ! 1.+4)6 .+'2*(5 I% !) HI< D) )L):6 )./ *(&0) 3.!(5/1 84+A *(34/!1*(5 )+ 2/34/!1*(5< =.*1 )04(1 2*+2/ ?C +886 F0) 2*+2/ ?: 4/A!*(1 +88 1*(3/ I2: L MHI !) )L):< =.*1 '/!7/1 (+2/ I% 8'+!)*(56 !(2 3.!(5/1 *( )./ *(&0) 10&&'> 2*4/3)'> 3+0&'/ )+ (+2/ I%< =.016 +(3/ )./ *(&0) .!1 2/34/!1/2 F> HI @I*( L :NN MHI L :NCI"6 I2: F/3+A/1 &+1*)*7/6 !(2 2*+2/ 2: )04(1 +( !) )L)C< =.*1 &/51 (+2/ I% !) 54+0(2 0()*' )L)H ;./( )./ *(&0) 3.!(5/1 84+A 2/34/!1*(5 )+ *(34/!1*(5< ?*+2/ ?: )04(1 +88 !) )L)H6 !(2 (+2/ O F/3+A/1 8'+!)*(5 !1 I2C L MHI !) ).*1 &+*() *( )*A/< I% !5!*( 8+''+;1 3.!(5/1 *( )./ *(&0)6 ).01 ?C )04(1 +( ;./( )./ *(&0) 10&&'> .!1 *(34/!1/2 F> HI, I*( L M:NCI P )L)Q< R+2/ I% 4/A!*(1 !) HI 0()*' )./ 1+043/ 3.!(5/1 )+ 2/34/!1*(56 2*+2/ ?C )04(1 +886 !(2 )./ /()*4/ 3>3'/ 4/&/!)1< JST9$ 1*A0'!)*+(1 1.+; 1'*5.)'> 2*88/4/() 4/10')1 1*(3/ 4/!' 2*+2/ A+2/'1 !4/ 01/2B I2*+2/ U VI !4/ 4/W0*4/2 )+ )04( 2*+2/1 +(6 !(2 2*+2/ 4/7/41/ '/!G!5/ 3044/()1 3.!(5/ (+2/ 7+')!5/1 *( .*5.M*A&/2!(3/ 1)!)/16 */ )./ (+2/ *1 (+) 3+((/3)/2 )+ !(+)./4 (+2/ ).4+05. ! '+;M4/1*1)!(3/ &!).<
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!" $%&!'()% *+%'% ,+% !+-'.% /'01 )" !01%& /'01 -23 *+%'% (, .0%& $4'(2. ,+% 2%.-,(5% !6!7% 0/ ,+% (284, &(24&0(39 2%.-,(5% !+-'.%& -'% -33%3 ,0 :; <'(.+, 87-,% &+0',%3 ,0 .'0423 ,+'04.+ $;"= $4'(2. ,+% 80&(,(5% (284, !6!7%9 !+-'.% (& ,+%2 84&+%3 (2 ,+% 0880&(,% 3('%!,(02 ,0 ,+% 70-3 ,+'04.+ $>=
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