University Press of Florida
Calculus-Based Physics II
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Permanent Link: http://ufdc.ufl.edu/AA00011670/00001
 Material Information
Title: Calculus-Based Physics II
Physical Description: Book
Language: en-US
Creator: Schnick, Jeffrey W.
Publication Date: 2008
 Subjects
Subjects / Keywords: Conservation of Mechanical Energy, Kinetic Energy, Gravitational Potential Energy, Springs, Rotational Kinetic Energy,Conservation of Angular Momentum, Conservation of Momentum, One-Dimensional Motion, One-Dimensional Motion, relative velocity, Newton's Laws, Universal Law of Gravitation,Circular Motion: Centripetal Acceleration, Rotational Motion Variables, …
Mathematics, Physics
Mathematics
Science / Physics
 Notes
Abstract: Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students. this item is part two, for semester two. Only the textbook in PDF format is provided here. To download other resources, such as text in MS Word formats, problems, quizzes, class questions, syllabi, and formula sheets, visit: http://www.anselm.edu/internet/physics/cbphysics/index.html Calculus-Based Physics is now available in hard copy in the form of two black and white paperbacks at www.LuLu.com at the cost of production plus shipping. Note that Calculus-Based Physics is designed for easy photocopying. So, if you prefer to make your own hard copy, just print the pdf file and make as many copies as you need. While some color is used in the textbook, the text does not refer to colors so black and white hard copies are viable.
General Note: Expositive
General Note: Community College, Higher Education
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General Note: Jeffrey W. Schnick
General Note: Narrative text, Textbook
General Note: http://www.anselm.edu/internet/physics/cbphysics/index.html
General Note: http://florida.theorangegrove.org/og/file/e153a870-4e35-41f0-868d-11727676a502/1/cbPhysicsIIb24.pdf
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Source Institution: University of Florida
Holding Location: University Press of Florida
Rights Management: Calculus-Based Physics is a free physics textbook. You are encouraged to copy, edit, use, and share the book itself and the ancillary materials posted to this web site in accord with the Creative Commons Attribution-ShareAlike 2.5 License [see: http://creativecommons.org/licenses/by-sa/2.5/ ]. I wrote Calculus-Based Physics in MS WordTM to make it easy …
Resource Identifier: isbn - 9781616100186
System ID: AA00011670:00001

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PAGE 1

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nr % nrn;n n n n nEr() J F) /n)nnnnr7) ; n n) )rr);. nn n 'n) )'n)(=n7" )r 8nrnn n n ;n (n nD ))nr3 nr ) n )(n7 )nnr nn 'n @' 'n nnn 5n'nn5 nn5nrn nnnrn55)5 (nnrn5 nrnr rn n nn)n)n =n)nn5 ;rnn n 5)n5 r ;rnn 5K' nn nrnnn)(n n5nn(n n)nrn5 nr) nnnn5(nn r ;rnn )r( 2 *2 /55nn( rrnn rnn 5r8 )5nnAC n?/8n < 2 *2 8n )n nnE;(Fn n nnrn) (rnrn .5n 2 *2 nr. 2 *2 nL3) 2 *2 <(nrnn r n nnnn( nnrn n nn.n rn nn7 rrn 5((nD n((<(n(( rn nr8n n n( 2 n) 2 nn))) 2 n) n % 2 n n5 % 2 n 5) n nn 2=n (nn(( r (n5 n8 (nn5 n((;r( rn)(n nn 2 % 1 n n2 2222222222%Mrn nn ( ,nnrAn 9 '(C8nnrnn E(n rnnnF)nrEn nn 9n nrF)nrEr nr) n9n n nrF

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nr nr n&' n 2 2 n)n nn rr nn nrn n rn rnn n <(rnnnDnn (rnn n 'n En%2rnnnrn n5('nrn rF) rrnn &nD) 5( rrnn nn nrnD <(5((rnn Er nn n(n' Dnn (F2 nnr & nrnnDnn) (rn5 )((n) nrnnDn n +nnr'n n5 "nnn n) )(n ) rnn 5n n))n(? ;rrnn n5 3;( rnn 5 (rnn n5(r nnnD)n9) n) nrn5( nnrn n5))n5 )rn( rnn n5nE(F; E(Frnn 5 rn +rn(n r nnn nr nn8 nn rnr(5nnr) () ( nr nn) nr))nn 5( n5( n(nn nr n'n (n5 n(5 nn/n(n(rn5 nr nnN nrn Ar C8n (n nn rn5(nnrn 8nr)nn nrn nrnnnn n rn n n n nn n5 nn nn n nrn ( n nn)n.n ;nnn 5n(nrn5n n(n(n rnn r .n+n n n(nn rn nnr5(nnrn 8n (n rnnnrn5nn rnDr nr n 8nn nn (r(n5 nnn(r (n.rnrn

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nr n (n n nnnn ( n Errn Frn5n n rnnr n nn 8(n'nn rrr $ r !r" r 8(n5n nnn n nr5 nnDnrn5 nr #$#%r/n(nnnn nD/nr)( 5nn) n n(?nD& nnrn n(?nDn8 n nrr)(n nn(nD n(n/r nn)rn nrn5)n)nrn5rn 5(r;rn nnn.9))8n nr))rn (nn5r.n )nn nn n E nn nrn5rFr( n ;n5(nr (n nrn5n nnn ;rn nnnn r&(nnrnnn)rr( nn5nn nn)rnn8 n 5(nD) nnr('n nD rnn )5 = n ) nn (n8 (nnnnn nnn)) nnnnnnnn )rnnn rnD)n5 n n')n5 n )'5n 7 nDr(n n r8 nnnr n5Drn) n) n rnn5n ;n5& ;nA n n5 nnC
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nr 1 8 (nnnn nnnn nD5( nn nn))' nDnnnn nn)'nn nn n)(n nnnn'n n(n nD>7(&(nnD nn) nnnn nnn )nn) (n 'nn)nn' n n nn/n nDr'n )nn nn' n r&7n nnn rn rr n& n nn)5n n r>7(5(n ?n?rn5 5n nn <)n rrn5( 5(/n)n n n @)) nn n nn n nnn nn n n rrn9n)) rrn5nn 5nn)(n9 #n9n'n n ) n n rn5nn75 (?nnn n 5(rnn5 5n5 nn5 rn n9=n) 5(n n 5Dn nn5(n 5 () 'n n5)) +) 55n5 ( ))n ) n555 (
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! '"(r$$r#)*$+#( $< 5( ;nn8 n;( n n; nn( En n;F n ; r(n n???n ?n??5rr (n n;n ; nnnnn 5r n n; nn<5(n ;)n rn>) 5nn ;& n???n ?n??5r 5nn A Cn&n n 5n)nn n) n n &(rn n 8rnA5rC n( n ; n n(; nn /nA5rCn 58 nn )E5 rF; n E?F n 5r 5nnnn 5r &'n n n;( 5rnn n 5rEF n nE F5rn nr8nA C 8n8n8 n8nn A5rC) n ; n) n( n nnnn( nn rrnO )n; n( nnr@) nr8' r) 5n (8nn( n8 (n5nn)nn
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2 8) n nnnn ; Enn nn rn;F n n( n nn)rn n(nnn 5 )nn (nn n;nn Er nn ;F/n nn r(n)7n ) ? n r 2 "=H3rr)() 'n r(n =n)7r B 2nnrn n n ; nnn 25r F = 2E 2 =n5nnnr n n nnn n) nn ( = *$ 2 & nrn 8)n8n r'nnn (nn n rnnrrnnrrrnnnrnn#nr $rn%"nr n5(5rn n n 5r( n'nr n5nn ;)(nnnn n5(?n 5 nnn) n ( n; nn/n5(? n5 rnr"n 5 nnn nn;n $rn )nr nn n"rn N/n) ;rn r(n 2 "=H ) 2nnrEn B2nnr nF n; n F = 2E 2 = *$ 2 <5 nn5 n n rr = *$ 2

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8 )(r5r5 ) n r5 n .n nr' n5n5nnn n 5n/n n; ( n5( (nn ) (;nnnn nn n n 75n n n rn 5n/n r r(n n r n)n ) '= 2 % =nnnnE 2 *2 Fn & nn ;nnnN = 2 2 % F 2 *2 E = 2 2 1 nnnnrn n nn nnE B9nn nn nnF)r nn n55 r 8 );r)n nn) nE 2 *2 F n );r '= 2 % )5 = 2 2 % F 2 *2 E = 2 2 1 5nn5 nr n rn = 2 2 1 nn r nP9 nnnnnn <); < rnn(r

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n;n5(( (n nnn 8n;n n 5nnn ) r'n nnrn < nr n 5( 5nnr rnr n/n)5 n 5n)n5(nnn nr n;) 5(nn rr rn5(nn< 5r nr )n nr5n( ) 5nr n;n)nr @( =n7 )r; nn8 nr)n) 5 n(n rn) n;nnnn) ) ;n nrnnnrn8 5n(n n nn ); nn rnnnrnn5 n nr &'n (% )nr!n*" nn nr) ? /n nn)5 nrn5) r<5(nnn ;) 5n@ nr)5nn rr )nn 5n)r / nr) nnn(nn nr nr(nnn5(n nnn n nn
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" rrn)n (8 n nr .n) rn r5(Er(A nrCF) rr 5(rn) ;rn) r() r"r )n =+3> &/ )

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r! n $ ,"(r$$r#*
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r! n % nn)(nn5 /n)(nr(n5 '(nn'8nDn&'n n'n nn5n)(n nn nn5 n)(( nrn 5n<5(n) nn5n)5 5nE n???n ?n? ?5r5nFn(( nrn 5n/n)nn r nN&n nn n5 r n E=03+,8><33+&>
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r! n ;r(Q r(75( n;nnr( '5(.n r )5r nn ; n n nn n n5(? 5r ;nr5(? nn ;); n n;(nnn nn ) ! )

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r! n nnr rnn n ;()n)) nrn5n );nACr n r nrn5rnn nn nn n( n)n( (nnr E nrF En nF5n )n(((nn r 75n(9n)n 75n(;rn n n nrn5(? )5n(B (n Dn( nE nnn 5n())r5Fn n ;nn( nn n # %

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r! n 1 >;rn Dn(n 5(? ) nnn 5n n)5r)5rr)5r 5n( <)n)) nnrn5n ))(; nnEn) n 5); nnnnF
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r! n n+nnrrnnrrrnnr)nr!nn nn n nr n(n5 (n5 F5( (n n5n F5( (n 5n "F 5nnnr 5 $n$r8 rnnn)n nn 5(n5(n n n 5(n n5nrn nn nn)nn n nn n nrn 5nn n 5nn nn rnn n n 5nnnrn 5nnn) rr)5n )

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r! n 2 /n) n)(n'n r nn 5n n nnrn 5 E2)2F) E r) 2Fn E r)* 2 rF (nn5nnn n rn E 5nn Fnrn E 5nn F 3 nrn5)nn AP(nC(n &;nA 5n n C n( n 5n 5n n nrrn n;nA n C ;n nrn;)r A nr n C I r I r I r ; ( I r ; ( ) )

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r! n (nn r((9 nnr<(n n5 n nr 5n n ) nrn @n5nn)5n ( n ) nrn &rn nn )(n nn 5nnn5(n I r I r ( ) Ir I* 2 r nr nr nn n nn n nnn !nr nn n ;

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r! n rn)nr!nnr) r!rn nrnnnnr7 n nrn.n=r() J E"?F r(n )n )nn) nnrn r = 2 !! 1 ) n En F n ;)n nrn ) J5nA nrnn n Cn =nn n5n ;n J E& 5rn ;n ) nrn F8 5n.n J )'n n ) ()nr((n n n n;r) 5) 5 5n J )r n5n))n J n 5nn nA nrn )nnCn n n5) n )n; n( n5nEnn F))nn nn n5 nn nn 5n nnn&rn%8 nn ));nn ))5(.n ? J nn7( n nr(&;nAr(n Cnr9 n7n n n ) r(

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r! n 8) n;n ( 5( .n? 8 n 5(.n"? J 8 n )E F.n J n5nr' nA nr nn C /;nnn nn .n nn 5r n E F(.n? J ;n nnnr n; n( n'Q;n nArrCE F

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"r $ -#$#(r$$r#)r'nnnnn(rn n(n(5n5' n 'nn nrn5n(')) n)(7) n(r)'(n n5(n(n n(n ) (nr5nrn ))(n 5rn nnn(5rn rr n5(nnn)) (n5nn 5nn ) )nnnnn nr nnn rn )nn n )n n#(nnn n nn.nF/n(nnn nn ) () nr E (nF nn n nnnn nnnF3.n nn n? nr "F/n(nnrn(?) n) (?n En?; F nn) n nn)n nnn nn nnn $F3.n?" nn nn (?nE n5rF & nn5rn nrn5r&nn(;nn (n EF/( n5n(( n (nnr) rn) ) (n'n)5(

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"r % %F>nn(nn.n?$ n nnrn N>n5E) nn.nF F/n(nnn nn ) () nr E (nF nn n nnnn nnn<& nr &n)nn r5() nnnnnn n ;nr( E nn)nn (r n.nr5n(8n)(rn5F< nrnn nn ) )

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"r 1 rn Nnn ;rn n? nr ) )

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"r "2 n5/n)rn 87 rn(nnn ( nnnn n nn n( nrn5) 5nnn nn5 nrn5/n) r nr(n5 n 8n &n r n ) rnrn n + ) n 55nnrnn nnrn5n )5nnn nnn n=n) n n n nn >)n) n rrn nr(nnnn n EnF rn) (nnn ( nr Ann''Cn) rnn nnn n :5n) r nn n )n((r n nr) n n 5(; /n)n) nr n rrnn (nn) nnnn n EnF =;.n $F3.n?" nn nn (?nE n5rF )

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"r 85nn ) nn (nn8 ( ?; nnr n=nn rn5 rr' 'n nn)5nnn n > n nn(nnn 8) nr(nn (?n )nn) 9n.n%F>nn(nn.n?$ n nnrn Nnn nn) 5(n5n 9n nrnn5r n) n5n nrn nrn n <)nnr'( nnnnn(rn5n rn( n nn?nn (nn ))n 8 ) (nnrn (? nnDn) 5(n nDn r nn n nDEn nn nrn DF

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-!r./ !n $ 0"(r$$r*12 nnn5( E*?F nnn) I =r 2 !! 1 nnrn) n En) 'nF nn) )nn nr n 8n n? nr E nnF) nrn nn' nnr nn n?n??r n /n) n) n S ;nn n 'n( n n5rn 5rrn5n;; nr # n # &7r(n' F E # # 5n nrn r) n 'n 55( nn; ; nr # I # n # I # /n)nn # # ) # # r r # # # # r # # # #

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-!r./ !n $% $n$rrnnrn)nr(rnr&rnnn nnn )nn rn nnn5 nn )nn 5 )n nrn rn nn nn(rr) )rn nn 5nr )#$n nr5n( nE;)(Fn;?()n n nn P 2) nn B 2) r &n (nnE;)(Fn;?( r n nrn 8 n nr)8 (rn. nn nrn5(?) nn nr5(? # % P E #% F # %.

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-!r./ !n $* <(n r5. % # <(n r5 % # # % E#%F # %. # # % E#%F # % #

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-!r./ !n $&n nrn ) (n rn % # % # F ) E F ) E F E F ) E F ) E % # % # % # % # % # % # # % E #% F # %.

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01r2r'r'3 n $1 3(4+r $/#$/#!rnnn ; n(nnn n )n 8rn5n E
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01r2r'r'3 n $! 5n n(n 7n &'nn' I2
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01r2r'r'3 n %2 /rr9 <.n r( n 5(nn r5n n <.n 5( n 9 n'n( n rn5 nrnnn .n nnnnr. n (9n (nnrrrn)nr(rnr #(n'nn nn n =r() 5(n nn) 9nn nn nnnn)r(n (nrr n'n( n rn5 nrnnnn nnEnnn;rF)nn nnnr nn)9nr $rnr (n n nn nnr9nr n5( nn nnr5n r5=n5 r ) )9nn)nr(rnr/" &'nnn; n nnEnnD n;r nnF)5(n nnnr 5n n)((5 n rnr & n;n)Annn n %5n)Cr5 n n5(nn nn%5nn ( Er9nn n nrnnFHn nAnCErnn 9nn nF )nr(rnr*nnnr"n 8)n'nnn nn5 n nn nn)) n n nnn A n n<@C5n n @r 5n nn<

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01r2r'r'3 n % n
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01r2r'r'3 n % n8()nr n nnnnn n nnrn nn+n nn nnn nnnn nn n&nn nn)5nrn((n n nn@n/8n rr)n nn n(nr)r() r"n 0nr nnr$rnrnnn r) ?n? (???n ?n??5r nn?n?(? ??n ?n??5rn n& r"n (rn )n n).n nrn ))n nnnn n9nn n8 nnnnn n9n) nnA (Cnn 9nn n/n) (n rnDnn "25nE nnnnn 9nn nF)(n rnrr rnn rnD"25n n(n ( nrnD <(nrn5n(n(n ()nn(n( n') rnn'r5n)) 5n EnFn nn n)5n r EnFn nnn 2"%'nrnnr"n2rrn +(nnn(5nE nFn n5 n Er ) n) nr5F 5n 9nn n n8 )n nrn 5 n nr A.?C +n)'n A.?C +n)nn')n 9nnn'n () n n'n & ( n'n @)nn n'n );3 )5n rn5n nn) D;Qn7 nnn('5n 5n; 5n9nn rn5 n nnn5n))5n n7 nnn()( rn nnn(

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0/nr $ n*$n&*$n!nr n(nr; n.nnr @r nrn n? nrE(n n J J F E" $ ) ) n F)n; n nnr &nnnn(nr.5 n nnr ;nnnnD nn nn(r /nnDn5rnrnr 5( ) (7' nrnErn nnn rFB;n7 n rr rn;nnn E # )2)2F5rnrnrn nr ) n rn'nn)n 'nnrnn n n6n'n )(nnn nr; nB; nr n( r5E n(n) nnn) nr n)nrn9n rF ( n J J F E" $ ) ) n J J F E" $ % n F E" $ nnn5( F E ) & 5nnn r)r(E # )2)2F/5 ) n rnn )); nDn5 n )n ( ) + #$ % & % n F E" $ ( ) + #$ % & % n F E" $

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0/nr $" =n) (n @ % # @ % # )') E rn 'F5E # )2)2F)(n $ n # /n)'n n)nr n nn $ rEr nF) # 5 n"nr!n*nr"r"rnr&%"Bn
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0/nr $$ nn n( (nr nrnE r(n.n ) ) F &r 5n(n )n n)n) n5n r 5(n nr) nr) nr nr n))n 5( nnr (nrr nr( nr#n (nrnn n (nn nn r ' '

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4&'< $% 5#/&n(nrr
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4&'< $>77nrnnn 5nrnn >7n ))n' n nrn5nnY8 7rnnnn5 rn(n5 ((n r 5Enn nn5 rn5FX#'(nrn nn n ;nn r ? n nnn n5n85 nrn5) n9nnrn n r 5n5(n r n57D(45 nrn)n75n(E n5n(n F)r'nnnn =n)'(nrn ,'(n n( nr(nn)) nn 5nE5n(5nF )r()Ann C=n)'(n n n( nr(n n))nn )n(n nr (n(nr nn Ennn r(nn'nF)r (nn n(n )(nnnn On;rn nnn n;n n5r (nn=nrr(n') n (n nn5nn' nL nn'E5 nrn5F /n)r )nnn rrn5rnrn5 /n n()rn5r8 r n n;n(r @'n rr% r r=n'n r n r rn5/rn nrn5) r rrn5 & nn EFN nnnn 5rnnn) nnEnrn5 = / 37/.%

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4&'< $1 nr)5nrn5rn nF @Dnn5 nr7 r>5(n5n( (n rnnn nrn5( n5 5n35n(n rn )rnrn5 5 r/n5 "nr"r"" n nr nrrn5n rr8 r)r8 n ))n nr) r(5)r(5@ )5 nr nr rrn5/n nr r)5) nEnnr rr rn5nn( nrFrnnnr r nnnE nnr r)n( n(r)rn5F nr r)r5 r nn nnnnnr r)r( )nn'E5 nr n5Fn 7n r 5 nr>)nr rn5nn n( r5r n5 r 5nn(r &nnrrn5 ) =n5 )n r n5)rn5r nr)r @n ) nn)(n r n'5n(n 5nr)n r )5nnn 5n(5nr 8 n(nn(nn nn ,(r5( (n nn'nrn 8n5(n(n(rn ;r5n'

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4&'< $! nn'rn rn55n r) 7((A nCr En).5()((r AnCF &(n9)nr) (nr En55n(nnn 5F) ) rn r (nn 8rn5) rAnCnrn )r n (nn (nAn Cr Enr nFr(r r nn r'E5 r )n r )5nnn 5n(n r F) AnCr En r nF) nn (;r n(9> r(r n r ( nn8 )(n r.n nr@ n8 n(n)85nnrn n 8r(Arn r C87rnnr85Dn ()n nrn (78nn) !% )n nr 2""n "nrnnr"n$n nrrr$rn rnrnn""rn"nrnrnnr = / 37/.%

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4&'< %2 + n(rr rnn5(nr nrn nn5n &5n n r &8(nr n nn) )(nr )8'nrn r n()rn (nnnnn nn(' )nnn )nnn nA ?nCn E() nnn?nn ) nn rF=n)rr() nn(' 5n nnr rnn(?' ) 5n 8rnrn ) ?rn) r r=n (n5 ?n)r (n)n nn A(nCn?rn r)(nnnr'nn rn nrnn r (n

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4&'< % /nn rn5(E r F r ()r?n ?r? ???) n( )(n7.)n rn)nr nn) 8n! (. r nn)87r nnnnn n n nr n.r) n) F r 2 E r 22 K5 n) F r W 2 E r 22 F r W 2 E r 7r'rnrn ( 2 n n n5;n WF 2 E nrn 2 n n F r W 2 E r W 2 '2 n n

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4&'< % /nrn nnn nn 2 nnnn '2 ) nn nnn(n n n n n r rn '2 (n(nn r A C (nnAn)C) r ?5n5n &'n A(nn C ( '2 . )5n)5nnr n n( nnnnn n nn(n nnnn+ nnn n8)n 'nn nn()) 'n n5n n5n nnnn n5n n nnnnr' n5nn)n) n nrn? nnr(nr &'n n5nn r n5 nn(nn)( nn rn rr<) n n r) On n7n nn r n(9)) (nn n'nr 8 r(n(n 5n(nnn rn rr) ) nr)nr 5 nnnn rn 5nn r) nnOnnn 'n) $nn n r rrr"rn nr n5n(nn) D KA rr C nnn r n ( n n IE rr F nrn (nnn n.( "nr# nnn(nn=n ;( nnnnrn r n nn r ;5r0@ E:'F ;n( r n r ;nrnn 5 r)&)5& r & n n n n n @C n

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4&'< %" (7)n( nnnnnnnn n rn r (nnnn) rn ; r C 3 @ rn nr'n nn I n nn 3 n nnnn r C @ n ;nnn 55n nn rn n 5 n nn58nn) r C C @ @ Knnn;n n (n n5 @ C 3 (7(;rn 87rnn (n5nn (nnn n%&r" nnnn nn)nn nn nnE nnF))5 rn r nn /nn r ;nn 3

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4&'< %$ @((7n 8n) @ C 3 n nnnn)nnn nnn n@) nnn5)r n I 3 rn n3n9)) I 3 @ C 3 nr r ;nn)5 3 C 3 @ @ C 3 3 5

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4&'< %% &5nnn) n&;( N) ;nn,n () r nn (rnn rn nn nn nn n8nn5 rn)n5 nnnnn n)5n rn nnrn n8n('rrn n n n<(r. rr nnnrn (rnnnrn n nnn( n r 7rnn nn ( r nnr n n nn A Cnnn n r
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59r''= *2)nr+nnr nrnn5 (n nn n
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@rn$: 1* '"= (r$$9& n 'n nn(n r ;nn(n 5r (n 5 r n( rn5nn ) I"22 2 1 rH@n( 5n; (rn5r =n n r ACrn5 n 8 nrn?n nn ) nrn 5n(n?? nn5n(n)r) 8nn) & n(rn n n 5 rnrnr)) r n.nn )) nnrn"n$rn >7rnrn n( 5rn n nn <
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@rn$: 1! n)5)5n)Z() rr((rQ r n r8rn 8 n5n (nn 5n .n nnn r 8n;) 8 n'nn .( nn(5)8 n 59\r ,n5"22?-%2 222,>9 $rr?r 8 -%2:>9?$"2>9-22r? $rr 0$"2?-%2>9$22?-22r K5n-%2?* 222>9%?$22r Z(* 222?%2 222 222>9 22*?%r :rr3(\%2 222 222>9[ 22*r =n5r(n n5nrr&) n?5)n? .(5 ))H5nn? 5? .(5<,nn n'>9, nn,>9n) (n<,n22r'(nn 5nn5n .(22'>95 "222r/(n,n 22r'(nn5nn5n .(22 ,>95"r &nnn r 5n)n r 5n) ,(n nr5n5 nnrn &r) ; nnr' rnn n;n rn n5) nnn 5 r ;n.nr?n? nr'r @nr(n n5 n nn 55n n n;n( )nrnr(n 'nnn r rn nn r8 nnnr#'r r )( n )n
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@rn$: !2 Dnr n>)nn r)n ; rn nn nnr r >nnr) (r(n nnr<9 ;rn nrn nrnnrn nrr n )r;n 5 5H nnr n;nnnr (nn nnn ) nn nrn( n n;nACn. rnn(> n'ArnC<) nrrnrnn' rnn ( nn n .(n nn n 58 r nnn5)n nnEnF rnr 8n nn n.?nr ') nn 5 n nr n(n n7nn)nr n r 8n (r ) n5 ( r(n n n() n5(5( 'n5( n n>)nn nr)) rn?' r n $nnnr 8n rr) 5n (n nrrnn 5 n 'n@)n5 nn n r5 nr( 'n) rn5rnn(nrn5 n5r&( n rr n 5rnn n 5rnn rr;n n) )n rr ;n nn rr) I" 22 2 1 rHn 5r))n rr @n 5;??n ? ??5r);n n (n.nE.rr )n5)5rF/nr 5 n;n nn n r "# 0r < 22 & "" :En'n >n(5F %

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@rn$: 'n nn r rn r n8 ( n n(n((n nn'nnrnnn 5( nr nnE nnr 5F)n)(nn) n .() n 'n)5(5 n&nDr (r;n 5 .EF) .(n n nnn 5 nnrn ( .( E' nFnnn nnn nD

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Ar&n+!B29 !" >7n(n nnn rn 5 nn) rACr9 E5nFrEn9n nF r+ ) rn5n (n( rQn )rn(' rnnn9nn r r @ @ K n 3 I

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Ar&n+!B29 !$ > nnn 9nn rr nrn ))n))n) )nr8r( n )rn(n(n EnrFD $ n 5n 5+ n)rrnQn 5nnn ;n))r n n n
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Ar&n+!B29 !% &rnnrrn nn 55n) 9r n ;nn rnn 5<;rn nn n nnn(n r 5n' <;rn n)n nnn 5)n I

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Ar&n+!B29 !* 8rnn'rn 9 nn n))7 n"r n nn n n) r n r(n ?n??rn nnn r 5nrr8 nnn n'n r)rn n 5#nnn5 nrrn5 >(7#5n55 n<5 n n 5 5(nn 558 )5 $nn 'n 55 ( (

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Ar&n+!B29 !5n n(nn (A Cnr n 5 n8nr(n nn nn5 n r r;rrnn rnrn5 5 n8 nnr)(n'nn n r;rr? ??? 5 n<) nn)5 nr' 'n @

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Ar&n+!B29 !1 (7# )nnn 5 n)n n ((5 n rr()n;n nrnn n I I

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Ar&n+!B29 !! &rrnnnn&(n?55nr' nn)nn )rE F(n)n); n '(nr; nnn( 'rnn r'8'n nr'r' n?nn(;n n5(r(r'n &nn n n9 nn r #nnnn(n)( r' '( 5rrn(59n ?' )r) n nn''

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Ar&n+!B29 22 nn < (n r'nn''nr nr rr'AnC ,n ()n 5n n r'/n %nr nr'E3n AnrCrAnC,'(n' nr(r %nr nr'nF +r')r (r') n 'n9n( n5 n (( n "n 8E'nn(; nFn r nrn) n n n >(7#nrn nrn nrn< nr nn nnn nrnAC nrr)) nn nn)rnn n8(9nrn)8rnnA 9nnrCnrn r'n nnr

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Ar&n+!B29 2 n 3 3 4 1(8r"$$ r $r% 87rnnn 5)n(nr'E nrn5F n=n)8rnn n5 nrn5 nrn5 K 3 4 3 2

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Ar&n+!B29 2 r $r% n nn n>(7#) nn 5 n n )5 r5 n nnnn) .n) r;rr nn& n(nn n55)n r'n)7r nn5En nn F5 nn ) .n) r;rr $
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Ar&n+!B29 2" =nn5 nn n)n5();n nrrn)5(nnnE ;AnnCnnF nrn r; 8 nrn()(nn nnnn( )rn5nn nnn<5( nnE;AnnCnn F) (n55 (rn) nr rn5)n n5 nr( 5 n+Ar( C5 n) r;rrn8rnn5 n rn5)rr;rr? E 5nF5 n) r r;rr?n5 n EF<)r n rr9( rn5
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Ar&n+!B29 2$ =n))E; nAnnnCn F)r;rE5 nnnF n r;rr?n?? 5n5 n)n n n#rnn r;rr??? 5n5 nn n<)8n rn nnr;rE r; F5(nnn nQ nnn5 n n)D n nr;rr?rn n &nn nn r;rn 5 ) >nn' Nn n nrn( nrn& n(r;rr??? 5 n nrn ))nrr)r;r r?n?? 5 n nrn&(n)5 n)nD n )) nr Ar&n+ B 2 9

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Ar&n+!B29 2% >nr;rr?n?? 5 n nr r;rr??? 5 n nr <); n5(nn)n n nn nn(? 5 n)nn 5 )nE r r nF;n nrnnr' r(
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Ar&n+!B29 2* 8 n5 (nnr nn5 (n ) 5 (nnn''(n r(n5 (n +'()7rn.587n( (n5nn(n n5n &nnn nn rrn r;r EFrrE')'9nF n8rnn(rnn 5r;rrnrrr nnr)n &rr;r2)))Vn'n nrr nn nrn5rr))" EnA2CrrrF)nn' n nrrn5n)85n rrr8 ()nrn nn r;rrn nrn))nn rrrn nr n8 n nrn;) ,
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Ar&n+!B29 28nr#&5n &5 1 r n(nn nnrrn @(nn r))n n(nn? n) nrn 5r nrn5<)(n nE; nr rnn)F 5Er;rr F5 nrn)5 nr n445nEr;rr F5 nrn)n5 nrn)n ) % n5/n)5n.5 () r;rrEn5 ) Fn I2 7 ?n?n ))5n nr 5n1&7n'n ;n n r;rr n) 7rn 7nn

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Ar&n+!B29 21 & 8 9 # & # # 8 # 9 n nn n 8rn5nrn 5 n 5 n nr ) ) ) $ nnnn(r nr /r()5 n nr 3 ) 3 ) 3 ) 3 $ nnnn(r nrrn)85 n nr nnn En Fnn r;r)) nrnrn n n r;rnn'rn)n 3 n nr5n r)n 3 ) 3 5n n@(r 5n ) 5 nrnn r 3 )) 5n rr 3 nE Fn5 n'(nn5 <( nr(n?n n5 n r nrnn)n) ) n5)n5) 5)n) nr)(rn 58 rn 5))5n 55 nrnn) rn 55 nrnn /n) n)5 )n5n n InP5 n I 1E I2)))VF nnn nn5 Ar&n+ B 2 9

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Ar&n+!B29 2! =n8n5r5n') n5 n)n nnr(n n n 8nrnn n r;rr )n r'n n nnnn )n? n5 rn nr r"n )nrK nr()85 rr n r;rn5 r'?n 8nnn (9 n nn n n

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Ar&n+!B29 2 +'()nr'n;rn/6N8n;r( .n!2 8) n nr)n6n!2 < n nrnn nnrn 8)9n? ;rnn ((nnrnn r n;rn.n)(() n;rn 6 "n r' r"n )r ; n n75nn' nnr nrn 5 n # 5 1I E I2)))VFE?F nn nr;rrn5 n ( nrrn ) r 5n) 5rn(rn 5 /n) n 5 E B]F 1I E I2)))VFE?F 5n n n n ) r;rrn n ?n n rn r;rr);n nn r;rr) n

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2nB2 ',r?r* $/? nn nrn8 )n r' n)r'n) r) )nn) n '8 nr(n n n? ))7. nr ? n(nr;>7nnr n()7 <) ?n nnnr)n' nn) r;rrn n n r;rrn( r;rr< r;rr r;rr < (n)8 nrrnr (;n nrrnn (n 8nr#&5 / ,'

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2nB2 /nn.n)AKnn nr(5 nnn n5NCn) 5 87rnnr'n (n8r =n8r5
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2nB2 nnn Hnr(n nn n? )'n n<)(n 'n)nn nnr(5 5)n)(rn 5 5/n)5 rrrn( E!2 F 1 E I2)))VF =nnnn.nn n # 8n(n (';&n; rnnrr) ; n ? .n rn"n rn 5En 5rn 5 Frnn nr rnnn
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2nB2 $ n nn rn 9n) n (9n8n9n <)5( rn n9nnr)5(r) 9n8 )nrn nr;rn)5 ( nnrrnrr& rnn n n nnr n 5nn 8 A< n CA@ n C)n5) A < n CA < n Cr 5(nr( 5 n A @n CA @ n C/n) n n E 5 Fnr'n ?r nn n <)rQ rn @n nnn <5(nn n (n n n 1 E I2)))VF >r ( HE rF/nn5 1 $ E I2)))VF < @ #n< #n@ #n< S #n@ S

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2nB2 % 7nn nr;r) nn) rn n nrrnrnnnn 5nn)5 1 1 r5 rrr ) %) ") 1 1 1 nrnnnn 5n nE nnn nF5 1 $ 1 $ r5rrr ) $ ) 2 ) *) 1 1 1 1 8 n nn n5 nn n) 1 ) rr 1 1 1 $ 1 r5rrr ) 1 ) 2 ) ) $ 1 1 1 1 8 nnn n n rr n D) r)5( rrr .n(rn 5 ) $) ") ) 1 1 1 1 1 E I))")VFE"?F &57 n(r;rn(( (nr r;rnnn ? 5nn (n nn nn)rr(n5 nr; r&)n( n)75 nnn n();r() r;rn;r(r(rr ?E2 F n;?r;rr) 'r;rr);( r(nrrr,nB"n&r*r&rrnnn n4 n'n 5'n )nnnr n)nn n n n? ;r r () nr)rnnnrrn? nn,nnnr? .(/(rnnnr 9n8)

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2nB2 (rnnnr) (nn n 5(nnnr .(n & nn n .8 5(nnnr .(n ) n n?n 8 (nrnn nn 5E5F 5n )(nr;n 5 H n8 (nr nnnrn .)(n rr nr n n5A C(r;rHn r?rnnn n n5nE n n? F n)5n )(nr( rn nnn 8n n'n 5 'nnn)r nrrn(nEn nrF& n(n 5)8rnn'n rn 8rn( n)n5n r 55n 85n rnn n nnn n 85(rnnr (n nn(nnnn
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-CB2: "1 ,0"D?9@n?/5n5(n r r(n )7n )n@n?/5 rrn ?( r' rnnn r r(n+(n nn)(n5nn r+ n) rn nnnr n n5n)n)'n rn 5n nr rn(nOn'n (n nnr $rn A8n)nr!n*nrr*rr"n n & r))n n) 'nrr @n?/55 rnn nr n n rrn ?( nnrn D@n?/5 @n?/5 n $ n nn n n n E"*?F @n?/5n n rnn r nn n

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-CB2: "! )#$n "*? r nn ( n9; n59n;n (nn r rrn ?(n nr'nn n n nr n 5n; nr rrE2) 2) @ S Fnn E # ) % ) @ F @ @ % # F E F E @ @ % # rn F E @ @ % # n nn n n 5nnB9nn; n nn n @ n &;n n )) n nn n n n@n?/5) n $ n nn n n n n ; ( 9 n E #%@ F @S

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-CB2: "2 H" n F E F E $ @ @ % # @ @ % # @ n H" n F E F E $ @ @ % # @ @ % # @ n H" n F E $ @ @ % # % # @ n H" n H" n F E $ F E $ @ @ % # @ # @ @ % # @ % n 7n'nnrnrn ;nrn)5 H" n F E $ @ @ % # @ % # 8n5@S nrn( r H" nF E $@ @ % # @ % '# 87rnnn nn5 nI@P@SIP @S)n)@S0P Kr5I@P@S@SI( nrn n nr5I@P@S@SI( nnrn n /n)nnr r rr r H" n$ % # % '# 8nnnnn rn rn n r H" n$ % # % '#

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-CB2: K F E # # # # r rr r nr(n nr44 ( % # ) ) # n nr)n n $ % # % # % '# =n)8n'rn ;n nn nn n )8n n nn .nnnrn@)8 5n ;n % # ).5n F E % # @ @ r(n5) En @ S nrFn5n 5/n)8 n nn .nn)87rnn5n n5 nnrn % # % # % # )n) n $ % # % # % '# 2 2 2 2 $ n% # % '# FE $ n% # % '# n % # % '# =n n(nrn3 H" n H" n F E $ F E $ @ @ % # @ # @ @ % # @ % n n) H" n F E $ @ @ % # @ # %

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-CB2: @); nrn P % ( # )r;n n # < n)EP % ;n n # # ;n n % F)) nn5 @Sn)n)n n(n7 n)(DAn n nC/n)n ( ; n ' DP % )n ;n n ; ) # 8nn)n5nnn n n)5 n % # # % /5n9nrnn;n H" n H" n F E $ F E $ @ @ % # @ # @ @ % # @ % n ) r5n9nrn /n n 9 ( ; ) ) ' n ) ) ;n n )E=r() @ % #' ' F)5 2 n n % # # % # % F E n # % % # .( % # D ).n n nr? (E r n) ) ;n9; nr nB F F E n # % rn)5n F E # % r % # # % F E>) 5n J rnF E # % 5( # % # % J );rr5 nn)5nF E # %

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-CB2: "" # % J F E / # % J F E nn;n F E n # % ( J n J n =nrn n)r( n )nr n nrn
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"-,;7.n "" n =+/6 n %r 23+K:> n nn n n