SOLUTIONS_OF_Ytha_Yu_Charles_Marut_Assem.pdf

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2. Preface …………………………………………………………………. 1 Ch.1 …………………………………………………………………. 2 Ch.2 …………………………………………………………………. 7 Ch.3 …………………………………………………………………. 14 Ch.4 …………………………………………………………………. 17 Ch.5 …………………………………………………………………. 32 Ch.6 …………………………………………………………………. 37 Ch.7 …………………………………………………………………. 58 Ch.8 …………………………………………………………………. 84 Ch.9 …………………………………………………………………. 93 Ch.10 …………………………………………………………………. 110 Appendix A (How to run a program)………………… .. 112 Appendix B ( Some useful procedure)………………… 117

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96. 6. I C M C= & +* C M C= ^ I C M = ^ I C 5 M C=5 & +* C M C=5^ I 5C C M5C=5^ 88 5C M5C=5^ ? ^ I C 1 M C=1 & +* C M C=1^ 1 2 5C C M ^ ?5^ =P 1^ G, 9,@X17 1*1 M1*, 17 G 2 ,>8X&7 9,@X17 9@1 M9,@ 17 ,>8X&7

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98. 64 6 # 8,* 9 ** #9@ 1J . #8 @ 85 < 8< T@<, @& , &9 DT #1 8, &> 2 1 I C U8 @ M L 89 I 89 C 1 ** &>8,1 I 8C M $ " 8C I 5C . M. V. = 8&I 5C 2+9< C 2+9< 8C M--------- I < 6 M *, 8C &>@ < 2 2 8C 2 2 C M C 1 ** +@8,1 2+9< 8C

99. 66 I @ < M---------- 2 2 C I 5C . I 8C 8&I 5C 1 ** +@8,1 M C 2+9< 8C M----------- I @ < 2 2 C 1 ** +@8,1 M C M---------- I < 1< M 8 9 &>@ < &> ,>82 &>1*+8, 1 ]@,9@] +@8,1# 9 &>1*+8, 1 ]@,9@]&>8,1# 9 ,>8 &> Q " 3 ! 1 @ ]

100. > < = ( R = ( 8 = > $ = ( 2 = # 8,* 9 ** #8 @ 9@ @ 85 < 8< <*7 85 P T < T R+ 85 P T R T 8& 85 P T 8 T >&1 85 P T > $ T 2,> 85 P T 2 T TDT #1 8, &> 2 1 I C U8 @ I 89 C M------------------------------------------------- 1 ** &>8,1 M C I 5* ( M 8 8&I 5* 88 * M1 >I, @ @ 8&S&@ I <*7 *

101. M---------------------- I * &1 * M---------------- 88 < M M--------------------------------------------------------- I < 6 M *, 8C 9@ @ &>@ <

102. M----------------- I < 1< &>@ < &> ,>82 &>1*+8, 1 ]@,9@]&>8,1# 9 ,>8 &>

103. # 8,* 9 ** #8 @ 85 < 8< T DT 85 < 8< T > DT 85 < 8< T ,9+*@ &9 DT #1 8, &> 2 1 I C U8 @ I 89 C I < 6 *, 8C &>@ < M-------- 1 ** &>8,1 M I 5C C M 5C I < 6 *, 8C &>@ < 1 ** &>8,1M > C 2+9< C M---------------- I < 6 *, 8C &>@ < I < M W # W I 8* T#T

104. ( &>@ < M---------------- 2 2 C C1<S C 5C M C 5C > O<&*,X I 1C I 8C & +* 1C M C= CV 8&I 5C 1 ** +@8,1 I C 8C M 1 2 8C G>, O<&*,X M---------------- M------------------------------ I < 1< &>@ < &> ,>82 &>1*+8, 1 ]@,9@]&>8,1# 9 &>1*+8, 1 ]@,9@] +@8,1# 9 ,>8 &>

105. . > : #" ('. 44'6 H

106. 0 4 # 8,* 9 ** #8 @ 85 < 8< T,>@, DT 85 < 8< T,>@, > DT 85 < 8< TS18 &9 DT #1 8, &> 2 1 I C U8 @ I 89 C M----------------- I < 6 *, 8C &>@ < 1 ** &>8,1 M 2+9< C M 3 I < 6 *, 8C &>@ < 1 ** &>8,1 M > 2+9< C M 3 > M------------- 2 2 5C 2 2 C * I 8C 8&I 5C M '> 1 2 8C G, S18X7 +>8 M5C &9 >

107. 4 I C 5C M > I 5C 8C M > G 2 * S18X7 +>8 I < 6 *, 8C &>@ @ < &> ,>82 &>1*+8, 1 ]@,9@] +@8,1# 9 &>1*+8, 1 ]@,9@]&>8,1# 9 ,>8 &>

108. 6

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110. #8 @ 9@X 8O ( 8+2 P #1 8, I 5C I 1C ( I 52 92 * I C O 8 2@ _52` I O 8 2@ 9@X _5C` C 88 52 88 5C * 2 *

111. 1 " " " , 0 1 2 - + ! % # - 3 " % ! V# 9 - Q $ % % 3 % % 3 # $ % , 0 1 32 - + 9 @ 9 " " H # Z % ! V# 5G - Q " % % $ @ 9 % % ! H $ " ! " # 9 - " % $ % $ # * $ " " " # - 5 $ " ! #

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116. 0 &>8,1 2 1 M , 8 >+ 5, &> >S, - 0.4 @ 0.0 M M C = ; 3 2+9< 5C 2+9< 1C 2+9< 8C M U5,S&> I @ < M TPT M = C 5C 5C M5C M " 3 = C 1C 1C M1C " M # I < &>@ < M # 1 2 * T-T M " G, U &>+9 M " 1 2 * T?T M " G, U2*+9 M " # G 2 U ,2, @ M " # !

117. 4 U &>+9 I 1C U2*+9 &>@ < M U ,2, @ M # % T T T6T 1 2 * T T M A=T TP G>S, U> @X8&S&@ M " # 1 2 * T6T M B=T6T P G>*, U> @X8&S&@ M 3 " >8 C 7< 2+9< C M = V ? " I C +* 5C 2 2 5C 88 5C C M I < &>@ < 1 2 * 8< M1 G>, U ,2, @ M 1 I C 5C M " 3 1C 1C G, U,C&@ >,S C M U,C&@ 2 2 8C 2 2 1C

118. 6 2 2 5C ,@ M " U> @X8&S&@ I @ @ < G 2 U5,S&> &>8,1 ,>82

119. &>8,1 2 1 M , 8 >+ 5, &> >S, - 0.4 @ 0.0 M M C = ; 3 2+9< 5C 2+9< 1C 2+9< 8C M U5,S&> I @ < M TPT M = C 5C 5C M5C M " 3 = C 1C 1C M1C " M # I < &>@ < M # 1 2 * T-T M " G, U &>+9 M " 1 2 * T?T M " G, U2*+9 M " # G 2 U ,2, @ M " # U &>+9 I 1C ! " #! $

120. U2*+9 &>@ < M U ,2, @ M # % T T T6T 1 2 * T T M A=T TP G>S, U> @X8&S&@ M " # 1 2 * T6T M B=T6T P G>*, U> @X8&S&@ M 3 " >8 C 7< 2+9< C M = V ? " I C +* 5C M---------------------------- 1 2 8C G>, U> @X8&S&@ M-------------------------- 2 2 5C 88 5C C M------------------------- G1 U> @X8&S&@ M-------------------- M I < &>@ < 1 2 * 8< M1 G>, U ,2, @ M 1 I C 5C M " 3 1C 1C

121. G, U,C&@ >,S C M U,C&@ 2 2 8C 2 2 1C 2 2 5C ,@ M " U> @X8&S&@ I @ @ < G 2 U5,S&> &>8,1 ,>82

122. +@8,1 2 1 2+9< C 2+9< 5C 2+9< 1C 2+9< 8C C C GS, U,>8X&7 2+9< C I 8* T-T I < &>@ < 2 2 C >,S C U,>8X&7 C 1C 1C I 5C 8 U ,2, @ C 8C 8C 8&I 5C 2+9< 8C &>1 1C !

123. C C G>, U ,2, @ I < U2 &>@X* 2 2 2 8C 8* < &>@ < * 2 U2 &>@X* 2 2 2 8C 2 2 1C 2 2 5C 2 2 C ,@ +@8,1 ,>82

124. ( &>5&> Q 2 1 C 5C 5C I < &>@ < O<&*,X 1 2 * 8< G, ,>8XO<&*, >8 * 7< 9<* 5C 5* * &>@ < G 2 O<&*,X ,>8XO<&*, ,@ &>5&> Q ,>82

125. . +@5&> Q 2 1 M C I 5C C I 1C . * * 5C G1 >, I @ < G 2 * >, I @ < * * 2 * ,@ +@5&> Q ,>82

126. 0 , 8X9@ 2 1 >, 2+9< 8& M = " 2+9< C M !=a C 5C 5C I < O<&*, &>@ < 1 2 * 8< G, ,>8XO<&*, 9@ 95 &>1 5C G 2 O<&*, ,>8XO<&*, 2 2 C 2 2 8& ,@ , 8X9@ ,>82

127. 4 8&92* QX9@ 2 1 >, 2+9< C M9& = 5,S&> 7 9@ &>S 2+9< 9& M&>2+@ 1C=a 7 1< @ 8&92* Q I @ < * * 895 I 8* * &>@ < * 2 * 2 2 9& 2 2 C ,@ 8&92* QX9@ ,>82

128. 6 @ $ " 5 O O , " -$ 6 ( (78 ( 2 , 39: ;:3;;<

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