Mathematic Methods HW Solutions 23

# Mathematic Methods HW Solutions 23 - where a = radius of...

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Chapter 5 2.1 3 2.2 - 18 2.3 4 2.4 8 / 3 2.5 e 2 4 - 5 12 2.6 2 . 35 2.7 5 / 3 2.8 1 / 2 2.9 6 2.10 5 π 2.11 36 2.12 2 2.13 7 / 4 2.14 4 - e (ln 4) 2.15 3 / 2 2.16 (ln 3) / 6 2.17 (ln 2) / 2 2.18 (8 2 - 7) / 3 2.19 32 2.20 16 2.21 131 / 6 2.22 5 / 3 2.23 9 / 8 2.24 9 / 2 2.25 3 / 2 2.26 4 / 3 2.27 32 / 5 2.28 1 / 3 2.29 2 2.30 1 - e - 2 2.31 6 2.32 e - 1 2.33 16 / 3 2.34 8192 k/ 15 2.35 216 k 2.36 1 / 6 2.37 7 / 6 2.38 - 20 2.39 70 2.40 3 / 2 2.41 5 2.42 4 2.43 9 / 2 2.44 7 k/ 3 2.45 46 k/ 15 2.46 8 k 2.47 16 / 3 2.48 16 π/ 3 2.49 1 / 3 2.50 64 / 3 3.2 (a) ρl (b) Ml 2 / 12 (c) Ml 2 / 3 3.3 (a) M = 140 (b) ¯ x = 130 / 21 (c) I m = 6 . 92 M (d) I = 150 M/ 7 3.4 (a) M = 3 l/ 2 (b) ¯ x = 4 l/ 9 (c) I m = 13 162 Ml 2 (d) I = 5 Ml 2 / 18 3.5 (a) Ma 2 / 3 (b) Ma 2 / 12 (c) 2 Ma 2 / 3 3.6 (a) (2 , 2) (b) 6 M (c) 2 M 3.7 (a) M = 9 (b) (¯ x, ¯ y ) = (2 , 4 / 3) (c) I x = 2 M , I y = 9 M/ 2 (d) I m = 13 M/ 18 3.8 2 Ma 2 / 3 3.9 (a) 1 / 6 (b) (1 / 4 , 1 / 4 , 1 / 4) (c) M = 1 / 24, ¯ z = 2 / 5 3.10 (a) s = 2 sinh 1 (b) ¯ y = (2 + sinh 2) / (4 sinh1) = 1 . 2 3.11 (a) M = (5 5 - 1) / 6 = 1 . 7 (b) ¯ x = 0, M ¯ y = (25 5 + 1) / 60 = 0 . 95, ¯ y = (313 + 15 5 ) / 620 = 0 . 56 3.14 V = 2 π 2 a 2 b , A = 4 π 2 ab , where a = radius of revolving circle, b = distance to axis from center of this circle.
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Unformatted text preview: , where a = radius of revolving circle, b = distance to axis from center of this circle. 3.15 For area, (¯ x, ¯ y ) = (0 , 4 3 r/π ); for arc, (¯ x, ¯ y ) = (0 , 2 r/π ) 3.17 4 √ 2 / 3 3.18 s = b 3 √ 2 + ln(1 + √ 2) B / 2 = 2 . 56 3.19 2 π 3.20 13 π/ 3 3.21 s ¯ x = b 51 √ 2-ln(1 + √ 2) B / 32 = 2 . 23, s ¯ y = 13 / 6, s as in Problem 3.18; then ¯ x = 0 . 87, ¯ y = 0 . 85 3.22 (4 / 3 , , 0) 3.23 (149 / 130 , , 0) 3.24 2 M/ 5 3.25 I/M has the same numerical value as ¯ x in 3.21. 3.26 2 M/ 3 3.27 149 130 M 3.28 13 / 6 3.29 2 3.30 32 / 5 23...
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