(a) v = in .NET framework

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29.11 (a) v =
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13 t4 13t 2 23 3 88 t3 t + 4; (b) x = + 4t; (c) at x = when t = 1, at x = when t = 3, and at x = when 3 3 12 6 12 4 3 t = 4; (d) t < 4 and 1 < t < 3. 29.13 (a) 3 s; (b) 99 ft. 29.14 7 units.
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29.12 (a) 160 ft/s; (b) 400 ft. 29.15 (a) y =
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2x 3 5x 1; (b) y = 6x 2 + x + 1. 3 8 . 3
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29.16 12.5 ft.
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29.17 (a) t 2 2t; (b) 0 < t < 2; (c) t = 2; (d) 0; (e)
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30.4 (a) 24; (b) 13 5 ; (c) . 3 3 30.5 A2 A1 A3 . 30.6 (c) 20. n(n + 1) 2 . 2 30.9 (a) . 11 . 5
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30.10 (a) 15; (b) 110; (c)
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3+ 3 ; (d) 15. 2
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30.12 (b)
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30.13 4 1 + 2 = 5.
31.10 (a) 24; (b) 31.11 (a)
8 5 25 5 2046 2 ; (c) 3; (d) ; (e) ; (f) . 2 5 2 2
9 13 26 1 35 3 1 ; (b) 27; (c) ; (d) ; (e) ; ( f ) ; (g) ; (h) 9. 2 2 3 3 3 6 2 450 522 254 248 56 113 226 + ; (f) [(11)3 (383) 256] = ; (g) ; 7 5 3 45 5 7 1 . 8
31.12 (a)
1 8 1 2 ; (b) ; (c) (1 2 2); (d) (2 2 1); (e) 2 2 3 3 1 8 5 223 4 (h) ; (i) ; ( j) ; (k) ; (l) (6 3 + 1); (m) 9 3 2 160 15 3 4 1 2 ; (b) ; (c) ; (d) . 4 3
31.13 (a)
ANSWERS TO SUPPLEMENTARY PROBLEMS 1 3 ; (b) c = ; (c) c = 3. 3 2 4 31.18 (a)
[ANS.
31.14 (a) c =
31.15 (a)
1 857 ; (b) . 35 6
. 4
x2 x1 . T
5 + 7x 2 ; (b) sin3 x; (c) 2 x 4 + 1. 25x . 125x 3 + 1
31.19 0.
31.20 (a) 6x 243x 10 + 1; (b) f (h(x)) h (x); (c) 3 3x and 31.21 b = n 3. 31.22 1. 31.23 0. 1 . 2 . 3
31.24 (a) 4x; (b) 2. 31.28 All three are equal.
31.25 (a) 0; (b) 31.29 c =
31.26 b = 4.
3 6.
31.30 All values such that x k is integrable on [0, 2]; these include all positive values. 31.31 (a) x = 13 m. 3 sin 3t 2 1 1 ; (b) ; (c) 0 < t < ; (d) and . 3 3 6 3 3 31.33 (a) 2 ; (b) 1. 31.34 0.33 as compared to 1 . 3
31.32 31.35
(2 2 + 1) 2.004559755 as compared to 2. 6 (c) 0.25.
31.36 (a) 0.2525, as compared to the exact answer 0.25; (b) 0.24875;
32.7 (a) 16 5 52 [Fig. A-22(a)]; (b) [Fig. A-22(b)]; (c) [Fig. A-22(c)]. 3 3 4
Fig. A-22
1 5 1 9 5 1 125 1 2 5 1 125 ; (b) ; (c) ; (d) ; (e) 2 1 ( f ) ; (g) ; (h) ; (i) ; ( j) 9; (k) ; (l) ; (m) ; (n) . 12 12 3 6 6 2 12 8 6 3 15 4 1 1097 17 33 ; (b) 10; (c) (80 10 13 13); (d) 9; (e) ; ( f ) 2 3; (g) ; (h) 21. 16 27 480 6
32.8 (a)
32.9 (a)
32.10 (a) 1.478942387; (b) 3.82018762; (c) 125.6601461.
ANS.]
ANSWERS TO SUPPLEMENTARY PROBLEMS
3 4 3 4 3 6 2 3 17 ; (b) ; (c) ; (d) ; (e) [r (r 2 a2 )3/2 ]; ( f ) (r a3 ) a(r 2 a2 ); (g) (64 ); (h) 2 2 ba2 ; 7 5 3 10 3 3 15 2 27 27 2 ; ( j) ; (k) ; (l) ; (m) 4 . (i) 3 5 2 3 1 2 3 3 1 1 1 4 3 33.9 (a) r ; (b) r ; (c) r 2 h; (d) ab c = abc. 3 9 3 3 2 6 33.8 (a) 33.10 (a) 27 14 . ; (b) 15 32 33.11 (a) 5 . 6 7324 226 ; (b) . 705 15 33.12 (a) See Fig. A-23; (b) (i) 4 , (ii) 64 . 5
33.13 (a) See Fig. A-24; (b)
Fig. A-23
33.14 (a) See Fig. A-25; (b) 81 1332 153 1152 ; (c) ; (d) ; (e) . 5 2 5 2
Fig. A-24
Fig. A-25
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