Exercises 3.1, page 88

1. $- 13$ $- 13$
3. $f (T - 10) = 9.1 + 0.08 T + 0.001 T^{2}$ $f (T - 10) = 9.1 + 0.08 T + 0.001 T^{2}$
5.
1. $A = π r^{2}$ $A = π r^{2}$
2. $A = \frac{1}{4} π d^{2}$ $A = \frac{1}{4} π d^{2}$
7. $d = \sqrt[3]{\frac{6 V}{π}}$ $d = \sqrt[3]{\frac{6 V}{π}}$
9. $A = \frac{1}{2} d^{2}, d = \sqrt{2 A}$ $A = \frac{1}{2} d^{2}, d = \sqrt{2 A}$
11. $A = 4 r^{2} - π r^{2}$ $A = 4 r^{2} - π r^{2}$
13. $7, - 9$ $7, - 9$
15. 6, 6
17. $\frac{3 - 2 π^{2}}{2 π}, - \frac{1}{2}$ $\frac{3 - 2 π^{2}}{2 π}, - \frac{1}{2}$
19. $\frac{1}{9} a - \frac{1}{3} a^{2}, 0$ $\frac{1}{9} a - \frac{1}{3} a^{2}, 0$
21. $3 s^{2} - 11 s + 16, 3 s^{2} + s + 8$ $3 s^{2} - 11 s + 16, 3 s^{2} + s + 8$
23. $- 6$ $- 6$
25. 62.9, 260
27. $- 299.7$ $- 299.7$
29. $f (x) = 3 x^{2} - 4$ $f (x) = 3 x^{2} - 4$
31. $f (x) = x^{3} - 7 x$ $f (x) = x^{3} - 7 x$
33. Square the input and add 2.
35. Cube the input and subtract this from 6 times the input.
37. Multiply by 3 the sum of twice the input added to 5.
39. $A = 5 e^{2}, f (e) = 5 e^{2}$ $A = 5 e^{2}, f (e) = 5 e^{2}$
41. $A = 5200 - 120 t, f (t) = 5200 - 120 t$ $A = 5200 - 120 t, f (t) = 5200 - 120 t$
43. 10.4 m
45. 75 ft, $2 v + 0.2 v^{2},$ $2 v + 0.2 v^{2},$ 240 ft, 240 ft
47. $31 lb/in .^{2}$ $31 lb/in .^{2}$
49. $d = 120 t + 65$ $d = 120 t + 65$
51.
1. f[f(x)] means “function of the function of x”.
2. $8 x^{4}$ $8 x^{4}$

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Table of Contents for Exercises 3.1, page 88