Basic Technical Mathematics, 11th Edition

Exercises 3.1, page 88

1. 1. $\hspace{0.17em}-\hspace{0.17em}13$

2. 3. $f(T\hspace{0.17em}-\hspace{0.17em}10)\hspace{0.17em}=\hspace{0.17em}9.1\hspace{0.17em}+\hspace{0.17em}0.08T\hspace{0.17em}+\hspace{0.17em}0.001T^2$

3. 5.

   1. $A\hspace{0.17em}=\hspace{0.17em}\pi r^2$

   2. $A\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{4}}\pi d^2$

4. 7. $d\hspace{0.17em}=\hspace{0.17em}\sqrt[3]{{\displaystyle \frac{6V}{\pi }}}$

5. 9. $A\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{2}}{d}^2\hspace{0.17em},\hspace{0.17em}d\hspace{0.17em}=\hspace{0.17em}\sqrt{2A}$

6. 11. $A\hspace{0.17em}=\hspace{0.17em}4r^2\hspace{0.17em}-\hspace{0.17em}\pi r^2$

7. 13. $7\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}9$

8. 15. 6, 6

9. 17. ${\displaystyle \frac{3\hspace{0.17em}-\hspace{0.17em}2{\pi }^2}{2\pi }}\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{1}{2}}$ 

10. 19. ${\displaystyle \frac{1}{9}}a\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{1}{3}}{a}^2\hspace{0.17em},\hspace{0.17em}0$

11. 21. $3s^2\hspace{0.17em}-\hspace{0.17em}11s\hspace{0.17em}+\hspace{0.17em}16\hspace{0.17em},\hspace{0.17em}3s^2\hspace{0.17em}+\hspace{0.17em}s\hspace{0.17em}+\hspace{0.17em}8$ 

12. 23. $\hspace{0.17em}-\hspace{0.17em}6$

13. 25. 62.9, 260

14. 27. $\hspace{0.17em}-\hspace{0.17em}299.7$

15. 29. $f(x)\hspace{0.17em}=\hspace{0.17em}3x^2\hspace{0.17em}-\hspace{0.17em}4$

16. 31. $f(x)\hspace{0.17em}=\hspace{0.17em}{x}^3\hspace{0.17em}-\hspace{0.17em}7x$

17. 33. Square the input and add 2.

18. 35. Cube the input and subtract this from 6 times the input.

19. 37. Multiply by 3 the sum of twice the input added to 5.

20. 39. $A\hspace{0.17em}=\hspace{0.17em}5e^2\hspace{0.17em},\hspace{0.17em}f(e)\hspace{0.17em}=\hspace{0.17em}5e^2$

21. 41. $A\hspace{0.17em}=\hspace{0.17em}5200\hspace{0.17em}-\hspace{0.17em}120t\hspace{0.17em},\hspace{0.17em}f(t)\hspace{0.17em}=\hspace{0.17em}5200\hspace{0.17em}-\hspace{0.17em}120t$

22. 43. 10.4 m

23. 45. 75 ft, $2v\hspace{0.17em}+\hspace{0.17em}0.2v^2\hspace{0.17em},\hspace{0.17em}$ 240 ft, 240 ft

24. 47. $31\text{ lb/in}{\hspace{0.17em}.\hspace{0.17em}}^2$

25. 49. $d\hspace{0.17em}=\hspace{0.17em}120t\hspace{0.17em}+\hspace{0.17em}65$

26. 51.

    1. f[f(x)] means “function of the function of x”. 

    2. $8x^4$