Basic Technical Mathematics, 11th Edition

Exercises 19.2, page 521

1. 1. 243

2. 3. 6400, 1600, 400, 100, 25

3. 5. ${\displaystyle \frac{1}{6}}\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{1}{2}}\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{3}{2}}\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{9}{2}}\hspace{0.17em},\hspace{0.17em}{\displaystyle \frac{27}{2}}$

4. 7. 128

5. 9. ${\displaystyle \frac{1}{125}}$

6. 11. ${\displaystyle \frac{100}{729}}$

7. 13. 1

8. 15. ${\displaystyle \frac{341}{8}}$

9. 17. 762

10. 19. ${\displaystyle \frac{3(2^{10}\hspace{0.17em}-\hspace{0.17em}{k}^{10})}{16(2\hspace{0.17em}+\hspace{0.17em}k)}}$

11. 21. $a_6\hspace{0.17em}=\hspace{0.17em}64\hspace{0.17em},\hspace{0.17em}{S}_6\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1365}{16}}$

12. 23. $a_1\hspace{0.17em}=\hspace{0.17em}16\hspace{0.17em},\hspace{0.17em}{a}_5\hspace{0.17em}=\hspace{0.17em}81$

13. 25. $a_1\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em},\hspace{0.17em}r\hspace{0.17em}=\hspace{0.17em}3$

14. 27. $n\hspace{0.17em}=\hspace{0.17em}7\hspace{0.17em},\hspace{0.17em}{S}_n\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{\mathrm{58,593}}{625}}$

15. 29. Yes; $r\hspace{0.17em}=\hspace{0.17em}{3}^x\hspace{0.17em};\hspace{0.17em}{a}_{20}\hspace{0.17em}=\hspace{0.17em}{3}^{19x\hspace{0.17em}+\hspace{0.17em}1}$

16. 31. 5

17. 33. ${\displaystyle \frac{x^2[\hspace{0.17em}1\hspace{0.17em}-\hspace{0.17em}{(\hspace{0.17em}-\hspace{0.17em}x)}^n]\hspace{0.17em}}{x\hspace{0.17em}+\hspace{0.17em}1}}$

18. 35. 1.4%

19. 37. 1.09 mA

20. 39. $366.76

21. 41. $5800\hspace{0.17em}°\hspace{0.17em}\text{C}$

22. 43. 43%

23. 45. $13,947

24. 47. $671,088.64

25. 49. The 5% bonus, $1,609,564.06 more

26. 51. 0.25 ft

27. 53. Yes, the ratio is squared.

28. 55. 8, 1, $\hspace{0.17em}-\hspace{0.17em}6\hspace{0.17em};\hspace{0.17em}$ 8, 16, 24; 1, $\hspace{0.17em}-\hspace{0.17em}6\hspace{0.17em},\hspace{0.17em}$ 36; 16, 24, 36