121616949-math.309 - a 3 √ a 3 √ b from charge A 6.1.32...

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Appendix B Selected Answers 295 6.1.5. 3 100 × 3 100 × 2 3 100, h/s = 2 6.1.6. w = l = 2 1 / 3 V 1 / 3 , h = V 1 / 3 / 2 2 / 3 , h/w = 1 / 2 6.1.7. 1250 square feet 6.1.8. l 2 / 8 square feet 6.1.9. $5000 6.1.10. 100 6.1.11. r 2 6.1.12. h/r = 2 6.1.13. h/r = 2 6.1.14. r = 5, h = 40 , h/r = 8 6.1.15. 8 6.1.16. 4 / 27 6.1.17. Go direct from A to D . 6.1.18. (a) 2, (b) 7 / 2 6.1.19. 3 6 × 3 6 + 1 2 × 1 4 - 3 12 6.1.20. (a) a/ 6, (b) ( a + b - a 2 - ab + b 2 ) / 6 6.1.21. 1 . 5 meters wide by 1 . 25 meters tall 6.1.22. If k 2 the ratio is (2 - ) / 4; if k 2 , the ratio is zero: the window should be semicircular with no rectangular part. 6.1.23. a/b 6.1.24. w = 2 r/ 3, h = 2 2 r/ 3 6.1.25. 1 / 3 58% 6.1.26. 18 × 18 × 36 6.1.27. r = 5 / (2 π ) 1 / 3 2 . 7 cm, h = 5 · 2 5 / 3 1 / 3 = 4 r 10 . 8 cm 6.1.28. h = 750 π 2 π 2 750 2 1 / 3 , r = 750 2 2 π 2 1 / 6 6.1.29. h/r = 2 6.1.30. The ratio of the volume of the sphere to the volume of the cone is 1033 / 4096 + 33 / 4096 17 0 . 2854, so the cone occupies approximately 28 . 54% of the sphere. 6.1.31. P should be at distance c 3
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Unformatted text preview: a/ ( 3 √ a + 3 √ b ) from charge A . 6.1.32. 1 / 2 6.1.33. $7000 6.1.34. There is a critical point when sin θ 1 /v 1 = sin θ 2 /v 2 , and the second derivative is positive, so there is a minimum at the critical point. 6.2.1. 1 / (16 π ) cm/s 6.2.2. 3 / (1000 π ) meters/second 6.2.3. 1 / 4 m/s 6.2.4.-6 / 25 m/s 6.2.5. 80 π mi/min 6.2.6. 3 √ 5 ft/s 6.2.7. 20 / (3 π ) cm/s 6.2.8. 13 / 20 ft/s 6.2.9. 5 √ 10 / 2 m/s 6.2.10. 75 / 64 m/min 6.2.11. 145 π/ 72 m/s 6.2.12. 25 π/ 144 m/min 6.2.13. π √ 2 / 36 ft 3 /s 6.2.14. tip: 6 ft/s, length: 5 / 2 ft/s 6.2.15. tip: 20 / 11 m/s, length: 9 / 11 m/s 6.2.16. 380 / √ 3-150 ≈ 69 . 4 mph 6.2.17. 81 km/hr...
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