College Algebra, 2013a

356 Rational Functions
4.3.3 Answers
1. x = − 6 7
2. x =1,x=2 3. x = −1
4. x = −6, x= 2 5. No solution 6. x =0,x= ±2 √ 2
7. (−2, ∞) 8. (−2, 3]
9. (−1, 0) ∪ (1, ∞) 10. [0, ∞)
11. (−∞, −3) ∪ (−3, 2) ∪ (4, ∞) 12. ( −3, − 1 3)
∪ (2, 3)
13. (−1, 0] ∪ (2, ∞) 14. (−∞, −3) ∪ (−2, −1) ∪ (1, ∞)
15. (−∞, 1] ∪ [2, ∞) 16. (−∞, −6) ∪ (−1, 2)
17. (−∞, −3) ∪ [ −2 √ 2, 0 ] ∪ [ 2 √ 2, 3 ) 18. No solution
19. [−3, 0) ∪ (0, 4) ∪ [5, ∞) 20. ( −1, − 1 2]
∪ (1, ∞)
21. 4.5 miles per hour 22. 24 miles per hour 23. 3600 gallons
24.
40
3
≈ 13.33 minutes 25. 3 hours
26. The absolute minimum of y = C(x) occurs at ≈ (75.73, 59.57). Since x represents the number
of game systems, we check C(75) ≈ 59.58 and C(76) ≈ 59.57. Hence, to minimize the average
cost, 76 systems should be produced at an average cost of $59.57 per system.
27. The width (and depth) should be 10.00 centimeters, the height should be 5.00 centimeters.
Theminimumsurfaceareais300.00 square centimeters.
28. The width of the base of the box should be ≈ 4.12 inches, the height of the box should be
≈ 6.67 inches, and the depth of the base of the box should be ≈ 5.09 inches; minimum surface
area ≈ 164.91 square inches.
29. The dimensions are ≈ 7 feet by ≈ 14 feet; minimum amount of fencing required ≈ 28 feet.
30. (a) V = πr 2 h (b) S =2πr 2 +2πrh
(c) S(r) =2πr 2 + 67.2
r
, Domain r>0 (d) r ≈ 1.749 in. and h ≈ 3.498 in.
31. The radius of the drum should be ≈ 1.05 feet and the height of the drum should be ≈ 2.12
feet. The minimum surface area of the drum is ≈ 20.93 cubic feet.
32. P (t) < 100 on (−15, 30), and the portion of this which lies in the applied domain is [0, 30).
Since t = 0 corresponds to the year 1803, from 1803 through the end of 1832, there were
fewer than 100 Sasquatch in Portage County.