Inverse Variation Handout
(Section 8.7, answers below)
| For problems 1 through 6, graph the function. | |
| 1. {(x, y): xy = 8} | 4. {(x, y): xy = -12} |
| 2. {x, y): xy = 1} | 5. {(x, y): xy + 10 = 0} |
| 3. {(x, y): xy = -6} | 6. {(x, y): xy -36 = 0} |
Determine each value of c for which both ordered pairs belong to the same inverse variation. |
|
| 7. (10, 25), (2, c) | 10. (5, 20), (c, c) |
| 8. (9, 28), (c, 42) | 11. (4/5, 2/3), (c, 6) |
| 9. (-60, -15), (-c, -c) | 12. (0.28, 0.32), (8, c) |
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| 13. {(4, 3), (-2, c)} is a subset of {(x, y): y varies inversely as x2} |
| 14. {(2, 6), (8, c)} is a subset of {(x, y): y varies inversely as x2} |
Graph each relation. |
|
| 23. {(x, y): xy < 100} | 26. {(x, y): xy > 24} |
| 24. {x, y): xy £ 4} | 27. {x, y): |x|y = 4} |
| 25. {(x, y): xy ³ 6} | 28. {(x, y): x|y| = 4} |
(Section 8.8, answers below)
| 1. The frequency of a radio wave is inversely proportional to the wave length. If a wave of 250 meters has a frequency of 1200 kilocycles per second, find the length of a wave with a frequency of 800 kilocycles per second. |
| 2. A pulley with a diameter 8 inches is running at 1452 revolutions per minute while belted to a 12-inch pulley. Find the speed of the larger pulley if the speeds of the pulleys are in inverse proportion to their diameters. |
| 3. Two meshed gears have 35 and 56 teeth respectively. If the speeds are inversely proportional to the number of teeth, at what speed should the second gear be driven in order to make the first gear run at 1450 revolutions per minute? |
| 4. A certain project can be completed by 28 men in 90 days. In order to get a bonus, the contractor hires extra men so that the job can be done in 84 days. How many extra men does he hire? |
| 7. A surface is now 10 feet from a source of light. How far from the source would the surface have to be in order to receive twice as much illumination, if the intensity of the illumintion varies as the square of its distance from the source of light? |
| 11. The weight of a body is inversely proportional to the square of its distance from the center of the earth. If a man weighs 147 pounds on the earth's surface, what will he weigh 200 miles above the earth? Assume the radius of the earth to be 4000 miles. |
8.7 ANSWERS: 1.
branches in Q I and Q III 2. branches in Q I and Q III 3.
branches in Q II and Q IV
4. branches in Q II and Q IV 5. branches in Q II and Q IV
6. branches in Q I and Q III 7. 125 8. 6
9. 30, -30 10. 10, -10
11. 4/45 12. 0.0112 13. 12
14. 3/8 23. draw branches in Q I and Q III
24. draw branches in Q I and Q III 25. draw branches in Q I and Q III
26. Hint: determine range!!!
27. Hint: determine domain!!!
8.8 ANSWERS: 1. 375 meters
2. 968 rpm 3. 906.25 rpm 4. 2
7. 7.07 feet 11. 133.3 pounds