6.4 Variation 327 Example 9 Combined Variation A varies jointly as B and C and inversely as the square of D. If A 1 = when B C 9, 4, = = and D 6, = determine A when B C 8, 12, = = and D 5. = Solution We begin with the equation A kBC D2 = We must first determine the constant of proportionality, k, by substituting the known values for A B C , , ,and D and solving for k. k k k 1 (9)(4) 6 1 36 36 1 2 = = = Thus, the constant of proportionality equals 1. Now we determine A for the corresponding values of B C, , and D. A kBC D A (1)(8)(12) 5 96 25 3.84 2 2 = = = = 7 Now try Exercise 53 Instructor Resources for Section 6.4 in MyLab Math • Objective-Level Videos 6.4 • PowerPoint Lecture Slides 6.4 • MyLab Exercises and Assignments 6.4 Exercises Warm Up Exercises In Exercises 1– 4, fill in the blank with an appropriate word, phrase, or symbol(s). 1. When the values of two related variables increase together or decrease together, it is an example of ________ variation. Direct 2. When one quantity increases while the other quantity decreases, it is an example of ________ variation. Inverse 3. A variation equation that relates one variable to two or more other variables using the operation of multiplication is called a(n) ________ variation equation. Joint 4. In the equation y kx, = k is called the constant of ________. Proportionality Practice the Skills In Exercises 5–18, determine whether the variation between the indicated quantities is direct or inverse. 5. The volume of air in a balloon and the radius of the balloon Direct 6. The time it takes to drive to work and the speed at which you drive Inverse 7. The time required to fill a pool with a hose and the volume of water coming from the hose Inverse 8. The distance between two cities on a map and the actual distance between them Direct 9. The interest earned on an investment and the interest rate Direct 10. The diameter of a hose and the volume of water coming out of the hose Direct 11. The speed of a runner and the time it takes the runner to complete a 10-kilometer race Inverse 12. The number of volunteers present and the time it takes to clean up the city park Inverse 13. The circumference of a circle and the radius of the circle Direct 14. The number of miles that a tire has been driven and the depth of the tread remaining on the tire Inverse 15. The width of the lawn mower and the time it takes to mow the lawn Inverse 16. On Earth, the weight and mass of an object Direct 17. The number of people in line at a bank and the amount of time required for the last person to reach the teller Direct SECTION 6.4
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