415 3.7 Variation Step 3 Substitute for k to find the relationship among the variables. n = 22T L Step 4 Now use the second set of values for T and L to find n. n = 22196 0.65 ≈43 Let T = 196, L = 0.65. The number of vibrations per second is approximately 43. S Now Try Exercise 43. CONCEPT PREVIEWFill in the blank(s) to correctly complete each sentence, or answer the question as appropriate. 1. For k 70, if y varies directly as x, then when x increases, y _______, and when x decreases, y _______. 2. For k 70, if y varies inversely as x, then when x increases, y _______, and when x decreases, y _______. 3. In the equation y = 6x, y varies directly as x. When x = 5, y = 30. What is the value of y when x = 10? 4. In the equation y = 12 x , y varies inversely as x. When x = 3, y = 4. What is the value of y when x = 6? Solve each problem. See Examples 1–4. 7. If y varies directly as x, and y = 20 when x = 4, find y when x = -6. 8. If y varies directly as x, and y = 9 when x = 30, find y when x = 40. 9. If m varies jointly as x and y, and m= 10 when x = 2 and y = 14, find m when x = 21 and y = 8. 10. If m varies jointly as z and p, and m= 10 when z = 2 and p = 7.5, find m when z = 6 and p = 9. 11. If y varies inversely as x, and y = 10 when x = 3, find y when x = 20. 12. If y varies inversely as x, and y = 20 when x = 1 4, find y when x = 15. 13. Suppose r varies directly as the square of m, and inversely as s. If r = 12 when m= 6 and s = 4, find r when m= 6 and s = 20. 14. Suppose p varies directly as the square of z, and inversely as r. If p = 32 5 when z = 4 and r = 10, find p when z = 3 and r = 32. 15. Let a be directly proportional to m and n2, and inversely proportional to y3. If a = 9 when m= 4, n = 9, and y = 3, find a when m= 6, n = 2, and y = 5. 16. Let y vary directly as x, and inversely as m2 and r2. If y = 5 3 when x = 1, m= 2, and r = 3, find y when x = 3, m= 1, and r = 8. 3.7 Exercises CONCEPT PREVIEWUsing k as the constant of variation, write a variation equation for each situation. 5. h varies inversely as t. 6. M varies jointly as g and h.
RkJQdWJsaXNoZXIy NjM5ODQ=