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Choose the correct answer. If y varies jointly as x and z, and y = 30 when x = 10 and z = 8, find y when x...

5) Choose the correct answer.
If y varies jointly as x and z, and y = 30 when x = 10 and z = 8, find y when x = 15 and z = 20.
20
112 1/2
120
75
6) Choose the correct answer.
Wind resistance varies jointly as an object's surface area and velocity. If an object traveling at 60 miles per hour with a surface area of 15 square feet experiences a wind resistance of 200 Newtons, how fast must a car with 45 square feet of surface area travel in order to experience a wind resistance of 250 Newtons?
25 miles per hour
12 miles per hour

Answer

  1. To solve for y when x = 15 and z = 20, we use the joint variation formula: y = kxz. Given y = 30 when x = 10 and z = 8, we find k: 30 = k * 10 * 8, so k = 30 / 80 = 3/8. Now, find y when x = 15 and z = 20: y = (3/8) * 15 * 20 = 112.5. The correct answer is 112 1/2.

  2. Let W = k * A * v, where W is wind resistance, A is surface area, and v is velocity. Given W = 200, A = 15, v = 60, find k: 200 = k * 15 * 60, so k = 200 / 900 = 2/9. Now, find v when W = 250 and A = 45: 250 = (2/9) * 45 * v, so v = 250 / 10 = 25. The correct answer is 25 miles per hour.

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