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Math Asked by a SnapAndSolve user · about 18 hours ago

Choose the correct answer. If y varies directly as x and inversely as z, and y = 25 when x = 5 and z = 3,...

3) Choose the correct answer.
If y varies directly as x and inversely as z, and y = 25 when x = 5 and z = 3, find y when x = 10 and z = 25.
4) Choose the correct answer.
If y varies jointly as x and z, and y = 8 when x = 12 and z = 4, find z when y = 5 and x = 7.

Answer

  1. To solve this, use the formula for direct and inverse variation: y = k * (x/z). First, find k using the given values: 25 = k * (5/3). So, k = 25 * 3 / 5 = 15. Now, find y when x = 10 and z = 25: y = 15 * (10/25) = 6. The correct answer is 6.

  2. For joint variation, use the formula: y = k * x * z. First, find k using the given values: 8 = k * 12 * 4. So, k = 8 / 48 = 1/6. Now, find z when y = 5 and x = 7: 5 = (1/6) * 7 * z. Solving for z gives z = 5 * 6 / 7 = 30/7 = 4 2/7. The correct answer is 4 2/7.

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