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If pp is inversely proportional to the square of qq, and pp is 27 when qq is 5, determine pp when qq is equal to 3.

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Final answer:

To find pp when qq is 3, we use the constant of inverse proportionality we've calculated from the given values, leading to pp being 75.

Step-by-step explanation:

The student's question involves a concept in mathematics known as inverse proportionality. When we say that pp is inversely proportional to the square of qq, we can express this relationship with the equation pp = k / qq^2, where k is a constant.

Given that pp equals 27 when qq is 5, we can find the constant using this information: 27 = k / 5^2, which simplifies to k = 27 * 25. To determine pp when qq is 3, we use the constant we've found and the inverse proportionality formula: pp = k / 3^2 = (27 * 25) / 9. Calculating this gives us pp = 75 when qq is 3.

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