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If p is inversely proportional to the square of q, and p is 8 when q is 3, determine p when q is

equal to 2.

User Jaylene
by
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1 Answer

1 vote

Answer:

p = 18

Explanation:

General inverse variation equation:

The general inverse variation equation is given by:

y = kx, where

  • y varies inversely as x,
  • and k is the constant of proportionality.

Since p is inversely proportional to the square of q, we can represent this with the equation p = k/q^2

Finding k (the constant of proportionality):

We can first find k by substituting 8 for p and 3 for q in p = k/q^2:

8 = k/(3^2)

(8 = k/9) * 9

72 = k

Thus, the constant of proportionality (k) is 72.

This means the equation we'll use for the last step is given by:

p = 72/q^2

Finding p when q is 2:

Now we can find p when q is 2 by substituting 2 for q in p = 72/q^2:

p = 72/(2^2)

p = 72/4

p = 18

Thus, p = 18 when q = 2.

User Chayim
by
8.4k points

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