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p varies directly as the square of q and inversely as r. If p = 36, when q = 36,...


Question

p varies directly as the square of q and inversely as r. If p = 36, when q = 36, when q = 3 and r = 4, find p when q = 5 and r = 2

Options

A) 72

B) 100

C) 90

D) 200

E) 125

The correct answer is D.

Explanation:

P \(\alpha\) \(\frac{q^2}{r}\)
P = \(\frac{kq^2}{r}\)
k = \(\frac{pr}{q^2}\)
= \(\frac{36 x 4}{(3)^2}\)
p = \(\frac{16q^2}{r}\)
= \(\frac{16 \times 25}{2}\)
= 200

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Dicussion (1)

  • P \(\alpha\) \(\frac{q^2}{r}\)
    P = \(\frac{kq^2}{r}\)
    k = \(\frac{pr}{q^2}\)
    = \(\frac{36 x 4}{(3)^2}\)
    p = \(\frac{16q^2}{r}\)
    = \(\frac{16 \times 25}{2}\)
    = 200