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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

A) 72

B) 100

C) 90

D) 200

E) 125

### 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

## 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