Given that p varies as the square of q and q varies inversely as the square root of r. How does p vary with r?

A.

p varies as the square of r

B.

p varies as the square root of r

C.

p varies inversely as the square of r

D.

p varies inversely as r

Correct answer is D

\(p \propto q^2\)

\(q\propto\frac{1}{\sqrt{r}}\)

\(p = kq^2\)

\(q = \frac{c}{\sqrt{r}}\)

where c and k are constants.

\(q^2 = \frac{c^2}{r}\)

\(p = \frac{kc^2}{r}\)

If k and c are constants, then kc\(^2\) is also a constant, say z.

\(p = \frac{z}{r}\)

p varies inversely as r.