If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.

A.

12

B.

8

C.

9

D.

16

Correct answer is C

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

\(\implies p = \frac{k}{\sqrt{q}}\)

when p = 3, q = 16.

\(3 = \frac{k}{\sqrt{16}}\)

\(k = 3 \times 4 = 12\)

\(\therefore p = \frac{12}{\sqrt{q}}\)

when p = 4,

\(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\)

\(\sqrt{q} = 3 \implies q = 3^2 \)

\(q = 9\)