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If $y \propto \frac{1}{\sqrt{x}}$ and x = 16 when y = 2, f...

If $y \propto \frac{1}{\sqrt{x}}$ and x = 16 when y = 2, find x when y = 24

A.

$\frac{1}{9}$

B.

$\frac{1}{6}$

C.

$\frac{1}{3}$

D.

$\frac{2}{3}$

View answer & explanation

Correct answer is A

$y \propto \frac{1}{\sqrt{x}}$

$y = \frac{k}{\sqrt{x}}$

When x = 16, y = 2.

$2 = \frac{k}{\sqrt{16}} \implies 2 = \frac{k}{4}$

$k = 8$

$y = \frac{8}{\sqrt{x}}$

When y = 24,

$24 = \frac{8}{\sqrt{x}}$

$\sqrt{x} = \frac{8}{24} = \frac{1}{3}$

$\therefore x = (\frac{1}{3})^2$

$x = \frac{1}{9}$

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