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If y varies directly as $\sqrt{n}$ and y = 4 when n = 4, f...

If y varies directly as $\sqrt{n}$ and y = 4 when n = 4, find y when n = 1 $\frac{7}{9}$

A.

$\sqrt{17}$

B.

$\frac{4}{3}$

C.

$\frac{8}{3}$

D.

$\frac{2}{3}$

View answer & explanation

Correct answer is C

y $\propto \sqrt{n}$

y = k $\sqrt{n}$

when y = 4, n = 4
4 = k $\sqrt{4}$

4 = 2k

k = 2

Therefore,

y = 2 $\sqrt{n}$

y = 2 $\sqrt{\frac{16}{9}}$

y = 2 $(\frac{4}{3})$

y = $\frac{8}{3}$

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