# Suppose that y varies directly as the square root of x, and the y=43 when x=324. What is y when x=172?

Apr 9, 2018

$y = \frac{43 \sqrt{43}}{9}$

#### Explanation:

y prop sqrt x or y = k *sqrt x ; k  is variation constant.

$y = 43 , x = 324 \therefore y = k \cdot \sqrt{x} \mathmr{and} 43 = k \cdot \sqrt{324}$ or

$43 = k \cdot 18 \therefore k = \frac{43}{18} \therefore$ The variation equation is

y = 43/18 * sqrt x ; x=172 , y= ?

$y = \frac{43}{18} \cdot \sqrt{172} = \frac{43}{18} \cdot 2 \sqrt{43}$ or

$y = \frac{43 \sqrt{43}}{9}$ [ Ans]