# If y varies directly as x and inversely as z^2, and y=3 when x=2 and z=4, what is the value of x when y=9 and z=4?

Feb 19, 2017

$\frac{3}{2}$

#### Explanation:

$y = k \frac{x}{z} ^ 2$ and (2, 3, 4) lies on this surface, So,

$k = \frac{\left(3\right) \left({4}^{2}\right)}{2} = 24$. The equation to the surface is

$x = \frac{1}{24} y {z}^{2}$ and

$x = \frac{1}{24} \left(9\right) \left(4\right) = \frac{3}{2}$, when $y = 9 \mathmr{and} z = 4$.