# If y varies inversely as x^2 and y = 10 when x=2 , find y when x = 0.5?

Jul 2, 2016

#### Answer:

$y = 160$

#### Explanation:

Write it as an inverse proportion first

$y \propto \frac{1}{x} ^ 2$

Change into an equation by multiplying by a constant.

$y = \frac{k}{x} ^ 2$

Find the value of the constant

$k = {x}^{2} \times y = {2}^{2} \times 10 = 40$

Use the constant in the equation

$y = \frac{40}{x} ^ 2$

Solve for y when x = 0.5

$y = \frac{40}{0.5} ^ 2 = 160$