# If y varies inversely as X^2 and X = 9 when y = 64, how do you find the value of y when x = 4?

May 2, 2017

$y = 324$

#### Explanation:

$\text{varies inversely means " 1/"variable}$

$\Rightarrow \text{the initial statement is } y \propto \frac{1}{{x}^{2}}$

$\text{to convert to an equation, multiply by k, }$
$\text{the constant of variation}$

$\Rightarrow y = k \times \frac{1}{x} ^ 2 = \frac{k}{x} ^ 2$

$\text{to find k, use the condition given}$

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

$\text{given " x=9" when } y = 64$

$\Rightarrow k = {9}^{2} \times 64 = 5184$

$\Rightarrow \text{ equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{5184}{x} ^ 2} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when x = 4 then}$

$y = \frac{5184}{16} = 324$