# If y varies inversely as x^2 and If y = 2 when x = 6, what is y when x = 3?

May 20, 2016

$y = \textcolor{g r e e n}{8}$ when $x = 3$

#### Explanation:

If $y$ varies inversely as ${x}^{2}$
then
$\textcolor{w h i t e}{\text{XXX}} y \cdot {x}^{2} = c$ for some constant $c$

Given that $\left(x , y\right) = \left(6 , 2\right)$ is a solution to this inverse relation:
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 2 \cdot {6}^{2} = c$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow c = 72$

So the complete relation is
$\textcolor{w h i t e}{\text{XXX}} y \cdot {x}^{2} = 72$
or
$\textcolor{w h i t e}{\text{XXX}} y = \frac{72}{{x}^{2}}$ provided $x \ne 0$

When $x = 3$
$\textcolor{w h i t e}{\text{XXX}} y = \frac{72}{{3}^{2}} = 8$