# Y is inversely proportional to the square of x when y =50, x=2, how do you find an equation connecting y and x?

Aug 1, 2015

$2 {x}^{2} y = 25$
$\textcolor{w h i t e}{\text{XXXX}}$(or some variation of that)

#### Explanation:

If $y$ is inversely proportional to the square of $x$, then
$\textcolor{w h i t e}{\text{XXXX}}$$y = \frac{c}{{x}^{2}}$$\textcolor{w h i t e}{\text{XXXX}}$for some constant $c$

We are told that when $y = 50$ then $x = 2$

So the proportional equation becomes
$\textcolor{w h i t e}{\text{XXXX}}$$50 = \frac{c}{{2}^{2}}$

$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow c = \frac{25}{2}$

So
$\textcolor{w h i t e}{\text{XXXX}}$$y = \frac{\frac{25}{2}}{x} ^ 2$
which could also be written as
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} y = \frac{25}{2}$
or
$\textcolor{w h i t e}{\text{XXXX}}$$2 {x}^{2} y = 25$