# If y varies inversely as the square of x and y=5 when x=2.5, what is the value of Y when X=9?

Apr 4, 2016

$y = \frac{31.25}{81}$

#### Explanation:

As $y \propto \frac{1}{x} ^ 2$, we have $y = \frac{k}{x} ^ 2$ or ${x}^{2} y = k$.

As when $x = 2.5$, $y = 5$,

${2.5}^{2} \times 5 = k$ or

$k = 6.25 \times 5 = 31.25$

Therefore ${x}^{2} y = 31.25$

Hence when $x = 9$, ${9}^{2} \times y = 31.25$

and $y = \frac{31.25}{81}$