# If y varies inversely as the square of x and y=4 when x=5, what is y when x is 2?

Jun 6, 2017

#### Answer:

$y = 25$

#### Explanation:

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

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

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

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

$y = 4 \text{ when } x = 5$

$y = \frac{k}{x} ^ 2 \Rightarrow k = {x}^{2} y = {5}^{2} \times 4 = 100$

$\text{the equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{100}{{x}^{2}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } x = 2$

$\Rightarrow y = \frac{100}{{2}^{2}} = \frac{100}{4} = 25$