Question

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

Answer 1

$y=25$
Explanation:
the initial statement is $y\propto \frac{1}{x^2}$
to convert to an equation, multiply by $k$, the constant of variation
$\Rightarrow y=k\times \frac{1}{x^2}=\frac{k}{x^2}$
to find $k$ use the given condition
$y=4$ when $x=5$
$y=\frac{k}{x^2}\Rightarrow k=x^{2}y=5^2\times 4=100$
the equation is $y=\frac{100}{x^2}$
when $x=2$
$\Rightarrow y=\frac{100}{2^2}=\frac{100}{4}=25$