Question

If $y$ varies inversely as the square of $x$, and $x=4$ when $y=3$, then value of $y$, when $x=2$ is .

• A. $12$
• B. $8$
• C. $6$

Answer 1

The correct option is A $12$

Given that $y\propto \frac{1}{x^2}\Rightarrow y=\frac{k}{x^2}$

Given: At $y=3,$ the value of $x=4$

$\Rightarrow 3=\frac{k}{4^2}\Rightarrow k=48$

At $x=2$

$\Rightarrow y=\frac{48}{2^2}\Rightarrow y=12$