Question

Suppose that $y$ varies inversely with the square of $x$, and $y=50$ when $x=4$. Find $y$ when $x=5$

Answer 1

The statement " $y$ varies inversely as $x$ means that when $x$ increases, $y$ decreases by the same factor. In other words, the expression $xy$ is constant:

$xy=k$

where $k$ is the constant of variation.

Here, it is given that $y$varies inversely with the square of $x$ and $y=50$ when $x=4$, therefore,

$x^{2}y=k\Rightarrow {\left(4\right)}^2\times 50=k\Rightarrow k=16\times 2500\Rightarrow k=40000$

Thus, the general equation is $x^{2}y=40000$.

Since $x=5$, therefore,

$x^{2}y=40000\Rightarrow {\left(5\right)}^{2}y=40000\Rightarrow 25y=40000\Rightarrow y=\frac{40000}{25}=1600$

Hence, $y=1600$ when $x=5$.