Question

Write an equation describing the relationship of the given variables Y varies inversely as the square of x and when x=3, y=4

Answer 1

ANSWER

$y=\frac{36}{x^2}$

EXPLANATION

We want to find the equation that describes the relationship of the given variables.

y varies inversely as the square of x. This implies that:

$\begin{gathered} y\propto\frac{1}{x^2} \\ \Rightarrow y=\frac{k}{x^2} \end{gathered}$

where k = constant of proportionality

When x = 3, y = 4. Substitute that into the equation above and solve for k:

$\begin{gathered} 4=\frac{k}{3^2} \\ 4=\frac{k}{9} \\ \Rightarrow k=4\cdot9 \\ k=36 \end{gathered}$

Hence, the equation that represents the relationship of the variables is:

$y=\frac{36}{x^2}$

That is the answer.