Question

Suppose that y varies inversely as the square of x, and that y = 8 when x = 4. What is y when x = 3? Round your answer to two decimal places if necessary.

Answer 1

If y varies inversely as the square of x you can say that:

`x^2y=k`

Where k represents a constant.

For x=4 and y=8, then

`\begin{gathered} (4)^28=k \\ k=128 \end{gathered}`

Then for x=3

`\begin{gathered} x^2y=k \\ y=(k)/(x^2) \\ y=(128)/((3)^2) \\ y=(128)/(9) \\ y=14.2 \end{gathered}`