Question

When y varies inversely as the square of x, x = 6 and y = 8. What is x when y = 2?

Answer 1

x = 12

Step-by-step explanation

If y varies inversely as the square of x, then it follows this rule:

`y=(a)/(x^2)`

To find a, we have to use the given point - x = 6 and y = 8 - and solve for a:

`\begin{gathered} a=y\cdot x^2 \\ a=8\cdot6^2 \\ a=8\cdot36 \\ a=288 \end{gathered}`

Then, the equation is:

`y=(288)/(x^2)`

Finally, we want to know the value of x when y = 2. Just replace y = 2 in the equation above and solve for x:

`\begin{gathered} x=\sqrt{(288)/(y)} \\ x=\sqrt[]{(288)/(2)} \\ x=\sqrt[]{144} \\ x=12 \end{gathered}`