Question

Correct Suppose that y varies inversely as the square of x, and that y = 9 when x = 12. What is y when x = 15? Round your answer to two decimal places if necessary.

Answer 1

we know that

If y varies inversely as the square of x,

then

the equation that represent this situation is equal to

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

we have

y=9 when x=12

Find the value of the constant of proportionality k

substitute the value of x and the value of y in the equation above

`\begin{gathered} 9=(k)/(12^2) \\ k=9(144) \\ k=1,296 \end{gathered}`

Find the value of y when the value of x=15

substitute in the equation

`y=(1,296)/(x^2)`
`\begin{gathered} y=(1,296)/(15^2) \\ y=5.76 \end{gathered}`

therefore

the answer is

y=5.76