we know that
If y varies inversely as the square of x,
then
the equation that represent this situation is equal to
[tex]y=\frac{k}{x^2}[/tex]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
[tex]\begin{gathered} 9=\frac{k}{12^2} \\ k=9(144) \\ k=1,296 \end{gathered}[/tex]Find the value of y when the value of x=15
substitute in the equation
[tex]y=\frac{1,296}{x^2}[/tex][tex]\begin{gathered} y=\frac{1,296}{15^2} \\ y=5.76 \end{gathered}[/tex]therefore
the answer is
y=5.76
