Respuesta :
ANSWER
x = 12
EXPLANATION
If y varies inversely as the square of x, then it follows this rule:
[tex]y=\frac{a}{x^2}[/tex]To find a, we have to use the given point - x = 6 and y = 8 - and solve for a:
[tex]\begin{gathered} a=y\cdot x^2 \\ a=8\cdot6^2 \\ a=8\cdot36 \\ a=288 \end{gathered}[/tex]Then, the equation is:
[tex]y=\frac{288}{x^2}[/tex]Finally, we want to know the value of x when y = 2. Just replace y = 2 in the equation above and solve for x:
[tex]\begin{gathered} x=\sqrt{\frac{288}{y}} \\ x=\sqrt[]{\frac{288}{2}} \\ x=\sqrt[]{144} \\ x=12 \end{gathered}[/tex]