Answer :
We know that y varies directly as x². This can be expressed as:
[tex]y=k\cdot x^2[/tex]where k is the constant of proportionality.
We know that y = 290 when x = 12.
We can find the value of k replacing x and y with the values:
[tex]\begin{gathered} y=k\cdot x^2 \\ k=\frac{y}{x^2} \\ k=\frac{290}{12^2} \\ k=\frac{290}{144} \\ k=\frac{145}{72} \end{gathered}[/tex]We then can calculate the value of y when x = 18 as:
[tex]\begin{gathered} y=\frac{145}{72}x^2 \\ y=\frac{145}{72}\cdot(18^2) \\ y=\frac{145}{72}\cdot324 \\ y=652.5 \end{gathered}[/tex]Answer: y = 652.5