Answer :

Given

z varies directly as x². If z = 18 when x = 3.

To find z, when x = 4.

Explanation:

It is given that,

z varies directly as x².

That implies,

[tex]z=kx^2\text{ \_\_\_\_\_\_\lparen1\rparen}[/tex]

Since z=18, when x=3.

Then,

[tex]\begin{gathered} 18=k(3)^2 \\ 9k=18 \\ k=\frac{18}{9} \\ k=2 \end{gathered}[/tex]

Therefore, (1) becomes,

[tex]z=2x^2[/tex]

Also, for x=4,

[tex]\begin{gathered} z=2(4)^2 \\ z=2(16) \\ z=32 \end{gathered}[/tex]

Hence, the value of z is 32 when x=4.