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.