Question

Z varies directly as x^2. If z = 18 when x = 3, find z when x = 4.

Answer 1

Given

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

To find z, when x = 4.

Step-by-step explanation:

It is given that,

z varies directly as x².

That implies,

`z=kx^2\text{ \_\_\_\_\_\_\lparen1\rparen}`

Since z=18, when x=3.

Then,

`\begin{gathered} 18=k(3)^2 \\ 9k=18 \\ k=(18)/(9) \\ k=2 \end{gathered}`

Therefore, (1) becomes,

`z=2x^2`

Also, for x=4,

`\begin{gathered} z=2(4)^2 \\ z=2(16) \\ z=32 \end{gathered}`

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