Question

z varies directly as x2 and inversely as y2. If z=128 when x=8 and y=9, find z if x=7 and y=4. (Round off your answer to the nearest hundredth.)

Answer 1

Answer:

z = 496.13

Step-by-step explanation:

Let the statement be written mathematically as follows:

`z\propto x^2\propto(1)/(y^2)`

So that:

`z=(kx^2)/(y^2)`

Where k is constant.

For z = 128, x = 8, and y = 9, we have:

`\begin{gathered} 128=(k*8^2)/(9^2) \\ \\ k=\frac{128*9^2}{8^2^{}}=162 \end{gathered}`

Using this value of k, we write the formula as:

`z=(162x^2)/(y^2)`

Now for x = 7, y = 4, we need to find z.

`z=(162*7^2)/(4^2)=496.13`