Question

If Z varies directly with x and inversely with y^2 when x=2 and y=5, z=8 what is the value of z when x=4 and y=9?

Answer 1

`z=4.9383`

Explanation:

Direct Variation is `y= kx`
Inverse Variation is `y = k/y`

If `z` varies directly to `x` the equation would be `z=kx`

If `z` varies inversely to `y^2` the equation would be `z=k/y^2`

Combining these two equations we get `z=(kx)/y^2`

We use the first set of values to solve for the constant of variation `k`

`x=2`
`y=5`
`z=8`

`8=(2k)/5^2`

`8=(2k)/25`

`8(25)=(2k)/cancel(25)cancel(25)`

`200=(2k)`

`200/2=(cancel2k)/cancel2`

`100 = k`

Now use the constant `k` with the second values to solve for `z`

`x=4`
`y=9`
`z=?`
`k=100`

`z=((100)(4))/9^2`

`z = 400/81`

`z=4.9383`