Question

Z varies directly with x and inversely with y2.

When x = 2 and y = 5, z = 8.
What is the value of z when x = 4 and y = 9?

Answer 1

The value of z is 4.938

Solution:

Given that,

z varies directly with x and inversely with
`y^2`

Which means,

`z \propto (x)/(y^2)\\\\z = k * (x)/(y^2)`

Where, "k" is constant of proportionality

Substitute x = 2 and y = 5, z = 8 in above

`8 = k * (2)/(5^2)\\\\8 = (2k)/(25)\\\\k = 25 * 4\\\\k = 100`

What is the value of z when x = 4 and y = 9?

Substitute k = 100 , x = 4 and y = 9 in above

`z = 100 * (4)/(9^2)\\\\z = 100 * (4)/(81)\\\\z = 4.938`

Thus value of z is 4.938