Question

Suppose z varies directly with x and inversely with the square of y. If z = 16 when x = 4 and y = 1 , what is z when x = 8 and y = 9 ?

Answer 1

z = 3.6

Explanation:

Given that,

z varies directly with x and inversely with the square of y. We can write it as :

`z\propto (x)/(y)\\\\z=(kx)/(y)`

Where

k is constant

Put z = 16 when x = 4 and y = 1

`16=(k* 4)/(1)\\\\k=4`

Now put k = 4, x = 8 and y = 9

`z=(4* 8)/(9)\\\\z=3.6`

So, the value of z is equal to 3.6.