Question

if y varies direrectly as x and inversely as the square of z. y=52 when x=16 and z=2. find y when x=18 and z=3.

Answer 1

y = 26

Explanation:

Given y varies directly as x and inversely as the square of z then the equation relating them is

y =
`(kx)/(z^2)` ← k is the constant of variation

To find k use the condition y = 52, x = 16, z = 2

k =
`(yz^2)/(x)` =
`(52(4))/(16)` = 13

y =
`(13x)/(z^2)` ← equation of variation

When x = 18 and z = 3, then

y =
`(13(18))/(9)` = 26