Question

y varies directly as x and inversely as the square of z. y=48when x=100 and z= 5. Find y when x=3 and z=12

Answer 1

y = 0.25

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 = 48 when x = 100 and z = 5

k =
`(yz^2)/(x)` =
`(48(25))/(100)` = 12

y =
`(12x)/(z^2)` ← equation of variation

When x = 3 and z = 12, then

y =
`(12(3))/(144)` = 0.25