Question

y varies directly as x and inversely as the square of z. y=20 when x=50 and z=5. Find y when x=3 and z=6.

Answer 1

y =
`(5)/(6)`

Explanation:

Given that 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 = 20 when x = 50 and z = 5, then

k =
`(yz^2)/(x)` =
`(x20(25))/(50)` = 10, thus

y =
`(10x)/(z^(2) )` ← equation of variation

Given x = 3 and z = 6, then

y =
`(10(3))/(36)` =
`(30)/(36)` =
`(5)/(6)`