Question

If y varies directly as the square if x. If y=27 when x=3, find x when y=81?

Answer 1

x = 3
`√(3)`

Explanation:

Given y varies directly as x², then the equation relating them is

y = kx² ← k is the constant of variation

To find k use the condition y = 27 when x = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

y = 3x² ← equation of variation

When y = 81, then

81 = 3x² ( divide both sides by 3 )

27 = x² ( take the square root of both sides )

x =
`√(27)` =
`√(9(3))` = 3
`√(3)`