Question

For the statement, find the constant of variation and the variation equation.

y varies directly as the cube of x; y = 4 when x = 2

Answer 1

see explanation

Explanation:

given y varies directly as x³ then the equation relating them is

y = kx³ ← k is the constant of variation

to find k use the condition y = 4 when x = 2 , then

4 = k × 2³ = 8k ( divide both sides by 8 )

`(4)/(8)` = k , that is

k =
`(1)/(2)`

y =
`(1)/(2)` x³ ← equation of variation