Question

If y varies directly as x to the power of 2 and y=6 when x=6, find the constant of variation

Answer 1

y varies directly as xto the power of 2 means

`(y)/(x^2)=k`

where k is constant of variation

when y=6 and x=6, find k

subsitute

`(6)/(6^2)=k`

`(6)/(36)=k`

`\frac{1}[6}=k`

the constant of variation is
`(1)/(6)`

Answer 2

y = kx²

y = 6 when x = 6

6 = k.6²

6 = 36k

k = 6/36

k = 1/6

The constant variation is 1/6