Question

The value of y varies directly as the square of x and y=27 when x=9. Find the equation represents this relationship. Report the proportionality constant as a reduced fraction when necessary.

Answer 1

The relation between x and y is

`y=\frac13 x^2`

Explanation:

Given that,

The value of y varies directly as the square of x.

`y\propto x^2`

`\Rightarrow y=rx^2`

where r is constant of proportional.

Given that,

y= 27 and x=9

Plug y= 27 and x=9 in above relation

`y=rx^2`

`\therefore 27=r(9)^2`

`\Rightarrow 27 = r.81`

`\Rightarrow r=(27)/(81)`

`\Rightarrow r=(1)/(3)`

The relation between x and y is

`y=\frac13 x^2`