Question

If y varies directly as the square of x. When x = 2, y = 20, how do you find y when x = 4?

Answer 1

`y=80`

Explanation:

Note - `color(blue)"the square of x is expressed as " x^2`

`rArrypropx^2`

Make into an equation by introducing k, the constant of variation.

`rArry=kxxx^2=kx^2`

To find k, use the condition given x = 2 when y = 20

`y=kx^2rArrk=y/x^2=20/4=5`

`"Thus " color(red)(bar(ul(|color(white)(2/2)color(black)(y=5x^2)color(white)(2/2)|)))`

`x=4toy=5xx4^2=80`