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

Answer:

The relation between x and y is

$y=\frac13 x^2$

Step-by-step 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

$y=rx^2$

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

$\Rightarrow 27 = r.81$

$\Rightarrow r=\frac{27}{81}$

$\Rightarrow r=\frac{1}{3}$

The relation between x and y is

$y=\frac13 x^2$