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 wh…

Question

asked Nov 1, 2021 24.3k views

1 Answer

AGrush · Answer 1 · 2021-11-07T20:21:52+0000

Answer:

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

$y=\frac13 x^2$