Question

If y is directly proportional to the square root of x and y = -67 when x = 9, find y if x = 81. (Round off your answer to the nearesthundredth.)

Answer 1

Given

y is directly proportional to square root of x.

And, y=-67, when x=9.

To find: y, if x=81.

Explanation:

It is given that,

y is proportional to square root of x.

That implies,

$\begin{gathered} y\propto\sqrt{x} \\ \Rightarrow y=k\sqrt{x} \end{gathered}$

Then, for x=9 and y=-67,

$\begin{gathered} -67=k(\sqrt{9}) \\ -67=k(3) \\ k=-\frac{67}{3} \end{gathered}$

That is,

$y=-\frac{67}{3}\sqrt{x}$

Then, for x=81,

$\begin{gathered} y=-\frac{67}{3}(\sqrt{81}) \\ =-\frac{67}{3}(9) \\ =-67\times3 \\ =-201 \end{gathered}$

Hence, the value of y is -201.