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.

Step-by-step explanation:

It is given that,

y is proportional to square root of x.

That implies,

`\begin{gathered} y\propto√(x) \\ \Rightarrow y=k√(x) \end{gathered}`

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

`\begin{gathered} -67=k(√(9)) \\ -67=k(3) \\ k=-(67)/(3) \end{gathered}`

That is,

`y=-(67)/(3)√(x)`

Then, for x=81,

`\begin{gathered} y=-(67)/(3)(√(81)) \\ =-(67)/(3)(9) \\ =-67*3 \\ =-201 \end{gathered}`

Hence, the value of y is -201.