Question

If y is directly proportional to the square root of x and y=22 when x=576, find y if x=331776. (Round off your answer to the nearest hundredth.)

Answer 1

We have the variable y, that is proportional to √x.

We can express as:

`y=k\cdot\sqrt[]{x}`

We know that y = 22 when x = 576.

Then, we can find the constant of proportionality k replacing y and x with the values:

`\begin{gathered} y=k\sqrt[]{x} \\ k=\frac{y}{\sqrt[]{x}} \\ k=\frac{22}{\sqrt[]{576}} \\ k=(22)/(24) \\ k=(11)/(12) \end{gathered}`

Knowing the value of k, we can calculate the value of y when x = 331776 as:

`\begin{gathered} y=(11)/(12)\sqrt[]{x} \\ y=(11)/(12)\sqrt[]{331776} \\ y=(11)/(12)\cdot576 \\ y=528 \end{gathered}`

Answer: y = 528