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:

$\begin{gathered} y=k\sqrt[]{x} \\ k=\frac{y}{\sqrt[]{x}} \\ k=\frac{22}{\sqrt[]{576}} \\ k=\frac{22}{24} \\ k=\frac{11}{12} \end{gathered}$

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

$\begin{gathered} y=\frac{11}{12}\sqrt[]{x} \\ y=\frac{11}{12}\sqrt[]{331776} \\ y=\frac{11}{12}\cdot576 \\ y=528 \end{gathered}$

Answer: y = 528