Question

on232428 29 30 312725 2632 33Y is inversely proportional to the square root of x. True or False: If Y=6 when x = 81, then Y= 9, when x is 36.

Answer 1

Solution

Step 1

Y is inversely proportional to the square root of x.

$y\text{ = }\frac{k}{\sqrt{x}}$

Step 2

Find the value of k if Y=6 when x = 81.

$\begin{gathered} 6\text{ = }\frac{k}{\sqrt{81}} \\ \\ 6=\text{ }\frac{k}{9} \\ \\ k\text{ = 6}\times9 \\ \\ k\text{ = 54} \end{gathered}$

Step 3

Let find y when x = 36

$\begin{gathered} y\text{ = }\frac{k}{\sqrt{x}} \\ \\ y\text{ = }\frac{54}{\sqrt{36}} \\ \\ y\text{ = }\frac{54}{6} \\ \\ y\text{ = 9} \end{gathered}$

Final answer

True