Question

Write an equation describing the relationship of the given variables y varies inversely as the square root of x and when x=64, y=9

Answer 1

Answer:

Concept:

Represent the statement below as

y varies inversely as the square root of x

$y\propto\frac{1}{\sqrt[]{x}}$

Note:

When the proportionality sign is changed to an equal to sign, a constant k is introduced

By applying this, we will have

$\begin{gathered} y\propto\frac{1}{\sqrt[]{x}} \\ y=\frac{k}{\sqrt[]{x}}----(1) \end{gathered}$

Step 2:

Substitute the values x=64 and y =9 in equation (1) above

$\begin{gathered} y=\frac{k}{\sqrt[]{x}}----(1) \\ 9=\frac{k}{\sqrt[]{64}} \\ 9=\frac{k}{8} \\ \text{cross multiply,we will have} \\ k=9\times8 \\ k=72 \end{gathered}$

Step 3:

Re place the value of k=72 in equation (1)

$\begin{gathered} y=\frac{k}{\sqrt[]{x}} \\ y=\frac{72}{\sqrt[]{x}} \end{gathered}$

Hence,

The final answer is

$\Rightarrow y=\frac{72}{\sqrt[]{x}}$