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

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=(k)/(8) \\ \text{cross multiply,we will have} \\ k=9*8 \\ 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}}`