Answer:
Concept:
Represent the statement below as
y varies inversely as the square root of x
![y\propto\frac{1}{\sqrt[]{x}}](https://img.qammunity.org/2023/formulas/mathematics/college/138ns13bhhqpm7duq5ac2bphdbfpuwl2fg.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/ndxjuom0wnbd53cpp67umlmef6d02nkl79.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/bquy2pewzr5znfjagf5f0ectk11qde23zd.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/college/ynba0olmhxc7v06n61efnba1jws6hhufqt.png)
Hence,
The final answer is
![\Rightarrow y=\frac{72}{\sqrt[]{x}}](https://img.qammunity.org/2023/formulas/mathematics/college/maugfvn075n0bbcyrh7kspwsxhpvoxc2sx.png)