Question

'y varies inversely as the square root of x and y = 5 when x = 36. Find the value of x when y = 10

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ y\alpha \frac{1}{\sqrt{x}} \\ \Rightarrow y\sqrt{x}=k\left(k\mathrm{is}\mathrm{a}\mathrm{constant}.\right) \\ \mathrm{We}\mathrm{have}: \\ 5\times \sqrt{36}=k\left(\because y=5\mathrm{when}x=36\right) \\ \Rightarrow k=5\times 6=30 \\ \mathrm{Equation}\mathrm{of}\mathrm{variation}: \\ y\sqrt{x}=30 \\ \mathrm{Also}, \\ 10\times \sqrt{x}=30\left(\because y=10\right) \\ \Rightarrow \sqrt{x}=\frac{30}{10}=3 \\ \Rightarrow x=9 \end{gathered}$$