Question

x ∝ $\frac{1}{\sqrt{y}}$ and when x = 40 then y = 16. If x = 10, find y.

Answer 1

It given that $x\propto \frac{1}{\sqrt{y}}$.

∴ $x=\frac{k}{\sqrt{y}}$, where k is constant of variation

⇒ $x\times \sqrt{y}=k$

When x = 40, y = 16.

∴ $k=40\times \sqrt{16}=40\times 4=160$

So, the equation of variation is $x\sqrt{y}=160$.

When x = 10,

$$\begin{gathered} 10\sqrt{y}=160 \\ \Rightarrow \sqrt{y}=16 \\ \Rightarrow y={16}^2=256 \end{gathered}$$