Question

Find constant of variation and write equation of variation for the example given below.

x ∝ \[\frac{1}{\sqrt{y}}\] ; if x = 15 then y = 9

Answer 1

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

\[\therefore x = \frac{k}{\sqrt{y}}\], where k is constant of variation

When x = 15, y = 9.

\[\therefore 15 = \frac{k}{\sqrt{9}}\]

\[ \Rightarrow 15 = \frac{k}{3}\]

\[ \Rightarrow k = 15 \times 3 = 45\]

So, the equation of variation is \[x = \frac{45}{\sqrt{y}}\] or \[x\sqrt{y} = 45\].