Question

y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.

Answer 1

It is given that y varies directly as square root of x i.e. $y\propto \sqrt{x}$.

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

When x = 16, y = 24.

$\therefore 24=k\times \sqrt{16}$

⇒ 24 = 4k

⇒ k = 6

So, the equation of variation is $y=6\sqrt{x}$.

Thus, the constant of variation is 6 and the equation of variation is $y=6\sqrt{x}$.