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  α  sqrtx`

∴  \[y = k\sqrt{x}\] , where k is constant of variation
When x = 16, y = 24.

∴ \[\ 24 = k \times \sqrt{16}\]

⇒ 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 \[y = 6\sqrt{x}\].