Question

`x ∝ 1/(sqrty) ` and when x = 40 then y = 16. If x = 10, find y.

Answer 1

It given that `x  α  1/sqrty`

`therefore x  = k/sqrty`, 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,

\[10\sqrt{y} = 160\]

\[ \Rightarrow \sqrt{y} = 16\]

\[ \Rightarrow y =  {16}^2  = 256\]