Question

y ∝ 1 √ x If y = 4 when x = 64 find, y when x = 16

Answer 1

Given:

$y\propto \dfrac{1}{\sqrt{x}}$

y = 4 when x = 64

To find:

The value of y when x=16.

Solution:

We have,

$y\propto \dfrac{1}{\sqrt{x}}$

$y=\dfrac{k}{\sqrt{x}}$           ...(i)

Where, k is the constant of proportionality.

We have, y = 4 when x = 64.

$4=\dfrac{k}{\sqrt{64}}$

$4=\dfrac{k}{8}$

$4\times 8=k$

$32=k$

Putting k=32 in (i), we get

$y=\dfrac{32}{\sqrt{x}}$

Putting x=16, we get

$y=\dfrac{32}{\sqrt{16}}$

$y=\dfrac{32}{4}$

$y=8$

Therefore, the value of y is 8 when x=16.