Question

Suppose that y is inversely proportional to the square root of x, and that y=45 when x=64. What
is y when x=25?

Answer 1

y is 28.125 when x = 25

Solution:

Given that,

y is inversely proportional to the square root of x

Therefore,

$y \propto \sqrt{x}\\\\y = c \sqrt{x}$ ----------- eqn 1

Where, c is constant of propotionality

y = 45 when x = 64

Substitute in eqn 1

$45 = c \times \sqrt{64}\\\\45 = c \times 8\\\\c = 5.625$

What  is y when x = 25?

Substitute x = 25 and c = 5.625 in eqn 1

$y = 5.625 \times \sqrt{25}\\\\y = 5.625 \times 5\\\\y = 28.125$

Thus y is 28.125 when x = 25