Question

Please assist me with this

Answer 1

Answer:

The answer is option A

Step-by-step explanation:

To find the value of x when y = 24, we must first find the relationship between them

$y \: \: \alpha \: \: \frac{k}{ \sqrt{x} }$

where k is the constant of proportionality

when

x = 16

y = 2

Substitute the values into the above formula and solve for k

That's

$2 = \frac{k}{ \sqrt{16} } \\ 2 = \frac{k}{4}$

Cross multiply we have the answer as

k = 8

So the formula for the variation is

$y = \frac{8}{ \sqrt{x} }$

Now when y = 24

We have

$24 = \frac{8}{ \sqrt{x} } \\ 24 \sqrt{x} = 8 \\ \sqrt{x} = \frac{8}{24} \\ \sqrt{x} = \frac{1}{3}$

Square both sides

$( { \sqrt{x} })^{2} = ( { \frac{1}{3} })^{2}$

We have the final answer as

$x = \frac{1}{9}$

Hope this helps you