Question

Please assist me with this

Answer 1

The answer is option A

Explanation:

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

`y \: \: \alpha \: \: (k)/( √(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 = (k)/( √(16) ) \\ 2 = (k)/(4)`

Cross multiply we have the answer as

k = 8

So the formula for the variation is

`y = (8)/( √(x) )`

Now when y = 24

We have

`24 = (8)/( √(x) ) \\ 24 √(x) = 8 \\ √(x) = (8)/(24) \\ √(x) = (1)/(3)`

Square both sides

`( { √(x) })^(2) = ( { (1)/(3) })^(2)`

We have the final answer as

`x = (1)/(9)`

Hope this helps you