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
[tex]y \: \: \alpha \: \: \frac{k}{ \sqrt{x} } [/tex]
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
[tex]2 = \frac{k}{ \sqrt{16} } \\ 2 = \frac{k}{4} [/tex]
Cross multiply we have the answer as
k = 8
So the formula for the variation is
[tex]y = \frac{8}{ \sqrt{x} } [/tex]
Now when y = 24
We have
[tex]24 = \frac{8}{ \sqrt{x} } \\ 24 \sqrt{x} = 8 \\ \sqrt{x} = \frac{8}{24} \\ \sqrt{x} = \frac{1}{3} [/tex]
Square both sides
[tex]( { \sqrt{x} })^{2} = ( { \frac{1}{3} })^{2} [/tex]
We have the final answer as
[tex]x = \frac{1}{9} [/tex]
Hope this helps you
