Answer:
[tex]Y = 441[/tex]
Step-by-step explanation:
Given
M = 27 when Y = 16 and X = 9
Required
Find Y when M = 7 and X = 2
We start by getting the algebraic representation of the given statement
[tex]X^2 \alpha \frac{1}{\sqrt Y} \alpha M[/tex]
Convert the variation to an equation; we have
[tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Where K is the constant of variation;
When M = 27; Y = 16; X = 9, the expression becomes
[tex]9^2 = \frac{K * 27}{\sqrt{16}}[/tex]
This gives
[tex]81 = \frac{k * 27}{4}[/tex]
Make K the subject of formula
[tex]K = \frac{81* 4}{27}[/tex]
[tex]K = \frac{324}{27}[/tex]
[tex]K = 12[/tex]
Solving for Y when M = 7 and X = 2
Recall that [tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Substitute values for K, M and X
[tex]2^2 = \frac{12 * 7}{\sqrt{Y}}[/tex]
[tex]4 = \frac{84}{\sqrt{Y}}[/tex]
Take square of both sides
[tex]4^2 = (\frac{84}{\sqrt{Y}})^2[/tex]
[tex]16 = \frac{7056}{Y}[/tex]
Make Y the subject of formula
[tex]Y = \frac{7056}{16}[/tex]
[tex]Y = 441[/tex]
