The square of X varies inversely as the square root of Y and directly as the variable M. When M = 27 and Y = 16, then X = 9. Find the exact value of Y when M = 7 and X = 2

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

Convert the variation to an equation; we have

Where K is the constant of variation;

When M = 27; Y = 16; X = 9, the expression becomes

This gives

Make K the subject of formula

Solving for Y when M = 7 and X = 2

Recall that

Substitute values for K, M and X

Take square of both sides

Make  Y the subject of formula

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation