Z is inversely proportional to the square root of M and Z=1 when M=9. Find M when Z=3/4

Answer 1

If Z is inversely proportional to the square root of M, we can write this relationship as:

Z = k / √M

Where k is the constant of proportionality.

We are given that when M = 9, Z = 1. Substituting these values into the equation, we can solve for k:

1 = k / √9
1 = k / 3
k = 3

Now we can substitute the value of k back into the equation:

Z = 3 / √M

We are asked to find M when Z = 3/4:

3/4 = 3 / √M

To remove the square root from the denominator, we can square both sides of the equation:

(3/4)^2 = (3 / √M)^2
9/16 = 9 / M
9M = 16 * 9
9M = 144
M = 144 / 9
M = 16

Therefore, when Z = 3/4, M = 16.