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