SOLUTION: Suppose M is jointly proportional to x and y and inversely proportional to the square of z. If x is doubled, y is decupled, and z is tripled, is the value of M changed, and if so,

Question 1047698: Suppose M is jointly proportional to x and y and inversely proportional to the square of z. If x is doubled, y is decupled, and z is tripled, is the value of M changed, and if so, by what factor?
Thanks!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
m1 = (x * y) / z^2

m2 = (2 * x * 10 * y) / (3 * z^2)

m2 / m1 = [(2 * x * 10 * y) / (3 * z^2)] / [(x * y) / (z^2)]

since (a/b) / (c/d) is the same as (a/b) * (d/c), your equation becomes:

m2 / m1 = (2 * x * 10 * y) / (3 * z^2) * (z^2) / (x * y)

this is equivalent to:

m2 / m1 = (2 * x * 10 * y * z^2) / (3 * z^2 * x * y)

the x and the y and the z^2 in the numerator cancel out the x and the y and the z^2 in the denominator and you are left with:

m2 / m1 = (2 * 10) / 3 which is equal to 20/3.

multiply both sides of this equation by m1 and you get:

m2 = 20 / 3 * m1

this says that m2 is 20/3 times as large as m1.

to see if this is correct, just provide random values for x, y, and z, and see if the ratio is correct.

i used:

x = 5
y = 10
z = 15

m1 = x * y / z^2 becomes m1 = (5 * 10) / (225) which becomes m1 = 50 / 225

m2 = (2 * x * 10 * y) / (3 * z^2) becomes m2 = (2 * 5 * 10 * 10) / (3 * 225) which becomes m2 = 1000 / 675.

if you take 50 / 225 and multiply it by 20 / 3, you get 1000 / 675.

this confirmed, for me, that the solution is good and that m2 is 20/3 times as large as m1.

i believe this is what you're looking for.

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