SOLUTION: x is inversely proportional to the cube of z. What happens to x when z is halved? I know x=K/z^3 but I do not know how to continue from there. Could you please explain what ste

Question 1127599: x is inversely proportional to the cube of z. What happens to x when z is halved?
I know x=K/z^3 but I do not know how to continue from there. Could you please explain what steps to take next?
My professor used "new" and "old" and I am very confused. His solution was Znew=z old/2
x new=K/z^3new = K/(8 old/2)^3 = 8K/z old^3 = 8 x old
There must be a more simple way to explain/solve this sort of problem?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x is increased by a factor of 8.
pick some numbers
x=k/z^3, let x=8 when z=4
8=k/64; k=512
Let z now be 2
x=512/8=64. That is 8 times the original x
it is 1/z^3, and when z is half of that it is 1/(1/8) or 8.
When z is decreased by (1/2), x is increased by 1/(1/2)^3 or 8 fold.
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