SOLUTION: If m and k are positive and 10m^2 * (k^-1) = 100m, what is m^-1 in terms of k?

Question 1189655: If m and k are positive and 10m^2 * (k^-1) = 100m, what is m^-1 in terms of k?
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

If and are positive and , what is in terms of?

than

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equation is:

10m^2 * k^-1 = 100m
simplify to get:
10m^2/k = 100m
multiply both sides of the equation by k to get:
10m^2 = 100m * k
divide both sides of the equation by 100m to get
10m^2/100m = k
simplify to get m/10 = k
solve for m to get:
m = 10k
raise both sides of the equation to the power of -1 to get:
m^-1 = (10k)^-1
your solution should be that:
m^-1 = (10k)^-1
to see if this is true, go back to the original equation.
that is 10m^2 * k^-1 = 100m.
let k = 50
then m^-1 = (10*50)^-1 which becomes:
m^-1 = 100^-1 which becomes:
m = 500.
you have:
when k = 50, m = 500.
using these values of m and k, the original equation of 10m^2 * k^-1 = 100m becomes:
10*500^2 * 1/50 = 100*500
this becomes:
10 * 250,000 / 50 = 50,000 which becomes:
10 * 5,000 = 50,000 which becomes:
50,000 = 50,000.
this confirms the values for m and k are good.

i'm not exactly sure what you're looking for, but, if i understand the problem correctly, then your solution should be:
m^-1 = (10k)^-1.
this is the same as:
1/m = 1/(10k) which is the same as:
m = 10k.

let me know if you have any questions.
theo

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