SOLUTION: Solve for the indicated letter. Solve the formula. S= 1/3 nr^2h + 4nrh for r.

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Question 314267: Solve for the indicated letter. Solve the formula.
S= 1/3 nr^2h + 4nrh for r.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for the indicated letter. Solve the formula.
S = 1%2F3nr%5E2h+%2B+4nrh for r.
:
1%2F3nr%5E2h+%2B+4nrh = S
Multiply by 3
nr%5E2h+%2B+3%284nrh%29 = 3S
:
nr%5E2h+%2B+12nrh = 3S
Factor out nh
nh(r^2 + 12r) = 3S
divide both sides by nh
r^2 + 12r = %283S%29%2F%28nh%29
Arrange as a quadratic equation
r^2 + 12r - %283S%29%2F%28nh%29 = 0
Solve for r using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: x = r a=1; b=12; c=-%283S%29%2F%28nh%29
r+=+%28-12+%2B-+sqrt%2812%5E2-4%2A1%2A%28%28-3S%29%2F%28nh%29%29+%29%29%2F%282%2A1%29+
:
r+=+%28-12+%2B-+sqrt%28144-4%28%28-3S%29%2F%28nh%29%29+%29%29%2F2+
:
r+=+%28-12+%2B-+sqrt%28144%2B4%28%283S%29%2F%28nh%29%29+%29%29%2F2+