SOLUTION: The volume of a rectangular based prism is x^3-13x^2+50x. What are the dimensions of the prism with a volume of 56cm^3?

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Question 177045: The volume of a rectangular based prism is x^3-13x^2+50x. What are the dimensions of the prism with a volume of 56cm^3?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
v%28x%29=x%5E3-13x%5E2%2B50x=56
x%5E3-13x%5E2%2B50x-56=0
Let's graph the function to see what we get.

+graph%28+300%2C+300%2C+-2%2C+10%2C+-10%2C+10%2C+x%5E3-13x%5E2%2B50x-56%29+
Looks like three possible answers, x=2,4,and 7.
Verify the solutions,
v%28x%29=x%5E3-13x%5E2%2B50x
v%282%29=2%5E3-13%282%29%5E2%2B50%282%29=8-52%2B100=56
v%284%29=4%5E3-13%284%29%5E2%2B50%284%29=64-208%2B200=56
v%287%29=7%5E3-13%287%29%5E2%2B50%287%29=343-637%2B350=56
All three x's (2,4,7) solve for v=56.