Question 1055963: Please help! I need assistance with this college level challenge problem! I worked out the problem but sadly, to no avail.
Link to the problem: https://www.scribd.com/document/329683850/Challenge-Problem-3
Any help would be much appreciated thank you!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Please help! I need assistance with this college level challenge problem! I worked out the problem but sadly, to no avail.
Link to the problem: https://www.scribd.com/document/329683850/Challenge-
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You want to make an 80 cubic inch out of a 10 by 12 inch sheet. Why not just say that? Are you a drama major?
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Cut squares of size x by x from each corner.
Vol = x*(12-2x)*(10-2x) = 80
4x^3 - 44x^2 + 120x - 80 = 0
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x^3 - 11x^2 + 30x - 20 = 0
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Try factors of 20 first, 1, 2, 4, 5, 10 & 20
f(x) = x^3 - 11x^2 + 30x - 20
f(1) = 0 --> x-1 is a factor.
Divide by x-1
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--> g(x) = x^2 - 10x + 20
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=20 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 7.23606797749979, 2.76393202250021.
Here's your graph:
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