SOLUTION: Eliana wants to make a diorama or an art contest contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama

Question 1120713: Eliana wants to make a diorama or an art contest contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open frontan open box front.
Describe how you could identify which points on a graph of v(x)=(12-2x)(8-2x)x correspond to a volume of 36 in.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Eliana wants to make a diorama or an art contest contest. SHE starts with a rectangular sheet of a cardboard box is 12 inches long and 8 inches wide. SHE PLANS to make the diorama box baby cute cutting identical squares from the corners and folding the sides to create a box with an open frontan open box front.
Describe how you could identify which points on a graph of v(x)=(12-2x)(8-2x)x correspond to a volume of 36 in.
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Solve:: v(x) = 36
x(2)(6-x)(2)(4-x) = 36
x(x-6)(x-4) = 9
x(x^2-10x+24) = 9
x^3-10x^2+24x-9 = 0
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Graph the cubic and find the roots of it.
x = 0 or x = 3 or x = 6.541..
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Since the dimensions of the box are x, 12-2x and 8-2x
only x = 3 would keep the dimensions positive.
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Cheers,
Stan H.
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