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Question 841341: in the shelving system includes a box-module, which may be made of thin plate with dimensions of 80 cm in length, and 50 cm in width. The plate is bent into shape that has length of 80-2x, with of 50 and height of x.
a) Estimate the height of x, given the box volume is as large as possible.
b) You must determine the volume of the box .
Hint: order of quadratic equation and use of the vertex formula
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! in the shelving system includes a box-module, which may be made of thin plate with dimensions of 80 cm in length, and 50 cm in width. The plate is bent into shape that has length of 80-2x, width of 50 and height of x.
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V = width*height*length
V = 50x(80-2x)
V = -100x^2 + 4000x
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a) Estimate the height of x, given the box volume is as large as possible.
Max occurs when x = -b/(2a) = -400/(2*-100) = 2
Ans: height = x = 2 cm
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b) You must determine the volume of the box .
V = 50*2(80-2*2) = 100(76) = 7600 cm^3
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Cheers,
Stan H.
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