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alex41 [277]
3 years ago
8

Pls help !!!

Mathematics
1 answer:
Step2247 [10]3 years ago
8 0
How is this 1st grade!? And also I think the answer is 3,000
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A lidless box is to be made with a volume of 256256 ft cubed 3. Find the dimensions of the box that requires the least amount of
sveta [45]

The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.

The dimensions of your box will be 8 ft square by 4 ft high.

_____

If the base dimension is x ft, the area (quantity of material) is

... a = x² + 4x(256/x²)

... a = x² + 1024x⁻¹

Then the derivative of area with respect to x is

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Setting this derivative to zero and solving for x gives the value of x for minimum area.

... 0 = 2x -1024/x²

... 512 = x³

... x = 8 . . . . . . . . same as above.

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I think its A

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