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jrjimenez
16.03.2020 •
Mathematics
You are constructing a cardboard box with the dimensions 4 m by 6 m. You then cut equal-size squares ( x by x squares) from each corner so that you may fold the edges to get a box. How long should x be to get a box with the maximum volume?? Round your answer to three decimal places. (enter numbers only)
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Ответ:
0.785 m
Step-by-step explanation:
(4-2x)(6-2x)x = Volume
Volume = 4x³ - 20x² + 24x
Max volume: dV/dx = 0
dV/dx = 12x² - 40x + 24 = 0
3x² - 8x + 6 = 0
x = 2.54858377, 0.784749563
Max when d²V/dx² < 0
d²V/dx² = 6x - 8
At x = 0.784749563
6x - 8 = -3.29 < 0
Ответ:
32/2 = 16% above 165 and also 16% below 135