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A one compartment vertical file is to be constructed by bending the long side of an 8 in by 10 in sheet of plastic along two lines to form a U shape How tall should the file be to maximize the volume?
Wiki User
∙ 14y ago
Assuming you mean bending parallel to the long side:
Volume (V) = 10*x*(8-2x) = -20x2+80x
To find the maximum, we find the zero of the first derivative.
dV/dx = -40x+80 = 0
x=2 inches tall
If you meant bending perpendicular to the long side:
V=8*x*(10-2x)=80x-16x2
dV/dx = 80-32x = 0
x = 80/32 = 5/2 = 2.5 inches tall
Wiki User
∙ 14y ago
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