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dusya [7]
3 years ago
10

A 120-inch strip of metal 12 inches wide is to be made into a small open trough by bending up two sides on the long side, at rig

ht angles to the base. The sides will be the same height, x. If the trough is to have a maximum volume, how many inches should be turned up on each side?
Mathematics
1 answer:
mezya [45]3 years ago
3 0

Answer:

x= 3 inch should be turned up on each side

Step-by-step explanation:

Let the height of trough be x.

Width of trough be 12 - 2x.

and length of trough = 120 inch

Volume of trough, V = L×W×H = 120 × (12-2x) × x = 120x(12 - 2x)

For maximum volume, we find V' = 0

i.e 1440 -480x = 0

or  x = \frac{1440}{480}

or  x= 3

Hence x= 3 inch should be turned up on each side

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