Can u help me in this pls
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Answer:
<em>work done is equal to 384279168 lb-ft</em>
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Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = = <em>30791.6 ft^3</em>
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = <em>1921395.84 lb</em>
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> <em>work done is equal to 384279168 lb-ft</em>
Reading that as
By the fundamental theorem of calculus, the first derivative is
and so the second derivative would be
which means
By the fundamental theorem of calculus, the first derivative is
and so the second derivative would be
which means