Consider a hemispherical tank with radius 10 ft. Suppose the tank is full to a depth of 7 ft with water of weight density 62.4 l
bs/ft3, and the top 5 ft of water are pumped out of the tank to a truck whose height is 5 feet above the top of the tank. Determine the total work required to pump the water into the truck.
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To solve this equation , we need to write it in quadratic form
To get the equation in quadratic form we replace x^2 with u
can be written as
, Replace u for x^2
So equation becomes
Now we factor the left hand side
-16 and -1 are the two factors whose product is +16 and sum is -17
(u-16) (u-1) = 0
u -16 = 0 so u=16
u-1 =0 so u=1
WE assume u = x^2, Now we replace u with x^2
Now take square root on both sides , x= +4 and x=-4
Now take square root on both sides , x= +1 and x=-1
So zeros of the function are -4, -1, 1, 4