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Paulie

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A 50/50 blend of engine coolant and water (by volume) is usually used in an automobile\'s engine cooling system. If your car\'s
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You just integrate pi (4-y^2) from -2 to 2, and you will get 32pi/3.
Just plot the graph of inverse function, you would see (2,-3) is the correct answer.
The inverse function is x = sqrt(9-y) If you differentiate the inverse function, you would get y' = -2 * sqrt(9-y) Then substitue x = sqrt(9-y) y' = -2x
The inverse function is x=y^2-4y+5 And the domain start from 1 to infinity to make one-to-one function. So, you get y' of inverse function = 1/(2y-4) where [1,infinity).
f(x) = x^2-4x+4 y = (x-2)^2 Inverse function x = (y-2)^2 Differentiate the inverse function, you would get y' = 1/(2sqrt(x))
Actually, f(x) = x^3+3/2x^2-18x+4 When you differentiate to find critical points which are -3 & 2, you would see from (-infinity,-3] and [2,infinity). Those two ranges make f(x) become one-to-one function.
It is C, I confirm.
Let h be the water level Each small slice of area from one end of parabola to the other end = 2*sqrt(y) dy Pressure exerting on small slice = density * (h-y) ; h-y is the depth of water from the surface. So, F = 62.5 integral of (h-y) 2*sqrt(y) dy from 0
W = 62.5 * 12 integral of (5-y) dy from 0 to 5 Area of each water slice = 12 You have to pump each slice out. An illustration would make you understand better, but I have no way to show you. So, the answer is 9375 lb-ft.
2) Cape Cod 3) Atlantic Coastla Plains 4) Brooks Range

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