Cooling towers at nuclear power plants have a "pinched" chimney shape formed by rotating a hyperbola x2 around an axis. The function y = 401/1+ for – 240 < < 100, where x and y are in feet, 10000 describes the shape of such a tower (laying on its side). Determine the volume of the tower by rotating the region bounded by the graph of y about the x-axis.

Q: y = Vx +1; x-axis ; y-axis ; x = 8

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Q: A container can be modeled by revolving the graph of       about the x-axis, where x and y are…

A: Given function  here R(x) = y(x)

Q: Find the largest area possible for a rectangle inscribed between the parabola y = 9 – x² and the x-…

A:

Q: z = 7+x+4y+x² , –2 < x < 1,–1< y < 1. | 1. A = 3V5 - ( 35 + 6/26 - In 4 %3D 17 17 35 + 6/26 2. A =…

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Q: 36. Volume of a domed stadium. The volume of a stadium with a domed roof can be approximated if the…

A:

Q: A rectangular package to be sent by a postal service can have a maximum combined length and girth…

A: To find the maximum of Volume we use dV/dx=0

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

A: Use double integral

Q: Use inscribed and circumscribed rectangles to find the area of the region to the right of the line x…

A: Concept: the area between the region y=f(x) and ==g(x) on the interval [a, b] Let us assume that…

Q: Determine the volume of the region inside the circle x2 + (y-b)2 = a2 (0<a<b); revolved about the…

A: To determine the volume of the region inside the circle x2+y-b2=a2 when revolved about x-axis.

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.