When studying the formation of mountain ranges, geologists estimate the amount of work required to lift a mountain from sea level. Consider a mountain that is essentially in the shape of a right circular cone C. Suppose that theweight density of the material in the vicinity of a point P is g(P) and the height is h(P).(a) Find a definite integral that represents the total work done in forming the mountain. (Assume a small amount of material is represented by AV.)Sch(P)g(P) dvIfJSISh(P)g(P)SoJJcJJJdVh(P)g(P)h(P)g(P)dvdvh(P)g(P) dvh(P)g(P) dv(b) Assume that Mount Fuji in Japan is in the shape of a right circular cone with radius 62,000 ft, height 12,400 ft, and density a constant 200 lb/ft³. How much work (in ft-lb) was done in forming Mount Fuji if the land was initially atsea level? (Round your answer to three significant digits.)ft-lb

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Answered: When studying the formation of mountain…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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At the bottom of a swimming pool, the pressure exerted at a given point is proportional to the depth of the water above it. In particular, the pressure at a given point of depth d is equal to 10, 000d Pascals. We will investigate the total pressure at the bottom of a swimming pool depending on its shape. You may view 3D models of the swimming pools for reference here (note that this is one model plotting the depth as a function of x and y, so represents essentially the pool flipped upside-down): https://www.geogebra.org/m/nnf4yhax (a) Suppose we have a rectangular pool that is 50 meters long and 25 meters wide. The pool has a shallow end that is 1 meter deep at the edge, a deep end 50 meters away that is 3 meters deep at the edge, and is such that the bottom of the pool forms a linear slant in between (so along a line segment parallel to the short side, the pool has constant depth, and along a line segment parallel to the long side, the pool's depth varies linearly). Set up and…
A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 2 cubic feet per minute. The reservoir is 4 feet deep, measures 6 feet across the top, and is 20 feet long (see figure). For any time t>=0, let H represent the depth of the water in the reservoir and let W represent the width of the rectangular region of water at the top. a. If the reservoir is initially empty, how long will it take to fill completely? b. How fast is the depth of the water in the reservoir changing when the reservoir is half-full? Remember to includes units. c. How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.

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