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 the weight 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.) II. O Jo O Ic O h(P) g(P) h(P)g(P) dv dv h(P) dv g(P) Ic III. Jl. h(P)g(P) dv h(P) dv g(P) h(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 at sea level? (Round your answer to three significant digits.) ft-lb
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 the weight 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.) II. O Jo O Ic O h(P) g(P) h(P)g(P) dv dv h(P) dv g(P) Ic III. Jl. h(P)g(P) dv h(P) dv g(P) h(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 at sea level? (Round your answer to three significant digits.) ft-lb
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text: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 the weight 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.)
Jl.
h(P)
g(P)
J h(P)g(P) dv
of dv
dV
O
h(P)
g(P)
dv
III. h(P)g(P) dv
h(P)
III.
g(P)
II.
dv
h(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 at sea level? (Round your answer to three significant digits.)
ft-lb
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