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Let E be the solid tetrahedron with vertices (0,0,0), (0,0,3), (0,2,0), and (4,0,0) where all measurements are in metres. Suppose it has uniform density of 1 kilogram per cubie metre. Determine the y coordinate of the centre of mass by evaluating the triple integral Hints: Determine the limits of integration first. Make sure the limits correspond to a tetrahedron and not a rectangular prism. Some of the integrals can get messy - in order to keep them simpler you can try using the reverse chain rule rather than expanding expressions.

Let E be the solid tetrahedron with vertices (0,0,0), (0,0,3), (0,2,0), and (4,0,0) where all measurements are in metres. Suppose it has uniform density of 1 kilogram per cubie metre. Determine the y coordinate of the centre of mass by evaluating the triple integral Hints: Determine the limits of integration first. Make sure the limits correspond to a tetrahedron and not a rectangular prism. Some of the integrals can get messy - in order to keep them simpler you can try using the reverse chain rule rather than expanding expressions.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let E be the solid tetrahedron with vertices (0,0,0), (0,0,3), (0,2,0), and (4,0,0) where all measurements are in metres. Suppose it has uniform density of 1 kilogram per cubic metre. Determine the y coordinate of the centre of mass by evaluating the triple integral y Hints: Determine the limits of integration first. Make sure the limits correspond to a tetrahedron and not a rectangular prism. Some of the integrals can get messy - in order to keep them simpler you can try using the reverse chain rule rather than expanding expressions.
Transcribed Image Text:Let E be the solid tetrahedron with vertices (0,0,0), (0,0,3), (0,2,0), and (4,0,0) where all measurements are in metres. Suppose it has uniform density of 1 kilogram per cubic metre. Determine the y coordinate of the centre of mass by evaluating the triple integral y Hints: Determine the limits of integration first. Make sure the limits correspond to a tetrahedron and not a rectangular prism. Some of the integrals can get messy - in order to keep them simpler you can try using the reverse chain rule rather than expanding expressions.
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