Chapter 13: Q 32. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the point’s distance from the -axis, find the mass of .
Short Answer
The mass is
Chapter 13: Q 32. (page 1039)
Let be triangular region with vertices
If the density at each point in is proportional to the point’s distance from the -axis, find the mass of .
The mass is
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Get started for freeIn Exercises 57–60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 3, 0 ≤ z ≤ 2}.
Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
Use the results of Exercises 59 and 60 to find the centers of masses of the laminæ in Exercises 61–67.
In the following lamina, all angles are right angles and the density is constant:
Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.
Identify the quantities determined by the integral expressions in Exercises 19–24. If x, y, and z are all measured in centimeters and ρ(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.
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