Chapter 13: Q. 73 (page 1041)
Prove that the centroid of a circle is the center of the circle.
Short Answer
the centroid of a circle is the center of the circle.
The centroid of a circleis atand the center is also at
Chapter 13: Q. 73 (page 1041)
Prove that the centroid of a circle is the center of the circle.
the centroid of a circle is the center of the circle.
The centroid of a circleis atand the center is also at
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Get started for freeFind the masses of the solids described in Exercises 53–56.
The solid bounded above by the plane with equation 2x + 3y − z = 2 and bounded below by the triangle with vertices (1, 0, 0), (4, 0, 0), and (0, 2, 0) if the density at each point is proportional to the distance of the point from the
xy-plane.
In 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 at each point in Ris proportional to the distance of the point from the xy-plane.
(a) Without using calculus, explain why the x- and y-coordinates of the center of mass are respectively.
(b) Use an appropriate integral expression to find the z-coordinate of the center of mass.
In the following lamina, all angles are right angles and the density is constant:
Evaluate the sums in Exercises .
Find the masses of the solids described in Exercises 53–56.
The first-octant solid bounded by the coordinate planes and the plane 3x + 4y + 6z = 12 if the density at each point is proportional to the distance of the point from the xz-plane.
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