Center of mass of constant-density solids Find the center of mass of the following solids, assuming a constant density. Use symmetry whenever possible and choose a convenient coordinate system . 56. The tetrahedron bounded by z = 4 – x – 2 y and the coordinate planes
Center of mass of constant-density solids Find the center of mass of the following solids, assuming a constant density. Use symmetry whenever possible and choose a convenient coordinate system . 56. The tetrahedron bounded by z = 4 – x – 2 y and the coordinate planes
Solution Summary: The author explains the density function and calculates the mass of the region.
Center of mass of constant-density solidsFind the center of mass of the following solids, assuming a constant density. Use symmetry whenever possible and choose a convenient coordinate system.
56. The tetrahedron bounded by z = 4 – x – 2y and the coordinate planes
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Identify the center and radius for each.
r? + y? = 49
x² + y? = 324
x² + (y + 2) = 64
(r + 2)² + y² = 64
(1 – 5)² + (y – 3)² = 144
(z+1) + (y – 10)? = 100
:: Center: (0, 2), r = 8
: Center (-1, 10), r = 10
: Center: (-2, 0), r = 8
:: Center: (1, – 10), r = 10
:: Center: (0, 0), r = 18
: Center: (5, 3), r = 12
: Center: (2, 0),r = 8
: Center. (0, 0), r =
7
: Center (-5,-3), r = 12
: Center (0, -2), r = 8
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
2, y =
13
y =
x2;
about the x-axis
%3D
V =
Sketch the region.
y
2.5
2.5
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.5
-2
-1
1
- 2
-1
1
-0.5
-0.5
-1.0F
-1.0F
y
y
1.5
1.5
1.0
1.0
0.5
0.5
-2
-2
-0.5
-0.5
Find the point lying on the intersection of the plane x +
+
z = 0 and the sphere x2 + y2 + z2 = 25 with the largest z-coordinate.
3
(х, у, 2) %
Chapter 16 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
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