A solid cube in the first octant is bounded by the coordinate planes and by the planes x = 1, y = 1, and z= 1. The density of the cube is 8(x,y,z) = x+y+z+ 7. Complete parts a through a. Find the mass of the solid. M = 8.5 (Simplify your answer. Use integers or fractions for any numbers in the expression.) b. Find the center of mass. X = 13 y= 13 Z= 13 (Simplify your answer. Use integers or fractions for any numbers in the expression.) c. Find the moments of inertia about the coordinate axes. x=2 ly=2 (Simplify your answer Use integers or fractions for any numbers in the expression) 1₂ = 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A solid cube in the first octant is bounded by the coordinate planes and by the planes x = 1, y = 1, and z= 1. The density of the cube is 8(x,y,z) = x+y+z+7. Complete parts a through c.
a. Find the mass of the solid.
M = 8.5
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
b. Find the center of mass.
13
13
3
13
3
3
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
c. Find the moments of inertia about the coordinate axes.
X =
y =
Z=
x = 2
ly = 2
¹₂ = 2
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Transcribed Image Text:A solid cube in the first octant is bounded by the coordinate planes and by the planes x = 1, y = 1, and z= 1. The density of the cube is 8(x,y,z) = x+y+z+7. Complete parts a through c. a. Find the mass of the solid. M = 8.5 (Simplify your answer. Use integers or fractions for any numbers in the expression.) b. Find the center of mass. 13 13 3 13 3 3 (Simplify your answer. Use integers or fractions for any numbers in the expression.) c. Find the moments of inertia about the coordinate axes. X = y = Z= x = 2 ly = 2 ¹₂ = 2 (Simplify your answer. Use integers or fractions for any numbers in the expression.)
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