SOLVED: Text: Math 254 10/29 Concept Check 12.7 Triple Integrals The formulas for the mass and center of mass for a 3D object are natural extensions of the formulas for a 2D object: m = âˆ­ p(x,y,z) d

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Text: Math 254 10/29 Concept Check 12.7 Triple Integrals
The formulas for the mass and center of mass for a 3D object are natural extensions of the formulas for a 2D object:
m =
âˆ p(x,y,z) dV
Myz âˆ x p(x,y,z) dV
Mxz âˆ y p(x,y,z) dV
Mxy âˆ 2 p(x,y,z) dV
Myz X = m
Mxz y = m
Mxy z = m
Suppose an object occupies the rectangular cube D = { (x,y,z) |-1<x <1,0 <y<4,-3<z <0} with a density function of p(x,y,z) = y. Find the total mass and center of mass:

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Transcript

So we have an tote. Tensity is to the z, 5 and 10. Defined is long to minus 1 to 1 y equal to 4 and z is minus 2 k, so we have to find x. Mass mass will be equal to the whole volume to x by d t so from here. We can write it as 0245. T y d d to d x is minus 1 to 1 and 2. As we can see, these are already determined that it has 5 steps 54 and the x minus 11 plus 1. So to get the answer to it to a ford 8 point now we have to find…

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