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Multivariable Calculus

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Difficult

Center of Tetrahedron

MVCALC-AX1YJE

Assume a tetrahedron is formed by the coordinates planes and the plane $x+y+z=1$ with constant density, find its center of mass.

A

$(\cfrac{1}{2},\cfrac{1}{2},\cfrac{1}{2})$

B

$(\cfrac{1}{4},\cfrac{1}{4},\cfrac{1}{4})$

C

$(\cfrac{1}{2}, \cfrac{1}{4}, \cfrac{1}{2})$

D

$(\cfrac{1}{4},\cfrac{1}{2},\cfrac{1}{4})$

E

None of the above