Find the mass and the center of mass of the solid E with the given density function $ \, \rho (x, y,z). $ E is the tetrahedron bounded by the planes $ x=0,\, y=0,\, z=0,\, x+y+z={\color{red}3}; \, \rho (x, y,z)={\color{red}2} y. $

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)