An elliptical galaxy has gravitational boundaries defiend by 9x²+16y²+144z²=144. A black hole at the center of the galaxy is interacting with dark matter producing a radiation envelope defined by the region inside the cone Z²=27x²+48y². If the energy density in this envelope is defined by ρ(x,y,z)=Κ |xyz|

Determine the following given the above with K >C

1. Find the volume of space inside the galaxy affected by the interaction using a triple integral transformed into u,v,w space with u=3x, v=4y, w=z

2.the total energy in the envelope.

3. the center of "mass of the energy in the upper and lower cones individually in the (x,y,z) system.

4.the average energy density , ρ, in each cone.

Note: for units you may use the following.  linear dimensions = 10^5 light year