Triple integral transformed, Mathematics

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

 

 

Posted Date: 2/27/2013 2:55:13 AM | Location : United States







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