Solve the Problem $z = \frac { 6 } { 7 } \sqrt { x ^ { 2 } + y ^ { 2 } }$

question 375

Multiple Choice

Solve the problem.
-Find the center of mass of the solid enclosed between the cone with equation $z = \frac { 6 } { 7 } \sqrt { x ^ { 2 } + y ^ { 2 } }$ and the plane with equation $z = 6$ if the density at any point is proportional to the distance from that point to the axis of the cone.

• A) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 9 } { 2 } \right)\)
• B) \(( \overline { \mathrm { x } } , \overline { \mathrm { y } } , \overline { \mathrm { z } } ) = ( 0,0,4 )\)
• C) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 15 } { 4 } \right)\)
• D) \(( \overline { \mathrm { x } } , \overline { \mathrm { y } } , \overline { \mathrm { z } } ) = \left( 0,0 , \frac { 24 } { 5 } \right)\)

---

Definitions:

DNA Methylation

A process in which gene inactivation is perpetuated by enzymes that add methyl groups to DNA.

Heterochromatin

Highly coiled and compacted chromatin in an inactive state. Compare with euchromatin.

Transcriptionally Inactive

Referring to genes or DNA regions that are not being transcribed into RNA, often due to regulatory mechanisms.

Chromatin

The complex of DNA and proteins, primarily histones, that forms the chromosomes within the nucleus of eukaryotic cells.