Find the Centroid of the Solid Region Bounded by the Graphs

question 41

Multiple Choice

Find the centroid of the solid region bounded by the graphs of the equations. Use a computer algebra system to evaluate the triple integral. (Assume uniform density and find the center of mass.) $$z = \frac { 9 } { y ^ { 2 } + 1 } , z = 0 , x = - 2 , x = 2 , y = 0 , y = 1$$

• A) \(\bar { x } = 2 , \bar { y } = \frac { 2 \ln ( 2 ) } { \pi } , \bar { z } = \frac { 2 + \pi } { 4 \pi }\)
• B) \(\bar { x } = 0 , \bar { y } = \frac { 2 \ln ( 2 ) } { \pi } , \bar { z } = \frac { 9 ( 2 + \pi ) } { 4 \pi }\)
• C) \(\bar { x } = 0 , \bar { y } = \frac { \ln ( 2 ) } { \pi } , \bar { z } = \frac { 9 ( 2 + \pi ) } { 4 \pi }\)
• D) \(\bar { x } = 0 , \bar { y } = \frac { 2 \ln ( 2 ) } { \pi } , \bar { z } = \frac { 9 ( 4 + \pi ) } { 4 \pi }\)
• E)\(\bar { x } = 2 , \bar { y } = \frac { ( 2 + \pi ) 9 } { 4 \pi } , \bar { z } = \frac { 2 \ln ( 2 ) } { \pi }\)

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Definitions:

Gestation

The period of development from the time of fertilization until birth in organisms that undergo embryonic and fetal development, notably humans.

Adoption Agency

An organization that facilitates placing children into adoptive families, ensuring the welfare of the child and assisting in the legal and logistical processes involved.

Average Gestation

The typical duration of pregnancy, measured from the first day of the woman's last menstrual period until the birth of the baby, usually around 40 weeks in humans.

Oocytes

Immature eggs in the ovaries that can develop into mature eggs during ovulation.