Solve the Problem $z = 4 - x ^ { 2 } - y ^ { 2 }$

question 131

Multiple Choice

Solve the problem.
-Find the center of mass of the hemisphere $z = 4 - x ^ { 2 } - y ^ { 2 }$ if the density is proportional to the distance from the center.

• A) \(\left( 0,0 , \frac { 6 } { 5 } \right)\)
• B) \(\left( 0,0 , \frac { 16 } { 15 } \right)\)
• C) \(\left( 0,0 , \frac { 4 } { 5 } \right)\)
• D) \(\left( 0,0 , \frac { 14 } { 15 } \right)\)

---

Definitions:

Allergic Reactions

Allergic reactions are the body's immune system responses to what it mistakenly identifies as harmful substances, leading to symptoms like sneezing, itching, and swelling.

IgG

A class of immunoglobulins that plays a major role in the body's immune response by identifying and neutralizing pathogens.

Circulating Antibodies

Antibodies present in the bloodstream, involved in identifying and neutralizing pathogens such as bacteria and viruses.

IgD

A class of immunoglobulin involved in the immune system's response, serving primarily as an antigen receptor on B cells.