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

question 272

Multiple Choice

Solve the problem.
-The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass.
Shell: portion of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ that lies in the first octant
Density: constant

• A) \(\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)\)
• B) \(\left( \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } \right)\)
• C) \(( 1,1,1 )\)
• D) \(( 2,2,2 )\)

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Definitions:

Higher Income Groupings

Refers to classifications of individuals or households that earn above a certain threshold of income, often compared within a broader economic context.

Lower Income Groupings

classifications of individuals or families that earn relatively less income compared to the median or average levels within a society.

Income Inequality

The unequal distribution of household or individual income across the various participants in an economy, leading to social and economic disparities.

Bottom Quintile

The lowest 20 percent segment of a population, often used in the context of income or wealth distribution.