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:

Truth Tables

A table used in logic to determine the truth value of a compound statement based on the truth values of its components.

Symbolic Form

Representation of logical statements or arguments using symbols and operators to abstract away from the content, focusing on structure.

Components

The individual parts or elements that make up a complex system or device.

Connective

A word or phrase in logic that connects propositions, such as "and", "or", "if...then", serving to create compound statements.