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

question 130

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: "nose" of the paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$ cut by the plane $z = 3$
Density: $\delta = \sqrt { x ^ { 2 } + y ^ { 2 } + 1 }$

• A) \(\left( 0,0 , \frac { 15 } { 8 } \right)\)
• B) \(\left( 0,0 , \frac { 96 } { 11 } \right)\)
• C) \(\left( 0,0 , \frac { 9 } { 11 } \right)\)
• D) \(( 0,0,8 )\)

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Definitions:

Unit Product Cost

The total cost associated with producing a unit of product, including both direct materials and labor, as well as allocated overhead.

Period Cost

Costs that are expensed in the period in which they are incurred, not directly tied to the production process.

Variable Costing

A financial recording method that counts only the variable expenses related to production (direct materials, direct labor, and variable manufacturing overhead) in the pricing of products.

Variable Costing

A financial recording approach that incorporates only variable manufacturing expenses, such as raw materials, direct workforce, and fluctuating production overheads, into the costs of goods produced.