$\text { Find } I _ { z } \text { for the lamina } z = x ^ { 2 } + y ^ { 2 } , 0 \leq z \leq 3$

question 12

Multiple Choice

$\text { Find } I _ { z } \text { for the lamina } z = x ^ { 2 } + y ^ { 2 } , 0 \leq z \leq 3$ with uniform density of 1 Use a computer algebra system to verify your result.

• A) \(\frac { \pi } { 50 } ( 16 \sqrt { 16 } + 1 )\)
• B) \(\frac { \pi } { 30 } ( 17 \sqrt { 16 } + 1 )\)
• C) \(\frac { \pi } { 60 } \left( 17 ( 13 ) ^ { 3 / 2 } + 1 \right)\)
• D) \(\frac { \pi } { 60 } \left( 15 ( 13 ) ^ { 3 / 2 } + 1 \right)\)
• E) \(\frac { \pi } { 30 } \left( 16 ( 13 ) ^ { 3 / 2 } + 1 \right)\)

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Definitions:

Rational Decision Maker

An individual or entity that makes choices that maximize benefits while minimizing costs, based on available information and logical analysis.

Shipping Fee

A charge applied for the transportation of goods from one location to another by sea, air, or land logistics.

Marginal Benefit

The additional satisfaction or utility that a person receives from consuming an additional unit of a good or service.

Marginal Cost

The increase in cost that arises from producing an additional unit of a good or service.