Using the Divergence Theorem, Find the Outward Flux of F

question 24

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $\mathbf { F } = x \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } \mathrm { i } + \mathrm { y } \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } \mathrm { j } + \mathrm { z } \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } \mathbf { k } ;$ D: the thick cylinder $5 \leq \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \leq 6,3 \leq \mathrm { z } \leq 4$

• A) \(728 \pi\)
• B) \(\frac { 728 } { 3 } \pi\)
• C) \(\frac { 1456 } { 3 } \pi\)
• D) \(\frac { 364 } { 3 } \pi\)

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Definitions:

Korsakoff's Syndrome

A chronic memory disorder caused by severe deficiency of thiamine (vitamin B1), often associated with alcoholism, characterized by short-term memory loss and confabulation.

Declarative Memory

A type of long-term memory that involves the ability to recall factual information, such as events, words, and concepts.

Short-Term Memory

The component of memory where small amounts of information can be stored for a short period of time, typically seconds to minutes.

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A region of the frontal lobe of the brain involved in decision making, planning, and personality expression.