Find the Flux of the Curl of Field F Through $\mathbf { F } = x ^ { 2 } \mathbf { i } + 6 x \mathbf { j } + 9 \mathbf { k } ; \mathrm { S }$

question 54

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = x ^ { 2 } \mathbf { i } + 6 x \mathbf { j } + 9 \mathbf { k } ; \mathrm { S }$ is the upper hemisphere of $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16$

• A) \(16 \pi\)
• B) 16
• C) \(96 \pi\)
• D) \(\pi\)

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Definitions:

Middle Term

In a syllogism, the term that appears in both premises but not in the conclusion, used to connect the other two terms of the argument.

Major Term

Refers to the predicate of the conclusion in a categorical syllogism, which is a key component in deductive reasoning.

Middle Term

In syllogistic logic, the term that appears in both premises but not in the conclusion, serving as a link between the major and minor terms.

Major Premise

The first statement in a syllogism, providing a general statement or condition for the argument.