Calculate the Flow in the Field F Along the Path

question 203

Multiple Choice

Calculate the flow in the field F along the path C.
- $\mathbf { F } = ( \mathrm { x } - \mathrm { y } ) \mathbf { i } - \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \right) \mathbf { j } ; \mathrm { C }$ is curve from $( 4,0 )$ to $( - 4,0 )$ on the upper half of the circle $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 16$

• A) \(8 \pi\)
• B) \(- 8 \pi\)
• C) \(\frac { 16 \pi - 1 } { 4 }\)
• D) \(16 \pi\)

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Definitions:

Fine

A monetary penalty imposed by an authority as punishment for a breach of law or rule.

Demand Curve

A graphical representation showing the relationship between the price of a good and the quantity demanded.

Negatively Sloped

Describing a line or curve on a graph that moves downward from left to right, indicating a negative relationship between two variables.

Output Sold

The total quantity of goods or services that have been sold within a specific period.