Calculate the Flow in the Field F Along the Path

question 12

Multiple Choice

Calculate the flow in the field F along the path C.
- $\mathbf { F } = - \frac { z y } { 6 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { i } + \frac { z x } { 6 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } j + \frac { z ^ { 3 } } { 3 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { k } , C$ is the curve $r ( t ) = 4 \cos 6 t i + 4 \sin 6 t j + 3 t k , 0 \leq t$ $\leq 1$

• A) \(\frac { 61 } { 9 }\)
• B) 21
• C) \(\frac { 61 } { 3 }\)
• D) 0

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Definitions:

Adverse Selection

A situation where incomplete or asymmetric information leads to a market failure, typically in insurance markets, where riskier individuals are more likely to select into plans.

Insurance Companies

Organizations that provide financial protection and compensation for losses to individuals and entities in exchange for premiums.

Adverse Selection

A situation where asymmetric information leads to the selection of undesirable alternatives in transactions, commonly seen in insurance markets.

Insurance Companies

Organizations that provide insurance policies to consumers, covering a variety of risks in exchange for premiums.