Determine Whether the Vector Field Is Conservative A) Conservative with Potential Function

question 82

Multiple Choice

Determine whether the vector field is conservative. If it is, find a potential function for the vector field. $$\overrightarrow { \mathbf { F } } ( x , y , z ) = 7 x ^ { 6 } y ^ { 8 } z ^ { 9 } \hat { \mathbf { i } } + 8 x ^ { 7 } y ^ { 7 } z ^ { 9 } \hat { \mathbf { j } } + 9 x ^ { 7 } y ^ { 8 } z ^ { 8 } \hat { \mathbf { k } }$$

• A) conservative with potential function \(f ( x , y , z ) = x ^ { 8 } y ^ { 8 } z ^ { 8 }\)
• B) conservative with potential function \(f ( x , y , z ) = x ^ { 7 } y ^ { 8 } z ^ { 9 }\)
• C) conservative with potential function \(f ( x , y , z ) = x ^ { 9 } y ^ { 8 } z ^ { 7 }\)
• D) conservative with potential function \(f ( x , y , z ) = x ^ { 9 } y ^ { 9 } z ^ { 9 }\)
• E) not conservative

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Definitions:

Reaction Time

Reaction time is the duration between the onset of a stimulus and the initiation of a response, often measured to assess sensory and cognitive processes.

Light Stimulus

A visual prompt used in experiments that involves the use of light to elicit a response from the study subject.

Margin Error

The amount of error allowed in the results of a statistical survey, reflecting the precision of the results.

Confidence Level

The probability or percentage that expresses how certain one can be about a confidence interval containing the true value of the parameter being studied.