Determine Whether the Vector Field Is Conservative $\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$

question 102

Multiple Choice

Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
$\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$

• A) conservative with potential function \(f ( x , y , z ) = x ^ { 10 } y\)
• B) conservative with potential function \(f ( x , y , z ) = x y ^ { 10 }\)
• C) conservative with potential function \(f ( x , y , z ) = x ^ { 11 } y\)
• D) conservative with potential function \(f ( x , y , z ) = x y ^ { 11 }\)
• E) not conservative

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Definitions:

Mean

The mean, often referred to as the average, is a statistic that represents the central or typical value in a set of data, calculated by dividing the sum of all values by the number of values.

Population Standard Error

A measure that estimates the variability of sample means around the population mean if multiple samples were taken from the population.

Confidence Interval

A band of values, yielded by analyzing sample data, which has a good chance of capturing the value of an unknown population variable.

Mean

The average value obtained by dividing the sum of all values in a set by the number of values.