For What Value of the Constant $b$ Is the Vector Field $\mathbf { F } = b x y ^ { 2 } \mathbf { i } + x ^ { 2 } y \mathbf { j }$

question 165

Multiple Choice

For what value of the constant $b$ is the vector field $\mathbf { F } = b x y ^ { 2 } \mathbf { i } + x ^ { 2 } y \mathbf { j }$ conservative?

• A) \(0\)
• B) \(\frac { 1 } { 4 }\)
• C)\(\frac { 1 } { 2 }\)
• D)\(\frac { 3 } { 4 }\)
• E)\(1\)
• F) \(\frac { 5 } { 4 }\)
• G)\(\frac { 3 } { 2 }\)
• H)No constant

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Definitions:

Short-term Results

Immediate or near-immediate outcomes or effects following an action or event, typically observable within a short time frame.

Negative Reinforcement

A type of conditioning where an unfavorable outcome or event is removed after a behavior, increasing the likelihood of that behavior being repeated in the future.

Punishment

A technique used in behavior modification that involves presenting an undesirable consequence or removing a desirable stimulus following unwanted behavior.

Partial Reinforcement

A conditioning schedule in which a response is sometimes reinforced, leading to more resistant behavior to extinction than continuous reinforcement.