Use Stokes' Theorem to Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$

question 85

Multiple Choice

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$ $\mathbf { F } ( x , y , z ) = 7 x y \mathbf { i } + 7 e ^ { x } \mathbf { j } + 7 x y ^ { 2 } \mathbf { k }$ S consists of the four sides of the pyramid with vertices (0, 0, 0) , (3, 0, 0) , (0, 0, 3) , (3, 0,3) and (0, 3, 0) that lie to the right of the xz-plane, oriented in the direction of the positive y-axis.

• A) 0
• B) 12
• C) 16
• D) 49
• E) 1

Comprehend the importance and wide applicability of learning principles across various behavioral scenarios.

Understand the role of reinforcers in decision-making processes related to self-control and prioritize long-term goals over immediate gratifications.

Recognize strategies for maintaining positive habits or breaking negative ones through the manipulation of environmental cues.

Understand the critical features that make an instrument negotiable.

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Definitions:

Saturated Solution

A solution containing the maximum concentration of a solute dissolved in a solvent at a given temperature and pressure.

Molarity

A measure of concentration expressing the number of moles of a solute per liter of solution.

Diluting

The process of reducing the concentration of a solute in a solution, usually by adding more solvent.

Molarity

An indicator of solute density within a solution, measured in moles per liter of the solution.