$y = 4$ And $z = 4 - x$ And the Coordinate Planes

question 63

Multiple Choice

$\text { Let } \mathbf { F } ( x , y , z ) = x y \mathbf { i } + z \mathbf { j } + ( x + y ) \mathbf { k } \text { and let } S \text { be the surface bounded by the planes }$ $y = 4$ and $z = 4 - x$ and the coordinate planes. Verify the Divergence Theorem by evaluating $\iint_{S} \mathbf{F} \cdot \mathbf{N} d s$ as a surface integral and as a triple integral. Round your answer to two decimal places wherever applicable.

• A) \(76.25\)
• B) \(85.33\)
• C) \(156.25\)
• D) \(64.00\)
• E) \(20.25\)

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Definitions:

Economies of Scale

Refers to the cost advantages that enterprises obtain due to their scale of operation, leading to a reduction in per-unit cost.

Capital Facilities

Physical assets such as buildings, machinery, and equipment used in the production of goods and services.

Principal-Agent Problems

Conflicts of interests that arise when one party (the agent) is expected to act in the best interest of another (the principal) but has an incentive to act in their own interest.

Monopoly

A market structure characterized by a single seller, selling a unique product in the market with no close substitutes and high barriers to entry.