$y = 4$ 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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Efficiently

Achieving maximum productivity with minimum wasted effort or expense.

Production Inefficiency

A situation where resources are not utilized in the best possible manner, resulting in wasted potential output.

Production Possibility Frontier

A graphical representation that shows the maximum combination of two goods or services that can be produced within a given time period, given available resources and technology.

Economic Growth

A growth in an economy's ability to generate goods and services when comparing two different time periods.