$z = 17 - x ^ { 2 } - y ^ { 2 }$

question 28

Multiple Choice

$\text { Let } \mathbf { F } ( x , y , z ) = x z \mathbf { i } + z y \mathbf { j } + 2 z ^ { 2 } \mathbf { k } \text { and let } S \text { be the surface bounded by }$ $z = 17 - x ^ { 2 } - y ^ { 2 }$
and $z = 0$ .
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.

• A) \(85,538,800.97\)
• B) \(63,235,739.36\)
• C) \(3,735,184.02\)
• D) \(63,235,747.36\)
• E) \(5,294,083.13\)

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Definitions:

Production Cycle

The series of steps involved in producing a good or service, from initial raw materials to the finished product.

Kanban

A visual scheduling system that controls the logistical chain from a production point of view, aiming to improve manufacturing efficiency by limiting work-in-progress items.

Safety Stock

Additional inventory kept on hand to guard against stockouts caused by uncertainties in demand and lead-time.

Kanbans

A scheduling system for lean manufacturing and just-in-time (JIT) production that signals the need to move materials within a production facility.