Let S Be the Closed Surface Which Is the Portion $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$

question 62

Multiple Choice

Let S be the closed surface which is the portion of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ with $- 2 \leq \boldsymbol { z } \leq 1$ topped by the disk in the plane $\bar { z } = 1$ , oriented outward.Then the flux of $\vec { r } = x \vec { i } + y \vec { j } + z \vec { k }$ through S is:

• A) \(9 \pi\)
• B) \(24 \pi\)
• C) \(27 \pi\)
• D) \(18 \pi\)
• E) \(36 \pi\)

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Definitions:

Encoded

Transformed into a coded form, often for the purpose of confidentiality, storage efficiency, or preparation for processing.

Parallel Processing

The brain's capability to process multiple information streams simultaneously, aiding in complex tasks like visual recognition.

Neural Networks

A series of algorithms that endeavor to recognize underlying relationships in a set of data through a process that mimics the way the human brain operates.

Different

Characterized by not being the same; showing a distinct or unique nature when compared to something else.