$\text { Find the flux of } \mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } - 2 z \mathbf { k } \text { through }$

question 32

Multiple Choice

$\text { Find the flux of } \mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } - 2 z \mathbf { k } \text { through }$
$S : z = \sqrt { 121 - x ^ { 2 } - y ^ { 2 } } , \iint _ { S } \mathbf { F } \cdot \mathbf { N } d S$ where $\mathbf { N }$ is the upward unit normal vector to $S$ .

• A) 8
• B) 11
• C) 1
• D) 0
• E) 4

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Definitions:

Antiaromatic

A type of cyclic compound that is destabilized by the delocalization of its electrons, failing to meet the criteria for aromatic stability.

Nonaromatic

Organic compounds that do not meet the criteria for aromaticity, lacking the special stability of aromatic systems.

Pyridine

A basic nitrogen-containing heterocyclic aromatic compound, resembling benzene but with one CH group replaced by a nitrogen atom.

Pyrrole

An aromatic heterocyclic organic compound, consisting of a five-membered ring with one nitrogen atom. It is the foundation for many natural and synthetic compounds including pharmaceuticals.