Using the Divergence Theorem, Find the Outward Flux of F $F = \sin y i + x z j + 5 z k$

question 52

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $F = \sin y i + x z j + 5 z k$ ; D: the thick sphere $4 \leq x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 9$

• A) \(135 \pi\)
• B) \(\frac { 76 } { 3 } \pi\)
• C) \(380 \pi\)
• D) \(\frac { 380 } { 3 } \pi\)

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Definitions:

Glial Cell

Nervous system cell that provides insulation, nutrients, and support and that aids in repairing neurons and eliminating waste products.

Neuron

A nerve cell that is the basic building block of the nervous system, responsible for transmitting information throughout the body.

Central Nervous System

The section of the nervous system that includes the brain and spinal cord, tasked with assimilating sensory data and reacting appropriately.

Glial Cells

Glial cells, or neuroglia, are non-neuronal cells in the central and peripheral nervous systems that do not conduct nerve impulses but are responsible for providing support and protection for neurons.