Find the Flux of the Curl of Field F Through $\mathbf { F } = ( 4 - \mathrm { y } ) \mathbf { i } + ( 3 + \mathrm { x } ) \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k } ; \mathrm { S }$

question 211

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = ( 4 - \mathrm { y } ) \mathbf { i } + ( 3 + \mathrm { x } ) \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k } ; \mathrm { S }$ is the upper hemisphere of $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16$

• A) \(64 \pi\)
• B) \(2 \pi\)
• C) \(32 \pi\)
• D) \(- 4 \pi\)

---

Definitions:

Aristotle

A Greek philosopher and polymath during the Classical period in Ancient Greece, known for his extensive contributions to various fields of philosophy and science.

Cultural Transmission

The process by which culture, including beliefs, social practices, and artifacts, is passed down from generation to generation.

Political Practices

Activities or actions taken within the context of formal politics or governance, including campaigning, legislation, and policy making.

Religious Customs

Traditional practices and rituals followed by members of a religion.