Solve the Problem $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 9 } ^ { \sqrt { 64 - r ^ { 2 } } } r d z d r d \theta$

question 4

Multiple Choice

Solve the problem.
-Let D be the smaller cap cut from a solid ball of radius 9 units by a plane 8 units from the center of the sphere. Set up the triple integral for the volume of D in cylindrical coordinates.

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 9 } ^ { \sqrt { 64 - r ^ { 2 } } } r d z d r d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 17 } } \int _ { 9 } ^ { \sqrt { 64 - r ^ { 2 } } } \mathrm { rdzdrd \theta }\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 17 } } \int _ { 8 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 145 } } \int _ { 8 } ^ { \sqrt { 81 - r ^ { 2 } } } r d z d r d \theta\)

Understand the key elements and phases of the writing process.

Identify and apply effective communication techniques, including verbal and nonverbal responses.

Recognize and implement the use of positive language to improve message tone.

Distinguish between effective and ineffective sentence structures in business writing.

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Definitions:

Acculturation

The process by which individuals adapt to and adopt elements of a different culture, often through exposure or migration.

Cultural Modification

The process by which an individual's or group's culture changes due to contact with other cultures, technologies, or ideas.

Hypertension

A condition where the force of the blood against the artery walls is too high, often leading to health issues such as heart disease.

Prejudice and Discrimination

Biased attitudes towards individuals or groups based on preconceived notions and unfair treatment stemming from those biases.