Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 69

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } ( x , y , z ) = \frac { x } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } } \mathbf { i } + \frac { y } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } } \mathbf { j } + \frac { z } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } } \mathbf { k }$ and S is the sphere $x ^ { 2 } + y ^ { 2 } + ( z - 5 ) ^ { 2 } = 9$ .

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Definitions:

Cross-lagged

A statistical technique used to analyze the directional relationships between variables at different points in time.

Cohort

A group of individuals with a shared characteristic, usually studied over a period of time to observe changes and effects within the group.

Respondents

Individuals who provide data or answers to a survey, questionnaire, or study.

Surveys

Research methods involving the collection of data from a predefined group of respondents to gather information and insights on various topics.