Let S Be the Sphere of Radius 4 Centered at the Origin

question 4

Multiple Choice

Let S be the sphere of radius 4 centered at the origin, oriented outward. Find $\vec { n }$ , the unit normal vector to S in the direction of orientation.

• A) \(\vec { n } = \frac { x } { 4 } \vec { i } + \frac { y } { 4 } \vec { j } + \frac { z } { 4 } \vec { k }\)
• B) \(\vec { n } = x \vec { i } + y \vec { j } + z \vec { k }\)
• C) \(\vec { n } = \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \vec { i } + \frac { y ^ { 2 } } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \vec { j } + \frac { z ^ { 2 } } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \vec { k }\)
• D) \(\vec { n } = \frac { x } { 16 } \vec { i } + \frac { y } { 16 } \vec { j } + \frac { z } { 16 } \vec { k }\)

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Definitions:

F-ratio

A statistical measure that is used to compare the variance among group means in a sample.

Null Hypothesis

The null hypothesis is a default hypothesis that there is no significant effect or difference present, to be tested against the alternative hypothesis.

GPAs

Grade Point Averages (GPAs) are numerical calculations used to assess a student's academic performance, typically on a scale from 0 to 4.0.

F-ratio

A statistical measure used in the analysis of variance (ANOVA) to compare the variability between groups to variability within groups.