What Region Of $\mathbb { R } ^ { 3 }$

question 6

Multiple Choice

What region of $\mathbb { R } ^ { 3 }$ is represented by the inequality $x ^ { 2 } + y ^ { 2 } \leq 1$ ?

• A)points inside a circular cylinder with axis the x-axis
• B)points inside a circular cylinder with axis the y-axis
• C)points inside a circular cylinder with axis the z-axis
• D)points inside a sphere of radius 1
• E)points inside a sphere of radius \(\sqrt { 2 }\)
• F)points inside a sphere of radius 2
• G)points inside a sphere of radius \(\sqrt { 3 }\)
• H)points inside a sphere of radius 3

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Definitions:

Nativism

The psychological theory that certain abilities or knowledge are innate and not acquired through learning or experience.

Learning Theory

A framework that describes how individuals absorb, process, and retain knowledge or skills through experience, study, or teaching.

Articles and Prepositions

Words used in language to specify grammatical relationships, with articles defining specificity (a, an, the) and prepositions indicating relationships in space and time (in, on, at).

Syntax

The set of rules, principles, and processes that govern the structure of sentences in a given language, especially in terms of word order and punctuation.