Write a Set of Parametric Equations for the Surface of Revolution

question 77

Multiple Choice

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function $y = x ^ { \frac { 3 } { 7 } } , 0 \leq x \leq 4$ about the $x$ -axis.

• A) \(x = u ^ { \frac { 3 } { 7 } } , y = u ^ { \frac { 3 } { 7 } } \cos v , z = u ^ { \frac { 3 } { 7 } } \sin v , 0 \leq u \leq 4,0 \leq v \leq 2 \pi\)
• B)\(x = u , y = u ^ { \frac { 3 } { 7 } } \cos v , z = u ^ {\frac { 3 } { 7 } } \sin v , 0 \leq u \leq 4,0 \leq v \leq 2 \pi\)
• C)\(x = u , y = u ^ { \frac { 3 } { 7 } } \sin v , z = u ^ { \frac { 3 } { 7 } } \cos v , 0 \leq u \leq 4 , v \geq 0\)
• D)\(x = u ^ { \frac { 3 } { 7 } } , y = u ^ { \frac { 3 } { 7 } } \sin v , z = u ^ { \frac { 3 } { 7 } } \cos v , u \geq 4,0 \leq v \leq 2 \pi\)
• E)\(x = v , y = v ^ { \frac { 3 } { 7 } } \cos u , z = v ^ { \frac { 3 } { 7 } } \sin u , u \geq 4 , v \geq 0\)

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Definitions:

Reinforcements

In psychology, the use of rewards or punishments to increase or decrease the likelihood of a specific behavior occurring again.

Behaviorism

A theory of learning based on the idea that all behaviors are acquired through conditioning, emphasizing the role of environmental factors over genetics.

Behaviorists

Psychologists who focus on observable behaviors and the ways in which learning influences behavior, excluding internal processes.

Structuralists

Psychologists who aimed to analyze the structure of the mind by breaking down mental processes into their most basic components.