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- Consider a circle of radius 5 in 2-dimensional space centered at the origin. We know we can parameterize this circle as r(t) = (5 cos(t), 5 sin(t)), where t runs from 0 to 27. (a) Find r' (t) and r'(t). (b) If this parameterization represents the motion of a particle around a circle, what is the speed of the particle? (c) Modify the parameterization so that the particle instead moves around the circle at a speed of 1.

- Consider a circle of radius 5 in 2-dimensional space centered at the origin. We know we can parameterize this circle as r(t) = (5 cos(t), 5 sin(t)), where t runs from 0 to 27. (a) Find r' (t) and r'(t). (b) If this parameterization represents the motion of a particle around a circle, what is the speed of the particle? (c) Modify the parameterization so that the particle instead moves around the circle at a speed of 1.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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- Consider a circle of radius 5 in 2-dimensional space centered at the origin. We know we can parameterize this circle as r(t) = (5 cos(t), 5 sin(t)), where t runs from 0 to 27. (a) Find r' (t) and r'(t). (b) If this parameterization represents the motion of a particle around a circle, what is the speed of the particle? (c) Modify the parameterization so that the particle instead moves around the circle at a speed of 1.
Transcribed Image Text:- Consider a circle of radius 5 in 2-dimensional space centered at the origin. We know we can parameterize this circle as r(t) = (5 cos(t), 5 sin(t)), where t runs from 0 to 27. (a) Find r' (t) and r'(t). (b) If this parameterization represents the motion of a particle around a circle, what is the speed of the particle? (c) Modify the parameterization so that the particle instead moves around the circle at a speed of 1.
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