Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center (0, 0) going counterclockwise (b) with center (1, 2) going counterclockwise (c) with center (1,2) going clockwise (d) Now modify this to be a path in 3 dimensional space, for a circle "above" the xy plane with a height of z = 3, with center (1,2,3), and moving counterclockwise as we look down from the positive z-axis. Hint: just set z = 3 and compute the other coordinates as in prior examples. (e) Find the formula for a helix that is found on a standard toilet roll interior (hard to come by?): Use centimeters for units. Note that the diameter is 4.2cm, and the height is 11.4cm, and the number of revolutions of the helix is 1 and 1/8th, i.e. 1.125.
Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center (0, 0) going counterclockwise (b) with center (1, 2) going counterclockwise (c) with center (1,2) going clockwise (d) Now modify this to be a path in 3 dimensional space, for a circle "above" the xy plane with a height of z = 3, with center (1,2,3), and moving counterclockwise as we look down from the positive z-axis. Hint: just set z = 3 and compute the other coordinates as in prior examples. (e) Find the formula for a helix that is found on a standard toilet roll interior (hard to come by?): Use centimeters for units. Note that the diameter is 4.2cm, and the height is 11.4cm, and the number of revolutions of the helix is 1 and 1/8th, i.e. 1.125.
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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Question
![Parametrize a path for the curve that is a circle in the x-y plane that has radius 2
(a) with center (0, 0) going counterclockwise
(b) with center (1, 2) going counterclockwise
(c) with center (1,2) going clockwise
(d) Now modify this to be a path in 3 dimensional space, for a circle "above" the xy plane
with a height of z = 3, with center (1,2,3), and moving counterclockwise as we look
down from the positive z-axis. Hint: just set z = 3 and compute the other coordinates
as in prior examples.
(e) Find the formula for a helix that is found on a standard toilet roll interior (hard to
come by?): Use centimeters for units. Note that the diameter is 4.2cm, and the height
is 11.4cm, and the number of revolutions of the helix is 1 and 1/8th, i.e. 1.125.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff452554f-6d0d-4bc0-879b-554ef167f54f%2F068d498f-8277-433a-a8d2-f90c8c056582%2Fj1az7ks_processed.png&w=3840&q=75)
Transcribed Image Text:Parametrize a path for the curve that is a circle in the x-y plane that has radius 2
(a) with center (0, 0) going counterclockwise
(b) with center (1, 2) going counterclockwise
(c) with center (1,2) going clockwise
(d) Now modify this to be a path in 3 dimensional space, for a circle "above" the xy plane
with a height of z = 3, with center (1,2,3), and moving counterclockwise as we look
down from the positive z-axis. Hint: just set z = 3 and compute the other coordinates
as in prior examples.
(e) Find the formula for a helix that is found on a standard toilet roll interior (hard to
come by?): Use centimeters for units. Note that the diameter is 4.2cm, and the height
is 11.4cm, and the number of revolutions of the helix is 1 and 1/8th, i.e. 1.125.
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