Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 9.2, Problem 35PS
To determine
To sketch the cylindrical surface
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4.
A cyclist is travelling in a straight path at a constant speed along a dirt
road with a button stuck to the outside of one of their wheels.
The movement of the button (as viewed from the side) can be described using the
equations of a cycloid,
I = r(t – sin t),
y = r(1 – cost)
where t represents the angle through which the wheel has rotated and r represents
the radius of the wheel.
See https://en.wikipedia.org/wiki/Cycloid or
https://www.youtube.com/watch?v=x0Z9OeJbRy4 for more details!
Every time the button touches the ground, it leaves a mark on the dirt. If the
marks are 647 cm apart, what is the radius of the tire wheel?
What value(s) of t correspond to the button touching the ground?
Show that when t = 27, we have = 0. Does this mean that the cyclist is
stopped? Why or why not?
dt
8. Find the values of z= V2+3i in rectangular form.
4. A cyclist is travelling in a straight path at a constant speed along a dirt road with a button
stuck to the outside of one of their wheels. The movement of the button (as viewed from the
side) can be described using the equations of a cycloid,
x = r(t - sin t), y = r(1 – cost)
where t represents the angle through which the wheel has rotated and r represents the radius of
the wheel.
See https://en.wikipedia.org/wiki/Cycloid or https://www.youtube.com/watch?v=x0Z9OeJbRy4
for more details!
(a) Every time the button touches the ground, it leaves a blemish on the dirt. If the blemishes
are 64TT cm apart, what is the radius of the tire wheel?
(b) What value(s) of t correspond to the button touching the ground?
(c) Show that when t = 21, we have dx/dt = 0. Does this mean that the cyclist is stopped? Why
or why not?
Chapter 9 Solutions
Calculus
Ch. 9.1 - Prob. 1PSCh. 9.1 - Prob. 2PSCh. 9.1 - Prob. 3PSCh. 9.1 - Prob. 4PSCh. 9.1 - Prob. 5PSCh. 9.1 - Prob. 6PSCh. 9.1 - Prob. 7PSCh. 9.1 - Prob. 8PSCh. 9.1 - Prob. 9PSCh. 9.1 - Prob. 10PS
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Prob. 58PSCh. 9.7 - Prob. 59PSCh. 9.7 - Prob. 60PSCh. 9 - Prob. 1PECh. 9 - Prob. 2PECh. 9 - Prob. 3PECh. 9 - Prob. 4PECh. 9 - Prob. 5PECh. 9 - Prob. 6PECh. 9 - Prob. 7PECh. 9 - Prob. 8PECh. 9 - Prob. 9PECh. 9 - Prob. 10PECh. 9 - Prob. 11PECh. 9 - Prob. 12PECh. 9 - Prob. 13PECh. 9 - Prob. 14PECh. 9 - Prob. 15PECh. 9 - Prob. 16PECh. 9 - Prob. 17PECh. 9 - Prob. 18PECh. 9 - Prob. 19PECh. 9 - Prob. 20PECh. 9 - Prob. 21PECh. 9 - Prob. 22PECh. 9 - Prob. 23PECh. 9 - Prob. 24PECh. 9 - Prob. 25PECh. 9 - Prob. 26PECh. 9 - Prob. 27PECh. 9 - Prob. 28PECh. 9 - Prob. 29PECh. 9 - Prob. 30PECh. 9 - Prob. 1SPCh. 9 - Prob. 2SPCh. 9 - Prob. 3SPCh. 9 - Prob. 4SPCh. 9 - Prob. 5SPCh. 9 - Prob. 6SPCh. 9 - Prob. 7SPCh. 9 - Prob. 8SPCh. 9 - Prob. 9SPCh. 9 - Prob. 10SPCh. 9 - Prob. 11SPCh. 9 - Prob. 12SPCh. 9 - Prob. 13SPCh. 9 - Prob. 14SPCh. 9 - Prob. 15SPCh. 9 - Prob. 16SPCh. 9 - Prob. 17SPCh. 9 - Prob. 18SPCh. 9 - Prob. 19SPCh. 9 - Prob. 20SPCh. 9 - Prob. 21SPCh. 9 - Prob. 22SPCh. 9 - Prob. 23SPCh. 9 - Prob. 24SPCh. 9 - 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