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 33PS
To determine
To sketch the cylindrical surface
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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,
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
15. Evaluate
x° ds where C is the part of the parabola y = x² from (0,0) to (2,4).
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
Ch. 9.1 - Prob. 11PSCh. 9.1 - Prob. 12PSCh. 9.1 - Prob. 13PSCh. 9.1 - Prob. 14PSCh. 9.1 - Prob. 15PSCh. 9.1 - Prob. 16PSCh. 9.1 - Prob. 17PSCh. 9.1 - Prob. 18PSCh. 9.1 - Prob. 19PSCh. 9.1 - Prob. 20PSCh. 9.1 - Prob. 21PSCh. 9.1 - Prob. 22PSCh. 9.1 - Prob. 23PSCh. 9.1 - Prob. 24PSCh. 9.1 - Prob. 25PSCh. 9.1 - Prob. 26PSCh. 9.1 - Prob. 27PSCh. 9.1 - Prob. 28PSCh. 9.1 - Prob. 29PSCh. 9.1 - Prob. 30PSCh. 9.1 - Prob. 31PSCh. 9.1 - Prob. 32PSCh. 9.1 - Prob. 33PSCh. 9.1 - Prob. 34PSCh. 9.1 - Prob. 35PSCh. 9.1 - Prob. 36PSCh. 9.1 - Prob. 37PSCh. 9.1 - Prob. 38PSCh. 9.1 - Prob. 39PSCh. 9.1 - Prob. 40PSCh. 9.1 - Prob. 41PSCh. 9.1 - Prob. 42PSCh. 9.1 - Prob. 43PSCh. 9.1 - Prob. 44PSCh. 9.1 - Prob. 45PSCh. 9.1 - Prob. 46PSCh. 9.1 - Prob. 47PSCh. 9.1 - Prob. 48PSCh. 9.1 - Prob. 49PSCh. 9.1 - Prob. 50PSCh. 9.1 - Prob. 51PSCh. 9.1 - Prob. 52PSCh. 9.1 - Prob. 53PSCh. 9.1 - Prob. 54PSCh. 9.1 - Prob. 55PSCh. 9.1 - Prob. 56PSCh. 9.1 - Prob. 57PSCh. 9.1 - Prob. 58PSCh. 9.1 - Prob. 59PSCh. 9.1 - Prob. 60PSCh. 9.2 - 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Prob. 34PSCh. 9.4 - Prob. 35PSCh. 9.4 - Prob. 36PSCh. 9.4 - Prob. 37PSCh. 9.4 - Prob. 38PSCh. 9.4 - Prob. 39PSCh. 9.4 - Prob. 40PSCh. 9.4 - Prob. 41PSCh. 9.4 - Prob. 42PSCh. 9.4 - Prob. 43PSCh. 9.4 - Prob. 44PSCh. 9.4 - Prob. 45PSCh. 9.4 - Prob. 46PSCh. 9.4 - Prob. 47PSCh. 9.4 - Prob. 48PSCh. 9.4 - Prob. 49PSCh. 9.4 - Prob. 50PSCh. 9.4 - Prob. 51PSCh. 9.4 - Prob. 52PSCh. 9.4 - Prob. 53PSCh. 9.4 - Prob. 54PSCh. 9.4 - Prob. 55PSCh. 9.4 - Prob. 56PSCh. 9.4 - Prob. 57PSCh. 9.4 - Prob. 58PSCh. 9.4 - Prob. 59PSCh. 9.4 - Prob. 60PSCh. 9.5 - Prob. 1PSCh. 9.5 - Prob. 2PSCh. 9.5 - Prob. 3PSCh. 9.5 - Prob. 4PSCh. 9.5 - Prob. 5PSCh. 9.5 - Prob. 6PSCh. 9.5 - Prob. 7PSCh. 9.5 - Prob. 8PSCh. 9.5 - Prob. 9PSCh. 9.5 - Prob. 10PSCh. 9.5 - Prob. 11PSCh. 9.5 - Prob. 12PSCh. 9.5 - Prob. 13PSCh. 9.5 - Prob. 14PSCh. 9.5 - Prob. 15PSCh. 9.5 - Prob. 16PSCh. 9.5 - Prob. 17PSCh. 9.5 - Prob. 18PSCh. 9.5 - Prob. 19PSCh. 9.5 - Prob. 20PSCh. 9.5 - Prob. 21PSCh. 9.5 - Prob. 22PSCh. 9.5 - Prob. 23PSCh. 9.5 - Prob. 24PSCh. 9.5 - Prob. 25PSCh. 9.5 - Prob. 26PSCh. 9.5 - Prob. 27PSCh. 9.5 - Prob. 28PSCh. 9.5 - Prob. 29PSCh. 9.5 - Prob. 30PSCh. 9.5 - Prob. 31PSCh. 9.5 - Prob. 32PSCh. 9.5 - Prob. 33PSCh. 9.5 - Prob. 34PSCh. 9.5 - Prob. 35PSCh. 9.5 - Prob. 36PSCh. 9.5 - Prob. 37PSCh. 9.5 - Prob. 38PSCh. 9.5 - Prob. 39PSCh. 9.5 - Prob. 40PSCh. 9.5 - Prob. 41PSCh. 9.5 - Prob. 42PSCh. 9.5 - Prob. 43PSCh. 9.5 - Prob. 44PSCh. 9.5 - Prob. 45PSCh. 9.5 - Prob. 46PSCh. 9.5 - Prob. 47PSCh. 9.5 - Prob. 48PSCh. 9.5 - Prob. 49PSCh. 9.5 - Prob. 50PSCh. 9.5 - Prob. 51PSCh. 9.5 - Prob. 52PSCh. 9.5 - Prob. 53PSCh. 9.5 - Prob. 54PSCh. 9.5 - Prob. 55PSCh. 9.5 - Prob. 56PSCh. 9.5 - Prob. 57PSCh. 9.5 - Prob. 58PSCh. 9.5 - Prob. 59PSCh. 9.5 - Prob. 60PSCh. 9.6 - Prob. 1PSCh. 9.6 - Prob. 2PSCh. 9.6 - Prob. 3PSCh. 9.6 - Prob. 4PSCh. 9.6 - Prob. 5PSCh. 9.6 - Prob. 6PSCh. 9.6 - Prob. 7PSCh. 9.6 - Prob. 8PSCh. 9.6 - Prob. 9PSCh. 9.6 - Prob. 10PSCh. 9.6 - Prob. 11PSCh. 9.6 - Prob. 12PSCh. 9.6 - Prob. 13PSCh. 9.6 - Prob. 14PSCh. 9.6 - Prob. 15PSCh. 9.6 - Prob. 16PSCh. 9.6 - Prob. 17PSCh. 9.6 - Prob. 18PSCh. 9.6 - Prob. 19PSCh. 9.6 - Prob. 20PSCh. 9.6 - Prob. 21PSCh. 9.6 - Prob. 22PSCh. 9.6 - Prob. 23PSCh. 9.6 - Prob. 24PSCh. 9.6 - Prob. 25PSCh. 9.6 - Prob. 26PSCh. 9.6 - Prob. 27PSCh. 9.6 - Prob. 28PSCh. 9.6 - Prob. 29PSCh. 9.6 - Prob. 30PSCh. 9.6 - Prob. 31PSCh. 9.6 - Prob. 32PSCh. 9.6 - Prob. 33PSCh. 9.6 - Prob. 34PSCh. 9.6 - Prob. 35PSCh. 9.6 - Prob. 36PSCh. 9.6 - Prob. 37PSCh. 9.6 - Prob. 38PSCh. 9.6 - Prob. 39PSCh. 9.6 - Prob. 40PSCh. 9.6 - Prob. 41PSCh. 9.6 - Prob. 42PSCh. 9.6 - Prob. 43PSCh. 9.6 - Prob. 44PSCh. 9.6 - Prob. 45PSCh. 9.6 - Prob. 46PSCh. 9.6 - Prob. 47PSCh. 9.6 - Prob. 48PSCh. 9.6 - Prob. 49PSCh. 9.6 - Prob. 50PSCh. 9.6 - Prob. 51PSCh. 9.6 - Prob. 52PSCh. 9.6 - Prob. 53PSCh. 9.6 - Prob. 54PSCh. 9.6 - Prob. 55PSCh. 9.6 - Prob. 56PSCh. 9.6 - Prob. 57PSCh. 9.6 - Prob. 58PSCh. 9.6 - Prob. 59PSCh. 9.6 - Prob. 60PSCh. 9.7 - Prob. 1PSCh. 9.7 - Prob. 2PSCh. 9.7 - Prob. 3PSCh. 9.7 - Prob. 4PSCh. 9.7 - Prob. 5PSCh. 9.7 - Prob. 6PSCh. 9.7 - Prob. 7PSCh. 9.7 - Prob. 8PSCh. 9.7 - Prob. 9PSCh. 9.7 - Prob. 10PSCh. 9.7 - Prob. 11PSCh. 9.7 - Prob. 12PSCh. 9.7 - Prob. 13PSCh. 9.7 - Prob. 14PSCh. 9.7 - Prob. 15PSCh. 9.7 - Prob. 16PSCh. 9.7 - Prob. 17PSCh. 9.7 - Prob. 18PSCh. 9.7 - Prob. 19PSCh. 9.7 - Prob. 20PSCh. 9.7 - Prob. 21PSCh. 9.7 - Prob. 22PSCh. 9.7 - Prob. 23PSCh. 9.7 - Prob. 24PSCh. 9.7 - Prob. 25PSCh. 9.7 - Prob. 26PSCh. 9.7 - Prob. 27PSCh. 9.7 - Prob. 28PSCh. 9.7 - Prob. 29PSCh. 9.7 - Prob. 30PSCh. 9.7 - Prob. 31PSCh. 9.7 - Prob. 32PSCh. 9.7 - Prob. 33PSCh. 9.7 - Prob. 34PSCh. 9.7 - Prob. 35PSCh. 9.7 - Prob. 36PSCh. 9.7 - Prob. 37PSCh. 9.7 - Prob. 38PSCh. 9.7 - Prob. 39PSCh. 9.7 - Prob. 40PSCh. 9.7 - Prob. 41PSCh. 9.7 - Prob. 42PSCh. 9.7 - Prob. 43PSCh. 9.7 - Prob. 44PSCh. 9.7 - Prob. 45PSCh. 9.7 - Prob. 46PSCh. 9.7 - Prob. 47PSCh. 9.7 - Prob. 48PSCh. 9.7 - Prob. 49PSCh. 9.7 - Prob. 50PSCh. 9.7 - Prob. 51PSCh. 9.7 - Prob. 52PSCh. 9.7 - Prob. 53PSCh. 9.7 - Prob. 54PSCh. 9.7 - Prob. 55PSCh. 9.7 - Prob. 56PSCh. 9.7 - Prob. 57PSCh. 9.7 - 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 - Prob. 25SPCh. 9 - Prob. 26SPCh. 9 - Prob. 27SPCh. 9 - Prob. 28SPCh. 9 - Prob. 29SPCh. 9 - Prob. 30SPCh. 9 - Prob. 31SPCh. 9 - Prob. 32SPCh. 9 - Prob. 33SPCh. 9 - Prob. 34SPCh. 9 - Prob. 35SPCh. 9 - Prob. 36SPCh. 9 - Prob. 37SPCh. 9 - Prob. 38SPCh. 9 - Prob. 39SPCh. 9 - Prob. 40SPCh. 9 - Prob. 41SPCh. 9 - Prob. 42SPCh. 9 - Prob. 43SPCh. 9 - Prob. 44SPCh. 9 - Prob. 45SPCh. 9 - Prob. 46SPCh. 9 - Prob. 47SPCh. 9 - Prob. 48SPCh. 9 - Prob. 49SPCh. 9 - Prob. 50SPCh. 9 - Prob. 51SPCh. 9 - Prob. 52SPCh. 9 - Prob. 53SPCh. 9 - Prob. 54SPCh. 9 - Prob. 55SPCh. 9 - Prob. 56SPCh. 9 - Prob. 57SPCh. 9 - Prob. 58SPCh. 9 - Prob. 59SPCh. 9 - Prob. 60SPCh. 9 - Prob. 61SPCh. 9 - Prob. 62SPCh. 9 - Prob. 63SPCh. 9 - Prob. 64SPCh. 9 - Prob. 65SPCh. 9 - Prob. 66SPCh. 9 - Prob. 67SPCh. 9 - Prob. 68SPCh. 9 - Prob. 69SPCh. 9 - Prob. 70SPCh. 9 - Prob. 71SPCh. 9 - Prob. 72SPCh. 9 - Prob. 73SPCh. 9 - Prob. 74SPCh. 9 - Prob. 75SPCh. 9 - Prob. 76SPCh. 9 - Prob. 77SPCh. 9 - Prob. 78SPCh. 9 - Prob. 79SPCh. 9 - Prob. 80SPCh. 9 - 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- Force Repeat Problem 43 for a 25.0-pound weight and a bench inclined at 12.5.arrow_forwardWhat is the equation of a line that is paralel to the ine that goes through the points (2.0) and (-2. a? Ov-x +6 Oy- +1/2) +7 Oy= (14) -2arrow_forward4. 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?arrow_forward
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