Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 11, Problem 15E
In each case, give an answer between 0° and 360°.
1. A clockwise rotation by an angle of 710° is equivalent to a counterclockwise rotation by an angle of________.
2. A clockwise rotation by an angle of 710° is equivalent to a clockwise rotation by an angle of_________.
3. A counterclockwise rotation by an angle of 7100° is equivalent to a clockwise rotation by an angle of______________.
4. A clockwise rotation by an angle of 71,000° is equivalent to a clockwise rotation by an angle of___________.
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This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
1. Consider the following preference ballots:
Number of voters
Rankings 6 5 4 2
1st choice A DCB
DC
2nd choice B B D
3rd choice DCBD
4th choice CA
AAA
For each of the four voting systems we have studied, determine who would win the election
in each case. (Remember: For plurality with runoff, all but the top two vote-getters are
simultaneously eliminated at the end of round 1.)
Chapter 11 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 11 - In Fig.1135_, indicate which point is the image of...Ch. 11 - Prob. 2ECh. 11 - Prob. 3ECh. 11 - In Fig. 11-38, P is the image of P under a...Ch. 11 - In Fig.11-39, l is the axis of reflection. a.Find...Ch. 11 - In Fig. 11-40, l is the axis of reflection. a....Ch. 11 - Prob. 7ECh. 11 - In Fig 11-42, P is the image of P under a...Ch. 11 - In Fig. 11-43, P is image of P under a reflection....Ch. 11 - Prob. 10E
Ch. 11 - In Fig. 11-45, A and B are fixed points of a...Ch. 11 - Prob. 12ECh. 11 - In Fig. 11-47, indicate which point is a. the...Ch. 11 - Prob. 14ECh. 11 - In each case, give an answer between 0 and 360. 1....Ch. 11 - Prob. 16ECh. 11 - Prob. 17ECh. 11 - Prob. 18ECh. 11 - Prob. 19ECh. 11 - Prob. 20ECh. 11 - Prob. 21ECh. 11 - Prob. 22ECh. 11 - In Fig. 11-54, indicate which point is the image...Ch. 11 - Prob. 24ECh. 11 - Prob. 25ECh. 11 - In Fig. 11-57, Q is the image of Q under a...Ch. 11 - In Fig. 11-58, D is the image of D under a...Ch. 11 - Prob. 28ECh. 11 - Prob. 29ECh. 11 - Prob. 30ECh. 11 - Prob. 31ECh. 11 - In Fig 11-63, P is the image of P under a glide...Ch. 11 - In Fig.11-64, B is the image of B and D is the...Ch. 11 - Prob. 34ECh. 11 - Prob. 35ECh. 11 - Prob. 36ECh. 11 - In Fig 11-68, D is the image of D and C is the...Ch. 11 - In Fig11-69, A is the image of A and D is the...Ch. 11 - Prob. 39ECh. 11 - Prob. 40ECh. 11 - Prob. 41ECh. 11 - Prob. 42ECh. 11 - Prob. 43ECh. 11 - Prob. 44ECh. 11 - Prob. 45ECh. 11 - Prob. 46ECh. 11 - Find the symmetry type for each of the following...Ch. 11 - Prob. 48ECh. 11 - Prob. 49ECh. 11 - Prob. 50ECh. 11 - Prob. 51ECh. 11 - Prob. 52ECh. 11 - Prob. 53ECh. 11 - Prob. 54ECh. 11 - Prob. 55ECh. 11 - Prob. 56ECh. 11 - Prob. 57ECh. 11 - Prob. 58ECh. 11 - Prob. 59ECh. 11 - Prob. 60ECh. 11 - Prob. 61ECh. 11 - Prob. 62ECh. 11 - Prob. 63ECh. 11 - Prob. 64ECh. 11 - Suppose that a rigid motion M is the product of a...Ch. 11 - Prob. 66ECh. 11 - Prob. 67ECh. 11 - Prob. 68ECh. 11 - Prob. 69ECh. 11 - Prob. 70ECh. 11 - Prob. 71ECh. 11 - Prob. 72ECh. 11 - Prob. 73ECh. 11 - Prob. 74ECh. 11 - Prob. 75ECh. 11 - Prob. 76ECh. 11 - Prob. 77ECh. 11 - Prob. 78ECh. 11 - Prob. 79ECh. 11 - Prob. 80E
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