Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 2.1, Problem 54E
To determine
To calculate: The value 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 2 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 2.1 - Prob. 1ECh. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Match each set in Group I with the appropriate...Ch. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - List all the elements of each set. Use set...Ch. 2.1 - List all the elements of each set. Use set...Ch. 2.1 - List all the elements of each set. Use set...Ch. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Denote each set by the listing method. There may...Ch. 2.1 - Denote each set by the listing method. There may...Ch. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Denote each set by the listing method. There may...Ch. 2.1 - Prob. 25ECh. 2.1 - 26 {(x, y) |x and y are integers, and
Ch. 2.1 - Denote each set by set-builder notation using x as...Ch. 2.1 - Denote each set by set-builder notation, using x...Ch. 2.1 - 29.
Ch. 2.1 - Denote each set by set-builder notation, using x...Ch. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Identify each set as finite or infinite.
35.
Ch. 2.1 - Identify each set as finite or infinite. {6,12,18}Ch. 2.1 - Identify each set as finite or infinite. {...Ch. 2.1 - Identify each set as finite or infinite. 3,6,9,Ch. 2.1 - Prob. 39ECh. 2.1 - Identify each set as finite or infinite.
40 {x|x...Ch. 2.1 - Identify each set as finite or infinite. {x|x is a...Ch. 2.1 - Identify each set as finite or infinite. {x|x is a...Ch. 2.1 - Find n (A) for each set. A=0,1,2,3,4,5,6,7Ch. 2.1 - Find n (A) for each set. A=3,1,1,3,5,7,9Ch. 2.1 - Find n (A) for each set.
45.
Ch. 2.1 - Find n (A) for each set. A=0,1,2,3,,2000Ch. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Find n (A) for each set. A={...Ch. 2.1 - Prob. 52ECh. 2.1 - Although x is a consonant why can we write x is a...Ch. 2.1 - Prob. 54ECh. 2.1 - Prob. 55ECh. 2.1 - Identify each set as well defined or not well...Ch. 2.1 - Prob. 57ECh. 2.1 - Prob. 58ECh. 2.1 - Fill each blank with either or to make each...Ch. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Prob. 64ECh. 2.1 - Fill each blank with either or to make each...Ch. 2.1 - The statement 96,86,76 is true even though the...Ch. 2.1 - Write true or false for each statement. 32,5,6,8Ch. 2.1 - Write true or false for each statement. m1,m,n,o,pCh. 2.1 - Prob. 69ECh. 2.1 - Write true or false for each statement. 2-2,5,8,9Ch. 2.1 - Write true or false for each statement....Ch. 2.1 - Prob. 72ECh. 2.1 - Write true or false for each statement....Ch. 2.1 - Prob. 74ECh. 2.1 - Prob. 75ECh. 2.1 - Prob. 76ECh. 2.1 - Prob. 77ECh. 2.1 - Prob. 78ECh. 2.1 - Prob. 79ECh. 2.1 - Prob. 80ECh. 2.1 - Write true or false for each statement in...Ch. 2.1 - Prob. 82ECh. 2.1 - Prob. 83ECh. 2.1 - Prob. 84ECh. 2.1 - 85. The human mind likes to create collections....Ch. 2.1 - Prob. 86ECh. 2.1 - Prob. 87ECh. 2.1 - Prob. 88ECh. 2.1 - Prob. 89ECh. 2.1 - Prob. 90ECh. 2.1 - Prob. 91ECh. 2.1 - Prob. 92ECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Insert or in each blank to obtain a true...Ch. 2.2 - Prob. 13ECh. 2.2 - {red, blue, yellow}_____{yellow, blue, red}Ch. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - 17. _____{0}
Ch. 2.2 - _____Ch. 2.2 - {0, 1, 2, 3}______{1, 2, 3, 4}Ch. 2.2 - 20.{ 56,98 }{ 65,89 }Ch. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - For Exercises 21-36, tell whether each statement...Ch. 2.2 - For Exercises 21-36, tell whether each statement...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - For Exercises 37-40, find (a) the number of...Ch. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Fly to California Drive to Califorina Higher cost...Ch. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 55ECh. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Prob. 59ECh. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Prob. 63ECh. 2.2 - Prob. 64ECh. 2.3 - Match each term in Group I with the appropriate...Ch. 2.3 - Match each term in Group I with the appropriate...Ch. 2.3 - Match each term in Group I with the appropriate...Ch. 2.3 - Match each term in Group I with the appropriate...Ch. 2.3 - Match each term in Group I with the appropriate...Ch. 2.3 - Match each term in Group I with the appropriate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Perform the indicated operations, and designate...Ch. 2.3 - Prob. 15ECh. 2.3 - 16.
Ch. 2.3 - Prob. 17ECh. 2.3 - 18.
Ch. 2.3 - (ZX)YCh. 2.3 - (TX)ZCh. 2.3 - X(XY)Ch. 2.3 - Prob. 22ECh. 2.3 - 23
Ch. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - (AB)(BA)Ch. 2.3 - 27.
Ch. 2.3 - (AB)CCh. 2.3 - Prob. 29ECh. 2.3 - TACh. 2.3 - Prob. 31ECh. 2.3 - TACh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - An accountant is sorting tax returns in her files...Ch. 2.3 - Prob. 37ECh. 2.3 - 38.
Ch. 2.3 - 39.
Ch. 2.3 - n(AB)=n(A)+n(B)(AB)Ch. 2.3 - For Exercises41-44 use your results in parts (a)...Ch. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - For Exercises 41-44 use your results in parts (a)...Ch. 2.3 - Prob. 45ECh. 2.3 - (2,13)=(13,2)Ch. 2.3 - 6,3=3,6Ch. 2.3 - 48.
Ch. 2.3 - Find and for A and B defined as follows.
49.
Ch. 2.3 - Prob. 50ECh. 2.3 - Use the given information to find n(AB) and n(BA)...Ch. 2.3 - n(A)=13 and n(B)=5Ch. 2.3 - Find the cardinal number specified. If n(AB)=72...Ch. 2.3 - Find the cardinal number specified. If n(AB)=300...Ch. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Use a Venn diagram similar to the one shown below...Ch. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Use a Venn diagram similar to the one shown below...Ch. 2.3 - Prob. 64ECh. 2.3 - Prob. 65ECh. 2.3 - Prob. 66ECh. 2.3 - Prob. 67ECh. 2.3 - Prob. 68ECh. 2.3 - Prob. 69ECh. 2.3 - Use a Venn diagram to shade each set (AC)BCh. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - Prob. 73ECh. 2.3 - Write a description of each shaded area Use the...Ch. 2.3 - Write a description of each shaded area Use the...Ch. 2.3 - Write a description of each shaded area Use the...Ch. 2.3 - Prob. 77ECh. 2.3 - Prob. 78ECh. 2.3 - Prob. 79ECh. 2.3 - Prob. 80ECh. 2.3 - Prob. 81ECh. 2.3 - Prob. 82ECh. 2.3 - Prob. 83ECh. 2.3 - Prob. 84ECh. 2.3 - Prob. 85ECh. 2.3 - Prob. 86ECh. 2.3 - Prob. 87ECh. 2.3 - Prob. 88ECh. 2.3 - Prob. 89ECh. 2.3 - Prob. 90ECh. 2.4 - Prob. 1ECh. 2.4 - 2.
a
b
c
d
e
Ch. 2.4 - 3 a ABC b ABC c. ABC d ABC e ABC f ABC g ABC h ABCCh. 2.4 -
4.
a
b
c.
d
e
f
g
h
Ch. 2.4 - In Exercises 5-10, make use of an appropriate...Ch. 2.4 - Find the value of n(AB) if n(A)=16,n(B)=28, and...Ch. 2.4 - Find the value of n (AB) if n(A)=20,n(B)=12, and...Ch. 2.4 - In Exercises 5-10, make use of an appropriate...Ch. 2.4 - 9. Find the value of n (A) if and
Ch. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - n(A)=25,n(B)=28,n(AB)=40,n(AB)=10Ch. 2.4 - 14.
Ch. 2.4 - Prob. 15ECh. 2.4 - ...Ch. 2.4 - 17
Ch. 2.4 - 18
Ch. 2.4 - Use Venn diagrams to work each problem.
19....Ch. 2.4 - Compact Disc Collection Gitti is a fan of the...Ch. 2.4 - Student Response to Classical Composers The 65...Ch. 2.4 - Financial Aid for Students At a southern...Ch. 2.4 - 23 Animated Movies A middle school counselor...Ch. 2.4 - 24 Non-Mainline Religious Beliefs 140 U S adults...Ch. 2.4 - Survey on Attitudes toward Religion Researchers...Ch. 2.4 - Prob. 26ECh. 2.4 - Hospital Patient Symptoms A survey was conducted...Ch. 2.4 - Song Themes It was once said that country-western...Ch. 2.4 - Prob. 29ECh. 2.4 - Sports Viewing A survey of 130 TV viewers was...Ch. 2.4 - Prob. 31ECh. 2.4 - Army Housing A study of U S. Army housing trends...Ch. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - In Exercises 1-14 let
Identify each statement as...Ch. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - In Exercises 1-14 let...Ch. 2 - n[(AB)C]=4Ch. 2 - In Exercises 1-14 let
Identify each statement as...Ch. 2 - Prob. 11TCh. 2 - In Exercises 1-14 let...Ch. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Give a word description for each set. {-3, -1, 1,...Ch. 2 - Give a word description for each set.
16. {Sun,...Ch. 2 - Express each set in set-builder notation.
17. {-1,...Ch. 2 - Express each set in set-builder notation.
18. {24,...Ch. 2 - Place both, or neither in each blank to make a...Ch. 2 - Place both, or neither in each blank to make a...Ch. 2 - Prob. 21TCh. 2 - Prob. 22TCh. 2 - Prob. 23TCh. 2 - Prob. 24TCh. 2 - 25 State De Morgan's laws for sets in words rather...Ch. 2 - Facts about Inventions The table lists ten...Ch. 2 - Prob. 27TCh. 2 - Prob. 28TCh. 2 - Prob. 29TCh. 2 - Financial Aid to College Students Three sources of...
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