Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 2.6, Problem 22E
To determine
The number of ways to choose 2 songs out of 9.
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Month PercentApr 1972 4.97May 1972 5.00Jun 1972 5.04Jul 1972 5.25Aug 1972 5.27Sep 1972 5.50Oct 1972 5.73Nov 1972 5.75Dec 1972 5.79Jan 1973 6.00Feb 1973 6.02Mar 1973 6.30Apr 1973 6.61May 1973 7.01Jun 1973 7.49Jul 1973 8.30Aug 1973 9.23Sep 1973 9.86Oct 1973 9.94Nov 1973 9.75Dec 1973 9.75Jan 1974 9.73Feb 1974 9.21Mar 1974 8.85Apr 1974 10.02May 1974 11.25Jun 1974 11.54Jul 1974 11.97Aug 1974 12.00Sep 1974 12.00Oct 1974 11.68Nov 1974 10.83Dec 1974 10.50Jan 1975 10.05Feb 1975 8.96Mar 1975 7.93Apr 1975 7.50May 1975 7.40Jun 1975 7.07Jul 1975 7.15Aug 1975 7.66Sep 1975 7.88Oct 1975 7.96Nov 1975 7.53Dec 1975 7.26Jan 1976 7.00Feb 1976 6.75Mar 1976 6.75Apr 1976 6.75May 1976…
Using FDF, BDF, and CDF, find the first derivative;
1. The distance x of a runner from a fixed point is measured (in meters) at an
interval of half a second. The data obtained is:
t
0
x
0
0.5
3.65
1.0
1.5
2.0
6.80
9.90
12.15
Use CDF to approximate the runner's velocity at times t = 0.5s and t = 1.5s
2. Using FDF, BDF, and CDF, find the first derivative of f(x)=x Inx for an input
of 2 assuming a step size of 1. Calculate using Analytical Solution and
Absolute Relative Error:
=
True Value - Approximate Value|
x100
True Value
3. Given the data below where f(x)
sin (3x), estimate f(1.5) using Langrage
Interpolation.
x
1
1.3
1.6
1.9
2.2
f(x)
0.14
-0.69
-0.99
-0.55
0.31
4. The vertical distance covered by a rocket from t=8 to t=30 seconds is given
by:
30
x =
Loo (2000ln
140000
140000
-
2100
9.8t) dt
Using the Trapezoidal Rule, n=2, find the distance covered.
5. Use Simpson's 1/3 and 3/8 Rule to approximate for sin x dx. Compare the
results for n=4 and n=8
Can you check if my step is correct?
Chapter 2 Solutions
Discrete Mathematics
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which (A − B) − C ≠ A...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - If A is a set containing m elements and B is a set...Ch. 2.1 - Under what conditions is A − B = B − A?
Ch. 2.1 - Under what conditions is A ⋃ B = A?
Ch. 2.1 - Under what conditions is A ⋂ B = A?
Ch. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prove the set equalities in Exercises...Ch. 2.1 - Prob. 39ECh. 2.1 - Prove that (A × C) ⋃ (B × D) ⊆ (A ⋃ B) × (C ⋃ D).
Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1-12, determine which of the...Ch. 2.2 - Prob. 6ECh. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - Prob. 8ECh. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - Prob. 12ECh. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - Prob. 17ECh. 2.2 - In Exercises 13–18, show that the given relation R...Ch. 2.2 - Prob. 19ECh. 2.2 - Write the equivalence relation on {1, 2, 3, 4, 5,...Ch. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Let R1 and R2 be equivalence relations on sets S1...Ch. 2.2 - Determine the number of relations on a set S...Ch. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - How many partitions are there of a set containing...Ch. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 33ECh. 2.3 - In Exercises 1–8, determine whether the given...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Consider the “divides” relation on the set of...Ch. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Determine formulas for the functions gf and fg in...Ch. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - Prob. 49ECh. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - Prob. 52ECh. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - Find a subset Y of the set of real numbers X such...Ch. 2.4 - Find a subset Y of the set of real numbers X such...Ch. 2.4 - Prob. 63ECh. 2.4 - If X has m elements and Y has n elements, how many...Ch. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.5 - Compute the Fibonacci numbers F1 through F10.
Ch. 2.5 - Suppose that a number xn is defined recursively by...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - In Exercises 7–10, determine what is wrong with...Ch. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - A sequence s0, s1, s2,… is called a geometric...Ch. 2.5 - A sequence, s0, s1, s2,… is called an arithmetic...Ch. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
4. C(12,...Ch. 2.6 - Evaluate the numbers in Exercises 1–12.
5. C(11,...Ch. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
8. C(13,...Ch. 2.6 - Evaluate the numbers in Exercises 1–12.
9. C(n,...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
12.
Ch. 2.6 - Prob. 13ECh. 2.6 - How many nonempty subsets of the set {a, e, i, o,...Ch. 2.6 - At Avanti’s, a pizza can be ordered with any...Ch. 2.6 - If a test consists of 12 questions to be answered...Ch. 2.6 - Prob. 17ECh. 2.6 - Jennifer’s grandmother has told her that she can...Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 33ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2 - Prob. 1SECh. 2 - Prob. 2SECh. 2 - Prob. 3SECh. 2 - Prob. 4SECh. 2 - Prob. 5SECh. 2 - Prob. 6SECh. 2 - Prob. 7SECh. 2 - Prob. 8SECh. 2 - Prob. 9SECh. 2 - Draw Venn diagrams depicting the sets in Exercises...Ch. 2 - Prob. 11SECh. 2 - Prob. 12SECh. 2 - Prob. 13SECh. 2 - Prob. 14SECh. 2 - Prob. 15SECh. 2 - Prob. 16SECh. 2 - Prob. 17SECh. 2 - Prob. 18SECh. 2 - Prob. 19SECh. 2 - Prob. 20SECh. 2 - Prob. 21SECh. 2 - Prob. 22SECh. 2 - Prob. 23SECh. 2 - Prob. 24SECh. 2 - Prob. 25SECh. 2 - Prob. 26SECh. 2 - Prob. 27SECh. 2 - Prob. 28SECh. 2 - Prob. 29SECh. 2 - Prob. 30SECh. 2 - Prob. 31SECh. 2 - Prob. 32SECh. 2 - Prob. 33SECh. 2 - Prob. 34SECh. 2 - Prob. 35SECh. 2 - How many equivalence relations on S = {a, b, c}...Ch. 2 - Prob. 37SECh. 2 - Prob. 38SECh. 2 - Prob. 39SECh. 2 - Prob. 40SECh. 2 - Prob. 41SECh. 2 - Prob. 42SECh. 2 - Prob. 43SECh. 2 - Prob. 44SECh. 2 - Prob. 45SECh. 2 - Prob. 46SECh. 2 - Prob. 47SECh. 2 - Prob. 49SECh. 2 - Prob. 50SECh. 2 - Prob. 51SECh. 2 - Prob. 52SECh. 2 - Prob. 53SECh. 2 - Prob. 54SECh. 2 - Prob. 55SECh. 2 - Prob. 56SECh. 2 - Prob. 57SECh. 2 - Prob. 58SECh. 2 - Prob. 59SECh. 2 - Prob. 60SECh. 2 - Prob. 61SECh. 2 - Prob. 62SECh. 2 - Prob. 63SECh. 2 - Prob. 64SECh. 2 - Prove the results in Exercises 63–72 by...Ch. 2 - Prob. 66SECh. 2 - Prob. 67SECh. 2 - Prob. 68SECh. 2 - Prob. 69SECh. 2 - Prob. 70SECh. 2 - Prob. 71SECh. 2 - Prob. 72SECh. 2 - Prob. 1CPCh. 2 - Prob. 6CPCh. 2 - Prob. 7CPCh. 2 - Prob. 12CP
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