Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 3.5, Problem 26E
To determine
The size of the check matrix associated with the generator matrix
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please solve with full steps please
4. Identify at least two mistakes in Francisco's work. Correct the mistakes and
complete the problem by using the second derivative test.
2f
2X
2. Find the relative maximum and relative minimum points of f(x) = 2x3 + 3x² - 3, using the
First Derivative Test or the Second Derivative Test.
bx+ bx
6x +6x=0
12x-
af
24
=
0
x=0
108
-2
5. Identify at least three mistakes in Francisco's work. Then sketch the graph of the
function and label the local max and local min.
1. Find the equation of the tangent line to the curve
y=x-2x3+x-2 at the point (1.-2).
Sketch the araph of y=x42x3+x-2 and the tangent line at (1,-2)
y' = 4x-6x
y' (1) = 4(1) - 667 - 2
=
4(-2)4127-6(-2)
5-8-19-20
=
Chapter 3 Solutions
Discrete Mathematics
Ch. 3.1 - In Exercises 1–8, find the quotient and remainder...Ch. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - In Exercises 1–8, find the quotient and remainder...Ch. 3.1 - In Exercises 1–8, find the quotient and remainder...Ch. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - In Exercises 9–16, determine whether p ≡ q (mod...Ch. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - In Exercises 17–36, perform the indicated...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - In Exercises 17–36, perform the indicated...Ch. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - In Exercises 17–36, perform the indicated...Ch. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - A hospital heart monitoring device uses two feet...Ch. 3.1 - Prob. 39ECh. 3.1 - Use Example 3.2 to determine the correct check...Ch. 3.1 - Prob. 41ECh. 3.1 - Federal Express packages carry a 10-digit...Ch. 3.1 - Prob. 43ECh. 3.1 - Use the formula in Example 3.7 to determine all...Ch. 3.1 - Let A denote the equivalence class containing 4 in...Ch. 3.1 - Prob. 46ECh. 3.1 - Let R be the equivalence relation defined in...Ch. 3.1 - Show that there exist integers m, x, and y such...Ch. 3.1 - Prob. 49ECh. 3.1 - A project has the nine tasks T1, T2, T3, T4, T5,...Ch. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.2 - List, in increasing order, the divisors of 45
Ch. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - List, in increasing order, the common divisors of...Ch. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - In Exercises 5–10, make a table such as the one...Ch. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - In Exercises 13–18, make a table such as the one...Ch. 3.2 - Prob. 19ECh. 3.2 - In Exercises 19–22, use the Euclidean algorithm to...Ch. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - In Exercises 23–26, use the extended Euclidean...Ch. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.3 - Prob. 1ECh. 3.3 - In Exercises 1–4, change the given plaintext...Ch. 3.3 - Prob. 3ECh. 3.3 - In Exercises 1–4, change the given plaintext...Ch. 3.3 - Prob. 5ECh. 3.3 - In Exercises 5–10, apply the modular...Ch. 3.3 - Prob. 7ECh. 3.3 - In Exercises 5–10, apply the modular...Ch. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - In Exercises 11–14, find b corresponding to the...Ch. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - In Exercises 15–22, use the extended Euclidean...Ch. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Suppose n = 93, E = 17, and the ciphertext message...Ch. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.4 - In Exercises 1–8, determine the parity check digit...Ch. 3.4 - In Exercises 1–8, determine the parity check digit...Ch. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - In Exercises 1–8, determine the parity check digit...Ch. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - In Exercises 9–16, use formula (3.1) to determine...Ch. 3.4 - Prob. 13ECh. 3.4 - In Exercises 9–16, use formula (3.1) to determine...Ch. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - In Exercises 17–24, determine the Hamming distance...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - In Exercises 25–32, add the given codewords using...Ch. 3.4 - In Exercises 33–36, suppose that the minimal...Ch. 3.4 - In Exercises 33–36, suppose that the minimal...Ch. 3.4 - In Exercises 33–36, suppose that the minimal...Ch. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 41ECh. 3.5 - Prob. 1ECh. 3.5 - In Exercises 1–4, determine the number of words in...Ch. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - In Exercises 5–8, suppose that the generator...Ch. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - In Exercises 9–12, determine the size of the check...Ch. 3.5 - In Exercises 9–12, determine the size of the check...Ch. 3.5 - If the check matrix of a matrix code is a 9 × 3...Ch. 3.5 - If the check matrix of a matrix code is an 11 × 4...Ch. 3.5 - Prob. 15ECh. 3.5 - In Exercises 15–20, determine all the codewords...Ch. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - In Exercises 21–28, determine the check matrix...Ch. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Exercises 29 and 30, the check matrix A* for a...Ch. 3.5 - Prob. 31ECh. 3.5 - In Exercises 31–38, use Theorem 3.8(b) to...Ch. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Consider the (3, 7)-code with generator...Ch. 3.5 - Prob. 41ECh. 3.5 - Find the generator matrix of the code that encodes...Ch. 3.5 - Prob. 43ECh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - In Exercises 1–8, determine the syndrome of each...Ch. 3.6 - In Exercises 1–8, determine the syndrome of each...Ch. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - In Exercises 9–28, the given word was received...Ch. 3.6 - Prob. 21ECh. 3.6 - In Exercises 9–28, the given word was received...Ch. 3.6 - In Exercises 9–28, the given word was received...Ch. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - In Exercises 29 and 30, a check matrix and a list...Ch. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - In Exercises 31–34, determine the minimal value of...Ch. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - In Exercises 35–38, determine the smallest values...Ch. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prove by mathematical induction that r2 + 1 ≤ 2r...Ch. 3 - Prob. 1SECh. 3 - Prob. 2SECh. 3 - Determine whether each statement in Exercises 1–4...Ch. 3 - Prob. 4SECh. 3 - Prob. 5SECh. 3 - Prob. 6SECh. 3 - Prob. 7SECh. 3 - Prob. 8SECh. 3 - Prob. 9SECh. 3 - Prob. 10SECh. 3 - Prob. 11SECh. 3 - Prob. 12SECh. 3 - Prob. 13SECh. 3 - Prob. 14SECh. 3 - Prob. 15SECh. 3 - Prob. 16SECh. 3 - Prob. 17SECh. 3 - Prob. 18SECh. 3 - Prob. 19SECh. 3 - Prob. 20SECh. 3 - Prob. 21SECh. 3 - Prob. 22SECh. 3 - Prob. 23SECh. 3 - Prob. 24SECh. 3 - Prob. 25SECh. 3 - Prob. 26SECh. 3 - Prob. 27SECh. 3 - Prob. 28SECh. 3 - Prob. 29SECh. 3 - Prob. 30SECh. 3 - Prob. 31SECh. 3 - Prob. 32SECh. 3 - Prob. 33SECh. 3 - Prob. 34SECh. 3 - Prob. 35SECh. 3 - Prob. 36SECh. 3 - Prob. 37SECh. 3 - Prob. 38SECh. 3 - Prob. 39SECh. 3 - Prob. 40SECh. 3 - Prob. 41SECh. 3 - Prob. 42SECh. 3 - Prob. 43SECh. 3 - Prob. 44SECh. 3 - Prob. 45SECh. 3 - Prob. 46SECh. 3 - Prob. 47SECh. 3 - Prob. 48SECh. 3 - Prob. 49SECh. 3 - Prob. 50SECh. 3 - Prob. 51SECh. 3 - Prob. 52SECh. 3 - Prob. 53SECh. 3 - Prob. 54SECh. 3 - Prob. 55SECh. 3 - Prob. 56SECh. 3 - Prob. 57SECh. 3 - Prob. 58SECh. 3 - Prob. 59SECh. 3 - Prob. 60SECh. 3 - Prob. 62SECh. 3 - Prob. 63SECh. 3 - Prob. 64SECh. 3 - Prob. 65SECh. 3 - Prob. 66SECh. 3 - Prob. 67SECh. 3 - Prob. 68SECh. 3 - Prob. 69SECh. 3 - Prob. 70SECh. 3 - Prob. 71SECh. 3 - Prob. 72SECh. 3 - Prob. 73SECh. 3 - Prob. 2CPCh. 3 - Prob. 3CPCh. 3 - Prob. 4CPCh. 3 - Prob. 5CPCh. 3 - Prob. 6CPCh. 3 - Prob. 7CP
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