Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter A.3, Problem 8E
To determine
To prove: The theorem “If a divides b, then
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(9) (16 points) Let
F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k
=
-
= (x²+y4,3xy, 2x2 + 2²).
(a) (4 points) Calculate the divergence and curl of F.
(b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² =
16, z ≥ 0.
(c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] ×
[0,1] x [0,1].
(8) (12 points)
(a) (8 points) Let C be the circle x² + y² = 4. Let
F(x, y) = (2y + e²)i + (x + sin(y²))j.
Evaluate the line integral
JF.
F.ds.
Hint: First calculate V x F.
(b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux
integral
√(V × F)
F).dS.
Justify your answer.
Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle.
a = 13, b = 15, C = 68°
Law of Sines
Law of Cosines
Then solve the triangle. (Round your answers to four decimal places.)
C = 15.7449
A = 49.9288
B = 62.0712
×
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Chapter A Solutions
Discrete Mathematics
Ch. A.1 - Prob. 1ECh. A.1 - Prob. 2ECh. A.1 - Prob. 3ECh. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - Prob. 9ECh. A.1 - Prob. 10E
Ch. A.1 - Prob. 11ECh. A.1 - Prob. 12ECh. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - Prob. 16ECh. A.1 - Write the negations of the statements in Exercises...Ch. A.1 - Prob. 18ECh. A.1 - Prob. 19ECh. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - Prob. 22ECh. A.1 - Prob. 23ECh. A.1 - Prob. 24ECh. A.1 - Prob. 25ECh. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Prob. 30ECh. A.1 - Prob. 31ECh. A.1 - Prob. 32ECh. A.1 - Prob. 33ECh. A.1 - Prob. 34ECh. A.1 - Prob. 35ECh. A.1 - Prob. 36ECh. A.2 - Prob. 1ECh. A.2 - In Exercises 1–10, construct a truth table for...Ch. A.2 - In Exercises 1–10, construct a truth table for...Ch. A.2 - Prob. 4ECh. A.2 - Prob. 5ECh. A.2 - Prob. 6ECh. A.2 - Prob. 7ECh. A.2 - Prob. 8ECh. A.2 - Prob. 9ECh. A.2 - Prob. 10ECh. A.2 - Prob. 11ECh. A.2 - Prob. 12ECh. A.2 - Prob. 13ECh. A.2 - Prob. 14ECh. A.2 - Prob. 15ECh. A.2 - Prob. 16ECh. A.2 - Prob. 17ECh. A.2 - Prob. 18ECh. A.2 - Prob. 19ECh. A.2 - Prob. 20ECh. A.2 - Prob. 21ECh. A.2 - Prob. 22ECh. A.2 - Prob. 23ECh. A.2 - Prob. 24ECh. A.2 - Prob. 25ECh. A.2 - Prob. 26ECh. A.2 - Prob. 27ECh. A.2 - Prob. 28ECh. A.2 - Prob. 29ECh. A.2 - The statement [(p → q) ∧ ~q] → ~p is called modus...Ch. A.2 - Prob. 31ECh. A.2 - Prob. 32ECh. A.2 - Prob. 33ECh. A.2 - Prob. 34ECh. A.3 - Prove that ~(p ∧ ~q) is logically equivalent to p...Ch. A.3 - Prove that the law of syllogism is a tautology.
Ch. A.3 - Prove that if m is an integer and m2 is odd, then...Ch. A.3 - Prove, as in Example A.14, that there is no...Ch. A.3 - Prove the theorems in Exercises 5–12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5–12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5–12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5–12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5-12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5–12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5-12. Assume that...Ch. A.3 - Prove the theorems in Exercises 5-12. Assume that...Ch. A.3 - Prove or disprove the results in Exercises 13–22....Ch. A.3 - Prove or disprove the results in Exercises 13–22....Ch. A.3 - Prove or disprove the results in Exercises 13–22....Ch. A.3 - Prove or disprove the results in Exercises 13–22....Ch. A.3 - Prove or disprove the results in Exercises 13–22....Ch. A.3 - Prove or disprove the results in Exercises 13-22....Ch. A.3 - Prove or disprove the results in Exercises 13–22....Ch. A.3 - Prove or disprove the results in Exercises 13-22....Ch. A.3 - Prob. 21ECh. A.3 - Prob. 22ECh. A.3 - Prob. 23ECh. A.3 - Prob. 24ECh. A.3 - Prob. 25ECh. A.3 - Prob. 26ECh. A.3 - Prob. 27ECh. A.3 - Prob. 28ECh. A - Prob. 1SECh. A - Prob. 2SECh. A - Prob. 3SECh. A - Prob. 4SECh. A - Prob. 5SECh. A - Prob. 6SECh. A - Prob. 7SECh. A - Prob. 8SECh. A - Prob. 9SECh. A - Prob. 10SECh. A - Prob. 11SECh. A - Prob. 12SECh. A - Prob. 13SECh. A - Prob. 14SECh. A - Prob. 15SECh. A - Prob. 16SECh. A - Prob. 17SECh. A - Prob. 18SECh. A - Prob. 19SECh. A - Prob. 20SECh. A - Prob. 21SECh. A - For each statement in Exercises 21–24, write (a)...Ch. A - Prob. 23SECh. A - Prob. 24SECh. A - Prob. 25SECh. A - Prob. 26SECh. A - Prob. 27SECh. A - Prob. 28SECh. A - Prob. 29SECh. A - Prob. 30SECh. A - Prob. 31SECh. A - Prob. 32SECh. A - Prob. 33SECh. A - Prob. 34SECh. A - Prob. 35SECh. A - Prob. 36SECh. A - Prob. 37SECh. A - Prob. 38SECh. A - Prob. 39SECh. A - Prob. 40SECh. A - Prob. 41SECh. A - Prob. 42SECh. A - Prob. 43SECh. A - Prob. 44SE
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