Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 4, Problem 35E
To determine
To prove: That
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7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
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Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x.
h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1
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Chapter 4 Solutions
Introductory Combinatorics
Ch. 4 - Prob. 1ECh. 4 - Determine the mobile integers in
.
Ch. 4 - Use the algorithm of Section 4.1 to generate the...Ch. 4 - Prove that in the algorithm of Section 4.1, which...Ch. 4 - Let i1i2 … in be a permutation of {1, 2, …, n}...Ch. 4 - Determine the inversion sequences of the following...Ch. 4 - Construct the permutations of {1, 2, …,8} whose...Ch. 4 - How many permutations of {1, 2, 3, 4, 5, 6}...Ch. 4 - Show that the largest number of inversions of a...Ch. 4 - Bring the permutations 256143 and 436251 to 123456...
Ch. 4 - Let S = {x7, x6,…, x1, x0}. Determine the 8-tuples...Ch. 4 - Let S = {x7, x6,…, x1, x0}. Determine the subsets...Ch. 4 - Generate the 5-tuples of 0s and 1s by using the...Ch. 4 - Prob. 14ECh. 4 - For each of the following subsets of {x7, x6, …,...Ch. 4 - For each of the subsets (a), (b), (c), and (d) in...Ch. 4 - Which subset of {x7, x6, … , x1, x0} is 150th on...Ch. 4 - Build (the corners and edges of) the 4-cube, and...Ch. 4 - Give an example of a noncyclic Gray code of order...Ch. 4 - Prob. 20ECh. 4 - Construct the reflected Gray code of order 5...Ch. 4 - Prob. 22ECh. 4 - Determine the immediate successors of the...Ch. 4 - Prob. 24ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Determine the 7-subset of {1, 2, … , 15} that...Ch. 4 - Generate the inversion sequences of the...Ch. 4 - Prob. 31ECh. 4 - Generate the 4-permutations of {1, 2, 3, 4, 5,...Ch. 4 - In which position does the subset 2489 occur in...Ch. 4 - Consider the r-subsets of {1, 2, …, n} in...Ch. 4 - The complement of an r-subset A of {1, 2, … , n}...Ch. 4 - Prob. 36ECh. 4 - Let R′ and R″ be two partial orders on a set X....Ch. 4 - Let (X1, ≤1) and (X2, ≤2) be partially ordered...Ch. 4 - Let (J, ≤) be the partially ordered set with J =...Ch. 4 - Prob. 40ECh. 4 - Show that a partial order on a finite set is...Ch. 4 - Describe the cover relation for the partial order...Ch. 4 - Prob. 43ECh. 4 - Prob. 44ECh. 4 - Prob. 45ECh. 4 - Let m be a positive integer and define a relation...Ch. 4 - Consider the partial order ≤ on the set X of...Ch. 4 - Prob. 50ECh. 4 - Let n be a positive integer, and let Xn be the set...Ch. 4 - Verify that a binary n-tuple an − 1, ⋯ ,a1a0 is in...Ch. 4 - Continuing with Exercise 52, show that can be...Ch. 4 - Let (X, ≤) be a finite partially ordered set. By...Ch. 4 - Prob. 56ECh. 4 - Prob. 57ECh. 4 - Prob. 58ECh. 4 - Prob. 59E
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- x-4 Let f(x)=5x-1, h(x) = Find (fo h)(0). 3 (fo h)(0) = (Type an integer or a fraction.)arrow_forwardFill in the blanks to write the calculus problem that would result in the following integral (do not evaluate the interval). Draw a graph representing the problem. π/2 So/² 2xcosx dx Find the volume of the solid obtained when the region under the curve 38,189 on the interval is rotated about the axis.arrow_forwardLet f(x) = -5x-1, g(x) = x² + 5, h(x) = · x+4 3 Find (hog of)(1). (hogof)(1)= (Simplify your answer. Type an integer or a decimal.)arrow_forward
- For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y= f(x) = x²+x; x=-1,x=2 a. Which of the following formulas can be used to find the slope of the secant line? ○ A. 2-(-1) f(2) f(-1) 2+(-1) C. 1(2)+(-1) The equation of the secant line is 1(2)+(-1) О в. 2+(-1) f(2)-(-1) D. 2-(-1)arrow_forwardplease do not use chat gptarrow_forwardUse technology to find f'(4), f'(16), f'(-5) for the given function when the derivative exists. f(x) = -2x² + +10xarrow_forward
- 42. Consider the following joint probability table. B₁ B2 B3 B4 A 0.09 0.22 0.15 0.20 A 0.03 0.10 0.09 0.12arrow_forwardEXERCISES 4.3 Mechanics 41. Consider the following contingency table. B B A 26 34 Ac 14 26 a. Convert the contingency table into a joint probability table. b. What is the probability that A occurs? ن فة What is the probability that A and B occur? d. Given that B has occurred, what is the probability that A occurs? e. Given that A has occurred, what is the probability that B occurs? f. Are A and B mutually exclusive events? Explain. g. Are A and B independent events? Explain. 42. Consider the following joint probability table. B₁ B2 B3 BA A 0.09 0.22 0.15 0.20 Ac 0.03 0.10 0.09 0.12arrow_forwardStem1: 1,4 Stem 2: 2,4,8 Stem3: 2,4 Stem4: 0,1,6,8 Stem5: 0,1,2,3,9 Stem 6: 2,2 What’s the Min,Q1, Med,Q3,Max?arrow_forward
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