EBK BASIC TECHNICAL MATHEMATICS
11th Edition
ISBN: 9780134508290
Author: Evans
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 2.1, Problem 3E
To determine
The adjacent angles from the given figure.
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
(b) How many edges does BL(T) have?
Prove that your answers are correct.
4. [10 marks]
Find both a matching of maximum size and a vertex cover of minimum size in
the following bipartite graph. Prove that your answer is correct.
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Chapter 2 Solutions
EBK BASIC TECHNICAL MATHEMATICS
Ch. 2.1 - What is the measure of the complement of in Fig....Ch. 2.1 - Prob. 2PECh. 2.1 - In Exercises 1–4, answer the given questions about...Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...
Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 5–12, identify the indicated angles...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 13–15, use Fig. 2.11. In Exercises...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 19–24, find the measures of the...Ch. 2.1 - In Exercises 25–30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 25-30, find the measures of the...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 31–34, find the indicated distances...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 35–40, find all angles of the given...Ch. 2.1 - In Exercises 41-46, solve the given problems
41. A...Ch. 2.1 - In Exercises 41–16, solve the given...Ch. 2.1 - In Exercises 41-46, solve the given problems
43. A...Ch. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.2 - Prob. 1PECh. 2.2 - Prob. 2PECh. 2.2 - Prob. 3PECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 5–8, determine ∠A in the indicated...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 9–16, find the area of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 17–20, find the perimeter of each...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 21–26, find the third side of the...Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - In Exercises 27–30, use the right triangle in Fig....Ch. 2.2 - Prob. 30ECh. 2.2 - In Exercises 31–58, solve the given problems.
31....Ch. 2.2 - In Exercises 31–58, solve the given problems.
32....Ch. 2.2 - In Exercises 31–58, solve the given problems.
33....Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given problems.
35....Ch. 2.2 - In Exercises 31–58, solve the given problems.
36....Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - In Exercises 31–58, solve the given...Ch. 2.2 - Prob. 50ECh. 2.2 - In Exercises 31–58, solve the given problems.
51....Ch. 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. 2.3 - Prob. 1PECh. 2.3 - Prob. 2PECh. 2.3 - Prob. 3PECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 5–12, find the perimeter of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - In Exercises 13–20, find the area of each...Ch. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - In Exercises 21–24, set up a formula for the...Ch. 2.3 - In Exercises 25–46, solve the given...Ch. 2.3 - What conclusion can you make about the two...Ch. 2.3 - Find the area of a square whose diagonal is 24.0...Ch. 2.3 - Noting the quadrilateral in Fig. 2.67, determine...Ch. 2.3 - The sum S of the measures of the interior angles...Ch. 2.3 - Express the area A of the large rectangle in Fig....Ch. 2.3 - Express the area of the square in Fig. 2.69 in...Ch. 2.3 - Part of an electric circuit is wired in the...Ch. 2.3 - A walkway 3.0 m wide is constructed along the...Ch. 2.3 - An architect designs a rectangular window such...Ch. 2.3 - Find the area of the cross section of concrete...Ch. 2.3 - A beam support in a building is in the shape of a...Ch. 2.3 - Each of two walls (with rectangular windows) of an...Ch. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.4 - Prob. 1PECh. 2.4 - Prob. 2PECh. 2.4 - Prob. 3PECh. 2.4 - In Exercises 1-4, answer the given questions about...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 5-8, refer to the circle with center...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 9–12, find the circumference of the...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 13–16, find the area of the circle...Ch. 2.4 - In Exercises 17 and 18, find the area of the...Ch. 2.4 - In Exercises 17 and 18, find the area of the...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 19–22, refer to Fig. 2.86, where AB...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 23–26, refer to Fig. 2.87. Determine...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 27–30, change the given angles to...Ch. 2.4 - In Exercises 31–34, find a formula for the...Ch. 2.4 - In Exercises 31–34, find a formula for the...Ch. 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 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - In Exercises 35–58, solve the given...Ch. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.5 - Prob. 1PECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - In Exercises 7–18, calculate the indicated areas....Ch. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - In Exercises 19–22, calculate the area of the...Ch. 2.6 - Prob. 1PECh. 2.6 - Prob. 2PECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - In Exercises 5–22, find the volume or area of each...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - In Exercises 5–22, find the volume or area of each...Ch. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 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 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - In Exercises 23–46, solve the given problems.
36....Ch. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - In Exercises 23–46, solve the given problems.
44....Ch. 2.6 - In Exercises 23–46, solve the given problems.
45....Ch. 2.6 - Prob. 46ECh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - In Exercises 19–26, find the perimeter or area of...Ch. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - In Exercises 27–32, find the volume of the...Ch. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - If the dimensions of a plane geometric figure are...Ch. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - In Exercises 55–84, solve the given problems.
69....Ch. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Find the surface area of a tennis ball whose...Ch. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PT
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