Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 12, Problem 21E
To determine
To prove: The regions obtained in dividing a plane by a finite number of straight lines can be colored with two colors in such a way that the regions which share a boundary are colored differently.
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Two cables tied together at C are loaded as shown. Given: Q = 130 lb.
8
30°
C
B
Q
3
4
Draw the free-body diagram needed to determine the range of values of P for which both cables remain taut.
Cable AB is 103 ft long and the tension in the cable is 3900 lb.
56 ft
A
50°
20°
B
x
C
Identify the angles 0.0, and 8, that define the direction of force.
1
By
N
2
Match each of the options above to the items below.
142.1°
57.1°
73.3°
3
8.
In the given figure, P = 51 lb .
65°
C
25°
35°
75 lb
P
Determine the corresponding magnitude of the resultant.
The corresponding magnitude of the resultant is|
lb.
Chapter 12 Solutions
Introductory Combinatorics
Ch. 12 - Prob. 1ECh. 12 - Prob. 2ECh. 12 -
Prove that the chromatic polynomial of a...Ch. 12 -
Prove that the chromatic number of a cycle graph...Ch. 12 - Prob. 5ECh. 12 -
Prove that a graph with chromatic number equal to...Ch. 12 - Prove that the greedy algorithm always produces a...Ch. 12 - Let G be a graph of order n ≥ 1 with chromatic...Ch. 12 - Let G be a graph of order n whose chromatic...Ch. 12 - Prob. 10E
Ch. 12 -
Prove that the chromatic polynomial of the graph...Ch. 12 -
What is the chromatic number of the graph...Ch. 12 - Prob. 13ECh. 12 -
Prove that the chromatic polynomial of a cycle...Ch. 12 - Prob. 15ECh. 12 -
Prove that the polynomial k4 − 4k3 + 3k2 is not...Ch. 12 - Prob. 17ECh. 12 -
Give an example of a planar graph with chromatic...Ch. 12 - A plane is divided into regions by a finite number...Ch. 12 - Prob. 22ECh. 12 - Prob. 23ECh. 12 - Prob. 26ECh. 12 - Let G be a planar graph of order n ≥ 2. Prove that...Ch. 12 - Find a solution to the problem of the 8 queens...Ch. 12 - Prob. 33ECh. 12 - Prob. 34ECh. 12 - Prob. 36ECh. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Prob. 45ECh. 12 - Prove that the edge-connectivity of Kn equals n –...Ch. 12 - Prob. 53ECh. 12 - Prob. 54ECh. 12 - Prob. 55ECh. 12 - Determine the edge-connectivity of the complete...Ch. 12 - Prob. 63E
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- Cable AB is 103 ft long and the tension in the cable is 3900 lb. 56 ft D y A B 20° 50° x C Identify the x, y, and z components of the force exerted by the cable on the anchor B. 1 F. FI 3 Fy 2 Match each of the options above to the items below. 2,120 lb 1,120 lb -3,076 lbarrow_forwardIn the given figure, P = 51 lb. 65° 25° 35° 75 lb P B Determine the required tension in cable AC, knowing that the resultant of the three forces exerted at point C of boom BC must be directed along BC. The required tension in cable AC is lb.arrow_forwardhelp on this question about Laplace transformation?arrow_forward
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