Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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Chapter B, Problem 6E
To determine
Three ordered pairs from the table:
| x | y |
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d₁ ≥ ≥ dn ≥ 0 with di even.
di≤k(k − 1) + + min{k, di}
vi=k+1
T2.5: Let d1, d2,...,d be integers such that n - 1
Prove the equivalence of the Erdos-Gallai conditions:
for each k = 1, 2, ………, n and the Edge-Count Criterion: Σier di + Σjeл(n − 1 − d;) ≥ |I||J| for
all I, JC [n] with In J = 0.
T2.4: Let d₁
T2.3: Prove that there exists a connected graph with degrees d₁ ≥ d₂ >> dn if and only
if d1, d2,..., dn is graphic, d ≥ 1 and di≥2n2. That is, some graph having degree
sequence with these conditions is connected.
Hint - Do not attempt to directly prove this using Erdos-Gallai conditions. Instead work with a
realization and show that 2-switches can be used to make a connected graph with the same degree
sequence. Facts that can be useful: a component (i.e., connected) with n₁ vertices and at least
n₁ edges has a cycle. Note also that a 2-switch using edges from different components of a forest
will not necessarily reduce the number of components. Make sure that you justify that your proof
has a 2-switch that does decrease the number of components.
Chapter B Solutions
Trigonometry (11th Edition)
Ch. B - Concept Check Fill in the blank to correctly...Ch. B - Concept Check Fill in the blank to correctly...Ch. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - For each equation, (a) give a table with at least...Ch. B - Prob. 20ECh. B - Prob. 21ECh. B - For each equation, (a) give a table with at least...Ch. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48E
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- T2.2 Prove that a sequence s d₁, d₂,..., dn with n ≥ 3 of integers with 1≤d; ≤ n − 1 is the degree sequence of a connected unicyclic graph (i.e., with exactly one cycle) of order n if and only if at most n-3 terms of s are 1 and Σ di = 2n. (i) Prove it by induction along the lines of the inductive proof for trees. There will be a special case to handle when no d₂ = 1. (ii) Prove it by making use of the caterpillar construction. You may use the fact that adding an edge between 2 non-adjacent vertices of a tree creates a unicylic graph.arrow_forward= == T2.1: Prove that the necessary conditions for a degree sequence of a tree are sufficient by showing that if di 2n-2 there is a caterpillar with these degrees. Start the construction as follows: if d1, d2,...,d2 and d++1 = d = 1 construct a path v1, v2, ..., vt and add d; - 2 pendent edges to v, for j = 2,3,..., t₁, d₁ - 1 to v₁ and d₁ - 1 to v₁. Show that this construction results vj in a caterpillar with degrees d1, d2, ..., dnarrow_forward4 sin 15° cos 15° √2 cos 405°arrow_forward
- 2 18-17-16-15-14-13-12-11-10 -9 -8 -6 -5 -4-3-2-1 $ 6 8 9 10 -2+ The curve above is the graph of a sinusoidal function. It goes through the points (-10, -1) and (4, -1). Find a sinusoidal function that matches the given graph. If needed, you can enter π-3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = > Next Questionarrow_forwardketch a graph of the function f(x) = 3 cos (표) 6. x +1 5 4 3 3 80 9 2+ 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3+ -4 5 -6+ Clear All Draw: пи > Next Questionarrow_forwardDraw the following graph on the interval πT 5π < x < 2 2 y = 2 sin (2(x+7)) 6. 5. 4 3 3 2 1 +3 /2 -π/3 -π/6 π/6 π/3 π/2 2π/3 5π/6 π 7π/6 4π/3 3π/2 5π/311π/6 2π 13π/67π/3 5π Clear All Draw:arrow_forward
- ketch a graph of the function f(x) = 3 cos (표) 6. x +1 5 4 3 3 80 9 2+ 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3+ -4 5 -6+ Clear All Draw: пи > Next Questionarrow_forward3 2 20-10-18-17-16-15-14-13-12-11-10-9 -8 -7 -6 -$4-3-2-1 -1 -2 -3 4- -5+ The curve above is the graph of a sinusoidal function. It goes through the points (-8, -4) and (6,-4). Find a sinusoidal function that matches the given graph. If needed, you can enter π=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = > Next Question Barrow_forwardX Grades for X Assignmen X A-Z Datab XE Biocultural X EBSCO-Ful X Review es/119676/assignments/3681238 Review Quiz 8.1-p2 points possible Answered: 3/5 ● Question 1 4+ 3. 2 1 13 /12-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4- 5 2 6 The curve above is the graph of a sinusoidal function. It goes through the points (-7,0) and (3,0). Find a sinusoidal function that matches the given graph. If needed, you can enter π=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = > Next Question 申 J % F 刀 Q Search S € t ח Y 7 I * 00 J ப I Darrow_forward
- 2 d) Draw the following graph on the interval k 5π Next Questionarrow_forwardDraw the following graph on the interval 5л Next Questionarrow_forwardDraw the following graph on the interval πT 5π < x < x≤ 2 2 y = 2 cos(3(x-77)) +3 6+ 5 4- 3 2 1 /2 -π/3 -π/6 Clear All Draw: /6 π/3 π/2 2/3 5/6 x 7/6 4/3 3/2 5/311/6 2 13/67/3 5 Question Help: Video Submit Question Jump to Answerarrow_forward
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