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(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed graph with L2 edges. If G has 6 vertices every of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can have? (c) Explain the truth value for each of the following statements: (i) 4 + 3 = 6 AND 3 + 3 = 6(ii) 5 + 3 = 8 OR 3 + 1 = 5(d) Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k is a positive integer. Also estimate f(n) if f is an increasing function. (e) Show the sufficient conditions of Dirac and Ore for a graph to be Hamiltonian. Give an instance of a graph that does not satisfy Dirac's condition, but satisfies Ore's condition. (f) Measure -25 + 75 using 2's complement.
x ?8x ?16x ? 0, x?0? ? 0, x?0? ? 2
If two vertices of an equilateral triangle are (0, 0) and (3, 0), find the third vertex. [Ans: 3/2 , 3/√ 3/2 or 3/2, -3√ 3/2] Ans: OA = OB = AB OA 2 = OB 2 = AB 2
John is planning to buy an irregularly shaped plot of land. Referring to the diagram, determine the total area of the land. a. 6,400 m 2 b. 5,200 m 2 c. 4,500 m 2 d.
a lending library has a fixed charge for the first three days and an additional charge for each day thereafter. sam paid Rs 27 for a bookkept for 7 days while jaan paid Rs 21 for t
a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
Calculate the edges in an undirected graph along with two vertices of degree 7, four vertices of degree 5, and the remaining four vertices of degree are 6? Ans: Total degree of
Example of Word problem: There is a man who is 21 years older than his son. 5 years ago he was four times as old as his son. How older are both now? Solution: Step 1
Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.
Ask question I have 2 problems I need them after 7 hours
Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3
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