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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.
Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x) dx Solution This kind of integral approximately falls into the form given in 3c. It is a quotient of ta
In this section we will be looking exclusively at linear second order differential equations. The most common linear second order differential equation is in the type. p (t ) y
no the parallel lines do not meet at infinity because the parallel lines never intersect each other even at infinity.if the intersect then it is called perpendicuar lines
Hypothesis Testing Of The Difference Between Proportions Illustration Ken industrial producer have manufacture a perfume termed as "fianchetto." In order to test its popul
A rescue and ?re squad places a 15 ft ladder against a burning building. If the ladder is 9 ft from the base of the building, how far up the building will the ladder reach? a. 8
Example 1: Multiply 432 by 8. Solution: 432 × 8 -------------- 3,456 In multiplying the multiplier in the units column to the multiplica
nc6:n-3c3=91:4
Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on
Type I and type II errors When testing hypothesis (H 0 ) and deciding to either reject or accept a null hypothesis, there are four possible happenings. a) Acceptance of a t
In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti
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