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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.
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Compute the dot product for each of the subsequent equation (a) v → = 5i → - 8j → , w → = i → + 2j → (b) a → = (0, 3, -7) , b → = (2, 3,1) Solution (a) v →
This time we are going to take a look at an application of second order differential equations. It's now time take a look at mechanical vibrations. In exactly we are going to look
a. Random or probability sampling methods they involve: Simple random sampling Systematic sampling Stratified sampling Multi stage sampling b.
Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.
explanation
On the Assessment page for the module Moodle site you will find five frequency response functions for the frequency range 20 to 100 Hz in the EXCEL spreadsheet "FRF_Data". These a
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