Let G be a connected graph that is not Eulerian. Prove that it is possible to add a single vertex to G together with some edges from this new vertex to some old vertices so that the new graph is Eulerian. Please see attachment for background and hints.
1. We noticed that a graph with more than two vertices of odd degree cannot have an Eulerian trail... (please see the attached file).
11. Let G be a graph with n>= 2 vertices. a) Prove that if G has at least (n-1) + 1 edges the G is connected. ( 2 ) b) Show that the result in (a) is best possible; that is, for each n>= 2, prove there is a graph with (n- 1)
Find the total area of the region between the graph of F and the x-axis. (see attachment)
Attached photo in word doc, please use zoom for better viewing.
(-x^2/2(x+1)^3/2) + (2x/(x+1)^1/2)=0 See attached file
X^2 + 1 = 6x
1. Calculate the ambiguity function of a signal with an envelope u(t) = Bexp(-t^2)T^2). What should be the value of B that will make the signal of the unit energy? 2. Calculate the ambiguity of a signal with a complex envelope u(t) = Bexp(-t^2/T^2)exp(jpikt^2). Note that this is the same signal as above, except for the additi
Show that the 1 dimensional problem with equation of motion (FUNTION1) has a stable equilibrium point at x=1, and show that the period of small oscillations about the point is (FUNCTION2). (PLEASE SEE ATTACHMENT FOR FUNCTIONS)
Let f(x)=invertedCOS(x) for EQUATION1 (the principal branch of EQUATION2) Find the polynomial of degree two EQUATION3 which minimizes EQUATION4. *(Please see attachment for all equations)
See attached for details
Suppose that F is a continuous function on [0,1] and f(x) is in [0,1] for each x. Prove that f(x)=x for some x.
Please graph the attached trend line slope
Please see the attached file for the fully formatted problems. Please, find analytically inverses of the following functions. a. f(x)= √(x-a)/(√(x-a) + √(b-x)) b. f(x)= (x-a)^2.5/((x-a)^2.5 + (b-x)^2.5) Where a and b are constants. Please, note that analytical solution does not require substitu
Project 4A 1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method. 1. In Washington DC, there is a large grassy area south of the White House known as the Ellipse. It is actually an ellipse wi
How do I find the equation of the ellipse with foci at (-8, 0) and (8, 0) and y-intercepts at (0, -6) and (0,6).
If P is any point on the parabola y = x^2 except for the origin, let Q be the point where the normal line intersects the parabola again. Find the shortest possible length of the line segment PQ.
List all the values of x for which the given function is not continuous f(x)= x^2 if x is less than or equal to 2 9 if x>2
F(x)= square root of x - 2(the 2 is not a part of the square root)/ x-4 ; x=2 decide if the given function is continuous at the specified value of s.
F(x)= (x^2-1 if x is less than or equal to 2) (3 if x is greater than 2)
Obtain the composite functions f(g(x)) and g (f(x)), and find all (if any) values of x such that f(g(x)) = g (f(x)) f(x)= the square root of 2x+1, g(x)= 1-3x
F(u) = u^2, g (x) = 1/x-1
1 In a class, there are 20 men and 15 women. Find the ratio of the number of men to the number of students in the class. First express the ratio as a fraction reduced to lowest terms. Then re write the ratio using a second method. 2.Determine whether each of the ordered pair is a solution of 3x-4y>7: (0,0), (3,-6), (-
Locate all zeros and singularities for each of the attached functions.
I need help understanding the following problem set. 1. Mark a point at the intersection of two rulings. The lattice point. Seven units to the right and four units up, mark another. Use a ruler to find the distance from one point to the other, using the distance between two parallel rulings as the unit. What degree of ac
What is the graphical relationship between z and -iz? Use induction to prove the identity.
A. Is a directed graph weakly connected if there is a path from a to b and from b to a whenever a and b are vertices in the graph? b. If two trees have the same number of vertices and the same degrees, are the two trees isomorphic?
A. The length of the longest simple circuit in K5 is ???? b. If T is a tree with 999 vertices, then T has ???? edges.
If F(x)=x/x+1 find F(x+h)-F(x)/h where h is not 0. This problem wants you to substitute F(x+h)-F(x)/h into F(x)=x/x+1.
Find the inverse function of F(x) sqr root of x-2