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Graphs and Functions

Slope and Intercept

8. The slope and x-intercept of the line 4x + 6y + 24 = 0 are a) -2/3 and (-6, 0) b) -3/2 and (0, -4) c) -4 and (-24, 0) d) none of the above 9. The slope of the line passing through (1,1) and (1,-1) is a) 1 b) 0 c) 2 d) inf

Pade Approximation

Let f(x) = cos(x) = ; then, consider the following rational approximation r(x) = called the Pade Approximation. Determine the coefficients of r in such a way that f(x) - r(x) = γ8x8 + γ10x10 + ...... Please see the attached file for the fully formatted problems.

Hamiltonian and Nonhamiltonian Graphs

4.15 Show that this theorem 1 is sharp, that is, show that for infinitely many n>=3 there are non-hamiltonian graphs G of order n such that degu+degv>=n-1 for all distinct nonadjacent u and v. Can you explain this theorem,please Theorem1: If G is a graph of order n>=3 such that for all distinct nonadjacent vertices u and

Hamiltonian Graphs

4.12 a) Prove that K_r,2r,3r is hamiltonian for every positive integer r. b) Prove that K_r,2r,3r+1 is hamiltonian for no positive integer r. (K_r means k sub r) Can you explain how is the graph K_r,2r,3r, what do subindices r,2r and 3r mean? Can you explain it step by step and draw a graph,plea

Determining Order Quantity

At Dot Com, a large retailer of popular books, demand is constant at 32,000 books per year. The cost of placing an order to replenish stock is $10, and the annual cost of holding is $4 per book. Stock is received 5 working days after an order has been placed. No backordering is allowed. Assume 300 working days a year. a)What

Graphing Line Equations

Graph the line with slope -3/4 through the pint (-5,-5) See attached file for full problem description.

Prove Let D be a nontrivial connected digraph.

4.4 Prove Let D be a nontrivial connected digraph. Then D is Eulerian if and only if od(v)=id(v) for every vertex v of D. Od means the outdegree of a vertex v of a digraph D. (is the number of vertices of D that are adjacent from v. id means the indegree of a vertex v of a digraph D.( is the number of vertices of D adjace

K-connected graph

3.17 Let v_1,v_2,...,v_k be k distinct vertices of a k-connected graph G. Let H be the graph formed from G by adding a new vertex of degree k that is adjacent to each of v_1,v_2,...,v_k. Show k(H)=k. k(G)=is the vertex connectivity

Intercepts of a Line

Find both the X-intercept and the Y-intercept of the line given by the equation - 9x + 4y + 13 = 0

Connected digraph

Prove that a nontrivial connected digraph D is Eulerian if and only if E(D) can be partitioned into subsets E_i , 1<=i<=k, where [E_i] is a cycle for each i. <= means less and equal. Please can you explain this step by step and can you draw a graph.

Strongly Regular Graph

Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both). Show that this is a strongly regular graph, and find its parameters.

Find examples of four types of graphs.

Relate the application to the specific graph (line, parabola, hyperbola, exponential). Describe the characteristics of each application as related to the graph. All of the graphs in this lesson occur in real life. Using the Cybrary, web resources, and other course materials, find a real-life application of each graph. ? R

Piecewise Functions

F(x) = {x if 0<= x <=1} {2-x if 1< x <=2} {0 if x > 2} Define a new function g, whose domain consists of all numbers x such that 0 &#8804; x &#8804; 4, and whose value g(x) for such x is given as follows: g(x) = the area between the graph of the function f and the horizontal axis from 0 to x. Problem: Find a f

Connected Graphs

Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G? Prove your findings! Let G be a connected graph and sq(G) be a graph which contains all vertices and edges of G and moreover edges joining every pair of vertices that were in G at distance 2. In other words, xy is

Finding Slope

Find the slope of the line that goes through each pair of points: (-5, -2) and (-2,1). What is the steepness of the line? (i.e. 3 units up and 5 units right)

Cylindrical Coordinates

What are the cylindrical coordinates of the point whose rectangular coordinates are x = - 4 , y= 2, and z = 4 ? r = (20)^(1/2) theta = z = 4 *need help finding theta in radians*