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Graphs and Functions

Directed Graphs

Given the adjacency relation p = {(1,4), (1,5) (1,6), (6,2), (6,3), (6,5)} on the set N ={1,2,3,4,5,6}, find the corresponding directed graph and adjacency matrix.

Graphs and Their Representations

If all the nodes of a simple, connected, planar graph have degree 4 and the number of arcs is 12, into how many regions does it divide the plane?

Big-Oh Function

Please see the attached file for the fully formatted problems. I need to find the best big-oh function for the function. I need to choose my answer from among the following: 1, log2 n, n, n log2 n, n2, n3,..., 2n, n!. A. f(n) = 1 + 4 + 7 + ... + (3n + 1). B.

Cost Problem (Using Graph - Slope)

If 9 pounds of pears cost x dollars, then what is the price per pound? Use the equation of a straight line and call y = "x $" and x = "9 pounds" and solve for the slope "m"

Moment generating function

1. X is uniform on {1,2,3,4,5,6} m_x(s)=? m_x(s)=E(e^sX) Which is called the moment generating function of X (or the distribution of X)


Which functions are one-to-one? Which functions are onto? Describe the inverse function A)F:Z^2-N where f is f(x,y) x^2 +2y^2 B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd) C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd) D)h:N^3 -> N where h(x,y,z) = x + y -z

Question about onto functions

Let P be the power set of {A, B} and let S be the set of all binary strings of length 2. A function f: P -> S is defined as follows: For A in P, f(A) has a 1 in the high-order bit position (left end of string) if and only if a is in A. f(A) has a 1 in the low-order bit position (right end of string) if and only if b is in A. Is

Equation of the tangent line

Find the equation of the line to y = x^(sin x) at the point [(pie/2),(pie/2)] Show all work and reduce to lowest terms.


Find the Taylor polynomial of degree 4 of at c=4 and determine the accuracy of the polynomial at x=2.

Simple Function Operations

1a.)Is y=x^4 a single- or multi-valued function? b.)Is y=f(x)=x^2+4x an even, odd, or neither function? c.)What is the inverse function of y=x^4 d.)What is the inverse function of (b.),y=x^2+4x? e.)Is the inverse function from (d.), odd, even, or neither?

Will Meteorites Travelling on a Parabolic Path Strike the Earth?

The earth with center at the origin has equation of xsquared + ysquared =65 where x and y are distances in thousands of kilometers. Will either of these two meteorites whose equations I will give you strike the earth? The first meteorite is a parabola whose equation is 18x-ysquared = -144. Please show all steps in sketching and

Draw the Graphs for Three Equations and Find a Common Point

Using first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Add a third equation figure to out the one point that all three conic sections meet. First equation is 9(x-squared)+25(y-squared)-72x=81 Second equation is 9(x-squared)-15(y-squared)=9 Graph these two conical

Linear Models : Choosing Between Point-Slope, Slope-Intercept and Standard Forms

Find an example, of the BMI between man/woman and estimate a best fit line graphically. Develop an approximate linear model using the point slope form, the slope-intercept form or the standard form line. You are not to graph the line here but help illustrate your point . You are only required to use the line of the forms to iden

Brouwer's Fixed Point Theorem

Please see the attached file for the fully formatted problems. Prove that if D is the closed disc |x| =< 1 in R2, then any map f E C2[D --> D] has a fixed point: f(x) = x. The proof is by contradiction, and uses Stokes theorem. Follow the steps outlined below. (1) Define a new map F(x) = ... ..... Show that F has no fixe

Spanning Tree Graph : Movie Collaboration (Kevin Bacon Game)

If you were required by a professor to find a spanning tree of the movie collaboration graph (where each node corresponds to an actor with finite Kevin Bacon number, and two nodes are connected by an edge if the corresponding actors have been in a movie together), how would you do it? Why would you choose your method over other

Spanning Trees and Graphs

Does every graph have a spanning tree? If not, then can you tell from the number of nodes and the number of edges a graph has whether it has a spanning tree, or do you need more information?

Functions, Inverse Functions and Graphs

1. Let h(x) = (8x - 5)/(7-x). (a) Find the inverse of the function h. Show work. (b) What is the domain of h? What is the domain of the inverse of h? 2. Use a calculator (standard scientific calculator or the online graphing calculator) to find each of the following values. Write your answer rounded to 4 decimal places.

Moment generating function

The discrete rv W has the pmf pw(W) = klog[(w+1)/w] for w = 2,3,4,5; 0 otherwise k = 1/ log(3) (a) deduce the mgf of W (b) Calculate E[W] and var[W] using the mgf (c) Determine and sketch the distribution function of W

Straight Line and slope

A) Explain what is the y-intercept and which letter represents it in the equation y = mx +b. b) If a and b are positive numbers, what is all the information we can deduce about the relationship between the lines: L1: y = - ax + b and L2: y = (1/a)x + b?