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Graphs and Functions

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?

Polar Function : Graphing an Ellipse

Graph an ellipse as a polar function with a focus at the pole and parameterized by the eccentricity e and the distance d between the focus and a vertical directrix. ----------------------------------------------------- Please show me how step-by-step on how you would graph this. Thanks

Polar function

Graph an ellipse as a polar function with center at the pole and parameterized by the lengths of the semi-major and semi-minor axes. Can someone please show me step-by-step on how to do this?

Functions : Radius of Convergence and Approximations

Please see the attached file for the fully formatted problems. Let f be the function defined by f(x) = sigma (starting at n=1 ending at infinity) xnnn /(3n n!) for all values of x for which the series converges. a) Find the radius of convergence of this series b) Use the first three terms of this series to approximat

Algebra : Graphing, Distance between Points and Equations of Lines

Please see the attached file for the fully formatted problems. Can you please help me with the following circled problems? Page 187 1. a) 12, b) 14, c) 16, d) 18 (Check for all four of our symmetries SY, SX, SO, SI; consult in WEEK7 NOTES, in COURSE CONTENT. Practice graphing these using the downloaded graphing utility Gr

Duality and Saddle Points

Please see the attached file for the fully formatted problem. I am working on a way to find the minimum of a function J(Y) with the constraint set C = {X E R^N such that gt(x) =<0 Vi E [1,n]} Let L(Y, mu) = J(Y) + SIGMA m --> i = 1 muigi(Y) be the lagrangean of the problem. I am having trouble proving the following

Lines through Non-Colinear Points

Given three points, there is one line that can be drawn through them if the points are colinear. If the three points are noncolinear,there are three lines that can be drawn through pairs of points. For three points, three is the greatest number of lines that can be drawn through pairs of points. Determine the greatest number of

Conic graph

Identify and sketch the graph of the conic described by the quadratic equation x^2 + 4xy + y^2 - 12 = 0. Do this by writing this equation in matrix form; then change the equation to a sum of squares of the form x'^T Dx' where D is a diagonal matrix.

Critical Point : Non-Degenerate

Please see the attached file for full problem description. Show that f(x) = x1x2 + x2x3 + x3x1 has a non - degenerate critical point at x = 0 and describe the shape of f as concretely as possible.

Division of functions

Divide 6x^3 - 29x^2 + 36x - 4 by x-2 in the traditional way and find the quotient. Note that the remainder will come out to be zero


If g(x)=x^2+1, find the formulas for g^3(x) and (gogog)(x).

Cantor's Diagonal Process

I am trying to use Cantor's diagonal process to prove that there are uncountably many functions from N into the set {e, pi}.

Findin the Equation of a Reflecting Line

Determine if the following orthogonal matrix represents a rotation or a reflection of the plane with respect to the standard basis. Find the equation of the reflecting line. - - |3/5 4/5 | |4/5 -3/5 | - -