Graphs and Functions

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Approximation of 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)

Proof f(x)=x

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.

Compute by double false position, to three decimal places, the root of: x^3 - 36x + 72 =0 that lies between 2 and 3. * He gave us the following formula to use when using double false position: x(subscript 2)y(sub1)-x(sub1)y(sub2)/y(sub1)- y(sub2) I couldn't figure out how to get subscripts to show up! PLEASE SHOW EACH S

Trend Line Slope (Graph)

Please graph the attached trend line slope ALL I NEED TO GO WITH THIS IS A TREND LINE SLOPE THIS IS MY 3RD REQUEST. On March 1st the stock price was: $28.41 (Pi) On April 1st the stock price was: $28.91 (Pf) The slope is defined as: The trend predicts that the stock price will increase 0.5 dollars every month.

Function : Analytically Find the Inverse

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

Vectors, graphs, and counting

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

Equation of an ellipse

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).

Shortest Length of Line Intersection

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.

Discontinuous and Continuous Function

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

Continuous Functions for a Given Value

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.

Write an equation for the line with the given properties

Through (-2,3) and parallel to the line x + 3y = 5

Sketch the graph of the given function. All x and y intercepts

F(x)= (x^2-1 if x is less than or equal to 2) (3 if x is greater than 2)

Find the Composite Function

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.

Composite Function Found

F(u) = u^2, g (x) = 1/x-1

Word problems, graphs and equations, etc.

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

Locate all zeros and singularities for each of the attached functions. SHOW ALL WORK SHOW ALL STEPS ANSWER ALL PARTS OF THE QUESTION SEND RESPONSE AS ATTACHMENT. Answer b, c, d, and e. (b) Zero at z = n*pi, where n is any integer. Singularity at z = 0 (isolated) f(z) = . (c) Zero at z = 0, Singul

Graphing equations

Plot the graph of the equations 2x + 4y = 10 and 3x + 6y = 12 and interpret the result.

Lattice Point and Distance Formula

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

Verifying an Inner Product for Continuous Functions

Please see the attached file for the fully formatted problems. Suppose f(x) and g(x) are continuous real-valued functions defined for [0,1]. Define vectors in n, F= ( f(x1), f(x2), ...,f(xn)) and G= g(x1), g(x2), ...,g(xn)), where xk = k/n. Why is <F,G>n = 1/n  f(xk) g(xk) dx not an inner product for the spa

Graphical relationship between z and -iz? Use induction

What is the graphical relationship between z and -iz? Use induction to prove the identity.

Directed Graphs and Trees

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?

Simple Circuits Tree Trans

A. The length of the longest simple circuit in K5 is ???? b. If T is a tree with 999 vertices, then T has ???? edges.

Function substitution

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.

Inverse of a Given Function

Find the inverse function of F(x) sqr root of x-2

Directed Graphs Adjacency Relation

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.

Nodes - 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.

Graph and Slope Situation

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)

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