Using a calculator or computer, graph the functions. Describe briefly in words the interesting features of the graph including the location of the critical points and where the function in increasing/decreasing. Then use the derivative and algebra to explain the shape of the graph. 9. Try graphing the x values from -5 t
Complete the square and sketch a graph of the following ellipse. Give the coordinates of the centre and the four vertices. What is the length of the major axis? 4x^2 + y^2- 8x + 4y -8 = 0 Solve and graph your solutions on the number line and express your answers in interval notation. 1. |3x - 7| >= 23 2. 1/2 |5-2x|
Name: __________________________ Date: _____________ 1. Which of the ordered pairs (6, 1), (8, 0), (4, -2), (-4, 6) are solutions for the equation x + 2y = 8? 2. A small company did a poll of how their employees commuted to work. The data is shown in the bar graph below. (a) How many people commute to work v
Differentiate 7. Find an equation of the tangent line to y = 2x/(x + 1) at the point (1, 1).
By contracting an edge e = uv, we mean removing e and identifying the vertices u and v as a single new vertex. Let num_T(G) denote the number of spanning trees of the graph G. a. Show that the following recursive formula holds: num_T(G) = num_T(G - e) + num_T (G * e) where G * e means the multigraph obtained from G by contrac
A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct elements from the set {0,1,...,q} in such a way that the induced edge labeling, which assigns the integer |i - j| to the edge ij, assigns the labels 1,2,...,q to the q edges of G. The graceful tree conjecture states that every tree i
Please see the attached file for the fully formatted problems. 1. Let . Tabulate the change of over the intervals (i) , (ii) , (iii) , (iv) , (v) . Graph together with the secant line passing through and . Estimate how quickly is changing at .
We define the floor function [[x]] to be the greatest integer not exceeding x. For example[[4]]=4 [[2.37]]=2 [[-1]]=1[[-1.2]]-2 Sketch by hand the graph y=[[x]] by first tabulating the values pf [[1]] for several numbers x. Then compare your graph with the plot from a graphing calculator. What are the discontinuities of f(x
Given f(x) = x^3 + x^2 - 5x +2, on what interval(s) is it decreasing?
Let G be a graph that is randomly eulerian from a vertex v. Show that if deg u = Delta(G)"max degree in G", then G is randomly eulerian from u.
Let F be a forest. Add a vertex x to F and join x to each vertex of odd degree in F. Prove that the graph obtained in this way is randomly Eulerian from x, and every graph randomly Eulerian from x can be obtained in this way.
Recall that a graph G is randomly Eulerian from a vertex x if and maximal trail starting at x in an Euler circuit. (If T = xx_1 ... x_l, then T is a maximal trail starting at x iff x_l is an isolated vertex in G - E(T).) Prove that a nonempty graph G is randomly Eulerian from x iff G has an Euler circuit and x is contained in ev
Let G be a graph. The line graph L(G) of G is defined to be the graph whose vertices are the edges of G and where two vertices of L(G) are adjacent if the corresponding edges of G are adjacent. Prove that if G is connected, then L(G) is eulerian if vertices of G are all odd or all even.
Give examples of eulerian grpahs that are randomly eulerian from exactly none, one, two or all of their vertices.
Let G be an eulerian graph of order n >= 3. Prove that G is randomly eulerian from exactly none, one, two or all of its vertices.
Please see the attached file for the fully formatted problems.
Please see the attached file for the fully formatted problems. 1) Find the domain of the following: a) Answer: Show your work or explain how you obtained your answer here: b) Answer: Explain how you obtained your answer here: c) Answer: Show your work or explain how you obtained your answer he
1) find the area of the enclosed region between the curve and the coordinate axes x^2/8 + y^2/6 =9 the graph is just the coordinate system with an ellipse draw over it, no numbers or letter are present 2) if f(x) =x^2 (x>=0) and f(inverse) = x^1/2, show that the slopes of the graphs of f(x) and f(inverse) are recipr
Does this equation have one real solution, two non-real solutions or two real solutions? x^2+6=0
Quadratic Equations. See attached file for full problem description.
Please see the attachment below for problems. I figured out number 1 and 2. I don't understand the rest of them.
Differential Equations From Equilibria and the Phase Line.
O For noninteger answers, please write your answer as a fraction rather than a decimal. To show your work, you will need to include o the algebra used to compute the solution to any equations. o the formula with substituted values. o the final calculated answer with units. 1) State the doma
Use two equations to write the equation for the Laplacian in cylindrical coordinates. See attached file for full problem description.
See attached file for full problem description.
Your manager is very pleased with your presentations and being able to show your calculations in a detailed fashion. He has asked that you help him prepare for the upcoming company summit. Before you get together, he has asked that you give him a little review on polynomial functions and how you would apply them to everyday use.
I need to understand how to find the vertex of a parabola two ways. Show examples
Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is: Max 2M + 3B Min 4000 (M + B) Max 8000M + 12000B Min 2M + 3B.
I do not understand how to conduct these equations I Excel so that I can show a graph of each. Choose a second-order/third-order (e.g., x2/x3) and a third-order/second-order (e.g., x3/x2) rational function. Provide a graph for the second-order rational function (e.g., x2), choosing x values in the range from -10 through +10.
I am pretty sure I have a and b. I am not sure how to get the time it would be at maximum height and what the maximum height is. The path of a falling object is given by the function s = -16t^2 + v0t + s0, where represents the initial velocity in ft/sec and represents the initial height in feet. a) If a rock is thrown u