Page 90, Theorem 4.6 ( To show that a digraph is hamiltonian if and only if for each vertex v, indegree (v) =outdegree (v) Page 92 Exercise problem 4.1 ( A modified version of konigsberg problem where, two extra bridges are built. ) Page 93, Figure 4.5 need to show as Hamilton. (Show that dodecahedron is hami
(1) For the function: (see attached) a) Give the y values for x = -1, 0, 1, 2, 3, 4. b) Using these points, draw a curve. (2) For the equation , perform the following: (a) Solve for all values of x that satisfies the equation. (b) Graph the functions y = x and on the same graph (by plotting points if necessary). Sho
Find the relative extrema for y = (x^2+5x+3)/(x-1).
Explain why it is not necessary to plot points to graph when using y = a(x - h)^2+ k.
(1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: (a) Solve by factoring. (b)Solve by using the quadratic formula. (2) For the function y = x2 - 6x + 8, perform the following tasks: (a) Put the function in the form y = a(x - h)2 + k. (b) What is the equation for the line of symmetry for t
Give the domain for f(x, y) = ln ( 1 - x^(2) - y^(2)).
Please see the attached file for the fully formatted problems. Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept 1. Slope: -2; y-intercept: (0, 4) 2. Slope: 5; y-intercept: (0, -2) 3. Slope: ; y-intercept: (0, 8) 4. Find the slope of any line pe
All of the graphs in occur in real life. Find a real-life application of each of the below graph and describe the characteristics of each application as related to the graph. line parabola hyperbola exponential
A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare. 2) If the number of riders are a function of the fare charged. Gr
Identify the attached graphs and give the domain and range for each graph. See the attached file for the full problem description and diagrams of the graphs.
1.A body has an a equation of motion measured in metres after t seconds such that s=4t3-14t2+40t+8. a) When and where is the body momentarily at rest? b) For what time interval is it moving forward? c) During what times is its acceleration negative? d) Draw three separate graphs for acceleration, velocity, and displaceme
Find the equation of the line shown: Please see the attached file for the fully formatted problems.
1. Draw a sign graph to determine where the following function is increasing or decreasing. Identify all stationary points. y=2x^4-4x^2+1 2. Find the intervals where the following curve is concave up or down. Also find the coordinates of any points of inflection. y=2x^3 - x^2 +3x+5 3
Suppose the constant function y(t) = 2 for all t is a solution of the differential equation dy = f(t,y). dt (a) What does this tell you about the function f(t,y)? (b) What does this tell you about the slope field? In other words, how much of the slope field can you sketch using this information? (c) What does this
Years (t) A = (1.10)t amount after t years (A) 0 A = (1.10)(0) 1 1 A = (1.10)(1) 1.1 2 A = (1.10)(2) 1.21 3 A = (1.10)(3) 1.331 4 A = (1.10)(4) 1.4641.
An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function and
G o g (x) = f(x)=2/x+5 and g(x)= 2/x +5.
1). The volume of a cylinder (think about the volume of a can) is given by V = pir2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters. Write h as a function of r. Keep "pi" in the function's equation. 2). What is the measurement of the height
Graph and state domain and range y=-2|x-1|+4
Determine whether each relation is a function 1. |4x|=|2y| 2. y=sqrt x-5
If P(x) = -2x^3 +5x^2 -12, find P(5)
1. Graph the functions y=x and y= square root of x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs. 2. A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the sid
X -2 -1 0 1 2 y .25 .5 1 2 4 Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. For the function, y= 1/x-1 a) Give the y
Sketch the graph of the function f(x) = x^3/4 /(x+2), locating all cusps, critical points, vertical tangents and asymptotes.
Use the method of differentials to estimate each of the following values to four decimal places. Hint: f(a + h) = f(a) + f'(a)h a) cot(46') b) 242^1/5 [Hint: 3^5 = 243]
56. Graph the function f defined by -1 if x <= -1 f(x) = x if -1 < x <= 3/2 x^2 if 3/2 < x Specify the domain on which this function is continuous, and the points of discontinuity. 62. Use the Intermediate Value Theorem to prove that the function defined by f(x) = x^3 + 4x^2 + x -1 has three r
Write an equation of the line that passes through the given point and is perpendicular to the given line. Write the answer in slope-intercept form. (0, 0), y = 4x -7
Find the slope of the line that passes through the points (9, 1) and (-2, 8).
See attached file for full problem description. Need help with 6,8,9,12,15 of exercise 13.2.
#1: In the real world, what might be a situation where it is preferable for the data to form a relation but not a function? ******************************** There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points: Fahrenheit Cels