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Graphs and Functions

Find an equation in slope-intercept form (where possible) for each line.

Find an equation in slope-intercept form (where possible) for each line. Through (-2,6), perpendicular to 2x-3y=5 Use slope to show that the square with vertices at (-2, 5) (4,5), (4 -1) and (-2,1) has diagonals that are perpendicular Graph each equation. 2x-3y= 12 Exercise To achieve the maximum benefit for the hear

Applications of Graphing

Section 6.1, pp. 510-511 24, 46, 48 Complete the ordered pairs so that each is a solution for the given equation. 24. ( 0,), 46. Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula . .

9 geometry problems

1. Angles ABC and CBD are complementary and the measure of CBD is twice of the measure of ABC. Angles ABD and DBE are supplementary angles. a) Draw a sketch illustrating these angles. b) Determine the measure of ABC. c) Determine the measure of DBE. 2. Form the converse of each of the following statements. State whether

Various Problem in Group Project

1) 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 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 s

Relations and Functions

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 Celsius Freezing point of water 32 0 Boil

Determine whether the diagram given in part 1 is a graph. Find the chromatic number of the graph given in part 2, and the number of colors needed to color the regions of the graph in part 3 (to ensure that adjacent regions have different colors).

The three questions are stated in an attached .doc file (1.doc). In part 1, a diagram is given, and whether the object depicted in the diagram is a graph is to be determined. In part 2, a graph is given and its chromatic number is to be determined. In part 3, a graph is given and the number of colors needed to color the

Undefined Tangent Values and Latitude

1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this? 2. A nautical mile depends on lat

Graphing, Trends and Forecasting : Cancer and Heart Disease

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year

Various Algebra Problems

See attached file for full problem description. 1. Find the missing coordinates in the following table: 2. Graph the following equation. Plot at least five points for the equation: x + 4y = 5 3. Demand Equation. Helen's Health Foods usually sells 400 cans of Pro Pac Muscle Punch per week when the price is $5 per can. Af

Justifying An Increased Line of Credit

Case 3: Justifying An Increased Line of Credit 1. A monthly regression analysis is to be conducted using monthly data for each demand variable. Formulate your empirical model using the additive functional form. 2. Using economic theory what are the hypothesized signs of parameters in the demand model. 3. Interpret your

Linear Equations, Midpoints and Distance Between Two Points

6. Consider the points (4, -1) and (7, 8). (a) Find the midpoint of the line segment with the given endpoints. (b) Find the distance between the points. Give an exact answer (simplified as much as possible), and also an approximation to three decimal places. Show some work. (c) Find the slope of the line passing through the

Comparing plots on graphs for a linear equation

You are the financial manager of a furniture company. It is your job to create supply and demand graphs that show the break-even point for the company. The functions that describe how the company can break even will be represented with linear equations. Linear inequalities will be used to graph conditions where the company exper

Arithmetic and Geometric Series

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

Equivalence relations, surjective maps, partitions and fibers.

Consider any surjective map f from a set X onto another set Y. We can define a relation on X by x_1 ~ x_2 if f(x_1) = f(x_2). Check that this is an equivalence relation. Show that the associated partition of X is the partition into "fibers" f^(-1) (y) for y in Y. I would like to understand what this question is asking me a

Monte Carlo Methods : Cumulative Density Function

Show that if the value of a variable x is selected by inverting the cdf (cumulative density function), x = F^-1 (RN), the distribution of the x values is given by the function f(x). See attached file for full problem description.

Graph Theory, Necessary and sufficient condition digraphs to be Eulerian.

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

Evaluating and Graphing Functions and Trigonometry Word Problems

(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

Quadratic Functions

(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

Graphing Linear Equations an Geometry of Coordinate Points

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

Graphing Linear Equations Word Problems

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

Derivatives and Rate of Change Word Problems: Motion and Relative Speed

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

Curve Sketching

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

Slope Fields

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

Maximizing the Volume of an Open Top Box by Graphing

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

Relations and Functions; Celsius / Fahrenheit Temperature Conversions

#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