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Graphs and Functions

Objective function calculations

A college cafe receives a profit of $1.25 for each cup of house tea that the sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special blend that they sell. Develop an objective that maximizes profit.

construct a circle graph

Online travel websites A sample of 500 travelers who used the internet to book a trip were asked to which travel website they used. There responses are given in the table below. Use this information to construct a circle graph illustrating the percent of people who gave each response. Online travel website

Show that any constant function is measurable

Using the definition of a measurable function, show that any constant function is measurable. definition of a measurable function: the function f is measurable on the interval [a,b] if for all c in R, the set {x in [a,b] : f(x) >c} is measurable.

Stem and Leaf Plot for Oil Usage

The table below shows the number of gallons of heating oil delivered to a residential customer each December from 1986 to 1993. Year 1986 1987 1988 1989 1990 1991 1992 1993 Gallons of oil 42 61 53 59 53 51 75 100 Make a stem-and - leaf plot of the data Find the mean,median, and mode of the d

sequence of continuously differentiable functions

Prove that if {f_n:R→R} is a sequence of continuously differentiable functions such that the sequence of derivatives {f_n^':R→R} is uniformly convergent and the sequence {f_n (0)} is also convergent, then {f_n:R→R} is pointwise convergent. Is the assumption that the sequence {f_n (0)} converges necessary? Pl

Graphing Functions: Example Problems

Y = 2x - 1 - y = (-3/4)x + 5 - y = x2 - 4 - y = -3x2 - 6x - 5 Label each axis and all intercepts. When I try to complete the problem and graph my line is not straight so I am doing something wrong. For the first problems I got (.5,0) and (0,-1). I need help with the steps.

Graphs

Write a short paper describing a graph or a series of graphs that would represent a real life situation or problem from your own life. An example might be a graph of your personal spending habits throughout the year, or the amount of time you spend watching TV each day of the week. Describe this graph in words and provide a co

Graphing: key information

When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -10t^2 + v*t + k gives the height of the ball at any time, t in seconds, where "v" is the initial velocity (speed) in meters/sec and "k" is the initial height in meters (as if you were on top of a tower or building). Make up a scenario wh

Profit Maximization

If total cost function and demand function are as under, TC = 10,000 + 100Q + 0.02Q^2 Qd =20,000 - 100 P how do I determine the short-run profit maximizing price and quantity? How do I determine the maximum profit accruable to the firm ?

slope of the line problems

1) How can the graph of f(x) = -(x -1 )2 be obtained from the graph of y = x2? A) Shift it horizontally 1 units to the right. Reflect it across the x-axis. B) Shift it horizontally 1 units to the left. Reflect it across the x-axis.. C) Shift it horizontally 1 units to the right. Reflect it across the y-axis. D) Shift it hor

Limit of a Function True

Provide an appropriate response. Given lim as x approaches 0- f(x) = Ll , lim as x approaches 0+ f(x) = Lr , and Ll ≠ Lr, which of the following statements is true? I. lim as x approaches 0 f(x) = Ll II. lim as x approaches 0f(x) = Lr III. lim as x approaches 0 f(x) does not exist. a. I b. II c. III d. none

Graphing, Substitution, Elimination

Please set-up the system described below, justify which method you would use to solve, by graphing, substitution, or elimination then solve. 

An apartment building contains 50 units. The one-bedroom units rent for $425 per month and the two-bedroom units rent for $550 per month. When the building is entirely rented,

Slope Intercept Form and Missing Coordinates

1. Write the equation in slope-intercept form y + 2= -6(x - 1) 2. Graph each inequality Y ≥ x-6 X ≥ -6 3. Use the given equation to find the missing coordinates in the tables. Y = -x - 14 X Y -2 0 2 0 -2 4. Graph each equation. Plot at least five points for each equation. X - 2y = 6 5. Demand equ

Cylindrical drum graph

Rates of change apply to many different situations, not just distance-time or motion. While we have not discussed these specific types of problems, try and apply what you have learned about rates of change to answer the questions. a. Water pours out of the bottom of a cylinder and out of a cylindrical cone (see diagram) at a c

Modelling and Simulation - Ln-test for a Power Model

Please refer to the attached Microsoft Word document pertaining to homework instructions. Consider the following results of measurement of a function y(x): x 1 2 3 4 5 y 0.4 0.65 0.86 1.06 1.23 Assume that the data set can be modeled by a power function y = a xb. a) Use a Ln-test (logarithm) to decide whether a powe

Quadratic Equations

MTH133 Unit 1-2 Individual Project (IP3 in Unit 2)VC 1. The following graph shows the growth of the median home value in a particular region of the United States starting in 1996. The graphs starts in 1996 and shows the trend through the year 2000; therefore x = 0 represents the year 1996 and x = 4 is 2000. X - axis (hor

Stem and Leaf Plot Construction

A medical equipment manufacturing company tested the reliability of blood pressure monitors. It measured the time to failure of 20 randomly sampled monitors it produced. Listed below are the 20 measurements (in months) for the time to first failure. 14 37 36 23 37 1 27 6 19 15 14 41 6

Algebra - Functions and Graphs

Amy, the owner of Amy's pottery can produce china pitchers at a cost of .... Use Synthetic division to divide ... Determine the equations of all asymptotes and sketch the graph of the function on the grid provided Please kindly assist with these 3 questions. (File attached) Thank you

Formulate objective function, constraint, optimal solution

A firm has two fixed resources that impose limits on its production activities. For a particular period of time it has 30 hours of resource 1 available and 80 hours of resource 2. Suppose that the firm considers making only two products and desire to know the Maximum profit program with Minimize of the costs. It has the fol

Perimeter of rectangle

1. Write equations for vertical and horizontal lines passing through the point (-6,5) in (x,y) coordinates. Vertical line: Horizontal Line: 2. A line passes through the point (x,y)= (-9,-5)and has a slope of -8. Write an equation for the line. 3. Write an equation of the line when y=4 and x=8.

Scale of a Map

Use the metric ruler to measure the distance between two points (Robinson and Neale) on the map. Map to Scale = 0-5miles Robinson and Neale = 2 centimeters Using the scale of the map find the approximate actual distance by air (not by roads) between the two points. Approximately how many square miles are shown o

global extrema of the function

Find the global extrema of the function f(x,y)= x^4 + 3y^2 on the closed region given by: [0 (< or equal to) x (< or equal to)(pi)]and [0 (< or equal to) y (< or equal to) 1]. You must provide a complete analysis of the function both inside the region and on each of the boundary lines. Be sure to clearly indicate the maximum

Math

Show your work for all problems Part I Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. a. (X+2)2 + (Y-4)2 = 36 b. Y = 3X2 c. Y = X2 + X d. (X-1)2 + (Y-8)2 = 16 Par

Calculating Optimum Run Size and Number of Runs per Year

The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,000 per day. FSF suppies hot dogs to local restaurants at a steady rate of 250 per day. The cost to prepare the equipment for producting hot dogs is $66. Annual holding costs are 45 cents per hot dog. The factory operates 300 days a year. Find: a) The op

function is not continuous by showing the limit does not exist.

Recall that if a function f of one variable is differentiable at x_0, it has a derivative at x_0 (via the limit definition of derivative). As one consequence, we know that f is continuous at x_0. This is not necessarily so in the case of a function of two or more variables. Consider the function: f(x,y) = (xy^2) / (x^2 + y^

Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

Gaussian plot print histogram

Central Limit Theorem Exercise Write a computer program or Excel spreadsheet that: a. takes a given distribution function (f(x), as given below), for x between: 0 and 1.0, b. randomly samples this function at n points and determines the mean for that sample c. repeats b. N times d. plots a histogram of the result of the