Question: A rancher plans to fence a rectangular
A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fencing, and no fencing is needed along the river (see figure).
a. Write the area A of the pasture as a function of x, the length of the side parallel to the river. What is the domain of A?
b. Graph the area function and estimate the dimensions that yield the maximum amount of area for the pasture.
c. Find the dimensions that yield the maximum amount of area for the pasture by completing the square.
> Dryden Company is an auto parts supplier. At the end of each month, the employee who maintains all of the inventory records takes a physical inventory of the firm’s stock. When discrepancies occur between the recorded inventory and the physical count, th
> Select one of the following companies (or any company of your choosing) and use the Internet to explore the company’s most recent annual report. Required: 1. Calculate the company’s overall return on investment (ROI).
> Refer to the data in the exercise 13-27 for Golden Gate Construction Associates. The company has two divisions: the real estate division and the construction division. The divisions’ total assets, current liabilities, and before-tax ope
> Golden Gate Construction Associates, a real estate developer and building contractor in San Francisco, has two sources of long-term capital: debt and equity. The cost to Golden Gate of issuing debt is the after-tax cost of the interest payments on the de
> Read Exercise 13–32. Instead of answering the requirements listed in the exercise, discuss the implications of SOX sections 302 and 404 for the company’s internal control issues. Data from Exercise 13-32: Dryden Company is an auto parts supplier. At the
> Refer to the data for Exercise 13–24. Assume that the company’s minimum desired rate of return on invested capital is 11 percent. Required: Compute Dakota Division’s residual income for the year. Data from Exercise 13-24: The following data pertain to
> Refer to the exercise 13-24: Required: Demonstrate two ways Dakota Division’s manager could improve the division’s ROI to 25 percent. Data from Exercise 13-24: The following data pertain to Dakota Division’s most recent year of operations. Income ……………
> The following data pertain to Dakota Division’s most recent year of operations. Income …………………………………………………….. $ 4,000,000 Sales revenue …………………………………………….. 50,000,000 Average invested capital ……………………………… 20,000,000 Required: Compute Dakota
> Data Screen Corporation is a highly automated manufacturing firm. The vice president of finance has decided that traditional standards are inappropriate for performance measures in an automated environment. Labor is insignificant in terms of the total co
> Hiawatha Hydrant Company manufactures fire hydrants in Oswego, New York. The following information pertains to operations during May. Required: Compute the following operational measures: (1) manufacturing cycle efficiency; (2) manufacturing cycle time;
> Fly High Tech, an early-stage start up, reports to its investors using a balanced scorecard that is prepared at the end of each quarter. During the first and second quarters of the current year, the company had the following results: The following additi
> Refer to the list of companies in Exercise 12–33. Required: Choose one of the companies, research it online, and prepare an abbreviated balanced scorecard for that company. Your scorecard should include • The company&
> Think carefully about the overall mission and goals of a nongovernmental organization (NGO), such as Doctors Without Borders or The Nature Conservancy. Required: 1. How does the task of building a balanced scorecard for an NGO differ from that for a pro
> Visit the website for one of the following companies, or a different company of your choosing. Required: Read about the company’s activities and operations. Then do as good a job as you can in preparing an organization chart for the f
> Lackawanna Community College has three divisions: Liberal Arts, Sciences, and Business Administration. The college’s comptroller is trying to decide how to allocate the costs of the Admissions Department, the Registrar’
> What does it mean to say that the concept of risk exposure may be the key to making SOX sections 302 and 404 more effective?
> Saddle River Electronics Company manufactures complex circuit boards for the aerospace industry. Demand for the company’s products has fallen in recent months, and the firm has cut its production significantly. Many unskilled workers have been temporaril
> The following data pertain to Aurora Electronics for the month of February. Required: Compute the sales-price and sales-volume variances for February.
> Refer to the data in Exercise 11–22 for Crystal Glassware Company. Prepare journal entries to • Record the incurrence of actual variable overhead and actual fixed overhead. • Add variable and fixed ov
> Montoursville Control Company, which manufactures electrical switches, uses a standard-costing system. The standard production overhead costs per switch are based on direct-labor hours and are as follows: The following information is available for the mo
> Refer to DCdesserts.com’s activity-based flexible budget in Exhibit 11–11. Suppose that the company’s activity in June is described as follows: Required: 1. Determine the flexible budgeted cost for e
> You brought your work home one evening, and your nephew spilled his chocolate milk shake on the variance report you were preparing. Fortunately, knowing that overhead was applied based on machine hours, you were able to reconstruct the obliterated inform
> The controller for Rainbow Children’s Hospital, located in Munich, Germany, estimates that the hospital uses 30 kilowatt-hours of electricity per patient-day, and that the electric rate will be .10 euro per kilowatt-hour. The hospital also pays a fixed m
> Evening Star, Inc. produces binoculars of two quality levels: field and professional. The field model requires three direct-labor hours, while the professional binoculars require five hours. The firm uses direct-labor hours for flexible budgeting. Requi
> Choose a city or state in the United States (or a Canadian city or province), and use the Internet to explore the annual budget for the governmental unit you selected. For example, you could check out the annual budget for Houston, Texas, at www.houstont
> Refer to the data in the Exercise 11–22 for Crystal Glassware Company. Draw graphs similar to those in Exhibit 11–7 (variable overhead) and Exhibit 11–9 (fixed overhead) to depict the overhead varianc
> As a group, stage an in-class debate about the future of the Sarbanes–Oxley Act. At least three positions can be staked out: leave SOX as is, repeal SOX, and modify SOX.
> Briefly describe the overall intent of the Sarbanes–Oxley Act of 2002.
> Test for symmetry with respect to each axis and to the origin. y = 9x − x2
> Convert the radian measure to degree measure. -2π / 3
> Convert the radian measure to degree measure. 11π / 4
> Convert the radian measure to degree measure. π / 6
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. -900º
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. -480º
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. 300º
> Convert the degree measure to radian measure as a multiple of π and as a decimal accurate to three decimal places. 340º
> Determine whether the function is even, odd, or neither. Then find the zeros of the function. Use a graphing utility to verify your result. f(x) = √x3 + 1
> determine whether the function is even, odd, or neither. Then find the zeros of the function. Use a graphing utility to verify your result. f(x) = x4 - x2
> A rancher has 300 feet of fencing to enclose two adjacent pastures (see figure). a. Write the total area A of the two pastures as a function of x. What is the domain of A? b. Graph the area function and estimate the dimensions that yield the maximum amou
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = √x - 2 g(x) = x2
> Test for symmetry with respect to each axis and to the origin. y = x2 – 6
> Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com.
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = 3x + 1 g(x) = −x
> What is the minimum degree of the polynomial function whose graph approximates the given graph? What sign must the leading coefficient have? a. / b. / c. / d. /
> Use a graphing utility to graph f(x) = x3 − 3x2. Use the graph to write a formula for the function g shown in the figure. a. / b. /
> Determine whether y is a function of x. x = 9 – y2
> Determine whether y is a function of x. xy + x3 – 2y = 0
> Use the Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x2 - y = 0
> Use the Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x + y2 = 2
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. g(x) = √x + 1
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = 4 / 2x – 1
> Find any intercepts. y = 2x − √x2 + 1
> Find the domain and range of the function. h(x) = 2 / x + 1
> Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. ( √x2 – 4) − y = 0
> Find the domain and range of the function. f(x) = -│x + 1│
> Find the domain and range of the function. g(x) = √6 - x
> Find the domain and range of the function. f(x) = x2 + 3
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 2x - 6 f(x) – f(1) / x - 1
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 4x2 f(x + ∆x) – f(x) / ∆x
> Consider the graph of the function f shown below. Use this graph to sketch the graphs of the following functions. To print an enlarged copy of the graph, go to MathGraphs.com. a. f(x + 1) b. f(x) + 1 c. 2f(x) d. f(−x) e. âˆ&#
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = x3 – 2x f(-3) f(2) f(-1) f(c - 1)
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 5x + 4 f(0) f(5) f(-3) f(t + 1)
> A contractor purchases a piece of equipment for $36,500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour. Write a linear equation for the cost C of op
> Find any intercepts. x2 y − x2 + 4y = 0
> The purchase price of a new machine is $12,500, and its value will decrease by $850 per year. Use this information to write a linear equation that gives the value V of the machine t years after it is purchased. Find its value at the end of 3 years.
> Find equations of the lines passing through (2, 4) and having the following characteristics. a. Slope of – (2/3) b. Perpendicular to the line x + y =0 c. Parallel to the line 3x – y =0 d. Parallel to the x-axis
> Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x − y2 = 0
> Find equations of the lines passing through (−3, 5) and having the following characteristics. a. Slope of 7/16 b. Parallel to the line 5x – 3y = 3 c. Perpendicular to the line 3x + 4y = 8 d. Parallel to the y-axis
> Find an equation of the line that passes through the points. Then sketch the line. (-5, 5), (10, -1)
> The Heaviside function H(x) is widely used in engineering applications. a. H(x) – 2 b. H(x − 2) c. −H(x) d. H(−x) e. 1/2H(x) f. −H(x − 2) + 2
> Find an equation of the line that passes through the points. Then sketch the line. (0, 0), (8, 2)
> Sketch the graph of the equation. 3x + 2y = 12
> Sketch the graph of the equation. y = 4x – 2
> Sketch the graph of the equation. x = -3
> Find any intercepts.
> Sketch the graph of the equation. y = 6
> Find the slope and the y-intercept (if possible) of the line. 9 - y = x
> Find the slope and the y-intercept (if possible) of the line. y – 3x = 5
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (5, 4) Slope: m = 0
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = x + √4 − x2
> There are two tangent lines from the point (0, 1) to the circle x2 + (y + 1)2 = 1 (see figure). Find equations of these two lines by using the fact that each tangent line intersects the circle at exactly one point. /
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (-3, 0) Slope: m = - 2/3
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (-8, 1) Slope: m is undefined
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (3, -5) Slope: m = 7/4
> Plot the pair of points and find the slope of the line passing through them. (-7, 8) , (-1, 8)
> Plot the pair of points and find the slope of the line passing through them. (3/2, 1) , (5, 5/2)
> Find any intercepts.
> Find the points of intersection of the graphs of the equations. x2 + y2 = 1 -x + y = 1
> Find the points of intersection of the graphs of the equations. x − y = −5 x2 – y = 1
> Find the points of intersection of the graphs of the equations. 2x + 4y = 9 6x – 4y = 7
> Find the points of intersection of the graphs of the equations. 5x + 3y = −1 x – y = -5
> Consider the circle x2 + y2 − 6x − 8y = 0 as shown in the figure. Find the center and radius of the circle. Find an equation of the tangent line to the circle at the point (0, 0). Find an equation of the tangent line t
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = │x − 4│ − 4
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = √9 − x2
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = 2 √4-x
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y2 = 9 – x
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = 9x − x3
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = −x2 + 4
> Find any intercepts. y = (x − 1)√x2 + 1
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The graph of a function of x cannot have symmetry with respect to the x-axis.
