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mathematics
calculus

Questions and Answers of Calculus

The median income for workers ages 20 to 62 is shown in the following table.(a) Use a scatter plot of the data with x equal to the age and y equal to the median income in dollars to decide what type
The table shows the national expenditures for health care in the United States for selected years, with projections to 2020. Year __________________ National Expenditures for Health Care
The following table gives the online sales, in billions of dollars, from 2000 and projected to 2017.(a) Find the power function that models these data, with x as the number of years past 1990.(b)
The table gives the U.S. population, in millions, for selected years from 1950 and projected to 2050.(a) Create a scatter plot for the data in the table. Use x as the number of years past 1950.(b)
Find the equation of the function of the specified type that is the best fit for the given data. Plot the data and the equation.1. Linear2. Linear 3. Quadratic 4. Quadratic
Find the real solutions to each quadratic equation.1. 3x2 + 10x = 5x2. 4x - 3x2 = 03. x2 + 5x + 6 = 04. 11 - 10x - 2x2 = 0
Solve each equation by using a graphing utility to find the zeros of the function. Solve the equation algebraically to check your results.1. 4z2 + 25 = 02. z(z + 6) = 273. 3x2 - 18x - 48 = 04. 3x2 -
Approximate the real solutions to each quadratic equation to two decimal places? 1. 23.1 - 14.1x - 0.002x2 = 0 2. 1.03x2 + 2.02x - 1.015 = 0
Find the vertex and determine if it is a maximum or minimum point, find the zeros if they exist, and sketch the graph. 1. y = ½ x2 + 2x 2. y = 4 - 1/4 x2 3. y = 6 + x - x2 4. y = x2 - 4x + 5
Use a graphing utility to graph each function. Use the vertex and zeros to determine an appropriate window. Be sure to label the maximum or minimum point?1 y = 1/3 x2 - 32. y = 1/2x2 + 23. y = x2 +
A graph is given. Use the graph to(a) Locate the vertex,(b) Determine the zeros, and(c) Match the graph with one of the equations A, B, C, or D.a. y = 7x - 1/2x2b. y = 1/2x2 - x - 4c. y = 8 - 2x -
Sketch a graph of each of the following basic functions? (a) f(x) = x2 (b) f(x) = 1/x (c) f(x) = x1/4
IfFind the following (a) f(-2) (b) f(0) (c) f(1) (d) f(2)
Graph each function1.2. (a) f(x) = (x - 2)2 (b) f(x) = (x + 1)3
Use a graphing utility to graph each function. Find any turning points?1. y = x3 + 3x2 - 9x2. y = x3 - 9x
Graph each function. Find and identify any asymptotes? 1. y = 1 / x - 2 2. y = 2x - 1 / x + 3
Consider the data given in the table.(a) Make a scatter plot.(b) Fit a linear function to the data.(c) Try other function types and find one that fits better than a linear function.
Consider the data given in the table.(a) Make a scatter plot.(b) Fit a linear function to the data.(c) Try other function types and find one that fits better than a linear function.
1. A ball is thrown into the air from a height of 96 ft above the ground, and its height is given by S = 96 + 32t - 16t2, where t is the time in seconds.(a) Find the values of t that make S = 0.(b)
By using U.S. Energy Information Administration data from 2012 and projected to 2040, the total U.S. employment in manufacturing, E in millions, can be modeled byE(t) = 0.0052t2 + 0.080t + 12Were t
A rectangular lot is to be fenced in and then divided down the middle to create two identical fenced lots (see the figure). If 1200 ft of fence is to be used, the area of each lot is given by(a) Find
Graph the first-quadrant portion of the supply function? p = 2q2 + 4q + 6
Graph the first-quadrant portion of the demand function? p = 18 - 3q - q2
(a) Suppose the supply function for a product is p = 0.1q2 + 1 and the demand function is p = 85 - 0.2q - 0.1q2. Sketch the first-quadrant portion of the graph of each function. Use the same set of
The supply function for a product is given by p = q2 + 300, and the demand is given by p + q = 410. Find the equilibrium quantity and price?
If the demand function for a commodity is given by the equation p2 + 5q = 200 and the supply function is given by 40 - p2 + 3q = 0, find the equilibrium quantity and price?
If total costs for a product are given by C(x) = 1760 + 8x + 0.6x2 and total revenues are given by R(x) = 100x - 0.4x2, find the break-even quantities?
If total costs for a commodity are given by C(x) = 900 + 25x and total revenues are given by R(x) = 100x - x2, find the break-even quantities?
Find the maximum revenue and maximum profit for the functions described in Problem 58. In problem 58, If total costs for a commodity are given by C(x) = 900 + 25x and total revenues are given by R(x)
Given total profit P(x) = 1.3x2 - 0.01x2 - 30, find maximum profit and the break-even quantities and sketch the graph?
Given C(x) = 360 + 10x + 0.2x2 and R(x) = 50x - 0.2x2, find the level of production that gives maximum profit and find the maximum profit?
A certain company has fixed costs of $15,000 for its product and variable costs given by 140 + 0.04x dollars per unit, where x is the total number of units. The selling price of the product is given
The rise of adult diabetes in the United States is a growing concern for health professionals. Using Centers for Disease Control and Prevention data for selected years from 2010 and projected to
The amount y of photosynthesis that takes place in a certain plant depends on the intensity x of the light present, according to y = 120x2 - 20x3 for x ( 0 (a) Graph this function with a graphing
Suppose the cost C, in dollars, of eliminating p percent of the pollution from the emissions of a factory is given by(a) What type of function is this? (b) Given that p represents the percent of
The Borough Municipal Authority of Beaver, Pennsylvania, used the following function to determine charges for water.Where C(x) is the cost in dollars for x thousand gallons of water. (a) Find the
The table shows the times that it takes a Subaru WRX to accelerate from 0 mph to speeds of 30 mph, 40 mph, etc., up to 90 mph, in increments of 10 mph.(a) Represent the times by x and the speeds by
The tables below give Social Security Administration data for the U.S. average annual wage from 2011 and projected to 2021 and for selected years from 2012 and projected to 2050.(a) Make a scatter
Obesity (BMI ( 30) is a serious problem in the United States and is expected to get worse. Being overweight increases the risk of diabetes, heart disease, and many other ailments, but the severely
The makeup of various groups within the U.S. population may reshape the electorate in ways that could change political representation and policies. The following table shows U.S. Department of Labor
Use the following matrices for the following Problems.1. How many rows does matrix B have? 2. What is the order of matrix E? 3. Which matrices have the same order as G? 4. Write the negative of D? 5.
Perform the operations, if possible.1. C + D2. A - F3. A + F4. Z + GT
Find x, y, z, and w.1.2.3.4.
Solve for x, y, and z if
Find x, y, z, and w if
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2012.United StatesForeign (a) Write a matrix A that contains
The following tables show important demographics for China, Bangladesh, and the Philippines for 2012 and projected for 2062.(a) Create matrix B for the 2012 table and matrix A for the 2062 table.(b)
The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars.(a) Use a calculator or spreadsheet to
The following tables give U.S. Census Bureau data and projections of the population (in thousands) by selected age groups and sex in the United States.(a) If matrix M gives the male data and Matrix F
Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2015 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in
A poll of 3320 people revealed that of the respondents that were registered Republicans, 843 approved of their representative's job performance, 426 did not, and 751 had no opinion. Of the registered
The following table gives the years of life expectancy at birth for Blacks and Whites born in the United States in selected years from 2000 and projected to 2020.(a) Make a matrix A containing the
The following table shows median weekly earnings for men and women of different ages in 2012.(a) Use the data to make a 2 Ã— 4 matrix with each row representing a gender and each column
The following tables give U.S. energy imports, exports, and consumption data and projections (in quadrillion BTUs) for various energy types (with liquid fuels and petroleum abbreviated as LF&P)
Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The following matrix gives the amounts of debt and the terms for the companies
A sales associate's expense account for the first week of a certain month has the daily expenses (in dollars) shown in matrix A.(a) The associate finds that expenses for the second week are 5% more
When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The
Management is attempting to identify the most active person in labor's efforts to unionize. The following diagram shows how influence flows from one employee to another among the four most active
In order to rank the five members of a school's chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2.(a)
Operating from two plants, the Book Equipment Company (BEC) produces bookcases and filing cabinets. Matrix A summarizes its production for a week, with row 1 representing the number of bookcases and
1. The following figure depicts the mean (average) flow time for a job when the critical-ratio rule is used to dispatch workers at several machines required to complete the job. In the figure, WHN 1,
Suppose that for the workers and the work centers described in the matrix in Problem 51, changes in rules cause efficiency to decrease by 0.01 at work centers 2 and 5 and to decrease by 0.02 at work
1. For the data in Problem 51, use a computer spreadsheet to find the average efficiency for each worker over the first four work centers. Which worker is the least efficient? Where does this worker
Multiply the matrices.1. (a)(b) 2. (a) (b)
Use the matrices below. Perform the indicated operations.1. AB 2. BA 3. CD 4. DC
Use matrices A through F. In Problems, perform the indicated operations, when possible.1. CD 2. DC 3. DE 4. CF
Is it true for matrices (as it is for real numbers) that AB equals a zero matrix if and only if either A or B equals a zero matrix? (Refer to Problems 23-32.)
(a) Find AB and BA ifAnd (b) For B to exist, what restriction must ad - bc satisfy?
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to see whether the values are the solution of the equation.1.2. 3. 4.
Use technology to find the product AB of the following matrices.1.2.
A car dealer can buy midsize cars for 12% under the list price, and he can buy luxury cars for 15% under the list price. The following table gives the list prices for two midsize and two luxury
A clothing manufacturer has factories in Atlanta, Chicago, and New York. Sales (in thousands) during the first quarter are summarized in the matrix below.During this period the selling price of a
Delivered energy is energy provided by a vendor, such as an electric company. For households with solar panels, windmills, wood-burning furnaces, or other on-site energy sources, only a portion of
Matrix A below gives the fraction of the earth's area and the projected fraction of its population for five continents in 2050. Matrix B gives the earth's area (in square miles) and its projected
Suppose that, for a certain metropolitan area and the surrounding counties, during each 5-year period an average of 20% of the metropolitan population M moves to the surrounding counties and the rest
Suppose the weights (in grams) and lengths (in centimeters) of three groups of laboratory animals are given by matrix A, where column 1 gives the lengths and each row corresponds to one group.If the
Use matrix A to encode the message "Waste not, want not."
Use matrix A to encode the message "To be or not to be"?
When gasoline is refined from crude oil, each gallon of regular, mid-grade, and premium uses a different blend of two different grades of crude oil according to the following matrix.In addition, the
A manufacturer of small kitchen appliances has the following unit costs for labor and materials for three of its products: a blender, a mixer, and a food processor.Furthermore, the quarterly demand
The annual budget of the Magnum Company has the following expenses, in thousands of dollars, for selected departments.(a) Write a matrix B for these budget amounts. (b) Write a matrix A so that BA
Accounting Consider the original budget matrix in Problem 53. Assume there is a 20% increase in manufacturing, a 3% increase in office, a 5% increase in sales, a 20% increase in shipping, a 5%
Use the indicated row operation to change matrix A, where1. Add - 3 times row 1 to row 2 of matrix A and place the result in row 2 to get 0 in row 2, column 1. 2. Add - 4 times row 1 to row 3 of
Use row operations on augmented matrices to solve the given systems of linear equations?1.2. 3. 4.
A system of linear equations and a reduced matrix for the system are given.(a) Use the reduced matrix to find the general solution of the system, if one exists.(b) If multiple solutions exist, find
How can you tell that a system of linear equations has no solution by just looking at its reduced matrix?
May have unique solutions, an infinite number of solutions, or no solution. Use matrices to find the general solution of each system, if a solution exists.1.2.3.4.
Write the augmented matrix associated with each system of linear equation?1.2. Each matrix is an augmented matrix used in the solution of a system of linear equations in x, y, and z. What is the
Use technology to solve each system of equations, if a solution exists?1.2.3.4.
A preschool has Campbell's Chunky Beef soup, which contains 2.5 g of fat and 15 mg of cholesterol per serving (cup), and Campbell's Chunky Sirloin Burger soup, which contains 7 g of fat and 15 mg of
A 3500-seat theater sells tickets for $75 and $110. Each night the theater's expenses total $245,000. When all 3500 seats sell, the owners want ticket revenues to cover expenses plus earn a profit of
A man has $235,000 invested in three properties. One earns 12%, one 10%, and one 8%. His annual income from the properties is $22,500 and the amount invested at 8% is twice that invested at 12%.(a)
A bank lent $1.2 million for the development of three new products, with one loan each at 6%, 7%, and 8%. The amount lent at 8% was equal to the sum of the amounts lent at the other two rates, and
A car rental agency in a major city has a total of 2200 cars that it rents from three locations: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return patterns are
A psychologist studying the effects of nutrition on the behavior of laboratory rats is feeding one group a combination of three foods: I, II, and III. Each of these foods contains three additives, A,
The following table gives the calories, fat, and carbohydrates per ounce for three brands of cereal. How many ounces of each brand should be combined to get 443 calories, 5.7 g of fat, and 113.4 g of
A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3
Suppose that portfolios I and II in Problem 56 are unchanged and portfolio III consists of 2 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. A customer wants 12 blocks of
Each ounce of substance A supplies 5% of the required nutrition a patient needs. Substance B supplies 15% of the required nutrition per ounce, and substance C supplies 12% of the required nutrition
A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein, and 1 g of carbohydrates. A quarter pound of lean red meat provides 3.4 mg of iron, 22 g of protein, and 20 g of carbohydrates. Two

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