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Math Mathematical Applications for the Management, Life, and Social Sciences

Projectiles Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by y = − 0.0013 x 2 + x + 10 and y = − x 2 81 + 4 3 x + 10 where x is the horizontal distance and y is the vertical distance, both is feet. Determine which projectile goes higher by locating the vertex of each parabola.

Projectiles Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by y = − 0.0013 x 2 + x + 10 and y = − x 2 81 + 4 3 x + 10 where x is the horizontal distance and y is the vertical distance, both is feet. Determine which projectile goes higher by locating the vertex of each parabola.

Solution Summary: The author compares the given function with the quadratic function f(x) to find the values of a, b and c.

Mathematical Applications for the Management, Life, and Social Sciences

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Textbook Question

Chapter 2.2, Problem 39E

Projectiles Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by

y = − 0.0013 x 2 + x + 10 and

y = − x 2 81 + 4 3 x + 10 where x is the horizontal distance and y is the vertical distance, both is feet. Determine which projectile goes higher by locating the vertex of each parabola.

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Chapter 2.2, Problem 38E

Chapter 2.2, Problem 40E

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Chapter 2 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 2.1 - The factoring method for solving a quadratic...Ch. 2.1 - Solve the following equations by factoring. Ch. 2.1 - Prob. 3CP Ch. 2.1 - Prob. 4CP Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 6E

Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 8E Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 10E Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 12E Ch. 2.1 - In Problems 5-14, solve each question by...Ch. 2.1 - Prob. 14E Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - Prob. 18E Ch. 2.1 - In Problems 15-20, solve each equation using the...Ch. 2.1 - Prob. 20E Ch. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - In Problems 21-26, find the exact real solutions...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - In Problems 27-36, use any method to find the...Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - In problems 37-42, solve each equation using a...Ch. 2.1 - Prob. 40E Ch. 2.1 - In problems 37-42, solve each equation using a...Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - In Problems 43-46, multiply both sides of the...Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Applications Profit If the profit from the sale of...Ch. 2.1 - Profit If the profit from the sale of x units of a...Ch. 2.1 - Profit Suppose the profit from the sale of x units...Ch. 2.1 - Profit Suppose the profit from the sale of x units...Ch. 2.1 - Flight of a ball If a ball is thrown upward at 96...Ch. 2.1 - Flight of a ball A tennis ball is thrown into the...Ch. 2.1 - Wind and pollution The amount of airborne...Ch. 2.1 - Drug sensitivity The sensitivity S to a drug is...Ch. 2.1 - 57. Corvette acceleration The time t, in seconds ,...Ch. 2.1 - 58.Consumer Price Index Using Social Security...Ch. 2.1 - 59. Marijuana use For the years since 2001 , the...Ch. 2.1 - Prob. 60E Ch. 2.1 - 61. Percent profit Ace Jewelry Store sold a...Ch. 2.1 - Prob. 62E Ch. 2.1 - 63. National health care Using data from 2002 and...Ch. 2.1 - 64. Velocity of blood Because of friction from the...Ch. 2.1 - 65. Body-heat loss The model for body-heat loss...Ch. 2.1 - 66. Depth of Fissure A fissure in the earth...Ch. 2.2 - Name the graph of a quadratic function. Ch. 2.2 - (a) What is the coordinate of the vertex of ? (b)...Ch. 2.2 - Prob. 3CP Ch. 2.2 - Prob. 4CP Ch. 2.2 - Prob. 5CP Ch. 2.2 - In Problems 1-6,(a)find the vertex of the graph of...Ch. 2.2 - Prob. 2E Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problem 1-6,(a)find the vertex of the graph of...Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problems 1-6,(a) find the vertex of the graph...Ch. 2.2 - In Problems 7-12,determine whether each...Ch. 2.2 - In Problems7-12,determine whether each functions...Ch. 2.2 - In Problems 7-12,determine whether each function’s...Ch. 2.2 - In Problem 7-12, determine whether each function’s...Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - In Problems , graph each function with a graphing...Ch. 2.2 - Prob. 21E Ch. 2.2 - In Problem 21 and 22, find the average rate of...Ch. 2.2 - In Problems , find the vertex and zeros and use...Ch. 2.2 - Prob. 24E Ch. 2.2 - Prob. 25E Ch. 2.2 - Prob. 26E Ch. 2.2 - Prob. 27E Ch. 2.2 - Prob. 28E Ch. 2.2 - Prob. 29E Ch. 2.2 - Prob. 30E Ch. 2.2 - 31. Profit The monthly profit from the sale of x...Ch. 2.2 - 32. Profit The monthly profit from the sale of x...Ch. 2.2 - 33. Crop Yield The yield in bushels from a grove...Ch. 2.2 - 34. Stimulus-response One of the early results in...Ch. 2.2 - Drug Sensitivity The sensitivity S to a drug is...Ch. 2.2 - 36. Maximizing an enclosed area Iffeet of fence ...Ch. 2.2 - Photosynthesis The rate of photosynthesis R for a...Ch. 2.2 - 38. Projectiles A ball thrown vertically into the...Ch. 2.2 - Projectiles Two projectiles are shot into the air...Ch. 2.2 - Flow rates of water The speed at which water...Ch. 2.2 - Prob. 41E Ch. 2.2 - Prob. 42E Ch. 2.2 - Apartment rental The owner of an apartment...Ch. 2.2 - Revenue The owner of a skating rink rents the...Ch. 2.2 - Pension resources The Pension Benefit Guaranty...Ch. 2.2 - Prob. 46E Ch. 2.2 - Health care costs per capita Rising health care...Ch. 2.2 - Women in the workforce Using U.S. Census Bureau...Ch. 2.2 - Prob. 49E Ch. 2.2 - E-commerce Online sales in the United States are...Ch. 2.3 - The point of intersection of the revenue function...Ch. 2.3 - If and , finding the break-even points requires...Ch. 2.3 - Prob. 3CP Ch. 2.3 - Prob. 4CP Ch. 2.3 - BREAK-EVEN POINTS AND MAXIMIZATION 1.The total...Ch. 2.3 - 2. If a firm has the following cost and revenue...Ch. 2.3 - 3.If a company has total costs And total revenues...Ch. 2.3 - 4. If total costs are and total revenues Are ,find...Ch. 2.3 - Given that profit is P(x)=11.5x-0.1x2-150 And that...Ch. 2.3 - 6.If the profit function for a firm is given by...Ch. 2.3 - 7.Find the maximum revenue for the revenue...Ch. 2.3 - 8.Find the maximum revenue for the revenue...Ch. 2.3 - 9.If in a monopoly market the demand for a...Ch. 2.3 - 10.If in a monopoly market the demand for a...Ch. 2.3 - The profit function for a certain commodity is...Ch. 2.3 - The profit function for a firm making widgets is ...Ch. 2.3 - (a) Graph the profit function . (b) Find the...Ch. 2.3 - Prob. 14E Ch. 2.3 - (a) Form the profit function for the cost and...Ch. 2.3 - Prob. 16E Ch. 2.3 - 17. Suppose a company has fixed costs of and...Ch. 2.3 - 18. Suppose a company has fixed costs of and...Ch. 2.3 - The following table gives the total revenues of ...Ch. 2.3 - The data in the table give sales revenue and costs...Ch. 2.3 - Prob. 21E Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - In Problems 22-24, a supply function and a demand...Ch. 2.3 - 25. If the supply function for a commodity is and...Ch. 2.3 - If the supply function for a commodity is and the...Ch. 2.3 - If the demand function for a commodity is given by...Ch. 2.3 - If the supply and demand functions for a commodity...Ch. 2.3 - If the supply and demand functions for a commodity...Ch. 2.3 - If the supply and demand functions for a certain...Ch. 2.3 - The supply function for a product is , while the...Ch. 2.3 - The supply and demand for a product are given by ...Ch. 2.3 - For the product in problem 31, if a $22 tax is...Ch. 2.3 - Prob. 34E Ch. 2.4 - All constant functions [such as ] have graphs that...Ch. 2.4 - Which of the following are polynomial...Ch. 2.4 - A third-degree polynomial can have at most _____...Ch. 2.4 - Prob. 4CP Ch. 2.4 - Prob. 5CP Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problems 1-12, match each of the function with...Ch. 2.4 - In problem 13, decide whether each function whose...Ch. 2.4 - In problem 14, decide whether each function whose...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - In Problems 15-22, match each equation with the...Ch. 2.4 - Ch. 2.4 - Prob. 24E Ch. 2.4 - Prob. 25E Ch. 2.4 - Prob. 26E Ch. 2.4 - Prob. 27E Ch. 2.4 - In Problems 23-28, graph the function. 28. Ch. 2.4 - Prob. 29E Ch. 2.4 - Prob. 30E Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Prob. 33E Ch. 2.4 - 34. If find the following. (b) (c) (d)...Ch. 2.4 - In Problems 35-40, (a) graph each function with a...Ch. 2.4 - In Problems 35-40, (a) graph each function with a...Ch. 2.4 - [Type here] In Problems 35-40, (a) graph each...Ch. 2.4 - [Type here] In Problems 35-40, (a) graph each...Ch. 2.4 - Prob. 39E Ch. 2.4 - Prob. 40E Ch. 2.4 - 41. Postal restrictions If a box with a square...Ch. 2.4 - Prob. 42E Ch. 2.4 - Latin American Internet use Using data from and...Ch. 2.4 - Prob. 44E Ch. 2.4 - 45. Pollution Suppose that the cost (in dollars)...Ch. 2.4 - Average cost If the weekly total cost of producing...Ch. 2.4 - Area If 100 feet of fence is to be used to enclose...Ch. 2.4 - Water usage The monthly charge for water in a...Ch. 2.4 - Prob. 49E Ch. 2.4 - Commercial electrical usage The monthly charge (in...Ch. 2.4 - First-class postage The postage charged for...Ch. 2.4 - Income tax In a given year, the U.S. federal...Ch. 2.4 - Prob. 53E Ch. 2.4 - Prob. 54E Ch. 2.4 - Prob. 55E Ch. 2.5 - The following table gives the Social Security...Ch. 2.5 - Prob. 2CP Ch. 2.5 - Prob. 1E Ch. 2.5 - Prob. 2E Ch. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - Prob. 5E Ch. 2.5 - In Problems 1-8, determine whether the scatter...Ch. 2.5 - Prob. 7E Ch. 2.5 - Prob. 8E Ch. 2.5 - Prob. 9E Ch. 2.5 - Prob. 10E Ch. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 12E Ch. 2.5 - Prob. 13E Ch. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 15E Ch. 2.5 - In Problems 9- 16, find the equation of the...Ch. 2.5 - Prob. 17E Ch. 2.5 - Prob. 18E Ch. 2.5 - Prob. 19E Ch. 2.5 - Prob. 20E Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - In Problems 17-24, (a) plot the given points, (b)...Ch. 2.5 - Prob. 24E Ch. 2.5 - Prob. 25E Ch. 2.5 - emission The following table gives the millions...Ch. 2.5 - Disposable income Disposable income is the amount...Ch. 2.5 - Diabetes As the following table shows ,...Ch. 2.5 - Wind chill The table gives the wind chill...Ch. 2.5 - Developing economies The developing economies’...Ch. 2.5 - Prob. 31E Ch. 2.5 - Prob. 32E Ch. 2.5 - Prob. 33E Ch. 2.5 - Prob. 34E Ch. 2.5 - Prob. 35E Ch. 2.5 - National health care The table shows the national...Ch. 2.5 - Prob. 37E Ch. 2.5 - Prob. 38E Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - In Problem 1-10, find the real solutions to each...Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - For each function in Problems 19-24, find the...Ch. 2 - For each function in Problems 19-24, find the...Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - [Type here] In Problems 25-30, use a graphing...Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - In Problems 25-30, use a graphing calculator to...Ch. 2 - The supply function for a product is 2pq10=0,...Ch. 2 - The supply and demand for a product are given by...Ch. 2 - 33.For the product in Problem 31,if a $22 tax is...Ch. 2 - Prob. 34RE Ch. 2 - In Problems 33-36, a graph is given. Use the graph...Ch. 2 - Prob. 36RE Ch. 2 - 37. Sketch a graph of each of the following basic...Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - In Problems 40 and 41 ,graph each function. 40. ...Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - 49.Profit The profit for a product is given by...Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - 54. Market equilibrium (a) Suppose the supply...Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Break-even points If total costs for a product are...Ch. 2 - Break-even points If total costs for a commodity...Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Maximum profit Given and , find the level of...Ch. 2 - Break-even and profit maximization A certain...Ch. 2 - 63. Diabetes The rise of adult diabetes in the...Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - 68. Average annual wage The tables below give...Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 1T Ch. 2 - Prob. 2T Ch. 2 - Prob. 3T Ch. 2 - Prob. 4T Ch. 2 - Which of the following three graphs is the graph...Ch. 2 - Prob. 6T Ch. 2 - Prob. 7T Ch. 2 - Prob. 8T Ch. 2 - Prob. 9T Ch. 2 - Prob. 10T Ch. 2 - Prob. 11T Ch. 2 - Prob. 12T Ch. 2 - Prob. 13T Ch. 2 - Prob. 14T Ch. 2 - Prob. 15T Ch. 2 - Prob. 16T Ch. 2 - Suppose the supply and demand functions for a...Ch. 2 - Suppose a company’s total cost a product is given...Ch. 2 - Prob. 19T Ch. 2 - Prob. 20T Ch. 2 - Prob. 1EAGP1 Ch. 2 - Prob. 2EAGP1 Ch. 2 - Prob. 3EAGP1 Ch. 2 - Prob. 4EAGP1 Ch. 2 - Prob. 5EAGP1 Ch. 2 - Prob. 6EAGP1 Ch. 2 - Prob. 7EAGP1 Ch. 2 - Prob. 1EAGP2 Ch. 2 - Prob. 2EAGP2 Ch. 2 - Prob. 3EAGP2 Ch. 2 - Prob. 4EAGP2 Ch. 2 - Prob. 5EAGP2 Ch. 2 - Prob. 6EAGP2 Ch. 2 - Prob. 7EAGP2 Ch. 2 - Prob. 8EAGP2

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