Finite Mathematics for the Managerial, Life, and Social Sciences
12th Edition
ISBN: 9781337405782
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter 3.3, Problem 2E
In Exercises
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A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?
Consider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.
Chapter 3 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
Ch. 3.1 - a. What is the difference between the graph of the...Ch. 3.1 - Prob. 2CQCh. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...
Ch. 3.1 - Prob. 9ECh. 3.1 - In Exercises 110, find the graphical solution of...Ch. 3.1 - In Exercises 11-18, write a system of linear...Ch. 3.1 - In Exercises 11-18, write a system of linear...Ch. 3.1 - In Exercises 11-18, write a system of linear...Ch. 3.1 - In Exercises 11-18, write a system of linear...Ch. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - In Exercises 11-18, write a system of linear...Ch. 3.1 - In Exercises 11-18, write a system of linear...Ch. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - In Exercises 2340, determine graphically the...Ch. 3.1 - Prob. 24ECh. 3.1 - In Exercises 2340, determine graphically the...Ch. 3.1 - Prob. 26ECh. 3.1 - In Exercises 2340, determine graphically the...Ch. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - In Exercises 2340, determine graphically the...Ch. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - In Exercises , determine graphically the solution...Ch. 3.1 - In Exercises 2340, determine graphically the...Ch. 3.1 - In Exercises 23 - 40, determine graphically the...Ch. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - In Exercises 2340, determine graphically the...Ch. 3.1 - CONCERT ATTENDANCE The Peninsula Brass Band will...Ch. 3.1 - MANUFACTURING FERTILIZERSAgro Products makes two...Ch. 3.1 - Investments Louisa has earmarked at most 250,000...Ch. 3.1 - DIET PLANNING A dietitian whishes to plan a meal...Ch. 3.1 - Prob. 45ECh. 3.1 - In Exercises 45-48, determine whether the...Ch. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.2 - What is a Linear programming problem?Ch. 3.2 - Suppose you are asked to formulate a linear...Ch. 3.2 - Prob. 3CQCh. 3.2 - Formulate but do not solve each of the following...Ch. 3.2 - Formulate but do not solve each of the following...Ch. 3.2 - Formulate but do not solve each of the following...Ch. 3.2 - Formulate but do not solve each of the following...Ch. 3.2 - PRODUCTION SCHEDULING A division of the Winston...Ch. 3.2 - PRODUCTION SCHEDULING Refer to Exercise 5. If the...Ch. 3.2 - ALLOCATION OF FUNDS Madison Finance has a total of...Ch. 3.2 - ASSET ALLOCATION A financier plans to invest up to...Ch. 3.2 - ASSET ALLOCATION Justin has decided to invest at...Ch. 3.2 - CROP PLANNING A farmer plans to plant two crops, A...Ch. 3.2 - MINIMIZING MINING COSTS Perth Mining Company...Ch. 3.2 - MINIMIZING CRUISE LINE COSTS Deluxe River Cruises...Ch. 3.2 - PRODUCTION SCHEDULING Acoustical Company...Ch. 3.2 - FERTILIZERS A farmer uses two types of...Ch. 3.2 - MINIMIZING CITY WATER COSTS The water-supply...Ch. 3.2 - PRODUCTION SCHEDULING Ace Novelty manufactures...Ch. 3.2 - DIET PLANNING A nutritionist at the Medical Center...Ch. 3.2 - OPTIMIZING ADVERTISING EXPOSURE Everest Deluxe...Ch. 3.2 - MINIMIZING SNIPPING COSTS TMA manufactures 37-in....Ch. 3.2 - SOCIAL PROGRAMS PLANNING AntiFam a hunger-relief...Ch. 3.2 - MINIMIZING SHIPPING COSTS The Green Company...Ch. 3.2 - Prob. 22ECh. 3.2 - MINIMIZING SHIPPING COSTS Singer Motor Corporation...Ch. 3.2 - OPTIMIZING ADVERTISING EXPOSURE As part of a...Ch. 3.2 - PRODUCTION SCHEDULING Custom Office Furniture...Ch. 3.2 - Prob. 26ECh. 3.2 - ASSET ALLOCATION Ashley has earmarked at most...Ch. 3.2 - Prob. 28ECh. 3.2 - MINIMIZING SHIPPING COSTS Acrosonic of Example 4...Ch. 3.2 - OPTIMIZING PRODUCTION OF COLD FORMULAS Beyer...Ch. 3.2 - OPTIMIZING PRODUCTION OF BLENDED JUICES Caljuice...Ch. 3.2 - MINIMIZING SHIPPING COSTS Steinwelt Piano...Ch. 3.2 - In Exercises 33 and 34, determine whether the...Ch. 3.2 - In Exercises 33 and 34, determine whether the...Ch. 3.3 - a. What is the feasible set associated with the...Ch. 3.3 - Prob. 2CQCh. 3.3 - In Exercises 16, find maximum and/or minimum...Ch. 3.3 - In Exercises 16, find maximum and/or minimum...Ch. 3.3 - In Exercises 16, find maximum and/or minimum...Ch. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - Prob. 16ECh. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - In Exercises 730, solve each linear programming...Ch. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - PRODUCTION SCHEDULING National Business machines...Ch. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - MINIMIZING SHIPPING COSTS TMA manufactures 37-in....Ch. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - The problems in Exercises 31-51 correspond to...Ch. 3.3 - TRANSPORTATION Complete the solution to Example 3,...Ch. 3.3 - MAXIMIZING INVESTMENT RETURNS Patricia has at most...Ch. 3.3 - VETERINARY SCIENCE A veterinarian has been asked...Ch. 3.3 - Prob. 55ECh. 3.3 - PRODUCTION SCHEDULING Bata Aerobics manufactures...Ch. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.4 - Suppose P=3x+4y is the objective function in a...Ch. 3.4 - Prob. 2CQCh. 3.4 - Prob. 3CQCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - SHADOW PRICES Refer to Example 2. a. Find the...Ch. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - MINIMIZING COSTS Perth Mining Company operates two...Ch. 3.4 - MINIMIZING CRUISE LINE COSTS Deluxe River Cruises...Ch. 3.4 - PRODUCTION SCHEDULING Soundex produces two models...Ch. 3.4 - Prob. 16ECh. 3.4 - PRODUCTION SCHEDULING Kane Manufacturing has a...Ch. 3.4 - Prob. 18ECh. 3.CRQ - Fill in the blanks. a. The solution set of the...Ch. 3.CRQ - Prob. 2CRQCh. 3.CRQ - Fill in the blanks. A linear programming problem...Ch. 3.CRQ - Prob. 4CRQCh. 3.CRQ - Fill in the blanks. In sensitivity analysis, we...Ch. 3.CRQ - Prob. 6CRQCh. 3.CRE - In Exercise 1 and 2, find the optimal value s of...Ch. 3.CRE - In Exercise 1 and 2, find the optimal value s of...Ch. 3.CRE - In Exercises 314, use the method of corners to...Ch. 3.CRE - In Exercises 314, use the method of corners to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corners to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - In Exercise 3-14, use the method of corner to...Ch. 3.CRE - FINANCIALANALYSIS An investor has decided to...Ch. 3.CRE - PRODUCTION SCHEDULING Soundex produces two model...Ch. 3.CRE - PRODUCTION SCHEDULING Kane Manufacturing has a...Ch. 3.CRE - MINIMIZING SHIPPING COSTS A manufacturer of...Ch. 3.BMO - Prob. 1BMOCh. 3.BMO - Prob. 2BMOCh. 3.BMO - Prob. 3BMOCh. 3.BMO - Prob. 4BMOCh. 3.BMO - Prob. 5BMO
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