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The velocity v of a freefalling skydiver is well modeled

Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall ISBN: 9780495561989 199

Solution for problem 12 Chapter 1.1

Differential Equations 00 | 4th Edition

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Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall

Differential Equations 00 | 4th Edition

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13
1
Problem 12

The velocity v of a freefalling skydiver is well modeled by the differential equation m dv dt = mg kv2, where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the diver during the dive. (Note that the constants m, g, and k are positive.) (a) Perform a qualitative analysis of this model. (b) Calculate the terminal velocity of the skydiver. Express your answer in terms of m, g, and k. Exercises 1315 consider an elementary model of the learning process: Although human learning is an extremely complicated process, it is possible to build models of certain simple types of memorization. For example, consider a person presented with a list to be studied. The subject is given periodic quizzes to determine exactly how much of the list has been memorized. (The lists are usually things like nonsense syllables, randomly generated three-digit numbers, or entries from tables of integrals.) If we let L(t) be the fraction of the list learned at time t, where L = 0 corresponds to knowing nothing and L = 1 corresponds to knowing the entire list, then we can form a simple model of this type of learning based on the assumption: The rate d L/dt is proportional to the fraction of the list left to be learned.Since L = 1 corresponds to knowing the entire list, the model isd Ldt = k(1 L),where k is the constant of proportionality.

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Chapter 1.1, Problem 12 is Solved
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Textbook: Differential Equations 00
Edition: 4
Author: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall
ISBN: 9780495561989

The full step-by-step solution to problem: 12 from chapter: 1.1 was answered by , our top Math solution expert on 01/02/18, 08:51PM. This textbook survival guide was created for the textbook: Differential Equations 00, edition: 4. This full solution covers the following key subjects: . This expansive textbook survival guide covers 90 chapters, and 1456 solutions. The answer to “The velocity v of a freefalling skydiver is well modeled by the differential equation m dv dt = mg kv2, where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the diver during the dive. (Note that the constants m, g, and k are positive.) (a) Perform a qualitative analysis of this model. (b) Calculate the terminal velocity of the skydiver. Express your answer in terms of m, g, and k. Exercises 1315 consider an elementary model of the learning process: Although human learning is an extremely complicated process, it is possible to build models of certain simple types of memorization. For example, consider a person presented with a list to be studied. The subject is given periodic quizzes to determine exactly how much of the list has been memorized. (The lists are usually things like nonsense syllables, randomly generated three-digit numbers, or entries from tables of integrals.) If we let L(t) be the fraction of the list learned at time t, where L = 0 corresponds to knowing nothing and L = 1 corresponds to knowing the entire list, then we can form a simple model of this type of learning based on the assumption: The rate d L/dt is proportional to the fraction of the list left to be learned.Since L = 1 corresponds to knowing the entire list, the model isd Ldt = k(1 L),where k is the constant of proportionality.” is broken down into a number of easy to follow steps, and 248 words. Differential Equations 00 was written by and is associated to the ISBN: 9780495561989. Since the solution to 12 from 1.1 chapter was answered, more than 668 students have viewed the full step-by-step answer.

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The velocity v of a freefalling skydiver is well modeled