Fundamentals of Differential Equations (9th Edition)

9th Edition

ISBN: 9780321977069

Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Publisher: PEARSON

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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A nkcschools.instructure.com Near the surface of any planet, the distance D fallen by a rock in time t is given by ct(this is a consequence of Newton's 2nd law of gravitation). Here we will D = measure D in feet and t in seconds. (a) A rock is dropped from two different heights. It takes the rock 5 times as long to hit the ground from the taller height. How do the heights compare? The taller height is times as tall as the other. (b) On Venus, a rock dropped from 70 feet above the surface takes 2.2 seconds to strike the ground. What is the value of c for Venus? Round your answer to 2 decimal places. (c) Another rock is dropped on Venus. How far has it fallen after 4 seconds? Round your answer to 2 decimal places and include an appropriate label.

A thermometer is removed from a room where the temperature is 70° F and taken outside, where the air temperature is 10° F. After a half a minute the thermometer reads 50° F. What is the reading of the thermometer at t = 1 minute? How long will it take for the reading on the thermometer to reach 15° F? Solve the problem as follows: a) construct a linear first-order DE that models the behaviour of Newton's Law of Cooling and state the initial condition; b) solve the DE and find the constant k using the fact that at half a minute the thermometer reads 50° F; c) what will the temperature T, be at = 1 minute; d) how long will it take the thermometer to display a reading of 15° F; e) sketch a rough graph of the solution in Question 3 (b) which displays the behaviour of the thermometer readings over time. Label the axes and relevant points on the graph;

Chapter 3 Solutions

Fundamentals of Differential Equations (9th Edition)

Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - A brine solution of salt flows at a constant rate...Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - A swimming pool whose volume is 10,000 gal...Ch. 3.2 - The air in a small room 12 ft by 8 ft by 8 ft is...Ch. 3.2 - Prob. 7E Ch. 3.2 - A tank initially contains s0 lb of salt dissolved...Ch. 3.2 - In 1990 the Department of Natural Resources...Ch. 3.2 - Use a sketch of the phase line (see Project B,...

Ch. 3.2 - Use a sketch of the phase line (see Project B,...Ch. 3.2 - Prob. 12E Ch. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14E Ch. 3.2 - In Problem 14, suppose we have the additional...Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Using the U.S. census data in Table 3.1 for 1900,...Ch. 3.2 - The initial mass of a certain species of fish is 7...Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.3 - A cup of hot coffee initially at 95C cools to 80C...Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - It was noon on a cold December day in Tampa: 16C....Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.4 - Prob. 1E Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Prob. 7E Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Prob. 17E Ch. 3.4 - When an object slides on a surface, it encounters...Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Prob. 24E Ch. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - The power generated or dissipated by a circuit...Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - A 108-F capacitor (10 nanofarads) is charged to 50...Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - Prob. 16E Ch. 3.6 - In many of the following problems, it will be...Ch. 3.6 - In Exercises 13-18, use a calculator or a computer...Ch. 3.6 - Prob. 19E Ch. 3.6 - Prob. 20E Ch. 3.7 - Prob. 1E Ch. 3.7 - Prob. 2E Ch. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - Prob. 5E Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Prob. 9E Ch. 3.7 - Prob. 10E Ch. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - Prob. 12E Ch. 3.7 - Prob. 13E Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - Prob. 16E Ch. 3.7 - Prob. 17E Ch. 3.7 - Prob. 18E Ch. 3.7 - Prob. 19E Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E

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