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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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. 3ECh. 3.2 - Prob. 4ECh. 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. 7ECh. 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. 12ECh. 3.2 - In Problem 9, suppose we have the additional...Ch. 3.2 - Prob. 14ECh. 3.2 - In Problem 14, suppose we have the additional...Ch. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 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. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.3 - A cup of hot coffee initially at 95C cools to 80C...Ch. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - It was noon on a cold December day in Tampa: 16C....Ch. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Early Monday morning, the temperature in the...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 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 - Unless otherwise stated, in the following problems...Ch. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - When an object slides on a surface, it encounters...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Escape Velocity. According to Newtons law of...Ch. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - The power generated or dissipated by a circuit...Ch. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - A 108-F capacitor (10 nanofarads) is charged to 50...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 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. 19ECh. 3.6 - Prob. 20ECh. 3.7 - Prob. 1ECh. 3.7 - Prob. 2ECh. 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. 5ECh. 3.7 - Prob. 6ECh. 3.7 - Prob. 7ECh. 3.7 - Prob. 8ECh. 3.7 - Prob. 9ECh. 3.7 - Prob. 10ECh. 3.7 - As in Exercises 3.6, for some problems you will...Ch. 3.7 - Prob. 12ECh. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Prob. 16ECh. 3.7 - Prob. 17ECh. 3.7 - Prob. 18ECh. 3.7 - Prob. 19ECh. 3.7 - Prob. 20ECh. 3.7 - Prob. 21E
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- A gear train consists of three gears meshed together (Figure 9). The middle gear is known as an idler. Show that the angular velocity of the third gear does not depend on the number of teeth of the idler gear (Gear 2).arrow_forwardA two-stage gear train consists of four gears meshed together (Figure 10). The second and third gears are attached, so that they share the same angular velocity (2=4). Find a formula giving the angular velocity of the fourth gear, 2, in terms of 1 and the values of n1,n2,n3andn4.arrow_forwardA mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = ?/12, ?/8, ?/6, ?/4, and 9?/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.)arrow_forward
- Earth and moon. Find the centripetal acceleration of the moon toward Earth, assuming that the orbit of the moon is a circle of radius 239,000 miles = 3.85 108 m, and the time for one complete revolution is 27.3 days = 2.36 106 s.arrow_forwardSuppose a rock falls from rest from a height of 100 meters and the only force acting on it is gravity. Find an equation for the velocity v(t) as a function of time, measured in meters per second. Hint What is the initial velocity of the rock?arrow_forwardQuestion b)arrow_forward
- An undamped spring-mass system contains a mass that weighs 8lb and a spring with spring constant 3lb/in. It is suddenly set in motion at t=0 by an external force of 7cos(4t)lb. Determine the position u, in feet, of the mass at any time t. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units. u(t) = ? ftarrow_forwardPlease also answer "This damped motion is" A. Overdamped B. Critically Damped C. Underdampedarrow_forwardThe weight of an individual walking is 824N. The hill they are walking on has a slope of 10 degrees. Assuming they are in a static equilibrium what is their normal force?arrow_forward
- A seasoned parachutist went for a skydiving trip where he performed freefall before deploying the parachute. According to Newton's Second Law of Motion, there are two forcës acting on the body of the parachutist, the forces of gravity (F,) and drag force due to air resistance (Fa) as shown in Figure 1. Fa = -cv ITM EUTM FUTM * UTM TM Fg= -mg x(t) UTM UT UTM /IM LTM UTM UTM TUIM UTM F UT GROUND Figure 1: Force acting on body of free-fall where x(t) is the position of the parachutist from the ground at given time, t is the time of fall calculated from the start of jump, m is the parachutist's mass, g is the gravitational acceleration, v is the velocity of the fall and c is the drag coefficient. The equation for the velocity and the position is given by the equations below: EUTM PUT v(t) = mg -et/m – 1) (Eq. 1.1) x(t) = x(0) – Where x(0) = 3200 m, m = 79.8 kg, g = 9.81m/s² and c = 6.6 kg/s. It was established that the critical position to deploy the parachutes is at 762 m from the ground…arrow_forward[25] An undamped spring-mass system has a mass that weighs 48 lb and a spring constant 0.5 lb/in. The mass is suddenly set in motion at t = 0 by an external force of 3 cos(2t) lb. Assume that the gravitational acceleration is g = 32 ft/s?. Find the position of mass as a function of time t.arrow_forward
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