
Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 4.10, Problem 2E
To determine
To sketch:
The frequency response curve (13) for the system.
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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below.
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars)
are as follows.
From
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Clermont
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Northwest Gas
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Chapter 4 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 4.1 - Verify that for b=0 and Fext(t)=0, equation (3)...Ch. 4.1 - If Fext(t)=0, equation (3) becomes my+by+ky=0. For...Ch. 4.1 - Show that if Fext(t)=0, m=1, k=9, and b=6, then...Ch. 4.1 - Prob. 4ECh. 4.1 - Verify that the exponentially damped sinusoid...Ch. 4.1 - An external force F(t)=2cos2t is applied to a...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - In Problems 79, find a synchronous solution of the...Ch. 4.1 - Undamped oscillators that are driven at resonance...
Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 1-12, find a general solution to the...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - In Problems 13-20, solve the given initial value...Ch. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - In Problems 22-25, use the method described in...Ch. 4.2 - Prob. 24ECh. 4.2 - In Problems 22-25, use the method described in...Ch. 4.2 - 26.Boundary Value Problems. When the values of a...Ch. 4.2 - In Problems 27 32, use Definition 1 to determine...Ch. 4.2 - In Problems 2732, use Definition 1 to determine...Ch. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - In Problems 2732, use Definition 1 to determine...Ch. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Wronskian. For any two differentiable functions y1...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - In Problems 3741, find three linearly independent...Ch. 4.2 - Prob. 38ECh. 4.2 - In Problems 3741, find three linearly independent...Ch. 4.2 - In Problems 3741, find three linearly independent...Ch. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Solve the initial value problem: y2yy+2y=0;...Ch. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.3 - In Problems 1-8, the auxiliary equation for the...Ch. 4.3 - In Problems 1-8, the auxiliary equation for the...Ch. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - In Problems 1-8, the auxiliary equation for the...Ch. 4.3 - In Problems 1-8, the auxiliary equation for the...Ch. 4.3 - In Problems 1-8, the auxiliary equation for the...Ch. 4.3 - In Problems 1-8, the auxiliary equation for the...Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution. u+7u=0Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution. yy+7y=0Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution....Ch. 4.3 - In Problems 9-20, find a general solution. yy+2y=0Ch. 4.3 - In Problems 21-27, solve the given initial value...Ch. 4.3 - In Problems 21-27, solve the initial value...Ch. 4.3 - In Problems 21-27, solve the given initial value...Ch. 4.3 - In Problems 21-27, solve the given initial value...Ch. 4.3 - In Problems 21-27, solve the given initial value...Ch. 4.3 - Prob. 26ECh. 4.3 - In Problems 21-27, solve the given initial value...Ch. 4.3 - To see the effect of changing the parameters b in...Ch. 4.3 - Find a general solution to the following...Ch. 4.3 - Prob. 30ECh. 4.3 - Using the mass-spring analogy, predict the...Ch. 4.3 - Vibrating Spring without Damping. A vibrating...Ch. 4.3 - Vibrating Spring with Damping. Using the model for...Ch. 4.3 - Prob. 34ECh. 4.3 - Swinging Door. The motion of a swinging door with...Ch. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prove the sum of angles formula for the sine...Ch. 4.4 - In Problem 1-8, decide whether or not the method...Ch. 4.4 - In Problem 1-8, decide whether or not the method...Ch. 4.4 - In Problem 1-8, decide whether or not the method...Ch. 4.4 - In Problem 1-8, decide whether or not the method...Ch. 4.4 - In Problem 1-8, decide whether or not the method...Ch. 4.4 - Prob. 6ECh. 4.4 - In Problem 1-8, decide whether or not the method...Ch. 4.4 - Prob. 8ECh. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problem 9-26, find a particular solution to the...Ch. 4.4 - Prob. 12ECh. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - Prob. 16ECh. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - Prob. 18ECh. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - Prob. 20ECh. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 9-26, find a particular solution to...Ch. 4.4 - In Problems 2732, determine the form of a...Ch. 4.4 - In Problems 27 32, determine the form of a...Ch. 4.4 - In Problems 2732, determine the form of a...Ch. 4.4 - In Problems 2732, determine the form of a...Ch. 4.4 - Prob. 31ECh. 4.4 - In Problems 2732, determine the form of a...Ch. 4.4 - Prob. 33ECh. 4.4 - In Problems 3336, use the method of undetermined...Ch. 4.4 - Prob. 35ECh. 4.4 - In Problems 3336, use the method of undetermined...Ch. 4.5 - Given that y1(t)=cost is a solution to yy+y=sint...Ch. 4.5 - Given that y1(t)=(1/4)sin2t is a solution to...Ch. 4.5 - In Problems 3-8, a nonhomogeneous equation and a...Ch. 4.5 - In Problem 3-8, a nonhomogeneous equation and a...Ch. 4.5 - In Problem 3-8, a nonhomogeneous equation and a...Ch. 4.5 - In Problems 3-8, a nonhomogeneous equation and a...Ch. 4.5 - In Problems 3-8, a nonhomogeneous equation and a...Ch. 4.5 - In Problems 3-8, a nonhomogeneous equation and a...Ch. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - In Problems 9-16 decide whether the method of...Ch. 4.5 - In Problems 9-16 decide whether the method of...Ch. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - In Problem 17-22, find a general solution to the...Ch. 4.5 - In Problems 17-22, find a general solution to the...Ch. 4.5 - In Problems 17-22, find a general solution to the...Ch. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - In Problems 2330, find the solution to the initial...Ch. 4.5 - In Problems 2330, find the solution to the initial...Ch. 4.5 - Prob. 27ECh. 4.5 - In Problems 2330, find the solution to the initial...Ch. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - In Problems 3136, determine the form of a...Ch. 4.5 - In Problems 3136, determine the form of a...Ch. 4.5 - Prob. 34ECh. 4.5 - In Problems 3136, determine the form of a...Ch. 4.5 - In Problems 31 36, determine the form of a...Ch. 4.5 - In Problems 3740, find a particular solution to...Ch. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Discontinuous Forcing Term. In certain physical...Ch. 4.5 - Forced Vibrations. As discussed in Section 4.1, a...Ch. 4.5 - A massspring system is driven by a sinusoidal...Ch. 4.5 - Prob. 44ECh. 4.5 - Speed Bumps. Often bumps like the one depicted in...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - Prob. 3ECh. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - In Problems 18, find a general solution to the...Ch. 4.6 - Prob. 9ECh. 4.6 - In Problems 9 and 10, find a particular solution...Ch. 4.6 - In Problems 1118, find a general solution to the...Ch. 4.6 - In Problems 1118, find a general solution to the...Ch. 4.6 - Prob. 13ECh. 4.6 - In Problems 11-18, find a general solution to the...Ch. 4.6 - In Problems 11-18, find a general solution to the...Ch. 4.6 - In Problems 11-18, find a general solution to the...Ch. 4.6 - In Problems 11-18, find a general solution to the...Ch. 4.6 - In Problems 11-18, find a general solution to the...Ch. 4.6 - Prob. 19ECh. 4.6 - Use the method of variation of parameters to show...Ch. 4.6 - Prob. 21ECh. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - In Problems 22 through 25, use variation of...Ch. 4.6 - In Problems 22 through 25, use variation of...Ch. 4.7 - In Problems 1 through 4, use Theorem 5 to discuss...Ch. 4.7 - In Problems 1 through 4, use Theorem 5 to discuss...Ch. 4.7 - In Problems 1 through 4, use Theorem 5 to discuss...Ch. 4.7 - In Problems 1 through 4, use Theorem 5 to discuss...Ch. 4.7 - In Problems 5 through 8, determine whether Theorem...Ch. 4.7 - In Problems 5 through 8, determine whether Theorem...Ch. 4.7 - In Problems 5 through 8, determine whether Theorem...Ch. 4.7 - In Problems 5 through 8, determine whether Theorem...Ch. 4.7 - In Problems 9 through 14, find a general solution...Ch. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - In Problems 9 through 14, find a general solution...Ch. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - In Problems 15 through 18, find a general solution...Ch. 4.7 - In Problems 15 through 18, find a general solution...Ch. 4.7 - In Problems 15 through 18, find a general solution...Ch. 4.7 - Prob. 19ECh. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.7 - In Problems 21 and 22, devise a modification of...Ch. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Let y1(t)=t3 and y2(t)=|t3|. Are y1 and y2...Ch. 4.7 - Prob. 27ECh. 4.7 - Let y1(t)=t2 and y2(t)=2t|t|. Are y1 and y2...Ch. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - By completing the following steps, prove that the...Ch. 4.7 - Prob. 33ECh. 4.7 - Given that 1+t, 1+2t, and 1+3t2 are solutions to...Ch. 4.7 - Verify that the given functions y1 and y2 are...Ch. 4.7 - In Problems 37 through 39, find general solutions...Ch. 4.7 - Prob. 38ECh. 4.7 - In Problems 37 through 39, find general solutions...Ch. 4.7 - Prob. 40ECh. 4.7 - In Problems 41 through 44, a differential equation...Ch. 4.7 - In Problems 41 through 44, a differential equation...Ch. 4.7 - In Problems 41 through 44, a differential equation...Ch. 4.7 - In Problems 41 through 44, a differential equation...Ch. 4.7 - Find a particular solution to the nonhomogeneous...Ch. 4.7 - Find a particular solution to the nonhomogeneous...Ch. 4.7 - In quantum mechanics, the study of the Schrodinger...Ch. 4.7 - Prob. 48ECh. 4.7 - Prob. 49ECh. 4.7 - Prob. 50ECh. 4.7 - Prob. 51ECh. 4.7 - Prob. 52ECh. 4.8 - Show that if y(t) satisfies yty=0, then y(t)...Ch. 4.8 - Prob. 2ECh. 4.8 - Prob. 3ECh. 4.8 - Prob. 4ECh. 4.8 - a. Use the energy integral lemma to derive the...Ch. 4.8 - Prob. 6ECh. 4.8 - Prob. 7ECh. 4.8 - Use the energy integral Lemma to show that...Ch. 4.8 - Prob. 9ECh. 4.8 - Prob. 10ECh. 4.8 - Prob. 11ECh. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Use the mass-spring oscillator analogy to decide...Ch. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.9 - All problems refer to the mass-spring...Ch. 4.9 - Prob. 2ECh. 4.9 - All problems refer to the mass-spring...Ch. 4.9 - All problems refer to the mass-spring...Ch. 4.9 - Prob. 5ECh. 4.9 - Prob. 6ECh. 4.9 - Prob. 7ECh. 4.9 - Prob. 8ECh. 4.9 - A 2kg mass is attached to a spring with stiffness...Ch. 4.9 - A 1/4-kg mass is attached to a spring with...Ch. 4.9 - Prob. 11ECh. 4.9 - A 1/4-kg mass is attached to a spring with...Ch. 4.9 - Prob. 13ECh. 4.9 - For an underdamped system, verify that as b0 the...Ch. 4.9 - How can one deduce the value of the damping...Ch. 4.9 - Prob. 16ECh. 4.9 - Consider the equation for free mechanical...Ch. 4.9 - Consider the equation for free mechanical...Ch. 4.10 - Sketch the frequency response curve (13) for the...Ch. 4.10 - Prob. 2ECh. 4.10 - Determine the equation of the motion for an...Ch. 4.10 - Prob. 4ECh. 4.10 - An undamped system is governed by...Ch. 4.10 - Derive the formula for yp(t) given in 21...Ch. 4.10 - Shock absorbers in automobiles and aircraft can be...Ch. 4.10 - The response of an overdamped system to a constant...Ch. 4.10 - An 8-kg mass is attached to a spring hanging from...Ch. 4.10 - Show that the period of the simple harmonic motion...Ch. 4.10 - A mass weighing 8 lb is attached to a spring...Ch. 4.10 - A 2-kg mass is attached to a spring hanging from...Ch. 4.10 - A mass weighing 32lb is attached to a spring...Ch. 4.10 - An 8-kg mass is attached to a spring hanging from...Ch. 4.10 - An 8-kg mass is attached to a spring hanging from...Ch. 4.RP - In Problems 1-28, find a general solution to the...Ch. 4.RP - Prob. 2RPCh. 4.RP - Prob. 3RPCh. 4.RP - Prob. 4RPCh. 4.RP - Prob. 5RPCh. 4.RP - Prob. 6RPCh. 4.RP - Prob. 7RPCh. 4.RP - Prob. 8RPCh. 4.RP - In Problems 1 -28, find the general solution to...Ch. 4.RP - Prob. 10RPCh. 4.RP - Prob. 11RPCh. 4.RP - Prob. 12RPCh. 4.RP - Prob. 13RPCh. 4.RP - Prob. 14RPCh. 4.RP - Prob. 15RPCh. 4.RP - Prob. 16RPCh. 4.RP - Prob. 17RPCh. 4.RP - Prob. 18RPCh. 4.RP - Prob. 19RPCh. 4.RP - Prob. 20RPCh. 4.RP - Prob. 21RPCh. 4.RP - Prob. 22RPCh. 4.RP - Prob. 23RPCh. 4.RP - Prob. 24RPCh. 4.RP - Prob. 25RPCh. 4.RP - In Problems 1-28, find a general solution to the...Ch. 4.RP - Prob. 27RPCh. 4.RP - Prob. 28RPCh. 4.RP - Prob. 29RPCh. 4.RP - Prob. 30RPCh. 4.RP - Prob. 31RPCh. 4.RP - Prob. 32RPCh. 4.RP - Prob. 33RPCh. 4.RP - Prob. 34RPCh. 4.RP - Prob. 35RPCh. 4.RP - Prob. 36RPCh. 4.RP - Use the mass-spring oscillator analogy to decide...Ch. 4.RP - A 3kg mass is attached to a spring with stiffness...Ch. 4.RP - A 32lb weight is attached to a vertical spring,...
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