DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
3rd Edition
ISBN: 9781119764564
Author: BRANNAN
Publisher: WILEY
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Chapter 5.1, Problem 29P
In each of Problems
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MATH-Solve the following problems. (Feel free to use a calculator.)
DATE:
1. If you were asked to load 225 boxes onto a truck, and the boxes are crated,
with each crate containing nine boxes, how many crates would you need to load?
2. Imagine you live only one mile from work and you decide to walk. If you
walk four miles per hour, how long will it take you to walk one mile?
3. Add 3 feet 6 inches + 8 feet 2 inches + 4 inches + 2 feet 5 inches.
4. In a grocery store, steak costs $3.85 per pound. If you buy a three-pound
steak and pay for it with a $20 bill, how much change will you get?
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part 3 of the question is:
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
Chapter 5 Solutions
DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
Ch. 5.1 - In each of Problems 1 through 4, sketch the graph...Ch. 5.1 - In each of Problems through , sketch the graph of...Ch. 5.1 - In each of Problems 1 through 4, sketch the graph...Ch. 5.1 - In each of Problems 1 through 4, sketch the graph...Ch. 5.1 - In each of Problems through , determine whether...Ch. 5.1 - In each of Problems through , determine whether...Ch. 5.1 - In each of Problems 5 through 12, determine...Ch. 5.1 - In each of Problems through , determine whether...Ch. 5.1 - In each of Problems through , determine whether...Ch. 5.1 - In each of Problems through , determine whether...
Ch. 5.1 - In each of Problems 5 through 12, determine...Ch. 5.1 - In each of Problems 5 through 12, determine...Ch. 5.1 -
Find the Laplace transform of each of the...Ch. 5.1 - In each of Problems 14 through 17, find the...Ch. 5.1 - In each of Problems through , find the Laplace...Ch. 5.1 - In each of Problems through , find the Laplace...Ch. 5.1 - In each of Problems 14 through 17, find the...Ch. 5.1 - In each of Problems through , find the Laplace...Ch. 5.1 - In each of Problems through , find the Laplace...Ch. 5.1 - In each of Problems 18 through 21, find the...Ch. 5.1 - In each of Problems through , find the Laplace...Ch. 5.1 - In each of Problems 22 through 24, use the facts...Ch. 5.1 - In each of Problems 22 through 24, use the facts...Ch. 5.1 - In each of Problems through , use the facts that ...Ch. 5.1 - In each of Problems through , using integration...Ch. 5.1 - In each of Problems 25 through 30, using...Ch. 5.1 - In each of Problems through , using integration...Ch. 5.1 - In each of Problems through , using integration...Ch. 5.1 - In each of Problems through , using integration...Ch. 5.1 - In each of Problems 25 through 30, using...Ch. 5.1 - In each of Problems 31 through 34, determine...Ch. 5.1 - In each of Problems 31 through 34, determine...Ch. 5.1 - In each of Problems 31 through 34, determine...Ch. 5.1 - In each of Problems through , determine whether...Ch. 5.1 - A Proof of Corollary 5.1.7 (a) Starting from...Ch. 5.1 - The Gamma Function. The gamma function is defined...Ch. 5.1 - Consider the laplace transform of tp, where p1....Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems 1 through 10, find the Laplace...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems 1 through 10, find the Laplace...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems 1 through 10, find the Laplace...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - (a) Let F(s)=L{f(t)}, where f(t) is piecewise...Ch. 5.2 - In each of Problems through, transform the given...Ch. 5.2 - In each of Problems through, transform the given...Ch. 5.2 - In each of Problems 12 through 21, transform the...Ch. 5.2 - In each of Problems 12 through 21, transform the...Ch. 5.2 - In each of Problems 12 through 21, transform the...Ch. 5.2 - In each of Problems 12 through 21, transform the...Ch. 5.2 - In each of Problems through, transform the given...Ch. 5.2 - In each of Problems through, transform the given...Ch. 5.2 - In each of Problems 12 through 21, transform the...Ch. 5.2 - In each of Problems 12 through 21, transform the...Ch. 5.2 - In section 4.1 the differential equation for the...Ch. 5.2 - In each of Problems through, find the Laplace...Ch. 5.2 - In each of Problems 23 through 27, find the...Ch. 5.2 - In each of Problems 23 through 27, find the...Ch. 5.2 - In each of Problems 23 through 27, find the...Ch. 5.2 - In each of Problems 23 through 27, find the...Ch. 5.2 - The Laplace transforms of certain functions can be...Ch. 5.2 - For each of the following initial value problems,...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 1 through 8, find the unknown...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 9 through 24, using the...Ch. 5.3 - In each of Problems 25 through 28, use a computer...Ch. 5.3 - In each of Problems 25 through 28, use a computer...Ch. 5.3 - In each of Problems 25 through 28, use a computer...Ch. 5.3 - In each of Problems 25 through 28, use a computer...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems 1 through 13, use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems 1 through 13, use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems 14 through 19, use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems 14 through 19, use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems 14 through 19, use the Laplace...Ch. 5.4 - In each of Problems through , use the Laplace...Ch. 5.4 - In each of Problems through , use a computer...Ch. 5.4 - In each of Problems 20 through 24, use a computer...Ch. 5.4 - In each of Problems through , use a computer...Ch. 5.4 - In each of Problems 20 through 24, use a computer...Ch. 5.4 - In each of Problems 20 through 24, use a computer...Ch. 5.4 - Use the Laplace transform to solve the system...Ch. 5.4 - A radioactive substance R1 having decay rate k1...Ch. 5.5 - In each of Problems through , sketch the graph of...Ch. 5.5 - In each of Problems 1 through 6, sketch the graph...Ch. 5.5 - In each of Problems 1 through 6, sketch the graph...Ch. 5.5 - In each of Problems through , sketch the graph of...Ch. 5.5 - In each of Problems through , sketch the graph of...Ch. 5.5 - In each of Problems through , sketch the graph of...Ch. 5.5 - In each of Problems 7 through 12, find the Laplace...Ch. 5.5 - In each of Problems 7 through 12, find the Laplace...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems 13 through 18, find the...Ch. 5.5 - In each of Problems through , find the inverse...Ch. 5.5 - In each of Problems 13 through 18, find the...Ch. 5.5 - In each of Problems 13 through 18, find the...Ch. 5.5 - In each of Problems through , find the inverse...Ch. 5.5 - In each of Problems 13 through 18, find the...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems 19 through 21, find the...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems through , find the Laplace...Ch. 5.5 - In each of Problems 22 through 24, find the...Ch. 5.5 - (a) If f(t)=1u1(t), find L{f(t)}; compare with...Ch. 5.5 - Consider the function defined by
and has...Ch. 5.6 - In each of Problems 1 through 13, find the...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems 1 through 13, find the...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - In each of Problems 1 through 13, find the...Ch. 5.6 - In each of Problems 1 through 13, find the...Ch. 5.6 - In each of Problems through , find the solutions...Ch. 5.6 - Find an expression involving uc(t) for a function...Ch. 5.6 - Find an expression involving for a function that...Ch. 5.6 - A certain spring-mass system satisfies the initial...Ch. 5.6 - Modify the problem in Example 1 of this section by...Ch. 5.6 - Consider the initial value problem y+13y+4y=fk(t),...Ch. 5.6 - In Problem 19 through 23, we explore the effect of...Ch. 5.6 - In Problem 19 through 23, we explore the effect of...Ch. 5.6 - In Problem 19 through 23, we explore the effect of...Ch. 5.6 - In Problem 19 through 23, we explore the effect of...Ch. 5.6 - In Problem 19 through 23, we explore the effect of...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - In each of Problems 1 through 12, find the...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - In each of Problems 1 through 12, find the...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - In each of Problems 1 through 12, find the...Ch. 5.7 - In each of Problems 1 through 12, find the...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - In each of Problems 1 through 12, find the...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - In each of Problems through , find the solutions...Ch. 5.7 - Consider again the system in Example 3 of this...Ch. 5.7 - Consider the initial value problem y+y+y=(t1),...Ch. 5.7 - Consider the initial value problem
Where ...Ch. 5.7 - Consider the initial value problem
Where ...Ch. 5.7 - Problem 17 through 22 deal with effect of a...Ch. 5.7 - Problem 17 through 22 deal with effect of a...Ch. 5.7 - Problem 17 through 22 deal with effect of a...Ch. 5.7 - Problem 17 through 22 deal with effect of a...Ch. 5.7 - Problem 17 through 22 deal with effect of a...Ch. 5.7 - Problem 17 through 22 deal with effect of a...Ch. 5.7 - The position of a certain lightly damped...Ch. 5.7 - Proceed as in Problem 23 for the oscillator...Ch. 5.7 - a) By the method of variation of parameters, show...Ch. 5.8 - Establish the distributive and associative...Ch. 5.8 - Show, by means of the example f(t)=sint, that ff...Ch. 5.8 - In each of Problems 3 through 6, find the Laplace...Ch. 5.8 - In each of Problems 3 through 6, find the Laplace...Ch. 5.8 - In each of Problems through , find the Laplace...Ch. 5.8 - In each of Problems through , find the Laplace...Ch. 5.8 - In each of Problems 7 through 12, find the inverse...Ch. 5.8 - In each of Problems 7 through 12, find the inverse...Ch. 5.8 - In each of Problems through , find the inverse...Ch. 5.8 - In each of Problems through , find the inverse...Ch. 5.8 - In each of Problems 7 through 12, find the inverse...Ch. 5.8 - In each of Problems 7 through 12, find the inverse...Ch. 5.8 - (a) If f(t)=tm and g(t)=tn, where m and n are...Ch. 5.8 - In each of Problems through , express the total...Ch. 5.8 - In each of Problems through , express the total...Ch. 5.8 - In each of Problems through , express the total...Ch. 5.8 - In each of Problems through , express the total...Ch. 5.8 - In each of Problems 14 through 21, express the...Ch. 5.8 - In each of Problems through , express the total...Ch. 5.8 - In each of Problems 14 through 21, express the...Ch. 5.8 - In each of Problems 14 through 21, express the...Ch. 5.8 - Unit Step Responses. The unit step response of a...Ch. 5.8 - Consider the equation (t)+0tk(t)()d=f(t), in which...Ch. 5.8 - Consider the Volterra integral equation (see...Ch. 5.8 - In each of Problems 25 through 27:
Solve the given...Ch. 5.8 - In each of Problems 25 through 27: a) Solve the...Ch. 5.8 - In each of Problems 25 through 27:
Solve the given...Ch. 5.8 - There are also equations, known as...Ch. 5.8 - There are also equations, known as...Ch. 5.8 - There are also equations, known as...Ch. 5.8 - The Tautochrone. A problem of interest in the...Ch. 5.9 - Find the transfer function of the system shown in...Ch. 5.9 - Find the transfer function of the system shown in...Ch. 5.9 - If h(t) is any one of the functions,...Ch. 5.9 - Prob. 4PCh. 5.9 - Use Rouths criterion to find necessary and...Ch. 5.9 - For each of the characteristic function in...Ch. 5.9 - For each of the characteristic function in...Ch. 5.9 - For each of the characteristic function in...Ch. 5.9 - For each of the characteristic function in...Ch. 5.9 - For each of the characteristic function in...Ch. 5.9 - For each of the characteristic function in...Ch. 5.9 - In each of Problems 12 through 15, use the Routh...Ch. 5.9 - In each of Problems 12 through 15, use the Routh...Ch. 5.9 - In each of Problems through, use the Routh...Ch. 5.9 - In each of Problems through, use the Routh...Ch. 5.P1 - Find such that the Laplace transform of the...Ch. 5.P1 - Suppose that the impressed voltage is prescribed...Ch. 5.P1 - Suppose that the impressed voltage is prescribed ...Ch. 5.P2 - In the following problem, we ask the reader to...Ch. 5.P2 - In the following problem, we ask the reader to...Ch. 5.P2 - In the following problem, we ask the reader to...Ch. 5.P2 - In the following problem, we ask the reader to...Ch. 5.P2 - In the following problem, we ask the reader to...Ch. 5.P2 - In the following problem, we ask the reader to...Ch. 5.P2 - In the following problem, we ask the reader to...
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- Find the accumulated amount A, if the principal P is invested at an interest rate of r per year for t years. (Round your answer to the nearest cent.) P = $13,000, r = 6%, t = 10, compounded quarterly A = $ 31902 Need Help? Read It Watch It Viewing Saved Work Revert to Last Response SUBMIT ANSWER O/6.66 Points] DETAILS MY NOTES TANAPCALC10 5.3.003. EVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER Find the accumulated amount A, if the principal P is invested at an interest rate of r per year for t years. (Round your answer to the nearest cent.) P = $140,000, r = 8%, t = 8, compounded monthly A = $259130.20 X Need Help? Read It Watch Itarrow_forwardFind the present value of $20,000 due in 3 years at the given rate of interest. (Round your answers to the nearest cent.) (a) 2%/year compounded monthly (b) 5%/year compounded daily $ Need Help? Read It Watch It SUBMIT ANSWER [-/6.66 Points] DETAILS MY NOTES TANAPCALC10 5.3.009. ASK YOUR TEACHER PRACTICE ANC Find the accumulated amount after 3 years if $4000 is invested at 3%/year compounded continuously. (Round your answer to the nearest cent.) Need Help? Read It Watch Itarrow_forwardFind the effective rate corresponding to the given nominal rate. (Round your answers to three decimal places.) (a) 9.5%/year compounded monthly % (b) 9.5%/year compounded daily % Need Help? Read It Watch It SUBMIT ANSWER -/6.66 Points] DETAILS MY NOTES TANAPCALC10 5.3.007. ASK YOUR TEACHE Find the present value of $90,000 due in 7 years at the given rate of interest. (Round your answers to the nearest cent.) (a) 9%/year compounded semiannually (b) 9%/year compounded quarterly LAarrow_forward
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