Basic Technical Mathematics
11th Edition
ISBN: 9780134437705
Author: Washington
Publisher: PEARSON
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Chapter 3.5, Problem 61E
To determine
The time that the drug concentration will be reduced to below 1.5 mg per L, if the concentration of a drug in a patient’s bloodstream t hours after taking a pill is
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5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force
of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass
is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I
purposefully removed the units- don't worry about them. Assume no conversions are
needed.)
a) Find the equation for the displacement of the spring mass at time t.
b) Write the equation for the displacement of the spring mass in phase-mode form.
c) Characterize the damping of the spring mass system as overdamped, underdamped or
critically damped. Explain how you know.
D.E. for Spring Mass Systems
k
m* g = kLo
y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo
m
2
A₁ = √c₁² + C₂²
Q = tan-1
4. Given the following information determine the appropriate trial solution to find yp. Do not
solve the differential equation. Do not find the constants.
a) (D-4)2(D+ 2)y = 4e-2x
b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3x
9.7 Given the equations
0.5x₁-x2=-9.5
1.02x₁ - 2x2 = -18.8
(a) Solve graphically.
(b) Compute the determinant.
(c) On the basis of (a) and (b), what would you expect regarding
the system's condition?
(d) Solve by the elimination of unknowns.
(e) Solve again, but with a modified slightly to 0.52. Interpret
your results.
Chapter 3 Solutions
Basic Technical Mathematics
Ch. 3.1 - EXAMPLE 5
If , then substitute a3 for t
For the...Ch. 3.1 - EXAMPLE 7
For the functions f(x) = 5x − 3 and g(x)...Ch. 3.1 - In Exercises 1–4, solve the given problems related...Ch. 3.1 - Prob. 2ECh. 3.1 - In Exercises 1–4, solve the given problems related...Ch. 3.1 - Prob. 4ECh. 3.1 - In Exercises 5–12, find the indicated...Ch. 3.1 - In Exercises 5–12, find the indicated...Ch. 3.1 - In Exercises 5–12, find the indicated...Ch. 3.1 - In Exercises 5–12, find the indicated...
Ch. 3.1 - In Exercises 5–12, find the indicated...Ch. 3.1 - In Exercises 5–12, find the indicated...Ch. 3.1 - In Exercises 5–12, find the indicated functions.
A...Ch. 3.1 - In Exercises 5–12, find the indicated...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 13–24, evaluate the given...Ch. 3.1 - In Exercises 25–28, evaluate the given functions....Ch. 3.1 - In Exercises 25–28, evaluate the given functions....Ch. 3.1 - In Exercises 25–28, evaluate the given functions....Ch. 3.1 - In Exercises 25–28, evaluate the given functions....Ch. 3.1 - In Exercises 29–32, determine the function y =...Ch. 3.1 - In Exercises 29–32, determine the function y =...Ch. 3.1 - In Exercises 29–32, determine the function y =...Ch. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - In Exercises 39–42, write the equation as given by...Ch. 3.1 - In Exercises 39–42, write the equation as given by...Ch. 3.1 - In Exercises 39–42, write the equation as given by...Ch. 3.1 - In Exercises 43–52, solve the given problems.
A...Ch. 3.1 - In Exercises 43–52, solve the given...Ch. 3.1 - In Exercises 43–52, solve the given problems.
45....Ch. 3.1 - In Exercises 43–52, solve the given problems.
46....Ch. 3.1 - In Exercises 43–52, solve the given problems.
The...Ch. 3.1 - In Exercises 43–52, solve the given problems.
The...Ch. 3.1 - In Exercises 43–52, solve the given problems.
A...Ch. 3.1 - In Exercises 43–52, solve the given problems.
A...Ch. 3.1 -
(a) Explain the meaning of f [f(x)]. (b) Find f...Ch. 3.1 -
If f(x) = x and g(x) = x2, find (a) f [g(x)], and...Ch. 3.2 - Find the domain and range of the function .
Ch. 3.2 - Prob. 2PECh. 3.2 - In Example 8, find p as a function of r if there...Ch. 3.2 - In Exercises 1-4, solve the given problems related...Ch. 3.2 - Prob. 2ECh. 3.2 - In Exercises 1-4, solve the given problems related...Ch. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - In Exercises 15-20, find the domain of the given...Ch. 3.2 - In Exercises 15-20, find the domain of the given...Ch. 3.2 - Prob. 17ECh. 3.2 - In Exercises 15-20, find the domain of the given...Ch. 3.2 - Prob. 19ECh. 3.2 - In Exercises 15-20, find the domain of the given...Ch. 3.2 - Prob. 21ECh. 3.2 - In Exercises 21-24, evaluate the indicated...Ch. 3.2 - In Exercises 21-24, evaluate the indicated...Ch. 3.2 - In Exercises 21-24, evaluate the indicated...Ch. 3.2 - Prob. 25ECh. 3.2 - In Exercises 25-38, determine the appropriate...Ch. 3.2 - Prob. 27ECh. 3.2 - In Exercises 25-38, determine the appropriate...Ch. 3.2 - Prob. 29ECh. 3.2 - In Exercises 25-38, determine the appropriate...Ch. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - In Exercises 25-38, determine the appropriate...Ch. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.3 - Prob. 1PECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - In Exercises 3 and 4, determine (at least...Ch. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - In Exercises 15–18, determine the quadrant in...Ch. 3.3 - In Exercises 15–18, determine the quadrant in...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 -
In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given questions.
If...Ch. 3.3 - In Exercises 19–38, answer the given...Ch. 3.3 - In Exercises 19–38, answer the given questions.
On...Ch. 3.3 - Prob. 38ECh. 3.4 - Prob. 1PECh. 3.4 - Prob. 2PECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - In Exercises 5–36, graph the given functions.
5.
Ch. 3.4 - In Exercises 5–36, graph the given functions.
6. y...Ch. 3.4 - In Exercises 5–36, graph the given functions.
7. y...Ch. 3.4 - In Exercises 5–36, graph the given functions.
8. y...Ch. 3.4 - In Exercises 5–36, graph the given functions.
9. s...Ch. 3.4 - In Exercises 5−36, graph the given functions.
10....Ch. 3.4 - In Exercises 5–36, graph the given functions.
Ch. 3.4 - In Exercises 5–36, graph the given functions.
Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - In Exercises 5–36, graph the given functions.
Ch. 3.4 - In Exercises 5–36, graph the given functions.
y =...Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given functions.
24....Ch. 3.4 - In Exercises 5–36, graph the given functions.
y =...Ch. 3.4 - In Exercises 5–36, graph the given functions.
26....Ch. 3.4 - In Exercises 5–36, graph the given functions.
27....Ch. 3.4 - In Exercises 5–36, graph the given functions.
28....Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given functions.
Ch. 3.4 - In Exercises 5–36, graph the given...Ch. 3.4 - In Exercises 5–36, graph the given functions.
32....Ch. 3.4 - In Exercises 5–36, graph the given functions.
33....Ch. 3.4 - In Exercises 5–36, graph the given functions.
34....Ch. 3.4 - In Exercises 5–36, graph the given functions.
35....Ch. 3.4 - In Exercises 5–36, graph the given functions.
36....Ch. 3.4 - In Exercises 37–40, use the graph to determine the...Ch. 3.4 - In Exercises 37–40, use the graph to determine the...Ch. 3.4 - In Exercises 37–40, use the graph to determine the...Ch. 3.4 - In Exercises 37–40, use the graph to determine the...Ch. 3.4 - In Exercises 41–70, graph the indicated...Ch. 3.4 - In Exercises 41–70, graph the indicated...Ch. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - In Exercises 41–70, graph the indicated...Ch. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Prob. 57ECh. 3.4 - Prob. 58ECh. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.4 - Prob. 61ECh. 3.4 - Prob. 62ECh. 3.4 - Prob. 63ECh. 3.4 - Prob. 64ECh. 3.4 - In Exercises 41–70, graph the indicated...Ch. 3.4 - In Exercises 41–70, graph the indicated...Ch. 3.4 - Prob. 67ECh. 3.4 - Prob. 68ECh. 3.4 - Prob. 69ECh. 3.4 - Prob. 70ECh. 3.4 - In Exercises 71‒74, determine whether or not the...Ch. 3.4 - In Exercises 71–74, determine whether or not the...Ch. 3.4 - In Exercises 71–74, determine whether or not the...Ch. 3.4 - In Exercises 71–74, determine whether or not the...Ch. 3.5 - Prob. 1PECh. 3.5 - Prob. 2PECh. 3.5 - Prob. 3PECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - In Exercises 3–18, display the graphs of the given...Ch. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - In Exercises 19–28, use a graphing calculator to...Ch. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - In Exercises 41–48, a function and how it is to be...Ch. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - In Exercises 53–60, solve the indicated equations...Ch. 3.5 - In Exercises 53–60, solve the indicated equations...Ch. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.5 - Prob. 61ECh. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.6 - Prob. 1PECh. 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 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3 - Prob. 1RECh. 3 - Determine each of the following as being either...Ch. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - In Exercises 29–38, plot the graphs of the given...Ch. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Prob. 49RECh. 3 - Prob. 50RECh. 3 - Prob. 51RECh. 3 - Prob. 52RECh. 3 - Prob. 53RECh. 3 - Prob. 54RECh. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - Prob. 57RECh. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RECh. 3 - Prob. 61RECh. 3 - Prob. 62RECh. 3 - Prob. 63RECh. 3 - Prob. 64RECh. 3 - Prob. 65RECh. 3 - Prob. 66RECh. 3 - Prob. 67RECh. 3 - Prob. 68RECh. 3 - Prob. 69RECh. 3 - Prob. 70RECh. 3 - Prob. 71RECh. 3 - Prob. 72RECh. 3 - Prob. 73RECh. 3 - Prob. 74RECh. 3 - Prob. 75RECh. 3 - Prob. 76RECh. 3 - Prob. 77RECh. 3 - Prob. 78RECh. 3 - Prob. 79RECh. 3 - Prob. 80RECh. 3 - Prob. 81RECh. 3 - Prob. 82RECh. 3 - Prob. 83RECh. 3 - Prob. 84RECh. 3 - Prob. 85RECh. 3 - Prob. 86RECh. 3 - Prob. 87RECh. 3 - Prob. 88RECh. 3 - Prob. 89RECh. 3 - Prob. 90RECh. 3 - Prob. 91RECh. 3 - Prob. 92RECh. 3 - Prob. 93RECh. 3 - Prob. 94RECh. 3 - Prob. 95RECh. 3 - Prob. 96RECh. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 10PTCh. 3 - Prob. 11PTCh. 3 - From the table in Problem 11, find the voltage for...
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