Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 1.4, Problem 2E
To determine
Whether the expression
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Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO). Beginning
at time t = 0, cigarette smoke containing 4% CO is introduced into the room at a rate of 0.8 cubic feet per
minute. The well-circulated smoke and air mixture is allowed to leave the room at the same rate.
Let A(t) represent the amount of CO in the room (in cubic feet) after t minutes.
(A) Write the DE model for the time rate of change of CO in the room. Also state the initial condition.
dA
dt
A(0)
(B) Solve the IVP to find the amount of CO in the room at any time t > 0.
A(t)
(C) Extended exposure to a CO concentration as low as 0.00012 is harmful to the human body. Find the time
at which this concentration is reached.
t=
minutes
Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to
the temperature difference between the object and its surroundings. This can be modeled by the
differential equation
dT
dt
k(TA), where T is the temperature of the object after t units of time
have passed, A is the ambient temperature of the object's surroundings, and k is a constant of
proportionality.
Suppose that a cup of coffee begins at 178 degrees and, after sitting in room temperature of 61 degrees
for 12 minutes, the coffee reaches 171 degrees. How long will it take before the coffee reaches 155
degrees?
Include at least 2 decimal places in your answer.
minutes
Decide whether each limit exists. If a limit exists, estimate its
value.
11. (a) lim f(x)
x-3
f(x) ↑
4
3-
2+
(b) lim f(x)
x―0
-2
0
X
1234
Chapter 1 Solutions
Discrete Mathematics
Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...
Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - A small purse manufacturer has a single machine...Ch. 1.1 - What is the answer to the previous problem if the...Ch. 1.1 - A survey is to be made of grocery shoppers in Los...Ch. 1.2 - In Exercises 1–16, calculate the number...Ch. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - In Exercises 1–16, calculate the number...Ch. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - A baseball manager has decided who his 9 starting...Ch. 1.2 - A president, vice president, and treasurer are to...Ch. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Different prizes for first place, second place,...Ch. 1.2 - Prob. 23ECh. 1.2 - A farmer with 7 cows likes to milk them in a...Ch. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - A dinner special for 4 diners at a Chinese...Ch. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Show that if 0 ≤ 2r ≤ n, then .
Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Suppose that the rating/kilogram ratio is computed...Ch. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - How many subsets does {Dopey, Happy, …, Doc}...Ch. 1.3 - How many subsets does {Chico, Harpo, Groucho,...Ch. 1.3 - Prob. 24ECh. 1.3 - Suppose m and n are positive integers with m < n....Ch. 1.3 - Prob. 26ECh. 1.3 - A draw poker player may discard some of his 5...Ch. 1.3 - Suppose that in the previous problem no more than...Ch. 1.3 - How long would it take a computer that can check...Ch. 1.3 - Find a subset of the 12 experiments with a total...Ch. 1.4 - In Exercises 1–6, tell whether the given...Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - In Exercises 1–6, tell whether the given...Ch. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - Prob. 13ECh. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - In Exercises 15–18, make a table listing the...Ch. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - In Exercises 19–22, illustrate as in Example 1.5...Ch. 1.4 - In Exercises 19–22, illustrate as in Example 1.5...Ch. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - In Exercises 23–26, estimate how long a computer...Ch. 1.4 - In Exercises 27–30, tell how many elementary...Ch. 1.4 - In Exercises 27–30, tell how many elementary...Ch. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1 - Prob. 1SECh. 1 - Prob. 2SECh. 1 - Prob. 3SECh. 1 - Prob. 4SECh. 1 - Prob. 5SECh. 1 - Prob. 6SECh. 1 - Prob. 7SECh. 1 - Prob. 8SECh. 1 - Prob. 9SECh. 1 - Prob. 10SECh. 1 - Prob. 11SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 13SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 15SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 17SECh. 1 - In Cincinnati, chili consists of spaghetti topped...Ch. 1 - Five students decide to send a delegation to a...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20-23, tell whether each expression...Ch. 1 - Let P(x) = 3x3+4x−5. Compute the various values S...Ch. 1 - Repeat the previous problem, using Horner's...Ch. 1 - Let S = {1, 2, 3, 4}. Find the ordered sequence of...Ch. 1 - Illustrate the use of the bubble sort algorithm to...Ch. 1 - How long would it take a computer to do 25!...Ch. 1 - Apply the following algorithm to n = 18.
What is...Ch. 1 - Prob. 30SECh. 1 - Prob. 1CPCh. 1 - Prob. 2CPCh. 1 - Prob. 3CPCh. 1 - Prob. 4CPCh. 1 - Prob. 5CPCh. 1 - Prob. 6CPCh. 1 - Prob. 9CPCh. 1 - Prob. 10CP
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