Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Chapter 1.4, Problem 9TY
To determine
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The blanks in the given statement.
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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 With Applications
Ch. 1.1 - A universal statement asserts that a certain...Ch. 1.1 - A conditional statement asserts that if one...Ch. 1.1 - Given a property that may or may not be true, an...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - In each of 1—6, fill in the blanks using a...Ch. 1.1 - Given any real number, there is a number that is...Ch. 1.1 - The reciprocal of any postive real number is...Ch. 1.1 - Prob. 6ESCh. 1.1 - Rewrite the following statements less formally,...
Ch. 1.1 - For every object J, if J is a square then J has...Ch. 1.1 - For every equation E, if E is quadratic then E has...Ch. 1.1 - Every nonzero real number has a reciropal. All...Ch. 1.1 - Evaery positive number has a positive square root....Ch. 1.1 - There is a real number whose product with every...Ch. 1.1 - There is a real number whose product with ever...Ch. 1.2 - When the elements of a set are given using the...Ch. 1.2 - The symbol R denotes ____.Ch. 1.2 - The symbol Z denotes ______Ch. 1.2 - The symbol Q denotes__Ch. 1.2 - The notation {xP(x)} is read _______Ch. 1.2 - Prob. 6TYCh. 1.2 - Prob. 7TYCh. 1.2 - Given sets A,B, and C, the Cartesian production...Ch. 1.2 - A string of length n over a set S is an ordered...Ch. 1.2 - Prob. 1ESCh. 1.2 - Write in words how to read each of the following...Ch. 1.2 - Is 4={4}? How many elements are in the set...Ch. 1.2 - a. Is 2{2}? b. How many elements are in the set...Ch. 1.2 - Which of the following sets are equal?...Ch. 1.2 - For each integer n, let Tn={n,n2} . How many...Ch. 1.2 - Prob. 7ESCh. 1.2 - Prob. 8ESCh. 1.2 - Is3{1,2,3}? Is 1{1}? Is {2}{1,2}? Is...Ch. 1.2 - Is ((2)2,22)=(22,( 2)2)? Is (5,5)=(5,5)? Is...Ch. 1.2 - Prob. 11ESCh. 1.2 - Prob. 12ESCh. 1.2 - Prob. 13ESCh. 1.2 - Prob. 14ESCh. 1.2 - Let S={0,1} . List all the string of length 4 over...Ch. 1.2 - Let T={x,y} . List all the strings of length 5...Ch. 1.3 - Given sets A and B , relation from A to B is ____Ch. 1.3 - A function F from B is a relation from A to B that...Ch. 1.3 - If F is a function from A to B and x is an element...Ch. 1.3 - Let A={2,3,4} and B={6,8,10} and define a relation...Ch. 1.3 - Let C=D={3,2,1,1,2,3} and define a elation S from...Ch. 1.3 - Let E={1,2,3} and F={2,1,0} and define a relation...Ch. 1.3 - Let G=-2,0,2) and H=4,6,8) and define a relation V...Ch. 1.3 - Define a relations S from R to R as follows: For...Ch. 1.3 - Define a relation R from R to R as follows: For...Ch. 1.3 - Let A={4,5,6} and B={5,6,7} and define relations...Ch. 1.3 - Let A={2,4} and B={1,3,5} and define relations U,...Ch. 1.3 - Find all function from {01,} to {1} . Find two...Ch. 1.3 - Find tour relations from {a,b} to {x,y} that are...Ch. 1.3 - Let A={0,1,2} and let S be the set of all strings...Ch. 1.3 - Let A={x,y} and let S be the set all strings over...Ch. 1.3 - Let A={1,0,1} and B={t,u,v,w} . Define a function...Ch. 1.3 - Let C = (1,2,3,4) and D={a,b,c,d}. Define a...Ch. 1.3 - Let X=2,4,5) and Y=(1,2,4,6) . Which of the...Ch. 1.3 - Let f be the squaring function defined in Example...Ch. 1.3 - Let g be the successor function defined in Example...Ch. 1.3 - Let h be the constant function defined in Example...Ch. 1.3 - Define functions f and g from R to R by the...Ch. 1.3 - Define functions H and K from R to R by the...Ch. 1.4 - A graph consists of two finite sets: ______and...Ch. 1.4 - A loop in a graph is_____Ch. 1.4 - Two distinct edges in a graph are parallel if, and...Ch. 1.4 - Two vertices are called adjacent if, and only if,...Ch. 1.4 - An edge is incident on _______Ch. 1.4 - Two edges incident on the same endpoint...Ch. 1.4 - A vertex on which no edges are incident is________Ch. 1.4 - Prob. 8TYCh. 1.4 - Prob. 9TYCh. 1.4 - In 1 and 2, graphs are represented by drawings...Ch. 1.4 - In 1 and 2, graphs are represented by drawings....Ch. 1.4 - In 3 and 4, draw pictures of the specified graphs....Ch. 1.4 - Prob. 4ESCh. 1.4 - Prob. 5ESCh. 1.4 - In 5-7, show that the two drawings represent the...Ch. 1.4 - In 5-7, show that the two drawings represent the...Ch. 1.4 - For each of the graphs in 8 and 9: (i) Find all...Ch. 1.4 - For each of the graphs in 8 and 9: (i) Find all...Ch. 1.4 - Use the graph of Example 1.4.6 to determine...Ch. 1.4 - Find three other winning sequences of moves for...Ch. 1.4 - Another famous puzzle used as an example in the...Ch. 1.4 - Solve the vegetarians-and-cannibals puzzle for the...Ch. 1.4 - Two jugs A and B have capacities of 3 quarts and 5...Ch. 1.4 - Prob. 15ESCh. 1.4 - In this exercise a graph is used to help solve a...Ch. 1.4 - A deptnn1 war to ithechik final ezans that no...
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