Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
15th Edition
ISBN: 9781323047620
Author: Barnett, Ziegler, Byleen
Publisher: Pearson Education
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Textbook Question
Chapter B.3, Problem 4MP
Use the binomial theorem to find the fourth term in the expansion of (x – 2)20.
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Pidgeonhole Principle
1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined
as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest
integer greater than or equal to x. Try figuring out the answers to the following:
(a) [2.1]
(b) [2]
(c) [2.9]
(d) [2.1]
(e) [2]
(f) [2.9]
2. The simple pidgeonhole principle states that, if you have N places and k items (k> N), then at
least one hole must have more than one item in it. We tried this with chairs and students: Assume you
have N = 12 chairs and k = 18 students. Then at least one chair must have more than one student on
it.
3. The general pidgeonhole principle states that, if you have N places and k items, then at least one
hole must have [] items or more in it. Try this out with
(a) n = 10 chairs and k = 15 students
(b) n = 10 chairs and k = 23 students
(c) n = 10 chairs and k = 20 students
4. There are 34 problems on these pages, and we…
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
Q2.2
1 Point
Determine if the set of vectors spans R³.
they span R³
they do not span R³
Save Answer
23
Q2.3
1 Point
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
1111
1110
Q2.4
1 Point
Determine if the set of vectors spans R4.
O they span R4
they do not span IR4
1000;
111O'
The everything combined problem
Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to
directly connect a workstation to a server. For each server, only one direct connection to that server can be
active at any time.
1. How many cables would you need to connect each station to each server?
2. How many stations can be used at one time?
3. How many stations can not be used at any one time?
4. How many ways are there to pick 10 stations out of 15?
5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can
simultaneously access different servers via direct connections. What is the minimum number of direct
connections needed to achieve this goal?
Chapter B.3 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
Ch. B.3 - Evaluate. (A)4! (B)7!6! (C)8!5!Ch. B.3 - Find (A)5C2 (B)6C0Ch. B.3 - Use the binomial theorem to expand (x + 2)5.Ch. B.3 - Use the binomial theorem to find the fourth term...Ch. B.3 - In Problems 120, evaluate each expression. 1.6!Ch. B.3 - In Problems 120, evaluate each expression. 2.7!Ch. B.3 - In Problems 120, evaluate each expression. 3.10!9!Ch. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - In Problems 120, evaluate each expression. 5.12!9!Ch. B.3 - In Problems 120, evaluate each expression. 6.10!6!
Ch. B.3 - Prob. 7ECh. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - Prob. 9ECh. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - Prob. 12ECh. B.3 - Prob. 13ECh. B.3 - In Problems 120, evaluate each expression. 14.7C3Ch. B.3 - In Problems 120, evaluate each expression. 15.6C5Ch. B.3 - Prob. 16ECh. B.3 - In Problems 120, evaluate each expression. 17.5C0Ch. B.3 - In Problems 120, evaluate each expression. 18.5C5Ch. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - Prob. 20ECh. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Prob. 28ECh. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Prob. 32ECh. B.3 - Show that nC0 = nCn for n 0.Ch. B.3 - Prob. 34ECh. B.3 - The triangle shown here is called Pascals...Ch. B.3 - Explain why the sum of the entries in each row of...Ch. B.3 - Explain why the alternating sum of the entries in...Ch. B.3 - Prob. 38ECh. B.3 - Show that nCr1+nCr=n+1Cr for n r 1.
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