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Exercise 1: Let k 21 be a positive integer. Consider the set of ordered 2k-tuples Π...
Prove: Let k be a positive integer, and set n :=2k-1(2k – 1). Then (2k+1 –...
Prove: Let k be a positive integer, and set n :=2k-1(2k – 1). Then (2k+1 – 1)2 = 8n +1 Prove: Let n be a positive integer, and let s and t be integers. Show that Hire (st) = n(s) in (t) mod n.
Imprecise Counting - Long Runs in Binary Strings Let n=2^k for some positive integer k and...
Imprecise Counting - Long Runs in Binary Strings Let n=2^k for some positive integer k and consider the set Sn of all n-bit binary strings. Let c be an integer in {0,…,n−k}. Consider any j∈{1,…,n−k−c+1}. How many strings b1,…,bn∈Sn have bj,bj+1,…,bj+k+c−1=00…0? In other words, how many strings in Sn have k+c consecutive zeros beginning at position j? For each j∈{1,…,n−k+c+1}, let Xj be the subset of Sn consisting only of the strings counted in the previous question. Show that (n−k−c+1)∑(j=1)...
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we ...
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we would like to show that for all 0 SjSk-, the function satisfies the advancement operator equation (A -r)f0 (a) Show that this is true whenever J-0. You can use the fact that f(n) = crn satisfies (A-r)f = 0. (b) Suppose fm n) satisfies the equation when m s k-2 for every choice of c. Show that )...
Consider the following four problems: Bin Packing: Given n items with positive integer sizes s1,s2,...,sn, a...
Consider the following four problems: Bin Packing: Given n items with positive integer sizes s1,s2,...,sn, a capacity C for bins and a positive integer k, is it possible to pack the n items using at most k bins? Partition: Given a set S of n integers, is it possible to partition S into two subsets S1 and S2 so that the sum of the integers in S1 is equal to the sum of the integers in S2? Longest Path: Given...
do the problem no 1 Let r, r2 Tm be a given set of positive rational...
do the problem no 1
Let r, r2 Tm be a given set of positive rational numbers whose sum is 1. Define the function f by f(n) = n - nfor each positive integer n. Determine the minimum and maximum values of f(n) k=1 An acute angle XCY and points A and B on the rays CX and CY, respectively, are given such that |CX| < \CA = |CB| < \CY]. Show how to construct a line meeting the ray...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system ...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Please read the article and answer about questions. You and the Law Business and law are...
Please read the article and answer about questions. You and the Law Business and law are inseparable. For B-Money, the two predictably merged when he was negotiat- ing a deal for his tracks. At other times, the merger is unpredictable, like when your business faces an unexpected auto accident, product recall, or government regulation change. In either type of situation, when business owners know the law, they can better protect themselves and sometimes even avoid the problems completely. This chapter...
Using the book, write another paragraph or two: write 170 words: Q: Compare the assumptions of...
Using the book, write another paragraph or two: write 170
words:
Q: Compare the assumptions of physician-centered and
collaborative communication. How is the caregiver’s role different
in each model? How is the patient’s role different?
Answer: Physical-centered communication involves the specialists
taking control of the conversation. They decide on the topics of
discussion and when to end the process. The patient responds to the
issues raised by the caregiver and acts accordingly. On the other
hand, Collaborative communication involves a...
Prove: Let k be a positive integer, and set n :=2k-1(2k – 1). Then (2k+1 – 1)2 = 8n +1 Prove: Let n be a positive integer, and let s and t be integers. Show that Hire (st) = n(s) in (t) mod n.
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we would like to show that for all 0 SjSk-, the function satisfies the advancement operator equation (A -r)f0 (a) Show that this is true whenever J-0. You can use the fact that f(n) = crn satisfies (A-r)f = 0. (b) Suppose fm n) satisfies the equation when m s k-2 for every choice of c. Show that )...
do the problem no 1
Let r, r2 Tm be a given set of positive rational numbers whose sum is 1. Define the function f by f(n) = n - nfor each positive integer n. Determine the minimum and maximum values of f(n) k=1 An acute angle XCY and points A and B on the rays CX and CY, respectively, are given such that |CX| < \CA = |CB| < \CY]. Show how to construct a line meeting the ray...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Using the book, write another paragraph or two: write 170
words:
Q: Compare the assumptions of physician-centered and
collaborative communication. How is the caregiver’s role different
in each model? How is the patient’s role different?
Answer: Physical-centered communication involves the specialists
taking control of the conversation. They decide on the topics of
discussion and when to end the process. The patient responds to the
issues raised by the caregiver and acts accordingly. On the other
hand, Collaborative communication involves a...
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