Math Homework

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Suppose that n is a positive integer and that n = ab, where
Suppose that n is a positive integer and that n = ab, where a and b are relatively prime positive integers. Define a function f: Un → Ua × Ub by f([x]) = ([x], [x]). Prove that f is surjective.Start b… read more
NicoletaB45
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Question 3 tests your understanding of set notation, and your
Question 3 tests your understanding of set notation, and your ability to prove that one set is a proper subset of another. Consider the following subsets of R2: A = {(x, y) ∈ R2 : x2 + y2 ≤ 9}, B = {(… read more
Stevewh
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Define the function f : N → N as follows. f(n) =<: f(n) =1
Define the function f : N → N as follows. f(n) =<: f(n) =1 if n = 1 f(n) =5 if n = 2 f(n) =f(n − 1) + 2f(n − 2) if n ≥ 3 Prove that f(n) = 2n + (−1)n for all integers n ≥ 1.… read more
Dr Arthur Rubin
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Doctoral Degree
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Define the function f : N → N as follows. f(n) =<: f(n) =1
Define the function f : N → N as follows. f(n) =<: f(n) =1 if n = 1 f(n) =5 if n = 2 f(n) =f(n − 1) + 2f(n − 2) if n ≥ 3 Prove that f(n) = 2n + (−1)n for all integers n ≥ 1.… read more
Osbert12
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I have some multiple choice questions I need help with, due
I have some multiple choice questions I need help with, due within the next hour. Can you help?… read more
Dr. Dan
Doctoral Degree
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The equation x^2n+y^2n+z^2n 1, where n is a positive integer,
The equation x^2n+y^2n+z^2n=1, where n is a positive integer, describes a flattened sphere. Define the extreme points to be the points on the flattened sphere with a maximum distance from the origin. … read more
Dr. Dan
Doctoral Degree
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I want to make sure that I am doing something the right way
I want to make sure that I am doing something the right way for the below Discrete Math problem: The President assured the American people that "In all my years of public service, I have never obstruc… read more
Dr. Dan
Doctoral Degree
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(4) Let P(x) be the sentence the word x contains the letter
(4) Let P(x) be the sentence “ the word x contains the letter ‘a' or ‘c' but not both”. What are the truth values of the following? (a) 1. P(faulty) (b) 2. P(sensible)] (c) 3. P(cardboard)] (d) 4. P(c… read more
Dan
Doctoral Degree
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1.The following algorithm adds all entries in a square n *
1.The following algorithm adds all entries in a square n * n array A. Analyze this algorithm where the work unit is the addition operation Sum =0 For i=1 to n do For j=1 to n do Sum = sum + A[I,j] End… read more
Dan
Doctoral Degree
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2 For every positive odd integer n Prove that n^2 2n + 3
2 For every positive odd integer n Prove that n^2 = 2n + 3 for n = 3 5 A string of 0s and 1s is to be processed and converted to an even –parity string by adding a parity bit to the end of the string.… read more
Dan
Doctoral Degree
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I have a few number theory questions. 1) Suppose that m is
I have a few number theory questions. 1) Suppose that m is a number such that phi(m) divides m-1. Show that there does not exist a prime such that p^2 divides m. 2) Show that phi(2n) = the piecewise f… read more
Dan
Doctoral Degree
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1. Prove that the acute angle whose cosine is 3/7 cannot be
1. Prove that the acute angle whose cosine is 3/7 cannot be trisected with straightedge and compass. 2. Find the cardinality of the set of all lines in the plane. Prove that your answer is correct. 3.… read more
Dr. Dan
Doctoral Degree
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1. Use mathematical induction to prove that the statements
1. Use mathematical induction to prove that the statements are true for every positive integer n. A. 2 + 4 + 6 +…….. + 2n=n(n+1) B. 5 + 10 + 15 +…….. + 5n = 5n(n+1) -------- 2 2 For every positive odd… read more
Dr. Dan
Doctoral Degree
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1. Use the definition of the integral to prove that the function
1. Use the definition of the integral to prove that the function f defined by f(x)=1/x for x does not equal zero and f(0)=0 is not Riemann Integrable on [0,1]. 2. Prove that the function g:[0,1]->R… read more
Jim C
Master's Degree
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Let f R- R be a monotone and let D be the set of all points
Let f:R->R be a monotone and let D be the set of all points in R at which f is not continuous. Prove D is a countable set. Define functions f and g by f(x)={0, if x0 g(x)={((-1)^n)/(2^n), if x=1/n … read more
Jim C
Master's Degree
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1. Use the definition of Uniform Continuity to prove each statement a.
1. Use the definition of Uniform Continuity to prove each statement: a. h(x)= 4/(x^2) is uniformly continuous on [1,5) b. G(x)= x^3 is not uniformly continuous on [0,infinity) c. H(x) = x sin x is not… read more
Jim C
Master's Degree
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1.Let a, b, c and d be any real numbers such that a b, c d.
1.Let a, b, c and d be any real numbers such that a… read more
Ben Brown
Bachelor's Degree
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We say that f R- R is additive if for all x, y E R, f(x+y)
We say that f: R->R is additive if for all x, y E R, f(x+y) = f(x)+f(y). In what follows, f is an additive function. 1. Show that for each positive integer n and each real number x, f(nx)=n(x). &n … read more
Dr Arthur Rubin
Doctoral Degree
Doctoral Degree
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