2) A = Eriris rational number and paca). A numberM is said to be an upperbound of A if asM for allacA. Define B = Eq: 9 rational number andupper bound for A3.is anqA) Show B is non-empty.B Show B doesn't have a smallest elementCHint; 92=2, <2 or >2. Argue First two can'thappen).

Part (a): Show B is non-emptyTo show that is non-empty, we need to find at least one rational…

Answered: 2) A = Eriris rational number and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A movie rental company charges $17.50 per month for membership and $0.50 rental fee per movie. 40. Let x represent the number of movies rented in a month. Write an expression for the total cost per month based on x number of movie rentals. A) 17.50 +0.50x B) 18.00x C) 17.50(x +0.50) D) 0.50(17.50 +x) 41. Write an expression that represents the cost per movie rental. 17.50(x+0.50) A) 0.50(17.50+x) B) 18.00x C) 0.50 17.50 +0.50x D) 42. Write a rational equation to find the number of movies needed to be rented to make the cost per movie rental $1.75. 0.50(17.50+x) A) 17.50 +0.50x B) =1.75 =1.75 18.00x C) 0.50 17.50(x+0.50) D) =1.75 =1.75 43. Find the number of movie rentals needed to make the cost per movie rental $1.75. A) 12 movies B) 14 movies C) 15 movies D) 16 movies E) 18 movies
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x-894 Page P) sum of first three digit is 15• If the digits reversed the real valu decreased Aba 599
7a) Prove that if x is a rational number such that 2x- 3 and 5x-4 are integers then x must be an integer. 7b) For what integer values of x the fraction - is an integer 2л-3 5x-4
∀a ∈ℤ^+, ∃b,c∈Q such that bc≠0 and a^2=b^2+c^2 a. write the statement informally b. for a=1 and a=2 find rational numbers b and c such that bc≠0 and a^2=b^2+c^2 holds. explain. c. prove the statement stated in part a.
Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number. Show all your work.
R) The following proot seems to show that 2-1. Place a check mark In the step In which the error occurs. Step 1: Let a =b Step 2: a - ab Multiply by Step 1 Step 2 a- - ab -h stract Step 4: (a-5)(a+h) - ba-h) Factor Step 3 Step 3 Step 4 (e-ka Ma- - Step 5: Divide by la-) Step 6: a+b=b Simplify Step 5 Step 6 Step 7: b+b=b Step 8: 2h = b Since a=b %3D Simplify Step 7 Step 8 Step 9: 2 =1 Divide by b Step 9
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Use a proof by contradiction to show that the difference of any rational number and any irrational number is irrational.
Which property of equality justifies each conclusion? a) If 2x - 3 = 7, then 2x = 10. b) If 2x 10, then x 5.
1 is the only number that has just one positive divisor and we call it a unit. 1 divides every number. 3 is a number that has exactly two positive divisors. Its divisors are 1 and 3. A number with exactly two divisors is called a prime. 12 is a number with six divisors. Its divisors are 1,2,3,4,6,12. A number with more than two positive divisors is called composite. The smallest number that is a prime is The smallest number that is composite is There are primes that are less than 10. There are composites that are less than 10. The smallest prime greater than 50 is

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2) A = Eriris rational number and pacas. A number Mis said to be an upperbound of A if as M for all. ac A. Define B = Eq: 9 rational number and upper bound for A3." is an q A) Show B is non-empty. B) Show B doesn't have a smallest element Chint 2 happen). 92=2, <2 or 22. Argue First two can't