1. Let a and b be natural numbers, where a, b> 2, such that god(a, b) I and ab = (x + y)" for some natural number n and integers x and y. Prove that x+ y cannot be prime.

Q: Write in listing or roster form. N = ( x|x is a positive integer and is a divisor of 18) Choices: ...

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Q: Suppose f is a function that satisfies f(2) = 20 and f(2n) +nf(2) = f(2n + 2) for all positive integ...

A: It is given that, f(2)=20      ...(1) and  f(2n)+nf(2)=f(2n+2)     ...(2)   Here 'n' must be a posit...

Q: The solution of e² = –has the form x + i (y + 2nm)here n is an integer. What is the value of æ? What...

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Q: Part II. Solve the following IVP using Laplace Transform: 1. 4y" + y' + 5y = 0 y(0) = 2 y'(0) = 1 y"...

A: Given differential equation is 4y''' + y' + 5y = 0withy(0) = 2 , y'(0) = 1  and  y''(0) = -1

Q: Let W be a subspace spanned by the u's, an

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Q: Consider the argument below: "If you complete your computer training, then you can be eligible to wo...

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Q: debit card, and 6 customers used a credit card. Based on these results, express the prob

A: In this question, the concept of Probability is applied. Probability The ratio of the number of favo...

Q: Testing for a Vector Space In Exercises 13-36, determine whether the set, together with the standard...

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Q: The polynomial p(x) = 6x4 - ax3 - bx2 + 28x + 12 where a and b are constant, has factors (x+2) and (...

A: The given polynomial is p(x)=6x4-ax3-bx2+28x+12 since x+2 is the factor so x=-2 will make the polyno...

Q: HoW: Find xcn) if: +る Aras: xcn)=- 80 (+)"+ 80 (+)-52n (t)"+en (ts" + 12n2

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Q: 2 11 -1 2 3 2 -1 1] 3 W 2-2 ,X = [1 2 Y = and Z = %3D %3D L0 -1 2 3 1 Which of the following stateme...

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Q: root of 25 is 6". wing questions with either T (if true) or F (if false

A: the statement p: 8 mod 2 =1 since 2 divides 8 therefore 8 mod 2 =0≠1 (a) therefore the truth value o...

Q: 5) Determine whether the following integral is convergent or divergent: dx 9 + x² 0.

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Q: Use the two properties L1 and L2 to show that the following are linear transformations. (b) T:R² →R'...

A: To show that the given transformation is linear: T:R2→R3 defined asT(x,y)=(−y,x+y,3x−4y)

Q: 3. 6y" – 7y' – 5y = 2x + e-5 [5 marks]

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Q: Find the Laplace transform of the following: -. f(t) = e3t

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Q: Exercise 3.4.7 Show that the center Z(G) is a normal subgroup of the group G.

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Q: Identify the 4th term of the sequence.

A: A sequence is a set of numbers that has a particular order or obeys a general form. As per the conve...

Q: 4) Define the variables a,b and c as: a=5, b=-5, and c=2a+b Evaluate: ба a) ab+ ac - b. b) abla

A: Some of the properties of indices and surds  an= a·a·a......n times a0=1 abac=ab-c

Q: Q1) Find the average value of the area Ander the curve ( y= 1-x).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: 3. f(t) = cosh(3t) %3D

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Q: Among the proposed formulas, the IW axiom is Choose one or more answers: O a. (-(F → G)→(¬G →¬(F →G)...

A: We will use the basics of mathematical logic to answer this question.

Q: Let y= 2a, x" be the series solution to y" +x y' +y=0 about x,=0. Then a. a19 3 a17 19 1 b. a19 a17 ...

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Q: HoW: Find xcn)if: 2. ns: Kcn)=- 80 (+)+ 80(+)-527(ぎ+1en(ょ + 12n

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Q: 22 times 24

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Q: Dztermine the louent peitve poot of f(x)- 7e* in X-1 O Uing the lecant methool C three iterations on...

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Q: Xp X,2s>

A: We have to evaluate the definite integral ∫csc6xdx or antiderivative of  csc6x. As per the definitio...

Q: Find a simple, closed form for the generating function of the sequence defined by a, n2. %3D

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Q: Solve this 75 + 75.175 -110 -25.882 If your answer is 66.06 and you can prove to me that the answe...

A: 75+75.175-110+25.882 =(75+75.175+25.882)-110 =176.057-110

Q: 1. Apply the Sieve Process from 200 to 300.

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Q: Calculate the integral approximation S12 for 1 dx. x²+1 S12 =

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Q: 10 2. F (s) s2 +4s+4

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Q: Jared invested $1,900 at the beginning of every 6 months in an RRSP for 11 years. For the first 4 ye...

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Q: 10 2. F (s) s2 +4s+4

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Q: f(t) = e3t f(t) = t3 %3D

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Q: 2) Find volume from above Z = 14-a-yz below Z=o inside 2+y%=|

A: The given problem is to find the volume of the solid bounded by given region and inside the region x...

Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: Find f(1). S(2). S(3), and f (4) if S(n) is defined recur- sively by f(0) = 1 and for n-0, 1, 2, . a...

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you...

Q: Find all the normal subgroups of D4.

A: To find all the normal subgroups of D4 .

Q: With the growth of digital photography, a young entrepreneur is considening establishing a new busin...

A: Camera life in years = shutter life(weddings per year)(photos per wedding)   Shutter life = 108,000 ...

Q: determine whether the set Sis linearty independent or linearly dependent. 39. S- ((0, 0, 0, 1), (0, ...

A: Given S={(0,0,0,1), (0,0,1,1), (0,1,1,1), (1,1,1,1)} Definition:  A set of vectors is said to be lin...

Q: ds Find the solution 2- dt S 5t3S3

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Q: Let A = {1, 2, 3, 4} Let R be defined on A x A where a Ry if æ > y . a) Draw a mapping diagram of R ...

A: A mapping diagram consists of two parallel columns. The first column represents the domain of a func...

Q: Let R be defined on A x A where R = {(1, 1), (1, 2), (2, 3), (3, 2), (3, 3)} State a counterexample ...

A: Given that    R= { (1,1),(1,2),(2,3),(3,2),(3,3) }we have to show that .... (a) R is not relaxive.  ...

Q: Which of the following represents the ratio of the corresponding sides of △ABC▵A⁢B⁢C⁢ to △DEF? 1:1 ...

A: Introduction: Sometimes, the corresponding angles of two triangles are equal, but the length of side...

Q: Testing for Linear Independence In Exercises 27-40, determine whether the set S is linearly independ...

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Q: Which of the following are real vector spaces? Select all possible answers. The set of natural numbe...

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Q: The production function for a firm is p(x, y) = 68x"y"", where x and y are the number of units of la...

A: By Method of lagranges multiplier . To maximize f(x,y,z) subject to g(x,y,z)=k  Solve system of equa...

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Q: b, c e R such that abc

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