We say that a set A is denumerable if there exists a bijective function f: N→ A. Suppose that A is a denumerable set. Prove that there exist sets B and C such that BnC = and BUC = A.

Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

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Q: for question d in the first line, why is the derivative of u(x) 1/x^2 and not 2/x?

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Q: 2. Which one of the following functions will result in the following graph? M 2 A. 5+ 4 sin[3(x -…

A: Put x=0 and see the function values and then decide which will be the graph

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Q: 4. Periodic impulses. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is at…

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Q: Temple Trucking Co. just hired Ed Rosenthal to verify daily invoices and accounts payable. He took 7…

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Q: 2. Evaluate aydA, where R = {(x, y) : 4 ≤ a² + y² ≤ 9, a ≤ 0, y ≥ 0}. x R

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Q: Let a and BE R. Consider the linear optimization model: min s.t. x1 + x2 αX1 + βα2 > 1 x1 ≥ 0,₂ € R.…

A: Let .Consider the linear optimization model (Pα,β)..Subject to:We need to write the linear…

Q: In Exercises 1-12, determine whether the given matrix A is diagonalizable. If A is diagonalizable,…

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Q: : Use the divergence theorem to find the total flux of flow field F out of the 6 sides of a…

A: We have to find the outward flux using divergence theorem where the flow field is given as F

Q: Parseval's Identity:

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Q: Consider the following matrix. 1 -7 2 [B] 2 -7 3 -1 -7 0 Find a basis for the column space of A. (If…

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Q: 3. For an odd prime p≥ 7, show that there are consecutive quadratic residues mod p, i.e., that there…

A: The exercise follows using multiplicative property of Legendre symbols

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Q: Calculate truncation error for e^2 with two and three terms in taylor expansion

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Q: 1. Evaluate the following Legendre symbols: (i) (ii) р 463 541 (iii) 8933 104729 (-).

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Q: . Suppose that p is a prime integer. (a) Show that if [x], [y] € Z and neither of which is [0], then…

A: Let's consider a prime integer p and the set Zp (integers modulo p).(a) To show that if [x],[y]∈Zp…

Q: • Standard deviation is the most common descriptive measures of there is no variability in the…

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Q: If A = -60000 5-6000 -4 -7 20 0 -89 3 -8 0 -2 -2 5 6 -9 then det (A): =

A: We have to find the determinant of the matrix .

Q: T F 106. The numbers 1073741824,1073741824, and 1073741824 are rational. T F 107. You should shy…

A: Since you have posted a multiple question according to guidelines I will solve first(106)  question…

Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral 0)

A: By using given definition of Laplace transform, we will find the Laplace of the given function.

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Q: | Let F =, use Green's Theorem to evaluate [F.dr where the curve C is the boundary of the region…

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Q: -42 18 (1 point) Let A = -90 39 Find two different diagonal matrices D and the corresponding matrix…

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A: Since you have asked more than one question, find the solution of the first one.

Q: et M = 10 6 In = -3 1 nd formulas for the entries of M", where n is a positive integer.…

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Q: #3: Let F(x, y, z) = (7y, 8x, 7y). Use Stokes' theorem to compute Sc F. dr = where C' is the…

A: We will use the stokes theorem to solve the following integral.

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A: Clearly slope field is parallel to x axis at y=0,1Hence .dy/dx=0 at y=0,1Forms two factor…

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A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: a) Calculate the flux of the vector field F(x, y, z) = 275k through a sphere of radlus 4 centered at…

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Q: Find the area bounded by the curves  y = 4x2 and y = x2 + 5.  (Round your answer to two decimal…

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Q: ctri shift t 1. tab caps lock f fn esc It Homepage | LAPC - с → I (? 17. The five top swimmers in an…

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Q: Give a basis for span(5) 3 # 1 0 Number of Vectors: 1 2 3 6 6 2 8

A: The given setThe augmented matrix

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Q: A Calculator is required for this problem. R Let R be the region enclosed by the x-axis and the…

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Q: 1. In the following problems, you don't need to understand the physics to complete the questions.…

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Q: How would I use those non-zero terms and make

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