Prove that a set A is countable if and only if there exist an injection of A into N.

Q: 1. Find the distance between (2, 8)and (–3, –4).

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Q: olve each problem . Point P is located at (-9, –5)and point Q is located at (-9, –8). What are the c...

A: Given points are P = (-9, -5) and Q = (-9, -8)

Q: Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent...

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Q: 820,A Lado a vert bottow HowD wall 1.4

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Q: prove that it is not possible to find four distinct prime numbers p, q, r, s such that ps − qr = 0.

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Q: Solve the IVP y′′ + 4y′ + 13y = 0, y(0) = 1, y′(0) = −5

A: To  Solve the IVP y′′ + 4y′ + 13y = 0, y(0) = 1, y′(0) = −5

Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? If p|rq, prove that p|r a...

A: Given that p, q and r are prime numbers and p≠q.

Q: Prove that the cartesian product of a countable set is countable

A: This is question related to set theory's topic countability.

Q: The functions f and g are continuous and differentiable with f (x) = g'(x). Selected values of the f...

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Q: 19, 2, 9, 5, 27, 6, 1, 7, 12, 15, 18 wisker plot

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Q: 1 Sketch the following four vectors: Let A = -2 -3 2 -2 • Aui • Auz Based on your sketch, which vect...

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Q: Obtain an asymptotic expansion for I(z) = S e-zy*/2 cos y² dy, as z → 00 along [0, 0).

A: Here, we need to find an asymptotic expansions for I(z)=∫-∞∞e-zy22cos y2dy, as z→∞ along [0, ∞). We ...

Q: Use parametric equations to describe the solution set of the linear equation below. Give the exact a...

A: Using parametric equations we describe the solution set of the given linear equation, using the vari...

Q: Q5) find the inverse of the following matrices: sin(0) lo 31 ,b) B = [ ]. •) R = [ coS(0) sin(8) 2 0...

A: according to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: 34. dyldx = 2(3x + y)² – 1; when x = 0, y = 1 Answer: y = tan (2x + a/4) – 3x

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the ...

Q: V f(x = - (x – 8) (x – 15) V g(x) = -x + (10,15) 15 V Label: (10, 15), (14,9) V Label: 10 (14, 9). P...

A: To find the area of region enclosed by functions f and g

Q: 5. Determine whether the given pair of graphs is isomorphic. u2 v2 V3 V4

A: The number of vertices in graph 1= 8 The number of vertices in graph 2 = 8  The number of vertices i...

Q: Find the inverse of the given matrix if the matrix is invertible, and check your answer by multiplic...

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Q: Find the generating function of the sequence {a;}k20 defined by ak = -3 if k even; a = 3 if k odd. %...

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Q: Solve the following system of congruences. By using Chinese Remainder Theorem X= 5 (mod 6) X = 4 (mo...

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Q: Find f(x) dx for each graph of y = f(x), where f(x) consists of line segments and circular arcs. Ay ...

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Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). %3D %3D = (0, 6) V = a b...

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Q: a=3,5, A=12.5°,C = 57.5°

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Q: Consider the following function: -9x2 + 5x + 6 if x 1 Step 1 of 2: At what x-value is the function ...

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Q: Determine which graph satisfies the following properties. (-2) 0 げ(-2) > 0 "(-2) < 0 Graph A Graph B...

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Q: The 25 staff members of an office decide to hold a Kris Kringle to celebrate the holidays and draw n...

A: Number of way r objects can be selected from n objects =nCr=n!r!×n-r! Also  we have to use Derangeme...

Q: a. For what vaiue(s) of a are the vectors r= (3, a, 9) and y (a, 12, 18) collinear? b. For what valu...

A: Collinear and perpendicular vectors

Q: Find S. Re z?dz clockwise around the boundary of the square with vertices 0,j,1+ j,1

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Q: Locate the highest real root of f(x) = 2x3 – 11.7x² + 17.7x – 5 a.) using fixed point iteration meth...

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Q: Premises: Vx(L(x) → H(x)) 3x (~ J(x) A L(x)) Conclusion: 3x (H(x) A - J(x))

A: Given that Premises:      ∀xLx→Hx                        ∃x~Jx A LxConclusion:  ∃xHx A ~Jx We have t...

Q: -1 1 5 1 Find 2 5 0 2 7 1

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Q: Prove that the union of countable set is countable

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Q: For the Euler differential operator, aind a utios to the homogeneous equation L=0, then use reductio...

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Q: 1. Three vectors , A , B and C are related as follows: = 2 @ В 180° , A + C = -5 + j 15 , C = conjug...

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Q: Drag and drop the equations matching the solution into the spaces provided. Infinitely many No solut...

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Q: Write in the form x+yi: 2+3i (a) 1+i -4+3i (b) -2 -i 4i (c) 2-i 1 (d) 2+3i 3- 2i (e) i p+qi (f) r+si

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Q: 4. Use variation of parameters to find a general solution of r'y" + 5a?y" + 2:ry/ – 2y = x³ log(x)

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Q: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure .r...

Q: 13. A lamina occupies the part of the disk a? + y <1 in the first quadrant. Find its center of mass ...

A: Given that a lamina occupies the part of the disk x2+y2≤1 in the first quadrant. The density at any ...

Q: Find the sum of the Fourier series of the function Ax) = e -1<x51 at x = -1 OA 3 O B. 3 OC. 3-e O D....

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Q: 3. Find the solution of the nonhomogeneous differential equation initial value prob- lem dy dy – 102...

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Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function f...

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Q: In connection with the deduction of the Black & Scholes formula for the price of an option (see Chap...

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Q: 6. Let f: A R be a continuous function. Show that if A is compact then sup f(A) e f(A).

A: Sup(A) under the continuous function

Q: Consider the following two ordered bases of R² {(1,-1), (-2,3)}, C = {(-1,1), (1, -2)}. B a Find the...

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Q: What can be said about the lines defined by the equations y = 0.25x + 8 and 3y - 3/4x - 24 = 0 recip...

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Q: (a) For what values of x is the following series convergent? Σ 00 n=0 (b) Find the value of x that s...

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Q: Each graph represents f"(x) (not the original function) Find the x-coordinates of all inflection poi...

A: We have to find the x- coordinates of Inflection point.

Q: Given the following vectors u' and v, find a vector w in R so that {u, v, w} is linearly independent...

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Q: What are the intersections of the conic section formed by the points A(0,1),B(2,3),C(5,4),D(1, −2),...

A: Below are graph and input view.