The coordinates coordinates of two points A and B are (3, 4) and (5, -2), respectively. Find the of points P if PA = PB and area of triangle PAB is 10 sq. unit.

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Q: Compute: ต 1 - -2 -4 51 3 -5 5 3 -4 04 -3 -3]

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Q: (b) Prove that Z/4Z is not a field.

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Q: State the domain of the function. 2 X-3 f(x) = The domain of the function f(x) is (Type your answer…

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Q: a. Given that v1 = eigenvalues. A₁ = X2 = [] and 72 = 4 are eigenvectors of the matrix -17 12 -18]…

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Q: ) A) Show that the set of all odd integers is countable, by producing a 1-1 unction F From J onto…

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Q: 3. Is the matrix 5 psd, pd, nsd, nd, or indefinite? Justify your answer.

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Q: What is the Laplace transform of sint cost? 1 OF +4 O O O 1 s+2 1 2t+2 1 2s+4

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Q: Show directly from the definition that the following are Cauchy sequences: ^(N+1) B (1 + 2/₁ + ... +…

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Q: Exercise 6.1.14: Find the Laplace transform of sin(w(t – a)).

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Q: Find the inverse of the function on the given domain. ƒ-¹ (x) = f(x) = (x6)², [6,∞)

A: Given function is f(x) = (x-6)2 ,[6, ∞).We have to find out the inverse of f.

Q: (14) Find two different reduced systems of residues modulo 8.

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Q: 8. Given that F (a, b, c, d) = (0, 1, 2, 4, 5, 7), derive the product of maxterms expression of F…

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Q: Given A = = -4A = -1 1 [4] compute -4A.

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Q: Find dy clx iy=(√x2-1 In (sin (8x3)) iiy y = 1+ sin² (3x)+sin 4 (3x) + sin 6 (3x)+...+ sin 2024 (3x)…

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. F(s) = 12 = s² +9 Your answer…

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Q: (9) Let a, b, and m be integers with m 21 and (a,m) = 1. Prove that the congruence ax=b (mod m) has…

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Q: S₁ = 3 S₁ = 5 and and Sn+1 = √√10S₁-17 for n≥1. n Sn+l = S₁ + 2 7 for n ≥ 1.

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Q: Use properties of determinants to evaluate the given determinant by inspection. 0200 -5000 0006 0 0…

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Q: Prove that every integer n ≥ 2 can be written as a product of prime numbers.

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Q: What is the likely amount of solutions to the problem xt = a in the field F*p and does is this…

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Q: Consider the function f(x)=2x-3 4 find its inverse and draw its graph

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