3. Let a, b, c EZ and n E N. Assume a = b (mod n). Prove that a + c = b + c (mod n).

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Q: 8. Show how the Gaussian quadrature rule can be used for a [₁1(a), 5 dr-f - V ( -√² ) + ( + √(√² )…

A: Given : I=∫abf(x)dx To prove : ∫-11f(x)dx≈59f-35+89f0+59f35 To find : ∫0π2 x dx

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Q: 57х3+4х+ уоб (+ 140x-29 лят(3жу) - 49*+3 + sin

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Q: What is the least squares line for data (1,1), (2,1.5),(3,3),(4,4.5),(5,5)? Ox+1 O x-1 O 1.1x -0.3 X

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Q: -2x Use Green's Theorem to evaluate [(3 ye^²* − 7 sin² (3x³)) dx + (5x² + 2x²y² +8e³¹²-7x+²) +2) dy…

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Q: Apply the inverse power method to approximate, for the matrix A , the ei­genvalue that is smallest…

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Q: 25. 0 2x+y=4 2 26. -1 у 0 y = ex 1 x

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Q: хочу dx + ²y = x²

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Q: Use Euclid's algorithm to find gcd(340, 144). Hence find Icm(340, 144). [Show your working.]

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Q: Q6. What is a11 for the geometric sequence with a₁ = 4 and r = 4?

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Q: Let A = [100 -2 1 1 3 -1 and D= A = PDP-¹. Find matrix P = -2 0 0 10 0 0 02] 0 a b c 3 1 2 d 07 . A…

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Q: a = 3 iff N(a) = G. also show that if G is finite, then a € 3 iff o(N E

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Q: (e) Check as to whether the group S3 is abelian or not [NB: You need not check that S3 is a group as…

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Q: 20. In a certain nation, every citizen is assigned an identification number consisting of the last…

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Q: QUESTION 1 Prove that ²+² n=1 9 = π coth 2a a 1 2q²¹ where a > 0.

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Q: Consider the matrix A = 10332 -3 3 1 3 1 10 06-1 4 -2 1 0-4-2 Its rank is 634215 → and its nullity…

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Q: 19. If S2 > T2, which of the following must be true? S>T 5² > T ST 0 |S| > |T| ST<0 A B D E

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A: If log a=b, then a=10b. The equation is provided as: M=23logE1011.8.

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Q: SET UP BUT DO NOT EVALUATE: integrals as specified to find the volume enclosed by √x² + y² and the…

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Q: (1) Prove that a sequence (fn)n converges to f in measure if and only if for every k N, lim m ({\fn…

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Q: Solve the followig non linear gebraic equation to fined one non Zevo root. P(x) = Sin [√ Secx + x…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…