If a is congruent to b mod m and a is congruent to b mod n, show that a is congruent to b mod mn. (note: m and n are relatively prime).

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A: Given: The generating function: 1+x+x21+x2+x4+x6x+x3+x5+x7+……….We need to formulate a problem that…

Q: 5 Prove: ACB iff Ax AC B x B

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A: Given:  Premises:1. If the steak is well done, it’s overcooked.2. If the steak is overcooked, the…

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A: 3rd option is correct answer.

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Q: let x = { a, b, c, d, e} T = ($₁ {a,b,c}, { lide}, {C}₂x} be a toponx is G = { a, b, c, d Connected…

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Q: THEOREM 1.7 (Gram-Schmidt process). Let X be an inner product space and let {₁,..} be a linearly…

A: The Gram-Schmidt process is a method to construct an orthonormal basis of a vector space from a…

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Q: Show that Q*, the group of all nonzero rational numbers under multipli- cation, is not isomorphic to…

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Q: 7. Let M be a 3 × 3 matrix. Prove that if M is upper triangular or lower triangular, then det (M) is…

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Q: What is the total differential: w = (x^2)(z^2) + sin(yz)

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Q: Use completing the square to write the following equation y=5x^2+30x-5 in the form y=a(x-h)^2+k…

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Q: -0.2 y 1.2 1.0 0.8 0.6 0.4 0.2 -0.2 R₁ R2 y=xx R3 y = x X 0.2 0.4 0.6 0.8 1.0 1.2 Find the volume of…

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Q: 3. Draw a number line like the one in Figu + 3 FIGURE 3.3

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Q: Imagine you are invited to a birthday party and you arrive late. The room is crowded and you can't…

A: The given distribution function is fx,y=5cosx3+cosy3 where x, y are the coordinates of the Cartesian…

Q: Consider the set A = {2, 3, 5, 10, 14, 19, 21} and the relation Va, b A, a Rb a = b mod 8. List all…

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Q: 2 A (left) stochastic matrix is one which has only non-negative (> 0) entries, and such that the…

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Q: (b)

A: Given: ddtxyz=-110-4-64-2-2axyz   To discuss: The stability of zero equilibrium of the given system…

Q: Consider the periodic step function graphed below. 51 11 (Click on graph to enlarge) This step…

A: From the graph, width of the vertical rectangle are 1.5 , 2.5 and 1 for a period.

Q: Find the multiplicative inverse of a mod n, using 2 different methods. Show your steps in each case…

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Q: Thank you for your response, since it was not included in the response,  is it possible to provide…

A: I gave the solution with more explaination.I hope it will help you.

Q: Find the equation of the hyperbola shown below. IN Gall ~ IN IN MU -CH- NP p N -2 114 IN Kell - X 4…

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Q: Construct the set S+T in the cases shown in Figs. (a) and (b). a Sb Figure (a) b a b Figure (b)

A: a) Given  S=(x,0)|a≤x≤b and T=(0,y)|c≤y≤d. So S+T is given by  S+T=x+y|x∈S and y∈T…

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Q: Consider the vector space R2×3 and the subset a = {[% b 0] -a b 0]|a,b=R}. H =

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Q: Let X be an exponential variable with unknown parameter \. We know that P (X ≤ 10) = §. Find the…

A: We are given that         X ~ exp(λ)     So, P(X ≤ x) = 1 - e-λx                       [cdf for…

Q: The length of an ellipse with axes of length 2a and 2b is given below, where e is the ellipse's…

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Q: What is (1 + i)?

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Q: Math Review: Light travels at a constant speed of 3.0 x 105 km/s. The distance between the Sun and…

A: We know that Distance = Speed * Time  So, Time = Distance/Speed. d=vt gives t=d/v.

Q: The least squares fit line for the points (3, 3.1), (2, 2.3), and (1, 2.1) has form y = mx + b.…

A: Given: It is given that the least squares fit line for the points 3, 3.1, 2, 2.3, and 1, 2.1 has…

Q: 1 Consider the infinite series The integral test can be used to verify convergence of the series…

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Q: Exi xo 1 प 23 10 4 1620 5 24 6 38 five of the 1- Rind F(x) fonform by Using five of given values. 2-…

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Q: The portion of the sphere x² + y² + z² = 4 in the first octant between the xy-plane and the cone z =…

A: Sol:- Parametrization Method: We can parametrize the surface of the sphere as follows: x = 2sinθcosφ…

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Q: A point is a polyhedron. Express the origin in the plane as the intersection of half-spaces. Specify…

A: Sol:- Since a point is a zero-dimensional polyhedron, the origin in the plane is also a polyhedron.…

Q: Estimate the minimum number of subintervals to approximate the value of (3t³ +6t) dt with an error…

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Q: 5. Evaluate the following. (b) 1²y² lim (y)+(0,0) + 3y fryz (T, y, z) if f(x, y, z) = (ry +zz+yz)²

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Q: find a reduced residue system modulo 28; state the value of theta 28

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Q: Which polynomial function is of a greater degree? f(x)=4-2x^(2)-5x^(4) g(x)=5x^(3)+12x^(2)+2x Select…

A: A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.…

Q: College of Letters and Science, the College of Fine Arts, the School of Business Administration, and…

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Q: Find the average value of on the interval [0,2]. f(x)=x²√√92 + x³ favg= Report all answers accurate…

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Q: if (~-~√/13) ₁ If is converted to polar coordinates (r, 0) with is in the interval (-, π], what is ?…

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Q: which, in this case since A is self-adjoint, is just A. Consider now the restriction of A to M…

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Q: Assume a, b, c, d ∈ Z. Prove each of the following. (a) If a|(15b−c) and 7c∼=5b (mod2a), then a|20c.…

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Q: Problem 1. Find all equilibrium solutions of the following system of differential equa- (a) tions:…

A: The given system of differential equation is ddtxy=-1-21-4xy+y2-x2     For the equilibrium solution…

Q: 3. For this question you should use the fact (given on Assn.4) that the matrix -3 6 6 4-5 1 4 2 8-9…

A: (a)  From given data the linear transformation T : R6→R4 defined as  T(x) = Ax       where  A=…

Q: For the linear program Max HA+ SB s.t. 14+ 28 58 SA 38 15 A, B 20 find the optimal solution using…

A: Given : A linear program Max C=4A+5B st. A+3B≤85A+3B≤15A≥0 B≥0 To Find : Optimal solution and value…

Q: u = [3, -4] and v = [6, k], what is the value of k if u is orthogonal to v?

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Q: Consider the function f(x) = −5x² + 70x + 6 on the interval [-3, 9]. Find the absolute extrema for…

A: The given problem is to find the absolute maximum and absolute minimum of the given function over…