2. Prove that if a = b( mod r) and c = d( mod r) then a – c= b – d( mod r)

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A: Solution :-

Q: Solve the following system of equations using the Gauss-Jordan elimination method. х - Зу + 7z = 15…

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Q: Question 1 1 -2 -1 1 2 -1 Let A= and assume that 1 2 -1 -2 0 -1 100 0 1 1 -1 0 0 0 0 0 0 -2 1 1 -1 B…

A: Given that                    A=1-21-1012-1012-10-1-21 To find: the basis of null space of A.

Q: Problem 3 The Silly Nut Company makes two mixtures of nuts: Mixture A and Mixture B. A pound of…

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Q: 18. Evaluate L (s² + 1)²

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Q: 10. What is the general solution of the nonhomogeneous differential equation (D² – D– 2)y = 6x +…

A: Given differential equation is D2 -D-2 y = 6x +6e-x  This is non homogeneous differential equation.…

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Q: Find the characteristic equation and eigenvalues of the matrix and a basis for each of the…

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Q: Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem)

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Problem 2: A diet to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200…

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A: This is the problem of modeling.

Q: A firm manufactures two types of Product A and B and sells them a profit of Rs. 12.00 on type A and…

A: 1st we will formed a linear program and then solve it using graphical corner point  method

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Q: Given that log, a+log, b=3, calculate all the possible integer values of a if b is also an integer…

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Q: Question 5. Given the following recurrence relations, fi %D

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Q: Let G be an abelian group, Ha subgroup of G, and n a fixed positive integer. (a) Let Hn = (aEGla"…

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Q: Solve the equation x dy + y dx = 2x^2y dx. Select one: O a. In |x+y| = X^2 + c O b. In |xy| = x^2 +…

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Q: 2 Let A be a fixed nonempty subset of set X and I= {Bc X | A Z B}. Show that (X,I) %3D is a matroid.

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

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Q: Let A = {2,6}. Consider the set B = A x P(A) (where P(A) is the power set of A). Define a partial…

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Q: For the graph shown below, compute for the total weight of a Hamiltonian cycle using the…

A: Here we use edge picking algo.

Q: QIV2 = {a + bv2| a, b e Q} -le, that is, Q[V2] is a field. Find the degree of the field extension…

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Q: 1. 4x + 2y +z = 11 -x + 2y 3 2x + y + 4z 16

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: TAYLOR SERIES Approximate f(7) of the function f(x) = sin(x) centered at 0, accurate to 3…

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Q: sin x - x limg0

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A: The given numbers are first converted to Base 10 numbers and multiplied together to find the food…

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A: To find- Find the volume of the figure with base bounded by the curves such that slices…

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Q: ( 1 if – 2 < x < 0, 2. Suppose that f(x) = { Let s(x) be the Fourier 2x if 0 < x < 2. series for…

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Q: 10.Sketch graph of the following multivariable functions a. z = +1 b. + c. z² = x² ++1 y2

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Q: Find the formula for the Riemann sum obtained by dividing the interval [ – 1, 0] into n equal…

A: To find the formula for the Riemann sum by dividing the interval in n equal sub intervals. The given…

Q: Question.2 Let f: [0,2] → R be a function f (x) = {x, ifx 1 Show that f is R – integrable. |

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Q: Determine the periodic payments on the given mortgage. HINT [See Example 5.] (Round your answer to…

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Q: Select all of the following that are equivalent to 1, for all natural numbers, n. A. O (1)! В. О B.…

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Q: (2) Construct the truth table for the statement (q - p)V ~ p.

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Q: What order of the taylor series expansion should be solve, to evaluate the exact value of:

A: This is the problem of counting and series expansion.

Q: Are the vectors 16 + 16x – 12x2, linearly independent + - 12 – 12x – 12x2 and 18 + 18x – 3x2…

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Q: A large corporation classifies its many divisions by their performance in the preceding year. Let P…

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Q: Indicate the cardinality of the set A, defined as the union of four sets of cardinalities 22, 31,…

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Q: + 6х, — 5х, — 2x4 + 5x3 5x, + 10х, + 6x2 + 8x4 +

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Q: Consider the function f(z) = z' + 5z2 - 14z. . Enter the factors and the roots separated by a comma.…

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Q: Write an expression equal to log, (5) + log,(6) using at most one log.

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Q: point P (x, y) moves such that it is always twice as far from (-5, -6) as it is from (2, -3). What…

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Q: Let's assume that we have the following system of linear equations Ax = b where 5 3 2. A = 3 7 -2 -3…

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Q: Five people are in an endurance race. Suppose you randomly pick and bet on two of them. What is the…

A: We will use permutation  ( arrangement ) Number of way r objects can be arranged by selecting  from…