Prove or disprove: There exists an integer a such that 14 | (3a – 5) and 21 | (2a +3).

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Q: Prove or disprove: For any integer a, 14 | (3a — 5) and 21 | (2a+3).

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Q: x-2y3z=0 3y + 3z = 0 3x + y 3z = -3

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Q: 6. Write in logarithmic form using base e: u = e".

A: Here we have to write the equation  in logarithmic form using base .

Q: Which of the following sets have a supremum in R? {ZEQ:0≤z ≤ √2} {z²-1: ze Z} {z² - 3z²+z 3 : ZEN}…

A: Which of the following sets have a supremum in ?1. 2. 3. 4.

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

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Q: 1. Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2,…

A: From first shifting theorem                                                       (…

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Q: Cantor's Theorem Let {F} be a sequence of non-empty subsets of satisfying:(i) each F is closed, and…

A: Consider the sequence of sets   as                             Clearly, (i) and (ii) are satisfied…

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Q: Then where a11 where C11 = a12 = C12 = a21 = C21 = a22 C22= A 1 = (§ 8), B= ( − 4 ³ ) ,0 = (1 ²).…

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Q: OBJECTIVE: G=2A + 3B CONSTRAINTS: A+B≥ 3 20A + 10B ≤ 80 B≤2A

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A: Yes this can be done by a human by hand written.

Q: Solve Completely to the final form of the 200 Solution as a Fourier Series the heat equation…

A: Given Heat equation is the following :Let, so we get By substitution ,we get

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Q: 27√94 188 26√ 94 189 27√94 189 25√√/94 100

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Q: Solve the system 21 X2 = I3 X4 4x₁5x₂ + 3x3 +3x4 +₂ +3x3 +2x4 3x₁4x2 +6x3 +5x4 -2x₁ +2x₂ +63 +4x4…

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Q: Suppose a) Find C₁ and C₂. 1 = 2 = c₂et Ge=¹ • [1] +₂³¹ H]₁ [3]. y(t)=c₁e ÿ(1) = b) Sketch the phase…

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Q: Let p, q be distinct primes. Show that √pq is irrational, use Euclids theorem and emphasis on proof…

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Q: 4. Let f(x) = -x³ cos x. With po = -1 and pi = Use the Secant method. 0, find p3. b. Use the method…

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Q: Use the first eight rules of inference to derive the conclusion of the symbolized argument below. M…

A: The objective is to prove the argument using rules of inference.

Q: Find the values of x and y for the following figure. A 30° 12 MathBits.com 60° 45⁰ X B C 60% y

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Q: Electricity bills: According to a government energy agency, the mean monthly household electricity…

A: Mean Standard deviation The amount is normally distributed.

Q: 2. Consider the linear transformation T: P₂ (R) → M2x2 (R) defined by ao + 2a2 T(a₂x² + a₁x + ao) =…

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Q: Let T: R³ R³ be a linear transformation with standard matrix A. Let P be a parallelepiped in R³. If…

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Q: Suppose A is an m by n matrix of rank r. Under what conditions on those numbers does (a) A have a…

A: Supose  that   is  an by   matrix  of rank .That  is  where   is  an matrix.(a) Suppose that .…

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Q: The Darmatis are leaving for Indonesia to visit relatives and will need $8,000. What will they need…

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Q: (a) possible number of colours. (b) . Write down a proper colouring of the graph below that uses the…

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Q: Determine the next pivot element for the tableau. u V M 1 0 0 -2 1 0 X 1 0 0 y -9 1 2 ol 18 0 6 1…

A: Given a simplex tableau, the objective is to find the next pivot element.

Q: 3. Let f(x) = x² - 6. With po = Use the Secant method. a. b. C. 3 and pi Use the method of False…

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Q: 7. Write in logarithmic form using base 10: x = 10%

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Q: (a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13. Show all your…

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Q: X V 12 3 1 4 -5 - 20 (a) The pivot element is (b) Find the next tableau. X u 1 0 0 y u V M 0 0 15 1…

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Q: The following graph is an example of... log (B1/B2) 3 2 -2 -3 -4 -4 -3 -2 -1 0 1 2 3 4 5 log (R1/R2)…

A: Given information:A graph is shown below:To find:Determine whether the graph…

Q: A square matrix A is idempotent if A² A. Let V be the vector space of all 2 × 2 matrices with real…

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Q: Find a polynomial that interpolates the following data points: (-1, −10), (1, 6), (2, 5).

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