Prove that 3" > n2 for every positive integer n.

Q: Exercise 3. Let A = 0 2 (a) Compute the eigenvalues of A and for each eigenvalue a corresponding eig...

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Q: region and a rectangular element of area. y = x2, y= 2 – x and x = = y3 49 sq. units 49 sq. units sq...

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Q: a) T(n) = T(n – 2) for n 2 2, T (0) = 5 and T(1) = -1. b) T(n) = -4T(n – 1) + 5T(n – 2) for n 2 2, T...

A: This is a problem of recurrence, generating function.

Q: Find the solution of the initial value problem substitution y-erX in to given defind

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Q: Let p: Man is rational. q: A century is 100 years. r: Today is Monday. General Instructions: 1.) Wri...

A: Given statement p: Man is rationalq: A century is 100 yearsr: Today is Monday We have to write state...

Q: Evaluate lim (tan-(t),e-2t,m²). t-1

A: We want to find given integral.

Q: Solve the initial value problem: (2x – 3y + 4)dx + (x – 1)dy = 0; y(-1) = 2. %3D

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Q: Find the area of the part of the surface ¤= (y/2 + z3/2) with y E [0, 2] and z E [0, 2]. Area =

A: For the solution of the problem follow the next step.

Q: 2. The figure below shows the region of integration for the integral SSI So *f(x,y,z) dydzdx. Rewrit...

A: This is the problem of multi variable calculus, triple integral.

Q: 3s-2 2s2-4s+2

A: The given function is                                             3s-22s2-4s+2

Q: Differentiate the two most common methods use for depreciation.

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Q: 1.6. Consider the arrow diagrams for the relations R and S and answer the questions related to them....

A: Since there are multiple questions, we will solve the first question.  Repost the question to get it...

Q: Choose the correct answer below. O A. f' is the average rate of change of f. B. f'is the tangent lin...

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Q: Two candidates are running for school president. The two choices are Emilio and Jose. The school's n...

A: What is the result of the vote after Paul entry.

Q: Q/ Solve the differential equetion (x²4)dy=zxy dx

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as o...

Q: 2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If d(x) = gcd(f(x), ...

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Q: 10. F(t) = te-4cost %3D 11. F(t) = -6t'et %3D 12. F(t) = e' u(t – 4) %3D

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Q: 1 4. 1. L s+9 s- 5 20 1 7 2. s+3 5s-3 6s-5 3. 4s+7

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Q: Calculate the results of the following expressions using the MATLAB Command Window. -3 (a) T - 1 (b)...

A: % MATLAB CODE(Command Window) :

Q: Use Cramer's rule to solve the system 2 X + 3Y-Z=10 5X + 2Y + 42Z=8 -x - 5Y + 2Z =4

A: We have a system of equations ,  2x + 3y - z = 105x + 2y + 4z = 8-x - 5y + 2z = 4 The system can be ...

Q: (5) Show that if n ɛ Z+ is odd which is divisible by k distinct primes, then the congruence x2 = 1 (...

A: Chinese Remainder Theorem: If a1,a2,...,ak are integers, and m1,m2,...,mk are pairwise relatively pr...

Q: The fox population in a certain region has an annual growth rate of 4 percent per year. It is estima...

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Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above ...

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Q: Find all complex numbers z of the form 2 =x+iy such that that ZZ = = 25 and *+ y = 7.

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Q: 2. Let the rref of a matrix A be, (1 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second...

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Q: 4. Use the Laplace transform to solve the IVP a" + 4x' + 4x = 4e24, r(0) = 0, r' (0) = 1.

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Q: > Σ Write nCnxn+2 + (n- 1)C,x"-1 as one power series. | n=0 n=1

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Q: xplain why F, contains a primitive nth root of unity if and only if p = 1 mod n. int: Use the discre...

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Q: O O O For which value of k the two vectors u=(3,k,-4) and v= (-4,8,1) are orthogonal? * None of thes...

A: Given  the two vector u = (3, k, -4) and v = (-4,8,1) we have to find for which value of k the two v...

Q: 4. Use the Laplace transform to solve the IVP r" + 4x' + 4x = 4e2", a(0) 0, r'(0) = 1. %3D

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Q: Find the g.c.d. in Z [i] of 2 and 3 + 5i.

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Q: Solve, 3 5 2 1 8 -8 7 4 1 - 5 0 6 3 4 det

A: Given matrix is A = 43520189-8741-5063

Q: Given : dy' j + 2k y'î + 4xĵ + 3* Varifng %3D 2.

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Q: Find the area of the region bounded by the given curves and find the volume of the solid formed when...

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Q: Let x be a continuous random variable that is normally distributed with mean u = 26 and standard dev...

A: This is a problem of Normal Distribution.

Q: 1 2 3 4 5 6 7 8 0 A = Calculating the inverse of A manually is probably not a pleasant work. Here th...

A: Let , A = 123456780 We need to find Inverse of A. We will Gauss-Jordan Elimination method, Since , w...

Q: 9. Consider an inhomogeneous differential equation f"(x) = e". a) 'Guess' a solution of the inhomoge...

A: Consider the inhomogeneous differential equation: f'''x=ex

Q: (b)(i) Use Mathematical Induction to prove that for all positive integers n 21 1 1. 1 一 -十 +... 1x3 ...

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Q: Determine the solution of the first-order ordinary differential equation: 2y' +4y- 4y cos x 0

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Q: 1. (C"B)A" 3 A = -1 B = -1 4 C = 1 2. tr(4ET – D) 1 1 1 2 6. 1 3 D = -1 1 E = -1 1 3 2 4 4. 3

A: To evaluate the given matrices. 

Q: 23. Let A be a non-empty set of positive numbers, which is bounded above and let B = {xe R: 1/xe A}....

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Q: In problems 1 - 5, determine if the sequence is bounded. If so, is it convergent? Find the magnitude...

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Q: (1) ,- (1 -2)"/3" (2) ,- nR/(2in+n) Z, -(-1)"-k +, where k is any integer.

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem....

Q: Hi I need step by step handwritten answer please

A: Note:- Some Laplace Transform:-  Ly't =s ys -y0Lsinat =as2+a2L eat =1s-a   Given system is 2dydt -y ...

Q: 2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If d(x) = gcd(f(x), ...

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Q: Peter bought a car which cost Php. 780,000. After using it for 3 years, how much will it be worth if...

A: Peter bought a car which cost Php. 780,000. After using it for 3 years, we have to find the current ...

Q: 5. Prove the following: (a) P(T) is the identity matrix if and only if a = idſn] - (b) P(T2 0 T1) = ...

A: Permutations: A permutation π of m elements is the function  π:1,2,...,m→1,2,...,m given by the 2×m ...

Q: Find the Maclaurin Series for tan¯(x). (If not possible to write in Summation Notation, write the fi...

A: Given: tan-1(x)

Q: Use Cramer’s rule to solve the system 2X+3Y-Z=10 5X +2Y +4Z =8 -x-5Y+2

A: Write the equation in matrix form 23-1524-1-52XYZ=1084 Find the determinant D D=23-1524-1-52=24+20-3...

Q: he Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requi...

A: Given The Well-built Company produces two types of wood chippers, economy and deluxe. The deluxe mod...