Let A = 8 -6 18 -13 a) Is matrix A diagonalizable? Yes b) If A is diagonalizable, find a matrix P along with its inverse and a diagonal matrix D such that A = PDP-¹.

Q: We want to approximate sin x on [-1,1] with an error smaller than 0.00001. What approximation should…

A: The function f(x)=sinx in [-1,1]The error is smaller than 0.00001

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A: Equipotent Sets: Two non-empty sets A and B are said to be similar/equipotent if there is a…

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Q: Consider the following second-order differential equation. 3y" + 2y' + y = 0 Find all the roots of…

A: The given equation is:3y11+2y1+y=0                                 ⇒(3D2+2D+1)y=0_____(1)Auxiliary…

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Q: f(x)= 3x+1 if x < -2 x-3 if x-2

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Q: the same nationality are

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Q: Determine the present value P you must invest to have the future value A at simple interest rate r…

A: Explanation of the answer is as follows

Q: we need to calculate an error measurement that gives weight based on each term's relative error, we…

A: we need to calculate an error measurement that gives weight based on each term's relative error, we…

Q: um value of -+ b + c c + a + a+b

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Q: 5 4 3 2 1 y=3x, 1 1.25 1.5 1.75 2 Ⓡ

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Q: A pair of dice is rolled. What are the odds of rolling a sum of 4 or a sum of 7? The odds of rolling…

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Q: (a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include…

A: fx=1-x-1

Q: 2. Assume that p > 1. (a) For all n> 1 prove that P-1 (n + 1)P (b) Prove that is convergent. NP <…

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Q: Solve the given integral equation or integro-differential equation for y(t). y'(t) + 27 (tv)y(v) dv…

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Q: 4. A spring with a mass of 3 kg has damping constant 30 and spring constant 123. (a) Find the…

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Q: Show how the division algorithm for complex numbers works. Give at least 3 illustrations

A: To show how the division algorithm for complex numbers works with the help of three examples.

Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

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Q: Average Cost Jesaki Water Sports incurs the following costs in producing a water ski vests in one…

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Q: Integral Representation for F₁ : T(c) T (b) T (c − b) √ ¹³-¹ (1 − p)²-b-1 (1 − x1)¯ª di − 1⁰-¹ - 2…

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Q: v1 = (-2, 3, 6) v2 = (4, 5, -1) v3 = (3, 3, 0)

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Q: Use Green’s Theorem to prove the area of an ellipse with semi-major and semi-minor axes lengths a…

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Q: H 6. Prove that the distinct equivalence classes of the relation of congruence modulo n are the sets…

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Q: Suppose f(x) > 0 and continuous for all x except x = 3, and Select the integrals that will…

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Q: et the terms a₁, a2, a3, ..., a, be in G.P. with common rat et S denote the sum of first k terms of…

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Q: The odds that tax revenue in a certain country comes from property taxes are 40:60. Find the…

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Q: What is the units digit of 31789?

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Q: A radio station runs a promotion at an auto show with a money box with 13 $25 tickets, 13 $5…

A: The box contains total (13+13+11+20) = 57 tickets.  So, 3 tickets can be drawn randomly from these…

Q: 11. a" = cm (mod n) for all integers m≥ 1 (Use mathematical induction on m.)

A: Given that  a ≡ c (mod n) and b ≡ d (mod n).   where  a, b, c, d, and n are integers. Now we will…

Q: Which of the following best describes the trend of the graph? Scatterplot of Salary vs Start Year…

A: Introduction: We know that Scatterplot is a one type of graphical representation between two…

Q: Consider the following linear system. 0 where the matrix A -- y' 0 -50 -51 y, yo 1 -50-51 (a)…

A: As per the question we are given a system of autonomous linear differential equations in matrix form…

Q: The differential equation used to model population growth, under the assumption that the…

A: To solve the differential equation

Q: Find the Taylor series, centered at c = 2, for the function f(x) The interval of convergence is: n=0…

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Q: Exercise 4.10.20 Are the following vectors linearly independent? If they are, explain why and if…

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Q: 4. A spring with a mass of 3 kg has damping constant 30 and spring constant 123. (a) Find the…

A: Mass m=3 kg Dumping constant c=30 Spring constant k=123 At t=0 it starts from initial velocity2 m/s…

Q: Find the area of the shaded region. x=y²-9 -10 -8 -6 -4 -2 y I 2 -2 y = 1 x = e 2 Hy=-1 4 X

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Q: Use the multiple-application Simpson's 1/3 rule in conjunction with a single application Simpson's…

A: Simpson's 1/3 rule:  ∫abf(x)≈h3[f(x0)+4f(x1)+2f(x2)+...2f(xn-1)+4f(xn-1)+f(xn)] n is an even number…

Q: Problem 3: For each of the two graphs below, determine whether they are planar. Justify your answer:…

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Q: Solve the given differential equation by undetermined coefficients. y" - 6y' +9y = 21x + 6 y(x) =

A: Solution:-

Q: Define P(n) to be the assertion that: n Σ₁²: j=1 (a) Verify that P(3) is true. b) Express P(k). c)…

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Q: The top six genres of podcasts in the year 2016 are listed in the table to the right. Use this…

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Q: dx dt +2X + dy dt. +6y= 2²- 2 dx + 3x + 3 dy dt dE +8y=1

A: To solve the system of ODE. dxdt+2x+dydt+6y=2et2dxdt+3x+3dydt+8y=1

Q: 1. Find the general solution to the system y' = Ay, where A is equal to: 4 0 1 -3 b) 3 1 81 -1 0 -1

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Q: let A, B ⊂ R, and suppose A and B are closed. Prove that A ∩B is closed. Hint: You might try showing…

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Q: 1. Let ƒ : R³ → R5 be the function given by f(x₁, x2, X3) = (x₁ + x2 − X3, 2x1 + 2x2 − X3, 3X1 + 3x2…

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Q: Use Green's Theorem to evaluate: LF F.n ds where F = (√x + 4y, 3x + 4y) and C is the boundary of the…

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Q: Consider the system: x+2y+3z=6 2x + 5y +3z=7 x + 8z = 14 a. Write the system as a matrix equation in…

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Q: 1₁ √9x² +25 da

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Q: 3x - 2y + 4z 8x + y - 9z passes through the point (-7, -2, 5). Solve your equation for z. Suppose…

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Q: DIFFERENTIAL EQUATIONS (PLEASE WRITE THE COMPLETE SOLUTIONS. NO LONG EXPLANATION NEEDED. BOX THE…

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