Show that n := e2™i/n is a primitive nth root of unity in C. Verify that (S3 - )? = -3 in C. Verify that (C8 + )? = 2 in C. Verify that (C5 + S$ – S3 – S3)² = 5 in C.

Q: -5-0 using Iterative fixed-point method by 2. Find one root of f(x) x+ choosing initial value as -2 ...

A: Given that fx=x3+4x2-5=0 To use iterative fixed point method to find one of the root of the above fu...

Q: Question 4, Let {an} be a sequence of real number. n starts from 1. Let a1 =1 and for any n 2 2, we ...

A: Solution is below.

Q: Find y as a function of t if 64y" + 144y' + 106y = 0, y(0) = 8, y' (0) = 3. y =

A: Given DE is  64y''+144y'+106y=0.....(1) Initial conditions are  y(0)=8,y'(0)=3......(2)

Q: Find the standard matrix of the linear transformation from R2 to R2 that first performs a vertical s...

A: Given ℝ2 is vector space over ℝ and standard basis of ℝ2 is e1=1, 0, e2=0, 1 Here given T:ℝ2→ℝ2 is a...

Q: 1) Is the graph in Fig.1 a) a connected graph? b) a complete graph? c) a tree? d) a weighted graph? ...

A: Questions from graph theory.

Q: Consider the following linear programming  problem  Minimize  Z=5X1+6X2+3X3 Subject to  5x1+5x2+3...

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Q: 1.8 (3-2) (7- y?) 2) (7 – s²) dz dy -1.8 -1.6 using an adaptive Gauss-Legendre Quadrature method.

A: The integral given is as follows: ∫-1.81.8∫-1.61.63-x27-y2dxdy We are asked to solve the integral us...

Q: What is the Laplace Transform of f(t)=Dv((1-cos(8t))/2)? O s/(s^2+16) O 4/(s^2+16) O 4/(s^2-16) s/(s...

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C () ...

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Q: r = 5 +4 cos 0 3. Draw and determine the area bounded by the curve in polar coordinates

A: We have to find the area bounded by the polar curve r = 5 + 4cos(theta)..

Q: Jenelle bought a home for $350,000, paying 18% as a down payment, and financing the rest at 6% inter...

A: Given that Total amount of home is $350000 down payment is 18% So down payment is 350000×18100=$6300...

Q: The price p (in dollars) and the demand x for a particular clock radio are related by the equation x...

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Q: 4.8a + 6.5v – 12.65 = -13.9 %3D 5.2a – 3.6v + 4.7S = 6.8 -3.3a + 6.4v – 8.7S = 13.5 %3D Find the val...

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Q: Find F'(x) if F(x) = cot-1 Your answer

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Q: Find all the critical points of each of the nonlinera system given. Then determine the type (or natu...

A: We Check others points (-1, -1), (1,-1)  If (-1, -1) , it is not satisfy x=-y and if (1, -1) it is n...

Q: 5х - Зу %3D 6 7x +у = 0 %3D

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Q: R-x, 0<x <n 0, Q7) Find the Fourier sine transform of f(x)3= otherwise

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Q: y = sin x ,x = 0, y = 1; about y = 1.

A: We have to find the volume of solid.

Q: E Divide 120 into 3 parts Such that he sum product faken 2 at a time Is a maximum. of the ir

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Q: 3. Let W5 be the vector space of all functions defined on [0, 1], and let W1, W2, W3, and W¼ be defi...

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Q: (0,1,1), v=(3,4,1) and w=(6,

A: Given,          U=(0,1,1), v=(3,4,1) and w=(6,2,1)            

Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

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Q: Let u be a solution of the heat equation U, –u = 0 u(0,1)= u(7,t)=0 ; u(x,0)= sin x+sin 2x ; 00 %3D ...

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Q: Suppose that over a certain region of space the electrical potential V is given by the following equ...

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Q: Is the following function a proper distance function? Why? Explain your answer. Measure the distance...

A: By the definition of distance function, distance between any element is non-negative. The given func...

Q: If u(x, t) is a solution of u, = uxx * u(x, 0) = 1 + x+ sin (ax) cos (Tx) u(0, t) = 1, u(1, t) = 2. ...

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Q: Suppose [1]. 7(t) = cet + cze' -1 -3 -2 -1 -1 -2 j(0) = A B (a) Find C1 and C2. C1 = - -3-2 - C2 = -...

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Q: Solve the following initial value problem. y" + 16y = sin 2x; y(0)= 1, y'(0) = 0 %3D The solution is...

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Q: Exercise 12.1 Which of the following subsets of R? are (a) path-connected (b) connected? Connected s...

A: We shall solve first three subparts only - for others kindly post again by mentioning properly.

Q: show that outer product for two vectors not rotation and not commulative ? justify your answer

A: The outer product is defined as, Consider x=x1x2x3⋮xn and y=y1y2y3⋮yn are two vectors from ℝn. Then ...

Q: | 20 yd 80 yd 40 yd An athletic field is a 40 yd - by - 80 yd rectangle, with a semicircle at each o...

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Q: Determine whether the Series is absi utely convergent, ordinergent 52ょ2n+3

A: Given series is ∑n=1∞-1n n2 +2n+35n3 +n+1 This is alternating series. Take an= -1n n2 +2n+35n3 +n+1

Q: *Sotve the fotowing tineat optimization Problem using the Latge M me thod- Max Z=Xx+8X2 Subject to Z...

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Q: canipaign has also started dueshould b lie above disk x²ty?LO single in fegral a bove (the disk x*+y...

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Q: Use layman's term to discuss Broyden's method for solving nonlinear equations.

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Q: Now we know the point on your curve y(x) occurs when t = x. Earlier you found y(t) = t2 +t + y(z) = ...

A: Solve the equation

Q: Your professor has 10 advanced statistics texts and 8 advanced calculus texts. (a) How many ways can...

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Q: A Fnd

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Q: Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed...

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Q: 3. The base of a cone is the unit circle centered at the origin in the r – y plane with vertex P = (...

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Q: NO. 5 Jenny Company produces two types of pants: long pants and short pants. The cost of making a pa...

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Q: The ingredients for your braised greens cost $1.32. You sell it for $4. What is your contribution ma...

A: Given that the ingredients for your braised greens cost $1.32. You sell it for $4.

Q: 3-11 A vertical plate is submerged (or partially submerged) in water and has the indicated shape. Ex...

A: We are only allowed to solve one question at a time so we will answer only the first question. Pleas...

Q: Find the augmented matrix of the system of equation. 2x – 14y + 9z = 47 -3x + 24y = - 52 2x -13z = 2...

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Q: Each of the following statements is an attempt to show that a given series is convergent or divergen...

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Q: Let A = {1, 6, 9, 10} and B = {5, 9, 10}. Indicate if each statement is true or false. 8 E A|Select ...

A: A={1, 6, 9, 10}B={5, 9, 10}

Q: 22n + 2" +1 (-1)* 1. 4n + 3n +5 n=1

A: Given: ∑n=1∞-1n22n+2n+14n+3n+5 To determine: Whether the given series is convergent or divergent.

Q: 1. . :) Determine the series solution to u' – tu = -ť², up to t.

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Q: 1. Find the value of ø(0) for a solution ø(x) to the initial value problem: 6y" + y' – 2y = 0; y(1) ...

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Q: How to avoid getting an estimate that is closest to the largest root when using Bisection Method to ...

A: The Bisection Method looks to find the value c for which the plot of the function f crosses the x-ax...