Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0 ≤ 0 ≤ 2n

Q: Solve the differential equation by variation of parameters. 1 6 + ex y" + 3y' + 2y =

A: y''+3y'+2y=16+ex we have to solver above differential equation using variation of parameters.

Q: Let -7√2 a and = +√₂ 3 be vectors in R3 equipped with the inner product generated by the matrix 122…

A: Given vectors as u¯=-72042 and u¯=-103

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Q: Consider the quadratic sequence: 72; 100; 120; 132 ; ... 2.1.1 2.1.2 2.1.3 Determine T,, the n term…

A: The given quadratic sequence is Qn=72,100,120,132,.... 2.1.2. We need to find "n" for which Qn is…

Q: Solve the following problems: Given the differential equation, c'"'+3c"+5c'+c=r""+4r"+6r'+r a. Poles…

A: As per the question we are given the the following trird order dynamic system : c''' + 3c'' + 5c' +…

Q: • Y _₂y = 4y + 8y = 2³x + 8x² - 3x -23 2X <-2X Ans: y = ₁2x + c₂xe + Cze 4 1 25 -3X 2 2³ + x² + x +…

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Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

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Q: Consider the IVP +20² dt² dx dt 4t- + 4x = 0, with x(1) = 0 and x' (1) = -3. Show that x₁(t) = t and…

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Q: How many integral solutions are there to the equation x+y=17 with x between 1 and 8 inclusive and y…

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: 4 Given integral is ∫0πsintdt. We have to estimate the given integral by using trapezoidal rule and…

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Q: Let BCR be the open ball of radius one centered at the origin, i.e. B = {(x₁,...,xn) € R" : x² + +…

A: As per the question we are given a n dimentional open ball B of radius 1 centered at the origin. And…

Q: 2. Suppose we want to compute the arclength of y = ln x from x = 1 to x = 3. (a) Write out the…

A: Solution 1: Given function is y=ln x  from x=1to x=3 So arclength is…

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Q: Evaluating and Solving an Linear and Exponential Applications Identify the information given to you…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: The present value of an annuity for ten years is $10000. find the quarterly payment or periodic…

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Q: The current student population of New Orleans is 1900. If the population increase at a rate of 13%…

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Q: Three different 2 x 2 matrices transform the plane R2 as follows. The matrix A rotates the plane…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00⁰).…

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Q: What is 1 + (COS ™n) when n = 4? 01 O -1 O2

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Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

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Q: Based on data given in table 1: k Xk Ук 0 3 0.5 Table 1 1 6 1.0 2 9 2.0 Estimate the following: a)…

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Q: -6 -5 -4 -3 -2 A CON 7 654 on 44 -4 -2 -3- --4-- -5 --6- flot 3 4 5 Find an equation for the graph…

A: We can see that the graph is modified form of f(x) = sec x which is vertically stretched thrice. So,…

Q: 7. Consider the inner product defined on P₂ by (p, q) = p(-1)q(−1) + p(0)q(0) + p(1)q(1). f₁(x) = x…

A: It is given that,  p, q = p(-1)q(-1) + p(0)q(0) + p(1)q(1) be an inner product on P2. f1(x) = x-x2 ,…

Q: Consider the differential equation x²y" - 7xy + 15y = 0; x³, x³, (0, ∞o). Verify that the given…

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Q: Question 27 Use algebraic techniques to determine whether the following function is even, odd, or…

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Q: Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4…

A: we are given the vector field as  F(x,y)=tan-1(2x)4i+(xy-y2+8x2)j to compute…

Q: True or False. Justify if answer is False. Give a counter example or a proof or well-written…

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = et In(t) y(t) =

A: Given differential equation is y''+2y'+y=e−tlnt. We have to find the solution of the given…

Q: True or False: The generating function of the sequence h₁=n+1 is 1/(1-x)². O True False

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Q: = 2x²-3x + 5 Question 26 f(x) Calculate the average rate of change for the function f(x) = over the…

A: The average rate of change of a function f(x) over the interval a≤x≤b is given by the equation; rate…

Q: Solve the following ODES by Inverse Operator method 2 (B³²+1) y = cos x X Ans & Y = C₁ C3 x + C₂…

A: First we'll find the roots of the auxiliary equation and form the complementary solution then we…

Q: Question 26 Calculate the average rate of change for the function f(x) = 2x² − 3x + 5 1 over the…

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Q: Define the binary operator by: ab=a² + b² and by: a b = 8a+ 8b Find the following. When simplifying,…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) OP: 30x + 120y + 30z =…

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Q: Show that (km) is the number of paths in a square grid from (0,0) to the point (m,n) on the diagonal…

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Q: Consider the differential equation 8x²y" + 10xy' + (x − 1)y = 0 Use Frobeniu's theorem to find two…

A: Given differential equation is 8x2y''+10xy'+x−1y=0......1. Let y=∑n=0∞cnxn be the power series…

Q: 3. Consider the following problem max 10 (1 - s) √kdt s.a. k = s√k = k(0) 1, k(10) libre, s(t) = [0,…

A: Given Data:   max ∫010(1-s) k dts.a k=skk(0)=1,k(10) libre,s(t)∈ [0,1], ∀t ∈[0,10]

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Define the binary operator & by: a & b = 2a + 5b + 3 Simplify each of the following. Do the order of…

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Q: Find the general solution of the given higher-order differential equation. y" - 2y" - 3y' = 0 y(x) =

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Q: ≤ t ≤t 1≤1 ≤ 2π O≤1≤t 1≤1 ≤ 2π with a period of 2π with a period of T

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Q: Consider the differential equation x²y" - 7xy' + 15y = 0; x³, x5, (0, co). Verify that the given…

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Q: Consider the differential equation x²y" 4xy' + 6y=0; x², x³, (0, 0). Verify that the given functions…

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Q: The given family of functions is the general solution of the differential equation on the indicated…

A: We have to find the solution of given differential equations.

Q: nd a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: 6. Evaluate the following real integrals by residue theorem 3 • 1= √² 88 15249 dx (x²+1)(x²+9) ans…

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Q: Determine the Root/s of the Mathematical Expression shown below. USE NEWTON-RAPHSON'S METHOD IN…

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Q: a) Given the curve y = f(x) as in Figure 1. y i. ii. iii. 3 N -1- lo 0 f(x) = 2 (3+x) (1+x²) 3…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…