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

Q: Exercise 68. Show that (V, B) is non-degenerate if and only if the matrix defining the bilinear form…

A: Hint: Use the given definition of non-degenerate to obtain the proof. Now, we have to proof "if…

Q: [32] (a) Find all nontrivial product solutions u(x, y) = X(x)Y(y) #0 of Uxx + Uyy = 0 (0 < x <∞,0…

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Q: This exercise refers to the hyperbolic paraboloid z = y² - x². (a) Find an equation of the…

A: Note: Hi! Thank you for your question. As per the guideline we can solve three subparts at a time in…

Q: QUESTION 1 A first order differential equation involving current i in a series R-L circuit is given…

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Q: Exercise 7.24. (a) Suppose : Z36 → G is a surjective homomorphism, where |G| (b) (a) Suppose : Z25 →…

A: (a) Here we have given that ϕ:ℤ36→G is a surjective homomorphism, where G=12. Now, by the first…

Q: Exercise 7.23. Let G be an Abelian group and let ne N. Let Gn Gn = {gge G}. Prove that G/Gn Gn. = {g…

A: Introduction: The isomorphism theorems are very important in studying group isomorphism. There are…

Q: la. Given the parabola below, f(t), has the following cartesian coordinates, determine an expression…

A: The main objective is to find the parabola equation f(t).

Q: You watch at a horizontal distance of 40 ft as a hot air balloon rises straight in the air at 10…

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Q: Find the associated half-life time or doubling time. (Round your answer to three significant…

A: Sol- Given  Q = 1800e-0.025tFor half -life time or doubling timeQ = 1800/2 = 900

Q: A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Pure water is then…

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Q: 14.24 Antibiotic Resistance. According to CDC estimates, at least 2.8 million people in the United…

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Q: Let= A+ iB. Calculate 1) the real and imaginary parts of (2-B)(A/C), real , imag =

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Q: y (0.2) 1.58 (a) Find approximate values of the solution of the given initial value problem at t =…

A: Since you have posted a multiple question according to guildlines I will solve first(a)   question…

Q: Find a basis for the null space of the matrix. -3 -6 A = 1 9 Basis for null(A) ={

A: Introduction: The null space of a matrix is the set of all solution that corresponds to the…

Q: :R³ R³ is Ci fa -3 -2 -2 1 0 4 2 3 A 0 la fan T

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Q: Consider the following. B E] X (a) Determine whether the graph is Eulerian. If it is, find an Euler…

A: Eulerian path and Eulerian Circuit 1. The Graph must be connected. 2. When exactly two varices have…

Q: List the elements of the set. The set of all outcomes of tossing a pair of distinguishable coins or…

A: Introduction: When we perform a random experiment, we obtain more than one possible results. The set…

Q: Let f(x) be a periodic function with period 27 and has the lof 2x -{² f(x)= -TWIN-T/2, -T/2 MINT.…

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Q: Determine the rate of change for a function that has the solutions in the following K 3 0 2 -1 1 y…

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Q: What is the initial value of f(t) if its Laplace transform is

A: Initial Value Theorem: The initial value theorem of Laplace transform enables us to calculate the…

Q: λ1 = -2, λ2=5  V1 = (1, -2)  V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find…

A: I have used eigenvalue and eigenvector method to solve the given system of ODE.

Q: Use the Laplace transform to solve the given initial-value problem. y" + 4y' + 13y = 8(tn) + 8(t -…

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Q: Using the methods of this article, determine the surface area A and volume V of the body formed by…

A: Given  t=17 mm r=44 mm h=11 mm The Surface is divided into three sections namely A,B and C. Seen as…

Q: 1 2 3 4 5 Q.5. Let A 0 1 2 3 -1 2012-2 " u || - 2 3 2 نیا 1 and v = 0 2 (a) Determine if u € NulA.…

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Q: Find the solution formula of u(x, y) for Uxx + Uyy = 0, uy(2,0)=0, u(x,b)=0, u(0, y) = 0, u(a, y) =…

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

Q: Find all values of primes p for which (¹¹) = 1 Р

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Q: What is the Fourier transform of

A: This is a problem of Fourier Transform.

Q: Model the data using an exponential function f(x) = Ab×. f(x) = X 0 12 f(x) 64 16 4

A: let y=f(x) then equation to be modelled is y=ABx x y=f(x) 0 64 1 16 2 4 y=ABx taking…

Q: Compute the indicated quantity. P(A n B) = P(A) = 0.1, P(B) = 0.4. A and B are independent. Find P(A…

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Q: A field is given as G = [25/(x² + y²)](xax + yay). Find (a) a unit vector in the direction of G at…

A: Vector field and vector

Q: [2][3][2]+[1]. ] + [ 1 ] e(t), y(t) = [1 − 1] [ 21 (1)] + e(t) (t) (t) d 1(t) dt x2(t) -1 0 For x₁…

A: given :             ddtx1tx2t =-1102x1tx2t +10 etyt=1-1x1tx2t+et To Find : Y(s)

Q: Find the general solution of the following equation: (D3+D2-D-1)y = 0 with y(0) = 1, y(2) = 0, Lim…

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Q: Consider the following. (Assume that what is observed are the numbers that face up.) HINT [See…

A: Since two indishtinguishable dice are rolled, the sample space S of the given experiment is   S =…

Q: A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles.…

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Q: (a) Sketch the graph of the given function for three periods. (b) Find the Fourier series for the…

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Q: The following table shows the frequency of outcomes when two distinguishable coins were tossed 5,000…

A: We want to find the relative frequency distribution.

Q: Find an explicit solution of the given initial-value problem. √₁ - y² dx - √1 - x² dy = 0, y(0) =…

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Q: 42 -(-433)X: X(0) - (1) is The solution of the system X'= Select the correct answer. O a. -2 °* x-((…

A: Solve by Matrix method

Q: Draw the graph of the following functions: y = x² y = |x| + 1 Find the inverse of function f(x) = 3x…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: COS1501 |U| = 140 100 (40-x)-X -(50-x) = x + 10 50-x 40-X X 45-X 80-(50-x) -X - (45-x) = x - 15…

A: We have to solve given problems:

Q: Let A = 64 -2 -3 Find the eigenvalues of A and, for each eigenvalue, find a corresponding…

A: Sol:- Find the eigenvalues for 64-2-3The eigenvalues of A are the roots of the characteristic…

Q: The definition of the error function also defines an "error term" E(x,y)E(x,y). Find E(x,y)E(x,y)…

A: By the Taylor's theorem E(x,y)=f(x,y)-L(x,y)E(x,y)=12fxx(c1 c2)(x-a)2+2fxy(c1 c2)(x-a)(y-b)+fyy(c1…

Q: The shaded portion in the following Venn Diagram represents B Select one: O a. (AUB) nC b. (CuAnB C…

A: Let us write the solution of the given Venn diagram problem in the next step.

Q: The following table shows the results of a survey of 500 authors by a publishing company. Total 160…

A: Consider the given table. We have to compute the relative frequency of the given event of  a…

Q: solve the system of equations

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Q: Given g(x) = 5x² − x + 7, find the following. (a) g(0) (b) g(−1) (c) g(r) (d) g(x + h)

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Q: Q.2. Let the set H :ab ≤2 (a) Is set H a vector space? Justify your answer. (b) Is the set H close…

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Q: 3. (i) Show that is an idempotent in M₂(Z12). e= the idempotent e of part (i). (13) 69 (ii) Give an…

A: To Prove: (i) e=4269 is an idempotent element in M2(ℤ12). To Find: (ii) explicit definition of…

Q: Q3. Derive the following formula for approximating the derivative f": ƒ™" (x) ≈ (f(x +3h) − 3f (x +…

A: To Derive: f'''(x)≈1h3f(x+3h)-3f(x+2h)+3f(x+h)-f(x). To find: Big-Oh error term from the above…

Q: Laplace transform of the convolution integral of

A: Note:- Convolution Integral Theorem:- If function ft  and  gt are the piece-wise continuous function…