Find the general solution of 2 y" - 2y + y = 10t (t > 0), given that y₁ (t) = t is a solution to the homogeneous part of the equation.

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A: Given, t (sec) 0 1 2 3 4 5 v (ft/sec) 26 -6 -38 -70 -102 -134 To find the linear function.

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A: 9.  (a) The given set is S={(x,y) | xy≥0 } . Let (1,2)∈Sand (-2,-1)∈S( Since 1×2=2>0 and…

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A: Let A be an m x n matrix, with singular value decomposition A = UΣV^T, where U is an m x m…

Q: QUESTION 12 Identify the law of logic used in the following simplification step: T^(p^ (qvr)) = p^…

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Q: 1) (5+1)+(7-2) = 2) (-3+12i)-(-6-3i)= 3) (12+23i)-(-16-13i)= 4) (-13+32i)+(-36-53i)= 5)…

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Q: a)Find the characteristic polynomial of A b)Find all the eigenvalues of A c)Find a basis for each of…

A: Find the characteristic polynomial of A b)Find all the eigenvalues of A c)Find a basis for each of…

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Q: A system consists of four components with A, B in series and C, D in parallel connected as shown…

A: Given, The probability that the component A,B,C and D fail is 0.10, 0.05, 0.10 and 0.20…

Q: QUESTION 6 Given two sets A = {1,2,3} and B={a,b,c}. Let AXB Answer part (a) and (b) with T if true…

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Q: Which price range(s) has a relative frequency greater than 0.18 and less than 0.27?

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Q: Find the equation of the graph given below. Notice that the sine function is used in the answer…

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Q: log.. 490 10 2 3

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Q: Calculate and simplify the Wronskian of the following two functions: y₁ (t) = 3t+3, 32(t) = 1² +1…

A: wornskain of the differential equations

Q: The 2×2 real symmetric matrix A has two distinct eigenvalues λ1 and λ2.If v1 =(1,2) is an…

A: Since A is a real symmetric matrix, it is guaranteed to have two distinct eigenvalues and two…

Q: Find the limit of the sequence as n →∞: (n+1)/(3+5n² + 4n²) ¹/2

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Q: 1. Use Fundamental Theorem of Calculus to evaluate (a) Jo sin zdz, C: arc eit, -≤ t ≤ 5; (b) Jedz,…

A: To Evaluate: The following integrals using Fundamental theorem of calculus: (a) ∫Csinz dz ,  C: eit,…

Q: Find the eigenvalues and eigenvectors of the following matrix: (5 0 21 0 30 3) 2 5 0

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Q: = 27. If f(x, y) = −3x² + 4y², find the value of the directional derivative at the point (1, -1) in…

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Q: 2. Is R Q first category, second category, both, or neither in R? Be sure to prove your claims.

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Q: write the equation of the tangent line to the graph of y-(8-6x + 1)(1+2x) at x-1. Check the…

A: Given that y=8x2-6x+11+2xAt x=1y(1)=8-6+11+2=3*3=9y(1)=9

Q: Question 2. Let A and B be any given sets. Using logical equivalences, prove that An (ANB) А Make…

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Q: Given x ∈ R3, definerij =(x2i+ x2j)1/2 i, j = 1, 2, 3For each of the following, determine a…

A: We want to find a Givens transformation matrix Gij that transforms the given vector x into a vector…

Q: Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given…

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Q: (a) Find the values of p for which the following integral converges: NINF 1 XP Input your answer by…

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Q: Before being allowed to enter a maximum-security area at a military installation, a person must pass…

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Q: x² - y²-2²-4x - 2z+3=0

A: The given surface is x2-y2-z2-4x-2z+3=0T is the trace of S using x=2.To find the two cordinate when…

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Q: . Determine the domain of the analyticity of the following function and explain why √₁2₁=2 f(2)dz =…

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Q: Prove that any Abelian group of order 45 has an element of order 15.Does every Abelian group of…

A: Let G be an Abelian group of order 45. By the fundamental theorem of finite Abelian groups, we know…

Q: y+ (2xy-e-2y) y' = 0

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Q: Q2/ Determined the area of the traverse shown below by Co-ordinate method. C (90,210) D (20,160)…

A: Given coordinate of points are C=(x1,y1)=(90,210) B=(x2,y2)=(150,170) A=(x3,y3)=(100,100)…

Q: In Exercises 3-6, with T defined by T(x) image under T is b, and determine whether x is unique. 3. A…

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Q: Give an example of a nonzero vector x ∈ R2 forwhich||x||∞ = ||x||2 = ||x||1

A: Let's first define what each of these norms means:   The Euclidean norm or L2 norm, denoted ||x||2,…

Q: A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring,…

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Q: Prove each of the following statements using mathematical induction. (a) Prove the following…

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

Q: An observer at a busy bus stop did a 30-minute study of 3 buses. Given the following -Alight time…

A: As per the question, we are tasked with determining the dwell time for three buses at a busy bus…

Q: A matrix A has a LU factorization if A = LU where L is a lower triangular matrix (a matrix with…

A: L=100-110201  U=43-50-22002LU=100-110201 43-50-22002     =43-5-4-5786-8     =A

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Q: For the simplex tableau, do parts (a) through (d). a. Determine which variable should be brought…

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Q: Use the graphical method to find the optimal solutions of the following LP Problem. Max. Z = 3x1 +…

A: Max Z=3x1+5x2s.t3x1+2x2≤18x1≤4x2≤6x1, x2≥0

Q: Prove that • Ụ ( ¹⁄2, ¹ − ¹ ) = (0, 1). 72 n>2 ● U ,1 - ¹] = (0, 1). 72 n>2 n (0,1/2) = 6. n>2 • U…

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Q: 0.0139 0.0055 0.0028 Let D = 0.0055 0.0111 0.0055 be a flexibility matrix, with flexibility measured…

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Q: Consider the homogenous system of differential equations given by: x² = ( ² ¹) x a. Find two…

A: Since you have posted multiple subpart question, we will solve the first three subparts. Please post…

Q: A model of a spring/mass system is 4x"+010. By inspection of the differential equation only, discuss…

A: Solution is given below:-

Q: How many of the following expressions can be simplified further? 3x²y - 2xy² + xy + 5x² x² - 4xy+3y²…

A: Given: Expressions :            3x2y-2xy2+xy+5x2 x2-4xy+3y2+6x2+7y 2x2y-5x2+7y-13We need to check…

Q: Prove that (2x choose x) is always even.

A: We need to prove that (2x choose x) is always even.

Q: Use the graph of f(x) = below to find a number & such that |ƒ (x) - 0.5| < 0.1 whenever 0 < |-2| <…

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Q: Prove each of the following statements using mathematical induction. (a) Prove the following…

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Q: alflife of 5760 year

A: Given  T1/2=5760 years we know that T1/2=ln2 /K