Using the Laplace transform pairs and the Laplace transform transforms for the following time functions: a. e-at sin wt u(t) b. e-at cos wt u(t) 2

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A: Piecewise function: A function which is defined according to interval. For each interval the…

Q: problem and find its transpose. Use "f" for the transpose. Minimize g = 4y₁ + 3y2 subject to 31 + y2…

A: Primal problem Min Zx=cixi subjected to Ax≥bxi≥0 Dual Problem Max Zy=bTiyi subjected to  ATy≤cTyi≥0…

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A: Since you have posted a multiple question according to guildlines I will solve first (Q.20)question…

Q: QUESTION 1 Find the approximate value of the expression (0.2) 2+3. (0.2) + 1 using the linearization…

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Q: Determine whether the following statements are TRUE, FALSE, OR INDETERMINATE (could be either true…

A: The given statements are: 4) EITHER a bat is a mammal OR crocodiles fly. 5) IF 5 is less than 10,…

Q: 4. Jocelyn and Mason built rockets from assembly kits and decide to launch them at the same time to…

A: Jocelyn's rocket modeled given by  J(t)=-16t2+180t Mason's rocket modeled given by  M(t)=-16t2+140t…

Q: . Evaluate 1 √₁-x²2-x²-y² | | | -1-√√1-x2 x² + y² (x² + y²)³/2 dzdydx

A: Solve the triple integrals using convert to cylindrical coordinates

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Q: 3. Determine whether the series converges or diverges. Show all work and give a clear explanation of…

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A: The quadratic interpolation technique is used to fit a data set into a quadratic equation of the…

Q: Find the area outside r = 2 +2 cos θ but inside r = 3 using double integrals.

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Q: • Now, find the equation of the tangent line at a = -2, and the equation of the secant line for the…

A: The given function is f(x)=400e-0.05x+10. (I)  To Find: equation for tangent line at a=-2. To Find:…

Q: Find the volume inside the sphere x² + y² + z² = 16 and outside the cilinder x² + y² = 4

A: Volume is the amount of space occupied by the closed surface. In this problem, we have to find the…

Q: The average inflation rate of the U.S. dollar over the last six years is 2.8% per year.  If a new…

A: Car cost six year ago = $29000 Inflation rate = 2.8%  r = 0.028 n = 6

Q: 9. For each of these collections of premises, what relevant conclusion or conclusions can be drawn?…

A: We need to determine the conclusion from given collections from premises. Here are some rules of…

Q: A laboratory blood test is 99% effective in detecting a certain disease, when it is in fact present.…

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Q: Use vectors to find the interior angles of the triangle with the given vertices. (Round your answers…

A: The given vectors are (2,3), (9,10), (8,11) We have to find the interior angles of the triangle…

Q: Use the Alternating Series Test to determine whether the series converges. 8 k Σ 1-1)k+1. 3k³ +1 k=1…

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Q: A box contains N coins, m of which are fair and the rest are biased. The probability of getting a…

A: Here the observed frequency of the experiment is as following:     f(head) = 1/2 = f (say)  Now it…

Q: In order to pay for college, the parents of a child invest $25,000 in a bond that pays 6% interest…

A: Bond Amount =$25000=P ROI = 6% = 0.06 Compounded semi annually so n =2

Q: Problems to be solved by the students: 1. Find the external reactions, the axial force,shear force…

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Q: (d) (e) Write down the interpolation error term for the above polynomial, and identify the…

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Q: Definition: A vector space is called the direct sun of W₁ and W2, denoted by V W₁ W2, where W₁ and…

A: Assume V = W1⊕W2 Let v be an element in V.  Since V = W1 + W2 there exists x1  ∈ W1 and x2  ∈ W2…

Q: Consider the recursively defined sequence (Hn)n>1 where 1. H₁ = 1 2. Hn+1 = Hn+n1 for n ≥ 1 >…

A: Table of H_{2^{n+1}} and H_{2^n}+1/2 for small values of n has been attached. This is just given an…

Q: Evaluate the following integral using a change of variables. SSE R y-x y + 2x + 1 4 y-x ¶(vY²xXx)**…

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Q: 6. Consider a spherical tumor of radius R that is covered with capillaries that provide oxygen at…

A: Given: Oxygen concentration=20 nM           Oxygen diffusion coefficient, D=1.8×10-9ms2…

Q: Discuss the hyperbolic length of the Euclidean segment AM

A: Here in the question it is said to discuss about the hyperbolic length of the Eucliedian segment.…

Q: 1 x²-6x+14 dx enter value of antiderivative for X = 3, C = 0.1

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Q: Find f. f(x)= Find f. f(t) = f"(x) = 20x³ + 12x² + 6, f(0) = 6, f(1) = 8 f"(t) = 9/√t, f(4) = 32,…

A: Find the function, using intial conditions

Q: Suppose T: R²→R³ is a linear transformation. Let u, v and w be the vectors given below, and suppose…

A: Given: T:ℝ2→ℝ3 is a linear transformation and u=12, v=25, w=512, Tu=9713 and Tv=211831. To find:…

Q: Translate the following into the language of congruence.  A) When e is even, then  leaves a…

A: The congruence a≡b mod m implies when  a is divided by m it leaves a remainder b. Or a - b is a…

Q: Given: f(x) = x³ + 2x² (x - 1)²¹ with f'(x) = x³ - 3x² - 4x (x − 1)³ - and f"(x) = 14x + 4 (x − 1)4*…

A: Given: The function fx is given by:        fx=x3+2x2x-12 The 1st derivative of the function fx is:…

Q: Define and give examples to all : what is dominating sets ? what is minimal dominating sets ? what…

A: We know that G=V, E is a graph. Here V=number of vertices in graph G. E=Number of edges in the graph…

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Q: An excercise: Let H be a subgroup of index 2 of a group G. Prove that H must be a normal subgroup of…

A: Given: H is a subgroup  of index 2 of a group G. To prove : H is a normal Subgroup.

Q: Solution is not complete. What is the combined power series of the function at zero?

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Q: The graph represents a function f (x). Use the graph to answer the following: y F What is the value…

A: Fro the given graph,we have to find the solution.

Q: Use the rational root theorem to list all possible rational roots for the equation. then find any…

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Q: A house sells for $574,000 and a 9% down payment is made. A mortgage is secured at 7% for 15 years.…

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Q: Find all solutions to the following system of equations. x = 1.5x(1x) - 0.3xy y = y + 2xy - 0.9y 0.0…

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Q: Solve for y. 2y² + 7y−13= (y+ 1)² If there is more than one solution, separate them with commas. y =…

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Q: One ISP (Internet Service Provider) has the following rate schedule for high speed internet service.…

A: The piecewise functions are used to describe the functions in more than one domain. Example:…

Q: 5% compounded every 4 months for 2 years. b) The number of compounding periods per year is  c) The…

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Q: 3. Evaluate the integral using polar coordinates. So Sy=z=1/² √² + y² dydz √1-(2-1)²

A: To find : ∫02∫1-x-124-x2 xx2+y2dy dx

Q: Prove that every nonzero coefficient of the Taylor series of (1-x+x²) ex about x = 0 is a rational…

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Q: pi/8 is wrong. it should be 0

A: Here M=∫01xsin-1x dx-∫01πx2dx Use by parts in part 1. M=sin-1x∫xdx-∫ddxsin-1x∫xdxdx01-πx2401…

Q: You may use a software to do calculations but you have to write down the details. The correspondence…

A: We see gcd(11, 27) = 1. Hence 11 has an inverse element mod 27. 11.5 = 5.11 = 55 (mod 27)…

Q: Let A = {1, 2, 3, 4, 5) and S = A³. Define an action o : S5 × S → S by σο(a1, 22, ag) (σ(a₁), σ(a₂),…

A: Given : A=1, 2, 3, 4, 5 and S=A3 Define an action o : S5×S→S by     σ o a1, a2, a3=σa1, σa2, σa3,…

Q: If Ju 1 8²u ax² c²at² and c = 3, determine the solution u = f(x, t) subject to the boundary…

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Q: 0. [Core content] John, Trey, and Miles want to know how many two- letter secret codes there are…

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