) Solve by using Laplace transform the partial differential equation a² y d'y =9 y(0,t)= 0, y(2,1)= 0, y(x,0) = 20 sin 2x-10 sin 5mx and 9 dt² Ox² dy(x,0) = 0 dt

Q: ) Solve by using Laplace transform the partial differential equation 8²y dt² =9. 90²y y(0,t) = 0,…

A: Solution

Q: After gym class you are tasked with putting the 28 identical dodgeballs away into 6 bins. a. How…

A: To find the given questions when there is restriction and there is no restriction :-

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Q: Given z = cos (2) + i sin (2241), where n is a po

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Q: Problem 13 Compute the three following inverse Laplace transforms: 72 8s 12 L-1 (²-3), 2-1(8+6}, and…

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Q: Use Laplace transform to solve the partial differential equation: d²ud²u du(x,0) t> 0, 0<x<1, u(x,0)…

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Q: 3. Find the area of the region bounded by y = x², y = 8 - x² and y = 4x + 12.

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Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

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Q: Consider numbers of the form a = a₁a2a3 . . . an, with n digits, each digit from the set {1, 2, 3,…

A: For n = 15 We have to find  a. How many such numbers are there. b. How many such numbers are there…

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

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Q: »pr«°C =m•22=4

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Q: Which are true?

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Q: (b) for 3-3.x 10 dx

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Q: ng Task 4: Given the equation x² + y² = 9. Differentiate using implicit differentiation. Express y…

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Q: 1.) Let G₁ = £1₁ 1₁ i -i) be group of 4 Complex numbers under mutiplication. a) is £1, i} a subgroup…

A: Given group under multiplicationG = 1, -1,  i , -i  A subset H of G will be subgroup of G if H…

Q: Let , ² be the complex cube roots of unity. Let z₁, z₂, z, be complex numbers such that z₁+z₂+z3 = A…

A: We will use properties of cube root of unity  ω3=1  and  1 + ω + ω2 =0

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Q: Q1: Solve ýex+y 2 = cosh x + √√cosh² x − 1 + 7e*

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Q: Write a note on Fourier Analysis for Composite Signals?!

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Q: he point of inflexion of the curve r = b0" are given by Love (a) r= b[-n(n+1)]"¹² (b) r =…

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Q: Find the Laplace transform of t², -8 + 3t, 2. g(t) = - 6)² + 2 cos cos (1-2), 6 0 2

A: given g(t) is defined in (0,2)

Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

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Q: b if it Se was Where a + 2b = 3 find the Value (2x + 3) dx a, b E R

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Q: 2. If a is an involution, then Baß is an involution for any transformation B.

A: It is given that α is an involution. So, we can say that α2=I.

Q: problem: Using the Laplace transform, solve the following initial value y" + 4y + 3y = e, y(0) = 1,…

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Q: Using the parity theorem and contradiction, prove that for any odd positive integer p,√2p is…

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Q: Use Laplace transform to solve the partial differential equation: d'y dy ox² ôt -+xt where y(x,0) =…

A: Introduction: Like other transforms, the Laplace transform converts one signal into another using a…

Q: For an arbitrary function f: XY, prove that the following relations hold: a) f(Uier Ai) = Uiel…

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Q: ) Solve by using Laplace transform the partial differential equation 8² 2² = 9. y(0,1)= 0, y(2,1)=…

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Q: x(n)= a"u(k − n) for k>0

A: Introduction: The Z-transform translates a discrete-time signal, which is a sequence of real or…

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Q: Find the image of |z + pi + 2p| = 4 under the mapping w = p√² (e¹²) z. about

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Q: Consider the positively oriented surface S₂ defined by the vector function R(u, v) = (u sin v-3, u…

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Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: If y = a e/, then radius of curvature p = a sec² 0 cosec 0, if (a) 0 = tan-12 (b) 0 = tan¨! a (c) 0…

A: The given equation of curve is y=aex/a

Q: How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b.…

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Q: Evaluate the integral of the equation using Romberg's Method h = 0.5. h/2=0.25 h/4 = 0.125 h/8 =…

A: We have to evaluate the integral of the equation using Romberg`s Method.   ∫12(3x+2x)2 h = 0.5

Q: ) Solve by using Laplace transform the partial differential equation 8² 2² = 9. dy(x,0) y(0,1)= 0,…

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Q: If f(x) is a polynomial of degree <3, f(a) a x-a

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Q: 7/ Find the optimal solution of the following (T.P) by using Least-Cost method. 6 40 50 70 90 90 100…

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Q: Find the Laplace transform of 1. f(t) = [1 − u₂n(t)](2 sin t - sin 2t) - 2

A: Properties of the Laplace transform Laf(t)+bg(t)=aF(s)+bG(s)Lsinat=as2+a2Luc(t)sinat=e-css2+a2

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Q: In a recent small survey of airline passengers, 27 said they had flown American in the last year, 23…

A: We will use  Addition theorem for  3 set

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