6 First Last Prove that 2 1² +2²+...+n² = n(n+i) (²n+1)/6) for positive integer. n. www

Q: Solve the wave equation utt = c²(uxx + Uyy) in the square D = {0 < x,y < } with homogeneous Neumann…

A: We are given the following wave equation with homogeneous Neumann conditions on the boundary and…

Q: 5. Evaluate the following integrals: (a) *³ ** cos(x) dx dy 4y -x²-y² (b) √ √ ² dy dx (Hint: Use…

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Q: Find the first derivative (i.e., general solution) then solve for the particular solution using 2nd…

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Q: 1. f(t) = 5t²u, (t) + 3(t-4)³ un(t)-9 sin()us(t)

A: This is a problem of Laplace Transformation.

Q: Let S be the following relation on C\{0}: S = {(x, y) = (C\{0})² : y/x is real}. Prove that S is an…

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Q: Q))Solve the Recurrence relation Xk+2 + Xk+1 - 6xk = 2k-1 where xo = 0 and x₁ = 0

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Q: 10. Particular solution of y" - 5y' = x-2, when x = 0, y = 0, y = 2

A: To find the particular solution of given differential equation :-

Q: 2s² + 10s 4. Find £¹2-2s +5 (s+1)]

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Q: √√/625 2 EVA tratical —

A: Here we use , (x^m)^n=x^mn                          (x^m)(x^n)=x^(m+n)

Q: Find the second derivative (i.e., general solution)

A: Note :  Since you have asked multiple question, we will solve the first question for you. If you…

Q: Given the differential equation: dy y +1 = − dx X with initial conditions y = 1 at x = 2.0, produce…

A: Given the differential equation: dydx+1=-yx with initial condition y=1, x=2 To find a numerical…

Q: Given the following characteristics, select the function family that is described. Shape: single…

A: Correct answer is quadratic. As end behaviour of a quadratic equatic equation is same.    Answer :-…

Q: y 1-i X Given: +1 must be an integer. 14 2+1 ; find xy (round up). Answer

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Q: Question 1 A body cools from 72°C to 60°C in 10 minutes. How much time (in minutes) will it take to…

A: Newton's cooling law is used

Q: Solve a part only

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Q: Given the 1st Order Ordinary Differential Equation and a corresponding Initial Value Condition: exy'…

A: To find the solution of the first order ordinary differential equation y'=fx,y with the initial…

Q: y" + 2y + 5y = t cos(5t)-6,y(0) = 1, y'(0) = -2

A: Here we use the table of Laplace transform and the partial fraction method to find solution.

Q: Below are two sets of real numbers. Exactly one of these sets is a ring, with the usual addition and…

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Q: b) Find the inverse Laplace transform of the following function: 3s +6 F(s) = s² +9s + 5.

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Q: 1. f(t) = 9t²u₁o(t) + 6(t-5)³u6(t) - 12 sin()us(t)

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

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Q: 2- Use Gauss Elimination method to solve the following system: 4x1 + 5x2 + x3 = 2 3x₁ + 2x2x3 = 4 -…

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Q: (b) If V = R", and U is a subspace of V prove that U is a subspace of V, where U² = {v € V: (u, v) =…

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Q: 2. Consider the spherical equation given by p = 4 cos sin o. Determine its corre- sponding equation…

A: Cartesian coordinates to spherical coordinates x2+y2+z2=ρ2 x=ρcosθsinϕ y=ρsinθsinϕ z=ρcosϕ

Q: Derive interpolating polynomial for log₁0 1=0, log₁, 2=0.3010, log, 3=0.4771, and hence calculate…

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

Q: -1²- 5. Evaluate the integral e dV, where E is the region between two cylinders z²+z² = 4 E and 2²…

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Q: @ Fs [ f ² (x)} = √√ = Pf (o) - P² Fs {f(x)} proof: How.

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Q: y" — y' — 6y = t²e³t — 4t², y(0) = 0, y' (0) = -1

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

A: Solution

Q: The face of a vertical dam has the shape of an isosceles triangle of altitude 4 m with an upper base…

A: Given a dam with face shape of isosceles triangle(OD=4m) and upper base(BC) of 6m. AD=3m Let us…

Q: Approximate the volume of the solid in the first octant bounded by the sphere x² + y² + z² = 64, the…

A: We have to find an approximate the volume of the solid in the first octant bounded by the sphere…

Q: 2. g(t) t, (t-7)², (11t-e21-30, t< 4 4≤t<7 t27

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Q: Q3) Prove or disprove 1. If (G, *) is an abelian group, then the map : G→ G defined by y(x) = x-¹ is…

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Q: A manufacturer is planning to sell a total of 300 machines to both foreign and domestic firms. The…

A: Given: Manufacturer supplies x machine to domestic market and y machines to the foreign market. The…

Q: 3. Mocca Blanca invested P45, 000 for 2 years and 8 months and earn P12,450 interest. What was the…

A: Mocca Blanca invested P45, 000  for 2 years and 8 months and earn P12,450 interest . We have to find…

Q: 22√9-12/9 6√x+18√√x+7√x 8a√17+11a√17

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Q: Consider the solid formed by the boundaries outside the elliptic paraboloid 4. x² + y² = z and…

A: Volume of a solid bounded by two surfaces z1=fx,y and z2=gx,y is given by V=∬z2-z1dydx Change of…

Q: Q3. Find the value of the following integration using Simpson method of integration: dx;n=6 √2x+1

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Q: a) the solid insider the paraboloid z = x² + y² and under the plane z = 4. Properly idenfity the…

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Q: 1. We are revising the catalogue of modules for a programme, so that each student should choose 4…

A: Given: Each student should choose 4 modules. Any choice of 4 different modules is allowed. There…

Q: Instruction: Setup the iterated double integral that gives the volume of the following solid.…

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Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 0 0 2 5 1 1 0 A = 3 7 2 2-2 9 20 7 -2 8…

A: Solution:-

Q: Use Laplace transform to solve the partial differential equation: d²u du = t> 0, 0<x<1, u(x,0) = sin…

A: Solution

Q: - The differential equation 1 d x² dr d (2²²) + v +y=0 has the solution y sin (a) Write down the…

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Q: Find a Maclaurin series for f(x) = x² e-x giving the first four nonzero terms and the general term.

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Q: Iteration Method Solve for the root of f(x) = 5x²-3x - 1 where xo = -4 3 Solve for the root of f(x)…

A: It is a Numerical Analysis problem and I used Fixed Point Iteration Method to find one real root of…

Q: Determine the Fourier series for the periodic function. f(x) = Problem 2 -2, when -π <x<0 +2, when…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: QUESTION 2 Let S be the following relation on C: S = {(x, y) = C²:y-x is real}. Prove that S is an…

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Q: Q2.Use Triangular method of integration, find the integral f dx. √√x²-9 5x4

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Q: The height and radius, respectively, of a cylindrical tank is 5 m and 2 m. If the tank is full of…

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