Find the solution of the following differential equation: d'a dr dz(0) +9x=32, 2(0) = 4, dt² dt Write your answer in the form of (t)= e(t) + xp(t), where xe(t) is the complementary solution and ap(t) is the particular solution. State what happens in the long term to the solution, as t→∞.

Q: B' B 1. Establish two perspectivities so that a projectivity is established between A, B, C and A',…

A: 1) By using Desargues theorem , we can established projectivity between A,B,C and A' , B' , C'.…

Q: Q11. If we assume a separable solution u(x, y) = X(x)Y(y) of Laplace's equation in a finit…

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Q: 4. Determine the number of possible routes from A to B if you travel only south or cast. a) A B b) A…

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Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Name three logs that would probably reveal the presence of shales. Explain your answers.

A: Following three logs: 1)Resistivity logs  2)Gamma ray logs 3)Induction logs

Q: ANSWER 5. For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality…

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Q: Prove that Define functions f(x) and g(x) as follows: 2 2 f(x) = 7/7 S e-tedt, g(x) = ²/1/²0 L…

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Q: Given a differential equation as d²y x2 dx² +4y=0. dx By using substitution of x = e' and t = ln…

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Q: Determine inverse z-transform of the following equations: Z 2² a. b. (z-2)² (z-1)(z-0.5)

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Q: Compute the Fourier series for the given function ? on the specified interval.

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Q: Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found…

A: Solution : Let A be quantity of radium present at time t. Decomposition equation, dAdt∝A dAdt=-kA…

Q: B/Find the oblique asymptote of the function f(x) = -3x²+2 x-1

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Q: Which cross-section absolutely cannot be used when solving the problem in the lesson? a. Disks b.…

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Q: Consider P2 (R) together with inner product: Find an orthogonal basis for P2 (R). (p(z),9(2) = Г'р…

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Q: Problem 1 Find the Fourier transform of the given function. f(t) = 2A -t + A, 7sts ≤t≤ 0; T 2 2A T…

A: Fourier transform of a function ft with respect to t Fft=∫-∞∞ ft eist dt Where i is a complex unit…

Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.

A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…

Q: Find the z-transform of the following equations: a. 2un+n b. cos(3n) + 2 sin(3n)

A: According to our guidelines I can answer only question no. (a)

Q: Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean…

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Q: 3. Consider the double-integral 2 2xy² + 2 dx dy where D is the triangle with vertices (0, 0), (5,…

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Q: Determine inverse z-transform of the following equations: a. (z-2)²

A: We will use partial fraction method and table of z transformation to find inverse z transformation…

Q: Evaluate. [ 10.xªtan (2x³ + 3) dx

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Q: 7. Find the Inverse Laplace Transform of 1 s²-8s+25

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Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D2 – 4D + 4)y = 0 ; when x = 0, y = 1, Dy = – 1.

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Q: Let W be the subspace of R4 spanned by {u₁ = (1, 1, 1, 1), u2 = (2, 4, 1, 5), u3 (2, 0, 4,0)). Using…

A: The solution is given as

Q: Find the Fourier transform of the given function. 2A f(t)==t+ A, St≤ 0; T 2A f(t)=== Ft+A, T f(t) =…

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Q: K(G) < K'(G) < 8(G).

A: Let κ(G), κ'(G) and δ(G) denote the vertex connectivity, edge connectivity and minimum degree of the…

Q: 4. Find the Fourier Series of the given periodic function. 4, f(t) = {_1 -π≤ t ≤0 0 < t < π

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Q: A solution of a differential equation free from arbitrary constants obtained from the general…

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Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: The matrix has eigenvalue > = 3 with an eigenspace of dimension 2. Find a basis for the…

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Q: K(G) < K'(G) < 8(G).

A: For a graph G ; κ(G)=Vertex connectivityκ'(G)= Edge coonectivityδ(G)=Minimum degree of G

Q: if i = 0 and q = 0 when t =0 find 20 92 O10et SW current (i) when t = 0.07 charge (q) when t = 0.07…

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: Force on spring to stretch it x unit of length  F=kx where  k is spring constant  Work done to…

Q: Let H be a Hilbert space, Mc H a convex subset, and (x₁) a sequence in M such that ||x₁|d, where d =…

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Q: Find the absolute maximum and minimum values of the function, subject to the given constraints. 2 2…

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Q: Using Secant Method in Excel, Given: f(x) = x^3 + 3x^2 - 1 = 0, how many iterations would you take…

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Q: Using Fixed-Point Iteration with an initial value of 1, find a value of x that will make the…

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Q: 3. Using the Gauss-Seidel method make three iterations for the linear system x(0) = 0, 4x - y -z =…

A: Solution :-

Q: For the function ƒ(x, y) = 4x³ + x² − 7, find the solution of the differential equation from x = 0…

A: We can solve this using mid point method

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: Given Fourier transform of the function ft with respect to t Fft=∫-∞∞ft e-iωt dt Fω=∫-∞∞ft e-iωt dt…

Q: Create a table wherein it shows your score or your • class interval • class width • frequency •…

A: To create a table where a data is shown with the frequency, class interval and cumulative frequency.

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: Let H be a Hilbert space, Mc H a convex subset, and (x₁) a sequence where d = inf ||x||. Show that…

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Q: 4. (-) Prove that a graph G is k-connected if and only -connected

A: We have to prove that graph G is k-connected graph if and only if  G∨Kr is k+r connected.

Q: What is the differential equation corresponding to the general solution y²=Cx³? dy 3x A dx 2y dy 2y…

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Q: y" - 3y' + 2y = 2x² + ex + 2xe* + 4e³x

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Q: Find the solution. (4D³-3D + 1)y=0 A y = (₁+₂) ²¹/²+c₂e² Get ® By y = (c₁ + ₁₂x) e */2² + c₂e²r x/2…

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Q: xdy + (3xy + y - e-³x) dx = 0

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Q: 2 2. y² dx + ( x² + 3xy + 4 y²) dy = 0 when x = 2, y = 1

A: Solution :-

Q: Solve the final solution for the differential equation with initial values: y(0) = 2 & y'(0) =6. Use…

A: The given initial value problem is                                             y''-3y'+2y=6 ;…