Use Fourier transform to solve the partial differential equation: du d'u du(0, y) 01 du(x, y) əx " = 0, lim u(x, y) = 0,

Q: Find the sum S of the following series (C, denotes "C,): S=C₁-C₂24+ C₂, C₂ C₂ 3 4 **+ (-1)"+1 C₂ n

A: Introduction: The harmonic series is an infinite series generated by adding all positive unit…

Q: For a data set of size 10, the highest order of a polynomial that could be fitted using Least…

A: Last option is correct i.e. 9

Q: 1. Prove or disprove (a). The order of the element (2, 3) € Z6X Z15 is 5. (b). The group Z7 × Z17×…

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Q: calculate the volume of G where G is bounded by 2= x² + y²₁ ²²+ y² = 4, 200 SS f d v

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Q: (a) Consider the feasible region in R² shown below (the red shaded region). 10 x+y=8 x+y=2 -3x - y =…

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Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

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

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Q: 0 Q4)(a) Find the maximum eigen value for the system A = x (0)=(0.02991) with initial vector

A: Let us find the maximum  eigenvalue of A using Power Method.

Q: Use Taylor series method to compute x(0.2) and given that d²x dx de -4x=0,x(0)=1,-(0)=2 dt² dt dr…

A: Taylor series of f(x) at x=0, is given by fx=f0+xf'0+x22!f''0+x33!f'''0+x44!f''''0+.....

Q: 6. Determine the Poisson brackets formed from the components of the angular momentum L.

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Q: 4) Find the largest eigen value for the matrix 1 ^-['s 2] wi A= with x (0)=(7/17_1) 54

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Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 11. D B C B A A

A: Introduction: A graph is a set of points, called nodes or vertices, which are interconnected by a…

Q: Find the basic solution for the following (T. d the optimal solution. 4 1 2 6 9 100 4 3 5 7 120 2 6…

A: Check if the problem is balanced by finding the sum of rows and columns 100+120+120=340…

Q: 1. Let f(x, y, z) = 9 (√x² + y² + z2²) 7 where g is some nonnegative function of one variable such…

A: Surface is the sphere with radius 2and centre at (0,0,0)

Q: [(9)se x². d²+xdx + (x²-n²) y=0_ by substitution x== 1102 at 2 pt souhen Hence show that it has no…

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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: ) Solve by using Laplace transform the partial differential equation 2², a² y dt² =9. ox² y(0,1)= 0,…

A: Solution :-

Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

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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

Q: Solve for the value of x. Points A and B are both centers of the given circles. 9 H 8 B

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Q: Solve: Subject to 2wt+3ux + 4u = 0 u (x,0) = x² in R. x [0,00)

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Q: 2. Find the general solution of cos² x sin x dy + (y cos³x - 1) dx = 0

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

A: Introduction: Laplace remodel is called in honour of the outstanding French mathematician, Pierre…

Q: So whats the final answer, whats the final unknown value?

A: Solution

Q: Consider a triangle ABC, on each of whose sides equilateral triangles are dra

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Q: How many permutations of {1, 2, 3, 4, 5, 6, 7, 8) leave exactly 1 element fixed?

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Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the given graph the four vertices A, B, E and F are of odd degree,hence by the Eulerian Graph…

Q: You have 14 presents to give to your 3 kids. How many ways can this be done if: a. The presents are…

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: Use the graph as in but now the dots (vertices) are locations inthecity of Stockholm, and the dashed…

A: The graph given is as follows: Given that α=10a  and  β=10b where a=1  and  b=2.

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

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Q: Describe the surface with cylindrical equation r=6. Hint The 8 and 2 components of points on the…

A: We have to find the surface whose cylindrical equation is given by: r = 6.

Q: show that, 8 = 1², when € IR³ we have x 1x)=870

A: Please five the answer in next step.

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

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Q: How many 9-bit strings start with 101 or end with 10 or both?

A: There are 9-bits, and we start with 101.It means there are 6 remaining bits.Therefore,there will be…

Q: 1. Use the following methods to solve for the root of the equation f(x) = xe * – sinx

A: Note:- The problem in second image has no solution as it is divergent according to the table. But,…

Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 10. B с A E D с E D B

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Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

A: Let us consider the curve y=f(x) and y=g(x). The volume obtained by rotating the curve about y-axis…

Q: If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is…

A: Introduction: The Fourier Transform may be used to deal with preliminary boundary cost problems at…

Q: GROUP holds four properties simultaneously: i) Closure, ii) Associative, iii) Identity element; 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: (iii) (1) Find the x-intercepts of the parabola. Give your answers in decimal form, correct to two…

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

A: Solution :-

Q: Calculate 2510 S. S. S. 2² r dz dv db (volume of D)

A: Triple integration

Q: Use Laplace transform to solve the partial differential equation: o²y_by -+xt where y(x,0) = 0,…

A: Solution

Q: II. Use Theorem 6.1.1 or Theorem 6.1.2 to solve the following problem: What are the equations of…

A: From the given data, Assuming the illustration in a 2D space. Let P=α,β Then, O be the origin.

Q: a non-planar graph that is not homeomorphic to K5or K3,3.

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

A: Solution

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: For X and Y normed linear spaces, let {T} be a sequence in L(X, Y) such that Tn → T in L(X,Y) and…

A: For X and Y normed linear spaces, let {Tn} be a sequence in L(X, Y) such that Tn → T in L(X,Y) and…