Find two fourier expansions for the function h(r) = sin(r). In one expansion, all the sine terms shoul have zero as their coefficient. In the other expansion, all the cosine terms should have zero as thei coefficient.

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Q: 4. Use the Laplace transform to solve the IVP a" + 4x' + 4x = 4e24, r(0) = 0, r' (0) = 1.

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Q: a) Find all cosets of 8Zin Z. b)Find all cosets of 8Zin 2Z.

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Q: Construct the dual

A: Given problem is max z = -x1 +x2s.t.        2x1  +2x2  ≤   10           x1  + x2   ≥ -2           x1...

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Q: Consider the matrix 7 7 -3 A = 4 -5 -3 4 -7 (a) Given that the matrix A has an eigenvector calculate...

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Q: Solve y//(t) – 6y/(t) + 8y(t) = e21 + sin (t) ; y(0) = 0 ; y/(0) = 1 -

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Q: 5. Find the solution of the differential equation y"(t) - 3y'(t) + 2y(t) = 4 y(0) =y'(0) = O using L...

A: Given differential equation is y''(t) - 3y'(t) + 2y(t) = 4 with y(0) = y'(0) = 0

Q: Does the following system have a unique solution? Explain. ​2x – 3y + z – 1 = 0 ​Y – z – 2 = 0 ​X...

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Q: Find all solutions of

A: Given,          0.3x + 0.1y  =  0.9 0.4x − 0.4y  =  1.6

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Q: 6s – 5 4s +7 3s – 2 s +8s+ 25 ) s+7 s(s² – 3s – 10) naL 3²L² +n?n?

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Q: 3. The area between the two loops of the limacon r = 1+2 sin e.

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Q: 2.x – 3iy + 4ix – 2y -5–10ix =x+ y– iy +2– (3 – x)i D. Find real numbers x and y such that

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Q: Give a recursive definition for each of the following. (You don’t need to prove your definitions are...

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Q: Compute the area of the shaded region. f(x) x 1 24 - In 5 12-In습 13 - In= 12 In 5

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Q: A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. Use Eq. (1.10) to compute v...

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A: If the Laplace transformation of the function: y(t) is Y(s), then it can be written that Ly(t)=Y(s) ...

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Q: Find the average of the function over the given interval. f(x) = x over [-2, 2] Plot the function an...

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Q: Given trna -2 0. 1. -1 -4 0. 1 0 2 -1 -1 1 3 -2 write -4 as a linear combination of the vectors -1 -...

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Q: Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined by a ...

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Q: QUESTION 3 a) Find all the cosets of (4)in Z12. b)Find all the cosets of (4>in (2> of Z12-

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Q: Suppose u = (1, –2, 6), v = (2, –5, –2) and w = (a, 2, –1). a) Show that u and v are orthogonal. b) ...

A: Given that                      u=1,-2,6, v=2,-5,-2 and w=a,2,-1. Here we will consider the inner pr...

Q: 4. Use the Laplace transform to solve the IVP r" + 4x' + 4x = 4e2", a(0) 0, r'(0) = 1. %3D

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Q: C. Find all complex numbers z of the form 2=x+y such that that zz = 25 and *+y = 7.

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Q: 7- Sketch the graph of y= cot x over the domain 0< x <2n 4

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