1) Find the volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane Z = 8.

Q: 1 -5e iwt dt + -jwt | 5e -jwt dt -1

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Q: Use the above formula to write each of the following limits as an integral (a) (b) Lm=0 nm-T lim n2…

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Q: Find all integral solutions of the linear Diophantine equations 6x + 11y = 41. Use attached photo…

A: Using division algorithm. Integral solution it may be positive, negetive or zero .

Q: Let D-{tx.y.2) : 2+y?s2s 1, z2 o}. Evaluate z dv.

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Q: Explain at least five disadvantages of utilising the direct approach of solution in numerical…

A: disadvantages of utilising the direct approach of solution in numerical analysis are  following

Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: my" + cy' + ky = F(t), y(0) = 0, y'(0) - 0 modeling the motion of a spring-mass-dashpot system…

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Q: Let E be the region that lies inside the cylinderx²+y² = 64 and outside the cylinder (x - 4)2 +y2…

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Q: Prove that 17 is the only prime number of the form n²- 64.

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Q: Let p be a prime such that p = 1 (mod 4). Prove that -lF, is a square in Fp.

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Q: 4). Let T: R4 → Rª be a linear transformation defined by T(x, y, z, w) = (x+z+w, -3x+3y+tz+w, -x+…

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Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

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Q: 4. Determine wether.the. Series..Camveryes. er.diverges n.. O. P.. 5 210- Jñ 3" n²+3

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Q: 4.1.17. Prove that deleting an edge cut of size 3 in the Petersen graph isolates a vertex.

A: Edge Connectivity: λ(G) or κ′(G) is the minimum size of edge set F s.t. G\F has more than one…

Q: in a graph What is a bond ? And give an example

A: To define bond in a graph.

Q: lve the following first order differential equations (

A: Given,          (x-2y)dy+ydx=0

Q: Domestic corporation X owns all of the stock of domestic corporation Y, which, in turn, owns all of…

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Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: A pattern has 5 no blue triangles to every 20 yellow triangles. What is the Ratio of yellow…

A: Solution:-

Q: 5. (D³ – 2D + 4)y = 0 ; y = – 2 , Dy = 8, D²y = 0, when x = 0.

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Q: from a deck of 52. A number card is one with value 2, 3, 4, 5, 6,7,8,9 or 10 so there are 36 number…

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Q: The region W lies between the spheres a? + y + z?= 1 and z +y+ z? =9 and V + y? with z>0, its…

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Q: The radius of the circle P rotates around is 1 meter: Priya is thinking about the windmill in an…

A: What do you think Priya means by rotating -π/2 radians ? Do you agree with Priya ?

Q: 1.0 1,0 -8 for 0 <a <7, for 7 <x <8. Let f(x) Compute the Fourier cosine coefficients for f(x). Ao…

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Q: Q4/ Solve the differential equation a) xy. = 1+ x+y+ xy b) = V 1+ sinx(1+ y²) when y(0)=1 dx

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Q: Find the convolution of the two functions: f (t) = 2t and g(t) Cos 3 t. %3D

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Q: Obtain the general solution unless otherwise instructed 3. (D² – 3D + 2)y = e2*(1+ e2x)¯1 SUMMARY OF…

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Q: Q4/ Solve the differential equation

A: Given,         xy·dydx=1+x+y+xy

Q: Four candidates are running for a lone position in the council of representatives. The results are…

A: Majority is a noun that in general means “the greater part or number; the number larger than half…

Q: 3. Let L: R4 → R³ be the following linear transformation: 2x + y – w + 4z -x + 4y + 5w + 2z x – 3y +…

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Q: log, (cot-1 x) 1- cosh(2") 3. lim I -00

A: 3 We have to evaluate the limit limx→−∞logπcot−1x1−cosh2x. Since, at x→−∞, cot−1x=0 And at x→−∞,…

Q: CatX dy す文 Suix - 00

A: To solve the given differential equation.

Q: dy = xy + x + y+1. dx

A: Solution :-

Q: Using the variation of parameters method to find a particular solution of a nonhomogeneous DE with 3…

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Q: The number of bacteria B(t) in a petri dish culture after t hours is given by B(t) = 400e0.876t When…

A: Given that The number of bacteria B(t) in a petri dish culture after t hours is given  To find When…

Q: Let n = pq where p and q are two distinct primes and consider Zn. Further, let [a] E Zn be an…

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Q: Q2: Find a root of x - 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that…

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Q: Let n = pq where and q are two distinct primes and consider Z,. Further, let [a] E Z, be an…

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Q: Q3: Construct a 3rd order Lagrange polynomial of the function f(x) = Inx.cosx where x e [1, 4]. Then…

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Q: 3. Consider the following formula f (x) = lim n-0 gn +1 Let D = {x € R: f(x) E R}. Calculate f(x)…

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Q: GRAD, DIV, CURL, V, DIRECTIONAL DERIVATIVE Let f = zy + yx, v = [y, z, 4: - x], w = [y2, z", x²].…

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Q: Q1: Determine the coordinates of point N (zero, ?, ?) located on the line AB where: A(-4,5,6) В…

A: Now to obtain the equation of a line passing through points A(x1, y1, Z1) and B(x2, y2, z2) we have…

Q: {t) + 4г(t) — exp( — 4t)сos(3t) + еxp( - 4t)sin(3) -

A: Continuing from the miscalculated step.

Q: on paper

A: Follow the steps.

Q: use two and three Points of Gaussian Guadrature xp = 1 %3D

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Q: 2. Find the Fourier series expansion of: | 0, f(x) = -1<x < 0 sin TX, 0 < x < 1 and then use it to…

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Q: the initial-value problem by finding series solutions about x-0: xy" – 3y = 0; y(0) = 1; y'(0) = 0…

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Q: (D + D, )u = 0 y

A: To find the solution of a homogeneous linear partial differential equation first we find auxiliary…

Q: Let B = . Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix %3D similar to…

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Q: Prove that 17 is the only prime number of the form n°- 64.

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