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Q: ·Expand. F. (X.). = 3x as a half._ ·∙range Fourier sine.... ・range.... series in the range FX. S.T..…

A: We expand f(x)=cosx as a half-range Fourier sine series in [0,π].

Q: Find the Laplace transform of the following: 2y+3y"-23y - 12y = 5t-7, y(0) = 0, y'(0) = 0, y" (0) =…

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Q: 1. 2. 3. 4. 2-1 1 s(s? + 4 1 sin2t.dt 6)=u (te-3(t - 1cosh4t S 25² + 18 - = us(t)e-2(t-2[cosh(4(t −…

A: Since you have posted multipart questions We are supposed to give solution of first four part only…

Q: The matrix has a singular value decomposition A = U EVT where and and The 2,2 entry of the…

A: The Moore-Penrose pseudoinverse A+A^+ of a matrix AA is a generalization of its inverse A−1A^{-1}.…

Q: Given the function f(z) = 2² +2² Z then find its real and imaginary parts.

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Q: 2 Ex: Expand fit) = +² o<t<2π in a Fourier Series expansion Sol: 2 L = 2 TT VA L = π -41 -21 2tr 27T…

A: We need to find , an  an = 1π ∫02π t2 cosnt dt Here , apply u - substitution. Plug , u = nt ⇒ du = n…

Q: Suppose gcd(a, n) = 1. Then a(") = 1 (n

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Q: b) Consider the system of equations Ax = b, where 1 3 3 2 A = 6 9 7 and b = 5 [5]. -1 -3 3 4 Find a…

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Q: a) Solve the difference equation Yt-3Yt-1 = 0 given Y₁ = 2 b) Find the limit of the geometric series…

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Q: i) ∀a,b ∈ K, [0 c

A: This is a question of Logic.

Q: Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's…

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Q: Q/ Integrate double integral the Function F(x₂y) = 1/xy over the For rectangle R: 1 √ x 15 2 1159152

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Q: mpotents in Z are {0, 1} elements of Z are non-zero divisors. in Q al Domain sian Integers Z[i] and…

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Q: y = x x², x = 0, x = 2, y = 0, about the ï — axis is 27 units³

A: We have to solve given problems:

Q: Find the volume of the region bounded by the sphere x+y+z² =9 and the planes x=0, y=0 and z = 0.

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Q: A motorboat and its load weigh 980 kg. Assume that the propeller force is constant and equal to 24…

A: Solution

Q: 100 000 61 383 52 279 Find the unknown number in between 45 000

A: It is known that: ∆=E-1, where ∆ is the forward difference operator and E is the shift operator.

Q: Let A be an invertible n x n-matrix. The natrix A(1 : k, 1: k) is invertible for k = 1 Fation, we…

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Q: 1. Helen sprays a weed killer to treat the weed problem in her lawn. The numb 100 hectare (ha)…

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Q: ADVANCED MATH (You may use excel for solving. Rate will be given.) See the following system of…

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Q: Let K be a commutative ring. For every AÃ ÃA = det (A) In- = quence, A is invertible iff det(A) is…

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Q: Find the order and degree of exy" - 3(y¹)² + 2xy = xe^ and write the differential equation in noxmal…

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Q: is not a Field Always because if we take the ideal I =¸ then Z12/ e map y: Z, -→ Z₂ such that y(x) =…

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Q: Question 2: 9 ma an Example for each of the following ( a) Two non-trivial idempotent elements in…

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Q: 7. For the following function : 4 0 <t<1 .f. (.t.)..=. -[ 1<t<2 a. Find the complex Fourier…

A: As you asked multiple question , we will answer first one as per the our policy statement. f(t) ={4…

Q: 2015 21504711201 2015 (a) LLLL 7/2015047 R₂ R₂ +3R3 on a 4 x 4 matrix? Justify your answer. What is…

A: Follow the steps.

Q: y” − 2y' + 5y 8e¯ª, y (0) ³, y (0) = 2, y’(0) = 12 =

A: It is known that: L{f(n)}=snF(s)−sn−1f(0)−sn−2f'(0)−⋯−sf(n−2)(0)−f(n−1)(0) Hence, it can be written…

Q: Without solving the ODE, determine the Wronskian of two t¹y" — 2t³y' — t³y = 0. - solutions to the…

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Q: Calculate the derivative dy for the parametric equation x=t7+t³+ln(5t + 1), y = e4t²_ +t6 giving…

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Q: An investigator's notes got smudged. Use out the smudged words and identify the a) Sketch of the…

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: A

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Q: 3. Find the constants bo, co, a1, b1, C₁ so that So(x)=1+ box + cox² + x³, S(x) = { S₁(x) = a₁ - 2x…

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Q: 100 000 61 383 52 279 Find the unknown number in between 45 000

A: Answer is in the image below.

Q: Let E and F be two vector spaces with the same finite dimension dim(E) = dim(F) For every linear map…

A: Follow the steps.

Q: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

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Q: 5. Find the half range cosine Fourier Series for the function..... X осхе 2 ....(x)...= TT-X <x<T…

A: Given function is ,  f(x) =     x         ; 0&lt;x&lt;π2π-x      ; π2&lt;x&lt;π (.)    Half range…

Q: an extremely simple human capital accumulation problem. Let ht denote human capital of generation t…

A: Given that ht denote human capital of generation t (i.e., the human capital of people born in year…

Q: - Sketch the set S = {z: |z − 2 − i|≤2}. Find the interior, exterior and boundary set of S. Then,…

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Q: A) Find all real eigenvalues of A, and give algebraic multiplicities, if it exists. B) Find the…

A: This is a problem of Linear Transformation

Q: F(x) X c) Obtain the "best-tit" model using 2nd order polynomial regression for the given Table. 0…

A: It is a regression problem where I used 2nd order polynomial regression  to obtain the "best fit"…

Q: Use the second forward, backward and central divided difference equations to estimate the second…

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Q: Let ABCD be a rectangle. The perpendicular bisector of the line segment BD intersects lines AB and…

A: let ABCD be a rectangle with vertex B at origin. let EF is the perpendicular bisector of line BD…

Q: See the below equations below: 4x + Ay = 4 Ax + y = -2 Solve the value of A such that the system…

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Q: 7) There is no proper non-trivial maximal ideals in (Z2₁, because is a maximal ideal in Z2₁, ,0 )…

A: Solution

Q: 4. Expand. f. (X.).=.03.x as a half._. - series in the range 0.₁FX F..... **** 8 - ans.: F.(x) = $…

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Q: A tank contains 200 liters of brine with 20 kg of salt in the solution. Bri containing 0.25 kg per…

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Q: Is every autonomous ODE separable? Justify your answer.

A: In mathematics, an autonomous differential equation is ordinary differential equation which does not…

Q: a) Find all critical points of the function f(x,y) = x³ + 3y - y³ - 3x and classify them as local…

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Q: show that the complex Fourier series of the *** function; f.(t) = t. .。.s.t.5.1... is... jant f (t)=…

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