5) USE THE LU FACTORIZATION 20 -3 0 20 - 4 A= b= 1 1 1 02 1 1 -3 4 (COLUMN OPERATIONS) 5 1 2 LAST DIGIT OF S.N.

Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π

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Q: The number of people in a small country town increases by 2% per year. If the population at the…

A: Solution :   Given that The principal population P0 = 12500 Increasing rate r = 2% = 2/100 = 0.02  n…

Q: Construct a truth table to verify the following implication. p⇒pvq Construct a truth table for the…

A: p⇒p∨q

Q: Let F be a field of characteristic not equal to 2. Let a, b E F such that b is not T CL If 1

A:

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Given z=ex2+y2, x2+y2=1, x2+y2=9, z=0

Q: Solving manually, the equation f(x) is given as x³ - x² + 4x -4 = 0. Considering the initial…

A: Option B is correct   I attach explanation in second step, i hope it will help you and you like my…

Q: I. Consider the vector-valued function In(2t + 1) Ŕ(t) = ²₁+ î+ t 1. Determine the domain of R. 2.…

A: This is a problem of Vector Calculus.

Q: II. Let F and G be vector-valued F(1) = (1,0,2), F'(1) = (1,1,2), G(1) = (2,1,3), G'(1) = (-1,…

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Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: Given: ∫021xdx To find: Definite integral

Q: Find of z= In(xy) 8²y

A: For a function of the form: z=f(x, y), the partial derivative with respect to y is calculated by…

Q: H.W: Use the chain rule to find the derivative of w= x² + y² with dw respect to t (dr), with x =…

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Q: Given that G is a group and H is a subgroup. What is the result of (b^-1)^-1 if b is an element of…

A: Given that     G is a group and H is a subgroup of G.    Inverse of an element:  Let G be a group…

Q: Prove that if f, g area analytic at ro and g(ro) #0 then f/g is analytic at ro

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Q: 16 Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from either one or…

A: Since you have asked a question with multiple subparts here, we will solve the first three sub parts…

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We will sketch the region bounded and find boundary curve to use polar co ordinate for volume .

Q: Determine the values of a where the function f (x) is not continuous. Label each discontinuity as…

A: Given function is continous for all real values of x.  As per given instructions,  Enter NA in both…

Q: (a) Find the curvature and the radius of curvature of the curve r(t) = 3 cos ti + 4 sin tj + tk at t…

A: Given curve is r→t=3costi^+4sintj^+tk^. We have to find the curvature and the radius of curvature at…

Q: Q/६ using integrat test: n - 14 (n+1)(n-4) Test the following series

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Q: 3. Solve the following differential equations using Laplace transforms: d³x d²x dx + + dx d²x b. +x=…

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Q: 4. Find the length of the curve defined by Ả(t) = (3t+1, 4t³/2, 4 – 3t²) from the point (1,0, 4) to…

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Q: What happened to the absolute value of e^-|2t|?

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Q: The number of bacteria in a container is given by an equation, Q(t)= Qoekt, where t is measured in…

A:

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We will sketch the region and also find boundary curve .Then convert every equation into polar curve…

Q: f(t) = 1, 0≤t≤ 0, <1<T f(t+T)= f(t), t≥ 0. T72 - T 3T/2 - 2T

A: This is a problem of Laplace Transform.

Q: (D² - 4D + 4)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: d²y (a) Solve the differential equation +y dx² y'(0) = 0. got up (4) pap = sin(x) + cos(x) with y(0)…

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Q: 5. Neil is traveling on a road at 60 miles per hour when he slams his foot on the brake pedal in…

A: S=(30Dfn) Here, S is speed of vehicle in miles/hour. 30 is constant.  D is skid distance in feet. f…

Q: Let Xn, Yn be any two sequences. If XnL, YnM, then Xn YnL M

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Q: c. 7 in Z10 under multiplication

A: Solution

Q: 1. Evaluate the definite integrals using (a) integration, (b) trapezoidal rule, (c) the mid-ordinate…

A: Here we have to evaluate a Integration  :  ∫2612x-1dx                             ⇒12∫2612x-1dx…

Q: SOLVE THE FOLLOWING NON-HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS.

A:

Q: 4. Suppose A € Mn,n (R) and A³ = A. Show that the the only possible eigenvalues of A are λ = 0, λ =…

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Q: 3. Let R be the region below bounded by the parabola y = 4-x²2 and the lines 3.x - 2y +3=0 and y =…

A: The region R is bounded by the parabola y=4-x2 and the line 3x-2y+3=0 and y=0. The region R is…

Q: xx/3 5 SS S 3p² sin o dp do de. 00 seco Evaluate the spherical coordinate integral

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Q: 8. Which one of the following statements is NOT true about this graph? B E Figure 1 OA) There is a…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Q6: Find the Fourier coefficients and Fourier series of the function f(x) defined by THAXNO f(x) =…

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Q: 8. Let a be the plane that goes through the origin and has normal (1,2,3) and let 3 be the plane…

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Q: 1. For each equation, first find the general form of the solution, and then apply the given Cauchy…

A: Note: As per our guidelines we will solve only first question. If you want any specific question to…

Q: Which of the following is cyclic? Justify. a. The set of positive integers under usual addition b.…

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Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x&lt;0xx≥0. If we take x=-2, then f-2=2…

Q: Use multiple equation Newton-Raphson method to determine one of the roots of the following…

A: Given x2+3y2=10x-22+y-12=3

Q: 9. Let u AB and v = =PQ where A=(-4, 6), B = (3, 3), P = (4, 5) and Q = (-3, 8). Can you verify that…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

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Q: y" + 2y' + y = −e* [(− x² + 4x+3)cos x + (− x² + 4x + 3)sin x]

A: As per the question we are given a second order linear non-homogeneous differential equation. And we…

Q: Reparametrize C: R(1) = (¹-²³, Vēts, ²+1) using the arc length is measured from the point P (3, -,0)…

A: We are given a 3d curve in paramatrized form. And we have to reparametrize it using the arc length…

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given vectors are y=466−1, u1=1101, u2=−120−1 and u3=−1011. Now, the formula of orthogonal…

Q: C -9 -3-15 0 -7 0 -6 5. Let A = where c is an unknown scalar. " 0 7 2 13 0 40 3 (a) Without using…

A: Given :                      A = c-9-3-150-7   0-60   7   2  130   0   03  Now for characteristic…

Q: 1. Is the following axiom system consistent/dependent? a. There are six points. b. There are three…

A: from the given statements: S1: Let there are six points A,B,C,D,E,F S2: there are three 3 point…

Q: 22. Find the moment of inertia form the given figure. 3

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Q: 1. "Let fE a[a, b]. For x E (a. b), set F(x)=ff. Prove that F is continuous on [a, b].

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