Factorize the matrix into LU decomposition. [0 5 41 A = 5 1 2 1 2 3.

Q: Find the solution. y'- y = -xyl/2

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Q: Let Dibe each o the fillowing whepar pmetrically. Be conte po, wing the formaliam you have practiond…

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Q: Consider the relation being described by the following arrow diagram. Which of the these statements…

A: (i) It is given that ;      S = {6, 7, 8}  and  T = {2, 4, 6} And the relation between S and T is :…

Q: b. 3 rows

A: the given rectangle is  draw a horizontal line as drawn in red Now there are 8  therefore one…

Q: We study the residue of functions of the form g(z) = 8 in a domain D. The singularities of g(2)…

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Q: 15

A: the given equation is -15e=3 solving for e multiply both sides by e -15e×e=3×e -15=3×e

Q: Solve the equation 1-x = 0.5 using the initial search region [0,2] and a maximum acceptable 1+x2…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

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Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 A y = x-2(1 + el+x) B x = y-(1 +el-x) © y =x-'(1 -…

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Q: 2. Alanna plans to add an extension on to her home. She applied for a loan of $30 000. Loans are…

A: Given: Loan amount = $30,000Interest rate r = 8.9%pa or 0.74% per monthPeriod n = 5 years or 60…

Q: i. Look for or create your own linear transformation T: R" → R". where n, and m are both R³, both…

A: In this question, we have to find the examples of linear transformations : (A) T : ℝ3→ℝ3(B) T :…

Q: Use the Laplace transform to solve x'-2y'=1;x'+y-x=0;x(0)=y(0)=0

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Q: Of a lot of 10 items, 2 are defective. The number of samples of 4 containing (1) no defectives is…

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Q: Find the area of the region bounded by y=x^2-6x+5, y=0 and the lines x=2 and x=5

A: We have to find the area of the region bounded by y=x2−6x+5, y=0 and the lines x=2 and x=5. The…

Q: Solve the variational problem 8 Ix (y ? +2y (x+y)] dx = 0, given y (1) = y (2) = 0. %3D

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Q: In how many ways can an employer select two senior staff from seven candidates, and three junior…

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Q: 3.1. Analyse and evaluate the role of problem-solving in the teaching and learning of Mathematics in…

A: Mathematics is not only about solving problems. The concept of solving a problem is a much more…

Q: 10. Let ø: Q(V2) → Q(v2) be the map given by ø(a+bv2) = a-bv2. Show that 6 is a Q-linear field…

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Q: Find the volume of a cone with a base diameter of 10 ft and a height of 11 ft. Write the exact…

A: Given that the diameter of the the base of a cone is 10 feet and the height of the cone is 11 feet.…

Q: Find the volume of a cone with a base diameter of 7 yd and a height of 6 yd. Write the exact volume…

A: Note: We have the volume of a cone  V=πr2h/3 cubic unit. r is the radius of the base and h is the…

Q: 04 Let f(x, y) = –2y² + 8xy. Assume f is subject to a constraint 2 + 2y = 24. At %3D which one of…

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Q: Water is running out of a conical funnel at the rate of 1 in3/ sec. If the radius of the base of the…

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Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

A: The solution of the problem is given in the next steps.

Q: undetermind cuefficien + चग-১৭४e 8 -22 -4

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Q: Consider the permutation (t aqgblvxh)(n skw fue)(ycodjr)(p z m i). (a) Showing your working, and…

A: The complete solution is in given below

Q: 4. Show that V2 ¢ Q(V3) and Q(/2, v3) = Q(/2+v3). Hence find the mmp of V2+ V3 over Q.

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Q: Find the solution. (4D³ + 4D² + D)y = 0 A y = c,+(c,+cx)e/2 /1- y = c,x+ (c,+c,)e½ © y = c,e-/+…

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Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Use the Laplace transform to solve x'-2y'=1;r'+y-x=0;x(0)=y(0)=0

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Q: How.L Find minima, bmakima and Saddle paints for the functionss foxy) -9x -4 xy 3- %3D f Cx,y) = 2…

A: (3) the given function is fx,y=9x3+y33-4xy Now we have to find ∂f∂x,∂f∂y,∂2f∂x2,∂2f∂y2 and ∂2f∂x∂y

Q: Given y4) – 9y" – 81y" + 729y' = t² – 10 +t sin t, determine a suitable form for Y(t) if the method…

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Q: y - 3y + 2y = 3e* + 2e2*

A: To solve the given Differential equation.

Q: 2. Consider a natural cubic spline model with two knots at ci and c2 given by y = Bo + B1r+ B2(r -…

A: Given, spline model, y=β0+β1x+β2x-c13+β3x-c33+∈                         β2+β3=0  ,  β2c1+β3c2=0…

Q: Which graph represents y as a linear function of x ? A y

A: Given: y is a linear function of x.

Q: b) Let T : P1 –→P1 defined by T(ax + b) = (4a – 26)x + b – 2a. V = P1, (p(x), q(x)) = Lo…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Determine the last three digits of 202220232024 + 20072002 + 2019

A: ............ 684 So last three digits is 684

Q: 5 Compute the Surface area f obtained by revoluing the line y=x around the y-aris. a cone whichü

A: To find the surface area of cone which is obtained by revolving y=x revolved around y-axis.

Q: Perform Gauss-Seidel Method to the given system of linear equations. using x, = 0, continue…

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Q: dy 2х-у-3 dx х+у-2

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Q: Problem 3: Consider the IVP y" + ay + by = et, _y(0) = 1, y'(0) = 1. 1. Write the second-order IVP…

A: Given y"-y'-6y=e3t, y0=1, y'0=1. Substituting y'=z and y"=z', we get z'-z-6y=e3tz'=z+6y+e3t.

Q: For what Vatuer of the Constant (k) that the funetion fayt=x'+kxy+y will have a- Saddle Point…

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Q: (Use decimal notation. Give your answer to five decimal places

A: Given,            f(x)=11x+15

Q: Question 25 Find the solution. (D2 + D - 6)y = 0 A y = c,e-+c,ez -3x -2r © y =c,e+c,e D

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Q: Find graphically approximate value of the root of the equation an 3 – x = e* - 1.

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Q: G.L.P for ARC2): Xe= X- li Xe- + la Xe-a+ ee Find the General Linear progression for AR(2). Please…

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Q: 11

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Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx