Write a rational function that has vertical asymptotes at x= 2 and x = -3, and a horizontal asymptote at y = 0.

Q: Question Let (X, B(R), u) be a Borel measure space. family of elements of B(R) such that An = Then,…

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Q: Consider the points A(-8, 0), B(4,0), and C(7,0). Find the coordinates of D if H(AB, CD).

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Q: Find the centre of mass of the 2D shape bounded by the lines y = +1.1x between x = 0 to 3.1. Assume…

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Q: s(1) = {" 0 1+ jwe ¹+jw (-w+j)² Given: f(t) a.) -t te -1<t<0 otherwise

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Q: Inverse Laplace F(8) = 4₁+3 (8-1) (5²+1)

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Q: Solve the following using Cramer's Rule 2x - 4y + 5z = -33 4x - y = -5 -2x + 2y - 3x = 19

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Q: 1-1 85 Determine angles a, banda

A: To find the given angle a,b,c . When we have l1 is parallel to l2 .

Q: Question 3 John went to the supermarket to check on a few items. The table below shows the…

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Q: Angela currently owes $6,000 to a friend who is charging her interest of 2.80% p.m. She is required…

A: Given information Value of loan today=$6000. Rate r=2.80% p.m=0.028 p.m Let us assume the equal…

Q: Find the inverse of the function on the given domain. f(x) = (x−5)^2, [5,00⁰) f-1(x) =

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Q: 3/ Find Valke of integral Sx dx

A: Value of the integration

Q: Let B be the sphere x² + y² + z² = 1. The volume of the portion of B contained in the first octant…

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Q: True or False 19 (a) By the law of quadratic reciprocity, (3) = (²9). 19 (b) If a is a quadratic…

A: We will use the basic knowledge of quadratic residue and Legendre's symbol to answer this question…

Q: Choose all the angles that must be congruent to 23 assuming that I, and le are parallel 4₁ 1₂ 4 3 6…

A: Line l1 and l2 are given the parallel lines and a third line intersected l1 and l2. Then by the…

Q: Let c be a positive constant and a be a variable positive parameter, with a > c. Consider the family…

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Q: the value of a and b. aº 55° bo 45°

A: The given lines are parallel Therefore use the result pair of alternate angles are equal

Q: Let f: A→ X X Y be defined as f (a) = (f₁ (a). f2 (a)) each a ≤ A, Then f is continuous if and only…

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Q: 8. ) Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…

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Q: Find two linearly independent solutions of 2x²y" - xy' + (−3x + 1)y = 0, x > 0 = x¹¹ (1 + α₁x + a₂x²…

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Q: P21. The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

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Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, mEnm-n is even. Is this an…

A: Here, E is an equivalence relation on Z. To show this,  we will show that E is reflexive relation,…

Q: 27. f(1) = 1 + e 29. f(1) = (1 + e²¹)² 31. f(t)=41²-5 sin 3r 28. f(t)=1²-e9¹ +5 30. f(t)=(e-e¹)² 32.…

A: Laplace transform of the function f(t)

Q: Given: vector-valued function Ř(t) = (3 cos 2t, 9t, −3 sin 2t) 1. Reparametrize R using the directed…

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Q: Please answer the subparts d and e. thank you!

A: Solution

Q: 1. Solve the linear system using Jacobi and Gauss-Seidel Method 2x − y=2 X - 3y +z = -2 -x+y=3z = -6

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Q: Solve the simultaneous linear equations using Inverse Matrix Method. 2x+y=7 3x-y=8

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Q: 6. Find the volume inside the paraboloid z = 9-x² - y², outside the cylinder x² + y² = 4, above the…

A: Relation between rectangular and polar coordinate  x=rcosθy=r sinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(2,0,2) on the…

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Q: Use the following methods to solve for the root of the equation f(x) = xe^* – sinx Solve for the…

A: Given function is fx =x e-x -sin2x Initial guess:- x1 =3,  x2 =3.5

Q: 7. Let S = [0, 1] × [0, 1] and ƒ: S → R be defined by f(x, y) (2x³+y², 10, Show that f is integrable…

A: Follow the steps.

Q: The region that lies inside the cardioid r= 7+ cos 8 and outside the circle r=7 is the base of a…

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Q: Find the sum of the series. 5η Σ gn! n = 0

A: The idea is to use the power series for the function e^x. The detailed solution typeset in LaTex is…

Q: (c) Let J be the linear transformation from R² → R² which is a reflection in the horizontal axis…

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Q: Find the general solution of the following Nonlinear first-order ODE.(show the detail of your work).…

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Q: bet FCK and KCL be field extensions, TA

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Q: At 11:04 pm, you find a secret agent murdered. Next to him is a martini that got shaken before he…

A: Please see the attachment

Q: Use Method of Variation of Parameters: [D²-8D+ 16]y = e4x sec²x

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Q: Let B be the sphere x² + y² + z² = 1. The volume of the portion of B contained in the first octant…

A: To find the volume in the first octant :-

Q: b) Consider the following metric: ds² = e²A(r) dt² - e²B(r) dr² — r² (d0² + sin² 0do²), with A(r)…

A: Solution :Consider the following 4D-curved spacetime metric.ds2 =…

Q: 2. Use Method of Undetermined Coefficients: y" - 2y + 5y = 4e* cos2x + x²

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Q: 8) An airplane is on a heading of 065° at 350 km/h and an 75 km/h wind is blowing from 310⁰.…

A: 0

Q: 8. Construct the graph of the following Matrices: Adjacency Matrix 1 2 3 3 4 1 0 1 10 1 2 10 1 1 30…

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Q: Solve the linear system using both gaussian and gauss-jordan elimination 2x₁ + x₂ 3x3 = 4 + 2x3 = 10…

A: Gaussian elimination method is used to find the solution of the system of linear equations using the…

Q: A B 3x-1 (1-x)(2-3x) in the form + - x 2-3x, where A and B are integers. (b) (i) Express 3x - 1 (ii)…

A: Binomial expansion

Q: 4. Evaluate the following limits. 2* a. lim 3x² -3/x e b. lim x+0 x² 2 In5 x c. limx→→+00 x² 1000 In…

A: This question is related to topic limit of function.

Q: 16 3. The value of 9 B) 4. The range of the function h(x)=0.5f(-x)+2 where f(x)=4* is: A) {y=R|y>2}…

A: 3. We want to find value of 169-0.5 As 169-0.5 = 9160.5 = 916 = 34 Hence Answer: A)   34

Q: a) u=r³-3ry² + 2xy + x, D) u= x² - y² +5, c) a= sinh rsing, d) u = e(y cos y + x siny), e)…

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Q: Find the least-squares solution of the system 4/3 x 4 2 -2 4 -27 2 4 12 [E] -20

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Q: Use the Simplex Method to solve for X1 and X2: Objective function: Maximize z = 4x₁ + 3x₂ Subject…

A: Please see the attachment

Q: laplace transform of f(t) = vin st sin ut

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