1-x Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line : 2+3 =y+1= 3 2 Find the intersection of and the plane II: 2x +2y-z + 3 = 0. Find a set of parametric equations of the line passing through the point P and perpendicular to both u and l.

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

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Q: (D³ + 4D² +9D + 10)y=-24e-* when x = 0, y = 0, y'= -4, y" = -10 ANSWER: y = e-2x + excos (2x) -sin…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan x)…

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Q: 8x Show that the three functions: f₁(x) = ex-8, f₂(x) = e³x, f(x) = 4(2x-2) are linearly dependent.

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Q: III. Let S be the quadric with equation 4x² − (y − 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Given: 4x2-y-32+4z2=4 To find: Plane

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Q: (d) The Cauchy problem u, + 2 uy = 0, u(x, y) = x² on y = r has: (A) a unique solution (C)…

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Q: B = 0 -2 12 4 −1 -1 3 4

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Q: Let C be the parametric curve defined by fa(t)=t²-t-6, y(t) = 4t³ + 3t² - 6t. Determine the point/s…

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A: To sketch and find the Laplace transform of the given break function.

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A: Given,C1 : r =2-cosθ  When θ =π2r =2⇒(r, θ) =(2 , π2)

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A: The following formulae are used to find the Fourier coefficients of the function fx on the interval…

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Q: Let f(2)= = csc(TZ) 22 Determine all isolated singularities off and find the residue at each…

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Q: Find the rank of A 1 2 3 A = 149 1 8 27 02 0 3 01

A: Rank: The rank of an m×n matrix is r if the number of linearly independent columns of the matrix is…

Q: Q1) Consider the group Z10X S5. Let g = (2, (345)) € Z10X S5. Find o(g). T LOV

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Problem 25. Find the Laurent expansion of f(z) = 1/[2(2-1)(z-2)] in i) 0 < z <1 ii) 1 < 2 <2 iii)…

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Q: Given the polar curves: C₁:r = 2 cos 0 ग 2 A(2,0) C2 B(0,0) C₂:r = 2 cos 30 Find the Cartesian…

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Q: Let f: MM' be an R-module homomorphism, then

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Q: d'y d³y - dx5 dx3 = 24.

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Q: Ex: If w = f(x, y, z), x = x(r, 0), y = y(r,0), z = z(r, 0), find wr, we? aw ax aw ay 1 aw

A: Chain rule for total derivative

Q: 1. Find the inverse of A = 1 1 0 1] 1 2 3 1 1 using the Gauss-Jordan method.

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Q: Consider the surface S given by 22² +2y² = a + 1 = 0. (a) Find the equations of the traces of S on…

A: A quadric surface is a graph of the function of two variables x and y in the three dimensional space…

Q: y = −2x4 + 4ax³ - 5x² - 8x + 1

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Q: Consider the initial value problem u" + p(t)u' + q(t)u = g(t), u(0) = uo, u'(0) = u Transform this…

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Q: Identify and sketch the graph of the following SURFACES. 2 = √9-y²

A: We have z=9-y2 Since z is square root of 9-y2 so z is positive always. We can write z=9-y2 as:…

Q: 6) Let f(z)=(2²-z-1)7. If a²+a+1=0 and Im(a)>0, then find f(a). a) 128a b) -128g c) 128g² d) -128g²…

A: Note: As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: Consider the polar curves C₁ : r = 3 (in blue) and C₂: r = 2-2 sin (in red) and let R be the shaded…

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Q: Solve the differential equation using inspection method d'y d³y dx5 dx³ = 24.

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Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: u(x, y) and let f and g be twice differentiable functions. The al solution to the equation uy2r + 2y…

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Q: Consider S as a quadric with equation 4x² − (y − 3)² + 4z² = 4 1. Find an equation of the trace of S…

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Q: Consider the vector-valued function Ŕ(t) = a. Find the domain of R. b. Determine if R is continuous…

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Q: the area bounded by the parabola x = 4y - y²

A: Given parabola as, x=4y-y2 and y=2x.

Q: 8 Find the value of x in the triangle below: xo A) 30° B) 32° C) 28° D) 36° E) 34° 31 17 78° fanny…

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Q: Let C be the parametric curve defined by fa(t)=t²-t-6, y(t) = 4t³ + 3t² - 6t. Determine the point/s…

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Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

Q: QUESTION 3 A manager wishes to simulate 10 days of operation of an inventory system. The beginning…

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Q: f(x) = 3 - 2x and g(x) = ln (x - 1) then (image attached) = 1. -2 2. None of these 3. 3 4. 1

A: Composite rule is used

Q: Solve the differential equation using inspection method d'y d³y dx5 dx³ = 24.

A: We have given a differential equation ,  d5ydx5 - d3ydx3 = 24 This would be written as ,  yv - y'''…

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Let us start solving the problem step by step  Centroid of the solid generated  When x2+y2-2y=0…

Q: Let (R, +,-) ring with properties X.XX, XER Cindempotent properties), show! @a = 0, x ER (b) x. y…

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Q: S- f(t) -fet-a, t>a J O ),^<a cring ка Se Shifting

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Q: be a linear operator on a vector space V(F). If = 0, t ce oft and null space of t. Also given an…

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Q: Problem 25. Find the Laurent expansion of f(z) = 1/[2(2-1)(z-2)] in i) 0< < 1 ii) 1 < x < 2 iii) 2 <…

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Q: Find the solution to the system 2x-8y + 5z =-5 2x+y=z=12 -5x+3y+9z=-17 . using (a) Jacobi Iterative…

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Q: 9. xy(1+xy2) = 1 Ans: + y² -2 =

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