Q1. Find the point of intersection of the lines L, and Ly whose equations are given as: L₁: (x = 1, y = -1 + 2, z = 1+1), L₂: (Sy-z=9, x-2y+4-0), then find the plane determined by the intersecting lines.

Q: The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0…

A: Problem is solved using concept of matrix eigenvalue and eigenvector.

Q: Does the following series converge or diverge? 4√n Σ 10n +7n+7 n=1 The series diverges. The series…

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Q: Using integration solve for an elliptical plate, major axis 6 ft minor axis 4 ft is submerged…

A: Given that the major axis of elliptical plate is 6 ft That is 2a=6⇒a=3 And the minor axis of…

Q: =C2e(-2x) - 6xel-3x) - 5e (2x) + C₂e(-2x) + 6xe(-3x) + 5e (2x)

A: option A is correct answer

Q: (c) If F(t) is an antiderivative of f(t), explain why the function F(t) is always increasing. (d)…

A: Let us start solving the problem step by step... D) given f(0)=0 Total rainfall=150 mm Which means…

Q: 2.) 3x + 3z = 0 2x +2y = 2 3y + 3z = 3

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Q: 55² +25-4 (5+₁) (S+₂) (S+ 3) Taking Laplace transform

A: First do partial fraction then find inverse Laplace transform by using standard formulas as in next…

Q: 1. An electric utility company is required to run a cable from a transformer station on the shore of…

A: An electric utility company is required to run a cable from a transformer station on the shore of a…

Q: Find the general Solution of the following PDES ди -5X -3x 17 9 = 2 ди +u, ucx;o) = ду + 2 е ax…

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Q: 1. The diagram below shows the left hand side of the main window (one period) of a periodic…

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Q: 3. 6, 10, 16, 24,... Find the explicit formula for an, where n ≥ 1. 4. 1 4 7 10' 15' 20' ... Find…

A: Part (3):-  Given sequence is 6, 10, 16, 24, .....

Q: 4Z is prime ideal of 2Z, but it is not Maximal ideal of Z. To fo

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Q: Solve the following differential equations, giving y in terms of x. (i) dy da = e+2y, given that y =…

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Q: Find the general Solution of the following PDES -X • з Их + 2 Иу =0 U (x,0) = = 4 é 2 (3y-2x)/2 ans…

A: The given PDE is                        3ux+2uy=0, u(x,0)=4e-x To solve this PDE we shall use the…

Q: -2 Evaluate: £²³₁²[(x²-y²)²] du dt

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Q: Define a relation T on R by xT y if and only if (sin^2) x + (cos^2) y = 1. (a) Prove that T is an…

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Q: (d) F = R, V = {ve R²: v+v ≤ 0}; * (e) F = C, V = {ve C²: v² - 2v₁v2 + ² = 0}; (f) F= C, V = R²;

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Q: cos(2³) COS 2 sin 2 2 (A) z = 0) is a simple pole (B) z = 0 is a removable singularity (C) Resf(0) =…

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Q: A fireplace arch must be constructed in the shape of a semi-ellipse. The opening must be 60 cm high…

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Q: An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 +0.25x² where…

A: Note:- As per our guidelines, we can answer the first of this problem as all the methods are…

Q: a. S f (x² - 2x + 1) e²x dx

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Q: 5. The variables x and y are related by the following differential equation. dy x+y = dr x-y By…

A: Solution :

Q: (a) X1 2x22x3 + 2x4 + 4x5 2x3 - 2x5 X4 2x5 - 0 0 (b) 3x1 9x1 6x1 x2 + 4x3 3x2 + 10x3 2x2 + 8x3 = - 0…

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Q: Solve the initial value problem. 4 -4 4 y' = 3 -3 - 10 2 15 y, y(0) 1 = 16 14 6

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Q: in Column B. Column A 1. f(x-4)³dx 2. f(x + 1)³dx 3. f(x - 5)*dx 4. f(2x³-5) 6x²dx 5. f(x5 +1) 75x*…

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Q: The following problem involves an equation of the form -= f(y). dy dt Sketch the graph of f(y)…

A: Given differential equation is dydt=y36−y2,   −∞<y0<∞

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: Determine the values of r for which the differential equation y" - y = 0 has solutions of the form y…

A: Given differential equation is y''-y=0. We have to find r such that y=ert is solution of this…

Q: Solve the following systems of linear equations via matrix algebra: –3x + 2y – z = –1 6x – 6y + 7z…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: Evaluate the line integral ²da + a²y dy where C' is the rectangle with vertices (0,0), (5,0), (5,4),…

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Q: Does the following series converge or diverge? 4√√n Σ 3/2 10n +7n+7 n=1

A: Solution :-

Q: bordinates where R: 0 < aw the solid R. th 2 2

A: We will use relation between Cartesian and cylindrical co ordinate system to get integral  x= r cosθ…

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: the value of 0.02 g/gal. NOTE: Round your answer to two decimal places

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Q: The equation y = C₁e(-x) + C₂e(-2) is the general solution of:

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Q: 3 Linear Mappings In which of the following cases is the mapping T: VW linear (F= R)? (a) V=W = R²,…

A: Note:- As per our guidelines, we can answer the first part and it's three sub - parts  as exactly…

Q: From the equation of x² + y² + z² = 25 and inside the equation x² + y² = 9 Calculate the volume of…

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Q: A. Sequences 1. Given that a2 = 6 and a6 = 96 are terms of a geometric sequence, find a4. 2. Given…

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Q: So SAF+1° y¹/3 x7 +1 (Hint: Change the order of integration to dy dx.) Y dx dy.

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Q: QUESTION 2 The height, h, of a cylinder is two times its radius, r. If the radius of the cylinder is…

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Q: Q1/ Find the determinant of the matrix [2 4 11 38 5 16 2 41

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Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable…

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Q: 7.5) A car, initially at rest, begins moving at time t = 0 with a constant acceleration down a…

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Q: Draw a direction field for the given differential equation. Based on the direction field, determine…

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Q: classify the following PDES :- 227 дх2 -2 822 буду +2 82 дуг =X+3y 2 2 X ох Ихх - 2ху Иху +у Иуу e

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Q: 4 The area of the surface S = {(x, y, z) € R³ : z — 5 — z² - y², z ≥ 3} equals (A) 4T (B) (C) (D)…

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Q: R. Map A A= {(8, 13), (8, 9), (9,8), (9, 11 ), ( 11, 8), ( 11, 9), (13, 8), (13, 14), ( 14, 16), (…

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Q: if it is a simple ring. Let R be a field of real number. Then Z8 is a subfield of R. 4Z is prime…

A: According to rule of bartleby  we can solve only first question or three sub question of first…

Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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