The object shown in the figure is axially symmetric and its curved surface is described in cylindrical coordinates by r = 4 – z for 0 < z < 12. ~ 3 Calculate the volume of this object.

Q: 3. Determination of integrating factors: 2y(x+ y+2)dx+(y² –x² - 4x -1dy = 0 4. Substitution…

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Q: 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: Given, three positive numbers whose sum is 18 and such that the sum of their square is as small as…

Q: Let A = [ 3*0 .8 = [ Jand C = [14-0 Jand c = [1* | Find the matrix X, if 8+0 -10 A? + 3X =C |B|

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Q: Calculate the curvature and radius of curvature of the graph of the function y = xe

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Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

A: Use the given differential and initial conditions.

Q: Relationship Y= (ax+bX) - Find the Linearizationof Nonlinear

A: This is the problem of application of differentiation.

Q: Relationship y= (ax+bX) - Find the Linearizationof Nonlinear

A: This is the question from linearization techniques. It involves the application of differential…

Q: Find the laplace of each f(t) 5. 2t'e 4t

A: Solution

Q: I. What is the use of Fourier Series? II. Why do we take Fourier Transform?

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Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. A) y(t) = sin…

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Q: a. Write down the 5 nonzero terms of the Taylor series around the point x=0 and find f(2.1) (4…

A: This is a problem of Taylor approximation.

Q: .Use the Monotone Convergence Theorem to show that the (2n)! {a)" is convergent.

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Q: . ndS over the 2 = 9, where F = is the unit outw

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Q: What is the general solution to the differential equation y- (9 - + = 0 ? dx In(Ay – 2) = Ax +B y2 =…

A: We have given a differential equation ,  yd2ydx2 - dydx2 + dydx = 0 This can be written as ,  y y''…

Q: Use Laplace transforms to solve the initial-value problem. x'' + 4x = cos t;   x(0)=0, x'(0)=0

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Q: Find the solution. dy x3 – 2y dx A y= 3x3 B 2y2 5 y3 D xy= + + II

A: To find the solution of a given differential equation first we will convert it into the form of…

Q: A function g whose domain is R, such that g is not continuous at 0, but g◦g is continuous at 0 what…

A: This is a problem of function.

Q: What value of x is in the solution set of 2x – 3 > 11 – 5x

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Q: Find the solution. (у -х + ху сotx) dx + x dy %3D 0 A xy sinx = c + sinx - xcosx xy tanx = ccosy…

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Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

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Q: Find the Laplace Transform of h(t) = t? sin(2t) = ='s 3s2-4 A H(s) = (s2+4) 2 482 – 3 B H(s) =…

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Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y(t) =…

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Q: d [dy dx [dx. What is the general solution to the differential equation бх + 3 ? y = 2x3 – 2x2 + Ax…

A: Solve by integrating.

Q: Find the solution. dy y dx A y = 8 8 (B y = 4 y-2 8 (D y = 8.

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Q: Evaluate the integral shown using Simpson's 3/8 Rule with 30 panels. 12 ) dx 4arctan O 32.52059525…

A: Given integral is ∫2124arctanx6dx

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: The given point is 4,-3,5. The given vectors are 2,6,1 &amp; 1,3,-5. The equation of plane having…

Q: 4xy V = -2xz XZ

A: relationship between voltage (V)  and uniform electric field (E) can be given by  E→=-dVdr=−∇→V…

Q: Integrate f(x) from x = 2 to 8 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000 + 24583x –…

A: We have fx=5000+24583x-7418x2+766x3-31x4+0.44x5 and x is from 2 to 8 The formula to integrate…

Q: . Describe ALL transformations from the parent function f(x) = x² to the function g(x) = -(x + 3)´ +…

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Q: In(n+ 2) n+ 2

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Q: the matrix -2 -3

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Q: х — 3 2. Graph the function f(x) = Identify asymptotes and holes in the х2 — 4х + 3 graph. Answer:…

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Q: Determine and draw the graph of the following equation in R3 : z = 1 – e® Also show the traces

A: A quadric surface is a graph in the three dimensional space ℝ3. The trace of a quadric surface is a…

Q: Find the area of the triangle with vertices P(1,5, -3), Q(0,0,0) and R(4,6, 1). NOTE: Enter the…

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Q: 1 In solving the antiderivative of f(x) = 2 – sin(x) by miscellaneous substitution, the substitution…

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Q: Prove the following using the rule of replacement and rule of inference. Let C = set of all students…

A: This is a problem of Logic.

Q: 16. Prove that an integer (a,-1an-2 · . . ao)10 is divisible by 11 if and only if ao + a2 + a4 + . .…

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Q: Using MOSA find the polynomlals that will approxlmate the solution to: y'= x2 + y; y(1)-1. y1(x). A…

A: y'=x2+y;    y(1)=1 f(x,y)=x2+y;    y0=1

Q: Match the following definitions to the correct terms.

A: # as per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: Find the solution. dy 2y dx A y = x(x+c) B y = x²(x-c) -2 y = x?(x+c)? O y = x'(x+c)³

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Q: 10. Suppose A is the n x n zero matrix (where all entries of A are zero), describe the solution set…

A: We have to find the solution set of system.

Q: Find the series solution of (1-x2)y’’+2xy’+y=0 using the Frobenius method

A: We have a given differential equation ,  1 - x2y'' + 2xy' + y = 0 Let , y = ∑n=0∞ anxn  be power…

Q: b) Given a linear system as below х — 2у + 3z %3 9, —х + Зу %3D — 4, 2х — 5у + 5z %3D 17 Find the…

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Q: Express the sum of integrals as an iterated integral in polar coordinates: r2/3 r4+V16–x² x dx dy +…

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Q: 2. Another key theorem is de Moivre's Theorem which states: (cos 0 + i sin 0)" = cos no + i sin ne.…

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Q: 9. Find all integers x, 0 < x < n, satisfying each of the fol- lowing congruences mod n. If no such…

A: Q (d),(g) asked and answered.

Q: When the insured knows more about their circumstances than the insurer, there is O propitious…

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Q: Find the Laplace transform of x(t) using differentiation theorem. d2 d a1z x(t) + 6x(t) + 5x(t) =…

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Q: 2. Find the power series representation of the following functions. And then write out their I.O.C..…

A: we have to find the power series representation of following f(x).

Q: Breathing is cyclic, and a full respiratory cycle from the beginning of inhalation to the end of…

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