Find the volume of the solid generated by revolving the area bounded by x – y? + 2y – 1 = 0 and X - y – 1 = 0 about y = -2.

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A: We are given e+f = 1T,e2=e,f2=f and e.f=0T where T is the rings containing elements e,f both not equ...

Q: A conical funnel is 200 mm tall and has a maximum diameter of 150 mm. Water is flowing into the funn...

A: 1st we will draw figure and using geometry find relation between radius and height of the funnel . T...

Q: uments a, b, c or d below) A. Modus ponens B. Modus tollens

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Q: sin-lds The antiderivative of -x sin sin-x+C A) True B) False

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Q: Given the vector function: 7(t) = (e', e' sin(t), e cos (t)) Determine the equations of the normal p...

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Q: Mathematical induction. Use mathematical induction to prove that 2^n > n^2 for any integer n > 4.

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Q: Use the method of Variation of Parameters to solve the following DE: у" — у %3D2х2 —х— 3.

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Q: Find the chromatic polynomials of the following graphs (a) (b) (c)

A: Since you have asked multiple questions, we will solve the first one for you. If you want any specif...

Q: Given f(z) = (y + 1) i(x³ – 3 x). Find the set of all points zo = xo + i Yo where f is differentiabl...

A: f(z)=(y3+1)i(x3-3x) f(x+iy)=(y3+1)i(x3-3x) f is differentiable if ux=vy, uy=-vx  

Q: Consider the differential equation: y" – 6y' + 9y = (x + 1)e3* Determine the function „, for the par...

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Q: Derive a composite matrix that transforms a square ABCD with coordinates A(0,0), B(1,0), C(1,1), D(0...

A: As per the question we have to find the affine transform which will transform the points A,B,C,D int...

Q: A cycle in a simple graph is a closed walk of length greater than m. What is the value of m?

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Q: Solve the differential equation y2dx - 2(y4 - x) dy = 0. If y = 1 when x = 3, determine x when y = 2...

A: We are given the differential equation as y2dx-2y4-xdy=0, y(3)=1. Here, M=y2 and N=-2y4-x. Now,     ...

Q: Find the value of f' (E) if f(x) = 2sc3x 15 in Your answer

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Q: +y²)dx + (x² – y²)dy where C is the triangle with vertices (0,0), (2,1) and (0,1).

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Q: Let A = {x | 5x + 1 E Q} and B be the set of all even integers. Prove that A and B have the same car...

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Q: Q2 Let A be a 4 × 5 matrix. If the column vectors a1, a2 and a4 are linearly independent and satisfy...

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Q: If F(x,y) = 3y. i+5x-j, find SF . •dr where Cis the straight-line path from (0,0) to (1,0), to (0,1)...

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Q: A point in the complex plane with both coordinates rational is called a rational point. The set of r...

A: Please find the answer in next step

Q: The values of C, and C2 so that y(x) = C, e²x + C, e-2* satisfies the following conditions: y(0) = 1...

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Q: A certain phenomenon has an initial value of 12 and grows at a rate of 8% per year. Give an exponent...

A: Given Initial value =12 (Grows rate) r=8% per year  

Q: 8 Find the inverse Laplace transform of F (s) = f (t) = 8"H(t) (Write eab as exp(a*b)). %3| ||

A: We have to find laplace inverse of F(s)

Q: Let Ax = b be a linear system whose augmented matrix has a reduced row echelon form given by: 1 0 -1...

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Q: I will accept a package whose combined height and perimeter of the base are at most 140 inches. Use ...

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Q: 1) A particle is in a one-dimensional box of width L. Find the probability that the particle is in t...

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Q: Exercises 41 O and 42 0: The graph of a polynomial f(x) is shown in the figure. Estimate the integer...

A: The graph of the polynomial function fx is given as follows: The graph touches x-axis at about x=-2...

Q: 5. For n > 0 let F(n) be the number of n xn matrices with entries 0 or 1. We define F(0) = 1. (a) Fi...

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.

Q: DÒ NOT include spaces in between characters. * Given F(x)=f(x)g(x) and f(2) = -3, f'(2) = 4, g(2) = ...

A: We want to find F'(2).

Q: of the ):305t=2 ;find at t:2 the area riDole

A: Given radius function is  r(t)=30t+2

Q: The following graph is k-edge connected. What is the value of k?

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Q: (d) How many subsets V of A are there so that 1 € V or VOB= Ø? Explain.

A: This question related to set theory . Solution is given below.

Q: find the area of the surface obtained by rotating the curve along the x-axis

A: Surface area along x-axis

Q: maximum Rate af change f faxiy)にろメこかyー2メり at (11) and the direction in which it occurs?

A: The maximum rate of change of F at (1,1) = 17 The direction of maximum change of F = <4,1>. Th...

Q: Evaluate f'(-2) if f(x) = x* – 5 + x=2 + 4x¬4.

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Q: 2. The equation of a curve C is given by y3 +y = x* + a° + 8. (a) Using implicit differentiation, fi...

A: We have to find slope of the curve at point P.

Q: Consider the initial value problem: y" – 2y' + 10 y = 0 y (0) = 0, y' (0) = 2 %3D Which of the follo...

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Q: Evaluate F dr, where F = (-6x²,9y², –12z?), %3D and C is the curve: 7(1) = (t, t? – 2r°, 21' – 1²), ...

A: Differentiate the expression of r→(t)=t,t2-2t3,2t3-t2 to obtain the expression of dr→. The power rul...

Q: Which of the following best describes the function below? _[3x² ifxs2 S(x) =- |x³ if 2<x A. Continuo...

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Q: Question * A natural cubic spline S(x), for a function f (x) is defined by x2 ax3 4 2' 1<x< 2 3 S(x)...

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Q: 1. Solve the given IVP: у(@ + 8у" + 16у %3D 0; у(0) 3 — 1, У (0) %3 5, у"(0) — —8, у" (0) — — 28.

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Q: Evaluate F dS, S where 4 F(x, y, z) = (3y, -2x, -), and S is the surface that is composed of the par...

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Q: Plot the point given in polar coordinates. (-3.-=) A/2 A/2 n/2 7/2 Find three additional polar repre...

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Q: Q3

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Q: A potato is launched vertically upward with an initial velocity of 123 ft/s from a potato gun at the...

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Q: 4. y (3x3 + 1)(-4x2 - 3)* (r3+4)5 5. y= 3xt-2 %3D

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Q: Which of the following is true about ƒ (x) = [x]? A. The function is continuous at r= 0. B. The func...

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Q: 2. Solve the initial value problem, y"(t) + 3y'(t) + 2y(t) = g(t) , y(0) = 0 , /(0) = -2

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Q: The exponential function N = 500 × 0.74t, where t is measured in years, shows the amount, in grams, ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: (x + y + z) for th ons ons

A: