In each of Problems 13 through 20, verify that each given function is a solution of the differential equation. -13- y"-y=0; y₁(t)= et, y₂(t) = cosh t

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

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Q: We have a semigroup (M, *), where M = R- {k} a a b = a + b-kab. Find also that, (M, *) is a group.…

A: Semi group will be a group if there exist an identity element and every element has inverse.

Q: 3. A small metal bar, whose initial temperature was 20° C, is dropped into a large container of…

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Q: 5. In how many ways can 7 boys be seated in a circular order?

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Q: y(2)=3/0 y (2) = 3/1 below. Use the graph to estimate the values of yo and 1. 5 "

A: Follow the steps.

Q: For circuit M, find out what orders its nonzero ones have elements and find their divisors of zero,…

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Q: 1. Let : Z25→ Ss be a homomorphism such that o(1) = (12468). (a) Find (22). (b) Determine kero. (c)…

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Q: 4. Use the Divergence Theorem to evaluate the flux integral JS, F-ndA over the surface of a…

A: Given that, F=(3xy3z5,3y,-xy3z6)F⇀=3xy3z5i^+3yj^-xy3z6k^ We have to evaluate the integral  ∫∫sF⇀.ndA…

Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

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Q: If the simple graph G has v vertices and e edges, how many edges does the complement of G have? Ⓒa.…

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: 4.In the mathematical Equation of Linear Regression y-a, + a₁x+e₁ (ao,a₁) refers to a. (Y-intercept,…

A: To find which of the following option is correct :-

Q: 53 ²5 dt +x³ 3 tcost

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Q: Find a general solution to the differential equation. y'"' + 2y = 2 tan 2t 3t -1/1e³t 4

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Q: a) Compute these two integrals shown below using one application of trapezoidal rule and Simpson's…

A: we have to calculate given two integral using Simpson's rule and trapezoidal rule.

Q: (b) How many partitions does the set [10]

A: This is a problem ofcounting.

Q: Determine the antiderivatives of the following functions: 1. f(x + 1)100 dx 2. f(x² + x)¹0 (2x +…

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Q: 2 x² = 3y² +4z²

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Solution.  In cylindrical coordinates  x=rcos(θ)  y = r sin(θ)  z = z  0<= r <=1, 0<= θ…

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

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Q: Write down the first four terms of the Taylor series expansion of the function x(t-h) about x(t),…

A: This Problem is solved using concept of Taylor series theorem.

Q: - 1. y(4) + y = 0, where y(0) = v'm "(0) = 0, y""(0) = 1

A: Follow the steps.

Q: 1-4 3. Let A = 3 0 and define T(x) = T₁(x) = Ax. [1 2 (a) Find T(x), the image of x = [4] under the…

A: The question is based on topic linear transformation in linear algebra.

Q: Using the Laplace transform solve ²+2 + 2q = tH (t-3), where q(0) = 0, q'(0) = 0.

A: 1l

Q: For x = x(y + 3), y = y(x - 1), find the trace of the Jacobian at the fixed point x = 0, y* = 0.

A: Given system is x˙ =xy+3y˙ =yx-1 Fixed point :  x* =0, y*=0   Take   x˙ =fx, y,    y˙ =gx, y   then…

Q: (b) compute an estimate of x(1) for the initial-value problem dx 1+x x(0) = -2 dt sin (t+1)'

A: Problem is solved using second-order predictor-corrector method.

Q: Prove or disprove the relation C on Z defined by C = {(x, y): x=y (mod 5)} satisfies the two…

A: I just used the definition of congruence and divisibility

Q: 7. Set-up the triple integral for the volume of the solid S enclosed by the paraboloid z = 4 + x² +…

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Q: Your parents helped you buy a car. You were supposed to pay then back $2000 sixty days ago and $1800…

A: Solution:-

Q: Write down the first three terms of the Taylor series expansions of the functions dx (t-h) and dx dt…

A: Problem is solved using concept of taylor series theorem.  Thaylor's theorem states that:

Q: 1 6. Suppose A is a 3 x 5 matrix. Find a 3 x 3 matrix E, such that EA is the result of multiplying…

A: 6. Taking a 3×5 matrix A as                  A=a11a12a13a14a15a21a22a23a24a25a31a32a33a34a35

Q: Find the standard equation of the hyperbola which satisfies the given condition: Foci (-4,-3) and…

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Q: 5. Show that T is a linear transformation by finding a matrix that implements the mapping. Note that…

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Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

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Q: 3. (a) How many positive integers divide 10!. (b) How many partitions does the set [10] = {1, 2,…

A: Given, set={1,2,3,4,5,6,7,8,9,10} we have to calculate number of partitions required in which each…

Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: ƒ(a + x) = f(a) + Σo_ x² d(n)f(x) an)f(x) = f(a) + xƒ'(a) + —ƒ"(a) + ¹ƒ''(a) + ·· . =1 n! dxn x=a By…

A: The Taylor series about a point a is already given . We will use this for f(x) = sin x and a=45°

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: given curves  0≤x≤10≤y≤1-x20≤z≤4-x2+y2

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Consider the given solid R, 0≤x≤10≤y≤1-x20≤z≤4-x2+y2 So, the diagram of the region is shown below,

Q: Prove: If A, B and C are sets then AU(BOC) and ((C- (AUB)) (B- (AUC))) are disjoint sets.

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Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: X[k] =a* [u[k] - u[k − N]]

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: We can solve this using given information

Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

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Q: Complete the table shown in Figure 2 for the N = 5 data points, and hence solve the following system…

A: Solution

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+32) sin(t)dt

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Q: y (4) + y" +y" = 0, where y(0) = y'(0) = y″(0) = 0, y″(0) = 1

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Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

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Q: Let X = {6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 zc N₁ x + z = y), where…

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Q: Which of the following functions are of exponential order? (a) t³ sint (b) 100e49 (c) e¹³

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