Q2: Using the rules, convert the following differe ntial equation into exact, then solve x* ydx-(x' + y')dy = 0

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A: Let x represents the number of buses and y represents the number of vans. Given that, the rental…

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Q: Bolue : Frih"x t1= Sech",

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Q: Use the second Taylor polynomial P (x) for f(x) = x² + cos(x) about xo = 0 and evaluate f f(x)dx. 7…

A: Evaluate the integral, using second order Taylor polynomial

Q: The composition of one or more rigid motions and a dilation is called a(n)?

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Q: Define the sequence {b,} as follows: bo = 1 bn = bn-i +n for n > 1 %3D n(n + 1) Use induction to…

A: Given- Define the sequence bn as follows: b0 = 1bn = bn-1 + n for n ≥ 1 To find- Use Induction to…

Q: 2x+5y =9 x+2y-z=3 -3x-4y+7z=1 a) Setup the augmented matrix. b) Solve the system by Gauss-Jordan…

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Q: Find the minimal distance from the point -18 10 P = to the plane V of R' spanned by 3 4 -4 4 -4 and…

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Q: Example 1.4.1 As an easy exercise, check that you believe that lim [0, 1- 1/n] = [0, 1) n-00 lim [0,…

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Q: B = f (2) da where f (x) > 0 for all a.Which of these statements is true about B? Bis the average…

A: The function fx represents a curve and since fx>0 it can be concluded that the curve lies above…

Q: Find the Inverse Laplace Transform. F (s) = 4(s+a)¯ – 2(s + 3)¯ -1 O 2e t-e-3t O 2e-at e-3t - O 2…

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Q: {an} = {} 4 2

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Q: Calculate the area of the region bounded by the curves x = = y² and x-y=2. a. 11/5 sq units O b. 9/2…

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Q: What is the coefficient of xy³ when (2y-x)° is expanded by the binomial theorem?

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Q: z = e(4+j3) In(6230°)

A: We evaluate  z=e(4+j3)ln(6<30°)

Q: Use a Taylor series to approximate the following definite integral. Retain as many terms as needed…

A: Introduction: The formula of the Taylor series of the function f(x) at x=0 is given by,…

Q: (a) A large water jug is full of water. After 24 litres of water are added, the jug is full. What is…

A: A large water jug is 1/4 full of water .After 24 litres of water are added the jug is 5/8 full . To…

Q: 3. Sketch the graph of the following functions by transforming the graph of their parent functions.…

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

Q: Use Newton's (or the Newton-Raphson) method and find p3 with po = 0 for f(x) = cos(Tx) – x. O -80 4.…

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Q: Example 1.3.1 Check lim inf[0, n/(n +1)) = lim sup[0, n/(n +1)) = [0, 1). n-00 We can now give an…

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Q: 7. (a) A computer is programmed to choose an integer between 1 and 99, inclusive, so that the…

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Q: Find the interval of convergence of 00 (x - 9)" In (5n) n=2 (Use symbolic notation and fractions…

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Q: 1. Use Euler's method to approximate the solution of the following initial-value problem at t = y' =…

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Q: Suppose that AJKL is isosceles with base LK. %3D Suppose also that mz L= (5x-17)° and mz K=(2x+22)°.…

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Q: Example 1.4.1 As an easy exercise, check that you be- lim [0, 1- 1/n] = [0, 1 lim [0, 1 – 1/n) = [0,…

A: Limit is the approximate value of the function .

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x = 5 using a…

A: Given function is y=cosx. We have to find the first derivative of y=cosx at x=π2 using a value of…

Q: Let W be the subspace of R* spanned by the vectors uj = (1,0,1,0), u2 = (0, 1, 1,0), and uz = (0,0,…

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Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: 5 =A

A: Here we use the definition of eigen values to find this-

Q: Find the volume of the parallelepiped with the given vertices. (0, 0, 0), (0, 4, 0), (-3, 0, 0),…

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Q: Find the midpoint M of the line segment joining the points C = (-3,-5) and D = (7, 5). %3D M = OD

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Q: Divide:(9x2 + 6x) ÷ 3x

A: We know , 1.(a+b) ÷ c = (a+b)/c = (a/c)+(b/c) 2. am/an= am-n 3. ao = 1

Q: Question 5*: 1130 lecture in the 2021 Fall term is 7. The average number of students at X University…

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Q: Reverse the order of integration and evaluate the integral: (a) / IT 2y° sin zy dy dz 2 dy dx (c) 0.…

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Q: a) V = R", (x, y) = (Ax) · (Ay) where A e Mn,n is invertible.

A: Given that, V∈Rn,  A∈Mn,n is invertible matrix, i.e  A≠0 we have to show that x,y=Ax.Ay is inner…

Q: The perimeter of the rectangle below is 116 units. Find the length of side RS. Write your answer…

A: length of the rectangle, using the perimeter of the rectangle

Q: NOW mezt Step 2 Gim En = lim n-s00 NoW PC En). %3D 1. 3/-

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Q: Find the Fourier transform of f(x) = sin x. In what sense does the Fourier transform exist?

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Q: What is the most appropriate translation of the given mathematical symbols below? * να R, α > 0,…

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: A brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the…

A: b) Let x represents the number of regular beer and y represents the light beer. From the given…

Q: Construct a symmetric matrix A with eigenvalues A1 = -3 and A2 = 10 and corresponding orthogonal…

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Q: 10 s(2-(z2 + 5)") dz =? 12z(z + 5)° +c (=+5) +c (22+5)

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Q: Let A E Mn.n: Show that AT A and AAT are similar.

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Q: Find the Inverse Laplace Transform. Y (s) (10s + 8) తాతి s3

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Q: An organization had 14 employees. There are 9 female employees and 5 male employees. How many teams…

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Q: 2. Let (x, y, Z, w) be a linearly independent set of vectors in R. Which of the following sets of…

A: Introduction: A set S={x,y,z} is known as a linearly independent set, if for some scalars is, a, b,…

Q: Q3 Please fill the blanks with correct answer Determine for each value on the constant of all…

A: Given: A system of linear equations, x+y+z=3ax+2y+(a+2)z=ax-(a+1)y-z=0 To find: Solution of given…

Q: L(0) = [B] Now, find the derivative, L'(0). Type theta for 0. L'(0) = [C] Once you find the value of…

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Q: 2. If the density of a random variable R is zero for x¢ the finite interval [a, b], show that NR(s)…

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Q: Question 2. Prove that a nonempty closed subset of R, if it is bounded from below, has a least…

A: The given question is related with real analysis. We have to prove that a nonempty closed subset of…