Write down the auxiliary (characteristic) equation and then find a general solution of the given ODE: (a) y"-3y'-4y=0 (b) y"-4y'+5y=0

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Q: a) Find the point on the graph of y = e where the tangent line has slope -4. b) Plot the graph of y…

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Q: show all steps please

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Q: Descriptive Statistics for the data set a = [3,7,2,4,8,4,1,3] find the first three moments by direct…

A: Answer:----.                   Date:----29/09/2021

Q: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

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Q: Find a value of k for which the function f(x,y) = x² + ky² + 5xy have a saddle point at (r, y) =…

A: Given: fx, y=x2+ky2+5xy

Q: At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula e At 099 A = 90…

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Q: 3. Matching a. r = 4 – sin 40 b. s = 1 – 4 sin 40 %3D C. r = 1+4cos 40 d. r = 4+ cos 40

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Problem 3. Suppose that we have postulated the model Y₁ = B₁x₁ + €i i = 1, 2, 3, where the e;'s are…

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Q: 2. Let P2 be the vector space of polynomials of degree at most 2. Let T: P2 → P₂ by T (p(x)) = p(x)…

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Q: Express the area of the shaded region in terms of (a) an integral with respect to x and (b) an…

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Q: Find the arc length of the curve below on the given interval. 3 y =-x 4 %=/3-+7 on [1,27) 8 The…

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Q: In a school picnic, a total of 43 students brought a backpack, a lunchbox, or both a backpack and a…

A: In this question, we will see how many students brought both a backpack and a lunchbox.

Q: Draw the graph represented by the adjacency matrix. 0 2 0 1 200 1 1 0 0 0 00 0 0 2 1. 1 0. 0.

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Q: Evaluate the line integral a) | 3x'yds, where Cis the curve r(t)=5ti + (3t-7)j. Ostsl. b) (xy +…

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Q: If the chance of rain on Sunday increases to 50% if it rains on Saturd. suppose you were away on…

A: *Answer: Solution: P(Sunday)=P(Saturday)+50%---------------------------1 Let Probability that it…

Q: 5. Let U = {(u₁, U2, U3) E R³|u₁ + u2 - u3 = 0} and V = {(V1, V2, V3) E R³v₁ - 3v2 +5v3 = 0}. (a)…

A: (a)

Q: d. Make a stem-and-leaf plot for the amount of bananas sold

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Q: Solve the initial value problem below using the method of Laplace transforms. 元 y"+4y'+3y = - 7…

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Q: find f(0), f'(0), g(1), g'(1), and (g o f)'(0)

A: The graphs of functions f and g are given belwo:

Q: Find the mass of the thin bar with the given density function. p(x) = 1+ sin x; for sxs Set up the…

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Q: e) Solve for P in the equation below. P + 100 3.6(304.8 – 2.2P) 1- cos 45

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Q: The population (in ten thousands) of a city from 2010 (t = 0) to 2018 (t = 8) is modeled by p(t) =…

A: We are given the model of the population by p(t)=0.25t2+98t+2400,  0≤t≤8. The average rate of change…