4) Consider the initial value problem " 8y +30y+25y = 0, y(0) = -2, y (0) = 8 What is the t-coordinate of the local extreme value of y = y(t) on the interval (0, ∞)? Enter your answer as a decimal accurate to three decimal places.

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A: Step 1: Step 2:

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Q: a) x(t) = rect(t − 3) b) x(t) = −3t rect(t) . c) x(t) = 2te 3u1(t) d) x(t) = e−2|t| 2. Sketch the…

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A: To solve the Euler-Lagrange equation for (I=∫(xy′2+x3y′′2)dx): Compute partial derivatives:…

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A: Step 1:Solve Equation (3) for xFrom x+5z=3X=3-5z Step 2:Substitute x=3−5z into Equation…

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A: The given values are:Value of FTSE 100 in July 2017: £7,455Value of FTSE 100 in July 2018:…

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A: Problem:Prove or give a counter-example: If {v1, ..., vn} is linearly independent and x ≠ 0, then…

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A: 1. The population of two towns is 265,846 and 486,720. How much less than 1,000,000 is this? 265,846…

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Q: 7. Rank and Nullity: 1 2 1 Let A - 2 4 2 a) Find the rank of matrix A. 3 6 3 b) Find the nullity of…

A: 7. a)To find the rank of the matrix A, we need to determine the number of linearly independent rows…

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A: Step 1: Define Dimensions for GridsWe'll set:First rectangle (a × b): a=7, b=8.This grid is 7 rows…

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Q: 1. Solve for x: 2. Simplify: 2x+5=15. (x+3)² − (x − 2)². - b 3. If a = 3 and 6 = 4, find (a + b)² −…

A: 1. Solve for x:  2x + 5 = 15 Let us Subtract 5 from both sides: 2x = 15 − 5 x = 10/2 = 5 Solution: x…

Q: x 1 3 5 7 f -1 3 15 35 7 • Sea) dx from the faible find: 1 f(x) dx by Sempeson method 8 2 if S .dx…

A: Step 1:            Step 2:

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A: Approach to solving the question:Freeform Detailed explanation: To determine the value of your…

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A: To solve the 1-dimensional wave equation problem with the given conditions, we can follow these…

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A: Step 1: Step 2: Step 3: Step 4:

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A: Please feel free to comment if you have any questions.

Q: Consider the initial value problem y"+y'-12y= 0, y(0) = a, y'(0) = 4 Find the value of a so that the…

A: Step 1: Step 2:

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Q: 7. Show that for R sufficiently large, the polynomial P(z) in Example 3, Sec. 5, satisfies the…

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Q: 2. Evaluate the following integral using cauchy integral theorem: ||=3 sin (22)+cos (22) (2-1)(2-2)…

A: The value of the integral is 4πi.

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A: Steps for Each Table:Table axy011142338419536Observe: The values do not follow a linear trend.…

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A: Here's detailed explanation:Part (a): Find the value of a_n using the given formula and stop when…

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A: Step 1: Step 2: Step 3: Step 4:

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A: See the actual solutions (generated using python)

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A: Thus, [A'|b'] has the same solution set S. [Proved]

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Q: 2.- Solve the following Homogeneous Differential Equation (xy + 3y²+x²)dx − (x² + 2xy)dy = 0 -

A: The value of the differential equation is tan−1(xy​)+ln∣1+x2y2​∣=ln∣x∣+C0​