LONH4. So ve the following initial value problem using Laplace transforms:y" + 3y + 2y = g(t)with y(0) = 0 and y (0) = -2 where%3D(2, t<6;g(t) = {t, 6 st< 10;4, t2 10.

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Answered: 4. So ve the following initial value…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Suppose a particle is traveling on a one-dimensional track with velocity v(t) = t² − 6t + 5 feet per second for 0 ≤ t ≤ 6. Further suppose that the position of the particle at time t = 0 is given by s(0) = 3 and that positive values mean the particle is traveling to the right. (a) (b) What is the position function s(t)? What is the acceleration function a(t)? (c) When is the particle at rest? The particle is at rest when the velocity is zero. Then graph the velocity function v(t).
2. You are standing at the point (1,1,3) on the hill whose equation is given by z = 5y – x² – y?. !! (a) If you decide to go straight northwest, will you be ascending or descending? At what rate? (b) If you decide to maintain your altitude, in what directions can you go?
4. A particle's position is given by the function p(t) = (1, 2t — e−¹) m (a) Find the magnitude of the displacement of the particle from times t = 0 seconds to t= 1 seconds. (b) Calculate the distance traveled by the particle from times t = 0 seconds to t = 1 seconds
1. A particle moves along a vertical coordinate axis so that its position at any time t20 is given by the function s() =r' - 6r² + 9t + 5, where s is measured in centimeters and t is measured in seconds. (e) Describe the motion of the particle for t20. Answer the following questions with justification: • When is the particle moving up? • When is the particle moving down?. • When is the particle at rest? • When is the particle speeding up? • When is the particle slowing down? because because because because because • Find the particle's acceleration each time the velocity is zero. • Find the total distance traveled by the particle from 0 to 3 seconds.
Solve for k if h(x) = 7x+k is tangent to f(x) = x^2 +3x - 8 (Problem 16) I don’t really know what the question is asking and it’s confusing me…please help lol
I keep getting the max as (-¼, 0, -1/4sqrte), the min as (-¼, 0, -1/4sqrte), and the saddle point as (0,0,0). However this seems to be wrong. The only thing I'm confident in is that x is +/-¼ but I went with y = 0 because when I try to find fy(x,y) = 0 I keep coming up with nothing.
7. Suppose that r(t) represents the position of the object at time t. Assume that a(t) = (1, 2, n² sin(Tt)), that the initial velocity is v(0) = (1,0,–7), and that the initial position of the object is 7(0) = (0,0,10). Find 7(10).
4. Suppose 4z² + 3xy + y² = 14, where both z and y are functions of time, t. At the point (1,2), -1. What is ?
11. Find y'if y = 2x + Vx -9x+3
14. Find the orthogonal trajectories of the family of curves 1 y = - (x + k)³ (a) y %3D (금z+ C)®i (d) y = (4x + C)*/* (b) y = (?x + C)"/³ (c)y = (¿x+C)"³ (e) y = (5x + C)/*
9. A bug is moving along a straight line such that its acceleration is given by the equation a(t)=2 cost +3 , with v(0)=-3 and s(0)=0. Find the position function, s(t), of the bug.

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4. So ve the following initial value problem using Laplace transfor y"+3y +2y = g(t) with y(0) =0 and y(0) = -2 where %3D 2, t<6; g(t) = {t, 6 st< 10;