# 04spex1 - (b(10 points Determine ±rom your sketch the...

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Math 320 First In-class Exam March 2, 2004 M´arton Bal´azs NAME: 1. (20 points) The Acela Express travels (between Boston and Washington DC) at a speed of 160 (miles/hour). A comfortable level of deceleration for trains is 8000 (miles/hour 2 ). At least how far from the terminus does the train have to begin braking in order to stay below the deceleration value above? How many minutes does it take until it comes to a full stop? 1

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2. (40 points) Solve the initial value problem x d y d x + 3 y = sin x x 2 , y ( π ) = 1 . 2
3. For d y d x = ( y - 3) (e y - 1) (a) (15 points) Sketch, roughly, a direction feld and classi±y the critical points.

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Unformatted text preview: (b) (10 points) Determine, ±rom your sketch, the asymptotic behavior o± the solution ±or y (0) = 1 as t → ∞ . 3 4. Solve the system 5 x 2 + x 3 =-8 x 1-2 x 2-x 3 = 2 6 x 1 + x 2-3 x 3 =-8 using (a) (20 points) Gauss-Jordan elimination, (b) (20 points) Cramer’s method. 4 5. Given the matrix A = 1 7 3-2-6-2 6-3-6-3-2 , (a) (20 points) compute A 2 and A 3 . (b) (15 points) Based on these results, determine the matrices A-1 and A 2004 . 5...
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## This note was uploaded on 08/11/2008 for the course MATH 475 taught by Professor Balazs during the Fall '05 term at University of Wisconsin.

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04spex1 - (b(10 points Determine ±rom your sketch the...

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