# Final fall 2014 solutions - Northwestern University Math...

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Northwestern UniversityMath 230Final examDecember 10, 2014Last name. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .First name. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Email. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NetID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Student ID. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Instructions:This exam has15problems and17pages. Please make sure that all pages are in-cluded.Read each problem carefully.Write legibly.Cross off anything you do not wish graded.Write in complete sentences.You may not use books, notes, calculators or phones.You have 120 minutes to complete this exam.DO NOTwrite outside of the box on each page.Good luck!
Problem 2 (18 points)A Frontier airplane follows the pathF(t) =h3-t, 1+t, 3tiand a Southwest airplanefollows the pathS(t) =h6-t,-1,-3-3ti. An observer on the ground notices that thelines of steam emitted from the planes appear to cross. Do they actually cross, and if so,at what point?
(4 pts for realizing that they need to solve a system of equations)

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