18-01F07-L13 - MIT OpenCourseWare http/ocw.mit.edu 18.01...

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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus, Fall 2007 Please use the following citation format: David Jerison, 18.01 Single Variable Calculus, Fall 2007 . (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms
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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus, Fall 2007 Transcript – Lecture 13 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Today we're going to keep on going with related rates. And you may recall that last time we were in the middle of a problem with this geometry. There was a right triangle. There was a road. Which was going this way, from right to left. And the police were up here, monitoring the situation. 30 feet from the road. And you're here. And you're heading this way. Maybe it's a two lane highway, but anyway it's only going this direction. And this distance was 50 feet. So, because you're moving, this distance is varying and so we gave it a letter. And, similarly, your distance to the foot of the perpendicular with the road is also varying. At this instant it's 40, because this is a 3, 4, 5 right triangle. So this was the situation that we were in last time. And we're going to pick up where we left off. The question is, are you speeding if the rate of change of D with respect to t is 80 feet per second. Now, technically that would be - 80, because you're going towards the policemen. Alright, so D is shrinking at a rate of - 80 feet per second. And I remind you that 95 feet per second is approximately the speed limit. Which is 65 miles per hour. So, again, this is where we were last time. And, got a little question mark there. And so let's solve this problem. So, this is the setup. There's a right triangle. So there's a relationship between these lengths. And the relationship is that x ^2 + 30 ^2 = D ^2. So that's the first relationship that we have. And the second relationship that we have, we've already written down. Which is dx / dt - oops, sorry. dD / dt = minus 80. Now, the idea here is relatively straightforward. We just want to use differentiation. Now, you could solve for x. Alright, x is the square root of D^2 - 30 squared. That's one possibility. But this is basically a waste of time. It's a waste of your time. So it's easier, or
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18-01F07-L13 - MIT OpenCourseWare http/ocw.mit.edu 18.01...

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