P16 - Project 16 MAC 2311 YOU MUST SHOW YOUR WORK TO...

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Project 16 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. An underwater pipe begins to leak oil that spreads outward in the shape of an expanding sphere. Recall that the volume of a sphere is V = 4 3 πr 3 , where r is the length of its radius. Suppose the company that owns the pipe takes some measurements and discovers that the volume (in cubic feet) of the spill has been V ( t ) = 3 + 2 t + t 2 , where t is the number of hours since the spill began ( t = 0). Calculate dr dV (first write r as a function of V ). Write a formula r ( t ) for the radius of the oil spill as a function of t and calculate r 0 ( t ). What does dr dt represent? What are its units? Draw a picture of the situation at the exact moment when t = 4 labelling the numerical values of the radius and volume of the sphere. At what rates are the volume and the radius of the spill changing at that time? At what rates are they changing after 100 hours? Include the units with your answers and round to the nearest hundredth. Show that as time passes, the radius of the spill will extend outward without
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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P16 - Project 16 MAC 2311 YOU MUST SHOW YOUR WORK TO...

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