# P13 - Project 13 MAC 2311 1. An underwater pipe begins to...

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Project 13 MAC 2311 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 of radius r is V = 4 3 πr 3 . The company that owns the pipe takes 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 dV dt and dr dV (write r as a function of V ﬁrst). What are the volume and radius of the spill after 1 hour? 4 hours? What are the values of dV dt and dr dV after 1 hour? 4 hours? Using only your previous answer, what is the value of dr dt after 1 hour? 4 hours? What do these numbers represent?. 2. Suppose y is deﬁned implicitly as a function of x by the equation y = x y + 1 . Calculate dy dx implicitly by using quotient rule, and then once more, but this time after ﬁrst multiplying the equation by y ﬁrst to clear the fractions. Are the answers different?? Show that there is a single point on the curve with

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## This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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P13 - Project 13 MAC 2311 1. An underwater pipe begins to...

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