Pre-Calc Homework Solutions 87

Pre-Calc Homework Solutions 87 - Section 3.5 d 4 3 r dr 3...

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31. (a) } d d V r } 5 } d d r } 1 } 4 3 } p r 3 2 5 4 p r 2 When r 5 2, } d d V r } 5 4 p (2) 2 5 16 p cubic feet of volume per foot of radius. (b) The increase in the volume is } 4 3 } p (2.2) 3 2 } 4 3 } p (2) 3 < 11.092 cubic feet. 32. For t . 0, the speed of the aircraft in meters per second after t seconds is } 2 9 0 } t . Multiplying by } 360 1 0 h sec }? } 1 1 00 k 0 m m } , we find that this is equivalent to 8 t kilometers per hour. Solving 8 t 5 200 gives t 5 25 seconds. The aircraft takes 25 seconds to become airborne, and the distance it travels during this time is D (25) < 694.444 meters. 33. Let v 0 be the exit velocity of a particle of lava. Then s ( t ) 5 v 0 t 2 16 t 2 feet, so the velocity is } d d s t } 5 v 0 2 32 t . Solving } d d s t } 5 0 gives t 5 } 3 v 2 0 } . Then the maximum height, in feet, is s 1 } 3 v 2 0 } 2 5 v 0 1 } 3 v 2 0 } 2 2 16 1 } 3 v 2 0 } 2 2 5 } v 6 0 4 2 } . Solving } v 6 0 4 2 } 5 1900 gives v 0 < 6 348.712. The exit velocity was about 348.712 ft/sec. Multiplying by } 360
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

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