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A circular ceiling fan rotates at a constant speed of 80 revolutions per minute. A point halfway between the center of the fan and the outer edge of the fan travels 90 inches in 2 minutes. How far (in inches) does a point on the outer edge of the fan travel in 30 minutes?

 May 29, 2021
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If  the halfway point  fan  travels   90 in  in 2 min.....then  it  must travel  45  in  in one minute

 

So  we  can  find  the  radius  of  this "smaller "  circle  that  the  halfway  point travels through as

 

45  =  80 * 2pi  *  r

 

45   =  160 pi  * r

 

45 / ( 160 pi)  =  r    =  9/ (32 pi)  in  

 

And  a point  at  the  outer  edge  must  travel   on  a  circle  with  a radius of  twice  as much  =  9 / (  16 pi)  in

 

So.....the  total  distqance  that this point  travels in  30 min =

 

(No. of  revs in 30 min) * ( 2 pi )  * (r)  =

 

30 ( 80)  ( 2pi)  ( 9 / (16 pi) )   =   2400  * 18  * (9/16)   =    2700  in

 

 

cool cool cool

 May 29, 2021

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