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Please help with the answer.

 

 Aug 30, 2020
 #1
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Let's call the fraction that it bounces back up "x"  

 

After the 1st bounce, the ball is  250 • x  high 

 

&, after the 2nd bounce, the ball is  (250 • x) • x  high 

 

&, after the 3rd bounce, the ball is [ (250 • x) • x ] • x  high 

 

All those parentheses aren't necessary, I just included them as a visual

to show that each bounce is x times the height of the previous. 

 

So.... anothe way of writing the height after the 3rd bounce is 250 • x3  

 

The height after the 3rd bounce is 16 so let's set the two expressions equal. 

 

                                                                       250x3  =  16  

                                                                             x3  =  16/250 

 

Let's change that to a decimal so I can

take the third root with my calculator                     x3  =  0.064 

 

Take the third root and obtain                                  x  =  0.

 

And, of course, 0.4 = 2/5  so the answer is .... wait for it .....   B. 2/5  

.

 Aug 30, 2020

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