document.write( "Question 978610: A Super Happy Fun Ball is dropped from a height of 8 feet and rebounds 12/13 of the distance from which it fell. \r
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Algebra.Com's Answer #599991 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Bounce Number         Rebound\r\n" );
document.write( "      \"1\"          \"%2812%2F13%29%2A8+=+96%2F13\"\r\n" );
document.write( "      \"2\"          \"%2812%2F13%29%2A%2896%2F13%29+=+1152%2F126\"\r\n" );
document.write( "      .\r\n" );
document.write( "      .\r\n" );
document.write( "      .\r\n" );
document.write( "      \"n\"           \"a%2Ar%5E%28n-1%29+=+%2896%2F13%29%2812%2F13%29%5E%28n-1%29\"\r\n" );
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document.write( "We set the nth bounce < 1\r\n" );
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document.write( "\"%2896%2F13%29%2812%2F13%29%5E%28n-1%29\"\"%22%22%3C%22%22\"\"1\"\r\n" );
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document.write( "Multiply both sides by \"13%2F96\"\r\n" );
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document.write( "\"%2812%2F13%29%5E%28n-1%29\"\"%22%22%3C%22%22\"\"13%2F96\"\r\n" );
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document.write( "Take logs of both sides:\r\n" );
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document.write( "\"log%28%28%2812%2F13%29%5E%28n-1%29%29%29\"\"%22%22%3C%22%22\"\"log%28%2813%2F96%29%29\"\r\n" );
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document.write( "\"%28n-1%29log%28%2812%2F13%29%29\"\"%22%22%3C%22%22\"\"log%28%2813%2F96%29%29\"\r\n" );
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document.write( "Divide both sides by \"log%28%2812%2F13%29%29\"\r\n" );
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document.write( "However since \"log%28%2812%2F13%29%29=-.0347621063\"\r\n" );
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document.write( "we are dividing an inequality through by a negative number\r\n" );
document.write( "and that will reverse the inequality from < to >:\r\n" );
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document.write( "\"n-1\"\"%22%22%3E%22%22\"\"log%28%2813%2F96%29%29%2Flog%28%2812%2F13%29%29\"\r\n" );
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document.write( "\"n-1\"\"%22%22%3E%22%22\"\"24.97915041\"\r\n" );
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document.write( "\"n\"\"%22%22%3E%22%22\"\"25.97915041\"\r\n" );
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document.write( "So the 26th rebound will be the first one less than 1 foot.\r\n" );
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document.write( "How far will the ball travel before it comes to rest on the ground? \r\n" );
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document.write( "--------------------------------------\r\n" );
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document.write( "Theoretically it will never stop bouncing, but that's theoretically,\r\n" );
document.write( "not actually.\r\n" );
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document.write( "However we treat it as an infinite series.\r\n" );
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document.write( "The first 8 feet that it fell must be added in separately.\r\n" );
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document.write( "It rebounded 96/13 feet and then fell 96/13 before it hit the ground\r\n" );
document.write( "the second time.  So the first term is 2×(96/13) = 192/13 and the common\r\n" );
document.write( "ratio is 12/13\r\n" );
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document.write( "To that we must add the 8 feet it fell in the beginning:\r\n" );
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document.write( "Answer: 192+8 = 200 feet.\r\n" );
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document.write( "Edwin
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