document.write( "Question 109830: A reboncing ball rebounces each time to a height equal to one half the height of the previous bounce. If it is dropped from a height of 16 mtrs. find the total distance it has travelled when it hits ground for the 10th time. \n" ); document.write( "
Algebra.Com's Answer #80030 by Edwin McCravy(20056)\"\" \"About 
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document.write( "From the picture, you can see that the ball falls 10 times \r\n" );
document.write( "but it only rises 9 times.\r\n" );
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document.write( "The \"falls\" form this geometric series with 10 terms, with\r\n" );
document.write( "first term 16, common ratio 1/2:\r\n" );
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document.write( "16+8+4+2+1+1/2+1/4+1/8+1/16+1/32\r\n" );
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document.write( "The \"rises\" form this geometric series with 9 terms, with\r\n" );
document.write( "first term 8, common ratio 1/2\r\n" );
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document.write( "8+4+2+1+1/2+1/4+1/8+1/16+1/32\r\n" );
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document.write( "The only difference in the two is the first \"fall\" of 16 ft. \r\n" );
document.write( "Let's find the sum of the geometric series of \"rises\" and then \r\n" );
document.write( "we can find the sum of the geometric series of \"falls\" by adding \r\n" );
document.write( "the first 16 foot \"fall\" to it:\r\n" );
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document.write( "The formula for the sum of a geometric series is\r\n" );
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document.write( "Sn = a1(1-rn)/(1-r)\r\n" );
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document.write( "For the \"rises\", a1 = 8, r = 1/2, n = 9\r\n" );
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document.write( "S9 = 8[1-(1/2)9]/(1-1/2)\r\n" );
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document.write( "S9 = 8[1-1/512]/(1/2)\r\n" );
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document.write( "S9 = 8[511/512]×(2/1)\r\n" );
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document.write( "S9 = (8×511×2)/(512)\r\n" );
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document.write( "S9 = 511/32 feet = sum of \"rises\" only.\r\n" );
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document.write( "The sum of the \"falls\" accounts for 16 feet more\r\n" );
document.write( "than the \"rises\" or\r\n" );
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document.write( "Sum of \"falls\" = 511/32 + 16 = 511/32 + 512/32 = 1023/32 feet\r\n" );
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document.write( "So, \"sum of rises\" + \"sum of falls\" = 511/32 + 1023/32 = \r\n" );
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document.write( "1534/32 = 767/16 feet = 47.9375 feet the ball travels.\r\n" );
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document.write( "Edwin
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