document.write( "Question 505613: A racetrack is in the shape of an ellipse 80 feet long and 40 feet wide. What is the width 10 feet from a vertex? \n" ); document.write( "
Algebra.Com's Answer #339936 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
A racetrack is in the shape of an ellipse 80 feet long and 40 feet wide. What is the width 10 feet from a vertex?
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document.write( "The equation of that ellipse is\r\n" );
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document.write( "2a = Major axis = 80, so a = semi-minor axis = 40\r\n" );
document.write( "2b = Minor axis = 40, so a = semi-minor axis = 20\r\n" );
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document.write( "Equation is of the form:\r\n" );
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document.write( "\"x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"x%5E2%2F40%5E2+%2B+y%5E2%2F20%5E2+=+1\"\r\n" );
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document.write( "\"x%5E2%2F1600+%2B+y%5E2%2F400+=+1\"\r\n" );
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document.write( "To find the width 10 feet from the vertex, we want to\r\n" );
document.write( "know the length of this green line:\r\n" );
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document.write( "We want to know the value of y when x = 30, so we substitute\r\n" );
document.write( "30 for x in\r\n" );
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document.write( "\"x%5E2%2F1600+%2B+y%5E2%2F400+=+1\"\r\n" );
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document.write( "\"30%5E2%2F1600+%2B+y%5E2%2F400+=+1\"\r\n" );
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document.write( "\"900%2F1600+%2B+y%5E2%2F400+=+1\"\r\n" );
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document.write( "\"9%2F16+%2B+y%5E2%2F400+=+1\"\r\n" );
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document.write( "Multiply through by 1600\r\n" );
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document.write( "\"900+%2B+4y%5E2+=+1600\"\r\n" );
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document.write( "\"4y%5E2+=+700\"\r\n" );
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document.write( "\"y%5E2=175\"\r\n" );
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document.write( "\"y+=+%22%22+%2B-+sqrt%28175%29\"\r\n" );
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document.write( "\"y+=+%22%22+%2B-+sqrt%2825%2A7%29\"\r\n" );
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document.write( "\"y+=+%22%22+%2B-+5sqrt%287%29\"\r\n" );
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document.write( "So the endpoints of that green line are\r\n" );
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document.write( "\"%28matrix%281%2C3%2C30%2C%22%2C%22%2C5sqrt%287%29%29%29\" and \"%28matrix%281%2C3%2C30%2C%22%2C%22%2C-5sqrt%287%29%29%29\"\r\n" );
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document.write( "and its length is \"10sqrt%287%29\" or about 26.46 feet.\r\n" );
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document.write( "Edwin
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