document.write( "Question 720326: A circle with circumference 12p has an arc with a 189° central angle.
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Algebra.Com's Answer #441826 by Edwin McCravy(20056) $\"\"$ $\"About$

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A circle with circumference 12p has an arc with a 189° central angle.
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document.write( "We want the length of the red arc:\r\n" );
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document.write( "The easy way is with the proportion:\r\n" );
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document.write( "Let the arc length be s:\r\n" );
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document.write( "Reduce the fraction on the right\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "40s = 252p\r\n" );
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document.write( "Divide both sides by 40\r\n" );
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document.write( "s = \r\n" );
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document.write( "s = \r\n" );
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document.write( "That's the exact answer.\r\n" );
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document.write( "The approximate answer is 19.792.\r\n" );
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document.write( "There is a harder way which some teachers require students \r\n" );
document.write( "to use so they will learn the formula for the length of an arc,\r\n" );
document.write( "and so they'll learn to convert degrees to radians, in cases\r\n" );
document.write( "when just the angle in degrees and the radius are given.\r\n" );
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document.write( "The formula for the length of an arc is: \r\n" );
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document.write( "s = q·r where font face=\"symbol\">q is\r\n" );
document.write( "measured in radians.\r\n" );
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document.write( "So we need to do two things:\r\n" );
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document.write( "1. Convert q = 189° to radians.\r\n" );
document.write( "2. Find the radius of the circle.\r\n" );
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document.write( "To convert 189° to radians we multiply it by  \r\n" );
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document.write( " q =  = \r\n" );
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document.write( "To find the radius of the circle, we use\r\n" );
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document.write( " C = 2pr\r\n" );
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document.write( "12p = 2pr\r\n" );
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document.write( "Divide both sides by 2p\r\n" );
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document.write( " = \r\n" );
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document.write( "6 = r\r\n" );
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document.write( "s = q·r\r\n" );
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document.write( "s = ·\r\n" );
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document.write( "s = ·\r\n" );
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document.write( "s = \r\n" );
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document.write( "s = \r\n" );
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document.write( "That's the exact answer.\r\n" );
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document.write( "The approximate answer is 19.792.\r\n" );
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document.write( "Edwin

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