document.write( "Question 1120315: \r
\n" ); document.write( "\n" ); document.write( "a point is moving along the positive y axis at a constant rate of 6 units per second. Find the rate of change of its distance from (1,0) when y=2\r
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Algebra.Com's Answer #735996 by ikleyn(52786)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I am here to fix an error in the @greenestamps solution.\r
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document.write( "The distance from the point (0,y), moving along the y-axis, to the point (1,0) fixed in the coordinate plane, is  D = \"sqrt%28y%5E2%2B1%29\"   (Pythagoras).\r\n" );
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document.write( "The rate of the distance change is the derivative \r\n" );
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document.write( "\"%28dD%29%2F%28dt%29\" = \"%281%2F2%29%2A+%282%2Ay%2A+%28%28dy%29%2F%28dt%29%29+%2F+sqrt%28y%5E2%2B1%29%29\" = \"y%2A+%28%28dy%29%2F%28dt%29%29+%2F+sqrt%28y%5E2%2B1%29\" = \r\n" );
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document.write( "    now substitute the given value of y= 2 and the given rate  \"%28dy%29%2F%28dt%29\" = 6 into the formula to get the rate of the distance change = \r\n" );
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document.write( "= \"%282%2A6%2Fsqrt%281%2B2%5E2%29%29\" = \"12%2Fsqrt%285%29\" units per second.\r\n" );
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document.write( "Answer.  The rate of the distance change = \"12%2Fsqrt%285%29\" units per second.\r\n" );
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