document.write( "Question 650829: A point is moving along the circle x2+y2= 25 in the first quadrant in such a way that its x coordinate changes at the rate of 2cm/sec. how fast is its y coordinate changing as the point passes through (3,4)? \n" ); document.write( "

Algebra.Com's Answer #407518 by Edwin McCravy(20086) $\"\"$ $\"About$

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A point is moving along the circle x² + y² = 25\r
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\n" ); document.write( "\n" ); document.write( ">>...x coordinate changes at the rate of 2cm/sec...<<
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document.write( "The vector pointing right is  = 2 cm/sec (right because it's\r\n" );
document.write( "positive. The vector pointing down is  = ? cm/sec.\r\n" );
document.write( "So the point is moving clockwise, and since the point is moving downard\r\n" );
document.write( "toward the x-axis,  vector is pointing downward, so we can\r\n" );
document.write( "expect its speed to be to be negative.  \r\n" );
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\n" ); document.write( ">>how fast is its y=coordinate changing as the point passes through (3,4)?<<
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document.write( "We want to know:  = ? when x=3 and y=4\r\n" );
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document.write( "CAUTION:\r\n" );
document.write( "x and y are varying as the point is moving before it reaches (3,4),\r\n" );
document.write( "so DO NOT substitute for x or y until after we have taken the derivative.\r\n" );
document.write( "Only then do we freeze the motion at the point (3,4)\r\n" );
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document.write( "                  x² + y² = 25\r\n" );
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document.write( "            2x + 2y = 0\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "              x + y = 0\r\n" );
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document.write( "                     y =  -x\r\n" );
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document.write( "                       =  ·\r\n" );
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document.write( "Now finally we can freeze the motion by substituting x=3, y=4,  = 2\r\n" );
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document.write( "                       =  ·(2)\r\n" );
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document.write( "                       =  \r\n" );
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document.write( "                       =  -1.5 cm/sec\r\n" );
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document.write( "That means that at the instant when the point passes through (3,4) \r\n" );
document.write( "it is falling toward the x-axis at a rate of 1.5 cm/sec.\r\n" );
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document.write( "Edwin

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