document.write( "Question 1160398: A 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 14 feet above the ground? \n" ); document.write( "

Algebra.Com's Answer #784122 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "x is the distance the foot of the 17-foot ladder is from the wall when the height the ladder reaches on the wall is y:

\n" ); document.write( " $\"x+=+sqrt%2817%5E2-y%5E2%29+=+%28289-y%5E2%29%5E%281%2F2%29\"$

\n" ); document.write( "Differentiate to find the rate of change in x for the given rate of change in y.

\n" ); document.write( "Square the given equation to avoid differentiating the square root function.

\n" ); document.write( " $\"x%5E2+=+289-y%5E2\"$
\n" ); document.write( " $\"2x%2A%28dx%2Fdt%29+=+-2y%2A%28dy%2Fdt%29\"$

\n" ); document.write( "dy/dt is given as -4 (ft/sec); when y=14, x is $\"sqrt%28289-196%29+=+sqrt%2893%29\"$ .

\n" ); document.write( " $\"2%2Asqrt%2893%29%28dx%2Fdt%29+=+-2%2814%29%28-4%29\"$
\n" ); document.write( " $\"dx%2Fdt+=+112%2F%282%2Asqrt%2893%29%29+=+56%2Fsqrt%2893%29\"$

\n" ); document.write( "When the top of the ladder is 14 feet above the ground, the foot is moving away from the wall at a rate of 56/sqrt(93) ft/sec, or about 5.8 ft/sec.

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