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Derivative applied to a ladder

  • Thread starter sporus
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Homework Statement



A 10 - foot ladder is placed against a vertical wall. The bottom of the ladder slides away from the wall at a constant rate of 2.9 ft/s. How fast is the top of the ladder sliding down the wall when the top of the ladder is 7.6 feet from the ground?
Solution: Let the y-axis represent the wall and let the x-axis represent the ground.


Homework Equations



100 = y^2 + x^2 = 7.6^2 + x^2
=> x= 6.5

y = (100 - x^2)^.5

The Attempt at a Solution



y' = 1/2 * (100 - x^2)^-.5 * -2x
y'(6.5) = -0.855
 

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