• anonymous we go with the ladder! Related Rates. 24' ladder hanging over a 7' fence - what is the rate the top is decending to the ground when the base is 7' away from the fence. I think I am trying to cal the rate change of the triangle? This is not a simple! Thanks
  • Stacey Warren - Expert
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  • chestercat
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  • anonymous
Looks like we need to use some implicit differentiation here. So we know the length of the ladder, 24 feet, and it rests over a 7 foot wall, so the total height of the ladder against the wall would be y+7. Using the pathagorean theorem, we have, \[24^2= x^2+(y+7)^2\] We differentiate with respect to x and get, \[0=2x+2(y+7)dy/dx\] We know the length of the ladder is not changing, so it's rate of change is zero. Now you can solve for dy/dx and you will have the rate of change of the y position of the ladder when you sub in 7 for x.

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