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A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4ft/s, how fast will the foot be moving away from the wall when the top is 11 feet from the ground.
 one year ago
 one year ago
A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4ft/s, how fast will the foot be moving away from the wall when the top is 11 feet from the ground.
 one year ago
 one year ago

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zepdrixBest ResponseYou've already chosen the best response.1
So our first step is to find x. The length of that side. I think we'll end up needing that :o Remember your Pythagorean Theorem for finding that side? :)
 one year ago

shann803Best ResponseYou've already chosen the best response.0
Ya so x would then be 11 as well because 14^211^2=121 and the square root of that is 11
 one year ago

shann803Best ResponseYou've already chosen the best response.0
wow lol my bad i mean it's the square root of 75 is x not 11 so like 8.66 is x :) miscalculated
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
So we'll call it ... 5sqrt3 i guess :D in simplified form.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Hmm I'm trying to remember how to do this type of problem XD Lol. I think we can do it like this. \[\large x^2 + y^2 = 14^2\] Taking the derivative from this point. (With respect to t, time).
 one year ago

shann803Best ResponseYou've already chosen the best response.0
so the derivative of x^2+y^2=14^2 is x/y?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large 2x\frac{ dx }{ dt }+2y \frac{ dy }{ dt }=0\] Since our derivative is with respect to t, Every time we differentiate a variable that is NOT t, we have to apply the chain rule multiplying by the d/dt term. For example when we differentiate x^2, we get 2x, but a dx/dt will pop out also.
 one year ago

shann803Best ResponseYou've already chosen the best response.0
yes yes I remember my teacher saying that!
 one year ago

shann803Best ResponseYou've already chosen the best response.0
so we plug in the dy/dt which is 4 and solve for dx/dt?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Heh :3 Ok cool. So now if we look at our problem. We now have 4 variables! Eeek! But we already KNOW 3 of them from the earlier! Yes plug in dy/dt, and also plug in y and x that we set up earlier :)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
from the earlier? what is wrong with me _ ugh..
 one year ago

shann803Best ResponseYou've already chosen the best response.0
so it's 2(5sqrt3)(dx/dt)+2(11)(4) is this right?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Hmm yes good good :) equals 0
 one year ago

shann803Best ResponseYou've already chosen the best response.0
so my answer is 5.08?
 one year ago

shann803Best ResponseYou've already chosen the best response.0
yes it's right!!1 THANK YOU SOOOO MUCH!! :)
 one year ago

shann803Best ResponseYou've already chosen the best response.0
I have another question going it's a problem solving like this but in the mathematics section do you think you can help me with that one too please?
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
When you do these problems, one way to check your work is this... You should get an answer that MAKES SENSE. If the ladder is sliding down the wall in the y direction at 4 ft/s Then our slide along the x direction should be a similar number.
 one year ago

shann803Best ResponseYou've already chosen the best response.0
true true, and yes the gravel problem lol :)
 one year ago
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