## shann803 Group Title 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

1. zepdrix Group Title

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2. zepdrix Group Title

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? :)

3. shann803 Group Title

Ya so x would then be 11 as well because 14^2-11^2=121 and the square root of that is 11

4. zepdrix Group Title

k cool :D

5. shann803 Group Title

wow lol my bad i mean it's the square root of 75 is x not 11 so like 8.66 is x :) miscalculated

6. zepdrix Group Title

Oh heh :3

7. shann803 Group Title

8. zepdrix Group Title

So we'll call it ... 5sqrt3 i guess :D in simplified form.

9. shann803 Group Title

sounds good

10. zepdrix Group Title

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).

11. shann803 Group Title

so the derivative of x^2+y^2=14^2 is -x/y?

12. zepdrix Group Title

$\large 2x\frac{ dx }{ dt }+2y \frac{ dy }{ dt }=0$ 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.

13. shann803 Group Title

yes yes I remember my teacher saying that!

14. shann803 Group Title

so we plug in the dy/dt which is -4 and solve for dx/dt?

15. zepdrix Group Title

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 :)

16. zepdrix Group Title

from the earlier? what is wrong with me -_- ugh..

17. shann803 Group Title

lol its fine :)

18. shann803 Group Title

so it's 2(5sqrt3)(dx/dt)+2(11)(-4) is this right?

19. zepdrix Group Title

Hmm yes good good :) equals 0

20. shann803 Group Title

yes of course lol :)

21. shann803 Group Title

22. shann803 Group Title

yes it's right!!1 THANK YOU SOOOO MUCH!! :)

23. zepdrix Group Title

Yay team \c:/

24. shann803 Group Title

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?

25. zepdrix Group Title

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.

26. zepdrix Group Title

the gravel problem?

27. shann803 Group Title

true true, and yes the gravel problem lol :)