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anonymous

  • 5 years ago

A 26 foot long ladder is leaning against a vertical wall. The foot of the ladder is 10 feet away from the base of the wall. The foot of the ladder is being pulled away from the base of the wall at a rate of 4 feet per second. How fast is the top of the ladder sliding down the wall at this instant? (related rates)

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  1. myininaya
    • 5 years ago
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    related rates problem awesome!

  2. anonymous
    • 5 years ago
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  3. myininaya
    • 5 years ago
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    cyter beat me

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  4. myininaya
    • 5 years ago
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    lol wrong problem

  5. myininaya
    • 5 years ago
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  6. anonymous
    • 5 years ago
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    could both answers be correct?

  7. myininaya
    • 5 years ago
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    lol there are two different answers let me see if i made a mistake

  8. anonymous
    • 5 years ago
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    You used 4 instead of 10

  9. myininaya
    • 5 years ago
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    cyter is right

  10. myininaya
    • 5 years ago
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    i used y' for y my bad

  11. myininaya
    • 5 years ago
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    cyter wins

  12. anonymous
    • 5 years ago
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    we both win because we spent energy working on the problem

  13. myininaya
    • 5 years ago
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    lol

  14. anonymous
    • 5 years ago
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    in the writing in the purple, isn't the derivative of s^2 2s, not just 2?

  15. anonymous
    • 5 years ago
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    yep

  16. anonymous
    • 5 years ago
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    the right hand side should have been 2s ds/dt I knew something was amiss.

  17. myininaya
    • 5 years ago
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    since s is a constant (it doesnt change) s'=0 so 2ss'=0

  18. myininaya
    • 5 years ago
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    so it doesnt change the answer

  19. anonymous
    • 5 years ago
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    yep it makes no difference but it looks logical

  20. myininaya
    • 5 years ago
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    right and it is best to be logical during to look crazy

  21. myininaya
    • 5 years ago
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    than not during*

  22. anonymous
    • 5 years ago
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    but what happens to the 2s? does it cancel out? and how does the x (dx/dt) becomes negative?

  23. myininaya
    • 5 years ago
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    2ss'=0

  24. myininaya
    • 5 years ago
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    the derivative of s^2 is 2ss' but since s doesnt change s'=0

  25. anonymous
    • 5 years ago
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    oo right, sorry

  26. anonymous
    • 5 years ago
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    factor out the 2 s and devide both sides by 2 0/2 = 0

  27. myininaya
    • 5 years ago
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    cyter did you draw that on the computer? it looks very mechanical like

  28. myininaya
    • 5 years ago
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    on some parts

  29. myininaya
    • 5 years ago
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    lol looks better than my horrible hand writing

  30. anonymous
    • 5 years ago
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    \[\text{2((xdx/dt)+(ydy/dt) = 2sds = 0/dt}\] dividing both sides by 2 we have \[\text{((xdx/dt)+(ydy/dt) = sds/dt = 0}\] now subtract both sides by (xdx/dt) we get \[\text{(ydy/dt) = -(xdx/dt)}\] and then divide both sides by y to get dy/dt alone \[\text{(dy/dt) = -(x/y)dx/dt}\] Then plug and play

  31. anonymous
    • 5 years ago
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    yes I used paint which isn't very good

  32. anonymous
    • 5 years ago
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    Your handwriting is legible, unlike mine where I have to use a drawing program on my computer

  33. myininaya
    • 5 years ago
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    i have a scanner haha

  34. myininaya
    • 5 years ago
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    lol

  35. anonymous
    • 5 years ago
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    ok i get it now, thank you both of you for your help

  36. anonymous
    • 5 years ago
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    glad to help

  37. anonymous
    • 5 years ago
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    Using cyter's solution diagram, \[y=x \text{Tan}[\text{ArcCos}[x/26]] \] then \[y=26 \sqrt{1-\frac{x^2}{676}} \] The total derivative of the above is: \[\text{Dt}[y]==-\frac{x \text{Dt}[x]}{26 \sqrt{1-\frac{x^2}{676}}} \] Replace x with 10 and Dt[x] with 4 and simplify, \[\text{Dt}[y]==-\frac{5}{3} \] I hope there are no errors. First DE solved in years.

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