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anonymous

  • one year ago

Sand is falling on a pile , having shape pf a cone, at the rate 1.5 m3/min. assime diameter of base is 3 times the altitiude, at what rate is the altitude increasing when the altitude is 2m?

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  1. anonymous
    • one year ago
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    @ganeshie8 @ParthKohli @Loser66

  2. anonymous
    • one year ago
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    whats is "r" equal too ?

  3. anonymous
    • one year ago
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    the question says 3d=h

  4. anonymous
    • one year ago
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    radius is half so 2/3r=h?

  5. anonymous
    • one year ago
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    other way around. d = 3h

  6. anonymous
    • one year ago
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    so r = 3h/2

  7. anonymous
    • one year ago
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    and V = πr²h/3, so make the substitution for r then take the derivative

  8. anonymous
    • one year ago
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    okey i did eberyhing i am getting 1/9pi and u ?

  9. anonymous
    • one year ago
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    i did somthing wrong

  10. anonymous
    • one year ago
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    yeah I got something different? What was your derivative?

  11. anonymous
    • one year ago
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    did u get 1/6pi?

  12. anonymous
    • one year ago
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    yes

  13. jim_thompson5910
    • one year ago
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    If you mean \[\Large \frac{1}{6\pi}\] then you are correct

  14. anonymous
    • one year ago
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    how ?

  15. anonymous
    • one year ago
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    oh, that's what I thought you meant

  16. jim_thompson5910
    • one year ago
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    what did you get for dV/dt ?

  17. anonymous
    • one year ago
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    my der was 9/12pih3 dh/dt?

  18. anonymous
    • one year ago
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    after putiing in 3/2h

  19. jim_thompson5910
    • one year ago
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    the h^3 part is incorrect

  20. anonymous
    • one year ago
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    how

  21. jim_thompson5910
    • one year ago
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    you will have h^3 in the V volume formula but after you derive, it turns into 3h^2

  22. anonymous
    • one year ago
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    the formula for cone is x=1/3r2h

  23. anonymous
    • one year ago
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    when 3/2h goes in it become h2 then h3 by timising the outside h

  24. anonymous
    • one year ago
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    |dw:1433903048615:dw|

  25. anonymous
    • one year ago
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    |dw:1433903137752:dw|

  26. anonymous
    • one year ago
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    ok what are the steps take the derv fist then sub?

  27. anonymous
    • one year ago
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    Sub for r first because we don't have a value for dr/dt, then take the derivative

  28. anonymous
    • one year ago
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    wait so (3h/2) doesnt equal 9h2/4? it eiqls 9h/4?

  29. anonymous
    • one year ago
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    oh wait i think i get it now

  30. anonymous
    • one year ago
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    you good?

  31. anonymous
    • one year ago
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    h is 2 right

  32. anonymous
    • one year ago
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    yes

  33. anonymous
    • one year ago
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    then 9(2)^2 = 36

  34. anonymous
    • one year ago
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    hold on the 1/3 is gone beacuse of derv right

  35. anonymous
    • one year ago
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    well the 1/3 was gone before the derivative. It was 3/4 after the substitution, and 9/4 after the derivative

  36. anonymous
    • one year ago
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    damn i am going to take 5 min brake

  37. dumbcow
    • one year ago
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    \[V = \frac{1}{3} \pi r^2 h\] \[r = \frac{3}{2} h\] \[\rightarrow V = \frac{1}{3} \pi (\frac{3}{2}h)^2 h = \frac{3}{4} \pi h^3\] Take derivative with respect to time \[\frac{dV}{dt}= \frac{9}{4} \pi h^2 \frac{dh}{dt}\] plug in dV = 1.5, h =2 , then solve for dh/dt \[\frac{dh}{dt} = \frac{1.5}{9 \pi}\]

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