calculus HELP ME PLEASE!

Discussion in 'Random Ramblings' started by arabookworm, Nov 22, 2009.

  1. arabookworm

    arabookworm Chillin' With My Peeps

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    Oct 27, 2008
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    two questions. I don't necessarily want them solved for me, I just can't figure out how to get started on them.

    1) prove the identity 2arcsinx=arccos(1-2x^2)

    2)a rain gutter is to be constructed from a metal sheet 30cm wide by bending up one third on each side to form angle a. what should angle a be in order to maximize the amount of water the gutter can hold?
     
    Last edited: Nov 22, 2009
  2. arabookworm

    arabookworm Chillin' With My Peeps

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    someone here must know calculus! PLEASE HELP ME!!!! [​IMG]
     
  3. Imp

    Imp All things share the same breath- Chief Seattle

    9. Worksheet for Level 4 Problem
    Set f(x) = 2 arcsin(x) − arccos(1 − 2x2). Since d
    dx (arcsin(x)) = − d
    dx (arccos(x)) = p 1
    1−x2, we
    have
    f0(x) = p 2
    1 − x2 − (−4x)p −1
    1 − (1 − 2x2)2
    = p 2
    1 − x2 − p 4x
    4x2 − 4x4
    = p 2
    1 − x2 − p 2
    1 − x2
    = 0
    for x > 0, thus f(x) = c for x > 0, for some constant c. Setting x = p1
    2 gives f

    p1
    2

    = 2(
    4 )−
    2 =
    0, and as f(0) = 0, 2 arcsin(x) = arccos(1 − 2x2) as asserted.


    Yes I know Calculus too. [​IMG]

    Imp-Knows nothing about gutters. Hope this helps
     
  4. The Poultry Peanut

    The Poultry Peanut lives under rock

    Quote:[​IMG]
     
  5. NoseyChickens

    NoseyChickens Feathers On The Ground

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    Well, that just made me feel stupid![​IMG]
     
  6. arabookworm

    arabookworm Chillin' With My Peeps

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    Quote:so the derivative of arcsinx is -d and the derivative of arccos(1-2x^2) is p1? but what are d and p? I hate identities right now... nope, strike that, I hate them always.
     
  7. newchickenfamily

    newchickenfamily Chillin' With My Peeps

    just thinking about calculus makes me want to [​IMG]
     
  8. Iowa Roo Mom

    Iowa Roo Mom Resistance Is Futile

    Apr 30, 2009
    Keokuk County
    [​IMG]
     
  9. Imp

    Imp All things share the same breath- Chief Seattle

    Arabookworm,

    Sorry I have no idea what any of this means. It has been decades since I've seen calculus. I googled

    this---> 2arcsinx=arccos(1-2x^2)

    and got lots of hits.

    This one seemed closest to what you were looking for----> www.math.siu.edu/mills/Math150Sum2003_ak_exam5_1.pdf

    Maybe you could try googling and find the answer you need

    Good luck.

    Just a guess, but shouldn't the angle on the gutter be the one that maximizes the area in the cut view of the gutter?--> \\_/. Thus maxing the volume of the gutter? I have no idea how to get there.

    Imp-Going to lie down now.
     
  10. With Geometry, I would be able to help you but Calculus? [​IMG] Didn't even take it in high school!
     

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