1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help word problem

  1. Oct 25, 2005 #1
    i dont know if one could do this without the diagram but...
    a rain gutter is to be made of aluminum sheets that r 12 inches wide by turning the edges 90 degrees. what depth would provide maximum cross-sectional area and hence allow the most water to flow?
     
  2. jcsd
  3. Oct 25, 2005 #2
    lets see what we know

    x = bottom of gutter

    y = sides

    so x + 2y = 12

    a = xy

    :y = 6 - x / 2

    sub in equation for a

    a = x ( 6 - (x/2))

    a = 6x - (x^2 / 2)

    da/dx = 6 - x

    set this to 0 so that

    6 - x = 0

    x = 6

    so the max will be at either the endpoints or at x = 6

    so we have

    6x - (x^2 / 2) = a

    f(0) = 0 -0 = 0 no.

    f(12) = 6(12) - (12^2 / 2) = 72 -72 = 0 no.

    f(6) = 6(6) - (6^2 / 2) = 18 yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Help word problem
  1. Help with word problem (Replies: 2)

  2. Help with Word Problem (Replies: 2)

Loading...