Results 1 to 2 of 2

Math Help - Density Function

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    11

    Density Function

    Seeds are dispersed from a tree in all directions uniformly. The density of seeds that land on the ground at a distance r away is approximately described by the function: s(r) = 50 sin (pi*r/10) seeds/m^2 , 0=<r=<10m

    a) At what distance from the tree are the seeds most densely distributed?
    b) What is the total number of seeds on the ground within a 10 m radius of the tree?

    For part a, I got 5m and for part b, I got 100pi^2. I have a final exam tomorrow and I desperately want to make sure I'm doing this correctly.
    Thanks!
    Last edited by mr fantastic; April 28th 2010 at 05:26 AM. Reason: Deleted incorrect part of post title.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    You are correct on the first part.

    For the second part, you need to integrate the density over the entire circular area. Since it is presented in polar coordinates, remember that you should use r \, dr \, d\theta.

    So:

    \int_0^{2\pi} \int_0^{10} 50 \sin \left( \frac{\pi r}{10} \right) r \, dr \, d\theta

    This gives a different answer than you gave. Is this how you set your integral up? If not, does this make sense why this is correct?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding a Cumulative Distribution Function and Density Function
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 17th 2011, 09:41 AM
  2. Replies: 4
    Last Post: October 27th 2010, 05:41 AM
  3. Replies: 1
    Last Post: April 10th 2009, 10:59 AM
  4. Density Function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 25th 2009, 05:08 AM
  5. Density Function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 9th 2009, 04:00 AM

Search Tags


/mathhelpforum @mathhelpforum