1. Limited time only! Sign up for a free 30min personal 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!

Question about rate of change

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the rate of change of an area of a square with respect to the length of its diagonal (r) when the square has a side length of 5 meters?

    2. Relevant equations



    3. The attempt at a solution

    Area of a square = s^2
    and if Area of a square = s^2 then it would = (r^2)/2

    Pythagorean Theorem to find the diagonal of the square:

    r^2 = s^2 + s^2
    r^2= 2s^2
    r=sqrt2s^2
    r=sqrt2 * s

    and then I did this:

    (dA)/(dr) and since we need A in terms of r (i hope that's what the question is asking)

    then ((d)/(dr))((r^2)/(2)) = (2r)/2 = r

    so then the final answer that I got is A = (5^2)/2 = 12.5
     
  2. jcsd
  3. Feb 5, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    They're not asking for A. Besides, when s = 5 meters, A = 25 m2.

    They're asking for (dA)/(dr) when s = 5 m. i.e. when r = 5/√(2) m.

    You essentially answered it earlier.
     
  4. Feb 5, 2012 #3
    so would that be the answer then? r = 5/√(2) m?
     
  5. Feb 5, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The answer to the question:
    "What is the rate of change of an area of a square with respect to the length of its diagonal (r) when the square has a side length of 5 meters?"​
    is 5/√(2) m, but that's not r .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about rate of change
Loading...