
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 2nd, 2010, 04:54 AM  #1 
Newbie Joined: May 2010 Posts: 1 Thanks: 0  optimization  rectangle in a semicircle
A piece of plexiglass is in the shape of a semicircle with radius 2m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass.  I tried isolating y from x^2 + y^2 = 4 and substituting it in the formula for the area of the rectangle f(A) = 2xy. Then I found the derivative of f(A) and set it to zero, but I just can't seem to factor it correctly. Can anyone help me out? According to the textbook the answer is supposed to be 1.42m by 0.71m. 
May 2nd, 2010, 06:36 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: optimization  rectangle in a semicircle
It won't factor, at least with integers. Use the quadratic formula!

May 2nd, 2010, 07:54 AM  #3 
Newbie Joined: May 2010 Posts: 4 Thanks: 0  Re: optimization  rectangle in a semicircle Does the picture look something like that? If so just solve it by using 3triangles. y=(square root (r^2x^2))*2 

Tags 
optimization, rectangle, semicircle 
Search tags for this page 
a piece of plexiglass is in the shape of a semicircle with radius 2m,a piece of plexiglass is in the shape of a semicircle with radius 2m . determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
a semicircle  Albert.Teng  Algebra  4  July 5th, 2013 10:45 AM 
Semicircle  johnny  Algebra  6  March 7th, 2011 02:03 PM 
How to calc sides of rectangle inside a rotated rectangle  mhurkman  Algebra  4  February 7th, 2011 11:40 AM 
Rectangle in Semicircle  symmetry  Algebra  5  February 2nd, 2007 04:53 PM 
Integrating Log Z along a semicircle contour  SuperMath  Complex Analysis  0  January 1st, 1970 12:00 AM 