November 9th, 2017, 01:42 PM  #1 
Newbie Joined: Nov 2017 From: Canada Posts: 4 Thanks: 0  Related rates  inscribed
A rectangle is inscribed in a semicircle of a radius 5m. Estimate the increase in the area of the rectangle using differentials if the length of its base along the diameter is increased from 6m to 6 1/6 m ?

November 9th, 2017, 06:39 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,865 Thanks: 768 
Show your work you lazy Canuck!! 
November 10th, 2017, 03:15 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,976 Thanks: 807 
A rectangle "inscribed in a circle" can't have its base "along the diameter". Your question makes no sense.

November 10th, 2017, 03:45 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,721 Thanks: 1536 
The problem states "inscribed in a semicircle", not "inscribed in a circle", so it does make sense.

November 10th, 2017, 03:56 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,976 Thanks: 807 
Right. Thanks, I misread it. Igorrrawr, set up a coordinate system with the origin at the center of the semicircle, the xaxis along its base. We can write the semicircle as $y= \sqrt{25 x^2}$. The vertices of the rectangle on the semicircle are of the form $\left(x, \sqrt{25 x^2}\right)$ and $\left(x, \sqrt{25 x^2}\right)$ for some positive x. The area is given by $A= 2x\sqrt{25 x^2}$. Initially, the base is 6 so x= 3 and $A= 6\sqrt{25 9}= 6(4)= 24$. Differentiate the formula for A to find dA in terms of x and dx, then set dx= 1/6. 

Tags 
inscribed, rates, related 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Related Rates help please!  efking  Calculus  5  October 19th, 2015 01:42 PM 
Related Rates  kagami08  Calculus  1  October 4th, 2015 08:58 PM 
Related Rates  ThePhantom  Calculus  2  April 16th, 2011 06:20 PM 
Related Rates  chocochippyx2  Calculus  3  March 24th, 2011 03:00 PM 
Related Rates?????????  imcutenfresa  Calculus  4  September 24th, 2009 12:22 PM 