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 Calculus Calculus Math Forum

 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: 14,597 Thanks: 1038 Show your work you lazy Canuck!!  November 10th, 2017, 03:15 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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: 20,966 Thanks: 2216 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: 3,264 Thanks: 902 Right. Thanks, I misread it. Igorrrawr, set up a coordinate system with the origin at the center of the semicircle, the x-axis along its base. We can write the semi-circle as $y= \sqrt{25- x^2}$. The vertices of the rectangle on the semi-circle 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. Thanks from igorrrawr Tags inscribed, rates, related Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post efking Calculus 5 October 19th, 2015 01:42 PM kagami08 Calculus 1 October 4th, 2015 08:58 PM ThePhantom Calculus 2 April 16th, 2011 06:20 PM chocochippyx2 Calculus 3 March 24th, 2011 03:00 PM imcutenfresa Calculus 4 September 24th, 2009 12:22 PM

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