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 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: 13,280 Thanks: 931 Show your work you lazy Canuck!!
 November 10th, 2017, 03:15 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 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: 19,697 Thanks: 1803 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: 3,261 Thanks: 894 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

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