Mathematics, 13.07.2019 01:40, jjmarie612
Arectangular field is to be bounded by a fence on 3 sides and a straight stream on the 4th side. find the dimensions of the field with maximum area that can be enclosed using 1000 ft of rope. this is in the applied maximum and minimum chapter btw.
Answers: 1
![\bf \stackrel{area}{A}=length\cdot width\implies A(w)=(1000-2w)w \\\\\\ \boxed{A(w)=1000w-2w^2} \\\\\\ \cfrac{dA}{dw}=1000-4w\implies 0=1000-4w\implies 4w=1000 \\\\\\ w=\cfrac{1000}{4}\implies \boxed{w=\stackrel{width}{250}} \\\\\\\ [1000-2(250)]\implies 1000-500\implies \boxed{l=\stackrel{length}{500}}](/tpl/images/0083/0466/16917.png)
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