anonymous
  • anonymous
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 16 ft, express the area A of the window as a function of the width x of the window.
Mathematics
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SOLVED
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chestercat
  • chestercat
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watchmath
  • watchmath
Let \(h\) be the height of the rectangle. Here \(x/2\) is the radius of the semicirlce. So perimeter= \(2h+x+\pi\cdot (x/2)=2h+(2\pi+1)x=160\) Solving for \(h\) we have \(h=80-(2\pi+1)(x/2)\). Now the area of the window is \(A=hx+\frac{1}{2}\pi(x/2)^2\) \(=80x-(2\pi+1)(x^2/2)-\pi(x^2/4)\) You can simplify more if you want :)
anonymous
  • anonymous
is the 160 suppose to be 16 ?
watchmath
  • watchmath
yes sorry, that was a typo then \(h=16-(2\pi+1)(x/2)\) and you continue from there :).

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anonymous
  • anonymous
okay thanks
watchmath
  • watchmath
I mean \(h=8-(2\pi+1)(x/2)\)

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