Posted by **Alex** on Monday, July 18, 2011 at 1:58pm.

A Norman window consists of a rectangle capped by a semi-circular regional. The perimeter of some particular Norman window must be 30 meters. The radius of the semi-circular region is "x" meters. The height of the rectangle is "h" meters. Find the values pf "x" and "h" such that this Norman window has a maximum area. That is, the Norman window will permit the most light to shine through.

- Calc -
**Reiny**, Monday, July 18, 2011 at 2:15pm
If the radius is x, then the base of the rectangle is 2x

let the height of the rectangle be h

Perimeter = 30 = (1/2)(2πx) + 2h + 2x

30 = πx + 2h + 2x

h = (30 - πx - 2x)/2

Area = A = 2xh + (1/2)πx^2

= 2x(30 - πx - 2x)/2 + (1/2)πx^2

I will let you finish it ...

simplify a bit, then differentiate,

set the derivative equal to zero and solve for x

- Calc -
**Anonymous**, Sunday, April 29, 2012 at 10:57am
63

- Calc -
**Anonymous**, Sunday, April 29, 2012 at 10:58am
54

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