At 12:36 AM +0100 10/31/03, Richard Brekne wrote: >A half circle is placed on top of a rectangle such that its diameter is >the top side of the rectangle. The length of the 3 remaining sides of >the rectangle, plus the circumference of the half circle is equal to 10 >cm. > >Question: What are the lengths of the sides of the rectangle when the >area of the combined figure is at its maximum ? It's a calculus problem (or resembles one I read in a calculus textbook), but that's not to say that I've got the numerical answer. But I started with your description (a rectangle with sides X and y): x+x*(pie/2)+2y=10 which yields: y=(10-2.5708*x)/2 I then took the product of these two to my computers graphing calculator, and got an inverted parabola. It looks as the the maximum product of these two occurs when x is slightly under 2. (Actually the graphing calculator yields the value at the apogee: x=1.94492, yielding y=7.5,minus a goat hair). That's on the assumption that when x*y has its maximum value, (x*y)+(x/4)*pie will be as well. But, hey! I'm with Barbie: "Math is hard." (I'm stepping aside for someone who has more than a high school diploma.) Bill Ballard RPT NH Chapter, P.T.G. "I go, two plus like, three is pretty much totally five. Whatever" ...........The new math +++++++++++++++++++++
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