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An architect wants to feature 100 feet square oval windows on the corporate headquarters of a large company. Each window will be in four sections - 2 semicircles and 2 rectangles with gold strips separating the glass sections and around the outside border. What values for a and b will require the shortest length of golden stripes?

2006-10-21 06:29:45 · 3 answers · asked by ? 1 in Science & Mathematics Mathematics

3 answers

What' are a and b? It's not clear.

2006-10-21 06:45:50 · answer #1 · answered by Steiner 7 · 0 1

Let a and b be the dimensions of the rectangle. Let a be the length of the side that borders the semicircles.

The surface area is 2ab + pi*(a/2)^2 = 100. Solve for b, and you get b = 50/a - pi*a/8.

The length of the gold stripes is 3a + 4b + pi*a. Substitute the above expression for b, and you get

(3+pi)a + 200/a - pi*a/2 = (3+pi/2)a + 200/a.

Differentiate and set the derivative equal to 0:

(3+pi/2) - 200/a^2 = 0

Multiply through by a^2:

(3+pi/2)a^2 - 200 = 0

Solve for a and get a = sqrt(200/(3+pi/2)) = 6.615 ft.

From before, b = 50/a - pi*a/8 = 4.961 ft.

2006-10-21 06:51:56 · answer #2 · answered by James L 5 · 1 0

explain better - what is a and b?

2006-10-21 06:41:34 · answer #3 · answered by ? 7 · 0 1

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