A Norman WindowDate: 16 Jan 1995 14:42:05 -0500 From: Jon Tienhaara Subject: calc quest. Dr. Math: My calculus teacher wanted me to give you this problem to see how you would do it. He says there are many ways: A Norman window is a window in the shape of a rectangle with a semicircle attached to the top. Assuming that the perimeter of the window is 12 feet, find the dimensions that allow the maximum amount of light to enter. Thank you! jtienhaa@esd122.wednet.edu Date: 17 Jan 1995 00:52:18 GMT From: Dr. Math Subject: Re: calc quest. Hello there! Well, probably the reason your _calculus_ teacher gave you this question is that it's a question that's ideally suited for calculus. So what I would do is first assign some variable r to the radius of the semicircular portion of the window. Then I would find an expression for the area of the window as a function of r. Then, as in most max/min problems, I'd take the derivative with respect to r of this function, set it equal to zero, and figure out what that gives me for r. Then, of course, you really have to figure out whether what you've found really is a maximum value, perhaps using the second derivative test. Anyway, give this a shot, and write back if you have difficulty. -Ken "Dr." Math |
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