Date: Mon, 8 Feb 1999 12:03:05 -0600 (CST)
Subject: a problem
Who is asking: Student
Hi again Katherine
If a is the length of the dog's leash then using calculus and polar coordinates the area of the portion of the garden that Dig can't reach is
Finding a value of a that makes this expression equal to 64 looks impossible, so lets try the other approach.
The garden has an area of 64 square meters and is approximately 3 so I drew a diagram and tried to estimate the length of the leash so that approximately one third of the area (64 square meters) would be beyond Dig's reach. My estimate lead me to guess that the configuration was as in the diagram, that is so that the line joining A and B goes through the center O of the circle that bounds the garden.
The area of the two "caps" is the area of the semicircle BCA minus the area of the triangle BCA, that is
Thus the area that Dig can dig is 64 - 64. Since the area of the entire garden is 64 , the arera that he can't reach is 64 square meters.So my guess was correct.
Chris and Harley
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