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31. Take any map and draw a circle on it anywhere (Figure 6). Prove that at any moment in time there exists a pair of diametrically opposite points A and B on that circle corresponding to locations where the temperatures at that moment are equal. Hint: Let 0 be an angular coordinate along the circle and let f (0) be the difference in temperatures at the locations corresponding to 0 and 0+r. B FIGURE 6 f(0) is the difference between the temperatures at A and B.

31. Take any map and draw a circle on it anywhere (Figure 6). Prove that at any moment in time there exists a pair of diametrically opposite points A and B on that circle corresponding to locations where the temperatures at that moment are equal. Hint: Let 0 be an angular coordinate along the circle and let f (0) be the difference in temperatures at the locations corresponding to 0 and 0+r. B FIGURE 6 f(0) is the difference between the temperatures at A and B.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 20T
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31. Take any map and draw a circle on it anywhere (Figure 6). Prove that at any moment in time there exists a pair of diametrically opposite points A and B on that circle corresponding to locations where the temperatures at that moment are equal. Hint: Let 0 be an angular coordinate along the circle and let f (0) be the difference in temperatures at the locations corresponding to 0 and 0+r. B FIGURE 6 f(0) is the difference between the temperatures at A and B.
Transcribed Image Text:31. Take any map and draw a circle on it anywhere (Figure 6). Prove that at any moment in time there exists a pair of diametrically opposite points A and B on that circle corresponding to locations where the temperatures at that moment are equal. Hint: Let 0 be an angular coordinate along the circle and let f (0) be the difference in temperatures at the locations corresponding to 0 and 0+r. B FIGURE 6 f(0) is the difference between the temperatures at A and B.
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