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M9.4.4

Understands that theories in mathematics are greatly influenced by practical issues; real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications.

Battle Strategies in the Bismarck Sea

Opposing naval commanders in a war must choose how to attack and defend rncritical areas.

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Motivating Honest Budgets and Hard Work Simultaneously

Motivating honest budgets and profit expectations is difficult because some rnsubordinate managers will provide overly optimistic budgets to "look good" to rntheir bosses, while others will lowball budgets so they will "look good" when they rnexceed expectations. This paper explains how to motivate accurate forecasts of rnbudgets and profits.

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Pilots, Airplanes, and the Tangent of Three (3) Degrees

When approaching an airport, pilots must learn to maneuver their aircraft visually, so that a stabilized approach to the runway can be flown at a constant approach angle. Precise approach planning insures a smooth transition to a landing within the Touchdown Zone (1) of the runway. Pilots must sometimes execute visual approaches that are varied in size, shape, and angle based upon a variety of factors such as: other aircraft, obstructions, noise abatement, or prevailing weather conditions. The standard approach angle however, is 3°.

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Logarithms: Taking the Curve Out

Logarithms are very handy when dealing with numbers at lots of different scales (see related PUMAS example: Just What is a Logarithm, Anyway?). But they also have another useful feature: they help us average measurements of physical phenomena that have nonlinear behavior. A common example in my field of study relates cloud "albedo" to cloud optical depth (Fig. 1); but similar examples may be found when examining many natural phenomena.

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