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# Theory Of Computation

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After having reviewed the problem-solving techniques in the textbook, for each of the following problems, determine what kind of problem it is (e.g., optimization) and briefly explain how you would set up a computer program to solve it. Don’t just say “this is an optimization problem.” Say which technique(s) you would use to solve it and why. Note that some of these might require techniques that were not discussed yet in class. In  CISC601 Scientific Computing II Page 7 of 10 these cases, you will have to do some extra reading on your own. You do not have to actually solve the problems. 1. The performance of an airplane wing is given by measurements a, b, c, and d and the equation � = 0.1298�* + 4.123�/ 0 . You wish to determine the best design to yield the best performance. 2. A banana is launched from a catapult at ground level on a completely flat surface at an angle of 16° with an initial velocity of 25km/h. You wish to determine when it will hit the ground again. 3. A circular glass-bottomed swimming pool with radius 10’ and height 6’ with a circular hole in the bottom of radius 5” is being filled with pure water from a hose at a rate of 3.2gal/min. You wish to determine if the pool will overflow. 4. Two bananas are launched from catapults facing each other over a completely flat surface at angles of 25° and 35°, each with initial velocities of 60km/h. You wish to determine if they will collide in midair. 5. A kind of yeast is discovered that produces a compound with antibacterial properties. The yeast grows at the rate defined by the following equation: � = *2 345.6242745.*28, where c is the temperature of the growing container in Celsius. At what temperature should the growing container be set? 6. You have plotted the growth rates of a bacterium over time using several combinations of temperature and humidity in the growing container. You wish to develop an equation that will yield an approximation of bacterial growth as a function of time, temperature, and humidity.

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