mel is designing a triathlon course which will have three legs in the
. Mel is designing a triathlon course, which will have three legs in the following order: biking, swimming,and running. She decides to make a course in the shape of a right triangle, with the hypotenuse as a3 kilometer swim down a straight stretch of the Charles River. Two possibilities are shown below. Mel knows the average triathlete swims at 2 km/hr, runs at 12 km/hr and bikes at 12/3 km/hr. In order to make her triathlon a real challenge, Mel wants to maximize the time it takes for an average triathlete to complete the course. In this problem, you'll help Mel by expressing this time as a function of one variable.
) Express the amount of time it takes for an average triathlete to complete the course as a function of 0, the angle between the running and swimming legs. What is the domain of the function you wrote in (a)? (c) Express the amount of time it takes for an average triathlete to complete the course as a function of the length of the biking leg. (d) What is the domain of the function you wrote in (c)?
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