A bicyclist leaves from her home at 9 a.m. and rides to a beach 40 mi away. Because of a breeze off the ocean, the temperature at the beach remains 60 °F throughout the day. At the cyclist's home the temperature increases linearly with time, going from 60 °F at 9 a.m. to 80 °F by 1 p.m.The temperature is assumed to vary linearly as a function of position between the cyclist's home and the beach.Determine the rate of change of temperature observed by the cyclist for the following conditions: (a)as she pedals 10 mph through a town 10 mi from her home at 10 a.m.; (b)as she eats lunch at a rest stop 30 mi from her home at noon; (c)as she arrives enthusiastically at the beach at 1 P.M.,pedaling 20 mph.

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