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Your new house sits at a perpendicular distance of 6 miles from the county highway...

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Your new house sits at a perpendicular distance of 6 miles from the county highway across a flatparcel of land. The town where you work is 15 miles down the highway from that point P. You aregoing to build a gravel road that will connect somewhere to the county highway. The maximum speedon your gravel road will be 25 mph and the maximum speed on the county highway is 50 mph. Youwould like to be able to drive to town in the shortest time.a. Write the equation you will be working with in this problem.b.Use Calculus to determine how far down the highway from the point P you should connect yourroad to the county highway.C. How much time can be saved by constructing the road as you indicated in part b.

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