A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road, The forest ranger can walk 3 miles per hour in the forest and travel 5 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the Highway left, and then along the road. Car The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car. Forest 5Vx +4 +3c – 3x 15 Forest Ranger T(x) = Toward what point on the road should the ranger walk in order to minimize the travel time to the car if... (a) c = 8 miles? (Numerical Answer ONLY) x = 1.5 (b) c = 1/2 miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY) x - 1.5 Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?

A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road, The forest ranger can walk 3 miles per hour in the forest and travel 5 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the Highway left, and then along the road. Car The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car. Forest 5Vx +4 +3c – 3x 15 Forest Ranger T(x) = Toward what point on the road should the ranger walk in order to minimize the travel time to the car if... (a) c = 8 miles? (Numerical Answer ONLY) x = 1.5 (b) c = 1/2 miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY) x - 1.5 Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from 306 kicks during games among top teams. In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks? E Click the icon to view the penalty kick data. Determine the null and alternative hypotheses. A. Ho: Jump direction is independent of kick direction. H: Jump direction is dependent on kick direction. O B. Ho: Goalkeepers jump in the direction of the kick. H,: Goalkeepers do not jump in the direction of the kick. O C. Ho: Goalkeepers do not jump in the…