Question: 1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on

1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. These questions refer to Lab 12A: More Optimization Problems. A swimmer is stranded 50 meters from shore, and you're standing 100 meters down the beach from the closest point to them (see the gure below). Assume that you can run at a speed of 4 meters/ second and you can swim at a speed of 2 meters/second. swimmer Q I\\ I \\ I \\ \\ ' \\ I \\ I \\ I \\ | \\ I \\ | \\ 50 I \\ I \\ I \\ I \\ \\ : . \\ I \\ ' \\ ' \\ I I 'I you ..O P a: 100 7 3: (a) If you run along the shore until you're :1: meters from the point P and then start swimming directly toward the stranded person, what is the total distance that you will run? What is the total distance that you will swim? You should have these answers in terms of X. (b) Let T(x) be the total time it takes to reach the stranded swimmer. Find the value of x in the domain [0, 50] that minimizes the total time T(x). (c) What is the total time T(x) that it takes you to reach the stranded swimmer? (d) What distance should you run and what distance should you swim to get to the swimmer as quickly as possible? This is the same question as (a), except now give numerical answers

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