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I need help with Part 2, Part 1 is given for context Part I: Complete the following steps: Reference: https://openstax.org/books/calculus-volume-1/pages/4-7-applied-optimization-problems Question 327 A lifeguard is

I need help with Part 2, Part 1 is given for context

Part I: Complete the following steps:

Reference: https://openstax.org/books/calculus-volume-1/pages/4-7-applied-optimization-problems

Question 327

A lifeguard is at point A of a circular pool with diameter 40 m. He must reach someone who is drowning on the exact opposite side of the pool, at position C. The lifeguard swims with a speed v = 3 m/s from point A to point B, and then runs around the pool from point B to point C at speed w = 9 m/s.

  1. Find a function that measures the total amount of time it takes to reach the drowning person as a function of the swim angle, expressed in radians.
  2. Find at what angle , in radians, the lifeguard should swim to reach the drowning person in the least amount of time.

Part II: Based on your work in Part I, discuss the following:

  1. Suppose the pool was rectangular. Respond to the following:
  2. Does it still make sense to parameterize using? Why or why not?
  3. If not, what parameter would you use?
  4. If so, how does the parameterization change?
  5. Set up, but do not solve, this problem with a rectangular pool.

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