Investigation A team of oceanographers is mapping the ocean floor to assist in the

Chapter 13, Problem 75

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Investigation A team of oceanographers is mapping the ocean floor to assist in the recovery of a sunken ship. Using sonar, they develop the model where is the depth in meters, and and are the distances in kilometers. (a) Use a computer algebra system to graph the surface. (b) Because the graph in part (a) is showing depth, it is not a map of the ocean floor. How could the model be changed so that the graph of the ocean floor could be obtained? (c) What is the depth of the ship if it is located at the coordinates and (d) Determine the steepness of the ocean floor in the positive direction from the position of the ship. (e) Determine the steepness of the ocean floor in the positive direction from the position of the ship. (f) Determine the direction of the greatest rate of change of depth from the position of the ship.