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 D is the depth in meters, and x and y 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 x = 1 and y = 0.5?

(d) Determine the steepness of the ocean floor in the positive x-direction from the position of the ship.

(e) Determine the steepness of the ocean floor in the positive y-direction from the position of the ship.

(f) Determine the direction of the greates

Transcribed Image Text:

'꼴 D = 250 + 30x2 + 50 sin 0 ≤x≤ 2, 0≤y≤2