Question 2 Suppose near a cargo ship, the depth of the sea is given by the function of: f(x, y) = 500 -0.02x² -0.03y², where x, y are measured in meters. Suppose a fisherman is on a small boat with coordinates (30, 40, 434). The positive x -axis points east and the positive y-axis points north. (a) (b) (c) Calculate the gradient of f (x, y) at (30, 40, 434). If the fisherman move towards North, is the water under the boat getting shallower or deeper when he departs? If the fisherman move towards to the cargo ship, will he start to ascend or descend? At what rate? (d) If the fisherman starts to moves, in which direction is the water under the boat getting deepest? What is the rate of change of the depth in that direction?
Question 2 Suppose near a cargo ship, the depth of the sea is given by the function of: f(x, y) = 500 -0.02x² -0.03y², where x, y are measured in meters. Suppose a fisherman is on a small boat with coordinates (30, 40, 434). The positive x -axis points east and the positive y-axis points north. (a) (b) (c) Calculate the gradient of f (x, y) at (30, 40, 434). If the fisherman move towards North, is the water under the boat getting shallower or deeper when he departs? If the fisherman move towards to the cargo ship, will he start to ascend or descend? At what rate? (d) If the fisherman starts to moves, in which direction is the water under the boat getting deepest? What is the rate of change of the depth in that direction?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with part (d)
Transcribed Image Text:Question 2
Suppose near a cargo ship, the depth of the sea is given by the function of:
f(x, y) = 500 -0.02x² -0.03y²,
where x, y are measured in meters. Suppose a fisherman is on a small boat with
coordinates (30, 40, 434). The positive x -axis points east and the positive y-axis points
north.
(a)
(b)
(c)
Calculate the gradient of f(x, y) at (30, 40, 434).
If the fisherman move towards North, is the water under the boat getting
shallower or deeper when he departs?
If the fisherman move towards to the cargo ship, will he start to ascend or
descend? At what rate?
(d)
If the fisherman starts to moves, in which direction is the water under the boat
getting deepest? What is the rate of change of the depth in that direction?
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