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Question 6 (a) Near a surface buoy the depth of a lake at the point with coordinates (x, y) is given by z = 100+ 0.05z² -0.02y² where x, y and z are measured in metres. The coxswain driving the small boat starts at the point (60, 30) and moves towards the buoy, which is located at (0,0). Is the water under the boat getting deeper or shallower when he departs? At what rate? Explain your answer. (b) Determine the equation of the tangent plane to the surface z+1=re" cos z at the point (1,0,0).

Question 6 (a) Near a surface buoy the depth of a lake at the point with coordinates (x, y) is given by z = 100+ 0.05z² -0.02y² where x, y and z are measured in metres. The coxswain driving the small boat starts at the point (60, 30) and moves towards the buoy, which is located at (0,0). Is the water under the boat getting deeper or shallower when he departs? At what rate? Explain your answer. (b) Determine the equation of the tangent plane to the surface z+1=re" cos z at the point (1,0,0).

Advanced Engineering Mathematics
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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Question 6 (a) Near a surface buoy the depth of a lake at the point with coordinates (x, y) is given by z = 100+ 0.05z² -0.02y² where x, y and z are measured in metres. The coxswain driving the small boat starts at the point (60, 30) and moves towards the buoy, which is located at (0,0). Is the water under the boat getting deeper or shallower when he departs? At what rate? Explain your answer. (b) Determine the equation of the tangent plane to the surface z+1=re" cos z at the point (1,0,0).
Transcribed Image Text:Question 6 (a) Near a surface buoy the depth of a lake at the point with coordinates (x, y) is given by z = 100+ 0.05z² -0.02y² where x, y and z are measured in metres. The coxswain driving the small boat starts at the point (60, 30) and moves towards the buoy, which is located at (0,0). Is the water under the boat getting deeper or shallower when he departs? At what rate? Explain your answer. (b) Determine the equation of the tangent plane to the surface z+1=re" cos z at the point (1,0,0).
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