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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).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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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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