Suppose that you are climbing a hill whose shape is given by 300). In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest? z = 764 – 0.04x2 - 0.04y, and that you are at the point (100, 40, If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 48E
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Suppose that you are climbing a hill whose shape is given by z = 764 0.04x? – 0.04y, and that you are at the point (100, 40,
300).
In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest?
If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?
Transcribed Image Text:Suppose that you are climbing a hill whose shape is given by z = 764 0.04x? – 0.04y, and that you are at the point (100, 40, 300). In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest? If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?
Expert Solution
Step 1

Given function is

z=764-0.04x2-0.04y2

and 

Point x,y,z=100,40,300

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