Suppose you are climbing a hill whose shape is given by the equation z = 1,300 -0.005x² -0.01y, where x, y, and z are measured in meters, and you are standing at a point with coordinates (80, 80, 1204). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend O ascend O descend descend? At what rate (in vertical meters per horizontal meter)? 1.6 vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? O ascend O descend At what rate (in vertical meters per horizontal meter)? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction is the slope largest? What is the rate of ascent (in vertical meters per horizontal meter) in that direction? (Round your answer to two decimal places.) vertical meters per horizontal meter At what angle (in degrees) above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)
Suppose you are climbing a hill whose shape is given by the equation z = 1,300 -0.005x² -0.01y, where x, y, and z are measured in meters, and you are standing at a point with coordinates (80, 80, 1204). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend O ascend O descend descend? At what rate (in vertical meters per horizontal meter)? 1.6 vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? O ascend O descend At what rate (in vertical meters per horizontal meter)? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction is the slope largest? What is the rate of ascent (in vertical meters per horizontal meter) in that direction? (Round your answer to two decimal places.) vertical meters per horizontal meter At what angle (in degrees) above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)
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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Suppose you are climbing a hill whose shape is given by the equation
z = 1,300 − 0.005x2 − 0.01y2,
where x, y, and z are measured in meters, and you are standing at a point with coordinates (80, 80, 1204). The positive x-axis points east and the positive y-axis points north.
Transcribed Image Text:Suppose you are climbing a hill whose shape is given by the equation z = 1,300 -0.005x² -0.01y², where x, y, and z are measured in meters, and you are standing at a point with coordinates (80, 80, 1204). The positive x-axis points east and the positive y-axis
points north.
(a) If you walk due south, will you start to ascend or descend?
O ascend
O descend
At what rate (in vertical meters per horizontal meter)?
1.6
vertical meters per horizontal meter
(b) If you walk northwest, will you start to ascend or descend?
O ascend
O descend
At what rate (in vertical meters per horizontal meter)? (Round your answer to two decimal places.)
vertical meters per horizontal meter
(c) In which direction is the slope largest?
What is the rate of ascent (in vertical meters per horizontal meter) in that direction? (Round your answer to two decimal places.)
vertical meters per horizontal meter
At what angle (in degrees) above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)
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