5) For the following situations, explain which concept, method, and/or formula from chapter 14 you would need to use to solve the problem, and why: a. I'm checking the size of an eagle's nest at the top of a tall tree for an ecological study. I want to know its volume, but due to its location, I must measure it from a distance and my measurements may be incorrect.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The options are Partial derivatives, tangent planes, directional derivatives, Gradient vector, optimization

5) For the following situations, explain which concept, method, and/or formula from
chapter 14 you would need to use to solve the problem, and why:
a. I'm checking the size of an eagle's nest at the top of a tall tree for an
ecological study. I want to know its volume, but due to its location, I must
measure it from a distance and my measurements may be incorrect.
b. I want to race a remote-controlled car up a mountain, but I know that the car
is very sensitive to steep slopes, so I want to find the most gradual path
possible so I can make it to the top without falling over.
c. I'm engineering a type of ultrasound process that uses energy reflected off of
multiple surfaces to combine at a single point. I need to position my surfaces
correctly, so the beams hit the same point after reflection.
d. I'm trying to make money in the stock market, and I've determined a revenue
function based on some stocks that are related in specific ways. I want to
make the most money possible, but there are constraints and ways the stocks
are connected that I have to take into account.
Transcribed Image Text:5) For the following situations, explain which concept, method, and/or formula from chapter 14 you would need to use to solve the problem, and why: a. I'm checking the size of an eagle's nest at the top of a tall tree for an ecological study. I want to know its volume, but due to its location, I must measure it from a distance and my measurements may be incorrect. b. I want to race a remote-controlled car up a mountain, but I know that the car is very sensitive to steep slopes, so I want to find the most gradual path possible so I can make it to the top without falling over. c. I'm engineering a type of ultrasound process that uses energy reflected off of multiple surfaces to combine at a single point. I need to position my surfaces correctly, so the beams hit the same point after reflection. d. I'm trying to make money in the stock market, and I've determined a revenue function based on some stocks that are related in specific ways. I want to make the most money possible, but there are constraints and ways the stocks are connected that I have to take into account.
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