The concentration of salt in a fluid at (x, y, z) is given by F(x, y, z) = 2x² + 3y + 4x²z² mg/cm³. You are at the point (1,-1,-1). (a) In which direction should you move if you want the concentration to increase the fastest? direction: (Give your answer as a vector.) (b) You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing? rate of change =
The concentration of salt in a fluid at (x, y, z) is given by F(x, y, z) = 2x² + 3y + 4x²z² mg/cm³. You are at the point (1,-1,-1). (a) In which direction should you move if you want the concentration to increase the fastest? direction: (Give your answer as a vector.) (b) You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing? rate of change =
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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Please answer both questions, thank you so much!
Transcribed Image Text:The concentration of salt in a fluid at (x, y, z) is given by F(x, y, z) = 2x² + 3y¹ + 4x²z² mg/cm³. You are at the point (1,−1, −1).
(a) In which direction should you move if you want the concentration to increase the fastest?
direction:
▶
(Give your answer as a vector.)
(b) You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration changing?
rate of change
Transcribed Image Text:Corn production, C, is a function of rainfall, R (in inches), and temperature, T (in degrees C). The first figure below shows how rainfall is predicted to
vary with time because of global warming; the second, how temperature is predicted to vary with time because of global warming.
Suppose that we know that (currently)
15
Hence, estimate dC/dt when t = 2020.
dC/dt =
14
13
27
25
23
2020
2040
Graph of rainfall, R vs. time, t
2020
2040
Graph of temperature, T vs. time, t
AC 3.8AR - 5.4AT
Use this to estimate the change in corn production between the year 2020 and the year 2021.
Change =
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