The concentration of salt in a fluid at is given by mg/cm . You are at the point . (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 cm/sec. How fast is the concentration changing? Rate of change = HINT: The rate of change of the perceived concentration F(x,y,z), by the Chain Rule, equals the dot product of the gradient vector of F and the velocity of the "particle". To find it, we need to know the norms (magnitudes) of both vectors and the angle between them. In this problem the angle is known.
The concentration of salt in a fluid at is given by mg/cm . You are at the point . (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 cm/sec. How fast is the concentration changing? Rate of change = HINT: The rate of change of the perceived concentration F(x,y,z), by the Chain Rule, equals the dot product of the gradient vector of F and the velocity of the "particle". To find it, we need to know the norms (magnitudes) of both vectors and the angle between them. In this problem the angle is known.
The concentration of salt in a fluid at is given by mg/cm . You are at the point . (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 cm/sec. How fast is the concentration changing? Rate of change = HINT: The rate of change of the perceived concentration F(x,y,z), by the Chain Rule, equals the dot product of the gradient vector of F and the velocity of the "particle". To find it, we need to know the norms (magnitudes) of both vectors and the angle between them. In this problem the angle is known.
The concentration of salt in a fluid at
is given by
mg/cm
. You are at the point
.
(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
cm/sec. How fast is the concentration changing?
Rate of change =
HINT: The rate of change of the perceived concentration F(x,y,z), by the Chain Rule, equals the dot product of the gradient vector of F and the velocity of the "particle". To find it, we need to know the norms (magnitudes) of both vectors and the angle between them. In this problem the angle is known.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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