The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z) = x6 + y3 + x2z2 &n...
The concentration of salt in a fluid at
(x,y,z) is given
by F(x,y,z)
= x6 + y3 +
x2z2 mg/cm3.
Suppose you are at the point (−1, 1, 1).
(a) In which direction should you move if you want the
concentration to increase the fastest? Give your answer as a
vector.
(b) You start to move in the direction you found in part (a) at a
speed of 7 units/sec. How fast is the concentration changing? Give
an exact answer.
Homework Answers
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The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z) = x6 + y3 + x2z2 &n...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 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? 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?
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 mg/cm3 You are at the point (1,1,1...
The concentration of salt in a fluid at (x,y,z) is given by F(x,y,z)=x^2+y^4+2x^2z^2 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? I keep getting <5,2,8> for this answer and it says it is incorrect 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?
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e...
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e e-3x2 – 3y2 – 2z2 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e...
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e e-3x2 – 3y2 – 2z2 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
a.You are standing above the point (5,1) on the surface z=30-(2x^2+y^2) In which direction should you walk to descend...
a.You are standing above the point (5,1) on the surface z=30-(2x^2+y^2) In which direction should you walk to descend fastest? (give your answer as a unit 2-vector) b. If you start to move in this direction what is the slope of your path?
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the r...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
Please give the answer symbolically, thank you. The temperature at a point (x, y, z) is...
Please give the answer symbolically, thank you.
The temperature at a point (x, y, z) is given by T(x, y, z) = 102-3x2 – 3y2 – 222 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z)...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
3 4. (4 pts) Consider the surface z = z = x²y + y3. (a) Find...
3 4. (4 pts) Consider the surface z = z = x²y + y3. (a) Find the normal direction of the tangent plane to the surface through (1,1,2). (b) Find the equation of the tangent plane in (a). (e) Determine the value a so that the vector 7= -7+27 +ak is parallel to the tangent plane in (a). (d) Find the equation of the tangent line to the level curve of the surface through (1,1).
For an imcomprresible fluid -y- direction velocity component on (x,y) plane given . İn this statement...
For an imcomprresible fluid -y- direction velocity component on
(x,y) plane given . İn this statement a
and v constant.For the flow area of this fluid find the vortex
vector of -z- direction component.? Note:X=0 for
U(x,y)=0
xy 2aV- = (و ,) ( +y)
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e e-3x2 – 3y2 – 2z2 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e e-3x2 – 3y2 – 2z2 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
Please give the answer symbolically, thank you.
The temperature at a point (x, y, z) is given by T(x, y, z) = 102-3x2 – 3y2 – 222 In which direction does the temperature increase fastest at the point (3, 1, 4)? Express your answer as a UNIT vector.
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
3 4. (4 pts) Consider the surface z = z = x²y + y3. (a) Find the normal direction of the tangent plane to the surface through (1,1,2). (b) Find the equation of the tangent plane in (a). (e) Determine the value a so that the vector 7= -7+27 +ak is parallel to the tangent plane in (a). (d) Find the equation of the tangent line to the level curve of the surface through (1,1).
For an imcomprresible fluid -y- direction velocity component on
(x,y) plane given . İn this statement a
and v constant.For the flow area of this fluid find the vortex
vector of -z- direction component.? Note:X=0 for
U(x,y)=0
xy 2aV- = (و ,) ( +y)
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