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?
Homework Answers
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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...
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 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.
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z +...
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...
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?
Given z = 2(x,y),X = x(s,t),y = y(s,t), and zx(-1,1)= 3, zy(-1,1)= 2, xs(-1,1)= -1, x,(-1,1)=...
Given z = 2(x,y),X = x(s,t),y = y(s,t), and zx(-1,1)= 3, zy(-1,1)= 2, xs(-1,1)= -1, x,(-1,1)= 3, ys(-1,1)= 1, z (1,2)=5, z (1,2)=3, x(1,2)= -1, y(1,2)= 1, y,(-1,1)= 4, xs(1,2)=3, xx(1,2)= -2, x(-1,1)= 1, y(- 1,1)=2, 7(1,2)=7, vs(1,2)=2, a. compute ( cas ? )ats = 1,t =2, b. if we plot the surface Z as a function of 5 and t, then at the point (1,2) in the st-plane, how fast is Z changing in the direction (-1,1) in the...
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.
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...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9.
Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9
Solve the following problem using Lagrange...
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...
Given z = 2(x,y),X = x(s,t),y = y(s,t), and zx(-1,1)= 3, zy(-1,1)= 2, xs(-1,1)= -1, x,(-1,1)= 3, ys(-1,1)= 1, z (1,2)=5, z (1,2)=3, x(1,2)= -1, y(1,2)= 1, y,(-1,1)= 4, xs(1,2)=3, xx(1,2)= -2, x(-1,1)= 1, y(- 1,1)=2, 7(1,2)=7, vs(1,2)=2, a. compute ( cas ? )ats = 1,t =2, b. if we plot the surface Z as a function of 5 and t, then at the point (1,2) in the st-plane, how fast is Z changing in the direction (-1,1) in the...
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.
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...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9.
Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9
Solve the following problem using Lagrange...
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