Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 3x2 - 4xy + xyz (a) Find the rate of change of the potential at P(4, 6, 6) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?
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Suppose you are climbing a hill whose shape is given by the equation z = 1600...
Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are me...
Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1366). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to...
Suppose you are climbing a hill whose shape is given by the equation below
Suppose you are climbing a hill whose shape is given by the equation below, where x, y, and z are measured in meters, and you are standing at a point with coordinates(60, 40, 1666). The positive x-axis points east and the positive y-axis points north.(a) If you walk due south, will you start to ascend or descend?ascenddescendAt what rate?___________(b) If you walk northwest, will you start to ascend or descend?ascenddescendAt what rate? (Round the answer to two decimal places.)_____________(c) In...
help.. 7. 67 points I Previaus Arawers SCacET8 146034 25 Submissions Used My Notes Ask Your Taachs Suppose you are climbing a hill whoss shape Is gven by the aquation-900-0.00x -o.oly. whera x, y, and...
help..
7. 67 points I Previaus Arawers SCacET8 146034 25 Submissions Used My Notes Ask Your Taachs Suppose you are climbing a hill whoss shape Is gven by the aquation-900-0.00x -o.oly. whera x, y, and z are measured in metons, and you are standing at a point with coordinatos (120, 80, 764). Tha positive -axls points east and tha poaitive y-axls point (a) If you walk dua south, will you start to ascand or descand? O ascent descend At what...
3. Suppose that you are climbing a hill whose shape is given by the equation z=1000...
3. Suppose that you are climbing a hill whose shape is given by the equation z=1000 - 0.01x-0.02y?, and you are standing at a point with coordinates (60, 100,764). In which direction should you proceed initially in order to reach the top of the hill fastest? 4. Find and classify all critical points of the function h(x,y) = 223+73 - 3x2 - 12. - 3y. Use the second derivative test when appropriate.
(9 points) Consider the bowl-shaped paraboloid z = f(x, y) = 4 + x2 + 3y2....
(9 points) Consider the bowl-shaped paraboloid z = f(x, y) = 4 + x2 + 3y2. (a) If you are located on the paraboloid at the point (2, - *), in which direction should you move in order to ascend on the surface at the maximum rate? What is the rate of change? (b) If you are located at the point (2, -), in which direction should you move in order to descend on the surface at the maximum rate?...
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?
Suppose that over a certain region of space the electrical potential V is given by the...
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x2 – 3xy + xyz (a) Find the rate of change of the potential at P(3, 6, 5) in the direction of the vector v = i + j - k. 56 15 (b) In which direction does V change most rapidly at P? 17 3 3 8V 721 '8V721 '8V (c) What is the maximum rate of...
We have a u-shaped conducting track on its side with the open part of the "U"...
We have a u-shaped conducting track on its side with the open part of the "U" the left A vertical 0.75 meter conducting bar is to slide left or right on the track There is magnetic field 0.06 Tesla directed out of the page. You are moving the bar to the right with a constant speed 400 meters per second Calculate the EMF induced in the circuit when the bar is 1.5 meters from the right of the sideways "U"...
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z)...
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
Name of All Group members Section At the end of this activity you will be able...
Name of All Group members Section At the end of this activity you will be able to: a. Add and Subtract vectors b. Resolve vectors into horizontal and vertical components c. Apply vector components to solve kinematic problems. Rank the magnitudes of the vectors from greatest to least. If two or more vectors have the same magnitude, the sequence in which you list them does not matter. 7Least Greatest 1 2 3 , 4 2. List all of the vectors...
Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1366). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to...
help..
7. 67 points I Previaus Arawers SCacET8 146034 25 Submissions Used My Notes Ask Your Taachs Suppose you are climbing a hill whoss shape Is gven by the aquation-900-0.00x -o.oly. whera x, y, and z are measured in metons, and you are standing at a point with coordinatos (120, 80, 764). Tha positive -axls points east and tha poaitive y-axls point (a) If you walk dua south, will you start to ascand or descand? O ascent descend At what...
3. Suppose that you are climbing a hill whose shape is given by the equation z=1000 - 0.01x-0.02y?, and you are standing at a point with coordinates (60, 100,764). In which direction should you proceed initially in order to reach the top of the hill fastest? 4. Find and classify all critical points of the function h(x,y) = 223+73 - 3x2 - 12. - 3y. Use the second derivative test when appropriate.
(9 points) Consider the bowl-shaped paraboloid z = f(x, y) = 4 + x2 + 3y2. (a) If you are located on the paraboloid at the point (2, - *), in which direction should you move in order to ascend on the surface at the maximum rate? What is the rate of change? (b) If you are located at the point (2, -), in which direction should you move in order to descend on the surface at the maximum rate?...
Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x2 – 3xy + xyz (a) Find the rate of change of the potential at P(3, 6, 5) in the direction of the vector v = i + j - k. 56 15 (b) In which direction does V change most rapidly at P? 17 3 3 8V 721 '8V721 '8V (c) What is the maximum rate of...
We have a u-shaped conducting track on its side with the open part of the "U" the left A vertical 0.75 meter conducting bar is to slide left or right on the track There is magnetic field 0.06 Tesla directed out of the page. You are moving the bar to the right with a constant speed 400 meters per second Calculate the EMF induced in the circuit when the bar is 1.5 meters from the right of the sideways "U"...
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
Name of All Group members Section At the end of this activity you will be able to: a. Add and Subtract vectors b. Resolve vectors into horizontal and vertical components c. Apply vector components to solve kinematic problems. Rank the magnitudes of the vectors from greatest to least. If two or more vectors have the same magnitude, the sequence in which you list them does not matter. 7Least Greatest 1 2 3 , 4 2. List all of the vectors...
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