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(8 points) The temperature at a point (x, y, z) is given by T(x, y, z)...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e?x2 ? 3y2 ? 7z2 where T is...
The temperature at a point(x, y, z)is given byT(x, y, z) = 100e?x^2 ? 3y^2 ? 7z^2where T is measured in °C andx, y, zin meters.(a) Find the rate of change of temperature at the point P(2, ?1, 2) in the direction towards the point(3, ?2, 3).(b) In which direction does the temperature increase fastest at P?(c) Find the maximum rate of increase at P.
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - 5y2 - 722 where Tis measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P12,-1, 3) in the direction towards the point (5, -3, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
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...
14. + -13 points SCalc8 14.6.032. 0115 Submissions Used The temperature at a point (x, y, z) is g...
14. + -13 points SCalc8 14.6.032. 0115 Submissions Used The temperature at a point (x, y, z) is given by T(x, y, z) - 300e-x2 - 3y2 -722 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -4, 3) °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate...
(a) The temperature T(x, y) at a point (x, y) on a plate is given by T(x, y) = 16 − x 2 − 2y 2 . ...
(a) The temperature T(x, y) at a point (x, y) on a plate is given by T(x, y) = 16 − x 2 − 2y 2 . i. What is the direction of greatest increase in temperature at the point P = (1, 3)? [3 marks] ii. What are the directions of zero change in temperature at the point P? [4 marks] iii. Find the path of greatest increase in temperature from the point P to the point of maximum...
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.
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.
Pt 3. The temperature (in C) at the point (r, y) (r and y are measured in em) is T(r.y). A bug cr...
pt 3. The temperature (in C) at the point (r, y) (r and y are measured in em) is T(r.y). A bug crawls along a path (see the picture below) from left to right toward the point P V T(P) (a) Find the directional derivative of the temperature at the point P in the direction of the bug's travel if the angle between this direction and VT(P) (the gradient of T at P) is r/3 and /VT(P)I-5 (b) At the...
A ship moves in space along the trajectory: rt,t,t]. The air pressure in this medium is given by ...
A ship moves in space along the trajectory: rt,t,t]. The air pressure in this medium is given by P(x,y,z)-e (cos(x ty)+1) a) Calculate the velocity vector of this trajectory b) Calculate the derivative of P in the direction of displacement of the trajectory r (t) at point P: (1,1,1) c) In which direction does the pressure at the point P: (1,1,1) increase fastest? d) What is the maximum rate of change of pressure in P (1, 1,1)?
A ship moves...
The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - 5y2 - 722 where Tis measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P12,-1, 3) in the direction towards the point (5, -3, 6). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.
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...
14. + -13 points SCalc8 14.6.032. 0115 Submissions Used The temperature at a point (x, y, z) is given by T(x, y, z) - 300e-x2 - 3y2 -722 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (6, -4, 3) °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate...
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.
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.
pt 3. The temperature (in C) at the point (r, y) (r and y are measured in em) is T(r.y). A bug crawls along a path (see the picture below) from left to right toward the point P V T(P) (a) Find the directional derivative of the temperature at the point P in the direction of the bug's travel if the angle between this direction and VT(P) (the gradient of T at P) is r/3 and /VT(P)I-5 (b) At the...
A ship moves in space along the trajectory: rt,t,t]. The air pressure in this medium is given by P(x,y,z)-e (cos(x ty)+1) a) Calculate the velocity vector of this trajectory b) Calculate the derivative of P in the direction of displacement of the trajectory r (t) at point P: (1,1,1) c) In which direction does the pressure at the point P: (1,1,1) increase fastest? d) What is the maximum rate of change of pressure in P (1, 1,1)?
A ship moves...
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