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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 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.
(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:
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...
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...
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.
(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...
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.
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...
y(m) 1. (10 points) The temperature of a plate in the ry-plane is given by 3 48 2 T(x, y) x2 2y2 2 1 T is in degrees Celsius (°C) and x, y are in meters (m). A contour plot of T(x, y) is shown at right. -3 -2 4 3 4 (a) At the point (-2,1) draw and label a vector in the direction 6 of VT(-2, 1 8 4 (b) At (-2, 1) draw and label both vectors...