The temperature at a point (x, y) is T(x,y), measured in degrees Celsius. A bug crawls...
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...
5. The temperature of a metal plate at (x,y) is e rate of 8ft/min (.e. -2). degrees. A bug is walking northeast at a dx dy dt dt a) From the bug's point of view, at what rate is the temperature changing with respect to distance as it crosses the origin? Label your answer with correct units. b) If the bug is sitting at the origin, in what direction should it start moving to experience the greatest rate of decrease...
6. The temperature at (x,y) is T(x,y) = 20 + 100%+++") degrees (in Celsius). A bug carries a tiny thermometer along the path c(t) = (cos(t - 2), sin(t -- 2)) where t is in seconds. What is the initial rate of change of the temperature t = 0.6s?
(20p) The temperature function T(x,y) is defined as T(x,y) = cos(-) at a specified location. Here x denotes the north direction and y denotes the east direction. So that Tx is the rate of change of the temperature with respect to distance if we travel north direction and Ty is the rate of change of the temperature with respect to distance if we travel east direction. Find the rate of change of temperature at the point ( 1) when we...
Let T(x,y)=6xy be the temperature at point (x,y). A snail craws so that its position after t seconds is given by x=1+t and y=2+13t How fast is the temperature rising on the snail's path after 3 second?
Using the Runge-Kutta fourth-order method, obtain a solution to dx/dt=f(t,x,y)=xy^3+t^2; dy/dt=g(t,x,y)=ty+x^3 for t= 0 to t= 1 second. The initial conditions are given as x(0)=0, y(0) =1. Use a time increment of 0.2 seconds. Do hand calculations for t = 0.2 sec only.
A wave is described by the equation y= 8sin[2pie(x/20 +t/2)] where all distances are measured in centimeters and time is measured in seconds. Which of the following is correct a. b. c. d.
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...
(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: