The path moved by the bug or displacement of bug is given by ;
The displacement is usually denoted by
We have to find rate of change of temperature at t=0.6
To find rate of change of temperature T , we use the chain rule
Now we have to find each part
6. The temperature at (x,y) is T(x,y) = 20 + 100%+++") degrees (in Celsius). A bug...
The temperature at a point (x, y) is T(x,y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = 4 + t, y = 8 where x and y are measured in centimeters. The temperature function satisfies Tx(5, 9) = 2 and Ty(5, 9) = 7. How fast is the temperature rising on the bug's path after 21 seconds? Step 1 We know that the rate of change of the temperature...
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...
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...
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...
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...
6. (10 points) (a) (6 points) The gradient of the function o(x, y, z) at (1,2,3) is the vector (2, 1, 1) and g(1,2,3) = 1 (1) (2 points) Find the equation of the tangent plane of the level surface g(r, y, z) = 1 at (1,2,3) (ii) (2 points) Find the maximum rate of change of g(x, y, z) at (1, 2, 3). hax. rarte ot change: 23 14 (iii) (2 points) Find the rate of change of g...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
6) 6 Distance x (cm) Temperatuire 100 93 70 6255 A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of thetemperature T(x), in degrees Celsius (°C), of the wire χ cm from the heated end. The function T is decreasing and is twice differentiable. a. Estimate T'(C7). Show the work that leads to your answer. Indicate units of measure b. Write an integral expression in terms of T(x) for the...
VBA The projectile motion equations are,x=x0+v0*cos(θ)*t, y=y0+v0*sin(θ)*t+0.5*g*t^2 where x and y are the current position at time t, x0 and y0 are the projectile’s initial position, v0 is the projectile’s initial speed, θ is the initial firing angle of the projectile, and g is the gravitational acceleration which is -9.81 m/s2 near Earth’s surface. The user (me) will input the initial x-position (m), y-position (m), speed (m/s), the firing angle (in degrees) in cells F2-F5 on Sheet2. Create a run...
F- [y - yz sin x,x + z cos x,y cos x] from OstsT/2 where the path is defined as follows x- 2t y = (1 + cost)2 z- 4(sint)3 m. F= [8xy®z, 12x2y®z, 4x2yaj from (2,0,0) to (0,2,π/2). The path is a helix of radius 2 advancing 1 unit along the positive z axis in one period of 2Tt. We were unable to transcribe this image F- [y - yz sin x,x + z cos x,y cos x] from...