34. The temperature at location (x, y) is T(x, y) = 20 + 0.1 (x^2 ? xy) (degrees

Question

34. The temperature at location (x, y) is T(x, y) = 20 + 0.1 (x^2 ? xy) (degrees Celsius). Beginning at (200, 0) at time t = 0 (seconds), a bug travels along a circle of radius 200 cm centered at the origin, at a speed of 3 cm/s. How fast is the temperature changing at time t = 3/Pi? 35. Suppose that gradient fp = (2, ?4,4). Is f increasing or decreasing at P in the direction v = (2, 1, 3)? 36. Let f(x, y) = xe^x^2?Y and P = (1, 1). (a) Calculate ||gradient fp||. (b) Find the rate of change of f in the direction gradient fp. (c) Find the rate of change of f in the direction of a vector making an angle of 45 degree with gradient fp.

Explanation / Answer

after t=pi/3

velocity in x= -3sin 30

velocity in y=-3cos 30

and coordinates will be (x,y)=(-200cos30,200cos60)

dT/dt=0.1(2x(Vx) - y (Vx) - x (Vy))

Substitute the values you will get the ans.

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