Question

Suppose that the celsius temperature at the point (x,y) in the xy-plane is T(x,y)=xsin(2y) and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at a constant rate of 2m/sec.

A) how fast is the temp experienced by the particle changing in degress cel per meter at the point: P(1/2, sqrt(3)/2)

Answer 1

1/2 = cos(2*t)sqrt(3) /2 = sin(-2*t)find tfind the time derivative of  x(t), y(t)(-2sin(2*t) , -2cos(2*t) )plug in the t you found to find the velocity vector.