Consider the following region r and the vector field f.

a. compute the two-dimensional curl of the vector field

b. evaluate both integrals in the circulation form of green's theorem and check for consistency.

c. state whether the vector field is conservative.

f = < 3y,-3x> ; r is the region bounded by y = sin x and y =0 for 0 \leq x \leq \pi

Suppose you are going to graph the data in the table. minutes temperature (°c) 0 -2 1 1 2 3 3 4 4 5 5 -4 6 2 7 -3 what data should be represented on each axis, and what should the axis increments be? x-axis: minutes in increments of 1; y-axis: temperature in increments of 5 x-axis: temperature in increments of 5; y-axis: minutes in increments of 1 x-axis: minutes in increments of 1; y-axis: temperature in increments of 1 x-axis: temperature in increments of 1; y-axis: minutes in increments of 5

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.

Given: circle o, cd is diameter, chord ab || cd. arc ab = 74°, find arc ca.