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

Use the following statements to write a compound statement for the conjunction or disjunction. then find its truth value. p: an isosceles triangle has two congruent sides. q: a right angle measures 90° r: four points are always coplanar. s: a decagon has 12 sides. a) a right angle measures 90° or an isosceles triangle has two congruent sides; true. b) a right angle measures 90° and an isosceles triangle has two congruent sides; true. c) a right angle measures 90° and an isosceles triangle does not have two congruent sides; false. d) a right angle measures 90° or an isosceles triangle does not have two congruent sides; true.