Use green's theorem to evaluate c f · dr. (check the orientation of the curve before applying the theorem.) f(x, y) = y2 cos(x), x2 + 2y sin(x) c is the triangle from (0, 0) to (1, 3) to (1, 0) to (0, 0).

Ms. sutton recorded the word counts and scores of the top ten essays in a timed writing contest. the table shows her data. how does the word count of an essay relate to its score in the contest? word count tends to decrease as the score decreases. word count tends to increase as the score decreases. word count tends to remain constant as the score decreases. word count has no apparent relationship to the score of the essay.

Atoy company is considering a cube or sphere-shaped container for packaging a new product. the height of the cube would equal the diameter of the sphere . compare the volume to surface area ratios of the containers. which packaging will be more efficient? for a sphere, sa =4πr²

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.