The function LaTeX: m\left(r\right)=31r^3m ( r ) = 31 r 3 models the mass in grams of a spherical zinc ball as a function of the ball's radius in centimeters. Write the inverse model to represent the radius r in centimeters of a spherical zinc ball as a function of the ball's mass m in grams. Then find the radius if the ball has a mass of 105 grams?

Algebraically prove that a clockwise and counterclockwise rotation of 180° about the origin for triangle abc are equivalent rotations.

In the triangle rst, rs = 65 and st = 60. which equation could be used to find the value of angle s?

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .