Match the vocabulary word with the correct definition 1. projection of a segment on a line the portion of a line with endpoints that are the projections of the endpoints of the segment 2. projection of a point on a line the point where a perpendicular through the point to the line intersects the line 3. altitude of a triangle For any positive real numbers a, b, and x, if then x is called the between a and b. Notice that or . 4. geometric mean in a triangle, the perpendicular line from a vertex to the opposite side

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 $ .