Uw pre calculus help (math 120)?
1. Angela, Mary and Tiff are all standing near the intersection of University and 42nd streets. Mary and Tiff do not move, but Angela runs toward Tiff at12 ft/sec along a straight line, as pictured. Assume the roads are50 feet wide and Tiff is60 feet north of the nearest corner. Where is Angela located when she is closest to Mary and when does she reach this spot?
2. The infamous crawling tractor sprinkler is located as pictured below, 100 feet South of a 10 ft. wide sidewalk; notice the hose and sidewalk are not perpendicular. Once the water is turned on, the sprinkler waters a cir-cular disc of radius 20 feet and moves North along the hose at the rate of 1 2 inch/second.
(a) Impose a coordinate system. Describe the initial coordinates of the sprinkler and find the equation of the line forming the southern boundary of the sidewalk.
(b) After 33 minutes, sketch a picture of the wet portion of the sidewalk; find the length of the wet portion of the Southern edge of the sidewalk.
(c) Find the equation of the line forming the northern boundary of the sidewalk. (Hint: You can use the properties of right triangles.)
3. Allyson and Adrian have decided to connect their ankles with a bungee cord; one end is tied to each person's ankle. The cord is 30 feet long, but can stretch up to 90 feet. They both start from the same location. Allyson moves 10 ft/sec and Adrian moves 8 ft/sec in the directions indicated. Adrian stops moving at time t =5.5 sec, but Allyson keeps on moving 10 ft/sec in the indicated direction.
(a) Sketch an accurate picture of the situa-tion at timet =7 seconds. Make sure to label the locations of Allyson and Adrian; also, compute the length of the bungee cord att =7 seconds.
(b) Where is Allyson when the bungee reaches its maximum length?
