Agnat takes off from one end of a pencil and flies around erratically for 18.6 seconds before landing on the other end of the same pencil. if the gnat flew a total distance of 7.15 meters, and the pencil is 6.13 cm long, find the gnat's average speed, as well as the magnitude of the gnat's average velocity vector.

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?