Asquare-based shipping crate is being designed that must contain a volume of 16 ft3 . the material that is used for the base and the lid costs 3 dollars/ft2 , while the material used for the sides costs 2 dollars/ft2 . what are the most cost-effective dimensions of such a crate?

You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.