One of your summer lunar space camp activities is to launch a 1210 kg1210 kg rocket from the surface of the moon. you are a serious space camper and you launch a serious rocket: it reaches an altitude of 203 km203 km . what gain in gravitational potential energy does the launch accomplish? the mass and radius of the moon are 7.36×1022 kg7.36×1022 kg and 1740 km1740 km , respectively.

Let f(x) = x4- 8x2 . find the relativeextrema of this function using the second derivative test.

The system is released from rest with the cable taut, and the homogeneous cylinder does not slip on the rough incline. determine the angular acceleration of the cylinder and the minimum coeffi cient s of friction for which the cylinder will not slip.

You are a sales representative for a company that makes a new alternate fuel for vehicles. you have prepared a presentation for the environmental engineers to sell your new product. what question do you expect the audience to ask regarding whether the new fuel will cause less damage to the environment? a. do we have to change any parts of the vehicle to use this alternate fuel? b. will the vehicles get better fuel mileage with the alternate fuel? c. how much greenhouse gas does your fuel produce compared with current fuel sources? d. is the alternate fuel more expensive than fossil fuel?