Me fill in the blanks most falling objects will experience air resistance. the air resistance will increase with *blank*. at the poiny when the air resistance equals the weight, there is no *blank* and the object will fall with *blank*.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

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?