A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a = a1 + Fm where a1 = 3.00 m/s2, F = 12.0 kg. m/s2 and m = 7.00 kg. First, which of the following is the correct step for obtaining a common denominator for the two fractions in the expression in solving for a? a. (m/m times a1/1) + (1/1 times F/m).
b. (1/m times a1/1) + (1/m times F/m).
c. (m/m times a1/1) + (F/F times F/m).
d. (m/m times a1/1) +(m/m times F/m ).

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.)

At very high pressures, gases become and will eventually a) more dense; become hotter b) more dense; change to a liquid or solid c) less dense; combust d) less dense; turn into a liquid

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). heavier cars tend to have lower fuel efficiencies (lower mpg ratings). which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context?