A dancer moves in one dimension back and forth across the stage. If the end of the stage nearest to her is considered to be the origin of an x axis that runs parallel to the stage, her position, as a function of time, is given by x(t) = [(0.02 m/s3)t3 − (0.41 m/s2)t2 + (1.82 m/s)t − 2.14 m]i. (a) Find an expression for the dancer's velocity as a function of time. (Assume SI units. Do not include units in your answer. Use the following as necessary: t.)

If you were on a jury, do you think you would expect individual characteristics in the evidence? why or why not? what effects might it have if individuals expect to have individuals characteristics presented? this question is for forensic science

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.)

The ph is the a.independent variable b.the dependent variable c.control group