Aparticle's position along the x-axis is described by. x(t)= at+bt^2where t is in seconds: x is in meters: and the constants a and b are given below. randomized variables a= -3.5 m/s b= 3.9 m/s^2 a. what is the velocity, in meters per second. of the particle at the time t1= 3.0 s? b. what is the velocity, in meters per second: of the particle when it is at the origm (x=0) at time to> 0?

An asteroid is discovered in a nearly circular orbit around the sun, with an orbital radius that is 2.47 times earth's. what is the asteroid's orbital period, its "year," in terms of earth years?

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.)

Researchers determine that the biodiversity in a woodland region is declining. they identify two major threats to the region's biodiversity, a method to address each threat, and the expected outcome of each method. this information is shown in the table. a) reforestation would not benefit many species because most forest species live on the ground. b) reforestation would take the longest time to be effective because trees take several years to grow. c) biological augmentation would benefit only a few species because is is typically not very effective. d) biological augmentation would take less time to ve effective because it targets the majority of prey species.