Why does the solar nebula theory imply planets are common? a. Planets formed from the spiral arms of matter encountered around the Sun. Most main-sequence stars pass spiral arms dozens of times in their lives. b. Planets formed from the Sun’s past binary partner star. Binary systems with different masses and evolution rates are common. c. Planets formed from the envelope of the Sun, ejected at the time of hydrogen fusion ignition. Stars commonly eject their envelopes. d. Planets formed from the disk of gas and dust that surrounded the Sun, and such disks are common around young stars.

Aprojectile is launched from ground level with an initial velocity of v 0 feet per second. neglecting air resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 t. find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when v 0equals112 feet per second. (a) find the time(s) that the projectile will reach a height of 192 ft when v 0equals112 feet per second. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Choose the most likely outcome of this scenario: jen decided to go bike riding without a helmet. while no one is around during her ride, she is thrown from her bike when her wheel goes into a pothole. she is not injured, but she is terrified to get back on her bike. what happens next? a. her physical health is affected even though she wasn't hurt. b. her mental and emotional health are affected because she is afraid to get back on her bike. c. her social health is affected because she is worried her friends saw the fall. d. her overall health is not affected at all by her fall.

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.)