5-kg mass is attached to a spring hanging from the ceiling, thereby causing the spring to stretch 4.9 m upon coming to rest at equilibrium. At time tequals0, an external force of Upper F (t )equalscosine t N is applied to the system. The damping constant for the system is 12 N-sec/m. Determine the steady-state solution for the system.

18 16 11 45 33 11 33 14 18 11 what is the mode for this data set

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.

Sara goes on a slingshot ride in an amusement park. she is strapped into a spherical ball that has a radius 3*10^2 of centimeters. what is the volume of air in the spherical ball? use this formula: volume of a sphere=4/3pi,r^3 , where r is the sphere’s radius.