The half-life of carbon-14 is 5730 years. how long will it take for 7/8 of a sample of carbon-14 to decay

Atwo-stage air compressor operates at steady state, compression 10m^3/min of air from 100 kpa and 300k to 1200 kpa. an intercooler between the two stages cools the air to 300k at a constant pressure of 350 kpa. the compression processes are isentropic. a) calculate the power required to run the compressor, in kw b) compare the result to the power required for isentropic compression from the same inlet state to the same final pressure.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants

Consider two less-than-desirable options. in the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. in the second option you are driving 30 mph and crash head-on into a stationary brick wall. in neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. which of these two situations would result in the greatest impact force?