A radioactive nucleus has a half-life of 5 x 108 years. Assuming that a sample of rock (say, in an asteroid) solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today?

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Dao makes a table to identify the variables used in the equations for centripetal acceleration. what quantities belong in cells x and y?

Find v1, the speed of the fluid in the left end of the main pipe. express your answer in terms of h1, h2, g, and either a1 and a2 or γ, which is equal to a1a2.