In a certain region of space, a force F(r) has an associated potential energy of the form U(r) = a r2 − b r + c , where a , b , and c are positive constants. What are the points, if any, where the force F(r) goes to zero?

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

At an oceanside nuclear power plant, seawater is used as part of the cooling system. this raises the temperature of the water that is discharged back into the ocean. the amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° c. what is the standard deviation of the temperature increase?

The diagram shows a series of volcanic island and a hot spot determine the direction of movement of the tectonic plate that for the island