Ina shoots a large marble (marble a, mass: 0.08 kg) at a smaller marble (marble b, mass: 0.05 kg) that is sitting still. marble a was initially moving at a velocity of 0.5 m/s, but after the collision it has a velocity of −0.1 m/s. what is the resulting velocity of marble b after the collision? be sure to show your work for solving this problem along with the final answer.

Adoctor administers a drug to a 38-kg patient, using a dosage formula of 50 mg/kg/day. assume that the drug is available in a 100 mg per 5 ml suspension or in 500 mg tablets. a. how many tablets should a 38-kg patient take every four hours? b. the suspension with a drop factor of 10 ggt/ml delivers the drug intravenously to the patient over a twelve-hour period. what flow rate should be used in units of ggt/hr? a. the patient should take nothing pills every four hours. (type an integer or decimal rounded to the nearest hundredth as needed.)

Amass weighing 16 pounds stretches a spring 8/3 feet. the mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. find the equation of motion if the mass is driven by an external force equal to f(t)=cos(2t).

Simplify using the distributive property. 1/4 (4x + 8)