Tank t_1 initially contain 50 gallons of pure water. starting at t_0 = 0, water that contains 1 pound of salt per gallon is poured into t_1 at the rate of 2 gal/min. the mixture is drained from t_1 at the same rate into a second tank t_2, which initially contains 50 gallons of pure water. also starting at t_0 = 0, a mixture from another source that contains 2 pounds of salt per gallon is poured into t_2 at the rate of 2 gal/min. the mixture is drained from t_2 at the rate of 4 gal/min. a) find a differential equation for the quantity q(t) of salt in tank t_2 at time t > 0. b) solve the equation derived in (a) to determine q(t). c) find lim_t rightarrow infinity q(t).

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.