If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from m dv dt = mg − kv2, k > 0. Let v(0) = 0, k = 0.125, m = 8 slugs, and g = 32 ft/s2.
a. Use the RK4 method with h = 1 to approximate the velocity v(5). (Round your answer to three decimal places.)
b. Use separation of variables to solve the IVP and then find the actual value v(5). (Round your answer to four decimal places.)

Julia chooses a card at random from her set of cards. what is the probability that the card is labeled cat or hamster?

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).