For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. it is believed that migrating fish try to minimize the total energy required to swim a fixed distance. if the fish are swimming against a current u (u < v), then the time required to swim a distance l is l / (v − u) and the total energy e required to swim the distance is given by e(v) = av3 · l v − u where a is the proportionality constant. (a) determine the value of v that minimizes e. note: this result has been verified experimentally.

The table above shows approximate conversions from gallons to liters. what is the value of x?

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.

Two years ago a man was six times as old as his daughter. in 18 years he will be twice as old as his daughter. determine their present ages.