Given that the acceleration vector is a(t)=(−9cos(−3t),−9sin(−3t),−t), the initial velocity is v(0)=(1,0,1), and the initial position vector is r(0)=(1,1,1), compute:

According to the law of conservation of mass, in a chemical reaction the total starting mass of all the reactants equal the total final mass of all the products. true or false?

Answer fast for how does the force exerted by two magnets change as the magnets are moved farther apart? the magnetic force increases. the magnetic force decreases. the magnetic force stays the same.

Lake happy times contains 100 km3 of pure water. it is fed by a river at a rate of 50 km3/yr. at time zero, there is a factory on one shore of lake happy times that begins introducing a pollutant to the lake at a rate of 2km3/yr. there is another river that is fed by lake happy times at a rate that keeps the volume of lake happy times constant. this means that the rate of flow from lake happy times into the outlet river is 52km3/yr. in turn, the flow from this outlet river goes into another lake, lake sad times, at an equal rate. finally, there is an outlet river from lake sad times flowing at a rate that keeps the volume of lake sad times at a constant 100 km3 . (a) find the amount of pollutant in lake sad times at the end of 3 months. (b) at the end of 3 months, observers close the factory due to environmental concerns and no further pollu- tant enters lake happy times. how long will it take for the pollutant in lake sad times (found in part (a)) to be cut in half?