Afarmer has a mixing tank of capacity 1200 liters which she half-filled with pure, fresh water. she pumps into the tank a concentrated liquid fertilizer (clf) at rate 3 liters/minute, containing 1/3 ∼ 0.333 kilo/liter of nitrate (a salt of nitric acid), aiming at getting a right concentration 0.11 kilo/liter for the type of soil she has in her field.
unfortunately, the tank is leaking: when the farmer checks it after 90 min (that is, 1.5 hr) she finds the tank containing only 330 liters of solution. assume the leak is at the bottom of the tank. then: (a) determine the leakage in liters/minute. (b) in what time would the tank become empty? what is (c) the amount n(t) and (d) the concentration c(t) of nitrate in the tank at the time the farmer checked it? write the ivp for n(t) which you use for solving (c). (e) how much of the clf in liters has been pumped in by the time she checked the tank?
in absence of leakage: (f) when would c(t) equal the right level 0.11, (g) how much of solution should be in the tank at that time?

1. the question asks the most appropriate, which seems to rule out "all of the above." your choice appears to be the correct one.

2. the protocol described is good for identifying correlation, but not cause and effect. for cause/effect, you need to devise a protocol that will assign the treatment (or not) to groups that have essentially the same "demographics" with respect to all the other variables. your choice regarding control group seems appropriate. random assignment of treatment (choice d) may be appropriate also. (i think you can argue that b and d are just different descriptions of the same method.)

3. d will randomize the birds, but may not guarantee there are 10 in each group. e will do both, so seems the better choice.

comment on question 2

based on the problem statement, it seems clear that confident, attentive drivers are more likely to use daytime running lights. so, the protocol might need to be devised in such a way that the lights would be turned on or off without the driver's knowledge. (an attentive driver will figure it out.) assigning a confident, attentive driver to a group required to drive without running lights might mess with his/her confidence and attentiveness. you don't want your experiment to do that. (nor do you want the experiment to subject a driver to greater risk of accident as a consequence of driving without running lights.) experiments involving human safety are always problematic.

i think it's c. i'm not sure but i think so.

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml