Water is leaking out of an inverted conical tank at a rate of 11600.011600.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. the tank has height 13.013.0 meters and the diameter at the top is 5.05.0 meters. if the water level is rising at a rate of 22.022.0 centimeters per minute when the height of the water is 4.04.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute

Win=436584.2477 cm3/min

Step-by-step explanation:

Volume for a conical tank

V=π/3 r^2 h

We need a relation between r and h

r/h=252.5/1301.3=0.194 --> r=0.194h

sust. in Volume equation

V=π/3 (0.194r)^2 h=0.0394h^3

taking derivative with time respect in both sides

dV/dt=3(0.0394) h^2 dh/dt    and we know when h=404cm, dh/dt=22.022 cm/min

dV/dt=3(0.0394)(404)^2 (22.022)=424984.2477 cm^3/min

Also, we know

dV/dt=Win-Wout and Wout=Win-11600.01160

Finally

Win=424984.2477+11600.0116

Answer

Win=436584.2477 cm3/min

me

step-by-step explanation:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.