Posted by COFFEE on Friday, July 13, 2007 at 4:36pm.
Please check my work below and comment.
A tank initially contains 80 gallons of fresh water. A 10% acid solution flows into the tank at the rate of 3 gallons per minute. The well-stirred mixture flows out of the tank at the rate of 3 gallons per minute. Find the amount of acid in the tank at the end of any time t. How much acid will be in the tank in 30 minutes? What will be the concentration (%) of acid in the tank after 30 minutes?
solution=0.3 gallons acid + 2.7 gallons H20
dy/dt = (rate in) - (rate out)
rate in = (0.3)(3) = 0.9 gallons/min
<-would this be gallons per min?
rate out = ((y(t))/80) * 3 gal/min
rate out = y(t)/(80/3)
Seperate into two intergrals:
-ln|(773/30)-y| = 3t/80+C, C=-ln|773/30|
-ln|(773/30)-y|=3t/80 - ln|773/30|
Is this the correct equation?
Then at 30 minutes, y(30) would be 17.4 gallons acid
Percentage after 30 minutes=17.4/80
correct procedure, however, one question: how did you get rate in .3*3? Wasn't it ten percent?
ah yes. Thank you!
Answer This Question
More Related Questions
- calculus - 500-gallon tank initially contains 200 gallons of brine containing ...
- math - A tank contains 50 gallons of a solution composed of 90% water and 10% ...
- math - Water is Pumped into an underground tank at a constant rate of 8 gallons ...
- CALC - A 200-gallon tank is currently half full of water that contains 50 pounds...
- calculus - Water is Pumped into an underground tank at a constant rate of 8 ...
- Algebra - A tank contains 150 gallons of water and fills at a rate of 8 gallons...
- chemical calculations - Brine from a first tank runs into a second tank at 2 ...
- linear - Suppose that we have a system consisting of two interconnected tanks, ...
- linear algebra - Suppose that we have a system consisting of two interconnected ...
- math - An inverted square pyramid has a height equal to 8m and a top edge to 3m...