Results 1 to 4 of 4

Math Help - rates

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    87

    rates

    A tank contains kg of salt and L of water. A solution of a concentration kg of salt per liter enters a tank at the rate L/min. The solution is mixed and drains from the tank at the same rate.

    Find the amount of salt in the tank after hours.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by amiv4 View Post
    A tank contains kg of salt and L of water. A solution of a concentration kg of salt per liter enters a tank at the rate L/min. The solution is mixed and drains from the tank at the same rate.

    Find the amount of salt in the tank after hours.
    You should know how to set up the differential equation that models this situation:

    \frac{dx}{dt} = (0.04)(8) - \left(\frac{x}{1000}\right) (8)

    where x is the amount (kg) of salt in the tank at time t. That is,

    \frac{dx}{dt} = \frac{40 - x}{125}, subject to the boundary condition x = 80 when t = 0.

    Solve the DE and hence solve for the value of x when t = 5.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    87
    k i solved it and got
    -ln(40-x) = t/125
    is that right cuz its not giving me the right answer
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by amiv4 View Post
    k i solved it and got
    -ln(40-x) = t/125
    is that right cuz its not giving me the right answer
    If you remember to include the arbitrary constant of integration and then use the given boundary condition to find its value then perhaps you might get the right answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 27th 2009, 08:30 PM
  2. rates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 7th 2008, 10:56 AM
  3. about rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 23rd 2008, 04:24 PM
  4. Rates and Related Rates!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 11:53 AM
  5. rates and related rates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 29th 2007, 10:51 PM

Search Tags


/mathhelpforum @mathhelpforum