Results 1 to 2 of 2

Math Help - Two tank brine problem

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    42

    Two tank brine problem

    I am studying for my final and this is one of the problems in out trial final, ive gone through it about 5-6 times and i can not for the life of me get it right.

    the pic and question is attached

    What i have is

    dx/dt=2-(3x/100)+(y/200)
    dy/dt=(3x/100)-(3y/200)

    I solve the second equation for x
    x=(dy/dt)(100/3)+(y/2) and that gives me x' as
    x'=(d^2y/dt^2)(100/3)+(dy/dt)(1/2)

    then i plug back into the equation and collect like terms and i get
    (100/3)(d^2y/dt^2)+(dy/dt)(1/2)=2-(3/100)[(dy/dt)(100/3)+(y/2)] +(y/200)

    which simplifies to

    (d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=2

    Then i find my two solutions for


    (d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=0

    and this is were it all goes wrong...

    Please help! Thank you
    Attached Thumbnails Attached Thumbnails Two tank brine problem-math-1.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,303
    Thanks
    1278
    Quote Originally Posted by acosta0809 View Post
    I am studying for my final and this is one of the problems in out trial final, ive gone through it about 5-6 times and i can not for the life of me get it right.

    the pic and question is attached

    What i have is

    dx/dt=2-(3x/100)+(y/200)
    dy/dt=(3x/100)-(3y/200)

    I solve the second equation for x
    x=(dy/dt)(100/3)+(y/2) and that gives me x' as
    x'=(d^2y/dt^2)(100/3)+(dy/dt)(1/2)

    then i plug back into the equation and collect like terms and i get
    (100/3)(d^2y/dt^2)+(dy/dt)(1/2)=2-(3/100)[(dy/dt)(100/3)+(y/2)] +(y/200)

    which simplifies to

    (d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=2

    Then i find my two solutions for


    (d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=0

    and this is were it all goes wrong...

    Please help! Thank you
    Okay, why does it "all go wrong"? I haven't checked the details but your general idea is correct. Now you have a linear equation with constant coefficients with characteristic equation r^2+ (9/200)r+ 3/10000= 0. By the quadratic formula, r= \frac{-(9/200)\pm\sqrt{(9/200)^2- 4(3/10000)}}{2}= 0.0225\pm 0.01436.

    What's wrong with that?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Tank Filling Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 14th 2011, 07:33 PM
  2. Mixing problem, brine solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: November 17th 2011, 11:45 PM
  3. Tank problem
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 30th 2009, 06:02 AM
  4. Tank Problem
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 11th 2009, 01:19 AM
  5. Concentration in brine solution
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 16th 2006, 02:48 PM

Search Tags


/mathhelpforum @mathhelpforum