Results 1 to 2 of 2

Thread: Last Quadratic work problem

  1. #1
    Sep 2007

    Last Quadratic work problem

    a hole is punched in the side of a cylindrical water tank and water begins to flow out. The hole is punched at time t=0 min. The volume of water in the tank, V litres, at any time t when the water is flowing out is given by V=t^2 - 16t + 100 .

    a. how much water is in the tank at the beginning? i got 100 litres bt from my calculations from the next question I think it may b wrong.
    b. How long does it take to empty the tank?is this just completing the square?
    c. How much water flows out of the tank and how much is left inside?
    d. Determine a formula for the time t when the tank has a given volume V. State the domain and range of this function.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member DivideBy0's Avatar
    Mar 2007
    Melbourne, Australia
    1. Yep, that's right

    2. Set $\displaystyle t^2-16t+100=0$
    If you check the discriminant of the expression you get $\displaystyle \Delta = (-16)^2-4 \times 100 \times 1= -144 < 0$, so there are no real solutions, and hence V never reaches 0. The tank never empties completely.

    3. You want to find the lowest value of V. Therefore, you need to find the turning point of the graph $\displaystyle V=t^2-16t+100$.
    Just complete the square here:

    $\displaystyle V = t^2-16t+64-64+100$

    $\displaystyle V = (t-8)^2+36$

    Hence, the turning point is located at (8, 36). So 64 litres flow out of the tank and 36 litres remains.

    4. Simply solve for t. Fortunately having it in 'complete the square' form makes it a lot easier to solve.

    $\displaystyle (t-8)^2=V-36$

    $\displaystyle t-8=\pm \sqrt{V-36}$

    $\displaystyle t=8 \pm \sqrt{V-36}$

    Notice since the parabola curves upwards again you will get two values of t for the one value of V.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: Aug 16th 2010, 05:20 AM
  2. Please Check My Work on Quadratic Equations
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Aug 11th 2010, 12:20 PM
  3. Another work problem??
    Posted in the Calculus Forum
    Replies: 10
    Last Post: Mar 18th 2010, 02:32 PM
  4. Quadratic Inequality (Why doesn't this work?)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Feb 13th 2010, 02:08 PM
  5. check my work on quadratic equations?
    Posted in the Algebra Forum
    Replies: 11
    Last Post: Dec 9th 2009, 01:45 AM

Search Tags

/mathhelpforum @mathhelpforum