SOLUTION: Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains is represented by the equation {{{ L=-5t^2-8t+120 }}} , where L represe

Algebra ->  Trigonometry-basics -> SOLUTION: Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains is represented by the equation {{{ L=-5t^2-8t+120 }}} , where L represe      Log On


   

Question 924604: Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains is represented by the equation +L=-5t%5E2-8t%2B120+ , where L represents the number of liters of water in the bathtub and t represents the amount of time, in minutes, since the plug was pulled. How many liters of water were in the bathtub when Barb pulled the plug? Round to the nearest tenth of a minute the amount of time it takes for all the water in the bathtub to drain.
Found 2 solutions by ewatrrr, jim_thompson5910:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
+L=+-5t%5E2-8t%2B120+
How many liters of water were in the bathtub when Barb pulled the plug? 120L
...
time it takes for all the water in the bathtub to drain.
-5t^2-8t+120 = 0 Solving (tossing out negative solution for unit measure)
t = 4.2 min to drain
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -5x%5E2%2B-8x%2B120+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-8%29%5E2-4%2A-5%2A120=2464.

Discriminant d=2464 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+2464+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+2464+%29%29%2F2%5C-5+=+-5.76386945839634
x%5B2%5D+=+%28-%28-8%29-sqrt%28+2464+%29%29%2F2%5C-5+=+4.16386945839634

Quadratic expression -5x%5E2%2B-8x%2B120 can be factored:
-5x%5E2%2B-8x%2B120+=+-5%28x--5.76386945839634%29%2A%28x-4.16386945839634%29
Again, the answer is: -5.76386945839634, 4.16386945839634. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B-8%2Ax%2B120+%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hints:

For the first part, you are plugging in t = 0 and evaluating.

So you need to compute +L=-5%280%29%5E2-8%280%29%2B120+


-------------------------------------------------------------------

For the second part, you need to solve +0=-5t%5E2-8t%2B120+ for t. You plug L = 0 into the equation because you want to know when the number of liters is 0. Make sure t is a positive number.

To solve +0=-5t%5E2-8t%2B120+ for t, you need to use the quadratic formula.

Let me know if these hints help or not. If not, then let me know. Thanks.