SOLUTION: I just need this question checked. Here it is.... A mining company has determined that the cost in dollars, c, per ton of mining a mineral is given by c(x)=0.2x2(squared)-2x+12 w

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I just need this question checked. Here it is.... A mining company has determined that the cost in dollars, c, per ton of mining a mineral is given by c(x)=0.2x2(squared)-2x+12 w      Log On


   

Question 21722: I just need this question checked. Here it is....
A mining company has determined that the cost in dollars, c, per ton of mining a mineral is given by c(x)=0.2x2(squared)-2x+12 where x is the number of tons of the mineral that is mined. Find the number of tons of the mineral that should be mined to minimize the cost. What is the minimum cost?
i got the minimum cost should be 7 is this right?
if not please help!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The "cost" equation is a quadratic with
a=0.2, b=-2, c=12
The min, max of this equation is at
x=-b/2a = 2/0.4 = 5 . Here is the graph.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.2x%5E2%2B-2x%2B12+=+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=%28-2%29%5E2-4%2A0.2%2A12=-5.6.

The discriminant -5.6 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -5.6 is + or - sqrt%28+5.6%29+=+2.36643191323985.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.2%2Ax%5E2%2B-2%2Ax%2B12+%29


Cheers,
Stan H.