The cost in millions of dollars, to remove x%of pollution in a lake is mideled by C=6.000/200-2x. A.) What is the cost to remove 80% of the pollutant? Remember that the cost is in millions of dollars. B.) For what value is the equation undefined? What does your answer mean?
To find the cost to remove 80% of the pollutant, we can substitute x = 80 into the equation C = 6.000 / (200 - 2x).
A.) Cost to remove 80% of the pollutant:
C = 6.000 / (200 - 2x)
C = 6.000 / (200 - 2(80)) [Substitute x = 80]
C = 6.000 / (200 - 160)
C = 6.000 / 40
C = 150
Therefore, the cost to remove 80% of the pollutant is $150 million.
B.) To find the value for which the equation is undefined, we need to look at the denominator. In this case, the denominator is (200 - 2x).
For an equation to be undefined, the denominator must be zero since division by zero is undefined.
So, to make the denominator equal to zero, we set (200 - 2x) = 0 and solve for x:
200 - 2x = 0
200 = 2x
x = 100
Therefore, the equation is undefined when x = 100.
When the equation is undefined at x = 100, it means that removing 100% of the pollutant is not possible. In this context, x represents the percentage of the pollutant being removed. So, when x = 100, it implies that the entire pollution cannot be removed from the lake.