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?
Whenever there is a division, insert parentheses to indicate the beginning and the end of the denominator, for example:
C=6.000/200-2x
is not the same as:
C=6.00/(200-2x)
I believe the expression supplied was the latter.
A. 80%
C=6.00/(200-2*80)=6/40=0.15 M$
B. When the denominator becomes zero, the expression for the cost is undefined.
If the denominator is (200-2x), when it becomes zero, then
(200-2x)=0
Solve for x.
When the expression is undefined, what does it mean in everyday terms?
To find the cost to remove a specific percentage of pollution, we can substitute that percentage into the given equation.
A.) To find the cost to remove 80% of the pollutant, we substitute x = 80 into the equation C = 6,000 / (200 - 2x):
C = 6,000 / (200 - 2 * 80)
C = 6,000 / (200 - 160)
C = 6,000 / 40
C = 150 million dollars
Therefore, the cost to remove 80% of the pollutant would be 150 million dollars.
B.) To find the value for which the equation is undefined, we need to look at the denominator because division by zero is not defined. In this case, the denominator is 200 - 2x.
To make the denominator zero, we set it equal to zero and solve for x:
200 - 2x = 0
2x = 200
x = 200 / 2
x = 100
So, when x = 100, the equation becomes undefined because it results in a division by zero. In this context, it means that removing 100% of the pollutant would not be possible or would result in an infinite cost.