10. Suppose the cost C of removing p% of the impurities from the waste water in a manufacturing process is given by
a) Where does the graph of this function have a vertical asymptote?
b) What does this tell us about removing the impurities from this process?
c) Removing how many percent of the impurities yield the cost of $10800?
Thanks in advance ;).
;). Thanks to anyone who tried, but i figured it out on my own.
If anyone is interested in the answer....
a) p=100
b) means they can't remove 100% of the impurities.
c) 18,00 = (3600p/100 - p)
10,800(100 - p) = 3600p
1,080,000 - 10,800 = 3600p
1,080,000 = 14400p
p = 75
removing 75% will cost $10800.
This is what i got, if i did anything wrong please correct me!
Oops, typo.
10,800 = (3600p/100 - p) ***
oh, and i just realized, the equation didn't show up when i asked the question.
Suppose the cost C of removing p% of the impurities from the waste water in a manufacturing process is given by C(p) = (3600p/100 - p)**
a) The graph of this function has a vertical asymptote when the denominator of the fraction is equal to zero. In this case, the denominator is 100 - p. So, the graph will have a vertical asymptote at p = 100.
b) The vertical asymptote at p = 100 indicates that it is not possible to remove 100% of the impurities from the waste water in this manufacturing process, as dividing by zero is undefined. Therefore, there will always be some impurities remaining in the water.
c) To find the percentage of impurities that yields a cost of $10800, we need to solve the equation C(p) = $10800.
The equation is:
C(p) = 50000 / (100 - p)
Setting C(p) = 10800:
10800 = 50000 / (100 - p)
To solve for p, we can start by multiplying both sides by (100 - p):
10800(100 - p) = 50000
Expanding the left side:
1080000 - 10800p = 50000
Rearranging the equation:
10800p = 1080000 - 50000
Simplifying:
10800p = 1030000
Dividing both sides by 10800:
p = 1030000 / 10800 = 95.37
Therefore, removing approximately 95.37% of the impurities will yield a cost of $10800 in this process.
a) To determine where the graph of the function has a vertical asymptote, we need to find the values of p for which the denominator of the fraction is equal to zero. In this case, the denominator is given by 100 - p.
Setting the denominator equal to zero, we have:
100 - p = 0
Solving for p, we subtract 100 from both sides of the equation:
p = 100
Therefore, the graph of the function has a vertical asymptote at p = 100.
b) The fact that the graph of the function has a vertical asymptote at p = 100 tells us that it is not possible to remove 100% of the impurities from the waste water in this manufacturing process. As p approaches 100, the cost of removing impurities approaches infinity, indicating that removing all impurities is theoretically impossible or impractical.
c) To find the percentage of impurities that yields a cost of $10800, we need to set the cost function equal to 10800 and solve for p.
Given the cost function: C = 50000 / (100 - p)
Setting C equal to 10800:
10800 = 50000 / (100 - p)
Multiplying both sides of the equation by (100 - p), we have:
10800(100 - p) = 50000
Expanding and rearranging the equation, we get:
10800(100) - 10800p = 50000
1080000 - 10800p = 50000
Subtracting 1080000 from both sides of the equation, we have:
-10800p = 50000 - 1080000
-10800p = -1030000
Dividing both sides of the equation by -10800 to solve for p, we get:
p = (-1030000 / -10800) = 95.37 (rounded to two decimal places)
Therefore, removing approximately 95.37% of the impurities will yield a cost of $10800.