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- Suppose that the daily cost C of manufacturing bicycles is given by C(x) = 80x + 5000. Then the average daily cost C' is given by C'(x) = 80x + 5000 x . How many bicycles must be produced each day for the average cost to be no more than $100?A firm can produce only 2500 units per month. The monthly total cost is given by C(x) = 400 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 350x −1/100 x2 dollars, how many items, x, should the firm produce for maximum profit?Suppose the percent of males who enrolled in college within 12 months of high school graduation is given by y= -0.126x + 55.72 and the percent of females who enrolled in college within 12 months of high school graduation is given by y= 0.73x + 39.7, where x is the number of years after 1960. Use graphical methods to find the years after these models indicate that the percent of females equaled the percent of males.
- Find the general solution using Reduction of Order: y''=2lnxthe topic is Elimination of Arbitrary Constants by Isolation of ConstantsSuppose the percent of males who enrolled in college within 12 months of high school graduation is given by y =-0.126x+55.72 and the percent of females who enrolled in college within 12 months of high school graduation is given by y=0.73x+39.7, where x is the number of years after 1960. Use graphical methods to find the year these models indicate that the percent of females equaled the percent of males.
- integral of (3x2+x+4)/(x4+3x2+2)Suppose that a construction zone can allow 50 cars per hour to pass through and that cars arrive randomly at a rate of X cars per hour. Then the average number of cars waiting in line to get through the construction zone can be estimated by: N(x)=x2/2500-50x Evaluate N(20), N(40), and N(49).Explain what happens to the length of the line as X approaches 50.If the average number of cars waiting in line is 1, find the average of cars per hour.Find and interpret the vertical asymptotes.One leukemic cell in an otherwise healthy mouse will divide into two cells every 12 hours, so that after x days the number of leukemic cells will be f(x) = 4x. (a) Find the approximate number of leukemic cells after 12 days. ________ cells (b) If the mouse will die when its body has a billion leukemic cells, will it survive beyond day 14? Yes or No