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- Break-Even The profit for a product is given byP = -3600 + 150x - x2, where x is the number ofunits produced and sold. How many units will givebreak-even (that is, return a profit of 0)?Ecology The cost C (in millions of dollars) of removing p of the industrial and municipal pollutants discharged into a river is given by C=225p100p,0p100. (a) Use a graphing utility to graph the cost function. (b) Find the costs of removing 10,40,and75 of the pollutants. (c) According to the model, is it possible to remove 100 of the pollutants? Explain.Viewing Earth: Astronauts looking at Earth from a spacecraft can see only a portion of the surface. See figure 2.47. The fraction F of the surface of Earth that is visible at a height h, in kilometers, above the surface is given by the formula F=0.5hR+h Here R is the radius of Earth, about 6380 kilometers. for comparison, 1 kilometer is about 0.62 mile, and the moon is about 380,000 kilometers from Earth. a. Make a graph of F versus h covering heights up to 100,000 kilometers. b. A value of F equal to 0.25 means that 25, or one-quarter, of Earths surface is visible. At what height is this fraction visible? c. During one flight of a space shuttle, astronauts performed an extravehicular activity at a height of 280 kilometers. What fraction of the surface of Earth is visible at that height? d. Is the graph of F concave up or concave down? Explain your answer in practical terms. e. Determine the limiting value for F as the height h gets larger. Explain your answer in practical terms.
- The bar graph shows the average dormitory charges at public and private four-year U.S. colleges. Use the information displayed by the graph to solve,a. Use the numbers shown by the bar graph to find the total dormitory charges at private colleges for a four-year period from the school year ending in 2010 through the school year ending in 2013. b. The model an = 198n + 5037 describes the dormitory charges at private colleges in academic year n, where n = 1 corresponds to the school year ending in 2010, n = 2 to the school year ending in 2011, and so on. Use this model and the formula for Sn to find the total dormitory charges at private colleges for a four-year period from the school year ending in 2010 through the school year ending in 2013. How does this compare with the actual sum you obtained in part (a)?Ecology The number N of trees of a given speciesper acre is approximated by the modelN = 3500(10−0.12x), 3 ≤ x ≤ 30where x is the average diameter of the trees (ininches) 4.5 feet above the ground. Use the model toapproximate the average diameter of the trees in a testplot when N = 22.Line p has a slope of -7/8 Line q is parallel to line p. What is the slope of line q? Simplify your answer and write it as a proper fraction, improper fraction, or integer.
- Time spent running (minutes) 0 15 30 45 60 75 Speed (mph) 13 11 10 9 8 0 Draw rectangles on this graph to help you underestimate the total distance traveled by the runner during the whole time. What underestimate did you obtain? Draw rectangles on this graph to help you overestimate the total distance traveled by the runner during the whole time. What overestimate did you obtain?ch12-1. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour.Find the equation that expresses the total fee in terms of the number of hours the equipment is rented. (Enter exact numbers as integers, fractions, or decimals.) y = _____ + _____ xExpressing rational numbers as decimals (1.)Write the fraction as a decimal 5/11 (2.) The average score on biology test was 72.1 Write The average score using a fraction?
- You are going down a road with a 10% grade. You are going down feet every feet horizontally. The slope of the road is . Express your answer as a reduced fraction or integer.Statistics show that the fractional part of a pair of flashlight batteries, P, that is still good after t hours of use is given by P=4-0.02t. What fractional part of the batteries is still operating after 50 hours of use? Express your answer as a fraction or as a decimal rounded to six decimal places.Cost-Benefit The percent p of particulate pollutionthat can be removed from the smokestacks of anindustrial plant by spending C dollars is given byp = 100C/8300 + C a. Find the percent of pollution that could be removedif spending were allowed to increase withoutbound.b. Can 100% of the pollution be removed? Explain.