for this page pls only answer questions 35,49,53,59,and 65topic: constructing function with variation.

2.6 Exercises 254 Chapter 2 Functions and Graphs 40. If q is directly proportional to the square root of h and in- MODELING The head is the vertical distance between the point of i For each formula that illustrates a type of variation, write the for- versely proportional to the cube of j, and q = 18 when h = 9 mula in words using the vocabulary of variation. The letters & and and j = 2, what is q when h = 16 and j = 1/2? Solve each problem. into the rock and the point of discharge such as a spring the length is the length of the flow from intake to disch represent constants, and all other letters represent variables. Determine whether the first variable varies directly or inversely with the other variable. Construct a function for the variation us- 53. First-Class Diver The pressure exerted by water at a point a certain sandstone a velocity of 10 ft per year has been below the surface varies directly with the depth. The pressure is corded with a head of 50 ft and length of 200 fu What 13. A = Fr 14. C = TD ing the appropriate variation constant. 4.34 1b/in. at a depth of 10 ft. What pressure does the sperm we expect the velocity to be if the head is 60 ft and the 15. y = 1 de 41. The length of a car in inches, the length of the same car in feet whale ( the deepest diver among the air-breathing mammals) is 300 ft? experience when it dives 6000 ft below the surface? 64. Cross-Sectional Area of a Well The rate of discharge PO 18. y = 4Vx - 3 12. The time in seconds to pop a bag of microwave popcorn, the well, V, varies jointly as the hydraulic gradient, i, and 247. T = 3W + 5 time in minutes to pop the same bag of popcorn 54. Second Place The elephant seal (second only to the sperm whale ) experiences a pressure of 2170 lb/ in.? when it makes cross-sectional area of the well wall, A. Suppose that 20. V = LWH with a cross-sectional area of 10 fi discharges 3 gal 19. a = KEN 43. The price for each person sharing a $20 pizza. the number of its deepest dives. At what depth does the elephant seal experi- ence this pressure? See the previous exercise, per minute in an area where the hydraulic gradient i hungry people dig another well nearby where the hydraulic gradie 21. H = KVI 22. B = 2vr and we want a discharge of 5 gal / min, then what s 44. The number of identical steel rods with a total weight of 55. Processing Oysters The time required to process a shipment cross-sectional area for the well? 40,000 lb, the weight of one of those rods of oysters varies directly with the number of pounds in the 2LJ shipment and inversely with the number of workers assigned. 23. D = 24. E = mck If 3000 lb can be processed by 6 workers in 8 hr, then how 65. Dollars per Death The accompanying table shows 45. The speed of a car in miles per hour, the speed of the same car amount of money that the National Institutes of He at the same time in kilometers per hour long would it take 5 workers to process 4000 1b? Find the constant of variation and construct the function that is ex- on disease research and the annual number of death pressed in each statement. 46. The weight of a sumo wrestler in pounds, the weight of the 56. View from an Airplane The view V from the air is directly diseases (www.nih.gov). Is the annual spending d same sumo wrestler in kilograms. (Chad Rowan of the United proportional to the square root of the altitude A. If the view portional to the annual number of deaths? Should 25. y varies directly as .x, and y = 5 when x = 9. States, at 455 lb, or 206 kg, was the first-ever foreign grand from horizon to horizon at an altitude of 16,000 ft is approxi- mately 154 mi, then what is the view from 36,000 ft? Table for Exercise 65 26. h is directly proportional to =, and h = 210 when = = 200. champion in Tokyo's annual tournament.) y 57. Simple Interest The amount of simple interest on a deposit Research JC 27. I' is inversely proportional to y, and 7 = -30 when y = 5. varies jointly with the principal and the time in days. If $20.80 Disease Spending AIDS $1.34 billion 28. H is inversely proportional to n, and H = 9 when n = -6. s earned on a deposit of $4000 for 16 days, how much interest would be earned on a deposit of $6500 for 24 days? Diabetes $295 million Heart disease $958 million C 29. m varies directly as the square of 1, and m = 54 when 1 = 3V2. 58. Free Fall at Six Flags Visitors at Six Flags in Atlanta get a brief thrill in the park's "free fall" ride. Passengers seated in a small 66. Bicycle Gear Ratio The gear ratio r for a bicy 30. p varies directly as the cube root of w, and p = V2/2 when cab drop from a 10-story tower down a track that eventually with the number of teeth on the chainring n. W = 4. curves level with the ground. The distance the cab falls varies and the diameter of the wheel w (in inches), an directly with the square of the time it is falling. If the cab falls with the number of teeth on the cog c, by the C31, y varies directly as x and inversely as the square root of z, and 16 ft in the first second, then how far has it fallen after 2 sec? harriscyclery.com). Find the missing entries y = 2.192 when x = 2.4 and z = 2.25. nying table. 59. Cost of Plastic Sewer Pipe The cost of a plastic sewer pipe 32. n is jointly proportional to x and the square root of b, and varies jointly as its diameter and its length, If a 20-ft pipe with n = - 18.954 when x = -1.35 and b = 15.21. Table for Exercise 66 a diameter of 6 in. costs $18.60, then what is the cost of a 16-ft pipe with a diameter of 8 in.? Solve each variation problem. Figure for Exercise 46 27 25 54 - 33. If y varies directly as x, and y = 9 when x = 2, what is y 60. Cost of Copper Tubing A plumber purchasing materials for a 50 40 26 13 45 when x = -3? renovation observed that the cost of copper tubing varies 27 67.5 jointly as the length and the diameter of the tubing. If 20 it of 34. If y is directly proportional to z, and y = 6 when z = V12, OC 47. The temperature in degrees Celsius, the temperature at the what is y when z = V75? same time and place in degrees Fahrenheit -in.-diameter tubing costs $36.60, then what is the cost of 100 ft of -in.-diameter tubing? 67. Grade on an Algebra Test Calvin believ college algebra test varies directly with 35. If P is inversely proportional to w, and P = 2/3 when 18. The perimeter of a rectangle with a length of 4 ft, the width of ge 61. Weight of a Can The weight of a can of baked beans varies spent studying during the week prior to th w = 1/4, what is P when w = 1 the same rectangle jointly with the height and the square of the diameter. If a 4-in.- with the number of hours spent at the Be high can with a 3-in. radius weighs 14.5 oz, then what is the leyball during the week prior to the test. 36. If H varies inversely as q, and H = 0.03 when q = 0.01, 49. The area of a rectangle with a length of 30 in., the width of the test when he studied 12 hr and played what is H when q = 0.05? same rectangle weight of a 5-in.-high can with a diameter of 6 in.? prior to the test, then what score should 37. If A varies jointly as L and W, and A = 30 when _ = 3 and 50. The area of a triangle with a height of 10 cm, the base of the 62. Nitrogen Gas Shock Absorber The volume of gas in a nitro- 9 hr and plays 15 hr? gen gas shock absorber varies directly with the temperature of W = 5V/2, what is A when L = 2V3 and W = 1/2? ame triangle the gas and inversely with the amount of weight on the piston. 68. Carpeting a Room The cost of carpeti 38. If J is jointly proportional to G and V, and J = V3 when 31. The number of gallons of gasoline that you can buy for $50. If the volume is 10 in.' at 80'F with a weight of 600 lb. then jointly as the length and width. Julie of $263.40 to carpet a 9-ft by 12-ft ro G = V2 and V = V8, what is J when G = V6 and V = 8? the price per gallon of that same gasoline what is the volume at 90 F with a weight of 800 lb? Stainmaster. Julie gave a customer a 52. The length of Yolanda's 40 ft- closet, the width of that closet 63. Velocity of Underground Water Darcy's law states that the peting a room with a width of 4 yd w 2 39. If y is directly proportional to u and inversely proportional to velocity V of underground water through sandstone varies but she has forgotten the length of th the square of v, and y = 7 when u = 9 and v = 6, what is y directly as the head / and inversely as the length / of the flow. length of the room? when u = 4 and v = 8