Numbers of factors



Graph to show men’s 100-metre world record progressionBy Cmglee - own work, CC BY-SA 3.0, pairs:What was Donald Lippincot’s world record time, set in 1912?What is Usain Bolt’s current world record time, set in 2009?Write down information about three world records set before 1977Write down information about three world records set after 1977What do the ‘whiskers’ mean?If it helps, an alternative graph of the same data is on the other sideSame data, different representation …source: Lippincott?United StatesJuly 6, 1912Jackson Scholz?United StatesSeptember 16, 192010.4Charlie Paddock?United StatesApril 23, 1921Eddie Tolan?United StatesAugust 8, 192910.3Percy Williams?CanadaAugust 9, 1930Eddie Tolan?United StatesAugust 1, 1932Eulace Peacock?United StatesAugust 6, 1934Chris Berger?NetherlandsAugust 26, 1934Takayoshi Yoshioka?JapanJune 15, 193510.2Jesse Owens?United StatesJune 20, 1936Harold Davis?United StatesJune 6, 1941Lloyd LaBeach?PanamaMay 15, 1948Barney Ewell?United StatesJuly 9, 1948McDonald Bailey?Great BritainAugust 25, 1951Heinz Fütterer?West GermanyOctober 31, 1954Bobby Morrow?United StatesMay 19, 1956Ira Murchison?United StatesJune 1, 195610.1Willie Williams?United StatesAugust 3, 1956Ira Murchison?United StatesAugust 4, 1956Leamon King?United StatesOctober 20, 1956Ray Norton?United StatesApril 18, 195910.0Armin Hary?West GermanyJune 21, 1960Harry Jerome?CanadaJuly 15, 1960Horacio Esteves?VenezuelaAugust 15, 1964Bob Hayes?United StatesOctober 15, 1964Jim Hines?United StatesMay 27, 1967Enrique Figuerola?CubaJune 17, 1967Paul Nash?South AfricaApril 2, 1968Oliver Ford?United StatesMay 31, 1968Charles Greene?United StatesJune 20, 1968Roger Bambuck?France June 20, 19689.9Jim Hines?United StatesJune 20, 1968Ronnie Ray Smith?United States June 20, 1968Charles Greene?United States June 20, 1968Eddie Hart?United StatesJuly 1, 1972Rey Robinson?United States July 1, 1972Steve Williams?United StatesJune 21, 1974Silvio Leonard?CubaJune 5, 1975Harvey Glance?United StatesApril 3, 1976Don Quarrie?JamaicaMay 22, 1976TimeAthleteNationalityDate9.93Calvin Smith?United StatesJuly 3, 19839.92Carl Lewis?United StatesSeptember 24, 19889.90Leroy Burrell?United StatesJune 14, 19919.86Carl Lewis?United StatesAugust 25, 19919.85Leroy Burrell?United StatesJuly 6, 19949.84Donovan Bailey?CanadaJuly 27, 19969.79Maurice Greene?United StatesJune 16, 19999.77Asafa Powell?JamaicaJune 14, 20059.74Asafa Powell?JamaicaSeptember 9, 20079.72Usain Bolt?JamaicaMay 31, 20089.69Usain Bolt?JamaicaAugust 16, 20089.58Usain Bolt?JamaicaAugust 16, 2009source: en.100 metresThe US athlete, Jesse Owens, once broke four different world records within 45 minutes at the same athletics event. A year later, during the 1936 Berlin Olympics, he won four gold medals.Public domainWhat was the lower bound of Owens’ record 100-metre time?What was the upper bound of his time?Write the error interval for Jesse Owens’ 1936 world recordWrite the error interval for Willie Williams’ 1956 world recordWrite the error interval for Donovan Bailey’s 1996 world record June 20 1968 is known as the ‘Night of Speed’ as three runners broke the world record at the same event. Was this the first time that a person had run 100 metres in less than 10 seconds? Explain your answer.Need more practice before moving on? Write down some more error intervals using the information in the tables.Tallest and shortestThe tallest man who ever lived, Robert Wadlow, was 2.72 metres tall to the nearest centimetre. Write the error interval for his height.The shortest man who has ever lived, Chandra Bahadur Dangi, was 54.6 centimetres tall to the nearest millimetre. Write the error interval for his height.Mount EverestWhen Mount Everest was first surveyed during the Great Trigonometric Survey of the 1850s, it was found to be exactly 29,000 feet high. It had taken years to find this result, and the surveyors were worried that people would think they had only estimated. So instead, they announced that Everest’s height was 29,002 feet.Imagine that 29,000 had been estimated to the nearest 1000 feet. What would the highest and lowest possible heights be? Write the error interval for this measurement.(Mount Everest is now thought to be 29,029 feet high)Kitchen cabinetsA kitchen cabinet has a width of 600 mm 2 mm. Write the error interval for the width of the cabinet.Georgina is designing a new kitchen. She wants to place 5 of these cabinets alongside each other on a wall that is 3 metres long. Will the cabinets fit? Explain your reasoning.VanA van can safely transport a load of 800 kg.? Andy is using the van to carry sacks of sand.? Each sack has a mass of 25 kg to the nearest kg.?How many sacks of sand can Andy transport safely?? Explain your thinking.Fibonacci Rectangle48006001117605 cm8 cm5 cm8 cmThe Fibonacci number sequence starts with the numbers 1, 1, …Each term is found by adding the two previous terms.The sequence continues as follows: 1, 1, 2, 3, 5, 8, 13, 21, …The dimensions of a rectangle are measured to the nearest centimetre. It is noted that they are two consecutive Fibonacci numbers: 5 cm and 8 cm.ProblemFind the upper bound for the area of the rectangleFind the lower bound for the area of the rectangleFind the difference between the upper and lower bounds for the area of the rectangle. Use your answer to form a conjecture. Explore further. Write down your results.Place the following statements in order to prove the conjectureThe bounds of b are b – 0.5 and b + 0.5The difference between the bounds of the area is (ab + 0.5a + 0.5b + 0.25) – (ab – 0.5a – 0.5b + 0.25) = 0.5a + 0.5a + 0.5b + 0.5b = a + bThe upper bound of the area is (a + 0.5)(b + 0.5) = ab + 0.5a + 0.5b + 0.25The bounds of a are a – 0.5 and a + 0.5Since a and b are two Fibonacci numbers then a + b is the next Fibonacci numberLet a and b be two consecutive Fibonacci numbers that are the dimensions of a rectangleThe lower bound of the area is (a – 0.5)(b – 0.5) = ab – 0.5a – 0.5b + 0.25 ................
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