In the episode Benderama of Futurama, Professor Farnsworth creates the Banach-Tarski Dupla-Shrinker, a duplicating and shrinking...

  
 
 
 

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In the episode Benderama of Futurama, Professor Farnsworth creates the Banach-Tarski Dupla-Shrinker, a duplicating and shrinking machine: M=22"-[2%] #WO In this episode, Bender the robot installs the Banach-Tarski Dupla-Shrinker in himself and starts duplicating himself. The series presented in the picture above is supposed to represent the total mass if Bender's duplicating and shrinking process continues forever. Question 1 If Mo represents the original mass of Bender and n is the generation order in the duplication and shrinking process, explain the sequence presented in the series given in the picture above. O Every generation will have one Bender with a mass of Mo Every generation will have one Bender with a mass of Mo 2" (n+1) Mo 2" (n+1) Every generation will have 2" (n+1) Benders, each with a mass of 2" Mo Every generation will have 2" Benders, each with a mass of 5 pts Question 2 What is the shrinking factor between generations? The shrinking factor between the n + 1 and the n generation is n+1 2(n + 2) 1 The shrinking factor between the n +1 and then generation is 2 The shrinking factor between the n + 1 and the 7 generation is n+1 n+2 3 The shrinking factor between the n +1 and the n generation is 5 Page 1 5 pts Question 3 5 pts During the episode, the professor states that the size of the duplicates is 60% of the original one. Is this statement correct? No, the size of each generation depends on the generation number and its limit is 50%. O Yes, the ratio is 3/5, which is 60%. Yes, the shrinking factor between the first two generations is 2/3 which is almost 60%. O Yes, the ratio is approximately 60%. O No, the shrinking factor is 50%. Question 4 Is the series convergent or divergent? O It converges by the comparison test. O It diverges by the limit test. It converges by the integral test. O It diverges by the limit comparison test. 5 pts In the episode Benderama of Futurama, Professor Farnsworth creates the Banach-Tarski Dupla-Shrinker, a duplicating and shrinking machine: M=22"-[2%] #WO In this episode, Bender the robot installs the Banach-Tarski Dupla-Shrinker in himself and starts duplicating himself. The series presented in the picture above is supposed to represent the total mass if Bender's duplicating and shrinking process continues forever. Question 1 If Mo represents the original mass of Bender and n is the generation order in the duplication and shrinking process, explain the sequence presented in the series given in the picture above. O Every generation will have one Bender with a mass of Mo Every generation will have one Bender with a mass of Mo 2" (n+1) Mo 2" (n+1) Every generation will have 2" (n+1) Benders, each with a mass of 2" Mo Every generation will have 2" Benders, each with a mass of 5 pts Question 2 What is the shrinking factor between generations? The shrinking factor between the n + 1 and the n generation is n+1 2(n + 2) 1 The shrinking factor between the n +1 and then generation is 2 The shrinking factor between the n + 1 and the 7 generation is n+1 n+2 3 The shrinking factor between the n +1 and the n generation is 5 Page 1 5 pts Question 3 5 pts During the episode, the professor states that the size of the duplicates is 60% of the original one. Is this statement correct? No, the size of each generation depends on the generation number and its limit is 50%. O Yes, the ratio is 3/5, which is 60%. Yes, the shrinking factor between the first two generations is 2/3 which is almost 60%. O Yes, the ratio is approximately 60%. O No, the shrinking factor is 50%. Question 4 Is the series convergent or divergent? O It converges by the comparison test. O It diverges by the limit test. It converges by the integral test. O It diverges by the limit comparison test. 5 pts

Answer rating: 100% (QA)

1 The 0th gen bender is the original bender Since each bender dupl... View the full answer