Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to stop. Jeff's data follow: Time since start (min) |0 15 30 45 60 75 90 Speed (mph) 14 12 8 (a) Assuming that Roger's speed is never increasing, give upper and lower estimates for the distance Roger ran during the first half hour. Lower estimate = i Upper estimate = i e Textbook and Media (b) Give upper and lower estimates for the distance Roger ran in total during the entire hour and a half. Lower estimate = i Upper estimate = i e Textbook and Media (c) How often would Jeff have needed to measure Roger's speed in order to find lower and upper estimates within 0.1 mile of the actual distance he ran?(a) Assuming that Roger's speed is never increasing, give upper and lower estimates for the distance Roger ran during the first half hour. Lower estimate = Upper estimate = i e Textbook and Media (b) Give upper and lower estimates for the distance Roger ran in total during the entire hour and a half. Lower estimate = i Upper estimate = i e Textbook and Media (c) How often would Jeff have needed to measure Roger's speed in order to find lower and upper estimates within 0. 1 mile of the actual distance he ran? Round your answer to the nearest integer. seconds e Textbook and MediaFor an closed cylinder with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 30 cms. NOTE: Enter exact answers, or round to three decimal places. r= cm h = cm