# Math

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1.) Your velocity is given by v(t) = t^2 + 6 in m/sec, with t in seconds.
Estimate the distance, S, traveled between t= 0 and t = 5.
Use an overestimate with data every one second.
The distance is approximately ___________ m.

Please show work and explain. I'm so confused!

For the next question, I just need someone to check my answers because I did a problem just like this, and the computer said it was wrong and this is my last chance to get it right so if I did it wrong, explain how to do it right.
2.) 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 13 12 12 10 9 0

In case the table messed up, the points are (0, 14) (15, 13) (30, 12) (45, 12) (60, 10) (75, 9) (90, 0)

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 = 375 miles
Upper estimate = 405 miles

b) Give upper and lower estimates for the distance Roger ran in total during the entire hour and a half.
Lower estimate = 840 miles
Upper estimate = 1050 miles

Thanks so much!

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