# Reimann Sums

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Category: Entertainment

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## Presentation Transcript

### Reimann Sums Project:

Reimann Sums Project Macy Jones

Destination!

### Camden to Augusta:

Camden to Augusta Distance: 41.0 miles Start Time: 12:10 pm Odometer Reading: 71666 miles

The Drive

### Data:

Data Time Elapsed (min) Velocity (MPH) 0 0 5 24 10 50 15 58 20 62 25 70 30 68 35 50 40 56 45 30 50 0 Final Reading: 71707 miles End time: 1:00 pm “ n ” = 11

### Graphs:

Graphs Time Elapsed Velocity

### Graphs:

Graphs Velocity Time Elapsed

### Calculations:

Calculations Distance Traveled = {(Left + Right) ÷ 2} + Error Number of subdivisions = 11 = “ n ” Convert miles per hour to miles per minute! Time Elapsed (min) Velocity (MPM) 0 0 ÷ 60 = 0 5 24 ÷ 60 = .4 10 50 ÷ 60 = .833 15 58 ÷ 60 = .966 20 62 ÷ 60 = 1.03 25 70 ÷ 60 = 1.16 30 68 ÷ 60 = 1.13 35 50 ÷ 60 = .833 40 56 ÷ 60 = .933 45 30 ÷ 60 = .5 50 0 ÷ 60 = 0 Left Hand: {5(0) + 5(.4) + 5(.833) + 5(.966) + 5(1.03) + 5(1.16) + 5(1.13) + 5(.833) + 5(.933) + 5(.5)} = 38.925 miles Right Hand: {5(.4) + 5 (.833) + 5(.966) + 5(1.03) + 5(1.16) + 5(1.13) + 5(.833) + 5(.933) + 5(.5) + 5(0) = 38.925 miles

### Distance Traveled:

Distance Traveled DT = {Left + Right}/2 + Error DT = {38.925 + 38.925}/2 + {38.925 – 38.925} = 38.925 miles Actual Distance Traveled = 41.0 miles Calculated Distance Traveled = 38.295 miles Error decreases when “ n ” approaches infinity