123 seconds. t (sec) v (ft/s) 12 264 17 374 25 550 41 902 60 1320 72 1884 123 4281 lower estimate of distance traveled = miles upper estimate of distance traveled = miles

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Estimating Distance from Velocity Data

When estimating distances from a table of velocity data, the time intervals don't need to be equally spaced. After a spaceship is launched, the following velocity data is recorded. Use this data to estimate the height above the Earth's surface at 123 seconds.

#### Velocity Data Table
| Time \(t\) (sec) | Velocity \(v\) (ft/s) |
|------------------|-----------------------|
| 0                | 0                     |
| 12               | 264                   |
| 17               | 374                   |
| 25               | 550                   |
| 41               | 902                   |
| 60               | 1320                  |
| 72               | 1884                  |
| 123              | 4281                  |

### Instructions
Calculate both a lower estimate and an upper estimate of the distance traveled using the given velocity data.

- **Lower estimate of distance traveled**: Calculate using the minimum velocity over each interval
- **Upper estimate of distance traveled**: Calculate using the maximum velocity over each interval

**Formulas to Use**:
Using the trapezoidal rule or considering endpoints of each interval helps in obtaining these estimates.

#### Fill in your estimates below:
- Lower estimate of distance traveled = [ ] miles
- Upper estimate of distance traveled = [ ] miles
Transcribed Image Text:### Estimating Distance from Velocity Data When estimating distances from a table of velocity data, the time intervals don't need to be equally spaced. After a spaceship is launched, the following velocity data is recorded. Use this data to estimate the height above the Earth's surface at 123 seconds. #### Velocity Data Table | Time \(t\) (sec) | Velocity \(v\) (ft/s) | |------------------|-----------------------| | 0 | 0 | | 12 | 264 | | 17 | 374 | | 25 | 550 | | 41 | 902 | | 60 | 1320 | | 72 | 1884 | | 123 | 4281 | ### Instructions Calculate both a lower estimate and an upper estimate of the distance traveled using the given velocity data. - **Lower estimate of distance traveled**: Calculate using the minimum velocity over each interval - **Upper estimate of distance traveled**: Calculate using the maximum velocity over each interval **Formulas to Use**: Using the trapezoidal rule or considering endpoints of each interval helps in obtaining these estimates. #### Fill in your estimates below: - Lower estimate of distance traveled = [ ] miles - Upper estimate of distance traveled = [ ] miles
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