please show clear steps and explanation ### Tutorial ExerciseA radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds. (Round your answer to two decimal places.)| \( t \) (s) | \( v \) (m/s) ||-----------------|---------------|| 0 | 0 || 0.5 | 4.62 || 1.0 | 7.33 || 1.5 | 8.81 || 2.0 | 9.74 || 2.5 | 10.29 || \( t \) (s) | \( v \) (m/s) || 3.0 | 10.52 || 3.5 | 10.68 || 4.0 | 10.73 || 4.5 | 10.86 || 5.0 | 10.86 |### Step 1The distance covered by the runner can be found by the integral of the velocity function evaluated over the time interval, distance \( = \int_{0}^{5} v(t) \, dt \).Using the table provided, we will approximate this using Simpson's Rule with \( \Delta t = \frac{1}{2} \) s and \( n = \_\_\_\_\_\_ \) subintervals.

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A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds. (R t (s) v (m/s) 0 0.5 99 4 1.0 1.5 2.0 2.5 0 4.62 7.33 8.81 8 9.74 10.29 t (s) v (m/s) 10.52 3.0 3.5 4.0 4.5 5 5.0 10.68 10.73 10.86 10.86

A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds. (R t (s) v (m/s) 0 0.5 99 4 1.0 1.5 2.0 2.5 0 4.62 7.33 8.81 8 9.74 10.29 t (s) v (m/s) 10.52 3.0 3.5 4.0 4.5 5 5.0 10.68 10.73 10.86 10.86

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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### Tutorial Exercise

A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds. (Round your answer to two decimal places.)

| \( t \) (s) | \( v \) (m/s) |
|-----------------|---------------|
| 0 | 0 |
| 0.5 | 4.62 |
| 1.0 | 7.33 |
| 1.5 | 8.81 |
| 2.0 | 9.74 |
| 2.5 | 10.29 |
| \( t \) (s) | \( v \) (m/s) |
| 3.0 | 10.52 |
| 3.5 | 10.68 |
| 4.0 | 10.73 |
| 4.5 | 10.86 |
| 5.0 | 10.86 |

### Step 1

The distance covered by the runner can be found by the integral of the velocity function evaluated over the time interval, distance \( = \int_{0}^{5} v(t) \, dt \).

Using the table provided, we will approximate this using Simpson's Rule with \( \Delta t = \frac{1}{2} \) s and \( n = \_\_\_\_\_\_ \) subintervals.

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