### Proportional Relationship Between Time and Depth of an Underwater Camera#### Problem Statement:The depth of an underwater camera on a cable anchored to the sea floor is proportional to the time. The table records the time in seconds (s) and depth in meters (m) of the camera. Fill in the missing values in the table.#### Given Table:| Time (s) | Depth (m) ||----------|-----------|| 0 | 0 || ? | -1 || 60 | ? || 100 | -5 || 240 | ? |To find the missing values, we can set up a proportional relationship between time (t) and depth (d). From the given values, we know:\[ \frac{t}{d} = k \]Given points:1. (100, -5)From this point:\[ k = \frac{100}{-5} = -20 \]Now using this value to find the missing entries:- When $ d = -1 $:\[ t = -1 \times -20 = 20 \]- When $ t = 60 $:\[ d = \frac{60}{-20} = -3 \]- When $ t = 240 $:\[ d = \frac{240}{-20} = -12 \]#### Completed Table:| Time (s) | Depth (m) ||----------|-----------|| 0 | 0 || 20 | -1 || 60 | -3 || 100 | -5 || 240 | -12 |This table shows the times at which the camera reaches specific depths underwater, demonstrating the proportional relationship between the time the camera has been descending and its depth in meters.

Given that, The depth of the camera under the water is proportional to the time. We have to fill up…

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The depth of an under proportional to the tim meters (m) of the came

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

### Proportional Relationship Between Time and Depth of an Underwater Camera

#### Problem Statement:
The depth of an underwater camera on a cable anchored to the sea floor is proportional to the time. The table records the time in seconds (s) and depth in meters (m) of the camera. Fill in the missing values in the table.

#### Given Table:
| Time (s) | Depth (m) |
|----------|-----------|
| 0 | 0 |
| ? | -1 |
| 60 | ? |
| 100 | -5 |
| 240 | ? |

To find the missing values, we can set up a proportional relationship between time (t) and depth (d). From the given values, we know:

\[ \frac{t}{d} = k \]

Given points:
1. (100, -5)
From this point:
\[ k = \frac{100}{-5} = -20 \]

Now using this value to find the missing entries:
- When $ d = -1 $:
\[ t = -1 \times -20 = 20 \]
- When $ t = 60 $:
\[ d = \frac{60}{-20} = -3 \]
- When $ t = 240 $:
\[ d = \frac{240}{-20} = -12 \]

#### Completed Table:
| Time (s) | Depth (m) |
|----------|-----------|
| 0 | 0 |
| 20 | -1 |
| 60 | -3 |
| 100 | -5 |
| 240 | -12 |

This table shows the times at which the camera reaches specific depths underwater, demonstrating the proportional relationship between the time the camera has been descending and its depth in meters.

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