Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F604a8397-7cad-4f94-b592-137fb3c84f4a%2Fce11fc18-3aac-4741-bb73-7407d4540eaa%2Fmga7wn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 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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