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Sagot :
Sure, let's go through the step-by-step process for determining each entry in the table given the measured distances and other provided information.
### Step 1: Measured Distance Across Anomalies (in cm)
The first step is to identify the measured distances across the anomalies from the map:
- Anomaly I: 1.25 cm
- Anomaly II: 1.50 cm
- Anomaly III: 1.75 cm
- Anomaly IV: 2.25 cm
These values are directly given in the problem.
### Step 2: Scale Conversion Distance Across Anomalies (in km)
The scale conversion distance for each anomaly is:
- 312.5 km
This means that each centimeter measured on the map corresponds to a real-world distance of 312.5 kilometers.
### Step 3: Scale Distance Across Anomalies Converted to cm
To understand the actual distance in centimeters, we multiply the scale conversion distance by 100,000 (since 1 km = 100,000 cm), which results in:
- [tex]\( 312.5 \text{ km} \times 100,000 \text{ cm/km} = 31,250,000 \text{ cm} \)[/tex]
Thus:
- For Anomaly I: 31,250,000 cm
- Similarly, for all other anomalies: 31,250,000 cm
### Step 4: Total Years of Anomalies
The total number of years each anomaly has been present is given as:
- 5,000,000 years
This value is constant across all anomalies.
### Step 5: Average Seafloor Spreading Rate (in cm/yr)
The average seafloor spreading rate can be found by dividing the scale distance (converted into cm) by the total years of anomaly. The formula is:
[tex]\[ \text{Average Seafloor Spreading Rate} = \frac{\text{Scale Distance} \text{ (cm)}}{\text{Total Years}} \][/tex]
Using the numbers:
[tex]\[ \text{Average Seafloor Spreading Rate} = \frac{31,250,000 \text{ cm}}{5,000,000 \text{ years}} = 6.25 \text{ cm/year} \][/tex]
For each anomaly, the average seafloor spreading rate is:
- 6.25 cm/year
### Summary
Here's the filled-in table based on the above calculations:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Pacific-Nazca Plates} (Use\ \text{line B}) & \text{Anomaly I} & \text{Anomaly II} & \text{Anomaly III} & \text{Anomaly IV} \\ \hline \text{Measured the distance across anomaly on the map (cm)} & 1.25\ \text{cm} & 1.50\ \text{cm} & 1.75\ \text{cm} & 2.25\ \text{cm} \\ \hline \text{Scale conversion distance across the anomaly (km)} & 312.5\ \text{km} & 312.5\ \text{km} & 312.5\ \text{km} & 312.5\ \text{km} \\ \hline \text{Scale distance across the anomaly converted to cm} & 31,250,000\ \text{cm} & 31,250,000\ \text{cm} & 31,250,000\ \text{cm} & 31,250,000\ \text{cm} \\ \hline \text{Total years of Anomaly} & 5,000,000\ \text{yrs} & 5,000,000\ \text{yrs} & 5,000,000\ \text{yrs} & 5,000,000\ \text{yrs} \\ \hline \text{Average Seafloor Spreading Rate (cm/yr) of Anomaly} & 6.25\ \text{cm/yr} & 6.25\ \text{cm/yr} & 6.25\ \text{cm/yr} & 6.25\ \text{cm/yr} \\ \hline \end{array} \][/tex]
And with this, we have a complete and detailed solution for the given question.
### Step 1: Measured Distance Across Anomalies (in cm)
The first step is to identify the measured distances across the anomalies from the map:
- Anomaly I: 1.25 cm
- Anomaly II: 1.50 cm
- Anomaly III: 1.75 cm
- Anomaly IV: 2.25 cm
These values are directly given in the problem.
### Step 2: Scale Conversion Distance Across Anomalies (in km)
The scale conversion distance for each anomaly is:
- 312.5 km
This means that each centimeter measured on the map corresponds to a real-world distance of 312.5 kilometers.
### Step 3: Scale Distance Across Anomalies Converted to cm
To understand the actual distance in centimeters, we multiply the scale conversion distance by 100,000 (since 1 km = 100,000 cm), which results in:
- [tex]\( 312.5 \text{ km} \times 100,000 \text{ cm/km} = 31,250,000 \text{ cm} \)[/tex]
Thus:
- For Anomaly I: 31,250,000 cm
- Similarly, for all other anomalies: 31,250,000 cm
### Step 4: Total Years of Anomalies
The total number of years each anomaly has been present is given as:
- 5,000,000 years
This value is constant across all anomalies.
### Step 5: Average Seafloor Spreading Rate (in cm/yr)
The average seafloor spreading rate can be found by dividing the scale distance (converted into cm) by the total years of anomaly. The formula is:
[tex]\[ \text{Average Seafloor Spreading Rate} = \frac{\text{Scale Distance} \text{ (cm)}}{\text{Total Years}} \][/tex]
Using the numbers:
[tex]\[ \text{Average Seafloor Spreading Rate} = \frac{31,250,000 \text{ cm}}{5,000,000 \text{ years}} = 6.25 \text{ cm/year} \][/tex]
For each anomaly, the average seafloor spreading rate is:
- 6.25 cm/year
### Summary
Here's the filled-in table based on the above calculations:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Pacific-Nazca Plates} (Use\ \text{line B}) & \text{Anomaly I} & \text{Anomaly II} & \text{Anomaly III} & \text{Anomaly IV} \\ \hline \text{Measured the distance across anomaly on the map (cm)} & 1.25\ \text{cm} & 1.50\ \text{cm} & 1.75\ \text{cm} & 2.25\ \text{cm} \\ \hline \text{Scale conversion distance across the anomaly (km)} & 312.5\ \text{km} & 312.5\ \text{km} & 312.5\ \text{km} & 312.5\ \text{km} \\ \hline \text{Scale distance across the anomaly converted to cm} & 31,250,000\ \text{cm} & 31,250,000\ \text{cm} & 31,250,000\ \text{cm} & 31,250,000\ \text{cm} \\ \hline \text{Total years of Anomaly} & 5,000,000\ \text{yrs} & 5,000,000\ \text{yrs} & 5,000,000\ \text{yrs} & 5,000,000\ \text{yrs} \\ \hline \text{Average Seafloor Spreading Rate (cm/yr) of Anomaly} & 6.25\ \text{cm/yr} & 6.25\ \text{cm/yr} & 6.25\ \text{cm/yr} & 6.25\ \text{cm/yr} \\ \hline \end{array} \][/tex]
And with this, we have a complete and detailed solution for the given question.
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