To determine how many meters the weather balloon rose each minute, we can first calculate the elevation change between the two given times.
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Calculate the altitude increase:
- At 4:05 p.m., the altitude was 1,482 meters.
- At 4:09 p.m., the altitude was 2,626 meters.
- The change in altitude is: \[ 2,626 \text{ m} - 1,482 \text{ m} = 1,144 \text{ m} \]
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Calculate the time elapsed:
- From 4:05 to 4:09, 4 minutes elapsed.
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Calculate the rise per minute:
- The rise per minute can be determined by dividing the change in altitude by the time elapsed: \[ \frac{1,144 \text{ m}}{4 \text{ min}} = 286 \text{ m/min} \]
So, the weather balloon rose 286 meters per minute.
Next, to determine how high the launch platform was, we need to find the altitude at t = 0 (when the balloon was released at 4:00 p.m.).
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Let’s establish a linear function based on the information we have: We know:
- At t = 5 minutes (4:05 p.m.), A = 1,482 m
- At t = 9 minutes (4:09 p.m.), A = 2,626 m.
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Using the rise rate we found (286 m/min):
- The altitude A can be expressed as: \[ A = 286t + h \] where \( h \) is the height of the launch platform.
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Substituting the information into the equations: For t = 5: \[ 1,482 = 286(5) + h \implies 1,482 = 1,430 + h \implies h = 1,482 - 1,430 = 52 \text{ meters} \]
So, the height of the launch platform is 52 meters.
Finally, we can write the equation that describes the relationship between the altitude A of the weather balloon in meters and the elapsed time t in minutes.
Based on our calculations:
- The rise rate is 286 meters per minute.
- The height of the launch platform is 52 meters.
Thus, the equation is: \[ A = 286t + 52 \]
Final Answers:
- The weather balloon rose 286 meters per minute.
- The height of the launch platform was 52 meters.
- The equation is \( A = 286t + 52 \).