3 is the correct answer
Please give the answer with explanation
a) Yes, The average speed of the train could have been greater than 145 km/h,
b) the new maximum average speed, correct to 2 decimal places, is approximately 2.46 km/minute.
a) To determine if the average speed of the train could have been greater than 145 km/h, we need to calculate the maximum possible average speed given the track length rounded to the nearest 10 km.
The track length is 290 km, rounded to the nearest 10 km. This means the actual track length could be anywhere between 285 km (290 km - 5 km) and 295 km (290 km + 5 km).
To find the maximum average speed, we'll assume the train took the minimum possible time (120 minutes) to cover the maximum possible track length (295 km):
Maximum Average Speed = (Maximum Possible Track Length) / (Minimum Possible Time)
Maximum Average Speed = 295 km / 120 minutes ≈ 2.4583 km/minute (rounded to 4 decimal places)
Since 2.4583 km/minute is greater than 145 km/h (which is approximately 2.4167 km/minute), the answer is:
Yes, the average speed of the train could have been greater than 145 km/h.
b) Now that we know the track was measured to the nearest 5 km, we'll calculate the new maximum average speed in km per minute based on the maximum possible track length (295 km) and the minimum possible time (120 minutes):
Maximum Average Speed = (Maximum Possible Track Length) / (Minimum Possible Time)
Maximum Average Speed = 295 km / 120 minutes ≈ 2.4583 km/minute (rounded to 4 decimal places)
So, the new maximum average speed, correct to 2 decimal places, is approximately 2.46 km/minute.
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e^x=3.4
2^x+6=3