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Problem 3: Set up an inequality for a farmer who needs at least 300 kg of maize and has already harvested y kg. Problem 4: Convert 126 km/h to m/s.

Mathematics

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Here are the solutions to the problems:

: Inequality for maize harvest

  1. Define the variables.

    Let yy be the amount of maize already harvested (in kg).
    Let xx be the additional amount of maize the farmer must harvest (in kg).

  2. Formulate the inequality based on the requirement.

    The farmer needs at least 300 kg300 \text{ kg} of maize. This means the total amount harvested (y+xy + x) must be greater than or equal to 300 kg300 \text{ kg}.

    y+x≥300y + x \ge 300
  3. Isolate xx to show how much more he must harvest.

    x≥300−yx \ge 300 - y

    The inequality showing how much more maize the farmer must harvest is x≥300−y\boxed{x \ge 300 - y}.

    : Convert speed from km/h to m/s

  4. Write down the given speed.

    The speed of the train is 126 km/h126 \text{ km/h}.

  5. Convert kilometers to meters.

    We know that 1 km=1000 m1 \text{ km} = 1000 \text{ m}.
    So, 126 km=126×1000 m=126000 m126 \text{ km} = 126 \times 1000 \text{ m} = 126000 \text{ m}.

  6. Convert hours to seconds.

    We know that 1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes} and 1 minute=60 seconds1 \text{ minute} = 60 \text{ seconds}.
    So, 1 hour=60×60 seconds=3600 seconds1 \text{ hour} = 60 \times 60 \text{ seconds} = 3600 \text{ seconds}.

  7. Perform the conversion.

    To convert 126 km/h126 \text{ km/h} to m/s\text{m/s}, we multiply by the conversion factors:

    Speed=126kmh×1000 m1 km×1 h3600 s\text{Speed} = 126 \frac{\text{km}}{\text{h}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} Speed=126×10003600ms\text{Speed} = \frac{126 \times 1000}{3600} \frac{\text{m}}{\text{s}} Speed=1260003600ms\text{Speed} = \frac{126000}{3600} \frac{\text{m}}{\text{s}} Speed=126036ms\text{Speed} = \frac{1260}{36} \frac{\text{m}}{\text{s}} Speed=35ms\text{Speed} = 35 \frac{\text{m}}{\text{s}}

    The speed of the train in m/s\text{m/s} is 35 m/s\boxed{35 \text{ m/s}}.

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