To determine how many miles the spacecraft will travel per year, we need to follow a series of steps:
1. Determine the total distance of the trip: The spacecraft will travel a total distance of [tex]\(3.5 \times 10^1\)[/tex] miles.
2. Know the duration of the trip: The total time for the journey is 9 years.
3. Calculate the rate of travel per year: To find the number of miles traveled per year, divide the total distance by the total duration of the trip. This is done as follows:
[tex]\[
\text{Miles per year} = \frac{\text{Total distance}}{\text{Total time}} = \frac{3.5 \times 10^1 \text{ miles}}{9 \text{ years}}
\][/tex]
4. Perform the division:
[tex]\[
\frac{3.5 \times 10^1}{9} = \frac{35}{9} \approx 3.888888888888889 \text{ miles per year}
\][/tex]
5. Round the result to the nearest hundredth: The value 3.888888888888889 rounded to the nearest hundredth is approximately 3.89.
Thus, the spacecraft will travel approximately [tex]\(3.89 \times 10^0\)[/tex] miles per year, which simplifies to 3.89 miles per year.
