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Julieta has been in the car with her family on a road trip for the past three hours. For the first hour, they went about 55 mph. Then, the speed limit changed and they started going about 70 mph. They are still going 70 mph.
B. What does the slope of your graph at any given time represent? Explain already done.
The slope of my graph shows how fast we are going in the car over time. When the line goes up a lot, it means we are going really fast, like when we were going 70 mph after the first hour. If the line is not steep, it means we were going slower, like when we were at 55 mph. So, the steeper the line on my graph, the faster we’re driving.
C. Create a piecewise function that models the distance Julieta's family has traveled over time. already done.
To show how far Julieta's family has traveled on their road trip, we can make a piecewise function. For the first hour, they went 55 mph, so the distance they traveled is just 55 miles (which is 55 miles per hour times 1 hour). After that, for the next two hours, they went 70 mph. So, for the second piece, they traveled 70 miles in each of those hours. The total distance traveled in the second part is 140 miles (which is 70 miles per hour times 2 hours). So, the piecewise function looks like this:
For 0 ≤ t < 1 (the first hour): Distance = 55t
For 1 ≤ t ≤ 3 (the second and third hours): Distance = 55 + 70(t - 1)
This means that in the first hour, they went 55 miles, and in the next two hours, they traveled 70 miles each hour after the first.
D. Two and a half hours into the road trip, how far had Julieta’s family traveled? Give your answer to a reasonable level of accuracy. Explain why your response cannot be perfectly accurate.
make it simple in a small paragraph and like a kid wrote it.
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Julieta has been in the car with her family on a road trip for the past three hours. For the first hour, they went about 55 mph. Then, the speed limit changed and they started going about 70 mph. They are still going 70 mph.
B. What does the slope of your graph at any given time represent? Explain already done.
The slope of my graph shows how fast we are going in the car over time. When the line goes up a lot, it means we are going really fast, like when we were going 70 mph after the first hour. If the line is not steep, it means we were going slower, like when we were at 55 mph. So, the steeper the line on my graph, the faster we’re driving.
C. Create a piecewise function that models the distance Julieta's family has traveled over time. already done.
To show how far Julieta's family has traveled on their road trip, we can make a piecewise function. For the first hour, they went 55 mph, so the distance they traveled is just 55 miles (which is 55 miles per hour times 1 hour). After that, for the next two hours, they went 70 mph. So, for the second piece, they traveled 70 miles in each of those hours. The total distance traveled in the second part is 140 miles (which is 70 miles per hour times 2 hours). So, the piecewise function looks like this:
For 0 ≤ t < 1 (the first hour): Distance = 55t
For 1 ≤ t ≤ 3 (the second and third hours): Distance = 55 + 70(t - 1)
This means that in the first hour, they went 55 miles, and in the next two hours, they traveled 70 miles each hour after the first.
D. Two and a half hours into the road trip, how far had Julieta’s family traveled? Give your answer to a reasonable level of accuracy. Explain why your response cannot be perfectly accurate.
make it simple in a small paragraph and like a kid wrote it.
Answers
Answered by
GPT-4o mini
Two and a half hours into the road trip, Julieta's family had traveled 55 miles from the first hour and then 70 miles for the next hour and a half. So, to find the total distance, we do: 55 miles (first hour) + 70 miles (second hour) + 35 miles (half of the third hour, since 70 times 0.5 is 35). That adds up to 55 + 70 + 35, which equals 160 miles. My answer can’t be perfectly accurate because I rounded the time when calculating how far they went in the last half hour. If I had more exact numbers, I could be sure!
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