Question
The table shows a truck drivers distance from home during one day's deliveries find the rate of change for each interval time(h) 0,1,4,5,8,10 distance(mi) 0,35,71,82,199,200 hour 0 to 1:
Answers
Answer
1 to 4:
Answer
4 to 5
Answer
5 to 8
Answer
8 to 10
Answer
The table shows a truck drivers distance from home during one day's deliveries find the rate of change for each interval time(h) 0,1,4,5,8,10 distance(mi) 0,35,71,82,199,200 hour 8 to 10:
Answered by
Downwithmath2010
The table shows a truck drivers distance from home during one day's deliveries find the rate of change for each interval time(h) 0,1,4,5,8,10 distance(mi) 0,35,71,82,199,200 hour 0 to 1:
What are the units on all your answers?
What are the units on all your answers?
Answered by
Downwithmath2010
The rate of change represents the average speed during which time interval what is the driver speed the greatest? Hour to
Answered by
GPT-4o mini
To find the rate of change of distance for the time interval from \(0\) to \(1\) hour, we use the formula for the rate of change, which is given by:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(0\) to \(1\):
- At \(t_1 = 0\) hours, the distance \(d(0) = 0\) miles.
- At \(t_2 = 1\) hour, the distance \(d(1) = 35\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(1) - d(0)}{1 - 0} = \frac{35 - 0}{1 - 0} = \frac{35}{1} = 35 \text{ miles per hour}
\]
So, the rate of change from \(0\) to \(1\) hour is **35 miles per hour**.
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(0\) to \(1\):
- At \(t_1 = 0\) hours, the distance \(d(0) = 0\) miles.
- At \(t_2 = 1\) hour, the distance \(d(1) = 35\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(1) - d(0)}{1 - 0} = \frac{35 - 0}{1 - 0} = \frac{35}{1} = 35 \text{ miles per hour}
\]
So, the rate of change from \(0\) to \(1\) hour is **35 miles per hour**.
Answered by
GPT-4o mini
To find the rate of change of distance for the time interval from \(1\) to \(4\) hours, we again use the formula:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(1\) to \(4\):
- At \(t_1 = 1\) hour, the distance \(d(1) = 35\) miles.
- At \(t_2 = 4\) hours, the distance \(d(4) = 71\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(4) - d(1)}{4 - 1} = \frac{71 - 35}{4 - 1} = \frac{36}{3} = 12 \text{ miles per hour}
\]
So, the rate of change from \(1\) to \(4\) hours is **12 miles per hour**.
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(1\) to \(4\):
- At \(t_1 = 1\) hour, the distance \(d(1) = 35\) miles.
- At \(t_2 = 4\) hours, the distance \(d(4) = 71\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(4) - d(1)}{4 - 1} = \frac{71 - 35}{4 - 1} = \frac{36}{3} = 12 \text{ miles per hour}
\]
So, the rate of change from \(1\) to \(4\) hours is **12 miles per hour**.
Answered by
GPT-4o mini
To find the rate of change of distance for the time interval from \(4\) to \(5\) hours, we again use the rate of change formula:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(4\) to \(5\):
- At \(t_1 = 4\) hours, the distance \(d(4) = 71\) miles.
- At \(t_2 = 5\) hours, the distance \(d(5) = 82\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(5) - d(4)}{5 - 4} = \frac{82 - 71}{5 - 4} = \frac{11}{1} = 11 \text{ miles per hour}
\]
So, the rate of change from \(4\) to \(5\) hours is **11 miles per hour**.
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(4\) to \(5\):
- At \(t_1 = 4\) hours, the distance \(d(4) = 71\) miles.
- At \(t_2 = 5\) hours, the distance \(d(5) = 82\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(5) - d(4)}{5 - 4} = \frac{82 - 71}{5 - 4} = \frac{11}{1} = 11 \text{ miles per hour}
\]
So, the rate of change from \(4\) to \(5\) hours is **11 miles per hour**.
Answered by
GPT-4o mini
To find the rate of change of distance for the time interval from \(5\) to \(8\) hours, we use the rate of change formula:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(5\) to \(8\):
- At \(t_1 = 5\) hours, the distance \(d(5) = 82\) miles.
- At \(t_2 = 8\) hours, the distance \(d(8) = 199\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(8) - d(5)}{8 - 5} = \frac{199 - 82}{8 - 5} = \frac{117}{3} = 39 \text{ miles per hour}
\]
So, the rate of change from \(5\) to \(8\) hours is **39 miles per hour**.
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(5\) to \(8\):
- At \(t_1 = 5\) hours, the distance \(d(5) = 82\) miles.
- At \(t_2 = 8\) hours, the distance \(d(8) = 199\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(8) - d(5)}{8 - 5} = \frac{199 - 82}{8 - 5} = \frac{117}{3} = 39 \text{ miles per hour}
\]
So, the rate of change from \(5\) to \(8\) hours is **39 miles per hour**.
Answered by
GPT-4o mini
To find the rate of change of distance for the time interval from \(8\) to \(10\) hours, we use the rate of change formula:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(8\) to \(10\):
- At \(t_1 = 8\) hours, the distance \(d(8) = 199\) miles.
- At \(t_2 = 10\) hours, the distance \(d(10) = 200\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(10) - d(8)}{10 - 8} = \frac{200 - 199}{10 - 8} = \frac{1}{2} = 0.5 \text{ miles per hour}
\]
So, the rate of change from \(8\) to \(10\) hours is **0.5 miles per hour**.
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
For the time interval from \(8\) to \(10\):
- At \(t_1 = 8\) hours, the distance \(d(8) = 199\) miles.
- At \(t_2 = 10\) hours, the distance \(d(10) = 200\) miles.
Now, plug in these values into the rate of change formula:
\[
\text{Rate of change} = \frac{d(10) - d(8)}{10 - 8} = \frac{200 - 199}{10 - 8} = \frac{1}{2} = 0.5 \text{ miles per hour}
\]
So, the rate of change from \(8\) to \(10\) hours is **0.5 miles per hour**.
Answered by
GPT-4o mini
The calculation for the interval from \(8\) to \(10\) hours was already provided, but let's go through it again step by step to ensure clarity.
To find the rate of change of distance for the time interval from \(8\) to \(10\) hours, we use the formula:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
**Given**:
- At \(t_1 = 8\) hours, the distance \(d(8) = 199\) miles.
- At \(t_2 = 10\) hours, the distance \(d(10) = 200\) miles.
**Plugging in these values**:
\[
\text{Rate of change} = \frac{d(10) - d(8)}{10 - 8} = \frac{200 - 199}{10 - 8} = \frac{1}{2} = 0.5 \text{ miles per hour}
\]
Thus, the rate of change from \(8\) to \(10\) hours is **0.5 miles per hour**.
To find the rate of change of distance for the time interval from \(8\) to \(10\) hours, we use the formula:
\[
\text{Rate of change} = \frac{\text{Change in distance}}{\text{Change in time}} = \frac{d(t_2) - d(t_1)}{t_2 - t_1}
\]
**Given**:
- At \(t_1 = 8\) hours, the distance \(d(8) = 199\) miles.
- At \(t_2 = 10\) hours, the distance \(d(10) = 200\) miles.
**Plugging in these values**:
\[
\text{Rate of change} = \frac{d(10) - d(8)}{10 - 8} = \frac{200 - 199}{10 - 8} = \frac{1}{2} = 0.5 \text{ miles per hour}
\]
Thus, the rate of change from \(8\) to \(10\) hours is **0.5 miles per hour**.
Answered by
GPT-4o mini
In the context of your question about the truck driver's distance from home and the calculated rates of change, the units are as follows:
- **Time** is measured in **hours (h)**.
- **Distance** is measured in **miles (mi)**.
- The rate of change is defined as the change in distance divided by the change in time, so the units for the rate of change will be in **miles per hour (mi/h)**.
Now, I've previously calculated the rates of change for each interval. Let me summarize them along with their units:
1. **From 0 to 1 hour:**
- Rate of change = **35 miles per hour (mi/h)**
2. **From 1 to 4 hours:**
- Rate of change = **12 miles per hour (mi/h)**
3. **From 4 to 5 hours:**
- Rate of change = **11 miles per hour (mi/h)**
4. **From 5 to 8 hours:**
- Rate of change = **39 miles per hour (mi/h)**
5. **From 8 to 10 hours:**
- Rate of change = **0.5 miles per hour (mi/h)**
So, the units for all the rates of change you requested are **miles per hour (mi/h)**.
- **Time** is measured in **hours (h)**.
- **Distance** is measured in **miles (mi)**.
- The rate of change is defined as the change in distance divided by the change in time, so the units for the rate of change will be in **miles per hour (mi/h)**.
Now, I've previously calculated the rates of change for each interval. Let me summarize them along with their units:
1. **From 0 to 1 hour:**
- Rate of change = **35 miles per hour (mi/h)**
2. **From 1 to 4 hours:**
- Rate of change = **12 miles per hour (mi/h)**
3. **From 4 to 5 hours:**
- Rate of change = **11 miles per hour (mi/h)**
4. **From 5 to 8 hours:**
- Rate of change = **39 miles per hour (mi/h)**
5. **From 8 to 10 hours:**
- Rate of change = **0.5 miles per hour (mi/h)**
So, the units for all the rates of change you requested are **miles per hour (mi/h)**.
Answered by
GPT-4o mini
To determine during which time interval the driver had the greatest average speed, we will summarize the calculated rates of change for each interval:
1. **From 0 to 1 hour:**
- Rate of change = **35 miles per hour (mi/h)**
2. **From 1 to 4 hours:**
- Rate of change = **12 miles per hour (mi/h)**
3. **From 4 to 5 hours:**
- Rate of change = **11 miles per hour (mi/h)**
4. **From 5 to 8 hours:**
- Rate of change = **39 miles per hour (mi/h)**
5. **From 8 to 10 hours:**
- Rate of change = **0.5 miles per hour (mi/h)**
### Conclusion
The greatest average speed occurs in the time interval from **5 to 8 hours**, where the rate of change is **39 miles per hour**.
So, the answer to your question is:
- The driver had the greatest speed during the interval from **5 hours to 8 hours**.
1. **From 0 to 1 hour:**
- Rate of change = **35 miles per hour (mi/h)**
2. **From 1 to 4 hours:**
- Rate of change = **12 miles per hour (mi/h)**
3. **From 4 to 5 hours:**
- Rate of change = **11 miles per hour (mi/h)**
4. **From 5 to 8 hours:**
- Rate of change = **39 miles per hour (mi/h)**
5. **From 8 to 10 hours:**
- Rate of change = **0.5 miles per hour (mi/h)**
### Conclusion
The greatest average speed occurs in the time interval from **5 to 8 hours**, where the rate of change is **39 miles per hour**.
So, the answer to your question is:
- The driver had the greatest speed during the interval from **5 hours to 8 hours**.
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