For each value below, enter the number correct to
four decimal places.
Suppose an arrow is shot upward on the moon with a
velocity of , then its height in meters after
seconds is given by . Find the
average velocity over the given time intervals.
[5, 6]:
[5, 5.5]:
[5, 5.1]:
[5, 5.01]:
[5, 5.001]:

Ask by Cole Mccoy. in Bahrain

Jan 25,2025

Question

For each value below, enter the number correct to
four decimal places.
Suppose an arrow is shot upward on the moon with a
velocity of , then its height in meters after
seconds is given by . Find the
average velocity over the given time intervals.
[5, 6]:
[5, 5.5]:
[5, 5.1]:
[5, 5.01]:
[5, 5.001]:

Ask by Cole Mccoy. in Bahrain

Jan 25,2025

UpStudy AI · Accepted Answer

To find the average velocity over each given time interval for the height function $$ h(t) = 47t - 0.83t^2 $$, we use the formula:

$$
\text{Average Velocity} = \frac{h(b) - h(a)}{b - a}
$$

where $$[a, b]$$ is the time interval.

### 1. Interval $$[5, 6]$$

$$
h(5) = 47(5) - 0.83(5)^2 = 235 - 20.75 = 214.25 \, \text{m}
$$
$$
h(6) = 47(6) - 0.83(6)^2 = 282 - 29.88 = 252.12 \, \text{m}
$$
$$
\text{Average Velocity} = \frac{252.12 - 214.25}{6 - 5} = 37.87 \, \text{m/s}
$$
$$
\boxed{37.8700 \, \text{m/s}}
$$

### 2. Interval $$[5, 5.5]$$

$$
h(5.5) = 47(5.5) - 0.83(5.5)^2 = 258.5 - 25.1075 = 233.3925 \, \text{m}
$$
$$
\text{Average Velocity} = \frac{233.3925 - 214.25}{5.5 - 5} = \frac{19.1425}{0.5} = 38.285 \, \text{m/s}
$$
$$
\boxed{38.2850 \, \text{m/s}}
$$

### 3. Interval $$[5, 5.1]$$

$$
h(5.1) = 47(5.1) - 0.83(5.1)^2 = 239.7 - 21.5883 = 218.1117 \, \text{m}
$$
$$
\text{Average Velocity} = \frac{218.1117 - 214.25}{5.1 - 5} = \frac{3.8617}{0.1} = 38.617 \, \text{m/s}
$$
$$
\boxed{38.6170 \, \text{m/s}}
$$

### 4. Interval $$[5, 5.01]$$

$$
h(5.01) = 47(5.01) - 0.83(5.01)^2 = 235.47 - 20.7583 = 214.7117 \, \text{m}
$$
$$
\text{Average Velocity} = \frac{214.7117 - 214.25}{5.01 - 5} = \frac{0.4617}{0.01} = 38.617 \, \text{m/s}
$$
$$
\boxed{38.6917 \, \text{m/s}}
$$

### 5. Interval $$[5, 5.001]$$

$$
h(5.001) = 47(5.001) - 0.83(5.001)^2 = 235.047 - 20.7583 = 214.2887 \, \text{m}
$$
$$
\text{Average Velocity} = \frac{214.2887 - 214.25}{5.001 - 5} = \frac{0.0387}{0.001} = 38.6999 \, \text{m/s}
$$
$$
\boxed{38.6999 \, \text{m/s}}
$$

### Summary of Average Velocities

- **[5, 6]:**  **37.8700 m/s**
- **[5, 5.5]:** **38.2850 m/s**
- **[5, 5.1]:** **38.6170 m/s**
- **[5, 5.01]:** **38.6917 m/s**
- **[5, 5.001]:** **38.6999 m/s**
The average velocities over the given intervals are: - [5, 6]: 37.8700 m/s - [5, 5.5]: 38.2850 m/s - [5, 5.1]: 38.6170 m/s - [5, 5.01]: 38.6917 m/s - [5, 5.001]: 38.6999 m/s

For each value below, enter the number correct to
four decimal places.
Suppose an arrow is shot upward on the moon with a
velocity of , then its height in meters after
seconds is given by . Find the
average velocity over the given time intervals.
[5, 6]:
[5, 5.5]:
[5, 5.1]:
[5, 5.01]:
[5, 5.001]:

Upstudy AI Solution

Answer

Solution

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For each value below, enter the number correct to four decimal places. Suppose an arrow is shot upward on the moon with a velocity of , then its height in meters after seconds is given by . Find the average velocity over the given time intervals. [5, 6]: [5, 5.5]: [5, 5.1]: [5, 5.01]: [5, 5.001]:

Upstudy AI Solution

Answer

Solution

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Latest Calculus Questions

For each value below, enter the number correct to
four decimal places.
Suppose an arrow is shot upward on the moon with a
velocity of , then its height in meters after
seconds is given by . Find the
average velocity over the given time intervals.
[5, 6]:
[5, 5.5]:
[5, 5.1]:
[5, 5.01]:
[5, 5.001]: