1 out of 2 parts have been answered.
A rocket is launched off the top of a 65 -foot building, and its trajectory is modeled by the function , where height is in feet
Determine the average rate of change of the height of the rocket between 2 seconds and 4 seconds.
Average Rate of Change:

Ask by Murphy George. in the United States

Mar 21,2025

Question

1 out of 2 parts have been answered.
A rocket is launched off the top of a 65 -foot building, and its trajectory is modeled by the function , where height is in feet
Determine the average rate of change of the height of the rocket between 2 seconds and 4 seconds.
Average Rate of Change:

Ask by Murphy George. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

**Step 1. Write down the function and time points:**

The height function is given by  
$$
H(t) = -16t^2 + 61t + 65
$$
We need to find the average rate of change between $$ t = 2 $$ and $$ t = 4 $$.

---

**Step 2. Calculate $$ H(2) $$ and $$ H(4) $$:**

For $$ t = 2 $$:
$$
H(2) = -16(2)^2 + 61(2) + 65 = -16(4) + 122 + 65 = -64 + 122 + 65 = 123
$$

For $$ t = 4 $$:
$$
H(4) = -16(4)^2 + 61(4) + 65 = -16(16) + 244 + 65 = -256 + 244 + 65 = 53
$$

---

**Step 3. Compute the average rate of change:**

The average rate of change is given by the formula:
$$
\text{Average Rate of Change} = \frac{H(4) - H(2)}{4 - 2}
$$

Substitute the computed values:
$$
\text{Average Rate of Change} = \frac{53 - 123}{2} = \frac{-70}{2} = -35 \text{ ft/s}
$$

---

**Final Answer:**

The average rate of change of the height of the rocket between 2 seconds and 4 seconds is  
$$
-35 \text{ ft/s}
$$
The average rate of change of the rocket's height between 2 seconds and 4 seconds is -35 ft/s.

1 out of 2 parts have been answered.
A rocket is launched off the top of a 65 -foot building, and its trajectory is modeled by the function , where height is in feet
Determine the average rate of change of the height of the rocket between 2 seconds and 4 seconds.
Average Rate of Change:

Upstudy AI Solution

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Solution

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1 out of 2 parts have been answered. A rocket is launched off the top of a 65 -foot building, and its trajectory is modeled by the function , where height is in feet Determine the average rate of change of the height of the rocket between 2 seconds and 4 seconds. Average Rate of Change:

Upstudy AI Solution

Answer

Solution

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1 out of 2 parts have been answered.
A rocket is launched off the top of a 65 -foot building, and its trajectory is modeled by the function , where height is in feet
Determine the average rate of change of the height of the rocket between 2 seconds and 4 seconds.
Average Rate of Change: