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The problem asks for the **average velocity** of an object with height given by the function:

\[
h(x) = -16x^2 + 149x + 94
\]

where \( x \) is time in seconds and \( h(x) \) is height in feet. You are tasked with finding the average velocity between \( x = 1 \) and \( x = 1.3 \).

### Average Velocity Formula
The average velocity between two points \( x_1 \) and \( x_2 \) is given by the formula:

\[
v_{\text{avg}} = \frac{h(x_2) - h(x_1)}{x_2 - x_1}
\]

### Step-by-Step Solution

1. **Find \( h(1) \)**:
   Substitute \( x = 1 \) into the function:

   \[
   h(1) = -16(1)^2 + 149(1) + 94 = -16 + 149 + 94 = 227 \, \text{feet}
   \]

2. **Find \( h(1.3) \)**:
   Substitute \( x = 1.3 \) into the function:

   \[
   h(1.3) = -16(1.3)^2 + 149(1.3) + 94
   \]
   \[
   h(1.3) = -16(1.69) + 193.7 + 94 = -27.04 + 193.7 + 94 = 260.66 \, \text{feet}
   \]

3. **Calculate the average velocity**:

   \[
   v_{\text{avg}} = \frac{h(1.3) - h(1)}{1.3 - 1} = \frac{260.66 - 227}{0.3} = \frac{33.66}{0.3} = 112.2 \, \text{feet per second}
   \]

Thus, the average velocity between \( x = 1 \) and \( x = 1.3 \) is approximately **112.2 feet per second**.

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Let me know if you want further clarifications or details!

### Related Questions:
1. How is the concept of average velocity different from instantaneous velocity?
2. Can you calculate the instantaneous velocity at \( x = 1 \) using derivatives?
3. How would the average velocity change if the interval was \( x = 1.3 \) to \( x = 1.5 \)?
4. How does the height function reflect the motion of the object (e.g., does it represent free fall)?
5. What is the significance of the coefficients in the quadratic height function?

### Tip:
When calculating average velocity over a small interval, you're approximating the instantaneous velocity at the midpoint of the interval!

The height h(x) of an object is given by the function h(x) = -16x^2 + 149x + 94 where x is time in seconds and h(x) is height in feet. Find the average velocity between x = 1 and x = 1.3. Round to one decimal place if necessary.

Learn how to calculate the average velocity between x = 1 and x = 1.3 for the quadratic function h(x) = -16x^2 + 149x + 94. This problem covers the concept of average velocity and rate of change for quadratic functions, ideal for students in Grades 10-12.

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