https://file.aiquickdraw.com/mathbot/file/1726671146835fxirc9u2.jpg

Let me guide you through the problem step by step based on the image provided:

### Part (b): Change in time (\(\Delta t\))
You already answered this part correctly:
\[
\Delta t = 10.4 - 5.6 = 4.8 \text{ hours}
\]

### Part (c): Change in height (\(\Delta h\))
The rate at which the candle burns is given as 1.8 inches per hour. Therefore, the change in height is calculated using the formula:
\[
\Delta h = -1.8 \times \Delta t
\]
Since \(\Delta t = 4.8\) hours:
\[
\Delta h = -1.8 \times 4.8 = -8.64 \text{ inches}
\]

So, the change in height \(\Delta h = -8.64\) inches.

### Part (d): Height after 10.4 hours
The initial height at \(t = 5.6\) hours is \(h_i = 9.92\) inches (from the graph). Using the formula:
\[
h = h_i + \Delta h
\]
Substitute the values:
\[
h = 9.92 + (-8.64) = 1.28 \text{ inches}
\]

So, the height of the candle at 10.4 hours after it was lit is 1.28 inches.

### Part (e): General formula for the candle height
The candle height decreases at a constant rate of 1.8 inches per hour. Given the height at \(t = 0\) as \(h_0 = 18\) inches (from the graph), the general formula for the height \(h\) at any time \(t\) is:
\[
h = h_0 - 1.8 \times t
\]

This formula will give the height of the candle for any given \(t\).

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Would you like to discuss any specific part in more detail?

Here are five related questions to practice:
1. What would be the candle height at \(t = 6\) hours using the general formula?
2. If the candle burns at 2 inches per hour, what would be the change in height over 5 hours?
3. How would the formula for \(h(t)\) change if the initial height was 20 inches?
4. What is the time \(t\) when the candle completely burns out if the height starts at 18 inches?
5. If the candle burned slower at 1 inch per hour, how long would it take to burn out?

**Tip:** Always track units during calculations, especially in rate problems involving time and physical dimensions!

We can represent an elapsed time of 10.4 hours after the candle was lit. What is the change in time from 5.6 hours to 10.4 hours after the candle was lit, and what is the corresponding change in the candle's height at this time?

This problem involves calculating the change in time and corresponding height of a candle burning at a constant rate of 1.8 inches per hour. Suitable for middle school students, it demonstrates the use of linear equations in real-life scenarios.

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