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Sagot :
Let's fill out the rest of the table step-by-step.
We start by noting the initial heights and the burn rates of the two candles:
1. The taller candle starts at 16 cm and loses 2.5 cm in height each hour.
2. The shorter candle starts at 12 cm and loses 1.5 cm in height each hour.
Next, let's calculate the heights for each candle from hour 2 to hour 7.
### Step-by-Step Calculation
- Time (hours) = 2:
- Tall candle height: \( 16 - 2 \times 2.5 = 16 - 5 = 11 \) cm
- Short candle height: \( 12 - 2 \times 1.5 = 12 - 3 = 9 \) cm
- Time (hours) = 3:
- Tall candle height: \( 16 - 3 \times 2.5 = 16 - 7.5 = 8.5 \) cm
- Short candle height: \( 12 - 3 \times 1.5 = 12 - 4.5 = 7.5 \) cm
- Time (hours) = 4:
- Tall candle height: \( 16 - 4 \times 2.5 = 16 - 10 = 6 \) cm
- Short candle height: \( 12 - 4 \times 1.5 = 12 - 6 = 6 \) cm
- Time (hours) = 5:
- Tall candle height: \( 16 - 5 \times 2.5 = 16 - 12.5 = 3.5 \) cm
- Short candle height: \( 12 - 5 \times 1.5 = 12 - 7.5 = 4.5 \) cm
- Time (hours) = 6:
- Tall candle height: \( 16 - 6 \times 2.5 = 16 - 15 = 1 \) cm
- Short candle height: \( 12 - 6 \times 1.5 = 12 - 9 = 3 \) cm
- Time (hours) = 7:
- Tall candle height: \( 16 - 7 \times 2.5 = 16 - 17.5 = -1.5 \) cm
- Short candle height: \( 12 - 7 \times 1.5 = 12 - 10.5 = 1.5 \) cm
### Completed Table
\begin{tabular}{|c|c|c|}
\hline
Time (hours) & 16 cm candle height (cm) & 12 cm candle height (cm) \\
\hline
0 & 16 & 12 \\
\hline
1 & 13.5 & 10.5 \\
\hline
2 & 11 & 9 \\
\hline
3 & 8.5 & 7.5 \\
\hline
4 & 6 & 6 \\
\hline
5 & 3.5 & 4.5 \\
\hline
6 & 1 & 3 \\
\hline
7 & -1.5 & 1.5 \\
\hline
\end{tabular}
The table now shows how the heights of both candles change over a period of 7 hours.
We start by noting the initial heights and the burn rates of the two candles:
1. The taller candle starts at 16 cm and loses 2.5 cm in height each hour.
2. The shorter candle starts at 12 cm and loses 1.5 cm in height each hour.
Next, let's calculate the heights for each candle from hour 2 to hour 7.
### Step-by-Step Calculation
- Time (hours) = 2:
- Tall candle height: \( 16 - 2 \times 2.5 = 16 - 5 = 11 \) cm
- Short candle height: \( 12 - 2 \times 1.5 = 12 - 3 = 9 \) cm
- Time (hours) = 3:
- Tall candle height: \( 16 - 3 \times 2.5 = 16 - 7.5 = 8.5 \) cm
- Short candle height: \( 12 - 3 \times 1.5 = 12 - 4.5 = 7.5 \) cm
- Time (hours) = 4:
- Tall candle height: \( 16 - 4 \times 2.5 = 16 - 10 = 6 \) cm
- Short candle height: \( 12 - 4 \times 1.5 = 12 - 6 = 6 \) cm
- Time (hours) = 5:
- Tall candle height: \( 16 - 5 \times 2.5 = 16 - 12.5 = 3.5 \) cm
- Short candle height: \( 12 - 5 \times 1.5 = 12 - 7.5 = 4.5 \) cm
- Time (hours) = 6:
- Tall candle height: \( 16 - 6 \times 2.5 = 16 - 15 = 1 \) cm
- Short candle height: \( 12 - 6 \times 1.5 = 12 - 9 = 3 \) cm
- Time (hours) = 7:
- Tall candle height: \( 16 - 7 \times 2.5 = 16 - 17.5 = -1.5 \) cm
- Short candle height: \( 12 - 7 \times 1.5 = 12 - 10.5 = 1.5 \) cm
### Completed Table
\begin{tabular}{|c|c|c|}
\hline
Time (hours) & 16 cm candle height (cm) & 12 cm candle height (cm) \\
\hline
0 & 16 & 12 \\
\hline
1 & 13.5 & 10.5 \\
\hline
2 & 11 & 9 \\
\hline
3 & 8.5 & 7.5 \\
\hline
4 & 6 & 6 \\
\hline
5 & 3.5 & 4.5 \\
\hline
6 & 1 & 3 \\
\hline
7 & -1.5 & 1.5 \\
\hline
\end{tabular}
The table now shows how the heights of both candles change over a period of 7 hours.
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