Final answer:
To find the candle's height after 9 hours, we add 1.2 cm (the product of 3 hours and the burning rate of 0.4 cm/hour) to the height at 12 hours, giving a result of 23.4 cm.
Step-by-step explanation:
The student is asking about the calculation of the height of a candle after a given time, knowing the slope of its burning rate and the height at another time point. This is a linear function problem in mathematics.
Given the slope (−0.4 cm/hour) and the height of the candle after 12 hours (22.2 cm), we can calculate the height after 9 hours.
The time difference between 12 and 9 hours is 3 hours. Since the candle decreases in height by 0.4 cm for each hour it burns, after 3 hours it would have burned down by 3 hours × 0.4 cm/hour = 1.2 cm. So, the height of the candle after 9 hours would have been 22.2 cm + 1.2 cm = 23.4 cm.
To find the height of the candle after 9 hours, we can use the slope of the linear function, which is -0.4. Since the slope represents the change in height per hour, we can multiply the slope by the number of hours to find the change in height.
So, the change in height after 12 hours is -0.4 * 12 = -4.8 centimeters. Since the height after 12 hours is 22.2 centimeters, we can subtract the change in height from the height after 12 hours to find the height after 9 hours: 22.2 - 4.8 = 17.4 centimeters.