Question

example 4: a burning candle - extended
a candle burns at a constant rate of 1.8 inches per hour. 5.6 hours after being lit, the candle is 9.92 inches tall. the candle burns continuously until completely consumed.
let h represent the candles height (in inches).
let t represent the elapsed time (in hours) since the candle was lit.
a. recall that the candle burns at a constant rate of 1.8 inches per hour. complete the following statements.
δh = 1.8 · δt preview 1.8 = 1.8
\frac{δh}{δt}=
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b. 5.6 hours after being lit, the candle is 9.92 inches tall. what is the reference point (t, h) given in the problem description?
(t, h) =
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question 17 points possible: 3
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Explanation:

Step1: Recall rate - change formula

Since the rate of change of height with respect to time is the constant burn - rate. If $\Delta h$ is the change in height and $\Delta t$ is the change in time, and the burn - rate is 1.8 inches per hour, then $\frac{\Delta h}{\Delta t}=1.8$.

Step2: Identify reference point

The reference point is given by the time and height values at a specific moment. Here, when $t = 5.6$ hours, $h=9.92$ inches. So the reference point $(t,h)=(5.6,9.92)$.

Answer:

a. $\frac{\Delta h}{\Delta t}=1.8$
b. $(t,h)=(5.6,9.92)$