Question

A candle burned at a steady rate. After 33 minutes, the candle was 11.2 inches tall. Eighteen minutes later, it was 10.75 inches tall. Use an equation in point-slope form to determine the height of the candle after 2 hours. Round the answer to the tenth place if necessary

Answer 1

Answer:

9.025 inches

Step-by-step explanation:

Let the length be represented by:

$L = mt+L_0$

Where $L$ is the length of candle at time $t$

$m$ is the rate at which the candle is burning.

And $L_0$ is the initial length of the candle.

As per the question statement, let us put the given values in the equation.

$11.2 = m\times 33 + L_0 .... (1)\\10.75 = m\times 51+L_0 ..... (2)$

Subtracting (1) from (2):

$0.45 = -18m\\\Rightarrow m = -0.025$

Putting the value of $m$ in the equation (1):

$11.2 = -0.025 \times 33+L_0\\\Rightarrow L_0 = 12.025$

Therefore, the equation becomes:

$L = -0.025t + 12.025$

Now, we have to find the height of candle after 2 hours.

2 hours mean 120 minutes.

$L = -0.025 \times 120 + 12.025\\\Rightarrow L = 9.025\ inches$

Therefore, the height of candle is 9.025 inches.