Answer:
9.025 inches
Step-by-step explanation:
Let the length be represented by:
[tex]L = mt+L_0[/tex]
Where [tex]L[/tex] is the length of candle at time [tex]t[/tex]
[tex]m[/tex] is the rate at which the candle is burning.
And [tex]L_0[/tex] is the initial length of the candle.
As per the question statement, let us put the given values in the equation.
[tex]11.2 = m\times 33 + L_0 .... (1)\\10.75 = m\times 51+L_0 ..... (2)[/tex]
Subtracting (1) from (2):
[tex]0.45 = -18m\\\Rightarrow m = -0.025[/tex]
Putting the value of [tex]m[/tex] in the equation (1):
[tex]11.2 = -0.025 \times 33+L_0\\\Rightarrow L_0 = 12.025[/tex]
Therefore, the equation becomes:
[tex]L = -0.025t + 12.025[/tex]
Now, we have to find the height of candle after 2 hours.
2 hours mean 120 minutes.
[tex]L = -0.025 \times 120 + 12.025\\\Rightarrow L = 9.025\ inches[/tex]
Therefore, the height of candle is 9.025 inches.
