Answer: the height after 10 hours is 21 cm
Step-by-step explanation:
Assuming the rate at which the height of the candle is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
If after seven hours of burning, a candle has high of 22.5 Centimeters, the expression is
22.5 = a + (7 - 1)d
22.5 = a + 6d - - - - - - - - - -1
If after 26 hours of burning, it's height is 13 cm. The expression is
13 = a + (26 - 1)d
13 = a + 25d - - - - - - - - - - - 2
9.5 = - 19d
d = 9.5/ - 19
d = - 0.5
Substituting d = - 0.5 into equation 1, it becomes
22.5 = a + 6 × - 0.5
22.5 = a - 3
a = 22.5 + 3
a = 25.5
The linear expression becomes
Tn = 25.5 - 0.5(n - 1)
The height of the candle after 10 hours would be
25.5 - 0.5(10 - 1)
= 25.5 - 4.5
= 21 centimeters
