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32831553
11/04/2022
Mathematics
High School
answered • expert verified
Allison just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 15 inches and the candle burned at a rate of 0.75 inches per hour. Make a table of values and then write an equation for L,L, in terms of t,t, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit.
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singhneha21
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The original length of the new candle was 10 inches. Using the given data points, the linear relationship between time (t) and the remaining unburned length (L) is (L = -t + 10).
To determine the original length of the new candle, we can use the equation of a straight line, which is given by:
L = mt + b
where:
- L is the length of the candle remaining unburned,
- t is the time in hours,
- m is the slope of the line,
- b is the y-intercept (the initial length of the candle).
We can use the given data points (1, 9), (6, 4), and (9.5, 0.5) to form a system of three equations and solve for m and b.
Using the point (1, 9):
9 = m(1) + b
Using the point (6, 4):
4 = m(6) + b
Using the point (9.5, 0.5):
0.5 = m(9.5) + b
Now, solve these equations simultaneously to find m and b.
1. 9 = m + b
2. 4 = 6m + b
3. 0.5 = 9.5m + b
Subtract equation (1) from equation (2):
-5 = 5m
Solve for m:
m = -1
Substitute m = -1 into equation (1):
9 = -1 + b
Solve for b:
b = 10
So, the equation for the relationship between t and L is:
L = -t + 10
Now, to determine the original length of the new candle, we find L when t = 0:
L = -(0) + 10 = 10
Therefore, the original length of the new candle was 10 inches.
The complete question is:
Allison just lit a new candle and then let it burn all the way down to nothing. Let L represent the length of the candle remaining unburned, in inches, t hours after candle was lit. The table below has select values showing the linear relationship between t and L. Determine the original length of the new candle.
t L
1 9
6 4
32831553
11/04/2022
Mathematics
High School
answered • expert verified
Allison just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 15 inches and the candle burned at a rate of 0.75 inches per hour. Make a table of values and then write an equation for L,L, in terms of t,t, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit.
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Expert-Verified Answer
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singhneha21
Virtuoso
7.2K answers
1.8M people helped
The original length of the new candle was 10 inches. Using the given data points, the linear relationship between time (t) and the remaining unburned length (L) is (L = -t + 10).
To determine the original length of the new candle, we can use the equation of a straight line, which is given by:
L = mt + b
where:
- L is the length of the candle remaining unburned,
- t is the time in hours,
- m is the slope of the line,
- b is the y-intercept (the initial length of the candle).
We can use the given data points (1, 9), (6, 4), and (9.5, 0.5) to form a system of three equations and solve for m and b.
Using the point (1, 9):
9 = m(1) + b
Using the point (6, 4):
4 = m(6) + b
Using the point (9.5, 0.5):
0.5 = m(9.5) + b
Now, solve these equations simultaneously to find m and b.
1. 9 = m + b
2. 4 = 6m + b
3. 0.5 = 9.5m + b
Subtract equation (1) from equation (2):
-5 = 5m
Solve for m:
m = -1
Substitute m = -1 into equation (1):
9 = -1 + b
Solve for b:
b = 10
So, the equation for the relationship between t and L is:
L = -t + 10
Now, to determine the original length of the new candle, we find L when t = 0:
L = -(0) + 10 = 10
Therefore, the original length of the new candle was 10 inches.
The complete question is:
Allison just lit a new candle and then let it burn all the way down to nothing. Let L represent the length of the candle remaining unburned, in inches, t hours after candle was lit. The table below has select values showing the linear relationship between t and L. Determine the original length of the new candle.
t L
1 9
6 4
9.5 0.5
Step-by-step explanation:
