Please help !Suppose that the height in centimeters of a candle is a linear function of them out of time in hours it has been burning after 12 hours of burning a candle has a height of 18.6 cm for 29 hours of running its height is 15.2 cm what was the height of the candle after 16 hours ?
I just did it .
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To find the height of the candle after 16 hours, we can use the concept of linear equations.
Let's consider the given information:
- After 12 hours of burning, the height of the candle is 18.6 cm.
- After 29 hours of burning, the height of the candle is 15.2 cm.
We need to find the height of the candle after 16 hours.
To set up a linear equation, we need two data points, which we already have. We can use the "point-slope form" of a linear equation:
y - y₁ = m(x - x₁)
Where:
- y and x are the variables (in this case, y represents the height of the candle, and x represents the time in hours).
- y₁ and x₁ are the coordinates of a point on the line (time and height we already know).
- m represents the slope of the line (rate at which the height changes with time).
Let's plug in the known values:
For the first point (12 hours, 18.6 cm):
x₁ = 12, y₁ = 18.6
For the second point (29 hours, 15.2 cm):
x = 29, y = 15.2
Now, let's find the slope (m):
m = (y - y₁) / (x - x₁)
m = (15.2 - 18.6) / (29 - 12)
m = -3.4 / 17
m = -0.2
Now we can form the linear equation using the point-slope form:
y - 18.6 = -0.2(x - 12)
Now, substitute the value of x as 16 (hours) into the equation and solve for y:
y - 18.6 = -0.2(16 - 12)
y - 18.6 = -0.2(4)
y - 18.6 = -0.8
y = -0.8 + 18.6
y = 17.8
Therefore, the height of the candle after 16 hours is 17.8 cm.