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Suppose that the height in centimeters of a candle is a linear function of the amount of time in hours it has been burning. after 10 hours of burning a candle has a height of 27 cm after 24 hours of burning its height is 23.4 cm what is the height of the candle after 21 hours?

User Nalo
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Final answer:

The height of the candle after 21 hours is 24.25 cm.

Step-by-step explanation:

To find the height of the candle after 21 hours, we need to determine the rate at which the height changes over time. Since the height of the candle is a linear function of the amount of time it has been burning, we can express this relationship as an equation of the form y = mx + b, where y represents the height, x represents the time, m represents the rate of change, and b represents the initial height of the candle.

Using the given information, we can form two equations:

Equation 1: 27 = 10m + b

Equation 2: 23.4 = 24m + b

By solving this system of equations, we can determine the values of m and b. Subtracting Equation 1 from Equation 2, we get:

23.4 - 27 = 24m - 10m + b - b

-3.6 = 14m

Simplifying, we find that m = -0.25.

Substituting the value of m into Equation 1, we get:

27 = 10(-0.25) + b

Solving for b, we find that b = 29.5.

Finally, we can use the equation y = mx + b to calculate the height of the candle after 21 hours:

y = (-0.25)(21) + 29.5 = 24.25 cm.

User Simar
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