Math Problem Statement
Solution
Let me guide you through the problem step by step based on the image provided:
Part (b): Change in time ()
You already answered this part correctly:
Part (c): Change in height ()
The rate at which the candle burns is given as 1.8 inches per hour. Therefore, the change in height is calculated using the formula: Since hours:
So, the change in height inches.
Part (d): Height after 10.4 hours
The initial height at hours is inches (from the graph). Using the formula: Substitute the values:
So, the height of the candle at 10.4 hours after it was lit is 1.28 inches.
Part (e): General formula for the candle height
The candle height decreases at a constant rate of 1.8 inches per hour. Given the height at as inches (from the graph), the general formula for the height at any time is:
This formula will give the height of the candle for any given .
Would you like to discuss any specific part in more detail?
Here are five related questions to practice:
- What would be the candle height at hours using the general formula?
- If the candle burns at 2 inches per hour, what would be the change in height over 5 hours?
- How would the formula for change if the initial height was 20 inches?
- What is the time when the candle completely burns out if the height starts at 18 inches?
- If the candle burned slower at 1 inch per hour, how long would it take to burn out?
Tip: Always track units during calculations, especially in rate problems involving time and physical dimensions!
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Math Problem Analysis
Mathematical Concepts
Time Calculations
Rate of Change
Linear Equations
Formulas
Change in time (Δt) = t_final - t_initial
Change in height (Δh) = rate * Δt
Height formula: h = h_i + Δh
Theorems
Linear Function Theorem
Suitable Grade Level
Grades 6-8