Math Problem Statement
Solution
Let's break down the problem described in the image:
- At 6 a.m., the temperature was 60°F.
- For the next 5 hours, the temperature increased by 1°F per hour. So by 11 a.m., the temperature would be:
- For the following 2 hours, the temperature rose 4°F per hour. So by 1 p.m., the temperature would be:
- The temperature remained steady at 73°F until 6 p.m..
- After 6 p.m., the temperature started dropping by 1°F per hour for the next 6 hours, reaching midnight. Therefore, by midnight, the temperature would be:
This temperature data can be plotted against the time of day, using 6 a.m. as the starting point and midnight as the ending point.
Step-by-step:
- 6 a.m.: Starting at 60°F.
- 6 a.m. to 11 a.m.: Temperature increases by 1°F each hour, reaching 65°F at 11 a.m.
- 11 a.m. to 1 p.m.: Temperature increases by 4°F each hour, reaching 73°F at 1 p.m.
- 1 p.m. to 6 p.m.: Temperature stays constant at 73°F.
- 6 p.m. to midnight: Temperature drops by 1°F each hour, reaching 67°F at midnight.
Would you like me to help you plot this graph step-by-step, or is there something specific you'd like assistance with?
Here are 5 relative questions:
- What would the temperature be at 3 p.m. given the data?
- How much total did the temperature increase between 6 a.m. and 1 p.m.?
- At what time did the temperature stop rising?
- How many hours did the temperature remain constant throughout the day?
- How would the temperature graph differ if the cooling period began at 4 p.m. instead of 6 p.m.?
Tip: When plotting graphs, always label the axes carefully and mark the points where changes in the rate of increase or decrease occur.
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Math Problem Analysis
Mathematical Concepts
Linear functions
Rate of change
Graphing
Formulas
y = mx + b (linear equation)
Slope = (change in temperature) / (change in time)
Theorems
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Suitable Grade Level
Grades 6-8
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