Math Problem Statement

The temperature dropped 28 degrees in 6 hours last night. The equation below can be used to find x, the average number of degrees the temperature dropped each hour during that time period. What was the average rate of change per hour in temperature last night?

Solution

The image shows a problem where the temperature dropped 28 degrees in 6 hours, and the equation 286=x-\frac{28}{6} = x is provided to find xx, the average rate of temperature change per hour.

To calculate xx:

x=286=4.6667x = \frac{-28}{6} = -4.6667

This simplifies to approximately 4.67-4.67 degrees per hour. Thus, the average rate of temperature change is about 4.67-4.67 degrees per hour.

Therefore, the closest answer should be "approximately 4.6-4.6 degrees per hour," which is the first option listed.

Do you have any questions or would you like further details?

Here are 5 related questions to expand on this concept:

  1. How would the rate change if the temperature dropped by 35 degrees over 7 hours?
  2. How is the average rate of change different from the instantaneous rate of change?
  3. Can the average rate of change be positive in some cases? Give an example.
  4. How would you interpret a positive average rate of change in the context of temperature?
  5. What is the significance of the negative sign in this context?

Tip: Always check the signs when working with rates of change; positive indicates increase, and negative indicates decrease.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rate of Change
Basic Arithmetic

Formulas

x = (-28) / 6

Theorems

Rate of Change

Suitable Grade Level

Grades 6-8