At 6 a.m., the temperature was $-8^{\circ} C$. By noon, the temperature had risen $6^{\circ} C$. The temperature at 6 p.m. was $-10^{\circ} C$. Which integer represents the temperature change between noon and 6 p.m.?
A. $-24$
B. $-12$
C. $-8$
D. $-4
Answer (2)
Calculate the temperature at noon: T n oo n = − 8 + 6 = − 2 ∘ C .
Calculate the temperature change between noon and 6 p.m.: Δ T = − 10 − ( − 2 ) = − 8 ∘ C .
The temperature change between noon and 6 p.m. is − 8 ∘ C .
The integer representing the temperature change is − 8 .
Explanation
Understanding the Problem We are given that the temperature at 6 a.m. was − 8 ∘ C . By noon, the temperature had risen 6 ∘ C . The temperature at 6 p.m. was − 1 0 ∘ C . We need to find the temperature change between noon and 6 p.m.
Calculating the Temperature at Noon First, we need to calculate the temperature at noon. Since the temperature rose by 6 ∘ C from 6 a.m., we add 6 to the temperature at 6 a.m.: T n oo n = T 6 am + 6 = − 8 + 6 = − 2 ∘ C
Calculating the Temperature Change Next, we calculate the temperature change between noon and 6 p.m. by subtracting the temperature at noon from the temperature at 6 p.m.: Δ T = T 6 p m − T n oo n = − 10 − ( − 2 ) = − 10 + 2 = − 8 ∘ C
Final Answer The temperature change between noon and 6 p.m. is − 8 ∘ C .
Examples
Understanding temperature changes is crucial in many real-world scenarios. For example, meteorologists use temperature variations to predict weather patterns. Similarly, engineers consider temperature changes when designing bridges and buildings to account for expansion and contraction of materials. In everyday life, knowing how temperature changes affect our environment helps us make informed decisions about clothing, outdoor activities, and energy consumption. The ability to calculate temperature changes accurately is essential for both practical applications and scientific understanding.
The temperature change between noon and 6 p.m. is − 8 ° C . This means the temperature decreased by 8 degrees Celsius. The correct answer is C. − 8 .
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