An oven's heating element turns on when the internal temperature falls to 20 degrees below the set temperature and turns off when the temperature reaches 5 degrees above the set temperature. You preheat the oven to 420 degrees before putting a cake in and baking it for an hour at 420. Write an inequality in terms of the temperature, T, that describes the temperature range of the oven while the cake is baking.
420 - 20 = 400
420 + 5 = 425
so
400</= T </= 425
To write an inequality that describes the temperature range of the oven while the cake is baking, we need to consider the heating element turning on and off based on the set temperature.
Let's denote the set temperature as S.
Since the heating element turns on when the temperature falls to 20 degrees below the set temperature, we can write the lower limit of the temperature range as:
T ≥ S - 20
Similarly, the heating element turns off when the temperature reaches 5 degrees above the set temperature, so the upper limit of the temperature range is:
T ≤ S + 5
Therefore, the inequality that describes the temperature range of the oven while the cake is baking is:
S - 20 ≤ T ≤ S + 5
To write an inequality that describes the temperature range of the oven while the cake is baking, let's break down the given information and consider the temperature conditions:
1. The oven's heating element turns on when the internal temperature falls to 20 degrees below the set temperature.
2. The oven's heating element turns off when the temperature reaches 5 degrees above the set temperature.
Let's assume the set temperature of the oven is T degrees.
Considering the first condition, the heating element turns on when the internal temperature falls to 20 degrees below the set temperature T. Therefore, the lowest temperature at which the heating element will turn on is T - 20 degrees.
Considering the second condition, the heating element turns off when the temperature reaches 5 degrees above the set temperature T. Therefore, the highest temperature at which the heating element will remain on is T + 5 degrees.
So, the range of temperatures during which the oven's heating element is on while the cake is baking can be expressed as:
T - 20 ≤ temperature ≤ T + 5
In the given scenario, since the oven was preheated to 420 degrees, we can substitute T with 420:
420 - 20 ≤ temperature ≤ 420 + 5
Simplifying the inequality, we get:
400 ≤ temperature ≤ 425
Therefore, the temperature range in which the oven is operating while the cake is baking is 400 to 425 degrees Fahrenheit.