you are preheating an oven to 350 degrees Fahrenheit before you bake muffins. several minutes later, the oven thermometer reads 346 degrees Fahrenheit. the measured temperature has an absolute deviation of at most 2 degrees Fahrenheit. write and solve an inequality to find the possible temperatures in the oven. should you continue to preheat the oven, or should you start baking the muffins?
|T-346| <= 2
344 <= T <= 348
so, keep heating.
To solve this problem, we need to set up an inequality to determine the range of possible temperatures in the oven.
Let's denote the target temperature of the oven as T (which is 350 degrees Fahrenheit in this case), and the absolute deviation as D (which is 2 degrees Fahrenheit).
The temperature reading on the oven thermometer is 346 degrees Fahrenheit, which is less than the target temperature.
Since the deviation is defined as the absolute difference between the measured temperature and the target temperature, we can write the inequality as:
|346 - T| ≤ D
Substituting the values, the inequality becomes:
|346 - 350| ≤ 2
Simplifying further, we have:
|-4| ≤ 2
Now, we can calculate the absolute value to get a positive value:
4 ≤ 2
Since this inequality is false, it means that the current oven temperature of 346 degrees Fahrenheit is not within the acceptable range (measured temperature ± absolute deviation) for preheating the oven.
Therefore, you should start baking the muffins as the oven has reached the desired temperature range.
To find the range of possible temperatures in the oven, we need to consider the absolute deviation of at most 2 degrees Fahrenheit from the target temperature of 350 degrees Fahrenheit.
Let's define the variable "x" as the actual temperature in the oven:
The absolute value of the difference between the measured temperature and the target temperature should be less than or equal to 2 degrees Fahrenheit:
|346 - x| ≤ 2
To solve this inequality, we can consider two cases:
Case 1: When the measured temperature (346) is greater than the target temperature (350):
346 - x ≤ 2
x ≥ 346 - 2
x ≥ 344
Case 2: When the measured temperature (346) is less than the target temperature (350):
x - 346 ≤ 2
x ≤ 346 + 2
x ≤ 348
Combining both cases, we can say that the possible temperature range in the oven is 344 to 348 degrees Fahrenheit.
Since the measured temperature is already within the acceptable range, there is no need to continue preheating the oven. You can start baking the muffins.