EMPERATURE A thermometer is guaranteed to give a temperature no more than 1.2°F from the actual temperature. If the thermometer reads 28°F, write and solve an equation to find the maximum and minimum temperatures it could be. (Note: Answer should be absolute equation, maximum value, minimum vale)
28-1.2 <= T <= 28+1.2
or,
|T-28| <= 1.2
So if the thermometer says 28°F it can only be 1.2°F above or below that so to find the maximum and minimum you add and subtract 1.2°F
28°F - 1.2°F = minimum
28°F + 1.2°F = maximum
solve for these and have a good day!
Let's call the actual temperature x.
According to the information given, the thermometer is guaranteed to give a temperature no more than 1.2°F from the actual temperature. This means that the thermometer reading can be from x - 1.2°F to x + 1.2°F.
Given that the thermometer reading is 28°F, we can set up the following equation:
28°F = x ± 1.2°F
To find the maximum value, we add 1.2°F to both sides of the equation:
28°F + 1.2°F = x + 1.2°F ± 1.2°F
29.2°F = x + 0°F
Therefore, the maximum temperature x could be is 29.2°F.
To find the minimum value, we subtract 1.2°F from both sides of the equation:
28°F - 1.2°F = x - 1.2°F ± 1.2°F
26.8°F = x - 0°F
Therefore, the minimum temperature x could be is 26.8°F.
In absolute equation form, the possible range of temperatures is:
|x - 28°F| ≤ 1.2°F
The maximum value is x = 29.2°F and the minimum value is x = 26.8°F.
To find the maximum and minimum temperatures that the thermometer could be reading, we can determine the range of temperatures by adding and subtracting the maximum error of 1.2°F to the given reading of 28°F.
Let's assume the actual temperature is represented by the variable T.
To find the maximum temperature, we add 1.2°F to the given reading of 28°F:
T + 1.2 = 28 + 1.2
T + 1.2 = 29.2
So the maximum temperature the thermometer could be reading is 29.2°F.
To find the minimum temperature, we subtract 1.2°F from the given reading of 28°F:
T - 1.2 = 28 - 1.2
T - 1.2 = 26.8
Therefore, the minimum temperature the thermometer could be reading is 26.8°F.
In absolute value terms, the equation can be written as:
|T - 28| ≤ 1.2
This means that the actual temperature T must be within 1.2°F of the given reading of 28°F. So the maximum temperature is 29.2°F and the minimum temperature is 26.8°F.