Question

engineering tolerance is an allowance made for imperfections in a manufactured object. the manufacturer of an oven specifies a temperature tolerance of ±15°f. this means that the temperature inside the oven will be within 15°f of the temperature to which it is set. write an absolute value equation to find the maximum and minimum temperatures inside the oven when the thermostat is set to 400°f. let t represent the temperature inside the oven.

Explanation:

Step1: Define the absolute value relationship

The temperature \( t \) inside the oven is within \( 15^\circ\text{F} \) of the set temperature \( 400^\circ\text{F} \). The absolute value of the difference between \( t \) and \( 400 \) should be equal to the tolerance, so we have \( |t - 400| = 15 \).

Step2: Solve for maximum temperature

To find the maximum temperature, we consider the positive case of the absolute value equation: \( t - 400 = 15 \). Adding \( 400 \) to both sides gives \( t = 400 + 15 = 415 \).

Step3: Solve for minimum temperature

For the minimum temperature, we consider the negative case: \( t - 400 = -15 \). Adding \( 400 \) to both sides gives \( t = 400 - 15 = 385 \).

Answer:

The absolute value equation is \( |t - 400| = 15 \). The maximum temperature is \( 415^\circ\text{F} \) and the minimum temperature is \( 385^\circ\text{F} \).