Final answer:
To find the boundary values for the acceptable diameters of the valve, set up an absoulte value equation |d - 5| = 0.001 and solve. The boundary values are 4.999mm and 5.001mm.
Step-by-step explanation:
To find the boundary values for the acceptable diameters of the valve, we can set up an absolute value equation:
|d - 5| = 0.001
Where d represents the diameter of the valve. In this equation, the absolute value represents the allowable difference between the diameter and 5mm. We can solve this equation by setting up two cases, one where d - 5 is positive and one where it is negative.
Case 1: (d - 5) = 0.001
Solving for d, we find d = 5.001
Case 2: -(d - 5) = 0.001
Simplifying, we get -d + 5 = 0.001.
Solving for d, we find d = 4.999
The boundary values for the acceptable diameters of the valve are 4.999mm and 5.001mm.