A company wants to make ball bearings that have a standard diameter, d, of 24.000 mm. Acceptable ball bearings measure within ± 0.025 mm of this standard. Determine the solution set for the diameter of these ball bearings
Dmin = 24.000 - 0.025 = 23.975 mm.
Dmax = 24.000 + 0.025 = 24.025.
To determine the solution set for the diameter of the ball bearings, we need to consider the acceptable range for the diameter.
The standard diameter, d, is given as 24.000 mm. Acceptable ball bearings measure within ± 0.025 mm of this standard.
To find the lower limit of the diameter, we subtract the tolerance (0.025 mm) from the standard diameter:
Lower limit = 24.000 mm - 0.025 mm = 23.975 mm
To find the upper limit of the diameter, we add the tolerance (0.025 mm) to the standard diameter:
Upper limit = 24.000 mm + 0.025 mm = 24.025 mm
Therefore, the solution set for the diameter of these ball bearings is any value between 23.975 mm and 24.025 mm, inclusive.
In interval notation: [23.975 mm, 24.025 mm]