The standard diameter of a golf ball is 42.67 mm.
A golf ball factory does quality control on the golf balls it manufactures. Golf balls are randomly measured to ensure the correct size. If the discrepancy in diameter is more than 0.004 mm, the production is stopped.
Which function could represent this situation?
[tex]\checkmark f(x)=|42.67-x|^2[/tex]
What are the acceptable diameters for the golf balls?
42.675 mm
42.6668 mm
42.664 mm
42.673 mm
72.676 mm
Answer (2)
The acceptable diameters for the golf balls manufactured are 42.6668 mm and 42.673 mm, as they fall within the specified tolerance of ±0.004 mm from the standard diameter of 42.67 mm. Other diameters provided do not meet the criteria. The process of quality control involves ensuring that the diameter does not deviate beyond acceptable limits.
;
Calculate the absolute difference between the standard diameter (42.67 mm) and each given diameter.
Check if the absolute difference is less than or equal to 0.004 mm.
Identify the diameters that meet the criteria.
The acceptable diameters are 42.6668 mm and 42.673 mm, so the final answer is 42.6668 , 42.673 .
Explanation
Understanding the Problem The problem states that the standard diameter of a golf ball is 42.67 mm. The factory stops production if the discrepancy in diameter is more than 0.004 mm. We are given a list of golf ball diameters and need to determine which ones are acceptable, meaning their difference from the standard diameter is within the allowed discrepancy.
Calculating Discrepancies To determine the acceptable diameters, we need to calculate the absolute difference between the standard diameter (42.67 mm) and each of the given diameters. Then, we check if this absolute difference is less than or equal to 0.004 mm.
Checking Each Diameter Let's analyze each diameter:
42.675 mm: ∣42.67 − 42.675∣ = ∣ − 0.005∣ = 0.005 Since 0.004"> 0.005 > 0.004 , this diameter is not acceptable.
42.6668 mm: ∣42.67 − 42.6668∣ = ∣0.0032∣ = 0.0032 Since 0.0032 ≤ 0.004 , this diameter is acceptable.
42.664 mm: ∣42.67 − 42.664∣ = ∣0.006∣ = 0.006 Since 0.004"> 0.006 > 0.004 , this diameter is not acceptable.
42.673 mm: ∣42.67 − 42.673∣ = ∣ − 0.003∣ = 0.003 Since 0.003 ≤ 0.004 , this diameter is acceptable.
72.676 mm: ∣42.67 − 72.676∣ = ∣ − 30.006∣ = 30.006 Since 0.004"> 30.006 > 0.004 , this diameter is not acceptable.
Final Answer Based on the calculations, the acceptable diameters are 42.6668 mm and 42.673 mm.
Examples
Quality control is essential in manufacturing to ensure products meet specific standards. In the golf ball factory, maintaining the correct diameter is crucial for performance. This problem demonstrates how absolute value and tolerance limits are used in real-world quality control to identify acceptable products and prevent defective items from reaching consumers. By setting a discrepancy limit, the factory can ensure that the golf balls produced are within the required specifications, leading to consistent and reliable performance on the golf course.
