The thread length of a screw is the part of the screw with threads. The function t(x) = |x – 63.75| can be used to find the difference, in millimeters, of a specific screw’s thread length, x, and the expected value. If a screw’s thread has a radius of 35.5 millimeters, the volume of the difference in thread can be calculated by the function V(t) = 1,260.25πt.
Answer
A
V(t(x)) = 1,260.25π|x – 80,347.3125|
B
V(t(x)) = |1,260.25πx – 80,347.3125|
C
V(t(x)) = |1,260.25πx – 63.75|
D
V(t(x)) = 1,260.25π|x – 63.75|
Explanation
Substitute t(x) = |x − 63.75| into V(t) = 1,260.25πt. This gives V(t(x)) = 1,260.25π|x − 63.75|, which is choice D. The absolute value applies to the difference between the actual thread length x and the expected length 63.75; it does not include the volume coefficient.
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