The thread length of a screw is the part of the screw with threads. The function t times x is equal to start absolute value x minus 63 point 7 5 end absolute value 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 point 5 millimeters, the volume of the difference in thread can be calculated by the function cap v times t is equal to 1 comma 260 point 2 5 pi t Which function can be used to find the volume of the difference in thread length depending on the total thread length?
Answer
A
cap v times open paren t times x close paren is equal to 1 comma 260 point 2 5 pi divides x minus 63 point 7 5 divides
B
V(t(x))=|1,260.25πx−80,347.3125|
C
V(t(x))=|1,260.25πx−63.75|
D
cap v times open paren t times x close paren is equal to 1 comma 260 point 2 5 pi divides x minus 80 comma 347 point 3 1 2 5 divides
Explanation
The difference in thread length is t(x) = |x − 63.75|. Substitute this into the volume function V(t) = 1,260.25πt to get V(t(x)) = 1,260.25π|x − 63.75|. This matches choice A. The absolute value applies to the difference from 63.75 millimeters, while the volume factor multiplies that difference.
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