Information:
A manufacturing process produces machine parts where dimensions satisfy , with representing geometric constraints and the part dimensions. Measurements have tolerance (0.1%). Analysis reveals .
What is the maximum relative uncertainty in the computed dimensions ?

Question

Information: 
 A manufacturing process produces machine parts where dimensions satisfy   , with    representing geometric constraints and    the part dimensions. Measurements have tolerance    (0.1%). Analysis reveals   . 
What is the maximum relative uncertainty in the computed dimensions   ?

Answer

Approximately 1200%, because    amplification applies when both    and    contain errors

Answer

Approximately 24%, because condition number amplifies the 0.1% measurement error by a factor of 240

Answer

Approximately 0.04%, because    reduces the error

Answer

Approximately 2.4%, since    for square-root scaling

Answer

Approximately 240%, since   , making the computed dimensions highly unreliable

Answer

Approximately 0.1%, matching the input tolerance, because solving linear systems preserves error magnitudes

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