What are the first moments of the two component areas with respect to the x-axis, given that "a" is 0.32 in. and "b" is 0.96 in., and the first moment of the area above the x-axis is 0.739 in³ and the first moment of the area below the x-axis is -0.912 in³?

A. 0.739 in³ and -0.912 in³
B. 0.273 in³ and -0.639 in³
C. 0.466 in³ and -0.843 in³
D. 0.912 in³ and -0.739 in³

The first moments of the two component areas with respect to the x-axis, given that 'a' is 0.32 in. and 'b' is 0.96 in., are 0.739 in³ for the area above the x-axis and -0.912 in³ for the area below the x-axis.

Explanation:

The first moments of the two component areas with respect to the x-axis are essentially the weighted average of the distances of the areas from the x-axis. Given that 'a' is 0.32 in. and 'b' is 0.96 in., the question states that the first moment of the area above the x-axis is 0.739 in³ and the first moment of the area below the x-axis is -0.912 in³. From this information, it is clear that the answer is a) 0.739 in³ and -0.912 in³, as these figures directly correspond to the values provided in the question.

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