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Answer :
Final answer:
By integrating the linear density function from 0 to 4 meters, the total mass of the rod is calculated as 36 kg, corresponding to option B.
Explanation:
To calculate the total mass of the rod with linear density s(x) = −9(½)x, we integrate s(x) over the length of the rod.
The integral of the linear density function from x = 0 to x = 4 m will give us the total mass:
Mass = ∫ s(x) dx = ∫ (−9(½)x) dx from 0 to 4
= −9(½) ∫ x dx from 0 to 4
= −9(½) [(½)x2] from 0 to 4
= −9(½) [(8/2) - (0/2)]
= −½ × 9 × 4
= −36 kg
Therefore, the total mass of the rod is 36 kg.
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