Final answer:
The total length of the object L is 8.62 m, and the absolute uncertainty ΔL is 0.42 m, giving a final result of L = 8.62 ± 0.42 m.
Step-by-step explanation:
To calculate the total length of an object, L, where L = A + B - C, and A, B, and C are given with their absolute uncertainties (delta A, delta B, and delta C), we use the given values:
- A = (10.4 ± 0.3) m
- B = (3.01 ± 0.06) m
- C = (4.79 ± 0.06) m
The value of L is calculated by summing A and B then subtracting C:
L = (10.4 m + 3.01 m) - 4.79 m = 13.41 m - 4.79 m = 8.62 m.
To find the absolute uncertainty in L, ΔL, we sum the individual absolute uncertainties:
ΔL = ΔA + ΔB + ΔC = 0.3 m + 0.06 m + 0.06 m = 0.42 m.
Therefore, the total length of the object L and its absolute uncertainty ΔL is L = 8.62 ± 0.42 m.