answer:1. **Identify the longest segment**: The longest segment inside the cylinder is the hypotenuse of a right triangle, where one leg is the height of the cylinder and the other leg is the diameter of its base. 2. **Calculate the diameter**: The diameter of the cylinder is (2 times 5 = 10) cm. 3. **Apply the Pythagorean theorem**: [ text{Length of the longest segment} = sqrt{(12)^2 + (10)^2} = sqrt{144 + 100} = sqrt{244} ] Simplifying (sqrt{244}) gives (2sqrt{61}). Therefore, the length of the longest segment that fits inside the cylinder is (boxed{2sqrt{61}}).

answer:**Analysis** This question examines the flexible application of the properties of an arithmetic sequence and is considered a basic question. **Solution** Given that a_3 + a_9 = 15 - a_6, by the properties of an arithmetic sequence, we have a_3 + a_9 = 2a_6 = 15 - a_6. Solving this equation, we get a_6 = 5. Therefore, the correct answer is boxed{C}.

answer:From f(x_{0})geqslant 0, we get -x_{0}^{2}+2x_{0}geqslant 0. Solving this, we find 0leqslant x_{0}leqslant 2. Using the formula for geometric probability, the probability that f(x_{0})geqslant 0 is dfrac {2-0}{3-(-1)}= dfrac {1}{2}. Therefore, the correct choice is boxed{C}. To solve the inequality f(x_{0})geqslant 0, we find the range of values for x_{0} that satisfy the condition. Using the formula for geometric probability, we can easily arrive at the conclusion. This problem mainly examines the calculation of geometric probability. Solving the quadratic inequality to find the range of solutions is key to solving this problem.

answer:To find the average speed for the entire trip, we need to find the total distance traveled and the total time taken. The first part of the trip: Distance = 8 km Speed = 11 km/hr Time = Distance / Speed = 8 km / 11 km/hr = 8/11 hours The second part of the trip: Distance = 11 km Speed = 8 km/hr Time = Distance / Speed = 11 km / 8 km/hr = 11/8 hours Total distance traveled = 8 km + 11 km = 19 km Total time taken = (8/11) hours + (11/8) hours To add these two times, we need a common denominator, which is 88 (11*8): Total time taken = (8*8)/(11*8) + (11*11)/(8*11) = 64/88 + 121/88 = (64+121)/88 = 185/88 hours Now, we can find the average speed for the entire trip: Average speed = Total distance / Total time Average speed = 19 km / (185/88) hours Average speed = 19 km * (88/185) hours^-1 Average speed = (19*88) / 185 km/hr Average speed = 1672 / 185 km/hr Average speed ≈ 9.04 km/hr Therefore, the average speed for the entire trip is approximately boxed{9.04} km/hr.