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High-difficulty problems in junior one mathematics
1) Every time the speed increases by 5 degrees, it will increase by 3 meters per second, and every time the speed increases by 1 degree, it will increase by 0.6 meters per second.

Let y represent the speed of sound, then y = 331+0.6x.

18 degrees means that the speed of sound is 331+10.8 = 341.8 seconds, and the distance is 34 1.8*5= 1709 meters.

2) If ∠AOB is X, ∠BOC is 2x ∠ AOD =1.5x.

∠ BOD =∠ AOD-∠ AOB = 0.5x = 14, then x = 28.

3) Five straight lines intersect, with at most 10 intersection points.

Article 100 has at most 4950 intersections.

N has at most 0.5*n*(n- 1) intersections.

The idea is that the nth straight line must intersect with the nth-1,and at most it is1+2+3+4+...+n- 1.

4) First question, the stop time after two scenic spots is 1 hour.

So it takes two hours to walk, with a speed of 2 kilometers per hour and a distance of 4 kilometers.

The distance of ce is: 4-1-1-1.6 = 0.4 km.

The second question C has two main routes between B and D.

Either follow the route of the first question, walk from point E to point B and then return, that is, A-E-B-E-C-D-A.

Not a-e-b-c-d-a.

The first time is 3+0.5+0.8/2=3.9 hours.

Stay at the second and third scenic spots 1.5 hours.

It takes 5.2/2=2.6 to drive 5.2 kilometers.

The total time is 1.5+2.6=4. 1.

So the first one takes less time.