2022英语周报4答案

21.解:(1)证明:∵PA⊥平面ABCD,AEc平面ABCD,∴PA⊥AE又∵PB⊥AE,PB∩PA=P,PB、PAC平面PAB,∴AE⊥平面PAB又ABC平面PAB,∴AE⊥AB又∵∴PA⊥平面ABCD,ABC平面ABCD,∴PA⊥AB又PA∩AE=A,PA、AEc平面PAE∴AB⊥平面PAE(2)解:由EC=-BC=2=AD,且ABCD为梯形,AD∥EC,且AD=DC=2则ADCE为菱形,所以AE=2由(1)得,AB⊥AE,又BE=4,所以∠ABE=30°,则∠AEC=120°从而有△CDE是边长为2的等边三角形在△PDE中:PE=PD=2√2,DE=2设C到平面PDE的距离为h-PDE△ECDPA=-S△PDEh1×1×2×√3×2=1×1×2×8-1×h解得h=2,即C到平面PDE的距离为2

One possible versionSeveral minutes later, the ice broke suddenly and Harry's feet sank into the water. It was noep, but his legs got wet to the knees. Harry was so upset that the accident would delay hisschedule. He had to find some firewood to build a fire to dry his clothes. He pulled off his glovestook out his matches, and lighted the fire. Seeing the burning fire, he had thought he was safe. Butsuddenly, without warming, a heavy mass of snow dropped down. The flame of hope was put outUnluckily, his dog ran away and the fear of death came over Harry. He had no choice but torun to save himself. However, he did not feel his feet when they hit the ground. Having falleneveral times, he decided to rest a while. As he lay in the snow, he noticed he was not shaking. Hecould not feel his nose or fingers or feet. A feeling of horror came into his mind. It was when herealized he was going to die that he heard a bark and the noise his friends made

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