题目

有人提出如下的圆周率的近似算法：在图3-2的单位正方形内均匀地取n个点Pi(xi,yi)(i∈{1,2,…,n}),然后统计出以xi,yi,1为边长的三角形中锐角三角形的个数m,则当n充分大时,π≈,试分析这种算法是否正确.          图3-2 答案：解：根据题中提出的算法,有0＜xi＜1,0＜yi＜1,所以以xi,yi,1为边长的三角形中,长为1的边所对角A为最大角,当且仅当0°＜A＜90°时,以xi,yi,1为边长的三角形为锐角三角形, +＞1,所以在图中的单位正方形内任意取一点Pi,满足以xi,yi,1为边长的三角形为锐角三角形的概率为P=阴影部分的面积/单位正方形的面积=1-,当n用所给单词的正确形式填空。6. Would you like to ask Mr. Hu for some ____________?（建议）7. I think diving is more _____________ than skating.（令人兴奋的）8. Why do you look so _____________? Can I help you?  (紧张)9. You must know that different people have different _______________(能力).10. Do you think what he said is ____________? (真实的)