先后投掷一颗骰子两次，将得到的点数分别记为a,b，则直线ax+by+4=0与x2+y2=1相交的概率为
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\uff081\uff09 \uff082\uff09 \u8bd5\u9898\u5206\u6790\uff1a\uff081\uff09\u5148\u540e2\u6b21\u629b\u63b7\u4e00\u679a\u9ab0\u5b50\uff0c\u5c06\u5f97\u5230\u7684\u70b9\u6570\u5206\u522b\u8bb0\u4e3aa,b,\u4e8b\u4ef6\u603b\u6570\u4e3a6\u00d76=36\uff0e \u2235\u76f4\u7ebfax\uff0bby\uff0bc=0\u4e0e\u5706x2\uff0by2=1\u76f8\u5207\u7684\u5145\u8981\u6761\u4ef6\u662f \u5373\uff1aa2\uff0bb2=25\uff0c\u7531\u4e8ea,b\u2208\uff5b1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6\uff5d\u2234\u6ee1\u8db3\u6761\u4ef6\u7684\u60c5\u51b5\u53ea\u6709a=3,b=4,c=5\uff1b\u6216a=4,b=3,c=5\u4e24\u79cd\u60c5\u51b5\uff0e \u2234\u76f4\u7ebfax\uff0bby\uff0bc=0\u4e0e\u5706x2\uff0by2=1\u76f8\u5207\u7684\u6982\u7387\u662f \uff082\uff09\u5148\u540e2\u6b21\u629b\u63b7\u4e00\u679a\u9ab0\u5b50\uff0c\u5c06\u5f97\u5230\u7684\u70b9\u6570\u5206\u522b\u8bb0\u4e3aa,b,\u4e8b\u4ef6\u603b\u6570\u4e3a6\u00d76=36\uff0e\u2235\u4e09\u89d2\u5f62\u7684\u4e00\u8fb9\u957f\u4e3a5\u2234\u5f53a=1\u65f6\uff0cb=5\uff0c\uff081\uff0c5\uff0c5\uff09 1\u79cd \u5f53a=2\u65f6\uff0cb=5\uff0c\uff082\uff0c5\uff0c5\uff09 1\u79cd \u5f53a=3\u65f6\uff0cb=3\uff0c5\uff0c\uff083\uff0c3\uff0c5\uff09\uff0c\uff083\uff0c5\uff0c5\uff09 2\u79cd \u5f53a=4\u65f6\uff0cb=4\uff0c5\uff0c\uff084\uff0c4\uff0c5\uff09\uff0c\uff084\uff0c5\uff0c5\uff09 2\u79cd \u5f53a=5\u65f6\uff0cb=1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6\uff0c\uff085\uff0c1\uff0c5\uff09\uff0c\uff085\uff0c 2\uff0c5\uff09\uff0c\uff085\uff0c3\uff0c5\uff09\uff0c\uff085\uff0c4\uff0c5\uff09\uff0c\uff085\uff0c5\uff0c5\uff09\uff0c\uff085\uff0c6\uff0c5\uff09 6\u79cd \u5f53a=6\u65f6\uff0cb=5\uff0c6\uff0c\uff086\uff0c5\uff0c5\uff09\uff0c\uff086\uff0c6\uff0c5\uff09 2\u79cd \u6545\u6ee1\u8db3\u6761\u4ef6\u7684\u4e0d\u540c\u60c5\u51b5\u5171\u670914\u79cd\u7b54\uff1a\u4e09\u6761\u7ebf\u6bb5\u80fd\u56f4\u6210\u4e0d\u540c\u7684\u7b49\u8170\u4e09\u89d2\u5f62\u7684\u6982\u7387\u4e3a \uff0e\u70b9\u8bc4\uff1a\u53e4\u5178\u6982\u578b\u8981\u6c42\u6240\u6709\u7ed3\u679c\u51fa\u73b0\u7684\u53ef\u80fd\u6027\u90fd\u76f8\u7b49\uff0c\u5f3a\u8c03\u6240\u6709\u7ed3\u679c\u4e2d\u6bcf\u4e00\u7ed3\u679c\u51fa\u73b0\u7684\u6982\u7387\u90fd\u76f8\u540c\uff0e\u5f04\u6e05\u4e00\u6b21\u8bd5\u9a8c\u7684\u610f\u4e49\u4ee5\u53ca\u6bcf\u4e2a\u57fa\u672c\u4e8b\u4ef6\u7684\u542b\u4e49\u662f\u89e3\u51b3\u95ee\u9898\u7684\u524d\u63d0\uff0c\u6b63\u786e\u628a\u63e1\u5404\u4e2a\u4e8b\u4ef6\u7684\u76f8\u4e92\u5173\u7cfb\u662f\u89e3\u51b3\u95ee\u9898\u7684\u5173\u952e\uff0e\u89e3\u51b3\u95ee\u9898\u7684\u6b65\u9aa4\u662f\uff1a\u8ba1\u7b97\u6ee1\u8db3\u6761\u4ef6\u7684\u57fa\u672c\u4e8b\u4ef6\u4e2a\u6570\uff0c\u53ca\u57fa\u672c\u4e8b\u4ef6\u7684\u603b\u4e2a\u6570\uff0c\u7136\u540e\u4ee3\u5165\u53e4\u5178\u6982\u578b\u8ba1\u7b97\u516c\u5f0f\u8fdb\u884c\u6c42\u89e3\uff0e
直线与单位圆相交，说明圆心到直线距离小于等于半径，4/根号（a^2+b^b)<=1所以，a^2+b^2>=16,总共有28种可能，总的情况共有36种，所以概率为28/36=7/9，公式不好打，不过应该能明白吧= =
如果相交的话 只要第一条直线的斜率与第二条直线的斜率不一样就行了 所以只要a和b的大小不一样就行了
先算不相交的概率 不相交的概率是a和b的大小一样的情况 一共是六种 而全部情况一共是6乘以6 一共是36种 所以不相交的概率是1/6
那么相交的概率就是5/6
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绛旓細锛1锛鍏堝悗2娆鎶鎺蜂竴鏋氶瀛愶紝灏嗗緱鍒扮殑鐐规暟鍒嗗埆璁颁负a锛宐锛屼簨浠舵绘暟涓6脳6=36锛庘埖鐩寸嚎ax+by+c=0涓庡渾x 2 +y 2 =1鐩稿垏鐨勫厖瑕佹潯浠舵槸 5 a 2 + b 2 =1 鍗筹細a 2 +b 2 =25锛岀敱浜巃锛宐鈭坽1...,8, 鍏堝悗2娆℃姏鎺蜂竴鏋氶瀛愶紝灏嗗緱鍒扮殑鐐规暟鍒嗗埆璁颁负a锛宐锛庯紙1锛夋眰鐩寸嚎ax+by+5=0涓庡渾...
绛旓細瑙ｏ細锛1锛夆憼鍏堝悗鎶鎺蜂竴鏋氶瀛愪袱娆★紝鍩烘湰浜嬩欢鍏36涓紝鍏朵腑婊¤冻a+b=4鐨勫熀鏈簨浠舵湁锛1锛3锛夛紝锛2锛2锛夛紝锛3锛1锛夛紝鍏3涓紝鎵浠ユ墍姹傛鐜囦负336=112锛涒憽婊¤冻a+b鈮4鐨勫熀鏈簨浠舵湁锛1锛1锛夛紝锛1锛2锛夛紝锛1锛3锛夛紝锛2锛1锛夛紝锛2锛2锛夛紝锛3锛1锛夛紝鍏6涓紝鎵浠ユ墍姹傛鐜囦负636=16锛涳紙2锛夊鍥...
绛旓細鎵浠^2+b^2鈮25 鑰宎銆乥鐨勫彲鑳藉彇鍊兼槸1銆2銆3銆4銆5銆6 婊¤冻a^2+b^2鈮25鐨勶紙a锛宐锛夊彧鏈夛紙1,5锛夈侊紙1,6锛夈侊紙2,5锛夈侊紙2,6锛夈侊紙3,4锛夈侊紙3,5锛夈侊紙3,6锛夈侊紙4,3锛夈侊紙4,4锛夈侊紙4,5锛夈侊紙4,6锛夈侊紙5,1锛夈侊紙5,2锛夈侊紙5,3锛夈侊紙5,4锛夈侊紙5,5锛夈侊紙5,6锛...
绛旓細(1)鍏堝悗閫忔敮涓ゆ楠板瓙锛鍏辨湁6脳6=36绉嶆儏鍐碉紝瑕佹眰a+b=5锛屽彲涓1+4銆4+1銆2+3銆3+2銆佸叡鏈夊洓绉嶏紝鏁呮鐜囦负4/36=1/9.(2)棰樼洰涓嶅畬鏁
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绛旓細鐩稿垏鐨勬墍鍖呭惈鐨勪簨浠朵釜鏁帮紝鍐嶇‘瀹氱洿绾 涓庡渾 涓嶇浉鍒囩殑鎵鍖呭惈鐨勪簨浠朵釜鏁帮紝鐒跺悗鏍规嵁鍙ゅ吀姒傚瀷姒傜巼璁＄畻鍏紡璁＄畻瑙ｏ細鎵鏈夌殑鍙兘缁撴灉鏈夛細锛1,1锛夛紝锛1,2锛夛紝锛1,3锛夛紝锛1,4锛夛紝锛1,5锛夛紝锛1,6锛夛紝锛2,2锛夛紝锛2,3锛夛紝锛2,4锛夛紝锛2,5锛夛紝锛2,6锛夛紝锛3,3锛夛紝锛3,4锛,(3,5),(...
绛旓細瑕佷娇 f(x)=x^2+mx+n^2 鏈夐浂鐐癸紝鍒欓渶鈻斥墺0 鍥犱负m锛宯涓虹偣鏁帮紝澶т簬闆 鎵浠ワ紝鍙渶m-2n鈮0 鍗砿鈮2n n=1 m=1,2,3,4,5,6 n=2 m=1,2,3,4,5,6 n=3 m=1,2,3,4,5,6 n=4 m=1,2,3,4,5,6 n=5 m=1,2,3,4,5,6 n=6 m=1,2,3,4,5,6 鎵浠(A)=9/36=...
