19.解析:(1)由已知A41⊥平面ABC,EFC平面ABC,所以AA1⊥EF又AB=AC,D是BC的中点,得AD⊥BC,又EF∥BC,故AD⊥EF因为A1,AD是平面A1D1D内的2条相交直线,所以EF⊥平面AA1D1D.…………4分(2)显然重心G在中线A0上,且AC=340,又EF∥BC,所AE=2ABAF由直棱柱性质和题设,DA1,D1B1,D1D两两互相垂直,建立如图所示的空间直角坐标系设A1=b,则A1(2,0.0,4(20,),B(0,0.-4)2(24)1,点D数学(理科)试题参考答案第3页书5设m=(x,y,)是平面A1E的法向量,则AA=(0,0,h),A1E(-}34+3y=0,取x=3,y=1,x=0得m=(3,1,0)6分设n=(x1,,)是平面AEF的法向量则E=(-1,,A),EF=(0,-2331+3y1+z1h=0取x1=31=01=是得(308分33y1=0因为锐二面角A-AE-F的大小是可,所以cs(mn,n)=3=1,10分解得h=所以AA12分

24.A推理判断题。由文章内容可知,本文是说吃播节目引起的食物浪费,所以在文章的开头提到Liulingyang是为了通过介绍吃播节目,引出食物浪费的话题。故选A项。C词义猜测题。根据画线单词所在句子的前半句food- wasting food shows are misleading可知thriftiness的意思应与 food-wasting相反 eating smartly意为“聪明地吃”: living healthily意为“健康地生活”;being economical意为“节俭的”: valuing food意为“重视食物”。放选C项26.C细节理解题。根据文章第五段中的 But as the market became more profitable, some people who can 'treally eat a huge amount of food, but still wanted to grab the money from audiences and advertisers,began to tum to fake eating可知,博主做吃播节目是为了赚钱。故选C项。27.D推理判断题。根据文章最后一段最后一句several live-streaming platforms have announced that theywill strengthen inspection of food shows, while some live-streamers voiced opposition to food waste andadvocated thriftiness可知些直播平台已经宣布,他们将加强对食品节自的检查,而些直播者则表示反对食品浪费,并主张节俭。由此可推断,吃播节目以后将会被仔细监管。故选D项m

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