mirror of https://gitee.com/XmacsLabs/planet.git
183 lines
117 KiB
Tcl
183 lines
117 KiB
Tcl
<TeXmacs|2.1.2>
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<style|<tuple|exam|std-latex|chinese>>
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<\body>
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<doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#5168\>\<#56FD\>\<#4E59\>\<#5377\>\<#FF08\>\<#6587\>\<#79D1\>\<#FF09\>>>
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\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>12\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>60\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<item>\<#96C6\>\<#5408\><math|M=<around|{|2,4,6,8,10|}>>\<#FF0C\><math|N=<around|{|x\|-1\<less\>x\<less\>6|}>>\<#FF0C\>\<#5219\><math|M*\<cap\>*N=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|<around|{|2,4|}>>>|<cell|B. <math|<around|{|2,4,6|}>>>|<cell|C.
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<math|<around|{|2,4,6,8|}>>>|<cell|D. <math|<around|{|2,4,6,8,10|}>>>>>>>
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<item>\<#8BBE\><math|<around|(|1+2*i|)>*a+b=2*i>\<#FF0C\>\<#5176\>\<#4E2D\><math|a>\<#FF0C\><math|b>\<#4E3A\>\<#5B9E\>\<#6570\>\<#FF0C\>\<#5219\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<cwith|2|2|1|2|cell-valign|c>|<cwith|2|2|1|2|cell-halign|l>|<table|<row|<cell|A.
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<math|a=1>\<#FF0C\><math|b=-2>>|<cell|B.
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<math|a=-1>\<#FF0C\><math|b=2>>>|<row|<cell|C.
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<math|a=1>\<#FF0C\><math|b=2>>|<cell|D.
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<math|a=-1>\<#FF0C\><math|b=-2>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#5411\>\<#91CF\><math|<wide|a|\<wide-varrightarrow\>>=<around|(|2,1|)>>\<#FF0C\><math|<wide|b|\<wide-varrightarrow\>>=<around|(|-2,4|)>>\<#FF0C\>\<#5219\><math|<around|\||<wide|a|\<wide-varrightarrow\>>-<wide|b|\<wide-varrightarrow\>>|\|>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|2>>|<cell|B. <math|3>>|<cell|C. <math|4>>|<cell|D. <math|5>>>>>>
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<item>\<#5206\>\<#522B\>\<#7EDF\>\<#8BA1\>\<#4E86\>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#4F4D\>\<#540C\>\<#5B66\><math|16>\<#5468\>\<#7684\>\<#5404\>\<#5468\>\<#8BFE\>\<#5916\>\<#4F53\>\<#80B2\>\<#8FD0\>\<#52A8\>\<#65F6\>\<#957F\>(\<#5355\>\<#4F4D\>\<#FF1A\>h)\<#FF0C\>\<#5F97\>\<#5982\>\<#4E0B\>\<#830E\>\<#53F6\>\<#56FE\>\<#FF1A\>
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7178BC1E18265113125F2EBBE08CE31DE4DC4AD675460902DC71CE7945DCD959D3AF57EF3E78FDED19F0A705645C0921A6D69E7D4D0A99E91581395E50E7EF54AEF9AB2281A8EBCAEC62CB5382405C3A426AD51F6A66F422827D8E623258B21F3753C662068C83FCBAF25938BF6DDCA4191A376996FCCB233868E0F6366A9AB96AEB2225225994461018C972B6F144E51C8F2C99335E6934CD6F646EDD545D6F14034084B292629B3E35D3C1624E02643B5B640DEB9882E6F1613047028E0E1BB0891327D6F71C8EE008EA14FF1FDD088678D9B2143D0000000049454E44AE426082>|png>|90pt|60pt||>
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\<#5219\>\<#4E0B\>\<#5217\>\<#7ED3\>\<#8BBA\>\<#4E2D\>\<#9519\>\<#8BEF\>\<#7684\>\<#662F\>
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A. \<#7532\>\<#540C\>\<#5B66\>\<#5468\>\<#8BFE\>\<#5916\>\<#4F53\>\<#80B2\>\<#8FD0\>\<#52A8\>\<#65F6\>\<#957F\>\<#7684\>\<#6837\>\<#672C\>\<#4E2D\>\<#4F4D\>\<#6570\>\<#4E3A\><math|7.4>
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B. \<#4E59\>\<#540C\>\<#5B66\>\<#5468\>\<#8BFE\>\<#5916\>\<#4F53\>\<#80B2\>\<#8FD0\>\<#52A8\>\<#65F6\>\<#957F\>\<#7684\>\<#6837\>\<#672C\>\<#5E73\>\<#5747\>\<#6570\>\<#5927\>\<#4E8E\><math|8>
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C. \<#7532\>\<#540C\>\<#5B66\>\<#5468\>\<#8BFE\>\<#5916\>\<#4F53\>\<#80B2\>\<#8FD0\>\<#52A8\>\<#65F6\>\<#957F\>\<#5927\>\<#4E8E\><math|8>\<#7684\>\<#6982\>\<#7387\>\<#7684\>\<#4F30\>\<#8BA1\>\<#503C\>\<#5927\>\<#4E8E\><math|0.4>
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D. \<#4E59\>\<#540C\>\<#5B66\>\<#5468\>\<#8BFE\>\<#5916\>\<#4F53\>\<#80B2\>\<#8FD0\>\<#52A8\>\<#65F6\>\<#957F\>\<#5927\>\<#4E8E\><math|8>\<#7684\>\<#6982\>\<#7387\>\<#7684\>\<#4F30\>\<#8BA1\>\<#503C\>\<#5927\>\<#4E8E\><math|0.6>
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<item>\<#82E5\><math|x>\<#FF0C\><math|y>\<#6EE1\>\<#8DB3\>\<#7EA6\>\<#675F\>\<#6761\>\<#4EF6\><math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x+y\<geq\>2,>>|<row|<cell|x+2*y\<leq\>4,>>|<row|<cell|y\<geq\>0,>>>>>|\<nobracket\>>>\<#5219\><math|z=2*x-y>\<#7684\>\<#6700\>\<#5927\>\<#503C\>\<#662F\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|-2>>|<cell|B. <math|4>>|<cell|C. <math|8>>|<cell|D. <math|12>>>>>>
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<item>\<#8BBE\><math|F>\<#4E3A\>\<#629B\>\<#7269\>\<#7EBF\><math|C:y<rsup|2>=4*x>\<#7684\>\<#7126\>\<#70B9\>\<#FF0C\>\<#70B9\><math|A>\<#5728\><math|C>\<#4E0A\>\<#FF0C\>\<#70B9\><math|B*<around|(|3,0|)>>\<#FF0C\>\<#82E5\><math|<around|\||A*F|\|>=<around|\||B*F|\|>>\<#FF0C\>\<#5219\><math|<around|\||A*B|\|>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|2>>|<cell|B. <math|2*<sqrt|2>>>|<cell|C. <math|3>>|<cell|D.
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<math|3*<sqrt|2>>>>>>>
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<item>\<#6267\>\<#884C\>\<#53F3\>\<#8FB9\>\<#7684\>\<#7A0B\>\<#5E8F\>\<#6846\>\<#56FE\>\<#FF0C\>\<#8F93\>\<#51FA\>\<#7684\><math|n=>
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<image|<tuple|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|png>|80pt|60pt||>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|y=<frac|-x<rsup|3>+3*x|x<rsup|2>+1>>>|<cell|B.
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<math|y=<frac|x<rsup|3>-x|x<rsup|2>+1>>>|<cell|C.
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<math|y=<frac|2*x<math-up|cos>x|x<rsup|2>+1>>>|<cell|D.
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<math|y=<frac|2<math-up|sin>x|x<rsup|2>+1>>>>>>>
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<item>\<#5728\>\<#6B63\>\<#65B9\>\<#4F53\><math|A*B*C*D-A<rsub|1>*B<rsub|1>*C<rsub|1>*D<rsub|1>>\<#4E2D\>\<#FF0C\><math|E>\<#FF0C\><math|F>\<#5206\>\<#522B\>\<#4E3A\><math|A*B>\<#FF0C\><math|B*C>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\>\<#5219\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<cwith|2|2|1|2|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F*\<bot\>>\<#5E73\>\<#9762\><math|B*D*D<rsub|1>>>|<cell|B.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F*\<bot\>>\<#5E73\>\<#9762\><math|A<rsub|1>*B*D>>>|<row|<cell|C.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F//>\<#5E73\>\<#9762\><math|A<rsub|1>*A*C>>|<cell|D.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F//>\<#5E73\>\<#9762\><math|A<rsub|1>*C<rsub|1>*D>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\><math|<around|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|3>\<#9879\>\<#548C\>\<#4E3A\><math|168>\<#FF0C\><math|a<rsub|2>-a<rsub|5>=42>\<#FF0C\>\<#5219\><math|a<rsub|6>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|14>>|<cell|B. <math|12>>|<cell|C. <math|6>>|<cell|D. <math|3>>>>>>
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<item>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<math-up|cos>x+<around|(|x+1|)><math-up|sin>x+1>\<#5728\>\<#533A\>\<#95F4\><math|<around|[|0,2*\<pi\>|]>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#FF0C\>\<#6700\>\<#5927\>\<#503C\>\<#5206\>\<#522B\>\<#4E3A\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|-<frac|\<pi\>|2>>\<#FF0C\><math|<frac|\<pi\>|2>>>|<cell|B.
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<math|-<frac|3*\<pi\>|2>>\<#FF0C\><math|<frac|\<pi\>|2>>>|<cell|C.
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<math|-<frac|\<pi\>|2>>\<#FF0C\><math|<frac|\<pi\>|2>+2>>|<cell|D.
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<math|-<frac|3*\<pi\>|2>>\<#FF0C\><math|<frac|\<pi\>|2>+2>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#7403\><math|O>\<#7684\>\<#534A\>\<#5F84\>\<#4E3A\><math|1>\<#FF0C\>\<#56DB\>\<#68F1\>\<#9525\>\<#7684\>\<#9876\>\<#70B9\>\<#4E3A\><math|O>\<#FF0C\>\<#5E95\>\<#9762\>\<#7684\>\<#56DB\>\<#4E2A\>\<#9876\>\<#70B9\>\<#5747\>\<#5728\>\<#7403\><math|O>\<#7684\>\<#7403\>\<#9762\>\<#4E0A\>\<#FF0C\>\<#5219\>\<#5F53\>\<#8BE5\>\<#56DB\>\<#68F1\>\<#9525\>\<#7684\>\<#4F53\>\<#79EF\>\<#6700\>\<#5927\>\<#65F6\>\<#FF0C\>\<#5176\>\<#9AD8\>\<#4E3A\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|<frac|1|3>>>|<cell|B. <math|<frac|1|2>>>|<cell|C.
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<math|<frac|<sqrt|3>|3>>>|<cell|D. <math|<frac|<sqrt|2>|2>>>>>>>
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</enumerate-numeric>
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\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>4\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>20\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<assign|item-nr|12><item>\<#8BB0\><math|S<rsub|n>>\<#4E3A\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\><math|<around|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|n>\<#9879\>\<#548C\>.\<#82E5\><math|2*S<rsub|3>=3*S<rsub|2>+6>\<#FF0C\>\<#5219\>\<#516C\>\<#5DEE\><math|d=><underline|<space|2cm>>\<#FF0E\>
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<item>\<#4ECE\>\<#7532\>\<#3001\>\<#4E59\>\<#7B49\><math|5>\<#540D\>\<#540C\>\<#5B66\>\<#4E2D\>\<#968F\>\<#673A\>\<#9009\><math|3>\<#540D\>\<#53C2\>\<#52A0\>\<#793E\>\<#533A\>\<#670D\>\<#52A1\>\<#5DE5\>\<#4F5C\>\<#FF0C\>\<#5219\>\<#7532\>\<#3001\>\<#4E59\>\<#90FD\>\<#5165\>\<#9009\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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<item>\<#8FC7\>\<#56DB\>\<#70B9\><math|<around|(|0,0|)>>\<#FF0C\><math|<around|(|4,0|)>>\<#FF0C\><math|<around|(|-1,1|)>>\<#FF0C\><math|<around|(|4,2|)>>\<#4E2D\>\<#7684\>\<#4E09\>\<#70B9\>\<#7684\>\<#4E00\>\<#4E2A\>\<#5706\>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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<item>\<#82E5\><math|f<around|(|x|)>=<math-up|ln>\|a+<frac|1|1-x>\|+b>\<#662F\>\<#5947\>\<#51FD\>\<#6570\>\<#FF0C\>\<#5219\><math|a=><underline|<space|2cm>>\<#FF0C\><math|b=><underline|<space|2cm>>\<#FF0E\>
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</enumerate-numeric>
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\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>7\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>80.0\<#5206\>\<#FF09\>
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\ (\<#4E00\>) \ \<#5FC5\>\<#8003\>\<#9898\>\<#FF1A\>\<#5171\> 60 \<#5206\>.
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<\enumerate-numeric>
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<assign|item-nr|16><item>\<#8BB0\><math|\<bigtriangleup\>*A*B*C>\<#7684\>\<#5185\>\<#89D2\><math|A>\<#FF0C\><math|B>\<#FF0C\><math|C>\<#7684\>\<#5BF9\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\><math|a>\<#FF0C\><math|b>\<#FF0C\><math|c>\<#FF0C\>\<#5DF2\>\<#77E5\><math|<math-up|sin>C<math-up|sin><around|(|A-B|)>=<math-up|sin>B<math-up|sin><around|(|C-A|)>>\<#FF0E\>
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(1)\<#82E5\><math|A=2*B>\<#FF0C\>\<#6C42\><math|C>:
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(2)\<#8BC1\>\<#660E\>\<#FF1A\><math|2*a<rsup|2>=b<rsup|2>+c<rsup|2>>\<#FF0E\><vspace|5cm>
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<item>\<#5982\>\<#56FE\>\<#FF0C\>\<#56DB\>\<#9762\>\<#4F53\><math|A*B*C*D>\<#4E2D\>\<#FF0C\><math|A*D*\<bot\>*C*D>\<#FF0C\><math|A*D=C*D>\<#FF0C\><math|\<angle\>*A*D*B=\<angle\>*B*D*C>\<#FF0C\><math|E>\<#4E3A\><math|A*C>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0E\>
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(1)\<#8BC1\>\<#660E\>\<#FF1A\>\<#5E73\>\<#9762\><math|B*E*D*\<bot\>>\<#5E73\>\<#9762\><math|A*C*D>;
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(2)\<#8BBE\><math|A*B=B*D=2>\<#FF0C\><math|\<angle\>*A*C*B=60<rsup|\<circ\>>>\<#FF0C\>\<#70B9\><math|F>\<#5728\><math|B*D>\<#4E0A\>\<#FF0C\>\<#5F53\><math|\<bigtriangleup\>*A*F*C>\<#7684\>\<#9762\>\<#79EF\>\<#6700\>\<#5C0F\>\<#65F6\>\<#FF0C\>\<#6C42\><math|C*F>\<#4E0E\>\<#5E73\>\<#9762\><math|A*B*D>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>\<#FF0E\>
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<item>\<#67D0\>\<#5730\>\<#7ECF\>\<#8FC7\>\<#591A\>\<#5E74\>\<#7684\>\<#73AF\>\<#586B\>\<#6CBB\>\<#7406\>\<#FF0C\>\<#5DF2\>\<#5C06\>\<#5C31\>\<#5C71\>\<#6539\>\<#9020\>\<#6210\>\<#4E86\>\<#7EFF\>\<#6C34\>\<#9752\>\<#5C71\>.\<#4E3A\>\<#4F30\>\<#8BA1\>\<#4E00\>\<#6797\>\<#533A\>\<#67D0\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#603B\>\<#6750\>\<#79EF\>\<#91CF\>\<#FF0C\>\<#968F\>\<#673A\>\<#9009\>\<#53D6\>\<#4E86\><math|10>\<#68F5\>\<#8FD9\>\<#79CD\>\<#6751\>\<#6728\>\<#FF0C\>\<#6D4B\>\<#91CF\>\<#6BCF\>\<#68F5\>\<#6751\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#800C\>\<#79EF\>(\<#5FC3\>\<#4F4D\>\<#FF1A\><math|m<rsup|2>>)\<#548C\>\<#6750\>\<#79EF\>\<#91CF\><math|<around|(|m<rsup|3>|)>>\<#FF0C\>\<#5F97\>\<#5230\>\<#5982\>\<#4E0B\>\<#6570\>\<#636E\>\<#FF1A\>
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<block*|<tformat|<table|<row|<cell|\<#6837\>\<#672C\>\<#53F7\><math|i>>|<cell|1>|<cell|2>|<cell|3>|<cell|4>|<cell|5>|<cell|6>|<cell|7>|<cell|8>|<cell|9>|<cell|10>|<cell|\<#603B\>\<#548C\>>>|<row|<cell|\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\><math|x
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<rsub|i>>>|<cell|0.04>|<cell|0.06>|<cell|0.04>|<cell|0.08>|<cell|0.08>|<cell|0.05>|<cell|0.05>|<cell|0.07>|<cell|0.07>|<cell|0.06>|<cell|0.6>>|<row|<cell|\<#6750\>\<#79EF\>\<#91CF\><math|y<rsub|i>>>|<cell|0.25>|<cell|0.40>|<cell|0.22>|<cell|0.54>|<cell|0.51>|<cell|0.34>|<cell|0.36>|<cell|0.46>|<cell|0.42>|<cell|0.40>|<cell|3.9>>>>>
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\<#5E76\>\<#8BA1\>\<#7B97\>\<#5F97\><math|<big|sum><rsup|10><rsub|i=1>x<rsub|i><rsup|2>=0.038>\<#FF0C\><math|<big|sum><rsup|10><rsub|i=1>y<rsup|2><rsub|i>=1.6158>\<#FF0C\><math|<big|sum><rsup|10><rsub|i=1>x<rsub|i>*y<rsub|i>=0.2474>\<#FF0E\>
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(1)\<#4F30\>\<#8BA1\>\<#8BE5\>\<#6797\>\<#533A\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#5E73\>\<#5747\>\<#4E00\>\<#68F5\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#4E0E\>\<#5E73\>\<#5747\>\<#4E00\>\<#68F5\>\<#7684\>\<#6750\>\<#79EF\>\<#91CF\>\<#FF1A\>
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(2)\<#6C42\>\<#8BE5\>\<#6797\>\<#533A\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#4E0E\>\<#6750\>\<#79EF\>\<#91CF\>\<#7684\>\<#6837\>\<#672C\>\<#76F8\>\<#5173\>\<#7CFB\>\<#6570\>(\<#7CBE\>\<#786E\>\<#5230\>0.01);
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(3)\<#73B0\>\<#6D4B\>\<#91CF\>\<#4E86\>\<#8BE5\>\<#6797\>\<#533A\>\<#6240\>\<#6709\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#FF0C\>\<#5E76\>\<#5F97\>\<#5230\>\<#6240\>\<#6709\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#603B\>\<#548C\>\<#4E3A\><math|186*m<rsup|2>>.\<#5DF2\>\<#77E5\>\<#6811\>\<#6728\>\<#7684\>\<#6750\>\<#79EF\>\<#91CF\>\<#4E0E\>\<#5176\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#8FD1\>\<#4F3C\>\<#6210\>\<#6B63\>\<#6BD4\>.\<#5229\>\<#7528\>\<#4EE5\>\<#4E0A\>\<#6570\>\<#636E\>\<#7ED9\>\<#51FA\>\<#8BE5\>\<#6797\>\<#533A\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#603B\>\<#6750\>\<#79EF\>\<#91CF\>\<#7684\>\<#4F30\>\<#8BA1\>\<#503C\>\<#FF0E\>
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\<#9644\>\<#FF1A\>\<#76F8\>\<#5173\>\<#7CFB\>\<#6570\><math|r=<frac|<big|sum><rsup|n><rsub|i=1><around*|(|x<rsub|i>-<wide|x|\<bar\>>|)>*<around*|(|y<rsub|i>-<wide|y|\<bar\>>|)>|<sqrt|<big|sum><rsup|n><rsub|i=1><around*|(|x<rsub|i>-<wide|x|\<bar\>>|)><rsup|2>*<big|sum><rsup|n><rsub|i=1><around*|(|y<rsub|i>-<wide|y|\<bar\>>|)><rsup|2>>>>\<#FF0C\><math|<sqrt|1.896>\<approx\>1.377>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=a*x-<frac|1|x>-<around|(|a+1|)><math-up|ln>x>.
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(1)\<#5F53\><math|a=0>\<#65F6\>\<#FF0C\>\<#6C42\><math|f<around|(|x|)>>\<#7684\>\<#6700\>\<#5927\>\<#503C\>;
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(2)\<#82E5\><math|f<around|(|x|)>>\<#6070\>\<#6709\>\<#4E00\>\<#4E2A\>\<#96F6\>\<#70B9\>\<#FF0C\>\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><math|E>\<#7684\>\<#4E2D\>\<#5FC3\>\<#4E3A\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#FF0C\>\<#5BF9\>\<#79F0\>\<#8F74\>\<#4E3A\><math|x>\<#8F74\>\<#FF0C\><math|y>\<#8F74\>\<#FF0C\>\<#4E14\>\<#8FC7\><math|A*<around|(|0,-2|)>>\<#FF0C\><math|B*<around|(|<frac|3|2>,-1|)>>\<#4E24\>\<#70B9\>
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(1)\<#6C42\><math|E>\<#7684\>\<#65B9\>\<#7A0B\>;
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(2)\<#8BBE\>\<#8FC7\>\<#70B9\><math|P<around|(|1,-2|)>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\><math|E>\<#4E8E\><math|M>\<#FF0C\><math|N>\<#4E24\>\<#70B9\>\<#FF0C\>\<#8FC7\><math|M>\<#4E14\>\<#5E73\>\<#884C\>\<#4E8E\><math|x>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\>\<#7EBF\>\<#6BB5\><math|A*B>\<#4EA4\>\<#4E8E\>\<#70B9\><math|T>\<#FF0C\>\<#70B9\><math|H>\<#6EE1\>\<#8DB3\><math|<wide|M*T|\<wide-varrightarrow\>>=<wide|T*H|\<wide-varrightarrow\>>>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#76F4\>\<#7EBF\><math|H*N>\<#8FC7\>\<#5B9A\>\<#70B9\>\<#FF0E\>
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</enumerate-numeric>
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<vspace|5cm>
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(\<#4E8C\>) \<#9009\>\<#8003\>\<#9898\>\<#FF1A\>\<#5171\> 10 \<#5206\>
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<\enumerate-numeric>
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<assign|item-nr|21><item>\<#5728\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#7CFB\><math|x*O*y>\<#4E2D\>\<#FF0C\>\<#66F2\>\<#7EBF\><math|C>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x=<sqrt|3><math-up|cos>2*t>>|<row|<cell|y=2<math-up|sin>t>>>>>|\<nobracket\>>(t>\<#4E3A\>\<#53C2\>\<#6570\><math|)>.\<#4EE5\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#4E3A\>\<#6781\>\<#70B9\>\<#FF0C\>
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<math|x>\<#8F74\>\<#6B63\>\<#534A\>\<#8F74\>\<#4E3A\>\<#6781\>\<#8F74\>\<#5EFA\>\<#7ACB\>\<#6781\>\<#5750\>\<#6807\>\<#7CFB\>\<#FF0C\>\<#5DF2\>\<#77E5\>\<#76F4\>\<#7EBF\><math|l>\<#7684\>\<#6781\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|\<rho\><math-up|sin><around|(|\<theta\>+<frac|\<pi\>|3>|)>+m=0>\<#FF0E\>
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(1)\<#5199\>\<#51FA\><math|l>\<#7684\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#FF1A\>
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(2)\<#82E5\><math|l>\<#4E0E\><math|C>\<#6709\>\<#516C\>\<#5171\>\<#70B9\>\<#FF0C\>\<#6C42\><math|m>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\><math|a.*b.*c>\<#4E3A\>\<#6B63\>\<#6570\>\<#FF0C\>\<#4E14\><math|a<rsup|<frac|3|2>>+b<rsup|<frac|3|2>>+c<rsup|<frac|3|2>>=1>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\>\
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<math|<around|(|1|)>*a*b*c\<leq\><frac|1|9>>;
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<math|<around|(|2|)><frac|a|b+c>+<frac|b|a+c>+<frac|c|a+b>\<leq\><frac|1|2*<sqrt|a*b*c>>>.
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</enumerate-numeric>
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<vspace|5cm>
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</body>
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<initial|<\collection>
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</collection>> |