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130 lines
390 KiB
130 lines
390 KiB
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x=a + r\\text{cos}\\theta \\ \r
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y=b + r\\text{sin}\\theta \r
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\\end{matrix}\\right. `},{value:`\\begin{array}{l} \r
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\\text{\u5BF9\u4E8E\u65B9\u7A0B\u5F62\u5982\uFF1A}x^{3}-1=0 \\ \r
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x_{1}=1,x_{2}= \\omega =\\frac{-1+\\sqrt{3}i}{2} \\ \r
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x_{3}= \\omega ^{2}=\\frac{-1-\\sqrt{3}i}{2} \r
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\\end{array} `},{value:`\\begin{array}{l} \r
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a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\ \r
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\\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\ \r
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\\left\\{\\begin{matrix} \r
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\\Delta \\gt 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u4E0D\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
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|
\\Delta = 0\\text{\u65B9\u7A0B\u6709\u4E24\u4E2A\u76F8\u7B49\u7684\u5B9E\u6839} \\ \r
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\\Delta \\lt 0\\text{\u65B9\u7A0B\u65E0\u5B9E\u6839} \r
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\\end{matrix}\\right. \r
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\\end{array} `},{value:`\\begin{array}{l} \r
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a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0 \\ \r
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\\Delta =\\mathop{{b}}\\nolimits^{{2}}-4ac \\ \r
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\\mathop{{x}}\\nolimits_{{1,2}}=\\frac{{-b \\pm \r
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\\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}} \\ \r
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\\mathop{{x}}\\nolimits_{{1}}+\\mathop{{x}}\\nolimits_{{2}}=-\\frac{{b}}{{a}} \\ \r
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\\mathop{{x}}\\nolimits_{{1}}\\mathop{{x}}\\nolimits_{{2}}=\\frac{{c}}{{a}} \r
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\\end{array} `}]}]},{name:E.formatMessage({id:"markdownEditor.geometry",defaultMessage:"\u51E0\u4F55"}),value:"\\Delta A B C ",children:[{data:[{value:"\\Delta A B C "},{value:"a \\parallel c,b \\parallel c \\Rightarrow a \\parallel b "},{value:"l \\perp \\beta ,l \\subset \\alpha \\Rightarrow \\alpha \\perp \\beta"},{value:`\\left.\\begin{matrix} \r
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a \\perp \\alpha \\ \r
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b \\perp \\alpha \r
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|
\\end{matrix}\\right\\}\\Rightarrow a \\parallel b`},{value:"P \\in \\alpha ,P \\in \\beta , \\alpha \\cap \\beta =l \\Rightarrow P \\in l "},{value:`\\alpha \\perp \\beta , \\alpha \\cap \\beta =l,a \\subset \\alpha ,a \\perp l \r
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\\Rightarrow a \\perp \\beta `},{value:`\\left.\\begin{matrix} \r
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a \\subset \\beta ,b \\subset \\beta ,a \\cap b=P \\ \r
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a \\parallel \\partial ,b \\parallel \\partial \r
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m \\subset \\alpha ,n \\subset \\alpha ,m \\cap n=P \\ \r
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a \\perp m,a \\perp n \r
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\\end{matrix}\\right\\}\\Rightarrow a \\perp \\alpha `},{value:`\\begin{array}{c} \r
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\\text{\u76F4\u89D2\u4E09\u89D2\u5F62\u4E2D,\u76F4\u89D2\u8FB9\u957Fa,b,\u659C\u8FB9\u8FB9\u957Fc} \\ \r
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a^{2}+b^{2}=c^{2} \r
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a \\gt b,c \\gt 0 \\Rightarrow ac \\gt bc \\ \r
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a \\gt b,c \\lt 0 \\Rightarrow ac \\lt bc \r
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\\end{array}`},{value:"\\left | a-b \\right | \\geqslant \\left | a \\right | -\\left | b \\right | "},{value:"-\\left | a \\right |\\leq a\\leqslant \\left | a \\right | "},{value:"\\left | a \\right |\\leqslant b \\Rightarrow -b \\leqslant a \\leqslant \\left | b \\right | "},{value:"\\left | a+b \\right | \\leqslant \\left | a \\right | + \\left | b \\right | "},{value:`\\begin{array}{c} \r
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a \\gt b \\gt 0,n \\in N^{\\ast},n \\gt 1 \\ \r
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\\left( \\sum_{k=1}^n a_k^2 \\right) \\left( \\sum_{k=1}^n b_k^2 \\right) `},{value:`\\begin{array}{c} \r
|
|
a,b \\in R^{+} \\ \r
|
|
\\Rightarrow \\frac{a+b}{{2}}\\ge \\sqrt{ab} \\ \r
|
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\\left( \\text{\u5F53\u4E14\u4EC5\u5F53}a=b\\text{\u65F6\u53D6\u201C}=\\text{\u201D\u53F7}\\right) \r
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\\end{array}`},{value:`\\begin{array}{c} \r
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a,b \\in R \\ \r
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|
\\Rightarrow a^{2}+b^{2}\\gt 2ab \\ \r
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|
\\left( \\text{\u5F53\u4E14\u4EC5\u5F53}a=b\\text{\u65F6\u53D6\u201C}=\\text{\u201D\u53F7}\\right) \r
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\\end{array}`},{value:`\\begin{array}{c} \r
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|
H_{n}=\\frac{n}{\\sum \\limits_{i=1}^{n}\\frac{1}{x_{i}}}= \\frac{n}{\\frac{1}{x_{1}}+ \\frac{1}{x_{2}}+ \\cdots + \\frac{1}{x_{n}}} \\ G_{n}=\\sqrt[n]{\\prod \\limits_{i=1}^{n}x_{i}}= \\sqrt[n]{x_{1}x_{2}\\cdots x_{n}} \\ A_{n}=\\frac{1}{n}\\sum \\limits_{i=1}^{n}x_{i}=\\frac{x_{1}+ x_{2}+ \\cdots + x_{n}}{n} \\ Q_{n}=\\sqrt{\\sum \\limits_{i=1}^{n}x_{i}^{2}}= \\sqrt{\\frac{x_{1}^{2}+ x_{2}^{2}+ \\cdots + x_{n}^{2}}{n}} \\ H_{n}\\leq G_{n}\\leq A_{n}\\leq Q_{n} \r
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\\text{\u5219}P \\left( A \\left| B\\right. \\right) =P \\left({B}\\right) \r
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\\forall A \\in S \\\\ \r
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P \\left( A \\right) \\ge 0 \r
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|
\\end{array}`},{value:"P \\left( \\bigcup \\limits_{i=1}^{n}A_{i}\\right) = \\prod \\limits_{i=1}^{n}P \\left( A_{i}\\right) "},{value:`\\begin{array}{c} \r
|
|
S= \\binom{N}{n},A_{k}=\\binom{M}{k}\\cdot \\binom{N-M}{n-k} \\\\ \r
|
|
P\\left ( A_{k}\\right ) = \\frac{\\binom{M}{k}\\cdot \\binom{N-M}{n-k}}{\\binom{N}{n}} \r
|
|
\\end{array}`},{value:`\\begin{array}{c} \r
|
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P_{n}=n! \\\\ \r
|
|
A_{n}^{k}=\\frac{n!}{\\left( n-k \\left) !\\right. \\right.} \r
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{"text":"What do we want?","key":-10,"loc":"-65 -324.305","group":-16,"figure":"Ellipse","fill":"white"},
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{"text":"What do our users want?","key":-11,"loc":"105 -334.305","group":-20,"figure":"Ellipse","fill":"#ffffff","color":"black"},
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{"text":"Meetings","key":-12,"loc":"-65 -444.305","group":-16,"figure":"TriangleDown","fill":"#ffffff"},
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{"text":"Reviews","key":-13,"loc":"105 -454.305","group":-20,"figure":"TriangleDown","fill":"#ffffff","color":"black"},
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{"text":"Can we solve it?","key":-14,"loc":"190 -140","color":"#7d33ff","fill":"#ffffff","figure":"Diamond","size":"140 80","thickness":3},
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{"isGroup":true,"text":"External","key":-20,"loc":"105 -394.305","fill":"#d5ebff","dash":null,"thickness":1,"group":-22},
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{"isGroup":true,"text":"Sources","key":-22,"loc":"20 -400","fill":"#a5d2fa","dash":[4,4],"color":"#3358ff"}
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> ${Le}-submenu > ${Le}-submenu-title`]:{height:fe,lineHeight:`${fe}px`},[`${Le}-item-group-list ${Le}-submenu-title,
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${Le}-submenu-title`]:{paddingInlineEnd:Et}}};var Be=Me=>{const{componentCls:Le,iconCls:fe,itemHeight:ze,colorTextLightSolid:je,dropdownWidth:it,controlHeightLG:vt,motionDurationMid:xt,motionEaseOut:Et,paddingXL:Dt,itemMarginInline:wt,fontSizeLG:Tt,motionDurationSlow:en,paddingXS:un,boxShadowSecondary:ln,collapsedWidth:Wt,collapsedIconSize:tn}=Me,nn={height:ze,lineHeight:`${ze}px`,listStylePosition:"inside",listStyleType:"disc"};return[{[Le]:{"&-inline, &-vertical":Object.assign({[`&${Le}-root`]:{boxShadow:"none"}},Ut(Me))},[`${Le}-submenu-popup`]:{[`${Le}-vertical`]:Object.assign(Object.assign({},Ut(Me)),{boxShadow:ln})}},{[`${Le}-submenu-popup ${Le}-vertical${Le}-sub`]:{minWidth:it,maxHeight:`calc(100vh - ${vt*2.5}px)`,padding:"0",overflow:"hidden",borderInlineEnd:0,"&:not([class*='-active'])":{overflowX:"hidden",overflowY:"auto"}}},{[`${Le}-inline`]:{width:"100%",[`&${Le}-root`]:{[`${Le}-item, ${Le}-submenu-title`]:{display:"flex",alignItems:"center",transition:[`border-color ${en}`,`background ${en}`,`padding ${xt} ${Et}`].join(","),[`> ${Le}-title-content`]:{flex:"auto",minWidth:0,overflow:"hidden",textOverflow:"ellipsis"},"> *":{flex:"none"}}},[`${Le}-sub${Le}-inline`]:{padding:0,border:0,borderRadius:0,boxShadow:"none",[`& > ${Le}-submenu > ${Le}-submenu-title`]:nn,[`& ${Le}-item-group-title`]:{paddingInlineStart:Dt}},[`${Le}-item`]:nn}},{[`${Le}-inline-collapsed`]:{width:Wt,[`&${Le}-root`]:{[`${Le}-item, ${Le}-submenu ${Le}-submenu-title`]:{[`> ${Le}-inline-collapsed-noicon`]:{fontSize:Tt,textAlign:"center"}}},[`> ${Le}-item,
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> ${Le}-item-group > ${Le}-item-group-list > ${Le}-item,
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> ${Le}-item-group > ${Le}-item-group-list > ${Le}-submenu > ${Le}-submenu-title,
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${Le}-submenu-arrow,
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${Le}-submenu-expand-icon
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