{"id":23,"date":"2023-02-08T18:53:37","date_gmt":"2023-02-08T23:53:37","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/?post_type=chapter&p=23"},"modified":"2024-01-11T14:02:36","modified_gmt":"2024-01-11T19:02:36","slug":"math","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/langarasandbox\/chapter\/math\/","title":{"raw":"MathJax Test","rendered":"MathJax Test"},"content":{"raw":"

1.1\u00a0 Length of a Vector<\/h3>\r\nIt follows from the Pythagorean formula that the length [latex]\\|\\mathrm{a}\\|[\/latex] of [latex]\\mathbf{a}=\\left\\langle a_{1}, a_{2}\\right\\rangle[\/latex] satisfies [latex]\\|a\\|^{2}=a_{1}^{2}+a_{2}^{2} .[\/latex]\r\n\r\nThis is shown in the following image:\r\n\r\n\"\"\r\n\r\nThus we get\r\n

[latex]\\|a\\|=\\sqrt{a_{1}^{2}+a_{2}^{2}} \\text {. }[\/latex]<\/p>\r\n\r\n\r\n

\r\n\r\n\u00a0<\/mn><\/math>\r\n\r\nExample: <\/strong>Use the graph of [latex]y=g(x)[\/latex] to sketch the graphs of:\r\n\r\n[latex]y=g\\left(x+2\\right)-1[\/latex]\r\n
<\/div>\r\n
This is different math [latex]A=\\pi\\ r^2[\/latex] that I think I know how it should sound.<\/div>\r\n
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This equation I can guess at:<\/div>\r\n
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[latex]x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}[\/latex]<\/div>\r\n
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1.1\u00a0 Length of a Vector<\/h3>\n

It follows from the Pythagorean formula that the length [latex]\\|\\mathrm{a}\\|[\/latex] of [latex]\\mathbf{a}=\\left\\langle a_{1}, a_{2}\\right\\rangle[\/latex] satisfies [latex]\\|a\\|^{2}=a_{1}^{2}+a_{2}^{2} .[\/latex]<\/p>\n

This is shown in the following image:<\/p>\n

\"\"<\/p>\n

Thus we get<\/p>\n

[latex]\\|a\\|=\\sqrt{a_{1}^{2}+a_{2}^{2}} \\text {. }[\/latex]<\/p>\n

\n

\u00a0<\/mn><\/math><\/p>\n

Example: <\/strong>Use the graph of [latex]y=g(x)[\/latex] to sketch the graphs of:<\/p>\n

[latex]y=g\\left(x+2\\right)-1[\/latex]<\/p>\n

<\/div>\n
This is different math [latex]A=\\pi\\ r^2[\/latex] that I think I know how it should sound.<\/div>\n
<\/div>\n
This equation I can guess at:<\/div>\n
<\/div>\n
[latex]x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}[\/latex]<\/div>\n
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