{"id":74,"date":"2017-07-17T15:14:46","date_gmt":"2017-07-17T15:14:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-oerguide\/chapter\/use-equations-formulas\/"},"modified":"2018-09-20T19:45:38","modified_gmt":"2018-09-20T19:45:38","slug":"use-equations-formulas","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-oerguide\/chapter\/use-equations-formulas\/","title":{"raw":"Use Equations & Formulas","rendered":"Use Equations & Formulas"},"content":{"raw":"The Lumen platform currently includes a utility that converts equations and formulas coded in LaTeX both inline (like $$x=\\frac{1+y}{1+2z^2}$$) and separately displayed (like below) as dynamically generated images. The original LaTeX code is included in the image in its \"alt\" attribute, which you can see by hovering your cursor over the images.\r\n\r\n[latex]\\int_0^\\infty e^{-x^2} dx=\\frac{\\sqrt{\\pi}}{2}[\/latex]\r\n\r\nThere are two LaTeX renderers\u00a0available, one generates cleaner looking images, and the other has the ability to handle more robust mathematical expressions including matrices. Please contact SUNY OER Services<\/a> for more information on which to use in your course.\r\n\r\nThe LaTeX code for the equation above is as follows, but note that you must surround the\u00a0equation or formula with the necessary double dollar sign ($$\\$\\$\\text{equation}\\$\\$ $$) or latex shortcode ([[latex]equation[\/latex]]) for it to be dynamically converted:\r\n
[[latex]\\int_0^\\infty e^{-x^2} dx=\\frac{\\sqrt{\\pi}}{2}[\/latex]]<\/pre>\r\nRead the official FAQ<\/a> of the WP LaTeX plugin.\r\n
Common Mathematical Expressions<\/h2>\r\nHere is LaTeX examples\u00a0for some common expressions you may use.\r\n\r\nAdding $$\\$\\$ $$ to the beginning and end of this statement:\r\n
$$\\$\\$ $$ C(g) = \\begin{cases} 25 ,\\ 0 < g < 2 \\\\ 25 + 10(g-2) , g \\ge 2\\\\ \\end{cases}$$\\$\\$ $$<\/pre>\r\nwill give: $$C(g) = \\begin{cases} 25 ,\\ 0 < g < 2 \\\\ 25 + 10(g-2) , g \\ge 2\\\\ \\end{cases}$$\r\n
[[latex]\\displaystyle{s}=\\sqrt{{\\frac{{\\sum{({x}-\\overline{{x}})}^{{2}}}}{{{n}-{1}}}}}{\\quad\\text{or}\\quad}{s}=\\sqrt{{\\frac{{\\sum{f{{({x}-\\overline{{x}})}}}^{{2}}}}{{{n}-{1}}}}}[\/latex]]<\/pre>\r\nwill give:[latex]\\displaystyle{s}=\\sqrt{{\\frac{{\\sum{({x}-\\overline{{x}})}^{{2}}}}{{{n}-{1}}}}}{\\quad\\text{or}\\quad}{s}=\\sqrt{{\\frac{{\\sum{f{{({x}-\\overline{{x}})}}}^{{2}}}}{{{n}-{1}}}}}[\/latex]\r\n
[[latex]\\displaystyle{B} = \\left[\\matrix{{1}&{2}&{7}\\\\{0}&{5}&{6}\\\\{7}&{8}&{2}}\\right][\/latex]]<\/pre>\r\nwill give: [latex]\\displaystyle{B} = \\left[\\matrix{{1}&{2}&{7}\\\\{0}&{5}&{6}\\\\{7}&{8}&{2}}\\right][\/latex]\r\n
Additional Equation Examples<\/h2>\r\n
[[latex]\\text{volume of lead cube}=2.00 cm\\times 2.00 cm\\times 2.00 cm={\\text{8.00 cm}}^{3}[\/latex]]<\/pre>\r\n[latex]\\text{volume of lead cube}=2.00 cm\\times 2.00 cm\\times 2.00 cm={\\text{8.00 cm}}^{3}[\/latex]\r\n
[[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{\\text{90.7 g}}{{\\text{8.00 cm}}^{3}}=\\frac{\\text{11.3 g}}{{\\text{1.00 cm}}^{3}}={\\text{11.3 g\/cm}}^{3}[\/latex]]<\/pre>\r\n[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{\\text{90.7 g}}{{\\text{8.00 cm}}^{3}}=\\frac{\\text{11.3 g}}{{\\text{1.00 cm}}^{3}}={\\text{11.3 g\/cm}}^{3}[\/latex]\r\n
[[latex]4.7\\cancel{\\text{g}}\\text{K}\\left(\\frac{\\text{mol K}}{39.10\\cancel{\\text{g}}}\\right)=0.12\\text{mol K}[\/latex]]<\/pre>\r\n[latex]4.7\\cancel{\\text{g}}\\text{K}\\left(\\frac{\\text{mol K}}{39.10\\cancel{\\text{g}}}\\right)=0.12\\text{mol K}[\/latex]\r\n
<\/p>","rendered":"
The Lumen platform currently includes a utility that converts equations and formulas coded in LaTeX both inline (like $$x=\\frac{1+y}{1+2z^2}$$) and separately displayed (like below) as dynamically generated images. The original LaTeX code is included in the image in its “alt” attribute, which you can see by hovering your cursor over the images.<\/p>\n
[latex]\\int_0^\\infty e^{-x^2} dx=\\frac{\\sqrt{\\pi}}{2}[\/latex]<\/p>\n
There are two LaTeX renderers\u00a0available, one generates cleaner looking images, and the other has the ability to handle more robust mathematical expressions including matrices. Please contact SUNY OER Services<\/a> for more information on which to use in your course.<\/p>\n
The LaTeX code for the equation above is as follows, but note that you must surround the\u00a0equation or formula with the necessary double dollar sign ($$\\$\\$\\text{equation}\\$\\$ $$) or latex shortcode ([latex]equation[\/latex]) for it to be dynamically converted:<\/p>\n
[latex]\\int_0^\\infty e^{-x^2} dx=\\frac{\\sqrt{\\pi}}{2}[\/latex]<\/pre>\n
Read the official FAQ<\/a> of the WP LaTeX plugin.<\/p>\n
Common Mathematical Expressions<\/h2>\n
Here is LaTeX examples\u00a0for some common expressions you may use.<\/p>\n
Adding $$\\$\\$ $$ to the beginning and end of this statement:<\/p>\n
$$\\$\\$ $$ C(g) = \\begin{cases} 25 ,\\ 0 < g < 2 \\\\ 25 + 10(g-2) , g \\ge 2\\\\ \\end{cases}$$\\$\\$ $$<\/pre>\n
will give: $$C(g) = \\begin{cases} 25 ,\\ 0 < g < 2 \\\\ 25 + 10(g-2) , g \\ge 2\\\\ \\end{cases}$$<\/p>\n
[latex]\\displaystyle{s}=\\sqrt{{\\frac{{\\sum{({x}-\\overline{{x}})}^{{2}}}}{{{n}-{1}}}}}{\\quad\\text{or}\\quad}{s}=\\sqrt{{\\frac{{\\sum{f{{({x}-\\overline{{x}})}}}^{{2}}}}{{{n}-{1}}}}}[\/latex]<\/pre>\n
will give:[latex]\\displaystyle{s}=\\sqrt{{\\frac{{\\sum{({x}-\\overline{{x}})}^{{2}}}}{{{n}-{1}}}}}{\\quad\\text{or}\\quad}{s}=\\sqrt{{\\frac{{\\sum{f{{({x}-\\overline{{x}})}}}^{{2}}}}{{{n}-{1}}}}}[\/latex]<\/p>\n
[latex]\\displaystyle{B} = \\left[\\matrix{{1}&{2}&{7}\\\\{0}&{5}&{6}\\\\{7}&{8}&{2}}\\right][\/latex]<\/pre>\n
will give: [latex]\\displaystyle{B} = \\left[\\matrix{{1}&{2}&{7}\\\\{0}&{5}&{6}\\\\{7}&{8}&{2}}\\right][\/latex]<\/p>\n
Additional Equation Examples<\/h2>\n
[latex]\\text{volume of lead cube}=2.00 cm\\times 2.00 cm\\times 2.00 cm={\\text{8.00 cm}}^{3}[\/latex]<\/pre>\n
[latex]\\text{volume of lead cube}=2.00 cm\\times 2.00 cm\\times 2.00 cm={\\text{8.00 cm}}^{3}[\/latex]<\/p>\n
[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{\\text{90.7 g}}{{\\text{8.00 cm}}^{3}}=\\frac{\\text{11.3 g}}{{\\text{1.00 cm}}^{3}}={\\text{11.3 g\/cm}}^{3}[\/latex]<\/pre>\n
[latex]\\text{density}=\\frac{\\text{mass}}{\\text{volume}}=\\frac{\\text{90.7 g}}{{\\text{8.00 cm}}^{3}}=\\frac{\\text{11.3 g}}{{\\text{1.00 cm}}^{3}}={\\text{11.3 g\/cm}}^{3}[\/latex]<\/p>\n
[latex]4.7\\cancel{\\text{g}}\\text{K}\\left(\\frac{\\text{mol K}}{39.10\\cancel{\\text{g}}}\\right)=0.12\\text{mol K}[\/latex]<\/pre>\n
[latex]4.7\\cancel{\\text{g}}\\text{K}\\left(\\frac{\\text{mol K}}{39.10\\cancel{\\text{g}}}\\right)=0.12\\text{mol K}[\/latex]<\/p>\n
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