89 lines
3.4 KiB
Plaintext
89 lines
3.4 KiB
Plaintext
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%html
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%head
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%script{:type => "text/x-mathjax-config"}
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MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
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%script{:type => "text/javascript", :src => "http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"}
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:css
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.solution {
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border-top: 1px dotted #222;
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}
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%body
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%h2 Solve for $l$:
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#solve-for-l-01.solution
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:escaped
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$$
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\begin{eqnarray}
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n & = & -5m + 3n - 16 \\
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-2lmn + 8m - 3n + 3n & = & -5m + 3n - 16 + 3n \\
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-2lmn + 8m & = & -5m + 3n - 16 + 3n \\
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-2lmn + 8m - 8m & = & -5m + 3n - 16 + 3n - 8m \\
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-2lmn & = & -5m + 3n - 16 + 3n - 8m \\
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\frac{-2lmn}{-2} & = & \frac{-5m + 3n - 16 + 3n - 8m}{-2} \\
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lmn & = & \frac{-5m + 3n - 16 + 3n - 8m}{-2} \\
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\frac{lmn}{mn} & = & \frac{\frac{-5m + 3n - 16 + 3n - 8m}{-2}}{mn} \\
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l & = & \frac{\frac{-5m + 3n - 16 + 3n - 8m}{-2}}{mn} \\
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l & = & \frac{\frac{-5m - 16 + 6n - 8m}{-2}}{mn} \\
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l & = & \frac{\frac{-16 + 6n - 13m}{-2}}{mn} \\
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l & = & \frac{8 - 3n - \frac{13m}{-2}}{mn} \\
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\end{eqnarray}
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$$
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#solve-for-l-02.solution
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:escaped
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$$
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\begin{eqnarray}
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n & = & -5m + 3n + 2 \\
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-2lmn + 8m - 3n + 3n & = & -5m + 3n + 2 + 3n \\
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-2lmn + 8m & = & -5m + 6n + 2 \\
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-2lmn + 8m - 8m & = & -5m + 6n + 2 - 8m \\
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-2lmn & = & -13m + 6n + 2 \\
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\frac{-2lmn}{-2} & = & \frac{-13m + 6n + 2}{-2} \\
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lmn & = & \frac{-13m}{-2} + \frac{6n}{-2} + \frac{2}{-2} \\
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lmn & = & \frac{-13m}{-2} + \frac{6n}{-2} - 1 \\
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lmn & = & \frac{-13m}{-2} + \frac{3n}{-1} - 1 \\
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lmn & = & \frac{-13m}{-2} - 3n - 1 \\
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\frac{lmn}{mn} & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
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l & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
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\end{eqnarray}
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$$
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#solve-for-l-03.solution
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:escaped
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$$
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\begin{eqnarray}
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-9 + -2lmn + 8m - 3n + 9 & = & -9 + -5m + 3n - 7 \\
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-2lmn + 8m - 3n & = & -9 + -5m + 3n - 7 \\
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-2lmn + 8m - 3n & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n & = & -5m + 3n + -7 + -9 \\
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-2lmn + 8m - 3n & = & -5m + 3n + -16 \\
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-2lmn + 8m - 3n + 3n & = & -5m + 3n + -16 + 3n \\
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-2lmn + 8m & = & -5m + -16 + 6n \\
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-2lmn + 8m - 8m & = & -5m + -16 + 6n - 8m \\
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-2lmn & = & -13m + 6n + -16 \\
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\frac{-2lmn}{-2mn} & = & \frac{-13m + 6n + -16}{-2mn} \\
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l & = & \frac{-13m + 6n + -16}{-2mn} \\
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l & = & \frac{13m - 6n + 16}{2mn} \\
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\end{eqnarray}
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$$
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%h2 Solve for $x$:
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#solve-for-x-01.solution
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:escaped
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$$
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\begin{eqnarray}
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x & = & -6y + -2 + -10 \\
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-2xy + 5xz - 5x & = & -6y + -12 \\
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-2xy + 5xz - 5xz - 5x & = & -6y - 12 - 5xz \\
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-2xy - 5x & = & -6y - 12 - 5xz \\
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-2xy + 2xy - 5x & = & -6y - 12 - 5xz + 2xy \\
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-5x & = & -6y - 12 - 5xz + 2xy \\
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\end{eqnarray}
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$$
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