add CI action; rm stale files
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"markdown": "# Related rates\n\n\n\nThis section uses these add-on packaages:\n\n``` {.julia .cell-code}\nusing CalculusWithJulia\nusing Plots\nusing Roots\nusing SymPy\n```\n\n\n\n\n---\n\n\nRelated rates problems involve two (or more) unknown quantities that are related through an equation. As the two variables depend on each other, also so do their rates - change with respect to some variable which is often time, though exactly how remains to be discovered. Hence the name \"related rates.\"\n\n\n#### Examples\n\n\nThe following is a typical \"book\" problem:\n\n\n> A screen saver displays the outline of a $3$ cm by $2$ cm rectangle and then expands the rectangle in such a way that the $2$ cm side is expanding at the rate of $4$ cm/sec and the proportions of the rectangle never change. How fast is the area of the rectangle increasing when its dimensions are $12$ cm by $8$ cm? [Source.](http://oregonstate.edu/instruct/mth251/cq/Stage9/Practice/ratesProblems.html)\n\n::: {.cell cache='true' hold='true' execution_count=4}\n\n::: {.cell-output .cell-output-display execution_count=5}\n```{=html}\n<div class=\"d-flex justify-content-center\"> <figure> <img src=\"data:image/gif;base64,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 truncated
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After Width: | Height: | Size: 13 KiB |
Reference in new issue
Block a user