视频流媒体月费与初装费线性不等式建模

视频流媒体月费与初装费线性不等式建模
几何画板及绘图内容加载中,请稍等……
2015-09-26 00:04
本范例演示视频流媒体月费与初装费累积的线性不等式现象。核心概念涉及一次函数建模与一元一次不等式求解。作图利用 GeoGebra 滑块控制变量,文本对象展示计算步骤,直线对象构建费用模型。适合初高中代数教学,辅助学生直观理解不等式在实际生活中的应用。

GeoGebra 命令及参数

  1. LaTeX("\text{Solve the inequality for the unknown variable.}") → text21
  2. LaTeX("\text{Write an inequality to represent the situation.}") → text8
  3. LaTeX("\text{Inequality from the previous step}") → text24
  4. LaTeX("\text{Simplify.}") → text29
  5. Line(A, B) → a_1
  6. LaTeX("\text{one term of the inequality.}") → text13
  7. LaTeX("\text{}") → text19
  8. LaTeX("\text{The total amount Cory has paid so far is the sum of the monthly rate and the one-time fee, }") → text15
  9. LaTeX((((("\text{The one-time fee is \textcolor{#000099}{" * b) * "}, so this value is represented by a constant:\textcolor{#000099}{") * b) * "}.}")) → text14
  10. LaTeX((((((((("\text{\textcolor{#000099}{" * c) * "}, write \textcolor{#000099}{") * a) * " m + ") * b) * "} on the left side of the less than symbol and \textcolor{#000099}{") * c) * "} on the right side of the symbol.}")) → text18
  11. LaTeX((((((("\text{ \textcolor{#000099}{" * a) * "m + ") * b) * " < ") * c) * "}}")) → text22
  12. LaTeX((("\text{Subtract \textcolor{#000099}{" * b) * "} from both sides.}")) → text25
  13. LaTeX((("\text{Divide both sides by \textcolor{#000099}{" * a) * "}.}")) → text26
  14. LaTeX((((("\text{ \textcolor{#000099}{" * a) * " m < ") * cb) * "}}")) → text23
  15. LaTeX((("\text{Cory could have been using the service for any number of months less than \textcolor{#000099}{" * s) * "}.}")) → text30
  16. Expand(((2 * x) * ((3 * x) - y))) → d
  17. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * a) * " m}{") * a) * "}< \frac{") * cb) * "}{") * a) * "}}}")) → text27
  18. LaTeX((("\text{ \textcolor{#000099}{m < " * s) * "}}")) → text28
  19. LaTeX("\text{that are not equivalent}") → text31_3
  20. LaTeX("\text{Since the problem uses the word under, use a less than symbol (\textcolor{#000099}{<}).}") → text11
  21. LaTeX("\text{Monthly rate \textendash}") → text2
  22. LaTeX((("\text{\textcolor{#000099}{" * a) * "}; One-time fee \textendash }")) → text5
  23. LaTeX("\text{Let \textcolor{#000099}{m} represent the number of months Cory has been subscribing to the service.}") → text9
  24. LaTeX((((((((("\text{so add the terms \textcolor{#000099}{" * a) * "m} and \textcolor{#000099}{") * b) * ": ") * a) * " m + ") * b) * "}.}")) → text16
  25. LaTeX((((((("\text{Therefore, the inequality is \textcolor{#000099}{" * a) * " m + ") * b) * " < ") * c) * "}.}")) → text20
  26. LaTeX((((("\text{The rate increases by \textcolor{#000099}{" * a) * "} for each month \textcolor{#000099}{m} that Cory subscribes. Therefore,\textcolor{#000099}{") * a) * "m} represents }")) → text12
  27. LaTeX((((((("\text{Cory has paid less than \textcolor{#000099}{" * c) * "} so far. Since what Cory has paid so far,\textcolor{#000099}{") * a) * "m + ") * b) * "}, is less than}")) → text17
  28. LaTeX((("\text{\textcolor{#000099}{" * c) * "}}")) → text7
  29. LaTeX((("\text{\textcolor{#000099}{" * b) * "}; Paid amount \textendash \textcolor{#000099}{under} }")) → text6
  30. LaTeX("\text{quantities are equal}") → text31_1
  31. LaTeX("\text{\mathbf{equation} a mathematical sentence that uses an equal sign (=) to show that two }") → text31
  32. LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between quantities }") → text31_2

AI 绘图提示语参考

绘制一个关于流媒体订阅成本的不等式建模教学图。画面中央展示一条坐标系中的斜线,标注为总费用随月份变化的线性函数图像。左侧放置变量滑块:每月费率a、一次性费用b、已支付总额c,以及变量m(订阅月数)。右侧依次显示推导步骤的文本框:设m代表订阅月数,建立不等式am+b<c,逐步移项化简得到m<s,结论为Cory最多订阅不到s个月。顶部说明等式与不等式的定义区别,突出关键词与符号关系,色彩以蓝黑为主,适合中学代数课堂直观演示。
以上提示语为根据原始绘图命令整理而来,仅供参考。