积极 AI Logo 积极 AI

深海潜水员的下潜距离

深海潜水员的下潜距离
几何画板及绘图内容加载中，请稍等……
2015-11-04 23:32
函数解析几何滑块动画函数图像
本例通过模拟深海潜水员每分钟下潜28英尺的过程，演示了线性函数的应用。核心数学概念包括线性函数和速度。使用了Line, Point, Segment, OrthogonalLine, Intersect, LaTeX, Sequence等GeoGebra命令，适合初中数学教学。

GeoGebra 命令及参数

  1. Line(I, J) → a_2
  2. Point(xAxis) → B_1
  3. Segment(A_1, B_1) → d
  4. OrthogonalLine(DPT1, xAxis) → c_1
  5. Segment(PO1, A_1) → e
  6. Point(xAxis) → C_1
  7. OrthogonalLine(C_1, c_1) → f
  8. Intersect(c_1, f) → D_1
  9. Segment(DPT1, D_1) → g
  10. OrthogonalLine(DPT2, f) → h
  11. Intersect(f, h) → G_1
  12. OrthogonalLine(G_1, h) → i
  13. Intersect(f, h) → H_1
  14. Point(f) → J_1
  15. Segment(I_1, J_1) → j
  16. Segment(I_1, DPT2) → k
  17. Segment(DPT2, G_1) → l
  18. Point(xAxis) → K_1
  19. Line(K_1, L_1) → m
  20. Point(xAxis) → N_1
  21. Line(M_1, N_1) → n
  22. Point(m) → O_1
  23. Point(n) → P_1
  24. Line(O_1, P_1) → r
  25. Point(m) → Q_1
  26. Point(n) → R_1
  27. Line(Q_1, R_1) → s
  28. Line(L_1, M_1) → t
  29. LaTeX("\text{Min}") → text2
  30. LaTeX("\text{Max}") → text2_3
  31. Sequence(Segment[AB + (d, 0), AB + (d, (-0.6))], d, 0, 10) → list1
  32. Sequence(Segment[AB + (d - 0.5, 0), AB + (d - 0.5, (-0.4))], d, 1, 10) → list2
  33. Segment(AB, AB2) → a
  34. LaTeX("\text{if she travels at the same rate?}") → MainQ_1
  35. LaTeX("\text{Write the rate of descent as a fraction.}") → Question1
  36. LaTeX("\text{\mathbf{Rate} a ratio that compares measurements with different kinds of units. }") → text1
  37. LaTeX((((("\text{A deep-sea diver descends \textcolor{#000099}{" * Va11) * "} feet every minute.How far does she descend in \textcolor{#000099}{ ") * Va12) * "} minutes}")) → MainQ
  38. LaTeX((((("\text{The diver descends \textcolor{#000099}{ " * Va11) * "} feet per minute,so the rate is \frac{\textcolor{#000099}{ ") * Va11) * "\; feet}}{\textcolor{#000099}{1\;minute}}.}")) → Question1text1
  39. LaTeX((("\text{Write an equivalent rate to determine how far she descends in \textcolor{#000099}{" * Va12) * "} minutes.}")) → Question1text3
  40. LaTeX((((("\text{Multiply the numerator and denominator by \textcolor{#000099}{" * Va12) * "} so that the denominator represents \textcolor{#000099}{") * Va12) * "} minutes.}")) → Question1Final
  41. LaTeX((((((((((("\text{ \frac{\textcolor{#000099}{ " * Va11) * "\; feet × \textcolor{#000099}{ ") * Va12) * "}}}{\textcolor{#000099}{1\;minute × \textcolor{#000099}{ ") * Va12) * "}}}=\frac{\textcolor{#000099}{") * Va3) * "\; feet}}{\textcolor{#000099}{") * Va12) * "\; minutes}} }")) → Question2
  42. LaTeX((((("\text{The diver descends \textcolor{#000099}{" * Va3) * "} feet in \textcolor{#000099}{") * Va12) * "} minutes.}")) → text7
  43. LaTeX((("\text{Depth descended per minute=" * Va11) * "\:feet}")) → text2_1
  44. LaTeX((("\text{Duration=" * Va12) * "}")) → text2_2