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Problem of Mixing - Addition of Solute - Percentage

Problem of Mixing - Addition of Solute - Percentage
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2018-05-07 12:25
Coordinate GeometryProbability & StatisticsGeometric ConstructionSlider AnimationGraphing
This example demonstrates the process of solving problems involving the addition of solute and percentage in mixtures, visually representing changes in solution proportions through dynamic graphics. Key mathematical concepts include addition, hypergeometric distribution, subtraction, ratios, logarithmic functions, and frequency distribution. The construction utilizes GeoGebra commands such as Ray, OrthogonalLine, Intersect, Line, Textfield, Segment, Midpoint, VerticalText, Min, Max, Sequence, KeepIf, Element, IndexOf, and Polygon. It is suitable for high school students studying probability & statistics and coordinate geometry, helping them understand mixture calculations and visualization.

GeoGebra Commands & Parameters

  1. Ray(A_4, B_4) → l
  2. OrthogonalLine(E_4, e_1) → m
  3. Intersect(l, m) → C_4
  4. Line(A_3, B_3) → f
  5. Line(A_2, C_2) → p
  6. Intersect(c, f) → C_3
  7. Textfield(m_11) → inputBoxm_11
  8. Textfield(m_21) → inputBoxm_21
  9. Textfield(w_11) → inputBoxw_11
  10. Textfield(m_32) → inputBoxm_32
  11. Line(A_1, C_1) → b
  12. Intersect(a, b) → B_1
  13. Segment(E_1, C_1) → b_1
  14. Segment(C_1, F_1) → c_1
  15. Segment(D_1, B_1) → a_1
  16. Segment(B_1, G_1) → d_1
  17. Segment(A_1, C_1) → g_1
  18. OrthogonalLine(G_2, t) → q
  19. Intersect(q, p) → B_2
  20. Segment(A_2, C_2) → g_2
  21. Segment(G_2, B_2) → d_2
  22. Segment(B_2, D_2) → a_2
  23. Segment(C_2, E_2) → b_2
  24. Segment(C_2, F_2) → c_2
  25. Segment(G_3, B_3) → d_3
  26. Segment(D_3, B_3) → a_3
  27. Line(B_4, C_4) → i
  28. Segment(G_4, B_4) → d_4
  29. Segment(B_4, D_4) → a_4
  30. Segment(F_4, C_4) → c_4
  31. Segment(C_4, E_4) → b_4
  32. Segment(A_4, C_4) → g_4
  33. Midpoint(D_2, E_2) → S_2
  34. Midpoint(D_4, E_4) → S_4
  35. Textfield(w_12) → inputBoxw_12
  36. Textfield(w_13) → inputBoxw_13
  37. Textfield(w_33) → inputBoxw_33
  38. Textfield(m_13) → inputBoxm_13
  39. Textfield(w_32) → inputBoxw_32
  40. Textfield(w_34) → inputBoxw_34
  41. Textfield(m_34) → inputBoxm_34
  42. Midpoint(D_1, E_1) → S_1
  43. VerticalText(Oy) → Oyv
  44. VerticalText(text2) → text3
  45. Min(w_13, w_23) → min3
  46. Max(w_13, w_23) → max3
  47. Sequence((100 * n), n, 0, 200) → list1
  48. KeepIf(0 < x ≤ 100, list21) → list31
  49. Element(list31, 1) → elem1
  50. IndexOf(elem1, list21) → index1
  51. Element(list1, index1) → scale
  52. Polygon(H_1, I_1, M_1, L_1) → poly1z1, a_5, b_5, c_5, d_5
  53. Polygon(H_1, I_1, J_1, K_1) → poly1b1, d, e, j, k
  54. Midpoint(D_3, E_3) → S_3
  55. Ray(F_3, C_3) → h
  56. Segment(A_3, C_3) → g_3
  57. Polygon(N_1, O_1, T_1, R_1) → poly1z2, n_1, o_1, t_5, r_5
  58. Polygon(N_1, O_1, P_1, Q_1) → poly1b2, n_2, o_2, p_5, q_5
  59. Polygon(U_1, V_1, W_1, X_1) → poly1b3, u_5, v_1, w_1, x_1
  60. Polygon(U_1, V_1, Z_1, Y_1) → poly1z3, u_6, v_2, z_1, y_1
  61. Segment(F_3, C_3) → c_3
  62. Segment(C_3, E_3) → b_3
  63. Polygon(H_2, I_2, J_2, K_2) → poly2b1, h_2, i_2, j_2, k_5
  64. Polygon(N_2, O_2, P_2, Q_2) → poly2b2, n_3, o_3, p_6, q_6
  65. Polygon(U_2, V_2, W_2, X_2) → poly2b3, u_7, v_3, w_2, x_2
  66. Polygon(H_2, I_2, M_2, L_2) → poly2z1, h_1, i_1, m_2, l_2
  67. Polygon(N_2, O_2, T_2, R_2) → poly2z2, n_4, o_4, t_6, r_6
  68. Polygon(U_2, V_2, Z_2, Y_2) → poly2z3, u_8, v_4, z_2, y_2
  69. Polygon(H_3, I_3, J_3, K_3) → poly3b1, h_3, i_3, j_3, k_6
  70. Polygon(N_3, O_3, P_3, Q_3) → poly3b2, n_5, o_5, p_7, q_7
  71. Polygon(U_3, V_3, W_3, X_3) → poly3b3, u_9, v_5, w_3, x_3
  72. Polygon(H_3, I_3, M_3, L_3) → poly3z1, h_4, i_4, m_1, l_3
  73. Polygon(N_3, O_3, T_3, R_3) → poly3z2, n_6, o_6, t_7, r_7
  74. Polygon(Y_3, U_3, V_3, Z_3) → poly3z3, y_3, u_{10}, v_6, z_3
  75. Polygon(H_4, I_4, J_4, K_4) → poly4b1, h_5, i_5, j_4, k_7
  76. Polygon(N_4, O_4, P_4, Q_4) → poly4b2, n_7, o_7, p_8, q_8
  77. Polygon(U_4, V_4, W_4, X_4) → poly4b3, u_{11}, v_7, w_4, x_4
  78. Polygon(H_4, I_4, M_4, L_4) → poly4z1, h_6, i_6, m_4, l_4
  79. Polygon(N_4, O_4, T_4, R_4) → poly4z2, n_8, o_8, t_8, r_8
  80. Polygon(U_4, V_4, Z_4, Y_4) → poly4z3, u_{12}, v_8, z_4, y_4
  81. Textfield(m_24) → inputBoxm_24
  82. Ray(E_4, C_4) → n
  83. OrthogonalLine(F_2, t) → g

AI Drawing Prompt Reference

Draw a mixture problem diagram with two containers A and B, showing the transfer of solution between them. Container A initially contains a certain amount of solution, and the amount of solute added can be adjusted using a slider. Observe the changes in solution proportions as the solution is transferred from A to B, with text boxes displaying the proportion changes.
The prompt above was compiled from the original drawing commands and is for reference only.