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Rectangler Probabilities - Sum of Areas

Rectangler Probabilities - Sum of Areas
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2015-11-02 11:42
CalculusProbability & Statistics
In collections Complex Math
This example demonstrates the calculation of rectangular probabilities by exploring the sum of areas. Key mathematical concepts include geometric transformations and area calculation. It uses commands like Vector, Point, Polygon, Integral, etc., in GeoGebra. Suitable for high school math education and learning, particularly in probability and statistics and geometric transformations.

GeoGebra Commands & Parameters

  1. Vector((0, c)) → w
  2. Vector((b, 0)) → v
  3. Vector((b, 0), (b, c)) → u
  4. Vector((b, c)) → d
  5. Vector((0, c), (b, c)) → m
  6. Point(m) → A
  7. Point(v) → B
  8. Point(w) → C
  9. Polygon(A, B, D, C) → poly1, a_1, b_1, d_1, c_1
  10. Integral(f, 0, 0.851) → p
  11. Integral(f, -500, 500) → Area
  12. Integral(f, -0.851, 0.851) → Area_σ
  13. Integral(poly1 - f(x), 0, 1) → ε_r
  14. Integral(poly1 - ε_r, 0, 1) → Δ_¬
  15. Name(Rectangle_¬) → A1
  16. Name(ρ_σ) → B1
  17. Name(ε_r) → D1
  18. Name(Δ_¬) → E1
  19. Integral(f(x) / σ, 0, 0.851) → probabilities
  20. Integral(1 / σ, 0, 1) → z_σ
  21. Name(σ) → C1

AI Drawing Prompt Reference

Draw a rectangular area and observe the sum of different rectangle areas by adjusting the width and height. Define the sides of the rectangle using vectors, construct the rectangle with points and polygons, and calculate the area and probability.
The prompt above was compiled from the original drawing commands and is for reference only.