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  "lines" : [
    {
      "id" : "2E2D7D7E-FD27-5F9C-8882-E208B7F2622F",
      "source" : "# Position, velocity, acceleration"
    },
    {
      "id" : "CD0C7351-1437-5F22-84F2-BF7D27DFFC23",
      "source" : "\/\/ position(t) = t³ - 6t² + 9t meters after t seconds."
    },
    {
      "id" : "8C53C033-7224-5F35-85A7-2D5AE24E9853",
      "source" : "position(t) = t³ - 6*t² + 9*t"
    },
    {
      "id" : "6FC1C6D5-3188-5330-A4E2-C03FC47F2A41",
      "source" : "velocity(t) = derivative(position(t), t)"
    },
    {
      "id" : "4BDA94C7-3862-5451-9CB9-C110338FC40C",
      "source" : "\/\/ Velocity works out to 3t² - 12t + 9; acceleration is its derivative."
    },
    {
      "id" : "4D894B53-9BA8-5D1B-A84B-4DC39F2F1624",
      "source" : "acceleration(t) = derivative(3*t² - 12*t + 9, t)"
    },
    {
      "id" : "5AC20203-7F09-583D-B8AE-89241E9A7A9F",
      "source" : "moment = 1 in 0 … 4"
    },
    {
      "id" : "845BC982-563B-5349-92CC-8E553CF9E702",
      "source" : "velocity(moment)"
    },
    {
      "id" : "E7598D24-818A-5417-A608-EE60A5157C0E",
      "source" : "acceleration(moment)"
    },
    {
      "id" : "04AB204C-9293-5AA5-BAA0-2B044CB985B5",
      "source" : ""
    },
    {
      "id" : "37C8BA7B-B87A-5EFB-8E1E-A5DC6BB34ADD",
      "source" : "# Related rates: the ladder"
    },
    {
      "id" : "C82DA7DB-0611-5993-93DC-D178F7B5ED2F",
      "source" : "\/\/ A 5 m ladder slides: base moves at 0.4 m\/s away from the wall."
    },
    {
      "id" : "EA3B963D-1111-5F84-B5AA-1ABD9834EE25",
      "source" : "ladder = 5 m"
    },
    {
      "id" : "FC3B310E-63C9-55BA-8C19-7D95E7539403",
      "source" : "base speed = 0.4 m\/s"
    },
    {
      "id" : "D6336434-59FB-59BB-AD3F-6A4366E2543D",
      "source" : "base distance = 3 m"
    },
    {
      "id" : "C42C14B9-B213-525F-AA7E-C1486AAD6E0E",
      "source" : "wall height = sqrt(ladder² - base distance²)"
    },
    {
      "id" : "002275CF-E305-5432-B42E-8369358A2077",
      "source" : "wall speed = -(base distance\/wall height)*base speed"
    },
    {
      "id" : "6F81C195-35A0-5100-BC50-365A24996754",
      "source" : "wall speed in m\/min"
    },
    {
      "id" : "76098741-3030-538C-88C9-F2F3D99428D5",
      "source" : ""
    },
    {
      "id" : "989287E3-57C3-5707-A0E3-7F26E7D5E84A",
      "source" : "# Optimization: fence area"
    },
    {
      "id" : "7E15E2AE-3740-5975-9B5A-2D032E781A39",
      "source" : "\/\/ A rectangular pen against a river uses 40 m of fence on three sides; the river side needs none."
    },
    {
      "id" : "48ECAB49-048A-5C84-84AE-E8350B63D13A",
      "source" : "fence = 40 m"
    },
    {
      "id" : "27AB668C-04C1-520D-9659-958A1A9D0C4D",
      "source" : "\/\/ depth is each side running away from the river."
    },
    {
      "id" : "1E8DE4D9-F816-5EFD-A9E4-92A34F30DDA9",
      "source" : "depth = 5 in 1 … 19"
    },
    {
      "id" : "F00DD6CC-D253-5BC3-8126-D67368C9D5E7",
      "source" : "width = fence - 2*depth*m"
    },
    {
      "id" : "4C8C3F7B-D181-5E47-95C9-63F4C3C5D2C6",
      "source" : "area = width*depth*m"
    },
    {
      "id" : "F20302F3-2866-5C61-8C4E-7C4996B740A4",
      "source" : "plot(area, depth, 1, 19)"
    },
    {
      "id" : "940D7A00-D70E-5878-8453-F8EEB8826053",
      "source" : "best depth = fence\/4"
    },
    {
      "id" : "E710C4C0-5ADB-5E77-960A-6B202B2E2866",
      "source" : "best width = fence - 2*best depth"
    },
    {
      "id" : "766F07CD-306F-595D-AE49-DAE40A95FAF6",
      "source" : "best area = best depth*best width"
    }
  ],
  "numberStyle" : {
    "decimal" : ".",
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    "secondaryGroupSize" : 3
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  "title" : "Motion and optimization"
}