{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Length of Shadow","Tip of Shadow","Sheet2"],"not_rendered":{"charts":8,"images":8,"macros":1,"defined_names":18,"comments":2},"read":"whole","date_system":"1900"}

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[null," Length of a Shadow Problem"]
[]
[null," This DIGMath module lets you investigate "]
[null,"the related rates calculus problem of finding"]
[null,"       the rate dS/dt at which the length S"]
[null,"          of a person's shadow increases"]
[null," as the person walks away from a lamppost "]
[null,null,"        at a given rate."]
[]
[]
["What is the height L of the lamppost (10 - 30 feet)?"]
[{"$nulls":3},10,{"$f":"#REF!+D12*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D12","v":10}]
[]
["How tall  is the person H (60-75, in inches)?"]
[{"$nulls":3},68,{"$f":"#REF!+D15*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D15","v":68}]
[]
["How fast is the person walking (1 - 6 feet per second)?"]
[{"$nulls":3},3,{"$f":"#REF!+D18*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D18","v":3}]
[]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":10},"   Select the distance from the lamppost: x0 =",{"$nulls":3},{"$f":"O23/5","v":26.6},"feet","Time =",{"$f":"x0/rate","v":{"v":8.866666666666667,"d":"8.9"}},"seconds"]
[null,null,"   Item 1",{"$nulls":11},133,{"$f":"Sheet2!#REF!+O23*(Sheet2!#REF!-Sheet2!#REF!)/100","v":{"$error":"#REF!"}}]
[null,null,"   Item 2"]
[null,null,"   Item 3",{"$nulls":10},"  The length of the shadow is",null,{"$f":"LOOKUP(x0+0.1,Sheet2!B3:B203,Sheet2!E3:E203)","v":{"v":61.384615384615245,"d":"61.4"}},"feet"]
[null,null,"   Item 4"]
[{"$nulls":11},"   The length of the shadow is growing at a rate of",{"$nulls":4},{"$f":"Sheet2!F4","v":{"v":2.3076923076923075,"d":"2.3"}}," feet per second"]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[null,"  Length of a Shadow Problem"]
[]
[null," This DIGMath module lets you investigate "]
[null,"the related rates calculus problem of finding"]
[null,"               the rate at which the tip"]
[null,"          of a person's shadow moves"]
[null," as the person walks away from a lamppost "]
[null,null,"        at a given rate."]
[]
[]
["What is the height L of the lamppost (10 - 20 feet)?"]
[{"$nulls":3},13,{"$f":"#REF!+D12*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D12","v":13}]
[]
["How tall  is the person H (60-75, in inches)?"]
[{"$nulls":3},68,{"$f":"#REF!+D15*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D15","v":68}]
[]
["How fast is the person walking (1 - 6 feet per second)?"]
[{"$nulls":3},3,{"$f":"#REF!+D18*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D18","v":3}]
[]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":9},"   Select the distance from the lamppost: x0 =",{"$nulls":3},{"$f":"N23/5","v":25},"feet","Time =",{"$f":"xx0/rate2","v":{"v":8.333333333333334,"d":"8.3"}},"seconds"]
[null,null,"   Item 1",{"$nulls":10},125,{"$f":"Sheet2!#REF!+N23*(Sheet2!#REF!-Sheet2!#REF!)/100","v":{"$error":"#REF!"}}]
[null,null,"   Item 2"]
[null,null,"   Item 3",{"$nulls":9},"The length of the shadow is",null,{"$f":"LOOKUP(xx0,Sheet2!B3:B203,Sheet2!E3:E203)","v":{"v":57.69230769230756,"d":"57.7"}},"feet"]
[null,null,"   Item 4",{"$nulls":9},"The distance from the lamppost to the tip =",{"$nulls":3},{"$f":"O25+xx0","v":{"v":82.69230769230757,"d":"82.7"}},"feet"]
[{"$nulls":10},"   The length of the shadow is growing at a rate of",{"$nulls":4},{"$f":"Sheet2!F4","v":{"v":2.3076923076923075,"d":"2.3"}}," feet per second"]
[{"$nulls":10},"    The tip of the shadow is moving at a rate of",{"$nulls":4},{"$f":"Sheet2!S5","v":{"v":6.000000000000002,"d":"6.0"}}," feet per second"]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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