{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Balloon","Sheet2","Sheet1"],"not_rendered":{"charts":4,"images":4,"macros":1,"defined_names":24,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"Balloon","index":0,"n_rows":35,"n_cols":20,"rows_kept":35,"merged":[[28,2,28,3]]}
[null,"Blowing Up A Balloon Problem"]
[]
[null," This DIGMath module lets you investigate "]
[null,"the related rates calculus problem of finding"]
[null,"       the rate dr/dt at which the radius r"]
[null,"                of a balloon is increasing"]
[null,"            when air is being blown into it "]
[null,null,"   at a given rate dV/dt."]
[]
[]
[]
["What is the maximum radius R (1 - 10 inches) of the balloon?"]
[{"$nulls":3},6,{"$f":"#REF!+D13*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D13","v":6}]
[]
["How fast (dV/dt) is air being blown "]
[null," into the balloon (1 to 25 cubic inches per sec)?"]
[{"$nulls":3},17,{"$f":"#REF!+D17*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D17","v":17}]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2",{"$nulls":8},"            Select the radius of the balloon: r =",{"$nulls":3},{"$f":"IF(O24/2>RMax, RMax,O24/2)","v":4.5},"inches","Time =",{"$f":"PI()*x0^3/rate","v":{"v":16.839860621080582,"d":"16.8"}},"seconds"]
[null,null,"   Item 3",{"$nulls":11},9,{"$f":"Sheet2!#REF!+O24*(Sheet2!#REF!-Sheet2!#REF!)/100","v":{"$error":"#REF!"}}]
[null,null,"   Item 4"]
[{"$nulls":13},"The volume of the balloon is",null,{"$f":"PI()*x0^3","v":{"v":286.2776305583699,"d":"286.3"}},"cubic inches"]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":10},"The volume of the balloon is increasing at a rate of",{"$nulls":4},{"$f":"3*PI()*x0^2","v":{"v":190.85175370557994,"d":"190.85"}}," cubic inches per second"]
["     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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