{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Cup","Sheet2","Sheet1"],"not_rendered":{"charts":4,"images":5,"macros":1,"defined_names":24,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"Cup","index":0,"n_rows":37,"n_cols":20,"rows_kept":37,"merged":[[36,2,36,3]]}
[null,"    Liquid into a Conical Cup"]
[]
[null," This DIGMath module lets you investigate "]
[null,"the related rates calculus problem of finding"]
[null,"       the rate dy/dt at which the height y"]
[null,"      of liquid in a conical cup is increasing"]
[null,"    when the liquid is flowing into the cup "]
[null,null,"   at a given rate dV/dt."]
[]
[]
["What is the height H of the cup (2 - 10 inches)?"]
[{"$nulls":3},5,{"$f":"#REF!+D12*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D12","v":5}]
[]
["What is the maximum radius R (1 - 6 inches) of the cup?"]
[{"$nulls":3},4,{"$f":"#REF!+D15*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D15","v":4}]
[]
["How fast (dV/dt) does liquid flow "]
[null," into the cup (1 to 10 cubic inches per sec)?"]
[{"$nulls":3},7,{"$f":"#REF!+D19*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D19","v":7}]
[]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":10},"       Select the height of liquid in the cup: y =",{"$nulls":3},{"$f":"IF(O24/5>L,L,O24/5)","v":0.4},"inches","Time =",{"$f":"LOOKUP(x0+0.01, Sheet2!D3:D103,Sheet2!C3:C103)","v":{"v":0.006127601671001804,"d":"0.01"}},"seconds"]
[null,null,"   Item 1",{"$nulls":11},2,{"$f":"Sheet2!#REF!+O24*(Sheet2!#REF!-Sheet2!#REF!)/100","v":{"$error":"#REF!"}}]
[null,null,"   Item 2"]
[null,null,"   Item 3",{"$nulls":10},"     The radius of the liquid is",null,{"$f":"x0*Area/H","v":{"v":0.5,"d":"0.50"}},"inches"]
[null,null,"   Item 4"]
[{"$nulls":11}," The height of the liquid is increasing at a rate of",{"$nulls":4},{"$f":"LOOKUP(x0+0.01,Sheet2!D3:D103, Sheet2!E3:E103)","v":{"v":19.25261408369701,"d":"19.3"}}," cubic inches per second"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]
[]
["To access/download all the DIGMath Apps for Calculus"]
["      Click this link:",null,"DIGMath for Calculus"]

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[null,"radius","t","Height","dy/dt"]
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