{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Trough","Sheet2","Sheet1"],"not_rendered":{"charts":4,"images":8,"macros":1,"defined_names":21,"comments":1},"read":"whole","date_system":"1900"}

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["   Filling a Trapezoidal Watering Trough"]
[]
[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 water in a trapezoidal trough "]
[null," is increasing when the water is flowing in "]
[null,null,"   at a given rate dV/dt."]
[]
[]
["What is the height H of the trough (20 - 50 cm's)?"]
[{"$nulls":3},22,{"$f":"#REF!+D12*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"2*D12","v":44}]
[]
["What is the length L (50 - 150 cm's) of the trough?"]
[{"$nulls":3},20,{"$f":"#REF!+D15*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"5*D15","v":100}]
[]
["What is the lower base a (5 - 15 cm's) of the trough?"]
[{"$nulls":3},10,{"$f":"#REF!+D18*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D18","v":10}]
[]
["What is the upper base b (15 - 40 cm's) of the trough?"]
[{"$nulls":3},21,{"$f":"#REF!+D21*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"D21","v":21}]
[]
["How fast (dV/dt) does the water flow ",{"$nulls":10},"          Select the height y of the water:   y =",{"$nulls":3},{"$f":"20+O24*(H-20)/100","v":27.68},"cm","Time =",{"$f":"Sheet2!C206","v":{"v":465.7160000000002,"d":"465.7"}},"seconds"]
[null," into the trough (30 to 150 cc's per second)?",{"$nulls":12},32,{"$f":"Sheet2!#REF!+O24*(Sheet2!#REF!-Sheet2!#REF!)/100","v":{"$error":"#REF!"}}]
[{"$nulls":3},16,{"$f":"#REF!+D25*(#REF!-#REF!)/100","v":{"$error":"#REF!"}},{"$f":"5*D25","v":80}]
[{"$nulls":13},"    The volume of the water is",null,{"$f":"Sheet2!E206","v":{"v":37257.28000000001,"d":"37257"}}," cc's"]
[]
[{"$nulls":10},"     The height of the water is increasing at a rate of",{"$nulls":4},{"$f":"Sheet2!H209","v":{"v":0.04728115872514175,"d":"0.047"}},"cm's per second at this point"]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[]
[]
[]
["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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