{"text_format":"3","workbook":"xlsx","n_sheets":2,"sheets":["SumOfSquares","Calcs"],"not_rendered":{"charts":2,"images":2,"macros":1,"defined_names":13,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"SumOfSquares","index":0,"n_rows":35,"n_cols":16,"rows_kept":35,"merged":[[26,2,26,3]]}
[null,"Optimizing the Sum of the Squares"]
[null,"               of Two Numbers"]
[]
[null,"     This DIGMath module lets you investigate "]
[null,"   the problem of finding two positive numbers"]
[null,"            for whom the sum of the squares"]
[null,"                is a maximum or a minimum."]
[]
[]
["What is the sum S of the two numbers?"]
[null,"          (1 - 25 )",null,"  Sum S =",{"$f":"D12","v":15}]
[{"$nulls":3},15]
[]
["The sum of the two numbers is S = x + y =",{"$nulls":3},{"$f":"S","v":15}]
["The formula for the sum of the squares SS =",{"$nulls":3},"x2 +  y2 =  x2 + (S - x)2"]
[{"$nulls":3},"= ",{"$f":"TEXT(S^2,0)&\" - \"&TEXT(2*S,\"0\")&\"x + 2x^2\"","v":"225 - 30x + 2x^2"}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[{"$nulls":10},"Select the value of x =",null,null,{"$f":"N29*dx","v":9.75}]
["Created by:  Sheldon P. Gordon   ",{"$nulls":12},130,{"$f":"Calcs!G7+N29*(Calcs!G8-Calcs!G7)/100","v":0}]
["                      Farmingdale State College    "]
["Development of this module was supported by the ",{"$nulls":9},"The associated value for y = ",{"$nulls":3},{"$f":"S-x0","v":5.25}]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160.",{"$nulls":9},"The sum of the squares is SS =",{"$nulls":3},{"$f":"Calcs!G14","v":{"v":122.62499999999997,"d":"122.63"}}]
[]
[{"$nulls":10},"      The value of the derivative is y' = ",{"$nulls":4},{"$f":"Calcs!H14","v":8.999999999999986}]

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