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{"sheet":"Sheet1","index":0,"n_rows":58,"n_cols":16,"rows_kept":58,"merged":[[0,1,0,16],[1,1,1,16],[2,1,2,16],[3,1,3,16],[4,1,4,16],[5,1,5,16],[7,2,7,7],[7,8,7,15],[8,2,8,3],[8,4,8,7],[8,9,8,14],[9,4,9,7],[9,9,9,14],[10,2,10,3],[10,4,10,7],[10,9,10,14],[11,2,11,4],[11,5,11,7],[11,9,11,14],[12,2,12,5],[12,6,12,7],[12,13,12,15],[13,1,13,16],[14,1,14,16],[15,2,15,7],[15,8,15,15],[16,2,16,3],[16,4,16,7],[16,9,16,14],[17,2,17,3],[17,4,17,7],[17,9,17,14],[18,2,18,3],[18,4,18,7],[18,9,18,14],[19,2,19,4],[19,5,19,7],[19,9,19,14],[20,2,20,5],[20,6,20,7],[20,13,20,15],[21,1,21,16],[22,1,22,16],[23,2,23,7],[23,8,23,15],[24,2,24,3],[24,4,24,7],[24,9,24,14],[25,2,25,3],[25,4,25,7],[25,9,25,14],[26,4,26,7],[26,9,26,14],[27,2,27,4],[27,5,27,7],[27,9,27,14],[28,2,28,5],[28,6,28,7],[28,13,28,15],[29,1,29,16],[30,1,30,16],[31,1,31,16],[32,1,32,16],[33,1,33,16],[34,1,34,8],[34,10,34,16],[35,1,35,16],[36,1,36,16],[38,1,38,16],[39,1,39,16],[40,5,40,13],[41,5,41,13],[42,5,42,13],[44,1,44,16],[45,1,45,16],[46,1,46,16],[47,1,47,16],[49,1,49,16],[50,1,50,16],[51,1,51,8],[51,10,51,16],[52,1,52,16],[53,5,53,13],[54,5,54,13],[55,5,55,13],[57,1,57,16]],"flags":["formulas_cached_only"]}
[null,"CREATED BY:  David@TechForText.com ©2010  To contact the author use the email address on the left. "]
[null,"Instructions for The Algebraic Calculator for Three Unknowns"]
[null,"AX+BY+KZ=M, DX+EY+FZ=N, GX+HY+JZ=W"]
[null,"The Algebraic Calculator for Three Unknowns solves the three equations presented above, for X, Y, and Z.  If the equations you want to solve do not look like the above, try to algebraically rearrange them to make them similar to the three equations on top of this page.  Then enter numbers for A, B, K, M, D, E, F, N, G, H, J, and W in the twelve white input boxes below.  Before entering or deleting numbers, left click with the mouse on the relevant white input box. For calculated results left click on the background. With the JavaScript version you can also press the calculation button, and with the spreadsheet version you can press the enter key. "]
[null,"Note: If less than 12 numbers are entered this Calculator will NOT function.  All twelve input boxes must contain numbers entered by the user.  While entering numbers, you may see error messages, which will stop when all the white input boxes have numbers."]
[null,"Note for the error-checking devices, which are on the left of the white input boxes.  An accuracy readout of 100% and an error readout of 0.00% is perfect.  An accuracy readout of less than or greater than 100% or an error readout less than or greater than 0.00% indicates some degree of error, which maybe insignificant if it is less than 1%.   Indications of inaccuracy, or any type of error message, usually relate to the numbers entered by the user.  This can involve numbers that do not satisfy the equations, calculations that exceed 300 digits, or there are one or more white input boxes without numbers.    (Very large and very small numbers are presented in scientific notation.)"]
[]
[null,null,"Error checking for AX+BY+KZ = M   ",{"$nulls":5},"Input Set One: input boxes for AX+BY+KZ = M"]
[null,null," Accuracy  %",null,{"$error":"#DIV/0!"},{"$nulls":3},"A=",{"$nulls":6},"X +"]
[null,null," Error %",null,{"$error":"#DIV/0!"},{"$nulls":3},"B=",{"$nulls":6},"Y +"]
[null,null,"AX+BY+KZ =",null,{"$error":"#DIV/0!"},{"$nulls":3},"K=",{"$nulls":6},"Z +"]
[null,null,"(AX+BY+KZ) - M =",null,null,{"$error":"#DIV/0!"},null,null,"M=",{"$nulls":6},"= M"]
[null,null,{"$error":"#DIV/0!"},{"$nulls":3},0,null,"X +",0,"Y+",0,"Z   =",0]
[null,"Above, right is a representation of the equation you entered. If an equation has numbers with more than four"]
[null," digits, look at the vertical representation of the equation, (right side of input boxes, blue numbers and letters) "]
[null,null,"Error checking for DX+EY+FZ = N  ",{"$nulls":5},"Input Set Two: input boxes for: DX+EY+FZ = N"]
[null,null,"Accuracy  %",null,{"$error":"#DIV/0!"},{"$nulls":3},"D=",{"$nulls":6},"X +"]
[null,null,"Error %",null,{"$error":"#DIV/0!"},{"$nulls":3},"E=",{"$nulls":6},"Y +"]
[null,null,"DX+EY+FZ =",null,{"$error":"#DIV/0!"},{"$nulls":3},"F=",{"$nulls":6},"Z +"]
[null,null,"(DX+EY+FZ) - N =",null,null,{"$error":"#DIV/0!"},null,null,"N=",{"$nulls":6},"= N"]
[null,null,{"$error":"#DIV/0!"},{"$nulls":3},0,null,"X +",0,"Y+",0,"Z   =",0]
[null,"Above, right is a representation of the equation you entered. If an equation has numbers with more than four"]
[null," digits, look at the vertical representation of the equation, (right side of input boxes, blue numbers and letters) "]
[null,null,"Error checking for GX+HY+JZ = W  ",{"$nulls":5},"Input Set Three: input boxes for: GX+HY+JZ = W"]
[null,null," Accuracy %",null,{"$error":"#DIV/0!"},{"$nulls":3},"G =",{"$nulls":6},"X +"]
[null,null,"Error %",null,{"$error":"#DIV/0!"},{"$nulls":3},"H =",{"$nulls":6},"Y +"]
[null,null,"GX+HY+JZ =",null,{"$error":"#DIV/0!"},{"$nulls":3},"J =",{"$nulls":6},"Z +"]
[null,null,"(GX+HY+JZ) - W =",null,null,{"$error":"#DIV/0!"},null,null,"W = ",{"$nulls":6},"= W"]
[null,null,{"$error":"#DIV/0!"},{"$nulls":3},0,null,"X +",0,"Y+",0,"Z   =",0]
[null,"Above, right is a representation of the equation you entered. If an equation has numbers with more than four"]
[null," digits, look at the vertical representation of the equation, (right side of input boxes, blue numbers and letters) "]
[null," The Multiple-Algebraic Calculator has a number of error-checking devices (above and below)."]
[null," These devices check the calculations and the numbers you entered to determine if they satisfy"]
[null," the equations. These devices provide feedback in words or numbers.  The calculations for "]
[null,"all of the error-checking devices are rounded to",{"$nulls":7},5,"decimal places.   You can change this,"]
[null,"by deleting the  blue number above, and entering the number of decimal places you prefer.  If you enter a number that is too high you may get false indications of errors. "]
[null,"Note: The number of zeros displayed is not affected by the blue number."]
[]
[null,"The Calculated Results, for X, Y, and Z are Displayed below  "]
[null,"( for AX+BY+KZ=M, DX+EY+FZ=N, GX+HY+JZ=W )"]
[{"$nulls":4},"X =",{"$error":"#DIV/0!"}]
[{"$nulls":4},"Y =",{"$error":"#DIV/0!"}]
[{"$nulls":4},"Z =",{"$error":"#DIV/0!"}]
[]
[null,"Spreadsheet formula for X is =(M-(B*Y+K*Z))/A"]
[null,"Spreadsheet formula for Y is =(A*N+D*K*Z-A*F*Z-D*M)/(A*E-D*B)"]
[null,"Spreadsheet formula for Z is"]
[null," =((A*E-D*B)*D*W-(A*E-D*B)*G*N-((D*H-G*E)*A*N)+(D*H-G*E)*D*M)/((D*H-G*E)*D*K-(D*H-G*E)*A*F-(A*E-D*B)*G*F+(A*E-D*B)*D*J)  "]
[]
[null," Displayed below are calculated values for X, Y and Z that  "]
[null,"have been rounded to specified number of decimal places  "]
[null,"Calculated results on this list are rounded to ",{"$nulls":7},5,"decimal places.  You can change this,   "]
[null,"by deleting the  blue number above, and entering the number of decimal places you prefer.  "]
[{"$nulls":4},"X =",{"$error":"#DIV/0!"}]
[{"$nulls":4},"Y =",{"$error":"#DIV/0!"}]
[{"$nulls":4},"Z =",{"$error":"#DIV/0!"}]
[]
[null,"CREATED BY:  David@TechForText.com ©2010  To contact the author use the email address on the left. "]