
CREATED BY: David@TechForText.com
©2010 To contact the author use the email address on the
left. 


The MultipleAlgebraic Calculator 


The MultipleAlgebraic Calculator demonstrates
that a number of complex calculations (involving 24 unknowns, calculus,
and trigonometry) can be carried out simultaneously, by devices created
with specialized design concepts in the JavaScript or spreadsheet
formats. When the user enters 12 numbers, and left clicks
with the mouse, the MultipleAlgebraic Calculator initially solves: AX+BY+KZ=M, DX+EY+FZ=N,GX+HY+JZ=W for X, Y and Z. With the calculated
values for X, Y, and Z, and the numbers entered by the user, additional
sets of calculations are automatically carried out involving
six double integrals, ratios, algebra and trigonometry.



Instructions 


To use the MultipleAlgebraic Calculator enter
twelve numbers in the twelve white input boxes, below. (To enter or delete
numbers, left click with the mouse on the relevant white input box.)
For calculated results left click with the mouse on the
background Alternatively, with the online JavaScript version
you can press the calculation button, and with the spreadsheet version you
can press the enter key. Numbers and words displayed in red
type are calculated results. 



Note: If less than 12 numbers are entered this
Calculator will NOT function properly. All twelve input boxes
must contain numbers entered by the user. 



To see all the equations, double
integrals, trigonometry and calculated results, scroll down. The
MultipleAlgebraic Calculator is approximately 20 times the height of a
typical computer screen. It is equivalent to a 15 page document.




Error
checking and input boxes for AX+BY+KZ = M 



Accuracy % 

A= 

X + 


Error % 

B= 

Y + 


AX+BY+KZ = 

K= 

Z + 


(AX+BY+KZ)  M = 

M= 

=M 








Z = 



Above, right is a representation of the
equation you entered. If an equation has numbers with more than four 


digits, look at the vertical
representation of the equation, (right side of input boxes, blue numbers
and letters) 


Error
checking and input boxes for DX+EY+FZ = N 


Accuracy % 

D= 

X + 


Error % 

E= 

Y + 


DX+EY+FZ = 

F= 

Z + 


(DX+EY+FZ)  N = 

N= 

=N 








Z = 



Above, right is a representation of the
equation you entered. If an equation has numbers with more than four 


digits, look at the vertical
representation of the equation, (right side of input boxes, blue numbers
and letters) 


Error
checking and input boxes for GX+HY+JZ = W 


Accuracy % 

G = 

X + 


Error % 

H = 

Y + 


GX+HY+JZ = 

J = 

Z + 


(GX+HY+JZ)  W = 

W = 

=W 








Z = 



Above, right is a representation of the
equation you entered. If an equation has numbers with more than four 


digits, look at the vertical
representation of the equation, (right side of input boxes, blue numbers
and letters) 


The MultipleAlgebraic Calculator
has a number of errorchecking devices (above and below). 


These devices check the
calculations and the numbers you entered to determine if they satisfy 


the equations. These devices
provide feedback in words or numbers. The calculations
for 


all of the errorchecking devices are rounded to


decimal places. You can change
this, 


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. 


Note: The number of zeros displayed is not
affected by the blue number. 





For AX+BY+KZ = M, DX+EY+FZ = N, GX+HY+JZ =
W 


The Calculated Results, for X, Y, and Z, are in
the three yellow boxes, below 




X = 








Y = 








Z = 






Spreadsheet formula for X is =(M(B*Y+K*Z))/A



Spreadsheet formula for Y is
=(A*N+D*K*ZA*F*ZD*M)/(A*ED*B) 


Spreadsheet formula for Z is 


=((A*ED*B)*D*W(A*ED*B)*G*N((D*HG*E)*A*N)+(D*HG*E)*D*M)/((D*HG*E)*D*K(D*HG*E)*A*F(A*ED*B)*G*F+(A*ED*B)*D*J)




The MultipleAlgebraic Calculator displays a
summary of 


calculated results for 24 unknowns,
below. This list does not 


include all the calculated
results. For all the results scroll down. 


Calculated results on this list are rounded
to 

decimal places. You can change
this, 


by deleting the blue number above,
and entering the number of decimal places you prefer. 


X = 

Da = 



Y = 

Ea= 



Z = 

Fa= 



P = 

Ga= 



V = 

Angle_A= 



S= 

Angle_B= 



T= 

Ja= 



Q = 

Ka= 



U = 

La 



Aa = 

Ma= 



Ba = 

Na= 



Ca = 

Pa= 




The three equations from the previous section,
(AX+BY+KZ=M, DX+EY+FZ=N, 



GX+HY+JZ=W are algebraically rearranged by
solving for Y as follows: 





Y= 
MAXKZ 

Y= 
NDXFZ 

Y= 
WGXJZ 







B 

E 

H 





In this section, calculations with
double integrals, will be carried out, for each 



of above. The calculations are
based on the following: 









The X axis will be based 0 to 





The Z axis will be based 0 to 






















































(MAXKZ)dxdz = 








B 








0 






0 




Spreadsheet formula for the above is
=(2*M*X*ZA*Z*(X^2)K*X*(Z^2))/(2*B) 









M = 



Y = 
MAXKZ 
These are the values 
A = 



B 
you entered in
the 
K = 






white input boxes. 
B = 






































(NDXFZ)dxdz = 








E 








0 







0 




Spreadsheet formula for the above is
=((2*N*X*ZD*Z*(X^2)F*X*(Z^2))/2*E) 










N= 




Y= 
NDXFZ 
These are the values 
D= 




E 
you entered in
the 
F= 







white input boxes. 
E= 




































(WGXJZ)dxdz = 







H 







0 






0 




Spreadsheet formula for the above is
=((2*W*X*ZD*Z*(X^2)F*X*(Z^2))/2*H) 









W= 



Y= 
WGXJZ 
These are the values 
G= 



H 
you entered in
the 
J= 





white input boxes. 
H= 




The three equations from the previous section,
(AX+BY+KZ=M, DX+EY+FZ=N, and 



GX+HY+JZ=W have been algebraically rearranged
by solving for Z as follows: 





Z= 
MAXBY 

Z= 
NDXEY 

Z= 
WGXHY 







K 

F 

J 





In this section, calculations with
double integrals, will be carried out, for each 



of above. The calculations are
based on the following: 









The X axis will be based 0 to 





The Y axis will be based 0 to 






































(MAXBY)dxdy = 








K 








0 






0 




Spreadsheet formula for the above is
=((2*M*X*ZA*Z*(X^2)K*X*(Z^2))/2*B) 









M = 



Z = 
MAXBY 
These are the values 
A = 



K 
you entered in
the 
K = 






white input boxes. 
B = 






































(NDXEY)dxdy = 








F 








0 







0 




Spreadsheet formula for the above is
=((2*N*X*ZD*Z*(X^2)F*X*(Z^2))/2*E) 










N= 




Z= 
NDXEY 
These are the values 
D= 




F 
you entered in
the 
F= 







white input boxes. 
E= 




































(WGXHY)dxdy = 







J 







0 






0 




Spreadsheet formula for the above is
=((2*W*X*ZD*Z*(X^2)F*X*(Z^2))/2*H) 









W= 



Z= 
WGXHY 
These are the values 
G= 



J 
you entered in
the 
J= 






white input boxes. 
H= 







A Ratio Problem Involving only X as an Unknown




In this section: the equations AX+BY+KZ=M,
DX+EY+FZ=N, and 




GX+HY+JZ=W and unknowns X, Y, and Z are
converted into a ratio 




problem, with only one unknown,
X. This is possible because the 




values for X, Y and Z have been
calculated. 



If P*X=Z 
If V*X=Y 



then P=Z/X 
then V=Y/X 



In terms of numbers 
In terms of numbers 



P= 

V= 




P*X= 

V*X= 





Z= 

Y= 





Thus, all of the unknowns represented 

Thus, all of the unknowns represented 




by Z can be replaced by P*X 

by Y can be replaced by V*X 



The three equations (AX+BY+KZ=M, DX+EY+FZ=N,
GX+HY+JZ=W) 


can now be rewritten in terms of
X, as follows: 







AX+BY+KZ=M 

DX+EY+FZ=N 

GX+HY+JZ=W 


In terms of X 

In terms of X 

In terms of X 


AX+BVX+KPX=M 

DX+EVX+FPX=N 

GX+HVX+JPX=W 


The above conclusions and calculations can be
checked as follows: 












AX+BY+KZ = 








AX+BVX+KPX = 








DX+EY+FZ= 








DX+EVX+FPX= 








GX+HY+JZ= 








GX+HVX+JPX= 












AX+BY+KZ=M rewritten in terms of X is
AX+BVX+KPX=M 





This can be restated in the form of a word
problem as follows: 












There are three numbers in the ratio of A, B*V,
and K*P, 







and the sum of the three numbers is M. 













In terms of calculated data the
three numbers are in the following RATIOS: 










A = 






B*V = 





K*P = 










The three numbers are as follows: 










A*X = 





B*V*X = 





K*P*X= 









The sum of the numbers is: 




The above should equal M = 










DX+EY+FZ=N rewritten in terms of X is
DX+EVX+FPX=N 





This can be restated in the form of a word
problem as follows: 












There are three numbers in the ratio of D, E*V,
and F*P, 







and the sum of the three numbers is N. 











In terms of calculated data the
three numbers are in the following RATIOS: 









D = 





E*V = 





F*P= 









The three numbers are as follows: 










D*X = 





E*V*X = 





F*P*X= 









The sum of the numbers is: 




The above should equal N = 










GX+HY+JZ=W rewritten in terms of X is
GX+HVX+JPX=W 




This can be restated in the form of a word
problem as follows: 










There are three numbers in the ratio of G, H*V,
and J*P, 






and the sum of the three numbers is W. 











In terms of calculated data the
three numbers are in the following RATIOS: 









G = 





H*V = 





J*P= 









The three numbers are as follows: 










G*X = 





H*V*X = 





J*P*X= 









The sum of the numbers is: 




The above should equal W = 























Miscellaneous Calculations: Solving for
Additional Unknowns 







This device solves for S 







A*(E+S)=B*KY 






S = 







Spreadsheet formula for the above is
=(B*KYA*E)/A 



1 







Spreadsheet formula for above
=ROUND(A*(E+S),Rd)=ROUND(B*KY,Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for T 




X+T+S=A*B*KY 




T= 





Spreadsheet formula for above =A*B*KYXS 








Spreadsheet formula for above =ROUND(X+T+S,
Rd)=ROUND(A*B*KY, Rd) 


` 

TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for U 




STA=B+Z+U 





U= 





Spreadsheet formula for above =S*TABZ 








Spreadsheet formula for above
=ROUND(S*TA,Rd)=ROUND(B+Z+U,Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Q 




T+SA = (S+Z+U+X) 




Q 




Q= 





Spreadsheet formula for above
=(S+Z+U+X)/(T+SA) 








Spreadsheet formula for above=ROUND(T+SA,
Rd)=ROUND(((S+Z+U+X)/Q),Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 









This device solves for Aa 




T*S+X+Y+Z=U+Q+Aa 




Aa = 





Spreadsheet formula for above
=(T*S+X+Y+Z)(U+Q) 








Spreadsheet formula for above =ROUND(T*S+X+Y+Z,
Rd)=ROUND(U+Q+Aa, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Ba 




T*S+X+Y+Z=U+Q*Aa*Ba 




Ba = 





Spreadsheet formula for above
=(T*S+X+Y+ZU)/(Q*Aa) 








Spreadsheet formula for above=ROUND(T*S+X+Y+Z,
Rd)=ROUND(U+Q+Aa*Ba, Rd) 



TRUE = NO Errors for this calculation 






FALSE = ERROR no result for the numbers you
entered. 









This device solves for Ca 




Ca*(X+Y+Z)=U+Q+Aa*Ba 





Ca= 






Spreadsheet formula for
above=(U+Q+Aa*Ba)/(X+Y+Z) 








Spreadsheet formula for above
=ROUND(Ca*(X+Y+Z), Rd)=ROUND(U+Q+Aa*Ba, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Da 




U*Q=U+Q+Aa*Ba+Da 




Da= 





Spreadsheet formula for above =U*Q(U+Q+Aa*Ba)









Spreadsheet formula for above =ROUND(U*Q,Rd)=
ROUND(U+Q+Aa*Ba+Da, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Ea 




X+Y+Z= Ea*(U+Q+Aa*Ba+Da+Ca) 




Ea = 





Spreadsheet formula for above
=(X+Y+Z)/(U+Q+Aa*Ba+Da+Ca) 








Spreadsheet formula for above
=ROUND(X+Y+Z, Rd)=ROUND(Ea*(U+Q+Aa*Ba+Da+Ca), Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Fa 




A*(Fa+X+Y+Z)= Ea+U+Q+Aa*Ba+Da+Ca





Fa = 





Spreadsheet formula for
above=((Ea+U+Q+Aa*Ba+Da+Ca)/A)(X+Y+Z) 








Spreadsheet formula for above
=ROUND(A*(Fa+X+Y+Z), Rd)=ROUND(Ea+U+Q+Aa*Ba+Da+Ca, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Ga 




A*(Aa+Ba+Ca+Da+Ea+Fa+U+Q) =X+Y+Z+Ga





Ga = 





Spreadsheet formula for
above=A*(Aa+Ba+Ca+Da+Ea+Fa+U+Q)(X+Y+Z) 








Spreadsheet formula for
above=ROUND(A*(Aa+Ba+Ca+Da+Ea+Fa+U+Q), Rd)=ROUND(X+Y+Z+Ga, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 






Miscellaneous Calculations Solving for
trigonometric Unknowns 






This device solves for Angle_A in radians





Tan(Angle_A)=Y/X 




Tan(Angle_A) = 






Spreadsheet formula for above = Y/X 





Angle_A= 





Spreadsheet formula for above = =ATAN(Y/X) 








Spreadsheet formula for above
=ROUND(TAN(Angle_A), Rd)=ROUND(Y/X, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 






This device solves for Tan(Angle_B), and
Angle_A in radians 



Tan(Angle_B)=X/Y 




Tan(Angle_B) = 





Spreadsheet formula for above =X/Y





Angle_B= 





Spreadsheet formula for above =ATAN(X/Y) 








Spreadsheet formula for above
=ROUND(TAN(Angle_B), Rd)=ROUND(X/Y, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Ja 




Ja+Sin(Angle_A)+Cos(Angle_A)=Tan(Angle_B)+A+B 




Ja = 




Spreadsheet formula for
above=TAN(Angle_B)+A+B(SIN(Angle_A)+COS(Angle_A)) 







Spreadsheet formula for
above=ROUND(Ja+SIN(Angle_A)+COS(Angle_A), Rd)=ROUND(TAN(Angle_B)+A+B, Rd)




TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Ka 




Ka*(Ja+Sin(Angle_A)) = Tan(Angle_B)+A+B+X





Ka = 




Spreadsheet formula for
above=(TAN(Angle_B)+A+B+X)/(Ja+SIN(Angle_A)) 







Spreadsheet formula for
above=ROUND(Ka*(Ja+SIN(Angle_A)), Rd)=ROUND((TAN(Angle_B)+A+B+X), Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for La 




La+Cos(Angle_A)=Tan(Angle_B)+Sin(Angle_A) 




La= 




Spreadsheet formula for
above=TAN(Angle_B)+SIN(Angle_A)(COS(Angle_A)) 







Spreadsheet formula for
above=ROUND(La+COS(Angle_A),Rd)=ROUND(TAN(Angle_B)+SIN(Angle_A), Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Ma 




Ma+La*Sin(Angle_A)=Tan(Angle_B)+A+K+D 




Ma = 





Spreadsheet formula for above
=TAN(Angle_B)+A+K+D(La*SIN(Angle_A)) 








Spreadsheet formula for
above=ROUND(Ma+La*SIN(Angle_A),Rd)=ROUND(TAN(Angle_B)+A+K+D, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Na 




D+Na*Sin(Angle_A) = Tan(Angle_A)+Ma+La+Ma





Na = 




Spreadsheet formula for
above=(TAN(Angle_A)+Ma+La+MaD)/(SIN(Angle_A)) 







Spreadsheet formula for above
=ROUND(D+Na*SIN(Angle_A), Rd)=ROUND(TAN(Angle_A)+Ma+La+Ma, Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 







This device solves for Pa 




Pa+Cos(Angle_B)=Tan(Angle_B)+Sin(Angle_B)AM





Pa= 




Spreadsheet formula for above
=TAN(Angle_B)+SIN(Angle_B)(COS(Angle_B))AM 







Spreadsheet formula for above
=ROUND(Pa+COS(Angle_B),Rd)=ROUND(TAN(Angle_B)+SIN(Angle_B)AM,Rd) 



TRUE = NO Errors for this calculation 




FALSE = ERROR no result for the numbers you
entered. 




CREATED BY: David@TechForText.com
©2010 To contact the author use the email address on the
left. 
