Manipulating Equations

on . Posted in Nomenclature & Symbols for Engineering, Mathematics, and Science

Mathematics and Management Rules and Symbols

 

Manipulating Equations Rules

  • The order of reareanging is important.
    • B E D M A S    Brackets  Exponents  Division  Multiplication  Addition  Subtraction
    • Solve ----->    B E D M A S    <----- Rearrange
    • Use the opposite both sides.
  • Every function has an opposite function.
    • \(+ \; to \;  -\)
    • \(\times \; to \;  \div\)
    • \(x^2 \; to\; \sqrt{x} \)
    • \(Sin \; to \;Sin^{-1}\)
  • Whatever you do to one side of the equation you must do to the other side.

 

Manipulating Equations
Formulas w/2
Formulas w/3Formulas w/4Formulas w/5Formulas w/6

\(\large{  a =  b \; c  }\)

\(\large{ b = \frac { a }{ c }   }\)

\(\large{ c = \frac { a }{ b } }\)

\(\large{ a =  b \; c \; d  }\)

\(\large{ b =  \frac{ a }{ c \; d }  }\)

\(\large{ c =  \frac{ a }{ b \; d }  }\)

\(\large{ d =  \frac{ a }{ b \; c }  }\)

\(\large{ a =  b \; c \; d \; e }\)

\(\large{ b =  \frac{ a }{ c \; d \; e }  }\)

\(\large{ c =  \frac{ a }{ b \; d \; e }  }\)

\(\large{ d =  \frac{ a }{ b \; c \; e }  }\)

\(\large{ e =  \frac{ a }{ b \; c \; d }  }\)

\(\large{  a =  b \; c \; d \; e \; f }\)

\(\large{ b =  \frac{ a }{ c \; d \; e \; f }  }\)

\(\large{ c =  \frac{ a }{ b \; d \; e \; f }  }\)

\(\large{ d =  \frac{ a }{ b \; c \; e \; f }  }\)

\(\large{ e =  \frac{ a }{ b \; c \; d \; f }  }\)

\(\large{ f =  \frac{ a }{ b \; c \; d \; e }  }\)

\(\large{  a =  b \; c \; d \; e \; f \; g }\)

\(\large{ b =  \frac{ a }{ c \; d \; e \; f \; g}  }\)

\(\large{ c =  \frac{ a }{ b \; d \; e \; f  \; g}  }\)

\(\large{ d =  \frac{ a }{ b \; c \; e \; f \; g }  }\)

\(\large{ e =  \frac{ a }{ b \; c \; d \; f \; g}  }\)

\(\large{ f =  \frac{ a }{ b \; c \; d \; e \; g }  }\)

\(\large{ g =  \frac{ a }{ b \; c \; d \; e \; f }  }\)

  

Manipulating Equations with Fraction
Formulas w/1
Formulas w/2Formulas w/3Formulas w/4Formulas w/5

 \(\large{ a = \frac{ b }{c} }\)

 \(\large{ b = a\;c }\)

 \(\large{ c = \frac{ b }{a} }\)

\(\large{ a = \frac{ b\;c }{d} }\)

\(\large{ b = \frac{ a\;d }{c} }\)

\(\large{ c = \frac{ a\;d }{b} }\)

\(\large{ d = \frac{ b\;c }{a} }\)

\(\large{ a = \frac{ b\;c\;d }{e} }\)

\(\large{ b = \frac{ a\;e }{c\;d} }\)

\(\large{ c = \frac{ a\;e }{b\;d} }\)

\(\large{ d = \frac{ a\;e }{b\;c} }\)

\(\large{ e = \frac{ b\;c\;d }{a} }\)

\(\large{ a = \frac{ b\;c\;d\;e }{ f } }\)

\(\large{ b = \frac{ a\;f }{ c\;d\;e } }\)

\(\large{ c = \frac{ a\;f }{ b\;d\;e } }\)

\(\large{ d = \frac{ a\;f }{ b\;c\;e } }\)

\(\large{ e = \frac{ a\;f }{ b\;c\;d } }\)

\(\large{ f = \frac{ b\;c\;d\;e }{ a } }\)

\(\large{ a = \frac{ b\;c\;d\;e\;f }{ g } }\)

\(\large{ b = \frac{ a\;g }{ c\;d\;e\;f } }\)

\(\large{ c = \frac{ a\;g }{ b\;d\;e\;f } }\)

\(\large{ d = \frac{ a\;g }{ b\;c\;e\;f } }\)

\(\large{ e = \frac{ a\;g }{ b\;c\;d\;f } }\)

\(\large{ f = \frac{ a\;g }{ b\;c\;d\;e } }\)

\(\large{ g = \frac{ b\;c\;d\;e\;f }{ a } }\)

          

 Manipulating Equations with \(\large{ \frac{1}{2} }\)
FormulaFormulaFormulaFormulaFormula

\(\large{ a = \frac{1}{2} \; b + c }\)

\(\large{ b = 2\;a - c }\)

\(\large{ c = 2\;a - b }\)

\(\large{ a = \frac{1}{2} \; b \; c^2 }\)

\(\large{ b = \frac{ 2\;a }{ c^2 } }\)

\(\large{ c = \sqrt{ \frac{ 2\;a }{ b }  } }\)

     

 

 Manipulating Equations
FormulaFormulaFormulaFormulaFormula

\(\large{ a =  b - c  }\)

\(\large{ b =  a + c  }\)

\(\large{ c =  b - a  }\)

 

\(\large{  a =  b + c\;d  }\)

\(\large{ b =  a - c\;d  }\)

\(\large{ c = \frac{ a - b }{ d }  }\)

\(\large{ d = \frac{ a - b }{ c }  }\)

 
 

\(\large{ a = - b \left( c - d \right) }\)

\(\large{ b =  \frac{ a }{ c \;-\; d } }\)

\(\large{ c = d \;- \; \frac{ a }{ b } }\)

\(\large{ d = \frac{ a }{ b } + c }\)

\(\large{ a = \frac{ b\;-\;c }{ d }  }\)

\(\large{ b = a\;d + c }\)

\(\large{ c = b - a\;d }\)

\(\large{ d = \frac{ b\;-\;c }{ a }  }\)

\(\large{ a = \frac{ b\;+\;c }{ d } }\)

\(\large{ b =  a \; d  - c  }\)

\(\large{ c =  b \; c  - b  }\)

\(\large{ d = \frac{ b\;+\;c }{ a } }\)

         

 Manipulating Equations
FormulaFormulaFormulaFormulaFormula

\(\large{ a = b\; \sqrt{ c\; d } }\)

\(\large{ b = \frac{a}{ \sqrt{ c\; d } } }\)

\(\large{ c = \frac{1}{d} \; \left( \frac{a}{b} \right)^2 }\)

\(\large{ d = \frac{1}{c} \; \left( \frac{a}{b} \right)^2 }\)

\(\large{ a = b\;c\; \sqrt{2\; d\; e }  }\)

\(\large{ b = \frac{a}{c\; \sqrt{2\; d\; e } } }\)

\(\large{ c = \frac{a}{b\; \sqrt{2\; d\; e } } }\)

\(\large{ d = \frac{\left( \frac{a}{b\;c} \right)^2 }{2\;e } }\)

\(\large{ e = \frac{\left( \frac{a}{b\;c} \right)^2 }{2\;d } }\)

 

\(\large{ a = 2\; \sqrt{ b^2 - c^2 } }\)

\(\large{ b = \sqrt{ \frac{a^2}{4} + c^2 } }\)

\(\large{ c = \sqrt{ \frac{a^2}{4} - b^2 } }\)


\(\large{a = \sqrt{\frac{b\;c}{d} }  }\)

\(\large{b = \frac{a^2\;d}{c}  }\)

\(\large{c = \frac{a^2\;d}{b}  }\)

\(\large{d = \frac{b\;c}{a^2}  }\)

 


     

 Manipulating Equations
FormulaFormulaFormulaFormulaFormula

\(\large{ a = \frac{ b^2\;c }{ d } }\)

\(\large{ b = \sqrt{  \frac{ a \; d }{ c }  }  }\)

\(\large{ c =  \frac{ a \; d }{ b^2 }  }\)

\(\large{ d = \frac{ b^2\;c }{ a } }\)

\(\large{ a = \frac{ b^2\;c\;d }{e} }\)

\(\large{ b = \sqrt{  \frac{ a \; e }{ c \; d }  }  }\)

\(\large{ c =  \frac{ a \; e }{ b^2 \; d }  }\)

\(\large{ d =  \frac{ a \; e }{ b^2 \; c }  }\)

\(\large{ e =  \frac{ b^2\;c\;d }{ a }  }\)

     

  

 Manipulating Equations
FormulaFormulaFormulaFormulaFormula

\(\large{ a = \frac{b}{\sqrt{ c\; d } } }\)

\(\large{ b = a\; \sqrt{ c\; d }  }\)

\(\large{ c = \frac{b^2}{a^2\;d } }\)

\(\large{ d = \frac{b^2}{a^2\;c } }\)

\(\large{ a = \frac{ b\;-\;c }{c\; \left( d\;-\;e  \right)  } }\)

\(\large{ b =  a \; c\; \left( d\;-\;e  \right)  + c  }\)

\(\large{ c = \frac{ b }{ a\; \left( d\;-\;e  \right) \;+\;1  } }\)

\(\large{ d = \frac{ d\;-\;e }{ a\;c } + c  }\)

\(\large{ e = b - \frac{ d\;-\;e }{ a\;c }  }\)

\(\large{  a =  \frac{ b\;c\;d  }{ e } + f }\)

\(\large{  b = a - f \; \frac{ e }{ c\;d }   }\)

\(\large{  c = a - f \; \frac{ e }{ b\;d }   }\)

\(\large{  d = a - f \; \frac{ e }{ b\;c }   }\)

\(\large{  e =  \frac{ b\;c\;d  }{ a \;-\; f } }\)

\(\large{  f = a - \; \frac{ b\;c\;d  }{ e } }\)

\(\large{ a  =  \frac{ b \;-\; c }{ d \;\left( \frac{ b }{ c } \right) }  }\) 

\(\large{ a  =  \frac{ b \;-\; c }{ d \; b \;-\; d  \; c } }\)

 

 

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