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Math Help - Transposition, analytical simultaneous Equations and indicial logarithms

  1. #1
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    Transposition, analytical simultaneous Equations and indicial logarithms

    Any help on these questions will be greatly appreciated

    Transposition
    e/f=1+r^(2)/1-r^(2) for r

    Simultaneous Equations
    y=5x-4-2x^(2) and y=6x-7

    Indicial Equation
    39=fe^(2x)+6e^(5x)/e^(3x)

    As I said above any solutions/help with these equations would be greatly apreciated

    Thankyou
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  2. #2
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    Quote Originally Posted by Andy1710 View Post
    Any help on these questions will be greatly appreciated

    Simultaneous Equations
    y=5x-4-2x^(2) and y=6x-7

    ...
    Hello,

    use substitution: Plug in the linear term of y into the first equation:

    6x - 7 = 5x - 4 - 2x

    0 = -2x - x + 3 ==>

    x = -(3/2) or x = 1 and
    y = -16 or y = -1

    That means the solutions are pairs of numbers: (-3/2, -16), (1, -1)
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  3. #3
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    Quote Originally Posted by Andy1710 View Post
    Any help on these questions will be greatly appreciated

    Transposition
    e/f=1+r^(2)/1-r^(2) for r

    ...
    Hello,

    I assume that you want express the variable r by e and f. If so:
    Code:
     e    1 + r
    --- = -------    multiply by the denominator
     f    1 - r
    
     e
    --- * (1 - r) = 1 + r  expand the brackets
     f
    
     e                e
    --- - 1 = r(1 + ---)
     f                f
    
          e - f
     r = -----
          e + f
    Calculate the square root of both sides of this equation.
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    Thank you very much for the help
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  5. #5
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    Quote Originally Posted by Andy1710 View Post
    Any help on these questions will be greatly appreciated
    ...
    Indicial Equation
    39=fe^(2x)+6e^(5x)/e^(3x)

    ...
    Hello,
    Code:
                   6e^(5x)
    39 = fe^(2x) + ------- = fe^(2x) + 6e^(2x)
                    e^(3x)
    
    39 = e^(2x)(f + 6)
    
      39 
    ------ = e^(2x)
    f + 6
    
    x = ln(39) - ln(f+6)
    Not sure if this is what you are looking for.
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