# Transposition, analytical simultaneous Equations and indicial logarithms

• May 20th 2007, 05:23 AM
Andy1710
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
• May 20th 2007, 06:45 AM
earboth
Quote:

Originally Posted by Andy1710
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 - 2x²

0 = -2x² - 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)
• May 20th 2007, 07:06 AM
earboth
Quote:

Originally Posted by Andy1710
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 + r² --- = -------    multiply by the denominator  f    1 - r²  e --- * (1 - r²) = 1 + r²  expand the brackets  f  e                e --- - 1 = r²(1 + ---)  f                f       e - f  r² = -----       e + f```
Calculate the square root of both sides of this equation.
• May 20th 2007, 11:06 AM
Andy1710
Thank you very much for the help :D
• May 20th 2007, 10:12 PM
earboth
Quote:

Originally Posted by Andy1710
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 = ½ln(39) - ½ln(f+6)```
Not sure if this is what you are looking for.