# Math Help - Transposition, analytical simultaneous Equations and indicial logarithms

1. ## 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

2. 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)

3. 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.

4. Thank you very much for the help

5. 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.