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log_{x} (7y+1) - log{x} (2y) =1 --> log_{x} [(7y+1)/2y]=1 (y =/= 0, Rules of logarithms i.e. difference of logarithms) --> x = [(7y+1)/2y] (x>0, Rules of logarithms i.e. log_{x} x = 1) --> 2yx...

A/(x-2) + B/(x+1) + C/(x+1)^2

if y=3x^2 + x -4 

then 

dy/dx = 6x + 1

setting this equal to zero gives

6x + 1 = 0

so then

x = -1/6

putting this x value back into the original equation gi...

a) y = 9 -6x^2 - 12x^4 

dy/dx = -12x - 48x^3 

b) At stationary points dy/dx = 0. 

-12x - 48x^3 = 0 

48x^3 + 12x = 0 

4x^3 + x = 0

x (4x^2 + 1) = 0 

Either ...

1. We the answer in question in the form A(1+B)^0.5 and we can do that by factorising out the 5. This gives 5^0.5(1+0.4x)^0.5. 2. Identify the formula we are going to use ...