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Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)). Notice that this looks a lot like a factorised quadratic equation, where <...
First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means: (19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction:
(19x - 2...
First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...
dy/dx = 24e6x - sin(x) + 6
2cosx - sinx = Rcos(x+a) = Rcos(x)cos(a)-Rsin(x)sin(a)
Implying
2cos(x)=Rcos(x)cos(a)
Rcosa = 2
Similarly: Rsin(a) = 1
Therefore tan(a) = 1/2
Meaning a=26.57 Degr...
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