Melody

Just add 0.9 to both sides.   Easy peazy :)))

Here is a you tube clip on it :)

1+1/87*85,9851

1+1/87*85,9851 = 1.9883344827586207

cos((3π/2) - ϴ)

\(cos((3π/2) - \theta)\\ =\text{change to degrees}\\ =cos(270-\theta)\\ =cos(180+(90-\theta))\\ =-cos(90-\theta)\\ =-sin(\theta)\)

I think Max is right in that not all this working is really needed.  

But it is easier for me to think through this way :)

Mr. Wong has 10 grandchildren. Assuming that the gender of each child is determined independently and with equal likelihood of male and female, what is the probability that Mr. Wong has more grandsons than granddaughters or more granddaughters than grandsons?

1 - (probability of 5 girls and 5 boys)

10C5(0.5)^5*(0.5)^5  =  10C5*(0.5)^10 = 0.24609375

1-0.24609375 = 0.75390625 = 75%

ln i =??

\(Let\\ \begin{align} i\theta& = ln(i)\\ e^{i\theta }&=e^{ ln(i)}\\ cos\theta+isin\theta&=0+i \end{align} so\\cos\theta=0 \quad and \quad sin\theta =1\\ \theta=\frac{\pi}{2}+2\pi n \qquad n\in Z\;\;(integer)\)

so 

\(ln(i)=(\frac{\pi}{2}+2\pi n)i\\ ln(i)=(\frac{1}{2}+2n)\pi i\\ ln(i)=(\frac{4n+1}{2})\pi i \qquad n \in Z \)

i^(2 n + 1) = i  for all positive integers n

\(i^1=i\\ i^2=-1\\ i^3=-i\\ i^4=+1\\ i^5=i\\ ...\\ i^{1+4k}=i\)

2n+1=4k+1     where n and k are both positive integers

2n    = 4k

n      = 2k

n = 2,4,6, .....   all positive even integers    

scale factor of 1\6 foot to 3 1/3 feet

\(\frac{1}{6}\;:\; \frac{10}{3}\\ \frac{1}{6}\;:\; \frac{20}{6}\\ 1:20 \)

find two consecutive even integers such that six times the first equals three times the second.

Let them be    2N  and  2N+2

6*2N = 3(2N+2)

4N    =   2N+2

2N    =        2

N=1

the numbers are   2 and 4

check:

2*6 = 3*4     True 

Roald Dahl thought it should be Tortoise backwards