Constructing an iterative signature function February 13

Please pardon my rather crude description of this problem, I am not very adept at mathematical notation and language, but I will do my best to describe it in a way as to be understandable.I have one number, lets call it K. I need to be able to modify

Problem on Time and Work February 13

$A$ can do a piece of work in $10$ days, $B$ can do in $20$ days and $C$ can do in $30$ days. If $A$ is assisted by $B$ and $C$ turn by turn in alternate days respectively, in how many days the work might have been finished?My attempt; In $10$ days,

what is a complex number in layman terms February 13

for an example, 3 is a real number and i can understand its value -like 3 apples.But i can't understand or visualize what a complex number is ! can anyone help me in understanding what really is a complex number ?

An exponential recurrence February 13    1

Is there any way to solve the recurrence$$x[n+1]=(x[n]+1)2^{x[n]+1}-1$$I know how to solve recurrences with z-transforms, but it doesn't look like that technique will yield anything useful here. I have a feeling I'll be able to work around this if wo

Help with combinatorics February 13

So if i have a set of 20 people.1) How can i count how many sets of 3 people can i nake out of those 20 if there is a list of them in alphabetical order But none two people from the set can be together on the list.And also: 2) how many different ways

Height and Distance problems February 13

A ladder rests against a wall at an angle $\alpha$ to the horizontal. When its foot is pulled away from the wall through a distance $a$, it slides a distance $b$ down the wall and makes an angle $\bet$ with the horizontal. Prove that : $$\frac{a}{b}=

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