## Help with counting possible ways of dividing a larger group into smaller groups 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

## How do I prove that sine is dependent only on the angle February 13

I did the following: Taking one triangle and writing the pythagorean formula to it: $a^2+b^2=c^2$ and hence: $$\frac{o}{h}=\frac{\pm \sqrt{c^2-a^2}}{\pm \sqrt{a^2+b^2}}$$I took another triangle and tried to assumed that the angle would be preserved.

## How many different ice cream cones with 31 different flavors and 2 kinds of cones February 13    1

I have been trying this for a while now. Using the formula for permutations, I am getting P(31, 2) = 10,230, but this seems way too high...An ice cream shop has 31 different flavors of ice cream and two kinds of cones. The rules are, cones can be one

## In how many different ways three persons A, B, C having 6, 7 and 8 one rupee coins duplicate February 13    2

This question already has an answer here: Combinatorics. Please explain me how to do it. 3 answers In how many different ways three persons A, B, C having 6, 7 and 8 one rupee coins respectively can donate Rs.10 collectivelyLet $a,b$, and $c$ be the

At an election three districts are to be canvassed by $10, 15$ and $20$ men respectively. If $45$ men volunteer, in how many ways can they be allotted to the different districts? Three groups of $10, 15, 20$ can be formed in $\frac{45!}{10! \cdot 15! ## Constructing an iterative signature function February 13 Please pardon my rather crude description of this problem, I am not very adept at mathematical notation and language, but I will do my best to describe it in a way as to be understandable.I have one number, lets call it K. I need to be able to modify ## Problem on Time and Work February 13$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 ? ## Show that multiplication is not definable on set of Natural Numbers with successor function February 13 I've shown that the theoty in the question admits quantifier elimination. If the F(x,y)=xy (multiplication) was definable on N with successor function and 0 then the statement A="There is x s.t for any y F(x,y)=x" is true. Now, I want to show th ## Can you discuss the convergence of$\prod_{k=2}^{\infty}\zeta(\sigma(n))$February 13 When I use the tool INFINITE PRODUCTS in the online calculator for products of Wolfram Alpha, I can type product zeta( DivisorSigma[1, k]), k=2 to infinity where$\zeta(s)$is the Riemann zeta function and$\sigma(m)$is the** sum of divisor function ## 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 ## Solution to recurrence relation:$f(x) = f(x-2)+f(x/2)$for even x,$f(x)=f(x-1)$for odd x. February 13 I need to find a solution for, or at least a way to compute efficiently, the following recurrence equation:f(x) = \begin{cases} f(x-2)+f(x/2), & \text{if$x$is even} \\ f(x-1), & \text{if$x$is odd} \end{cases}Also,$f(0)=f(1)=1$.I looked back a ## 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 ## Given triangle w/ two congruent perpendicular bisectors, is it isosceles February 13 1 Given any triangle with two congruent perpendicular bisectors (the segment that is inside the triangle), must it be isosceles? Why?Trying to construct a non-isosceles one doesn't seem to work. I attempted to prove it multiple times such as by drawing ## A question on subspace of a vector space February 13 I am having a hard time with this math question.Which of the following is not a subspaceS = { B(y) : B e F} where y is a fixed element of a vector space V over a field FS = {(x,-x,0): x e R } in R^3S = { (x 0) } { (0 -x) : x e R } in F the set of all ## 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 : $$\frac{a}{b}= ## Repeating something with (1/n)th chance of success n times February 13 3 Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every guess, giving in the end a probability of 1.If the ## Maximising returns Limiting Risk February 13 This is probably a simple question/solution, but I'm no math expert.I'm looking into a Facebook group that provides bet to try and get up to 50k, you may have heard of it. The premise being that you start at 50 and put all your winnings into each an ## How can I find the limit without using a closed form expression February 13 I am trying to evaluate this limit without using the closed form expression for the sum of natural numbers raised to kth power.$$\lim_{n \to \infty} \dfrac{ 1^n +2^n+\cdots +n^n}{n^n}$$## Expected error of simplifying to a geometric distribution February 13 While reading an answer related to solving a problem with a geometric distribution, the following question occurred to me.The answer gives two possibilities for replying the OP's question. In the second one (Changing number) he's actually using a geo You Might Also Like • I have run into some confusion while reading Newman Bak's Complex Analysis.The text states that if we wish t ... • What does weak convergence in$L^{2}(0,T;H^{-1}(\Omega))$means?$\Omega$is open, bounded, has boundary smoo ... • Introduction:I have proved the following:Suppose that Poisson events are occuring at the constant rate of$\ ...
• We are in $M_{n\times n}(\mathbb{R})$. Define $<A,B>=tr(AB^t)$. First I had to prove that this was ind ...
• When reading up on graph theory, I came across this puzzle and on further investigation, learned that a gene ...
• Suppose we have two finite sets $A,B\subset\mathbb Z$. I am interested in an upper bound on the number of tr ...
• Given an elliptic curve with a Weierstrass equation, is there any easy way to see whether it has got an isog ...
• I'm looking for a book on BILP, which focuses on algorithms / solutions methods. So far, I only found the fo ...
• Can you help me with this limit? It is one side limit. Please if it is possible tell me some trick(formula) ...
• Let T = {1, 2, 3, 4} and A = T * T. We can define a relation R on A; (a,b)R(c,d) <=> (a/b)=(c/d)For ex ...