# All Questions

12 views

### Tangent of Circles

$k_1$ is a circle with center $O_1$ and radius $r_1$. Similar for $k_2(O_2;r_2)$. $r_1 < r_2$. $AB$ and $CD$ are tangent lines to $k_1$ and $k_2$. Prove that $AP=DQ$.
16 views

6 views

### Compute a sum with finite and infinite elements

I would like to compute the following summation: $$s = \sum_{i=1}^n a_i \, \Phi^{-1}(u_i)$$ where $\Phi^{-1}$ is the inverse of the standard Gaussian distribution function, $a_i$ are some real ...
4 views

9 views

### Finding the average temperature over a certain amount of time

I'm assuming you use some time of equation such as the Mean Value Theorem of Integrals to find the average here, but the equation is not represented in the form of an integral, so I'm not entirely ...
10 views

### Question of probability .

the probab. that any one of the men A1,A2,A3,A4 is alive after 95 yr.s of age is 1/2 . the probab. that A1 will die at the age of 95 and will be the first to die is?
13 views

The width of a rectangular TV screen is 22.9 in longer then the height. Of the diagonal is 60 in find dimensions of the screen. 1. Using Pythagorean theorem express the given information in the ...
25 views

### Sumo Wrestler partial round robin tournament

A coworker of mine is a big fan of Sumo. He recently came to me with a problem he's been wondering about for years: In a professional sumo tournament there are 42 wrestlers. A tournament lasts 15 ...
27 views

### Error in linear algebra proof

In "The linear algebra a beginning graduate student ought to know" by Golan there is a proof that if $V$ is a vector space of over a field $F$ and $D$ is a maximal linearly-independent subset of $V$ ...
17 views

### Is the function max{x,y} defined if x and y take equal values?

If x and y take the same values, will the function return a result? I am asking this as maximum means greatest of two values. So if both the values are equal, the existance of the function confuses ...
10 views

### The geometry meaning of Riemann–Stieltjes integral

Maybe my question seems so strange but I want to know what is the geometry meaning of Riemann stieltjes integral ??
11 views

### What questions are independent from the axiom of constructibility?

Wikipedia gives a list of statements true in L which would be true also for set theory if the axiom of constructibility (V=L) holds. However I wonder about the converse: Are there any important open ...
21 views

### $X_n\rightarrow X$ in probability, but $\mathbb{E}(X_n)$ does not converge to $\mathbb{E}(X)$ [duplicate]

What is an example of a sequence $X_1,X_2,...$ such that $X_n\rightarrow X$ in probability, but $\mathbb{E}(X_n)$ does not converge to $\mathbb{E}(X)$?
21 views

### In a connected graph, if the maximum path you could make is of length 100, and there are two paths of length 100, aren't they the same path?

Here's the question: Let G be a connected graph. (Remember that this means that every two vertices of G can be joined by a path starting at one and ending at the other.) Suppose also that G ...
9 views

14 views

### Express one constant as a linear combination of two other constants?

Let a,b,n,m,o be nonzero rational scalars. How do I express o as a linear combination of n and m with coefficients a and b? Explicitly how to find a,b such that an + bm = o? I know how to do linear ...
10 views

### Finding volume of a cone given density

Let $C$ be the solid cone with the boundary surfaces $x^2 +y^2 = z^2$ and $z = 0$. The density of the solid at point $(x,y,z)$ is $z$. Find the volume of the solid using the integrals in both the ...
52 views

7 views

### Isomorphism from $SL_2(F_2)$ to Sym(3)

Can you help me find a isomorphism from $SL_2(F_2)$ to Sym(3). I supose that I have to use vectors. ex. $v_1 (1,0), v_2(1,1), v_3 (0,1)$, but I don't remeber how to do it.
15 views

### $p$-group acting on a finite set

Let $G$ be a $p$-group. Prove that if $G$ acts on a finite set $X$ and $p$ does not divide $|X|$, then $X$ contains some element that is fixed by every element in $G$. Any thoughts? I'm stumped ...
18 views

### How fast things con/diverge.

Is there some kind of standard listing for how fast common series converge/ diverge? For instance, is it true that this order holds (diverges faster closer to the top)? Pretend there's a ...
10 views

### Using var[ r ] = E[ r^2 ] − E[ r ]^2, obtain the formula σ^2 = w1^2σ1^2 + w2^2σ2^2 + 2w1w1σ12

Able to solve it using var(x)= E[(x-E(x))^2] but cannot get anywhere with this one
11 views

### Fourier inversion Lemma (Lars Hörmander)

I always like to have more than one proof for the same theorem. The other day I was browsing through my copy of Lars Hörmander's book on PDE (volume 1). When proving the fourier inversion formula (on ...

15 30 50 per page