# All Questions

97 views

### $f\cdot g=0 \implies f=0$ or $g=0$.

I know this is kind of an obvious thing to say: Let $f,g \in \Bbb K[x]$, then $$f\cdot g=0 \implies f=0 \text{ or } g=0$$ But to my surprise I couldn't prove it. What's a simple way to do this?
17 views

### Within what angle does she need to throw her stone at to hit her opponents?

In curling, it is often necessary to hit and displace an opponent’s stone to win the end. Olivia would like to hit her opponent’s stone with her own stone. If she releases her stone at the hog line, ...
15 views

### Question on complete spaces, longer, more specific question.

Let $S \subset C^2[0,1]$ (set of two times differentiable functions $f(x)$ on $[0,1]$) which satisfy the following: $$\int_0^1 f(x)\,dx\leq3$$ Question is $(S,d)$ is a complete metric space, ...
20 views

### Singularities of an integral

We have the integral : $$I(t)=-i\int_0^\infty \frac{\log\left[\frac{\sin(t\log\sqrt{1+ix})}{\log(1+ix)} \right ]-\log\left[\frac{\sin(t\log\sqrt{1-ix})}{\log(1-ix)} \right ]}{e^{2\pi x}-1} \, dx$$ I ...
11 views

### What is the difference between a lower bound and an upper bound in an Interval Graph $G(I)$

As I know that the maximal size of an independent set $IS$ of an interval Graph $G$ is a lower bound. Now what is exactly the upper bound, and when they might be equivalent to each other. are there ...
3 views

### How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
16 views

### How to get the equation for a one-to-one function given the coordinates. [on hold]

The one-to-one function is defined as: f(x)={(-8,4)(-6,1)(3,-6)(8,-2)}
28 views

### Tricky word problem

Two crews were assigned the job of setting a total of $960$ conduit hangers. By the time the job was completed, one crew had set on $7/8$ as many conduit hangers as the other crew. How many conduit ...
17 views

### Directional derivative for differentiable function

In the directional derivative formula $$\frac{\partial f}{\partial v} = \nabla f \cdot v$$ why must $v$ be a unit vector?
15 views

27 views

### conditional expectation

I got somewhat confused about this condition expectation here. Can anyone help me please? Let $v_1,v_2,v_3$ be 3 continuous random variables from an i.i.d distribution, does the equality below ...
35 views

### show that the function $\{x_n\}\mapsto \sum_{n=1}^\infty 2^{-n}x_n$ is continuous

This problem comes from an old Preliminary exam: Consider the space $[0,1]\times [0,1]\times \cdots$ (the countably infinite product of $[0,1]$ with the product topology) An element of $X$ may be ...
16 views

### Geometric meaning of directional derivative

Suppose $f(x,y)$ is a differentiable function and $v = (a, b)$ is a vector. If $(x_0,y_0) \in D_f$ and $\frac{\partial f}{\partial v}(x_0,y_0) = 0$. What is the meaning of this? Along the direction ...
19 views

### Poisson Distribution Word Problem

The image you are looking is a solution to a problem that has been cropped out. I'm certain the solution is incorrect since it does not include P(X=2). Just to be on the overly safe side, I decided ...
11 views

### Implicit function theorem conclusion notation?

I am working through implicit function theorem for the first time, and I have the following understanding. Given a system of $n$ equations, f_i(x_1,\dots ,x_m,y_1,\dots , y_n)=0,\ \ \ ...
In $7^{th}$ grade, in order to learn divisibility, memory, and focus, my math teacher had my pre-algebra class play a game called Frazzle. To play the game Frazzle, each person went around the room ...