general
Distribute black and white balls to maximize probability
Take the following problem: You have 100 balls (50 black balls and 50 white balls) and 2 buckets. How do you divide the balls into the two buckets so as t...
Apr 11, 2026
Archive: General
general
Is there a way to use a calculator for logarithmic form equations that aren't base 10 or base e?
Is there a way to use a calculator for logarithmic form equations that aren't base 10 or base e? I just find this really hard to believe and quite un...
Apr 11, 2026
general
Do four noncoplanar points determine space?
The title says it all. In the same way that: Two distinct points determine a line. Three noncollinear points determine a plane. My question is: Do four no...
Apr 11, 2026
general
Intuitive explanation of why the modified Gram-Schmidt is more stable than the classical one?
This may be an old question, and there are certainly some related posts which I will mention below. However, there seems no clear answer to me yet. The qu...
Apr 11, 2026
![partial derivative of matrix equation [duplicate]](https://news.conceivablytech.com/uploads/partial-derivative-of-matrix-equation-duplicate_720.jpg)
general
partial derivative of matrix equation [duplicate]
I want to see the following step in greater detail: $$\nabla_x~\bigg[(\vec{x}-\vec{\mu})^TP^{-1}(\vec{x}-\vec{\mu}) \bigg] ~~~~~(3)$$ $$= P^{-1}(\vec{x}-\...
Apr 11, 2026
general
Finding Particle Distance with Acceleration Function
I'm having a difficult time figuring out this problem. I'm thinking that you will need to solve the anti-derivative to get the velocity, and the...
Apr 11, 2026
general
Field extension of a finite field
Let $E$ be an extension field of a finite field $F$ , where $F$ has $q$ elements. Let $a \in E$ be algebraic over $F$ of degree $n$. Prove that $F(a)$ has...
Apr 11, 2026
![Number of multiples of 2 or 3 in range [1,100]](https://news.conceivablytech.com/uploads/number-of-multiples-of-2-or-3-in-range-1-100_720.jpg)
general
Number of multiples of 2 or 3 in range [1,100]
I am reading the problem: How many numbers between $[1, 100]$ are multiples of $2$ or multiples of $3$? (Caution to avoid double counting) My approach: Nu...
Apr 11, 2026
general
Find the limit points and exterior points of the following
Let $X=\mathbb R$, with the usual metric on $\mathbb R$ and $A=((0,1)\cap \mathbb Q)\cup$ {$2,3$}. Find the limit points of $A$, exterior points of $A$, $...
Apr 11, 2026
general
Deriving the sine function
How can the sine function be derived/proven? The definition for $\sin(x)$ is of course given as $\frac{\text{opposite}}{\text{hyoptenuse}}$ of a right-ang...
Apr 11, 2026
