general
Exponent outside parentheses, how interpret?
In this Khan Academy video $(a^3)^{^2}$ is interpreted as $a^6$. Considering the placement of the outer exponent, shouldn't it be $a^{3^2}=a^9$ inste...
Apr 12, 2026
Archive: General
general
Is it possible for a linear system to have infinitely many solutions without the augmented matrix having a row of zeroes?
Is it possible for an augmented matrix of a $4 \times 4$ system to have infinitely many solutions without having a row of zeroes? I think it's not bu...
Apr 12, 2026
![How do I prove that the sum of a rational and irrational number is irrational? [duplicate]](https://news.conceivablytech.com/uploads/how-do-i-prove-that-the-sum-of-a-rational-and-irrational-number-is-irrational-duplicate_720.jpg)
general
How do I prove that the sum of a rational and irrational number is irrational? [duplicate]
How do I prove that the following proposition is true? The sum of any rational number and any irrational number is irrational. I am currently a beginner a...
Apr 12, 2026
general
Can Mutually Inclusive events be dependent?
Existing Understanding: I understand that mutually exclusive events cannot be independent. If A and B are independent, the probability of A and B both hap...
Apr 12, 2026
general
Calculate point, given x, y, angle, and distance
Excuse my ignorance and use of incorrect terms, but... I have x and y coordinates, and the angle that the entity is facing on a 2D plane. I want to find t...
Apr 12, 2026
general
How tangent line gives us a slope at one point?
As we know that slope is the rate of change of one quantity with respect to the other. So we do always need two points to find the slope. But then its con...
Apr 12, 2026
general
What is the quickest way to find the sum of $x$ and $y$ in this system of equations?
$$ \begin{align*} 2\left( x-\frac{1}{3}\right) -\frac{3}{2}\left( y-\frac{1}{6}\right)&=0 \tag 1\\ 3\left( y-\frac{1}{2}\right) +\frac{8}{3}\left( x-\...
Apr 12, 2026
general
How to find how usual or unusual a probability is?
guys. Just doing some homework and I came I across a problem that I did not know how to do, Could someone explain, Please and thank you. Problem: a group ...
Apr 12, 2026
general
Example of a meromorphic function in $\mathbb{C}$ but not in $\mathbb{C}_{\infty}$
I need to produce an example of a meromorphic function on $\mathbb{C}$ but not meromorphic on the Riemann sphere $\mathbb{C}_{\infty}$. Will this work: $f...
Apr 12, 2026
general
Computing the angle between two vectors using the inner product
Question is: Consider $\mathbb{R}^3$ with the inner product $\langle u1,u2\rangle=x_1x_2+3y_1y_2+z_1z_2$ where $u_1=(x_1,y_1,z_1)$ and $u_2=(x_2,y_2,z_2)$...
Apr 12, 2026
