general
Find all points on which a function is discontinuous.
$ f(x,y) = \begin{cases} \dfrac{x^3+y^3}{x^2+y^2} &\quad\text{if} [x,y] \neq [0,0]\\[2ex] 0 &\quad\text{if}[x,y] = [0,0]\\ \end{cases} $ The only ...
Apr 21, 2026
Archive: General
general
Change of an angle in a triangle
I've a triangle ABC. Where AC is the hypotenuse and the angle ABC is 90 degress. AB is $15 km$ and changes with a speed of $600 km/h$. BC is $5 km$ a...
Apr 21, 2026
general
What's the difference between Independent Event and Mutually Inclusive Event?
What's the difference between Independent Event and Mutually Inclusive Event? Are all Independent Events mutually inclusive or vice verse?
Apr 21, 2026
general
"faces" of a non-planar graph
Good afternoon, I have a question concerning concepts in graph theory. Graph theory is a field quite strange to my knowledge, so my question is maybe stup...
Apr 21, 2026
general
Volume of a solid formed by 3 cylinders
I am trying to find the volume of the solid enclosed by three cylinders given by $x^2+y^2=1$, $x^2+z^2=1$, and $y^2+z^2=1$. I'm supposed to be using ...
Apr 21, 2026
general
Vertical Tangent line with Implicit Differentiation
The original equation is $$x^2-2xy+y^3= 4$$ and I hope the derivative to be $$\frac{dy}{dx} = \frac{2(x-y)}{2x-3y^2}$$ I know the vertical tangent is when...
Apr 21, 2026
general
When was $\pi$ first suggested to be irrational?
When was $\pi$ first suggested to be irrational? According to Wikipedia, this was proved in the 18th century. Who first claimed / suggested (but not neces...
Apr 21, 2026
general
Common tangent to two circles
Find the equations of the common tangents to the 2 circles: $$(x - 2)^2 + y^2 = 9$$ and $$(x - 5)^2 + (y - 4)^2 = 4.$$ I've tried to set the equation...
Apr 21, 2026
![Formula for number of 6 letter words from English alphabet if there is repetion and ordering [duplicate]](https://news.conceivablytech.com/uploads/formula-for-number-of-6-letter-words-from-english-alphabet-if-there-is-repetion-and-ordering-duplicate_720.jpg)
general
Formula for number of 6 letter words from English alphabet if there is repetion and ordering [duplicate]
Is there a formula or method to find the number of 6-letter words from the English alphabet if repetition is allowed, but they must appear in alphabetical...
Apr 21, 2026
general
What is the "official" name for these boolean algebra rules?
In boolean algebra, we have the following simplification rules: $$P + (\ldots P \ldots) = P + (\ldots 0 \ldots)$$ and $$P \cdot (\ldots P \ldots) = P \cdo...
Apr 21, 2026
