updates
Find all real solutions of $6^x+1=8^x-27^{x-1}$
Find all real solutions of $6^x+1=8^x-27^{x-1}$. Things I tried: We want solutions of $$2^x3^x+1 = (2^x)^3-\frac{(3^x)^3}{27}.$$ Write $a=2^x$ and $b=3^x$...
Apr 17, 2026
Archive: Updates
updates
Is proofwiki.org a reliable source of math proofs?
Is proofwiki.org a reliable source of math proofs? I'm inspired by this question about wikipedia. This site has much less traffic and not very known,...
Apr 17, 2026
updates
Rotate a Vector by Quaternion
I'm trying how to work out how to Rotate a Vertex using Quaternions, using a scientific calculator, or on paper. Exam preparation. My lecturer has gi...
Apr 17, 2026
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Characteristic time or time constant for diffusion (heat) equation
Is there a time constant or a characteristic time it takes for the diffusion equation $$\frac{\partial \psi(\vec{x}, t)}{\partial t} = D \nabla^2 \psi(\ve...
Apr 17, 2026
updates
average number of moves needed to complete a game of FreeCell
Sometimes finishing a game of FreeCell takes me 10 minutes, other times just one minute. I know that all but one of the FreeCell deals in windows can be w...
Apr 16, 2026
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Find a solution or show that there is none: $x^2 \mod 7 = 3 \; (x\in \mathbb{Z})$
Find a solution or show that there is none: $x^2 \mod 7 = 3\;(x\in \mathbb{Z})$ I've tried different ways to approach this problem, such as rewriting...
Apr 16, 2026
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Square divided by absolute value
First time posting on Math SE, with kind of a basic algebra question. Question Does the relation: $$\dfrac{(ab)^2}{|ab|} = \left|ab\right|$$ with $a,b \in...
Apr 16, 2026
updates
Equivalence classes and equivalent relationship
We define a relation S on the set of all integers by: $nSk$ iff $n^2$ $=$ $k^2$ Decide if S is an equivalence relation. If so, what is the equivalence cla...
Apr 16, 2026
updates
Limits for sine and cosine functions
Recently I took a test where I was given these two limits to evaluate: $\lim_\limits{h \to 0}\frac{\sin(x+h)-\sin{(x)}}{h}$ and $\lim_\limits{h \to 0}\fra...
Apr 16, 2026
![How does one solve trig functions by hand? [duplicate]](https://news.conceivablytech.com/uploads/how-does-one-solve-trig-functions-by-hand-duplicate_720.jpg)
updates
How does one solve trig functions by hand? [duplicate]
First of all, I am not very intelligent, so the question I am about to ask would sound inane--but I am just curious, that's all. We were always used ...
Apr 16, 2026
