MethodMath Math Questions and Answers

Theres this quote going around:

"If you get 1% better every day, after one year you'll be $1.01^{365} \approx 37.78$ times better!"

And the negative version: "If you get 1% worse every

Im a teacher and my students showed me something weird. If you type:

into different calculators, you get different answers! My Casio says 1 but my phone calculator says

If $0.\overline{9} = 1$, then does $0.\overline{8} = 0.\overline{9}$?

Wait no thats dumb. But hear me out:

If $0.999... = 1$, then what about $0.0999...$? Is that $0.1$?

And what about

This trick is all over Instagram:

To multiply $23 \times 47$:

Total: $800 + 140 + 120 + 21 = 1081$

But isnt this just FOIL? $(20+3)(40+7)$ expanded? So its not really a "trick" but

I'm studying A-Level calculus and I can state the Mean Value Theorem:

If $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, then there exists $c \in (a,b)$ such that:

I need to understand the logistic growth model:

where $r$ is the growth rate and $K$ is the carrying capacity.

I know this is a separable ODE, but I'd

I am studying linear algebra and I understand the formal definition:

For a square matrix $A$, if $A\mathbf{v} = \lambda\mathbf{v}$ for some scalar $\lambda$ and non-zero vector $\mathbf{v}$, then $\lambda$

In the $8 \div 2(2+2)$ debate, I keep hearing about "implicit multiplication" or "multiplication by juxtaposition" having higher priority than normal multiplication.

The argument is that $2(2+2)$ means $2$ is implicitly multiplied