\begin{align*} \frac{0}{0} &= \frac{100-100}{100-100} \\ &= \frac{10^2-10^2}{10(10-10)} \\ &= \frac{(10+10)(10-10)}{10(10-10)} \\ &= \frac...

A teacher asked me to prove the well known Crossbar theorem. I tried it in the following way:- Given: If $D$ is in the interior of $\triangle ABC$, then p...

I have some problems with this In response to an attack of 10 missiles, 500 antiballistic missiles are launched. The missile targets of the antiballistic ...

Please help me answering this problem! thank you :) Prove that for any nonsingular matrices $A$, $B$, and $C$, the equation $$(ABC)^{-1} = C^{-1}B^{-1}A^{...

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Suppose $\mathcal{A}$ and $\mathcal{B}$ are categories with products, and $T$ a functor between them. If $X$ and $Y$ are objects in $\mathcal{A}$, what do...

The simplification is: $$ \frac {r (1 + x)} {1 + 2x} $$ but I don't understand how one can arrive at the simplified formula from: $$ \frac { r } {1 +...

"When you draw a circle in a plane of radius $1$ you can perfectly surround it with $6$ other circles of the same radius." BUT when you draw a circle in a...

I am in Electronics Technician "A" School in the Navy and we are learning the basics of radars. In one module, we were exposed to this formula which confu...

I am new to the normal distribution topic. While I have understood and solved various different kind of questions, the normal distribution questions with ...