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Convert Degrees of Latitude to Feet
I need to check this formula I have to compute the distance of a point with latitude $lat$ from the equator: $$ \mathrm{feet} = \mathrm{lat} * 10000 \time...
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what is the derivative of $\ln(2x^2)$
In finding the derivative of $\ln(2x^2),\;$ I have applied the chain rule and obtained $2x / x^2.\;$ Is this correct? If not could some please explain how...
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Finding Tens Digit of Very Large Number
I think I can figure out the leading digit or the units digit, but how would one find the tens digit of, say, $$7^{100}$$ without having a calculator or w...
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Why isn't $\arctan \theta = \frac{\arcsin \theta}{ \arccos \theta}$?
Why is it that $\arctan \theta \neq \dfrac{\arcsin\theta}{\arccos\theta}$ ? Thanks for your help in figuring this out.
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Number of distinct connected digraphs with 4 vertices and 6 edges
I have been looking at graphs representing how people or things can move between states (vertices). Each directional move from one vertex directly to anot...
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Solving P vs NP with computer
Is it possible to build a computer program that would (eventually) bring a solution to the P vs. NP question?
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Textbook confusion in 8-bit representation
A textbook I'm following says the following in the section 8-Bit Representation of a Number: "Now consider the two’s complement of an integer n that ...
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How to prove a set is open
The problem is to prove $\{(x,y) \mid 2 \lt x^2 + y^2 \lt 4\}$ is open. So I have an arbitrary circle in this set, with a radius greater than $2$ and less...
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Understanding the definition of domain in Complex Analysis
I have a definition in my book which states, "a nonempty open set that is connected is called a domain." I understand what an open set is (a set containin...
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If a graph has a chromatic number $k$, then for any color there is a vertex of that color that has as neighbors all the other colors
Let $G$ a graph and $k= \chi(G)$. Prove that for all $k$-colorings of $G$ and for all colors $i \in \{1,\ldots,k\} $, there exists $u \in V(G)$ of color $...
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