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How to solve a bimatrix game?
Given a bimatrix game of $$\left(\begin{matrix}(0,-1) & (0,0)\\(-90,-6)&(10, -10)\end{matrix}\right)$$ Source How to find the nash equilibrium str...
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Finding the angle between two points
First of all, I am doing some mathematical background information for a software I am creating. What I want to achieve is the point on an object rotating ...
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What does "subject to" mean in math?
For instance, I saw the expression in the Wikipedia article on Lagrange multipliers: maximize $f(x, y)$ subject to $g(x, y) = c$ What does "subject to" mean?
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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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