Consider the vector differential equations \begin{equation} \mathbf{x}^{\prime}=\mathbf{A}(t)\cdot\mathbf{x}\tag{1} \end{equation} and \begin{equation} \m...

I am given these three problems: I think I understand the first question, it is basically asking me to find the formula for the sum of the first odd $n$ c...

I'm trying to solve a problem where I need to find a chord and the practically only information that I've been given is the length of the arc th...

How we can find exact value of $\sin(10^\circ)$? I tried trigonometric ways but I get this equation: $\ 8y^3-6y+1=0$ and $y = \sin(10^\circ)$ and all the ...

Whilst trying to explain the concept of an isomorphism to a non-mathematician, it didn't seem to suffice to me to just give a precise definition, or ...

There exists fast algorithm to approximate length of 2D vector - Alpha max plus beta min algorithm. It says that $\alpha\cdot\max(x,y)+\beta\cdot\min(x,y)...

I don't fully understand the steps to reach the answer. I've plotted the graph and I found out that the graph is an odd graph and that after ref...

Our instructor had given us an equation and we should get the derivative of it. But even him, he is confused what to do (funny college instructor) if we s...

Mutually exclusive events are also independent or not ? can some one explain with an example? Is it compulsory for independent event to be mutually exclus...

I have the following system: $$\begin{cases}\frac{dx}{dt} = (x+6)(x-7)(y-7)\\ \frac{dy}{dt} = (x^2-9)(y+5)\end{cases}$$ I have solved the system using the...