Let $P_n$ be the set of polynomials of degree at most $n$ with real coefficients. Is the set of polynomials of the form $p(t) = a + t^2,$ such that '...

It is usually stated in Precalculus textbooks that in polar coordinates when a relation between $r$ and $\theta$ passes a symmetry test then the curve des...

The question: Let $X$ and $Y$ be two sets, and let $S$ be an equivalence relation on set $X$ and $T$ be an equivalence relation on set $Y$. Define a relat...

I need to prove the following: Prove that $A\cup \!\, \varnothing \!\,=A$ and $A\cap \!\, \varnothing \!\,=\varnothing \!\,$ It's my understanding th...

Say I have a general tetrahedron, or in fact only the tip of a tetrahedron, being three triangles in 3-space sharing a single vertex and sharing edges pai...

I found this amazing wall clock picture on the internet but I really don't know a few things. I don't know what's $B'_L$, 3, ...

I have proven that the sum of any two irrational numbers is not always irrational and that a rational plus an irrational is irrational, however I am not s...

Calculate Inverse Discrete Time Fourier Transform of the following where $|a| < 1$: $$ X(e^{j\omega}) = \frac{1-a^2}{(1-ae^{-j\omega})(1-ae^{j\omega})}...

A particle moves in a straight line according to the rule $x(t)=t^3-2t+5$, where $x(t)$ is given in meters and where $t$ is given in seconds. Determine th...

What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$ I tried to factorize $n^3+100$, but $100$ is not a perfect cube. I wish it wer...