I think I have some good understanding of complex numbers. They are represented as a+ib where a,b are reals, and i² = -1. More precisely, multiplying a co...

Find the minimum distance from the origin to the intersection of $xy=6$ with $7x+24z=0$. Solution: We should minimize $f(x,y,z)=x^2+y^2+z^2$ subject to th...

If I'm not mistaken, in a ring with identity, the additive identity cannot have a multiplicative inverse. I'm trying to prove this. Here's ...

I am confused about this question. It says Disprove the statement by giving a counterexample. For all positive integers $n$, $n^2- 2n$ is positive. Then i...

What is the equation of the circle which passes through the point $(0,2)$ with radius $4$ and whose center lies on the line $y = x$?

This is going to be a long post due to information that I am going to have to present. A brief outline in what I am asking is, that I need to integrate a ...

Given the figure in this image (I don't know the correct name in English. I wish to know the length of the 4th side. How to calculate it and what...

If I consider the field extension $K=Q(\sqrt{5})$ and choose a basis , for example {$1,\sqrt{5}$} . I do not really understand the relation between calcul...

Solve the equation: $$\sqrt{3x-2} +2-x=0$$ I squared both equations $$(\sqrt{3x-2})^2 (+2-x)^2= 0$$ I got $$3x-2 + 4 -4x + x^2$$ I then combined like term...

How do I get rid of this square root so that I can integrate it? $$S = 2 \pi a ^2 \int_0^{\sqrt{2}} t \sqrt{4t^2 + 1}\ dt$$