Sorry if my question is poorly explained. Basically I want the name of the shape that always looks like a sphere in 3 dimensions when fed into 3d space st...

I'm preparing for the ACTM Sate contest, and I stumbled across this problem. I've never learned how to decipher equations like this, so could so...

Suppose we pick a random real number between 0 and 1 and call it $x$. There are $2^{\aleph_0}$ possible values, so the chance of picking any specific numb...

In this image I have counted 14 but others say 18. Is there a method to check exactly?

Let $A\in M(\mathbb F)_{n \times n}$ Prove that the trace of A is minus the coefficient of $\lambda ^{n-1}$ in the characteristic polynomial of A. I had s...

Let $p(z)=2z^4-2z^3+2z^2+7$. I'm trying to determine the number of roots of $p(z)$ that lie inside $\{z\in\mathbb{C}:|z|<2\}$ I used Rouche's...

For $x > 0$, the graph takes on a parabola-like shape. Is there a method to algebraically and not graphically determine the vertex of the graph? Desmos...

Is there any elementary way to solve (i.e. not involving derivatives etc.) $x^6 - 6x + 5 > 0$ ? I can divide it two times by $(x - 1)$ to get $x^6 - 6x...

The function is $f(x, y) = x^2 + 2y^2 + 2xy - 4y + 15$ here's what I did, $$f_x = 2x + 2y$$ $$f_y = 4y + 2x - 4$$ $$f_{xx} = 2$$ $$f_{yy} = 4$$ $$f_{...

The question is: what is the indefinite integral: $\int \sin^2(kx) \, \mathrm dx$? I get the correct answer using trig identities to change the $(\sin(kx)...