I was wondering how many different possible combinations are there for unlocking an Android phone. In order to do this, you have to choose a path from a g...

Let us start with the obvious. I know the formulae for angles. I know how to apply them. I also know the formulae involving $e$. But I don't understa...

If the ratios sine, cosine and tangent are applicable to right angled triangles, then how can they be applicable for the angles of 0, 180 and 360 degrees?...

I am trying to solve the following: $$y''(x)=\frac{4}{3} y(x)^3 y'(x)$$ given that $y(0)=1$ and $y'(0)=1/3$. This is a link to Wolfram Alp...

I would like know whether a circle is intersecting an ellipse. Here ellipse equation is $$Ax^2 + Bxy + Cy^2 + dx+ey + 1 = 0,$$ and the circle equation is ...

Good day to you all. I have a little problem I have been banging my head on for a while. I have come to think that it is impossible, but I hope you can sa...

Does the number of permutations of $n$ objects, $r$ alike of one kind and $n−r$ alike of another kind, always equal the combinations of n different object...

The wife and I are sitting here on a Saturday night doing some algebra homework. We're factoring polynomials and had the same thought at the same tim...

I understand how to find a limit. I understand the concept of the $\epsilon$-$\delta$ definition of a limit. Can you walk me through what we're doing...

Having read the classical proof of the existence of an Algebraic Closure (originally due to Artin), I wondered what is wrong with the following simplifica...