The product has only positive factors so it has zero as lower bound. Also the product is decreasing as all its factors are less than one. In conclusion th...

In the Eucledian 3D space, only one axis of rotation is possible at one time for a body, such as a sphere. So we have a 2D plane of rotation perpendicular...

I recently read about superperfect numbers: $σ^2(n) = 2n$, where $σ(n)$ is the divisor function. I saw that the first few numbers were: $2, 4, 16, 64, 409...

Question: What is the area of the region enclosed by the curves: $$2y = 4\sqrt{x},\quad y = 3,\quad \text{and} \quad 2y + 2x = 6. $$ I have tried calculat...

I don't understand this question. Verify that the indicated function $y=\phi(x)$ is an explicit solution of the given ODE. Consider $\phi$ simply as ...

With given category $\mathcal{C}$ and its objects $A$ and $B$, a hom-set $\hom_\mathcal{C}(A, B)$ is the collection of all morphisms from $A$ to $B$. Ther...

Question: A sphere of radius $R$ has total mass $M$ and density function given by $ρ = kr$, where $r$ is the distance a point lies from the centre of the ...

Consider the differential forms on $\mathbb{R}^3$, $\omega_1 = xy \space dx + z \space dy + dz$ , $\omega_2 = x \space dy + z \space dz$. I need to determ...

There are different categories of numbers that we use every day. Integers that written in decimal notation have $1, 2$ or $5$ as the leading figure, follo...

For $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blac...