general
Calculating Lagrange error of a Taylor polynomial approximation
So I am slightly confused when it comes to finding the error of a Taylor series approximation. I know the equation is : $ E_n(x)=\frac M {(n+1)!}(x-a)^{n-...
Apr 09, 2026
Archive: General
![how to find the cube roots of $-27i$? [closed]](https://news.conceivablytech.com/uploads/how-to-find-the-cube-roots-of-27i-closed_720.jpg)
general
how to find the cube roots of $-27i$? [closed]
i know to solve the question if it is given a+ib . but for this kind of question i can't solve it because it is only given 'ib' . for this ...
Apr 09, 2026
general
Moment of inertia of a sphere
My physics textbook said that the moment of inertia of a sphere is $\frac25mr^2$ where $m$ and $r$ are the mass and the radius of the sphere respectively....
Apr 09, 2026
general
Is a parallelogram with equal sides necessarily a rhombus? Is one with 4 right angles (or congruent diagonals) necessarily a rectangle?
We know that a rhombus is a parallelogram that has 1) equal sides and 2) diagonals that are perpendicular to each other. If, for instance, we are a told t...
Apr 09, 2026
general
How long would it take for light to go through a human eyeball and back to the other side
I couldn't find any TAGS that fit my question... I don't know if I'm doing this correctly. I want to know how long a "twinkling of an eye" ...
Apr 09, 2026
general
Proving that a subgroup of a finitely generated abelian group is finitely generated
A question says: Using the isomorphism theorems or otherwise, prove that a subgroup of a finitely generated abelian group is finitely generated. I would s...
Apr 09, 2026
general
Why Markov matrices always have 1 as an eigenvalue
Also called stochastic matrix. Let $A=[a_{ij}]$ - matrix over $\mathbb{R}$ $0\le a_{ij} \le 1 \forall i,j$ $\sum_{j}a_{ij}=1 \forall i$ i.e the sum along ...
Apr 09, 2026
general
What does "closed under ..." mean?
What exactly is meant by "closed under fill in the blank"? Thanks.
Apr 09, 2026
general
How to prove an Inequality
I'm beginner with proofs and I got the follow exercise: Prove the inequality $$(a + b)\Bigl(\frac{1}{a} + \frac{4}{b}\Bigr) \ge 9$$ when $a > 0$ a...
Apr 09, 2026
general
Describing sine in terms of cosine
The problem says: Show if $\sin{\theta} = \sqrt{1 - \cos^2{\theta}}$ if $\sin{\theta}$ is positive and $\sin{\theta} = -\sqrt{1 - \cos^2{\theta}}$ if $\si...
Apr 09, 2026
