In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$...

Given a square $n$-th order matrix, say $A=[a_{ij}]$, $a_{ii}$'s are referred to as diagonal entries $a_{ij}$'s, $i\neq j$ are referred to as of...

Looking into the intersection of abstract algebra and geometry, it's well known that it is impossible to double the cube with ruler and compass, sinc...

I've been studying Calculus of Variations and I came a cross with the term "perturb" in my study material, but the term was not defined. The sentence...

I have the following matrix: \begin{bmatrix}1&2\\3&4\end{bmatrix} and I'd like to find the vectors that span the kernel. The book I'm re...

I have checked the question upon this topic, but everytime the answer is the parity of zero is even because $0\times2=0$, and it is between two odd number...

Sine is usually defined as the ratio of the opposite side to an angle to the hypotenuse in a right angle triangle. Another common definition is based on t...

I am to find the vertical and horizontal asymptotes of this given function: $$f(x) = \frac{e^x(x + 1)}{e^{2x}(x^2 - 1)}$$ To find the vertical asymptote,I...

How this equality is verified. $$\arctan(2\sqrt2)+2\arctan(\sqrt2)=\pi$$

A triangle has angle measures of 15, 30, and 135 degrees. The side opposite the 15 angle is x feet, the side opposite the 30 angle is y feet, and the side...