I was asked this on an aptitude test recently Determine the next number in the sequence: $-2, 3, 27, 69, 129, \ ..$ A: $178$ B: $207$ C: $288$ D: $312$ I&...

How to show that it is impossible to have a cuboid for which the volume, the surface area and the perimeter are numerically equal ? The perimeter of a cub...

I just noticed there is a similarity between logic operations on propositions and the operations of set theory. It seems: $$\begin{array}{llll} \textrm{di...

Is this a correct expression of the mathematical statement, "Every positive real number has exactly two square roots."; expression: ∀x∃a∃b((x>0) → (a!=b)∧...

How do I construct a change of basis matrix? For example in $\mathbb R^3$, how to construct matrix changing basis from $A$ to $B$? $A=\begin{pmatrix} 1 \\...

I can't solve this problem, spent a lot of time, just no result $$ x^4-7x^3+14x^2-7x+1=0 $$ PLEASE HELP

Say you had a 3x3 grid, and could pick any square to start with. From that square, choose an adjacent or diagonal tile to move to, and draw an arrow to it...

I've read somewhere that the sine and cosine functions can be fully described by this theorem: $\sin(0) = 0, \cos(0) = 1$ $\sin(a-b) = \sin(a)\cos(b)...

We know that, in a triangle ABC, sine law and cosine law are well developed formulas. My questions are:- Why is that there is no tangent law? (If no, just...

Solve $\cos 2x - \sin x = 0$. \begin{align}\cos 2x = 1 - 2\sin^2 x &\iff 1 -2 \sin^2 x - \sin x = 0 \\ &\iff -2 \sin^2 x - \sin x + 1 = 0 \\ &...