I couldn't find out the exact value of this operation. $$1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32 \dots$$ You go 1 units right on the number line, half of i...

I am taking a course on abstract algebra, and the lector defined $T$ to be a set, and defined $G$ to be the set of all bijections from $T$ to itself: $$ G...

Let $A$ be an $m\times n$ matrix and $b\in \Bbb R^m;b\neq 0$. Pick the correct options: The set of all solutions of $Ax=b$ form a vector space. If $u,v$ a...

I am having some troubles with understanding some aspect of the problem below: Placing 3 INDISTINGUISHABLE rooks on a 6x6 board such that no two rooks att...

The book that I'm reading states that the identity permutation is an even permutation. But it gives no example, and at this point, I'm confused....

How do I show that $$\int_a^bf(x)dx - I_1 = - \frac{h^5}{90}f^{(4)} (\xi)$$ with $\xi \in [a,b]$ and $$I_1 := \frac{h}{3}(f(a) + 4f\left( \frac{a+b}{2}\ri...

Proof. Let $G$ be a group, and $x,y\in G$. Then, we have $xy(xy)^{-1}=e$, where $e$ is the identity element of $G$. Multiplying on the left by $x^{-1}$, w...

I'm in the process of learning game development and have a question regarding a simple rotation. So far, I'm visualizing the rotation as such: I...

From the existness and uniqueness Theorem,the initial value problem $$y'=3x(y-1)^{1/3} , y(3)=-7$$ has a unique solution on some open interval that c...

Alright so I have a cone with radius 59.75 and height 60.75. Given this I can find the volume of the cone. Now I need to find the volume of a cone that is...