Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 112

Have I sufficiently demonstrated the answer? A point is reached on an inclined plane that lies on a circle in the time take to fall directly.

Here is my calculation. When $frac{1}{2}alphasin A t^2=OQ$, $frac{1}{2}alpha t^2=OP$ Therefore, $frac{OQ}{sin A}=OP$ and $frac{OQ}{OP}=sin A$...

Asked on 02/23/2021 by OpenSauce

0 answer

Prove the existence and uniqueness of the adjoint function of a linear function

Definition Let be $V$ and $U$ two vector spaces equipped with an inner product. So given a linear transformation $f:Vrightarrow W$ a function $f^*:Urightarrow V$ is...

Asked on 02/23/2021 by Antonio Maria Di Mauro

1 answer

Optimal Strategy in Dice Game

In a recent interview I received the following question (an optimisation/strategy game)...which left me a bit stumped. The rules of play, you start with 0 points, then: Roll three fair...

Asked on 02/23/2021

3 answer

Proof of the fact that the closure of a set always contains its supremum and an open set cannot contain its supremum

I would like to ask, if my proof checks out and is completely sound. Exercise 3.2.4 from Stephen Abbot's Understanding Analysis.$newcommand{absval}[1]{leftlvert #1 rightrvert}$Let $A$ be non-empty subset...

Asked on 02/23/2021

2 answer

Show that $mathbb{Z}/5mathbb{Z} = langle arangle$

Show that $mathbb{Z}/5mathbb{Z} = langle arangle$. I have that $a$ is an element of the non zero complex numbers $mathbb{C}^*$ and $a^{5}=1$ where $a neq...

Asked on 02/23/2021 by user723228

2 answer

Is there a translation-invariant way to assign probabilities to infinite subsets of $mathbb{Z}$?

There is no uniform probability distribution over the integers. But I’m wondering whether the next best thing can be constructed. My question is, is there a meaningful way...

Asked on 02/23/2021

1 answer

Understanding Slope Better

Recently, I have realized how much I have taken for granted in understanding the slope of a line and the slope of a curve in general. With that said, I...

Asked on 02/22/2021 by Taylor Rendon

2 answer

Different representations of the perspective projection matrix?

So in the textbook, we want to map $(x,y,z,1)$ to $big(frac{x}{1-frac{z}{d}}, frac{y}{1-frac{z}{d}}, 0, 1big)$. Since we are working with homogenous coordinates, this is the same thing as mapping...

Asked on 02/22/2021

1 answer

To derive quantity $k=frac{2-p^2}{p+2}$ for positive rational $p$ such that $p^2>2$ and $(p+k)^2>2$

I am reading Baby Rudin and stuck at one small point.$A$ is set of all positive rationals $p$ such that $p^2<2$ and $B$ is set...

Asked on 02/22/2021 by Believer

3 answer

Question about theorem on homotopic curves for a holoorphic function. (stein and shakarchi)

The following theorem, is about the integral over two homotopic curves for a holomorphic function being equal in stein and shakarchi.: I don't...

Asked on 02/22/2021 by inquirer

2 answer

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