有向數及數線 | Directed Numbers and Number Line

If there is a tank of length, width, height of 40x10x30 respectively, and there are 8L of water in the tank. Then put a prism of base area 80cm square, height 60cm.The base of the prism touch the bottom of the tank.
Will the water overflowing？？？

28/07/2022 at 13:41

the capacity of the tank: 40x10x30=12000ml=12L,
the volume of prism: 80x60x1/3=1600ml=1.6L
the capacity of the tank > the volume of prism+8L
the water won’t overflowing

31/07/2021 at 02:56

Why (-2)^0.1 =1.01931714 + 0.331196214 i ?

Tony 11/06/2021 at 13:06

Is π digits random? (which means each digit appears very close to 10% of the time or not)

IDENTITY (Administrator) 13/06/2021 at 14:18

好有趣嘅問題，之前都冇諗過。上網見到呢篇 blog 寫得唔錯，結論係：未有 mathematical proof 證明到係 uniformly distributed (i.e. 10% chance of appearance)，但 empirical evidence 似乎話畀我哋知真係 10% chance。

https://blogs.sas.com/content/iml/2015/03/12/digits-of-pi.html

20/01/2021 at 18:56

how do i rationalise the denominator $\frac{1}{\sqrt{12}}$

IDENTITY (Administrator) 24/01/2021 at 01:01

Haha 你竟然知道呢度可以用 LaTeX。返返你嘅問題：

$\begin{align*} \frac{1}{\sqrt{12}}&=\frac{1}{\sqrt{12}}\times\frac{\sqrt{12}}{\sqrt{12}}\\ &=\frac{\sqrt{12}}{12}\\ &=\frac{\sqrt{3\times4}}{12}\\ &=\frac{\sqrt{3}\times\sqrt{4}}{12}\\ &=\frac{\sqrt{3}\times2}{12}\\ &=\frac{\sqrt{3}}{6} \end{align*}$

10/10/2020 at 12:09

New identity web

IDENTITY (Administrator) 11/10/2020 at 14:26

Haha a little surprise to the old IDENTITY users. Which one do you like better 🙂 ?

19/02/2022 at 11:55

The new one of course!

08/10/2020 at 22:13

Is 0 a directed number?

IDENTITY (Administrator) 11/10/2020 at 14:20

Short answer: I don’t think there’s a clear definition on that.

In fact, directed number is not a very rigorous mathematical definition. It’s just a fancy term to emphasize a number can be positive or negative. In that sense, arguing whether 0 is a directed number may not be very meaningful. After all, +0 = -0 = 0.

Jayden lee 08/10/2020 at 18:39

x(x-2)+A(x-1)≡x^2+B find the value of A and B

I don’t know how to do this question

08/10/2020 at 20:44

is it a =2 b=-2

IDENTITY (Administrator) 11/10/2020 at 14:23

Sorry for the late reply.
You’re right. A = 2 and B = -2. Well done!

16/04/2023 at 05:02

LHS=x(x-2)+A(x-1)
=x^(2)-2x+Ax-A
=x^(2)+(-2+A)x-A

RHS=x^(2)+B
-2+A=0
A=2
-2=B

28/09/2020 at 11:01

Anyone could explain the Mandelbrot Set?