Jeffes02

Oh XD I didn't read your explanation correctly, thanks for the reply :D

FINALLY! I'm not the only one who have a bunch of flat earth videos in my recommended section in youtube(sighs)

    If you think about it, it is actually very reasonable to still have people on Earth than still believes that it is flat, considering that billions of people can't even get proper education, and how many people that got proper education simply forgot what they have learned about astronomy, physics, and aerodynamics in a few years, not considering how many people can't even correctly memorize the eight planets and their moons.

    The problem with flat earthers that have internet not believing in that he Earth is flat is mainly because of the below reasons, and they are ignorant to accept facts & scientific proofs, using what every religion and conspiracy theory uses so they are able to survive in the information era:

1.Assume Fakery:

    Meaning: Assuming something is wrong, fake, or incorrect just because it defies their ideology, take an example:

    Example: You are watching your favorite national football team on TV on a sofa, you expected your own country's which you support to win, but instead, the team opposing yours won, if you are a not-that-kind person, you might think the team that won the game cheated and the game needs to be rematched although you have no evidence.

    Effect: Blocks information from entering the conspiracy. (i.e. Reinforcing your walls to protect your ideology from foreign intruders.)

2.Making Up:

   Meaning: Making up theories in your hypothesis, religion, & conspiracies to compensate for the fact that the ideology that you believe in have flaws in them.

   Example: The countless different kind of theory that the flat Earth society created to explain gravity doesn't exist, such as saying it is caused by some effects of electromagnetism (Which they have no idea in.), the Earth is accelerating upwards at exactly 9.8 m/s^2, or it is simply buoyancy of the air like how helium balloon floats and objects heavier than air sinks.

   Or the countless branches Christianity have made throughout the history, such as Oriental Orthodoxy, Eastern Orthodoxy, Roman Catholicism etc. creating countless conflicts and wars against each other, because Christians knew there are contradictions in the Bible, therefore they have to fix them by ways to make sure people will join their religion instead of disagreeing with them or some other religions, but Christians are across half of Earth by then, and every part of them have developed different ways to fix the contradictions themselves, thus creating more and more differ ones from the original.

   Effect: Reinforcing your conspiracy and beliefs in the society. (i.e. Upgrading your army & weapons against intruders.)

3.People's Vulnerability To Ideologies:

   Meaning: Having your mind being vulnerable to what people around you & powerful people on social medias says.

   Example: Does seeing a random guy in the comment sections of youtube's flat Earth videos saying "Earth is Flat! Praise the truth!" make you believe in it? Maybe not. How about if this world-famous American rapper with million of followers said the exact same thing? (A Flat-Earth theories believer.)

https://twitter.com/bobatl?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor

   If your answer is "Maybe?" then your mind is vulnerable to thoughts, this is how people indoctrinate others to believe in their ideology & beliefs, by weakening your walls first by sending you emails about how God must have created the Earth by looking at how beautiful it is, or a daily news on facebook about how celebrities believes that flat-Earth is a cover-up, and then commence a attack on your mind by recommending you flat-Earth videos & Sending you welcoming letters from neighboring churches, thus finalizing their goal of turning yourself into one of them.

  Effect: Having others to join your ideology and beliefs. (Recruiting soldiers from towns and villages to join your army.)

   In the end, conspiracies and religions are just like castles spreaded across lands, each with strong, well trained, and considerable quantity of soldiers willing to fight for their kings and queens, and thick, reinforced walls to protect citizens inside their castles. You might ask "How is it possible to defeat them?", that's easy, just call the hollow-Earthers, all the other hundred and thousand of gods, and make conflicts inside their own conspiracies by pointing out contradictions in their videos and holy books, that way, they will be attacked from both the inside and the outside, thus ultimately destroying themselves.

   I'm sorry if this offended anyone, forgive me for being such a straightforward person, but this is what humanity needs, the humanity needs no gods and hoaxes, but truths.

Your answer to the 2nd and the 3rd question is correct, good job! (You must have read a lot of books about classical physics didn't you.)

But for the 1st question, the question states that \(M_1>M_2\), that means their first Lagrangian point won't be midway between the two objects, but closer to \(M_2\), like how the point between the Sun and the Earth is closer to Earth than Sun does :D

*Read the question for 3 times and finally understood what it means*'

We know that the \(\frac{1}{9}\) part of the pyramid is above water,  since the pyramid is three-dimensional, the volume of it is equal to the third power of its sides.

Now since we know that \(\frac{8}{9}\) of the volume is underwater, therefore the volume of the smaller pyramid which is above the water would be 8 times of the remaining pyramid which is underwater

The height of the smaller pyramid \(=x\), with the height of the remaining pyramid \(=150-x\)

\(x^3:(150-x)^3=1:8\)

Therefore \(150-x\) would be \(\sqrt[3]{8}=2\) times larger than \(x\):

\(150-x=2x\)

\(3x=150\)

\(x=50 (meters)\)

Done :D

(Time spent \(\approx\) 2 hours)

There isn't a really a "reason" of why it is irrational, it just happens to be like this way, like Euler's constant \(e\approx2.71828183...\), \(π\) is similar to most other mathematical constants, they are so important in geometry (especially trigonometry), that they can't be plain simple integers or decimals.

Your answer is correct :)

This is a REALLY difficult question to answer (Atleast in my knowledge), but I will try my best:

Input:

Solve for x:

|3x-2|-1=|5-x|

Intepretation: Sove for \(x\) in the function \(|3x-2|-1=|5-x|\)

Step 1. Rewrite the expressions:

\(\sqrt{\left(3x-2\right)^2}-1=\sqrt{\left(5-x\right)^2}\)

Step 2. Square both sides:

\(({\sqrt{\left(3x-2\right)^2}-1})^2=(\sqrt{\left(5-x\right)^2})^2\)

Step 3. Expand x2:

\((3x-2)^2-2\sqrt{\left(3x-2\right)^2}+1=(5-x)^2\)

\(9x^4-12x+5-2\sqrt{\left(3x-2\right)^2}=x^2-10x+25\)

Step 4. Move the corresponding terms:

\(8x^2-2x-20=2\sqrt{\left(3x-2\right)^2}\)

Step 5. Square both sides again:

\((8x^2-2x-20)^2=(2\sqrt{\left(3x-2\right)^2})^2\)

\(64x^4-16x^3-160x^2-16x^3+4x^2+40x-160x^2+40x+400)=4(3x-2)^2\)

Step 6. Simplify:

\(64x^4-32x^3-316x^2+80x+400=36x^2-48x+16\)

Step 7. Move the terms again:

\(64x^4-32x^3-352x^2+128x+384=0\)

Step 8. Divide by their greatest common divisor (i.e. \(32\))

\(2x^4-x^3-11x^2+4x+12=0\)

Step 9. Factorize the function:

Now we use the rational root theorem:

For a polynomial \(ax^n+bx^{n-1}+cx^{n-2}+...+yx^1+z\)

The possible rational roots will be located at \(± \frac{all\space\space factors\space of\space a}{all\space factors\space of\space z}\)

Now find the factors of both \(a\) and \(z\)

9.1 The factors of \(12=z\) is: \(1,2,3,4,6,12\)

The factors of \(2=a\) is: \(1,2\)

9.2 Plug the factors in:

\(±\frac{1,2,3,4,6,12}{1,2}\)

9.3 Expand & List them out:

\(±1,2,3,4,6,12,1,\frac{3}{2},\frac{1}{2},2,3,6\)

9.4 Cancel & Reorganize the repeated possible roots:

\(±\frac{1}{2},1,2,\frac{3}{2},3,4,6,12\)

9.5 Plug all the numbers above into the equation

\(2x^4-x^3-11x^2+4x+12=0\)

Is it \(±\frac{1}{2}\)? No.

Is it \(±1\)? \(1\) doesn't, while \(-1\) does

We can deduct that \((x+1)\) is a factor of the polynomial:

9.6 Perform polynomial long division:

Solve for \(\frac{2x^4-x^3-11x^2+4x+12}{x+1}=(2x^3-3x^2-8x+12)\)

9.7 Factor \((2x^3-3x^2-8x+12)\)

Factor \(x^2\) from \(2x^3-3x^2\), \(-4\) from \(-8x+12\)

\(=x^2(2x-3)-4(2x-3)\)

Merge the terms:

\(=(x^2-4)(2x-3)\)

9.71 Factor \((x^2-4)\)

Use the law: \(a^2-b^2=(a+b)(a-b)\) with \(a=1\) and \(b=2\)

\(=(x+2)(x-2)\)

Therefore:

\(2x^4-x^3-11x^2+4x+12=(x+1)(x+2)(x-2)(2x-3)\)

Step 10.  Find the possible roots of \(x\)

\(x+1=0, x+2=0, x-2=0, 2x-3=0\)

\(x=-1\space or\space -2\space or\space 2\space or\space \frac{3}{2}\)

Step 11. Final Step:

Plug the four \(x\) above into \(|3x-2|-1=|5-x|\)

And making sure the left and the right side is the same:

In the end: \(x=-2,2\)

Therefore the final solution for \(|3x-2|-1=|5-x|\) is:

\(x=±2\)

(There must be an easier way to solve this.)

Not sure, my best guess is that it is related to how many like one gets with that answer & how popular the question is viewed, you can ask the staffs when they are online about that :)

The robots won't come for only the purpose to advertising, but used aswell to clog a server's internet connection by putting immense useless data on it, making the connection taking ages to created (i.e. DDoS attack), or to spam personal political messages like who to support in a presidential election etc., also adblock is used to block the ads you see on webpages on the blank spaces left or right to it (i.e. Sponsored content, that's how websites mostly get their funds and money from), not to block comments with ads encrusted in them.

It's called a captcha, and unfortunatly no, you can't disable it, if you can, then it would defy the purpose that it is created in the first place, since people who want to spam can just disable it and do whatever they want to do on websites.

It might be annoying but hey, atleast you won't see spam advertisements in this forum with their protection :D