all nostalgia aside, arras.io is so much better
Hint:
spoiler
Try out the following tasks before going for the big one
- Draw a circle of radius
a. - Animate a point on circle
a, let that be your rotational speed. - Animate a circle rolling horizontally (along the
xaxis) at your rotational speed. - Animate a point on that horizontally rolling circle.
You should now have an idea on how to draw a hypocycloid.
Draw a hypocycloid using a graphical calculator (such as Desmos or Geogebra).
Your hypocycloid should include
- Inner circle of radius `a
- Outer circle of radius `b
- As time
tincreases the point on the inner circle should trace out the pattern, you can animate the graph usingt.
Below is the link to a Desmos graph:
https://www.desmos.com/calculator/vzgog7xqrz
Hint
spoiler
If you are studying the algorithm, you are doing it wrong
Solution: https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd solutions/2024-08-04_extended-euclid.html
spoiler
- Given
nandmare coprime, show that there exist integern'such thatnn' mod m=1. - The extended Euclid's algorithm is given below without proof, which may be useful in your proof.
(I'm too lazy to type out the algorithm again, so look at the image yourself)
Hint:
spoiler
Let x mod y = a
Solution: https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd solutions/2024-08-01_multiple-of-modulus.html
spoiler
- Prove that
z(x mod y) = (zx) mod (zy)
Be rigorous
(trust me bro im gonna daily post trust me bro)
EDIT: assume all variables are integers
Hint:
spoiler
The size of a set is the number of possible values that an element can take.
I recently started reading TAOCP, in other words you can expect daily posts from me again, because I'll just take some of the cooler questions from there and repost them here.
because I have never heard of this argument before, ever. most media's stance on politics is "their party bad our party good", but the "all the parties are pretty hypocritical" argument has never been explored properly, because its depressing and nobody likes it.
I'm a Londoner, I used to have this friend (who is not a Londoner) we had a huge disagreement on topic unspecified. But after I've watched this video I think I see his viewpoint, which is true. I just don't see it at all because there's such a enormous disconnect between London and the rest of the country.
I would recommend you to watch the video as well, some arguments made in the video are slightly misleading, but the general picture is clear and true.
https://youtu.be/b5aJ-57_YsQ
yup thats the intended solution, im not really familiar with taylor series yet, but maybe for a person who knows taylor series would be able to see it right away
Hint
spoiler
The solution I have in mind is related to the Taylor series
Hint 2
spoiler
It converges to -ln(2), but why
Solution:
Here's a rly cool solution from stackexchange, which blows my average geometric solution out of the water
spoiler
I've shown that ln(n/n-1) is always larger than 1/n, so Σln(n/n-1) for all natural number n will be larger than the series 1+1/2+1/3+...
but I don't know how to make sure the sum of all ln(p/p-1) only when p is prime is larger than the provided series
the question is strongly suggesting its divergent, i just dont know how to show it
i pulled the image from a meme channel, so i dont know if its real or not, but at the same time, this below does look like a legit response
the background it likely ai generated anyways
(i took the meme off some discord channel, so i dont know how its made)
Hint:
spoiler
It is not a telescoping series
Solution:
Hint:
spoiler
e
Solution:
spoiler
zkfcfbzr solved it
i put everything into ln because i was scared of multiplication
yup there u go, btw can u please spoiler it so its harder for people to accidentally see it
i've been doing some 15 minutes of duolingo japanese for almost 10 months now, and i think i know a bit of japanese, and i could vaguely understand lyrics of songs if i stop it and read the text, i think the main issue for some people is that they only do it to "keep the streak", which is the case for a lot of my irl friends, and they barely learnt anything. One of my friend did do a large number of russian lessons daily, and i think he now knows quite a bit of russian (aka, can speak)
i dont think i'll be able to speak japanese in a daily convo in quite a while, cuz im too scared to speak, however im starting to understnad what they are speaking, so its not entirely accurate to say duolingo is pointless, cuz it really depend on ur attitude towards it
also, almost none of the anime kids ive met know any amount of japanese, the two topics couldnt be any more different