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siriusmart

@siriusmart@lemmy.world

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siriusmart OP Mod , (edited )
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Hint

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The solution I have in mind is related to the Taylor series

Hint 2

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It converges to -ln(2), but why

Solution:

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-06-02-alternating_harmonic.html
https://lemmy.world/pictrs/image/16bd1657-951e-4b81-a739-b076147fc0bd.png

siriusmart OP Mod ,
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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

siriusmart OP Mod ,
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Here's a rly cool solution from stackexchange, which blows my average geometric solution out of the water

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https://lemmy.world/pictrs/image/5747b508-d67d-4a3d-9c2e-f2e1003d2cc9.png

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

Hint:

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It is not a telescoping series

Solution:

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-18_not-a-telescoping-series.html
https://lemmy.world/pictrs/image/da6bb5e3-e42b-47c4-bcb0-9d7c6bec9227.png

siriusmart Mod ,
@siriusmart@lemmy.world avatar

i got the answers, but i dont really know why

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Challenges%20solutions/bound-f.html
https://lemmy.world/pictrs/image/9054b3da-3ca4-4321-9d9c-824c9e73ef54.png

siriusmart OP Mod , (edited )
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Solution (starter question):

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https://lemmy.world/pictrs/image/f4f24d39-5f28-4914-97bb-92728cdc4aa8.png

Please refer to the main post, if you don't like looking at the image.
https://gmtex.siri.sh/fs/1/School/Extra/Maths/Unsolved/1d-gravity.html

For the main question, you are encouraged to share your progress

spoiler

https://lemmy.world/pictrs/image/9ea15515-d6b7-468b-bfc5-ec708a6d0e09.png

You might be able to solve this with differential equations, or by solving the iterative functions, I dont know

siriusmart OP Mod , (edited )
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Hint:

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e

Solution:

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zkfcfbzr solved it

i put everything into ln because i was scared of multiplication

https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-16_telescoping-multiplication.html
https://lemmy.world/pictrs/image/1f096e4a-97f2-4bf1-b5d2-0037b9fbba98.png

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

i added the solution to the post, i didnt see the multiplication before someone mentioned it, but yeah if we put it to the power of e it will telescope again, which is clearly the main character of this sub at this point (jk)

siriusmart OP Mod , (edited )
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Hint:

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  • Try show that for the statement to be true, the derivative has to be defined.
  • There are 2 definitions for the derivative, either would be useful in the proof

Solution

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-15_differentiablility-implies-continuity.html
https://lemmy.world/pictrs/image/e297427c-59ad-46d9-99e8-bad9a90203c7.png

siriusmart OP Mod ,
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mb

siriusmart OP Mod ,
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i thought the "default" counter example is y=|x| lol

siriusmart Mod ,
@siriusmart@lemmy.world avatar

i got it, no calculator needed

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Challenges solutions/log-5and6.html
https://lemmy.world/pictrs/image/8d0e26f3-c103-4828-9a0d-0f43194ddddb.png

siriusmart Mod ,
@siriusmart@lemmy.world avatar

i get why 0 would work, but i dont get how it doesnt show up as a solution when i try to solve for it

siriusmart Mod ,
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i showed the question to my friend who isnt particularly bright in maths, he said 30 by just looking at it, i freaked out a bit but it might just have been a lucky guess

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

Solution:

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-14_lnx-differential.html
https://lemmy.world/pictrs/image/9486bc79-1bb6-4205-9a23-ed2d5dc0ffdf.png

siriusmart OP Mod , (edited )
@siriusmart@lemmy.world avatar

this one got some table slams from my friends

Hint:

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Find an example which satisfies the equation.

Solution:

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-13_irrational-powers.html
https://lemmy.world/pictrs/image/94a2af80-483f-4874-9864-ca1858e61546.png

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

that is simply genius

(i suppose it didnt come to me when i think of "irrational")

siriusmart OP Mod , (edited )
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Hint:

spoiler

It is often helpful to visualise the problem, build it in minecraft to see if u notice anything.

Note that the sum of first n natural numbers can be proven without induction, as shown below
https://lemmy.world/pictrs/image/854e5b2e-02ed-41a5-a93e-6c61355fbf30.png

Solutions:

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-09_sum-of-squares.html
https://lemmy.world/pictrs/image/167dcb2f-bca2-4f1d-99af-7d117b46b737.png

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

i took the second setup cuz thats what i saw when thinking of the problem, i'll read the first approach later

What is the area of the shaded region? ( lemmy.world )

An 8x5 rectangle. If the bottom left corner is considered (0, 0), then two lines are drawn within the rectangle, from (0, 4) to (8, 1) and from (1, 5) to (7, 0). The smaller two regions of the four these lines cut the rectangle into are shaded. What is their combined area?

siriusmart Mod ,
@siriusmart@lemmy.world avatar

I love doing things the wrong way, so

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https://lemmy.world/pictrs/image/9b9d277f-e642-45a6-9bf1-9e9f6f03e4fe.png

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

There seemed to be more than one ways to prove this.

Hint:

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Use a suitable substitution.

Solution:

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https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-08_e%5Ex-definition.html
https://lemmy.world/pictrs/image/27caff35-d892-4083-b262-b8b6d59e9937.png

siriusmart OP Mod , (edited )
@siriusmart@lemmy.world avatar

Hint 1:

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expand the expression

Hint 2:

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partial fractions

Solution:

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Link: https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-07_infinite-sum.html
https://lemmy.world/pictrs/image/b10bbfbe-728e-4873-ab6f-1758e61bbf13.png

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

mb, its now fixed

siriusmart OP Mod ,
@siriusmart@lemmy.world avatar

Solution (that is likely much better than yours): https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-06_equation-of-circle.html

spoiler

https://lemmy.world/pictrs/image/57380d29-1c7e-4bc5-9e26-98623c1298d0.png

siriusmart Mod ,
@siriusmart@lemmy.world avatar

holdup taking the side length of the unit square actually makes the working out a bit simpler, because the otherside is 1

idk i just saw the diagonal at first

2l+0.5 sqrt(2l^2)=1
l(2+0.5sqrt(2))=1
l=1/(2+0.5sqrt(2))
=(2-0.5sqrt(2))/3.5
=(4-sqrt(2))/7

also, all the public items on the drive is mean to be public, there are unlisted and private items u dont see

siriusmart OP Mod ,
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ggs

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