#help-0

1 messages ยท Page 500 of 1

tulip violet
#

ru sick of me..? ๐Ÿ˜ญ

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um

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the

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weird

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thingy

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ik

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what

heady cloak
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nope

tulip violet
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the

heady cloak
#

I suck at math

tulip violet
#

THE

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THINGY

#

UM

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SQUARE ROOT

mental python
mental python
tulip violet
mental python
#

take the square root of both sides

tulip violet
#

so the exact for

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m

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is the square root

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of 18

long shale
tulip violet
#

but not in america

marsh wedge
#

who

#

needs help

mental python
long shale
mental python
#

you get $x=\sqrt{18}$

ocean sealBOT
marsh wedge
mental python
tulip violet
marsh wedge
long shale
mental python
#

now to get the area, we can break it up into two parts

tulip violet
mental python
#

do you notice how the area we want is equal to the area of the quarter circle minus the area of the triangle?

tulip violet
#

wait

tulip violet
long shale
tulip violet
#

yes

#

bonk is cool

long shale
tulip violet
mental python
#

does this make sense?

image.png
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(sry for the bad drawing ๐Ÿ˜ญ)

tulip violet
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OH

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YEA

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I SEE IT NOW

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i think thats what my friend was trying to explain to me ngl

long shale
mental python
tulip violet
#

ok

mental python
#

so we need to find the area of the quarter circle

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and the area of the triangle

tulip violet
#

so i work out the quartercircle

mental python
#

yes?

tulip violet
#

eys

mental python
tulip violet
#

yes

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ok ok

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i can do that

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maybe

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ฯ€r^2?

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for area?

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of

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circle?

mental python
#

pi r^2 is the area of the full circle

tulip violet
#

yes

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1/4

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that

mental python
#

indeed

long shale
mental python
#

and what is our radius?

tulip violet
#

square root 18

mental python
#

yup

tulip violet
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omg

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ru proud of me

mental python
#

so then what is the area of the quarter circle?

mental python
tulip violet
#

square root 4.5 pi

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i cbf to do all the

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decimals

mental python
#

can you show how you got that answer?

tulip violet
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1/4 x 18

mental python
#

just keep it exact

tulip violet
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then add the sqaure root

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and

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hte pi

mental python
long shale
mental python
#

area of quarter circle: $\frac{\pi r^2}4$

ocean sealBOT
tulip violet
#

yes

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i did that

mental python
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you dont pull the 4 into the sqrt

tulip violet
#

wait

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hey

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HEY

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I FORGOT THE SQAURE

long shale
tulip violet
#

the radius

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๐Ÿ˜ญ

long shale
tulip violet
#

yes

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its so messy

mental python
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looks good

long shale
#

so when we square that term the square root and the square will get canceled each other which will only lrft 18

tulip violet
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yes

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i knew taht

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atha

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that

long shale
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so now pi *1/4 *18

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multiply these 3

tulip violet
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ok...

long shale
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you know the value of pi right??

tulip violet
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leave in exact..?

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3.14159

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this is pi followed by

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2653589

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circumference over diameter

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i forgto the rest

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trust

long shale
tulip violet
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im better at chem

mental python
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do not put it in decimals

tulip violet
#

ik

mental python
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keep it exact

tulip violet
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i have the pi

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thing

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in my

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thing

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thing

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CALCULATOR

mental python
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yes good

tulip violet
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that

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so

mental python
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so, what did we calculate again?

tulip violet
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4.5ฯ€???

mental python
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yes, but what is this for

tulip violet
#

the area..?

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of the

mental python
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of...?

tulip violet
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quarter

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thing

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circle

mental python
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indeed

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and now we need the area of the triangle, right?

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do you know how to calculate that

tulip violet
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uhhh

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1/2

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hight

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length

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smth like that

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dw

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i got this

mental python
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its 1/2 * base * height, yes

tulip violet
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yes

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see

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i got this

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wouldnt it be

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1/2 x square root 18 x square root 18

mental python
#

yup

tulip violet
#

so 9

mental python
#

that is indeed the area of the triangle

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so we have the area of the quarter circle

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and the area of the triangle

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what do we do now?

tulip violet
#

so

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4.5 ฯ€ - 9

mental python
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yup

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thats the answer

tulip violet
#

do i have to leave it in exact form now

mental python
#

it depends on what the quesiton asks

#

can you show the full question?

tulip violet
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it jsut says find the shaded area

mental python
#

then exact form is fine

tulip violet
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i dont like exact form

mental python
#

you can also do $\frac92\pi - 9\approx 5.14$ if you like

ocean sealBOT
mental python
tulip violet
#

i did that

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so

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the next questions

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is the same

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ish

long shale
tulip violet
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yes

long shale
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what do you think you can do by seeing this image

tulip violet
#

minus little sector from big sector

long shale
#

so how we are going to minus?

mental python
#

$\tikz{\fill[blue!40!yellow] (0,1) --++(1,0)arc[start angle=0,end angle=90,radius=1];} - \tikz{\fill[blue!40!yellow] (1,0) -- (0,1) -- (0,0) -- cycle;} = \tikz{\fill[blue!40!yellow] (1,0) arc (0:90:1);}$

ocean sealBOT
mental python
#

yes!

tulip violet
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i got 6.28cm^2

tulip violet
mental python
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ive been working on this for a while ๐Ÿ˜…

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(sry to interupt, continue :))

tulip violet
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alggg

long shale
mental python
tulip violet
long shale
tulip violet
#

i have 3 more pages of hw left

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yay

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(๐Ÿ˜ญ๐Ÿ˜ญ๐Ÿ˜ญ๐Ÿ˜ญ๐Ÿ˜ญ๐Ÿ˜ญ)

mental python
#

$\tikz{\fill[blue!40!yellow] (0,1) --++(1,0)arc[start angle=0,end angle=90,radius=1];} - \tikz{\fill[blue!40!blue] (1,0) -- (0,1) -- (0,0) -- cycle;} = \tikz{\fill[blue!40!yellow] (1,0) arc (0:90:1);\fill[blue!40!blue] (1,0) -- (0,1) -- (0,0) -- cycle;}$

ocean sealBOT
mental python
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(even more obvious now)

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or mby not idk

tulip violet
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ngl

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what u did

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helped

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so much

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thank uuuuu

mental python
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thats great to hear

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and im glad you understand it ๐Ÿ˜„

tulip violet
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i still got so much hw

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sa is

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killing me

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and volume

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i dont like

mental python
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continue with your calculation

tulip violet
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for which

mental python
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or are you done already?

tulip violet
#

is that solved??

tulip violet
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i got

mental python
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ah, you did it already

mental python
#

yes mb

tulip violet
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omg

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the thunder is rattling my windows

mental python
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btw

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the answer in exact form is just 2pi

tulip violet
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..

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hm

mental python
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i recommend going as far as possible writing it in exact form

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then answering it in decimal

tulip violet
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ok ok

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is the volume of a rectangular prism

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base times length times height

mental python
# tulip violet

like here you should do $\\begin{aligned}&\frac{30}{360}7^2\pi-\frac{30}{360}5^2\pi\=&\frac1{12}49\pi-\frac1{12}25\pi\=&\frac{24}{12}\pi\=&2\pi\end{aligned}$

mental python
tulip violet
#

i have a headache

tulip violet
#

yes

mental python
tulip violet
#

oh..

ocean sealBOT
tulip violet
#

hm

mental python
#

perhaps showing it like this is more obvious

tulip violet
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so

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wait

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idkzzz

mental python
tulip violet
tulip violet
mental python
mental python
tulip violet
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yay

mental python
#

youre doing b?

tulip violet
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yes

mental python
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ok

tulip violet
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why is there 10 and 14

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i am

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clndused

mental python
#

thats the diagonal

tulip violet
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confused

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the 10..?

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wait

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huh

mental python
#

this is when you look at it from the front

image.png
tulip violet
#

ohโ€ฆ

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hm

mental python
#

can you see that?

tulip violet
#

unfortunately

mental python
#

unfortunately?

tulip violet
#

yes

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i have to figure our

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both sides

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now

mental python
#

this is a bit more work than a, yes

tulip violet
#

what about the volume

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wait

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i got this

mental python
#

lets goo

tulip violet
#

ok

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SA=1721.6cm^2

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V=3571.2cm^3

mental python
#

can you show your calculations?

tulip violet
#

uhhh

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yes

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its messy

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ur gonna lecture me ๐Ÿ˜”๐Ÿ˜”๐Ÿ˜”

mental python
#

then make sure its clean next time ๐Ÿ™‚

tulip violet
tulip violet
mental python
#

(dont wanna scroll back up :))

tulip violet
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yes

mental python
#

whats A5?

tulip violet
#

uhhh

mental python
#

you just wrote 604.8

tulip violet
#

the bottom

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i tihkn

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yea

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...

mental python
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it is

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just write it down next time ๐Ÿ™‚

tulip violet
#

i tryyy

mental python
#

the area looks correct

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volume aswell

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seems like youre already quite comfortable with this topic

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youre doing very well

tulip violet
#

yay

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this is just

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this weeks hw

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i still have

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like

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2 and a half pages

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and its due on sunday

mental python
#

do as many as you can

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and ask a question if you need it

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or need your answer needs checking

tulip violet
#

oki

#

thanks

mental python
#

!done

lone heartBOT
#

If you are done with this channel, please mark your problem as solved by typing .close

tulip violet
#

metres ^3 into litres..?

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nvm

mental python
tulip violet
#

..?

mental python
#

10cm * 10cm * 10cm = 1 Liter

tulip violet
#

hm

mental python
mental python
tulip violet
#

i just times by 1000

mental python
#

yes

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thats correect

#

m^3=1000L

tulip violet
#

im doing this question now

mental python
tulip violet
tulip violet
mental python
tulip violet
#

dw

#

i got this

mental python
#

okay catthumbsup

tulip violet
mental python
#

this step is wrong

image.png
#

cm^3=L

#

anyway

#

you pretty much know how to answer these questions

#

i recommend you close this channel

tulip violet
#

ok

mental python
#

and open a new one if you have a new question

tulip violet
#

ima go bed anyways

mental python
#

(also i gotta go for lunch lol)

tulip violet
#

oof

mental python
tulip violet
#

timezones

#

australia

mental python
#

ahh

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thats i think +9 from me

#

so 10pm?

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or 11pm

tulip violet
#

yes

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11

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ur in

mental python
#

h, +10

tulip violet
#

europe..?

mental python
#

ofc

mental python
tulip violet
#

england?

mental python
#

nope

tulip violet
#

smth close..?

mental python
#

i seem british ig lol

mental python
tulip violet
#

france..?

mental python
#

ah wait, the channel doesnt extend upwards

#

no not france

tulip violet
#

uhhh

#

scotland

#

ireland

#

wales

#

smth

mental python
#

i doubt youre gonna guess it lol

tulip violet
#

IDK

#

IM NOT EUROPEAN

mental python
#

netherlands

tulip violet
tulip violet
mental python
tulip violet
#

DONT BEAT ME UP

mental python
#

you have geography though, no?

#

xd

#

grade 10?

tulip violet
#

we barely learn about the geography of other countrues

mental python
#

you only learn about australian geography?

tulip violet
#

netherlands is dutch..?

mental python
#

yes

tulip violet
tulip violet
#

im learning dutch

mental python
#

oh wow, this side of the country is alloutback

#

this other side

#

is also basically all outback

#

but some cities on the coast

#

๐Ÿ˜„

#

geography of australia done

tulip violet
#

cause im moving to europe this year

mental python
mental python
tulip violet
#

exchange student

mental python
#

in grade 10?

#

wait, how old are you?

tulip violet
#

14

#

im turning 15 soon

#

before i leave

mental python
#

and doing exchange??

tulip violet
#

yes

mental python
#

for how long

tulip violet
#

6 months

mental python
#

interesting

#

what for?

#

just cuz you can?

tulip violet
#

yes

mental python
#

lol

tulip violet
#

denmark wouldnt let me go there

#

cause apparently im too young

mental python
#

so youre just oging to school in europe for 6 months just cuz you can

tulip violet
#

i mean

#

its a good change

#

ive been going to basically the same schhool my whole life

long shale
tulip violet
#

with most of the same people

mental python
mental python
long shale
mental python
#

(uni mostly)

tulip violet
mental python
long shale
mental python
#

here youre in the same class for primary school

#

then highschool basically same ppl in the class aswell

tulip violet
#

youd move around

#

alot

#

but

#

ive been stuck in the same place

#

i mean

#

i travel alot

#

with my family

mental python
#

only time when you have different classmates is when you go from primary school -> high school and high school -> uni

tulip violet
#

but never had a change in culture or environment

mental python
tulip violet
#

in my big city

#

yea

mental python
#

even in a big city youll still just go to the same school

tulip violet
#

i mean

mental python
tulip violet
#

its โ€œdifferentโ€ highschool

#

its just

#

its right next to eachother

#

so most people

#

1/3 of our grade

#

is from our primary

mental python
#

ye okay sure

tulip violet
#

๐Ÿ˜ญ๐Ÿ˜ญ

mental python
#

sydney

#

wow what a surprise

tulip violet
#

yep

#

wow

#

def

mental python
#

i have family that lives in sydney ๐Ÿ˜„

tulip violet
#

oooo

#

thats fun

#

sydney sucks

mental python
#

lmao

tulip violet
#

too many murders now

mental python
#

???

tulip violet
#

so many

mental python
#

i read that NSW is the cocaine and gambling capital of the world lol

long shale
tulip violet
#

gambling

#

i didnt know about the cociane

mental python
#

pokies

tulip violet
#

they just busted the big weed place near me

tulip violet
#

for sure

tulip violet
#

dont kill the dogs

long shale
tulip violet
#

i acruals gotta sleep

#

ive got karate tmrw

#

at 9 am ๐Ÿ˜ญ๐Ÿ˜ญ๐Ÿ˜ญ

#

ill close this

long shale
tulip violet
#

thanks for the help

mental python
#

np !

tulip violet
long shale
tulip violet
#

ooo

tulip violet
mental python
#

,ti

ocean sealBOT
#

The current time for .bonk__ is 01:25 PM (CET) on Fri, 14/02/2025.

long shale
ocean sealBOT
#

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

tulip violet
#

hmmm

long shale
mental python
tulip violet
#

can i send friend request to u???

mental python
#

!done

lone heartBOT
#

If you are done with this channel, please mark your problem as solved by typing .close

tulip violet
#

IM

#

not good at sleeping

mental python
#

turn off the phone

#

or PC

#

whatever youre on

#

close your eyes and go to sleep

#

(also close the channel)

tulip violet
#

thats hard

tulip violet
#

i will

long shale
#

,ti

ocean sealBOT
#

The current time for xyruseditz is 05:57 PM (IST) on Fri, 14/02/2025.

long shale
tulip violet
#

whats ist

long shale
mental python
tulip violet
#

funn

tulip violet
#

the other night

#

i was like

#

ima go bed at 9 pm

#

i went to bed at 2 an

mental python
#

okay

#

but now

#

you can change it

#

and go to bed now

#

if you dont close the channel

tulip violet
#

and my crush is texting me

mental python
#

i will

tulip violet
#

so

#

how am i supoosed to sleep

mental python
#

he can wait for tmrw

tulip violet
#

ATLEAST ACCEPT MY FRIEND RQUEST

mental python
#

I ALREADY DID

long shale
tulip violet
#

you did..?.????

deep condor
#

no stay up

tulip violet
long shale
tulip violet
#

ok

#

bye bye

#

i got friends now

#

jk

mental python
#

๐Ÿ˜„

tulip violet
#

i have friends

mental python
#

๐Ÿ˜ฆ

tulip violet
#

i swear

mental python
#

!done

lone heartBOT
#

If you are done with this channel, please mark your problem as solved by typing .close

mental python
#

please

tulip violet
#

YES

#

.close

lone heartBOT
#
Channel closed

Closed by @tulip violet

Use .reopen if this was a mistake.

#
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โ€ข Type the command .close to free the channel when you're done.
โ€ข Be polite and have a nice day!

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little bough
#

Why is it that instead of subtracting the intervals at the end, we add them instead?

image.png image.png
lone heartBOT
fierce cipher
#

that exercise looks so familiar...

little bough
#

It does? lol

fierce cipher
#

i think i just did it this morning

little bough
#

Oh actually

#

Well im confused here and the teacher didnt explain why but dont we subtract at the end cause FTC or

#

This is for distance

fierce cipher
#

wdym

#

this part?

image.png
little bough
#

Lemme write it

#

no no lemme write

#

why at the end is it not 22/3 - 17/6

#

shouldnt it be that cause of FTC?

#

@fierce cipher

#

Im just confused why it switches to addition at the end

fierce cipher
#

,w -32/3 + 27/2

ocean sealBOT
little bough
#

right but then we subtract the results cause of ftc right

fierce cipher
#

this is the mistake

image.png
#

it's +

little bough
#

Oh

#

Well this is actually my teachers notes ๐Ÿ’€

#

Well thats cooked

fierce cipher
#

rip

little bough
#

Wait so with FTC

#

We disregard the negative?

#

Here?

#

F(b) - F(a) but ohhh

#

Is it cause distance

#

not displacement

fierce cipher
#

yea

little bough
#

right so essentially the absolute value of the entire function right so that turns to always positive

fierce cipher
#

ye

little bough
#

So in every case regarding distance would I always use positive using the FTC

fierce cipher
#

think simple

  • negative areas turn into positive
little bough
#

Right I see

#

Well this was informative appreciate it man

#

.close

lone heartBOT
#
Channel closed

Closed by @little bough

Use .reopen if this was a mistake.

fierce cipher
#

@little bough just wanna ask something

little bough
#

Yeah

fierce cipher
#

what country are u from

little bough
#

Oh no

#

I know why your asking ๐Ÿ˜‚

fierce cipher
#

i knew it

little bough
#

Yep ๐Ÿ™‚

lone heartBOT
#
Available help channel!

Send your question here to claim the channel.

Remember:
โ€ข Ask your math question in a clear, concise manner.
โ€ข Show your work, and if possible, explain where you are stuck.
โ€ข After 15 minutes, feel free to ping <@&286206848099549185>.
โ€ข Type the command .close to free the channel when you're done.
โ€ข Be polite and have a nice day!

Read #โ“how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

spare moss
#

need help if my proof is correct

lone heartBOT
spare moss
#

24

#

ax โ‰… by (mod 5)

#

(ax) - (by) = 5k
a*x * (-1) * b * y
(-1) * a * b * x * y
where a * b = 5n, x * y = 5m
(-1) * 5n * 5m = 5k
-25nm = 5k
5(-5nm) = 5k
let k = (-5nm)
5k = 5k

#

.close

lone heartBOT
#
Channel closed

Closed by @spare moss

Use .reopen if this was a mistake.

lone heartBOT
#
Available help channel!

Send your question here to claim the channel.

Remember:
โ€ข Ask your math question in a clear, concise manner.
โ€ข Show your work, and if possible, explain where you are stuck.
โ€ข After 15 minutes, feel free to ping <@&286206848099549185>.
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vivid heart
#

need help on simplifying this
was told this can be simplified to a cos(b) where a and b are constants and a is an integer

IMG_6785.png
lone heartBOT
vale wigeon
lone heartBOT
#

@vivid heart Has your question been resolved?

vivid heart
# vale wigeon

I've tried rewriting it with cos (3x) = 4cos^3 x- 3 cos x and the arctan into arccos but it didn't help

vale wigeon
#

hm well

#

hm

#

let theta = arctan(3sqrt(3))/3

#

then we know tan(3 theta) = 3 sqrt(3) and are interested in cos(theta)

#

does that help us at all

vivid heart
#

oh wait

#

let me try that

#

so cos(3theta) = sqrt(7)/14

lone heartBOT
#

@vivid heart Has your question been resolved?

lone heartBOT
#
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#
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blissful rapids
lone heartBOT
wild umbra
#

!status

lone heartBOT
# 
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
blissful rapids
#

1

wild umbra
#

we'll start by breaking it into two simpler terms

#

[
S = \frac{1}{(1 + \log_e 10^n)^r} \sum_{r=0}^{n} (-1)^r \binom{n}{r} + \frac{\log_e 10}{(1 + \log_e 10^n)^r} \sum_{r=0}^{n} (-1)^r \binom{n}{r} r.
]

blissful rapids
#

The denominator should be raised to r

#

(1 + ln(10^n))^r

wild umbra
#

oh right

ocean sealBOT
wild umbra
#

do you recall this property? [
\sum_{r=0}^{n} (-1)^r \binom{n}{r} = (1 - 1)^n = 0, \quad \text{for } n \geq 1.
]

ocean sealBOT
blissful rapids
#

Yes

blissful rapids
#

The denominator

#

Its not independent of r anymore

wild umbra
#

[
S = \sum_{r=0}^{n} (-1)^r \binom{n}{r} \frac{1}{(1 + \log_e 10^n)^r}

  • \sum_{r=0}^{n} (-1)^r \binom{n}{r} \frac{r \log_e 10}{(1 + \log_e 10^n)^r}
    ]
ocean sealBOT
blissful rapids
#

Btw how did you make the background black

#

With this bot

wild umbra
#

Do you recall this binomial summation property? [
\sum_{r=0}^{n} (-1)^r \binom{n}{r} x^r = (1 - x)^n
]

ocean sealBOT
blissful rapids
#

Yes

wild umbra
#

,tc white

ocean sealBOT
#

I don't recognise the option white. Use ,texconfig to see the list of options.

wild umbra
#

,tc dark

ocean sealBOT
#

I don't recognise the option dark. Use ,texconfig to see the list of options.

wild umbra
#

,tc color dar

ocean sealBOT
#
Couldn't parse your input!

Unknown colourscheme dar. Valid colourschemes:
โ€‹ โ€‹ โ€‹ โ€‹ โ€‹ โ€‹ white: Pure white background, with black text.
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trans_black: Transparent background, with black text. (May cause issues)

Use ,texconfig colour to see more detailed information about this setting.
wild umbra
#

,tc color dark

ocean sealBOT
#

You have switched to the dark colourscheme.

wild umbra
#

,tex yes this is how you do it

ocean sealBOT
blissful rapids
#

Thank you

wild umbra
blissful rapids
#

(-ln10)^n

wild umbra
#

[
\sum_{r=0}^{n} (-1)^r \binom{n}{r} \frac{1}{(1 + \log_e 10^n)^r}
= \left( 1 - \frac{1}{1 + \log_e 10^n} \right)^n
]

[
1 - \frac{1}{1 + \log_e 10^n} \quad = \quad \frac{\log_e 10^n}{1 + \log_e 10^n}
]

[
\left( \frac{\log_e 10^n}{1 + \log_e 10^n} \right)^n
]

ocean sealBOT
wild umbra
#

this is what you're supposed to get, and not (-ln10) raised to the power n

blissful rapids
#

I think I got how to do the second summation

wild umbra
#

for the second summation, we differentiate the binomial property

blissful rapids
#

$\binom{n}{r} = \frac{n}{r} * \binom{n - 1}{r - 1}$

wild umbra
#

once you're done simplifying both the summations, you will just need to add them and it should be equal to 1

ocean sealBOT
blissful rapids
#

Then cancel out the r

wild umbra
#

bro is this JEE

blissful rapids
wild umbra
#

oh alr

blissful rapids
#

Thank you

#

.close

lone heartBOT
#
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halcyon walrus
lone heartBOT
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grand pulsar
#

Is writing sum of sigmas like this correct?

image.png
lone heartBOT
grand pulsar
#

As in I have a sum called S, and it can be expressed as

image.png
#

Then we want to calculate S+S

#

Can I write it like I just did

tight pier
late turtle
#

k and -k cancel out

grand pulsar
#

Ok thanks!

#

.close

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#
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#
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odd pawn
lone heartBOT
mental python
#

use linearity

odd pawn
#

i had this question on a test and im not sure of my answer

#

it seemed too easy

mental python
#

what did you do on the test?

odd pawn
#

flipped the sign of the g(x) and then replaced the numbers in the function and got the answer 42

#

my friend said the answer will be 90 but were not sure whos correct yet

#

so i came here to see whos correct

mental python
#

its 48

#

lol

odd pawn
mental python
#

ill write it out

#

$\int_2^5 2f(x)+3g(x)+3\dd x\\2\int_2^5 f(x)\dd x-3\int_5^2 g(x)\dd x+\int_2^5 3\dd x\\2\cdot 30-3\cdot 7+3\cdot 3\\60-21+9 = 48$

ocean sealBOT
mental python
#

unless i made a mistake somewhere

odd pawn
#

i trust you stranger on the internet

#

we will see how the test will go from here

#

thank youuu

#

.close

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#
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lone heartBOT
#
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urban rain
#

Your opponent is playing a virtual computer game where their character opens a mystery box on each turn. The mystery box either has a green pill (55% chance) or a red pill (45% chance) inside. If the pill is green, they get +1 point, and if the pill is red, they get -1 point. If at the end of the game, your opponent has a positive score, you must give them $1000, and if they have a negative score, they must give you $1000. You can choose for them to either have to play exactly 3 turns, exactly 33 turns, or exactly 333 turns. Which number of turns do you choose? What if the green pill gives your opponent +3 points instead of +1? Explain your answers

lone heartBOT
topaz schooner
#

what is the probability of you winning the game when you play 1 turn?

lone heartBOT
#

@urban rain Has your question been resolved?

urban rain
#

55

#

percent

topaz schooner
#

no

#

45%

#

if they get a red pill they lose 1 point

#

and if their score is negative you win

urban rain
#

oh right yes

#

oops

#

my bad

#

the more turns the better right?

topaz schooner
#

the more turn the lower the probability of you winning

#

because youre taking out the luck

lone heartBOT
#
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#
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red crater
#

Can someone help explain why the trapezoidal rule divides f(X0) and f(Xn) by 2?

lone heartBOT
north rover
red crater
#

I looked it up, still trying to figure out why the formula looks like that

north rover
red crater
#

That works!

#

I get that now

#

how does this apply to the trapezoidal rule?

north rover
#

According to the trapezoidal rule.

red crater
north rover
red crater
#

Yea but what confuses me so much then is we do basically the trapezoid area formula for the end points summed up but then we have a sum we dont divide by two in the middle?

#

Like how is that?

red crater
north rover
#

I haven't dealt with that specific simplification method yet

#

๐Ÿ˜…

red crater
red crater
#

.close

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#
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#
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vague jolt
#

Hi guys

lone heartBOT
vague jolt
#

So I'm writing a combinatorial proof

#

for a summation identity

#

for integer n>= 1

#

How do I go abt this

vague jolt
mental python
#

!xy

lone heartBOT
#

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

vague jolt
mental python
#

well, ${n \choose i}$ is indep of j, thus $\sum_{i=0}^{n-1}\sum_{j=0}^{n-1} {n\choose i}{n\choose j}=\sum_{i=0}^{n-1}\left({n\choose i}\sum_{j=0}^{n-1}{n\choose j}\right)$

ocean sealBOT
vague jolt
#

I don't quite understand

mental python
#

you can pull one outside of the sum

vague jolt
#

Also there's no way that's the whole proof

#

๐Ÿ’€

mental python
#

nah you need to show a bit more

vague jolt
#

Do we not consider two subsets?

mental python
#

wdym?

vague jolt
#

Like

#

To prove it

mental python
#

but wdym two subsets

mental python
vague jolt
mental python
#

,w sum sum (n choose i)(n choose j), j=0 to n-1, i=0 to n-1

ocean sealBOT
mental python
#

cuz WA says (2^n-1)^2

vague jolt
#

Uhh

#

Idk how u feel abt this but I got an answer from GPT4 what do u think of it

mental python
#

!nogpt

lone heartBOT
#

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

vague jolt
#

Damn really?

#

I mean

#

Can I show u anyways

#

I mean it's not GPT4

mental python
#

all AI is shit for maths

vague jolt
#

It's a custom GPT that I gave a bunch of videos and slides to

#

I mean

#

Can I show u anyways

#

Everyone says AI is bad for math but tbh it's done me pretty well in recent history but probably because the math I do is really simple

mental python
#

is this the AI answer?

vague jolt
#

Yeah

mental python
#

yeah, youre wasting my time

vague jolt
#

Bro

#

I'm just wondering if it's a good answer to reference and learn from

#

๐Ÿ’€

#

I'm here to learn and I'm using AI as a tool

lone heartBOT
#

@vague jolt Has your question been resolved?

lilac lake
vague jolt
somber eagle
vague jolt
lilac lake
lilac lake
vague jolt
#

Why not

lilac lake
#

I'm dumb

vague jolt
#

Bruh why u guys here opening used help channels if u can't help

#

Bum boys

somber eagle
lilac lake
#

I feel offended

#

please take action

vague jolt
#

No way bro just @ all the moderators

#

Surely that doesn't actually work

lilac lake
#

you called me a bum

vague jolt
#

I called u a bum ironically

somber eagle
mental python
somber eagle
#

though idk what they will do here

vague jolt
#

I mean

tepid drum
#

lol

lilac lake
vague jolt
#

If anything he should get in trouble

lilac lake
#

take it back

vague jolt
#

For @ ing unnecessarily

lilac lake
vague jolt
#

He's also a new user

lilac lake
#

๐Ÿ˜”โœŠ

vague jolt
# lilac lake read the rules

Me calling u a bum boy is obviously an ironic joke and ur the one trolling right now so yeah if I was a mod I'd mute you

lilac lake
#

this man is verbally attacking me

#

I feel so offended

lilac lake
#

I take jokes seriously

vague jolt
#

Bro ur literally a child

lilac lake
vague jolt
#

Ur acting like one too bro

#

Nothing wrong w it

#

Just making a statement

#

Bro anyways

#

Stop this nonsense

#

I need help

#

LOL

lilac lake
vague jolt
#

Man I give up no one going to help me

#

Close the channel guys

mental python
lone heartBOT
vague jolt
#

.close

lone heartBOT
#
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lone heartBOT
#
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Remember:
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โ€ข Show your work, and if possible, explain where you are stuck.
โ€ข After 15 minutes, feel free to ping <@&286206848099549185>.
โ€ข Type the command .close to free the channel when you're done.
โ€ข Be polite and have a nice day!

Read #โ“how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

tough minnow
#

Is it possible to construct 3 nondegenerate right angle triangles with integer side lengths and the same hypotenuse such that the area of two of the triangles sum to the area of the last?
I'm trying to either prove it isn't possible or find a counterexample and I haven't really been able to make progress

lone heartBOT
#

@tough minnow Has your question been resolved?

limpid turret
#

by "degenerate" do you mean "similar" or "congruent"?

tough minnow
#

a triangle with a side that's 0 length would have 0 area and be a degenerate triangle

#

just means the side lengths are all nonzero

lone heartBOT
#

@tough minnow Has your question been resolved?

limpid turret
tough minnow
#

but even then I'm not sure it makes the problem that much easier

tight marten
#

ive tried playing around with algebra and not really gotten anywhere but i might just be missing smth

#

my gut says there probably does exist an example but probably you need really big numbers

tough minnow
#

yeah I did think of and then see this general circle construction before

rncua.png
#

if you fix the hypotenuse at 1 then the legs just have to be rational

#

but I don't think that helps much

clever scarab
#

Hear me out 2+2

pale herald
#

Hello Iโ€™m currently studying for a big test on algebra, Iโ€™m trying to find the square root of pie

clever scarab
#

Hello huzz @everyone

pale herald
#

Do you guys have any suggestions to get goon of your paper

tough minnow
pale herald
#

I got a little to excited

tough minnow
#

can someone get these trolls outta here

tight marten
#

ok made this so it now shows all of the points on the circle that give integer side lengths

tight marten
tough minnow
#

you need to make a new link

tight marten
#

ah

tough minnow
#

didn't know you could to that elipsis syntax to get a list of integers, cool

tight marten
#

yeah its super useful

#

ig shouldnt be too hard to throw together some crappy python code to do some manual searching

tough minnow
#

I already told chatGPT to

#

ages ago

#

up to 10k

#

and it didn't find it

#

which is promising

#

because I don't believe it's out there

tight marten
#

that isnt anything ih2s

#

chatgpt cant do maths

tough minnow
#

fine I'll code it myself later

tight marten
#

oh you mean it wrote some code

tough minnow
#

but I don't think it's going to find anything

#

yeah

tight marten
#

oh ok lol i thoguht you meant you asked it to check and it said "no" LOL

#

i mean so long as you checked the code over so that it was acc doing what you wanted then yeah thats fine

#

but i feel like the numbers may just be BIG

tough minnow
#

well I'm pretty sure if they do exist they're bigger than 10^14 but not certain

tight marten
#

whered that number come from ?

tough minnow
#

I derived this problem from another problem

#

as a condition that must be met for it to be possible

#

computer searches of the original problem have gone to 10^14 and found nothing

#

but my version with the triangles is a condition that's needed for it to be possible which means if I prove it's impossible I prove the original problem impossible

#

however if I prove it possible it doesn't nessisarily mean the original problem is possible

tight marten
#

whats the original problem?

tough minnow
#

the 3x3 magic square of perfect squares

#

for one to exist, there must be a solution to my triangle problem

tight marten
#

yeah ok i well now i dont feel so good about finding one of these sets of triangles ahha

tough minnow
#

yeah that's why I didn't say it upfront

#

because I knew it would put people off

tight marten
#

๐Ÿ’€

#

yeah rightfully so lmao

#

how do the problems link btw ?

tough minnow
#

that's quite a bit of math but I have a document of it

#

I'll get it

#

wrong one, that's older

#

yeah that's it

tough minnow
# tight marten how do the problems link btw ?

for each diameter going through the center you get this general form of (c^2-o,c^2,c^2+o) which can be converted into a Pythagorean triple in this weird way where o is 4 times the area of a right triangle of integer sides and c is the hypotenuse

#

for the two diagonals the value of o is x and y, and by considering the vertical column in the middle, it's o value can be called s for sum where s=x+y

image.png
#

now you get that x+y=s and those 3 values can be seen as 4 times the area of a triangle but the 4 cancels and you simply get the fact that the area of two of the triangles adds to the area of the third

#

and they all share the same hypotenuse because c is the central square they all share

#

and that forms it

tight marten
#

are the differences significant

tough minnow
#

nah

#

mostly just extra on the end

#

about porting it to triangles

tight marten
tough minnow
#

I'm about to give up so I was hoping that maybe I could nerdsnipe someone

tight marten
#

haha

tough minnow
#

and with the problem in a different form I thought that maybe someone could get a new perspective on it

tight marten
#

im still of the opinion that finding 3 triangles will be possible

#

which as you say wont really help your cause

tough minnow
#

well it tells me for sure that it's a dead end

#

which is still helpful

tight marten
#

true

tough minnow
#

to fully encode the whole problem

#

you just add one more triangle

#

which must have an area being the difference of the first two

#

but I feel like you don't need it for it to already be impossible

tight marten
#

starting to sound less possible but idk my intuition says thats out there

tough minnow
#

one thing that is known is that if it is out there, there are only finitely many relatively prime/coprime solutions

#

for the full thing

#

ignoring the difference triangle I can't say that for sure

tight marten
#

well i wish you the best of luck getting your 10k lmao

#

or perhaps a high five

tough minnow
#

I see you have been keeping up to date