help-39

[modest chasm]

😔 should I just trial and error it more and then try to confirm with my teacher if it works

[fair creek]

just try to go one step at a time

[modest chasm]

wait btw does the 100m distance change anything?

[fair creek]

not really

it means that at least one function

should make it to 100m

[modest chasm]

ohhhh

[fair creek]

(don't worry the parabola does)

[modest chasm]

😭😭 ty i’m so lost w all this

[fair creek]

i might've had a reading comprehension moment but for our case

uh

c can be 0

(it's not specified that it's non zero so it can be)

[modest chasm]

ohhh

OH

i didnt see it

[fair creek]

we're fine just substitute (0,0) then you get values

or relations for other variables

when they have to start at origin

[modest chasm]

substitute (0,0) into the functions? — how do you do this 😔

[fair creek]

i hope you understand all the functions here though

do you?

[modest chasm]

not really

[fair creek]

this is gonna be a bit hard then

[modest chasm]

😭😭 is this my sign to drop down to standard math or js drop it completely

[fair creek]

it's fine

just

be familiar with these functions

to be able to manipulate them

[modest chasm]

ohh tyy for clearing things up!1!1!1!!1

also how would you suggest to like familiarise with functions

[fair creek]

usually by plotting them...

just see what they look like

[modest chasm]

oh..

[fair creek]

that's all i'm asking

[modest chasm]

one last question where would i add the domain on the graphing calculator thingy

[fair creek]

domain for what 🤔

[modest chasm]

i think it’s for one of the variables so that it starts at the origin

[umbral widget]

desmos?

[fair creek]

i'm not sure what you mean but

[modest chasm]

i’m using geogebra

[fair creek]

for the first and second criteria just obtain relations by inputting (0,0) i.e. D=0, t=0

[modest chasm]

ohh

OHH

[fair creek]

the bottom two are easy if you know what the graphs look like

[modest chasm]

omg ty that makes a lot of sense

[umbral widget]

try to find youtube videos

someone can explain you how they work on a graph then you can try it yourself on geoalgebra

[modest chasm]

ohhh

[umbral widget]

its best if they are using geoalgebra too

[modest chasm]

i’ll do that b4 finishing this question so that i don’t mess everything up 😔

[umbral widget]

essentially look for tutorials

[fair creek]

(usually one would use desmos for analytic geometry and function stuff)

(but geogebra works too)

[umbral widget]

i think it's more of a school thinh

mandated by school i'm guessing

[modest chasm]

i’m moving to desmos 😔

[umbral widget]

desmos is super intuitive to use

you basically get nice sliders for your input

[modest chasm]

ooh

[umbral widget]

try it, you'll not be disappointed

at one point it becomes like playing a game lol

when you get familiar with it

[modest chasm]

wait i’m using desmos rn idk how to make the line show up

[umbral widget]

youtube! look up basic tutorial on youtube

it's got you covered

[modest chasm]

OH YA

ty i have bad memory

😔😔

[umbral widget]

np, you can close the chat now if you want

https://www.youtube.com/watch?v=xdRJBsOi7g8 this should be fine

[modest chasm]

okayy thank you parabolicinsanity and transience !!1!1! your help is really encouraging and helpful 😭❤️❤️❤️❤️

.close

[pearl pond]

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[fair creek]

happy mathing

[pearl pond]

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[charred hill]

I'm trying to solve this on my casio classpad:
Tn+1 = 2Tn + 4
T6 = 444
where I have to find T1

problem is, I've been trying to solve this on my classpad but it doesn't seem to allow me

[charred hill]

As A0 is unable to be changed to A6

it's not really a math problem but a niche calculator problem

[rustic tendon]

tbh the problem is not too hard to do by hand

[charred hill]

yeah I know but there could be harder versions of this kind of question

it would be useful to know how to input a term that isn't the first

[rustic tendon]

does the calculator allow negative values for n

[charred hill]

n? N is the term position, I don't understand what you mean by that

[rustic tendon]

yeah so

does it allow negative indices

[charred hill]

I've never been taught you could go negative in a sequence

[rustic tendon]

by definition a sequence doesn't have negative indices yeah

but it might be a quirk of your calculator

since it extends naturally

oh wait actually no

yeah nvm

[rustic tendon]

just look up your model and see if anything can be done

[pearl pond]

@charred hill Has your question been resolved?

[pearl pond]

@charred hill Has your question been resolved?

[next ore]

you can do it by hand right?

[charred hill]

Yeah, if you scroll up you would see that I’ve already said it

[pearl pond]

@charred hill Has your question been resolved?

[pearl pond]

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[fading raft]

In a computer program
X and Y
After graphing the functions, the coordinate axes were deleted and a grid of equal squares was added to the background, resulting in this image
According to this, f(0)=?

[fading raft]

Tnis problem is a dumb ripof but still i cant move my pencil😭

Help😱

[pearl pond]

@fading raft Has your question been resolved?

[autumn fossil]

were the X and Y axis horizontal and vertical or were they in the directions of the square grid

and whats that integral thing?

[fading raft]

Hmm mmmmmm🤔

[autumn fossil]

what does f(x) ve integral f(x) mean?

[fading raft]

The ss low quality?

[autumn fossil]

No, its okay

[fading raft]

İdk💀

[autumn fossil]

I just dont get what it means

what does "ve" mean?

[fading raft]

Ve mean and

[autumn fossil]

oh

so it probably shows graph of f(x) and integral of f(x)

[fading raft]

Same i didnt get what is asking too

[fading raft]

Yes👍

[autumn fossil]

yeah, that sounds sufficient to figure it out

[fading raft]

Bro its like the last time similar

But its look like i didnt learned

Cuz im failed on this

[autumn fossil]

What can you see on the graph? What are those shapes?

are they circles? Parabolas? Or what?

[fading raft]

İdk😱

[autumn fossil]

they are lines

2 lines

2 linear functions

[fading raft]

They look like f(x)=ax+b

[autumn fossil]

Yeah exactly

and one is an integral of the other

isnt that interesting?

[fading raft]

But with integral is it possible?

[autumn fossil]

Integral of linear functions is usually quadratic

[fading raft]

Wait abminuteeeeeeeeeeww

soo f(x)=c ????

[autumn fossil]

Exactlyyy

one of those functions is constant

[fading raft]

😱😱😱😱😱😱😱

[autumn fossil]

and the other is then cx + d

[fading raft]

Bro how unsaw it

[autumn fossil]

for some constant d

[fading raft]

Soo okey i get it
f(x)=c
İntegralf(x)=ax+b

Alr

İm starting

[autumn fossil]

you can get better than that

you can get a more precise expression for integral of f(x)

use f(x) = c and integrate it

[fading raft]

Ahh i didnt get it😨

You mean we can find a?

Cuz its slope?

[autumn fossil]

you can write integral f(x) = cx + a

f(x) = c
int f(x) = cx + a

just by integrating f(x)

now you have only 2 variables to find

[autumn fossil]

But yeah, this is the next step. You need to figure out the sloep

[fading raft]

Now we find slope?

[autumn fossil]

yes

the constant function can serve as the x-axis

you can also shift it up and down if you wish to

then you need to make good use of the square grid provided

[fading raft]

Ehh is it 11/6?

[autumn fossil]

lemme check

idts

im getting something over 3

3 + 2/3 is what im getting

im not sure about my result tho

[fading raft]

🤔🤔🤔i messed

[autumn fossil]

i just checked my calculations with a graphing calc, i think theyre correct

[autumn fossil]

i started by shifting the x-axis

[fading raft]

Did i were calculating another thin xd..... Distraction

Whatta hell is this i found

[fading raft]

Hmmmmm🤔🤔🤔🤔

Looks true tho

[autumn fossil]

I dont think these 2 angles are the same

[fading raft]

Hmm i thought we can use z rule

You right

But we are talkin about same right😭

Oh wait

You right

[autumn fossil]

oh this looks correct

just divide it by half

(11/6) / (1/2) = 22/6 = 11 / 3

= 3 + 2/3

same result as mine

[fading raft]

Bro why did i found 11/6...

Bruh alr

[autumn fossil]

you wrote (11/6) / (1/2)

anyway, now that you have the slope you have your c

c = 11/3

[fading raft]

Hmm alr

[autumn fossil]

might be a good time to look back at the question

[fading raft]

Alr im focusing no more misscalculating bye

Lol it was asking f(0)

İts same always

11/3..

Gg

[fading raft]

Thxman this is make me solving it

What would you rate this?

[autumn fossil]

This one was fun

original

9/10, I actually saved this to my collection lol

[fading raft]

Fr😱

[fading raft]

Do you remember the Derivative grid

İ think they stole it from this xd

[autumn fossil]

Yep

i think those questions were made by the same person

[pearl pond]

@fading raft Has your question been resolved?

[fading raft]

No the first one is the original one derivative grid from yks
This one inspired by yks

Ye im talking empty but i wanted to share this info

Anyways thx friend

.close

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[pearl pond]

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[ivory mortar]

<@&268886789983436800>

[pearl pond]

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[vagrant yoke]

Can someone explain what C and P are on the Casio calculator?

[dreamy tinsel]

can you provide an image?

[toxic lichen]

most likely combinations and permutations, but yeah show your calculator

[vagrant yoke]

you are right, and its too dark where I am

[toxic lichen]

does your phone camera not have flash

[vagrant yoke]

I don't have my phone right now

[toxic lichen]

rip

[vagrant yoke]

But you are correct

How do I apply the rules to real life?

<@&286206848099549185> im still stuck

[pearl pond]

@vagrant yoke Has your question been resolved?

[dreamy tinsel]

https://www.youtube.com/watch?v=XJnIdRXUi7A

[sharp quest]

combinations is the number of ways to select k objects from n objects without considering the order they're selected in (throwing things into a bag, or poker hands, or disorganized shelf, etc)
permutations is the same thing, but we care about the order of the selection (number of outcomes for a race, an organized shelf, a list, etc.)

[vagrant yoke]

thank you all

!close

/close

.close

[pearl pond]

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[eager jewel]

convert everything to sin and cos and tell me what you get

[stiff wraith]

Wha

[eager jewel]

do u know how to convert tan and sec to in sin and cos terms?

[stiff wraith]

?

.close

[pearl pond]

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[timid grail]

i've done up to 3, but i don't understand what 4 is asking

[timid grail]

State Regular Unleaded Diesel
OH 2.27 2.15
OH 2.25 2.35
OH 2.25 1.85
OH 2.25 2.47
OH 2.25 2.45
OH 2.29 2.47
OH 2.07 2.28
IN 2.15 2.28
IN 2.14 2.28
IN 2.07 2.29
IN 2.07 2.28
IN 2.14 2.28
IN 2.29 2.26
IN 2.25 2.24
IN 2.29 2.26
IN 2.25 2.27
IN 2.25 2.25
IL 2.19 2.39
IL 2.29 2.35
IL 2.29 2.35
IL 1.99 2.41
IL 1.99 2.45
IL 1.99 2.38
IL 1.99 2.47
IL 1.99 2.39
IL 1.99 2.47
IL 2.25 2.35
IL 2.19 2.38
IL 2.35 2.39
MO 2.19 2.06
MO 2.19 2.06
MO 2.17 2.06
MO 2.17 2.06
MO 2.17 2.07
MO 2.17 2.09
MO 2.19 2.06
MO 2.19 2.06
MO 2.06 2.13
MO 2.15 2.13
MO 2.04 1.99
MO 2.04 1.95
MO 1.89 2.05
MO 1.87 2.25
MO 1.99 2.07
MO 1.95 2.18
MO 1.99 2.21
MO 1.99 2.07
MO 1.99 2.09
MO 1.91 2.15
MO 1.87 2.18
MO 1.99 2.05
KS 2.05 2.04
KS 2.05 2.04
KS 1.97 2.34
KS 1.88 2.35
KS 1.87 2.23
KS 1.89 2.35
KS 1.89 2.16
KS 1.99 2.15
KS 2.25 2.18
KS 1.89 2.04
KS 2.09 2.27
KS 1.96 2.15
KS 1.99 2.33
KS 2.09 2.23
KS 2.11 2.19
KS 2.09 2.29
KS 2.09 2.34
KS 1.93 2.24
KS 1.93 2.39
KS 1.97 2.15
CO 2.14 2.18
CO 2.21 2.18
CO 2.05 2.37
CO 2.05 2.35
CO 2.15 2.28
CO 2.05 2.09
CO 2.19 2.09
CO 2.09 2.35
CO 2.07 1.99
CO 2.05 2.37
CO 2.09 2.19

[pearl pond]

@timid grail Has your question been resolved?

[timid grail]

<@&286206848099549185>

.close

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[plucky carbon]

I am stuck how do I get to x ?

[plucky carbon]

10x-174/11=46

I could move it to the other side but I don't see the point of doing that

[dapper kraken]

$$10x-\frac{174}{11}=46$$
$$\frac{10x-174}{11}=46$$
do you mean the first one or the second one?

[jolly parrot]

skissue.in.a.teacup

[plucky carbon]

first sir

[dapper kraken]

you would actually want to move the 174/11 to the other side to isolate x

[plucky carbon]

ok now I have 10x=46+174/11

[plucky carbon]

do I have to change 46 into a fraction and if yes how so

[dapper kraken]

yes, multiply it by 11/11 so that the denominator is the same with 174/11, so you can combine them

[plucky carbon]

so do 46 * 11/11 ?

[dapper kraken]

yes

so it will be like $\frac{46\cdot 11}{11}$

[jolly parrot]

skissue.in.a.teacup

[plucky carbon]

do I have to do the other side too ?

[dapper kraken]

nah

essentially you would make it $10x=\frac{46\cdot 11}{11}+\frac{174}{11}$

[jolly parrot]

skissue.in.a.teacup

[plucky carbon]

ok

so 506/11 + 174/11

which is 680/11

[dapper kraken]

sorry something came up i have to go, i hope you can finish this, if your still confused you can wait for somebody else to help you, goodluck!

[plucky carbon]

thanks

<@&286206848099549185>

[plush bramble]

Is this your x

[plucky carbon]

no

[plush bramble]

Or are you just simplifying the right side

[plucky carbon]

just simplifying rn I have 10x=680/11

[plush bramble]

If you have 10x = number, then what can you do to isolate x

[plucky carbon]

divide by 10

bruh how do i do (680/11) / 10

can i just type that shit in the calc

well I did and got 68/11

[plush bramble]

Idk can you

[plucky carbon]

I mean I didn't get a syntax error so I guess

[versed mica]

you needed a calc for that?

[plush bramble]

You can always plug 68/11 into the original equation to verify your answer

[versed mica]

what’s 69374747370/10?

[plucky carbon]

idk

[plucky carbon]

thanks

[versed mica]

tough

[plucky carbon]

it just got rid of the 0 i'm seeing a pattern here

[versed mica]

yep

[plucky carbon]

https://tenor.com/view/bigbrainbarnes-gif-6132461259902152472

.close

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[plucky carbon]

hey just had one like this but this is more confusing so its 6x+7(142/13)=-2

[plucky carbon]

so I did 7*142

which is 994

so u get 6x+994/13=-2

then I move it so its like this 6x=-2-994/13

but if I do -2*13/13 I get -26/13 which is -2 so what do I do ?

cause I can't get two fractions on the right so do I just divide by 6 ?

or can I leave it in fraction form as -26/13 and proceed

?

got it

.close

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[placid geyser]

Sketch the values of r between 1 + 2 sin theta

Where the bounds are pi/6 and pi

So, sketch the region in between the following equations:
Theta = pi/6
Theta = pi
R = 0
R = 1 + 2 sin theta

And shade the region in between

Wait, I'll send the graph

,rotate

[placid geyser]

This

Wdym?

No, u don't have to plug it

It's the region in between the 2 theta values such that it's also between r = 0 and r = 1 + 2 sin theta graph

[midnight haven]

https://tenor.com/view/minecraft-minecraft-movie-a-minecraft-movie-steve-jack-black-gif-4079785775268000209

[pearl pond]

@spring crystal Has your question been resolved?

[pearl pond]

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[worn turret]

For this question, why is P_1 and P_2 element of P_7 when proving closure under vector addition?

[harsh gyro]

because degree(P) = degree(P_1) + 2

so degree(P_1) < degree(P) <= 7

[worn turret]

shoudn't it be P_5 since x^2+7x+9 is a factor of p(x)?

[harsh gyro]

sure but P_5 is a subset of P_7

so it's still in P_7

[worn turret]

oh I see

that P_7 notation means at most degree 7 or less right?

[harsh gyro]

yes

[worn turret]

got it, thanks

.close

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[mighty nexus]

can anyone tell me how can i solve a equation?

show that, cos²θ/1+cos²θ = (1 + cosθ) (1 - cosθ)

pls help me with my maths homework

[pearl pond]

Please don't occupy multiple help channels.

[snow moss]

You need to show that cos²θ/1+cos²θ is the same (1 + cosθ) (1 - cosθ). So you need to rewrite one side of the equation
Try expanding (1 + cosθ) (1 - cosθ)

[toxic lichen]

duplicate channel?

or close your previous

[mighty nexus]

alr

sorry

[toxic lichen]

ok yeah im closing this one and you can continue in #help-5

.close

[pearl pond]

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[mighty nexus]

👍 pls help me there

[toxic lichen]

no guarantees, sorry.

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[heavy hill]

can someone explain how to do part ii)

[heavy hill]

these are the solutions but i dont understand how they got that

i thought that it would be this:

[toxic lichen]

the tunnel lengths after the n'th pickaxe is worn out follow an arithmetic progression

with 0th term 100 and common difference 40

[toxic lichen]

ngl your diagram doesnt make a lot of sense to me either

[compact ridge]

the 40s are distances

so they really should have put $\underbrace{40}$ I agree

[jolly parrot]

south

[merry carbon]

(also bear in mind that the miner starts their "shift" at the start of the tunnel: they travel the 100 metres to where it was dug, then dig the 40m (in the process travelling), then have to return that 140m to the start, then back the 140m to where they dug up to...)

[pearl pond]

@heavy hill Has your question been resolved?

[heavy hill]

hey!!! so that makes sense, but is that not what i did in my solution?

[merry carbon]

Where did you get the 360 from? (it seems like you're including some of the distance in that S_n which will make things out of line of what they want from you)

e.g. when the first pickaxe breaks (so n = 1), you'd have travelled 280m, but your formula doesn't get that

[merry carbon]

Actually I see, you've effectively included what you'd have when you've gotten two pickaxes broken

[merry carbon]

Hence my comment here

[pearl pond]

@heavy hill Has your question been resolved?

[pearl pond]

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[pearl pond]

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[west osprey]

I want to find the average amount of rolls it would take to get something of whatever rarity, but your luck increases by 0.25% each roll.

So a chance of 1% becomes 1.0025% in the second roll and so on.

[cold tapir]

hi bot can you help me with this question

[west osprey]

nope

[placid geyser]

I think I got something but am not too sure

Wait, for "avg number of turns", should the probability of obtaining it be above 99% or what?

I'm new to such type of questions

[west osprey]

I mean, if the chance is 1%, then the average number of rolls should be 100 normally

[placid geyser]

So, to get 100%

[west osprey]

maybe average is the wrong word, but idk

100/chance

[placid geyser]

What about "ideal number of turns"?

Okay

[cold tapir]

so what

some body help jhon-cena

[west osprey]

fr

[placid geyser]

How about this?

[placid geyser]

I was writing it down

[west osprey]

I'm not gonna lie, I don't even know what some of those symbols do

[cold tapir]

@west osprey yeah i too tried it out

[placid geyser]

$\sum$ and $\Pi$?

[jolly parrot]

Suika

[cold tapir]

bro what is this

[placid geyser]

Huh?

[cold tapir]

what is that

above

[placid geyser]

I'm asking whether these r the symbols john said he can't understand

Cause I can't think of any other complex symbols that I used

[cold tapir]

okay okay

[west osprey]

I know what Pi is but yeah that huge E I dont know

[cold tapir]

same here

[placid geyser]

No, they r symbols for sum and product

They r greek letters sigma (E like) and pi respectively

[west osprey]

Well, does the formula work for what I said?

[placid geyser]

Idk

It's hard to calculate

[west osprey]

😭

[placid geyser]

I think taking a = 0 would make things easier

https://www.vedantu.com/jee-main/chemistry-sigma-and-pi-notation

Read the "Summation Symbol" and "Pi Symbol" headings' details

Idk why it says chemistry in the link though

[west osprey]

I mean if you want me to understand all that, I'm gonna be here all day

[pearl pond]

@west osprey Has your question been resolved?

[west osprey]

I noticed you wrote that we need to have 100% of getting it before n turns. But I don't think that's what I'm asking.

Basically, if a 1% chance is an average of 100 rolls, how would a 0.25% increase in luck per roll affect that.

So in the second roll, that 1% chance is actually 1.0025%
Third roll is 1.005%
etc.

(It's not a hard +0.25 to the roll chance, it's +0.25% to your luck. So [roll chance+0.25%] in second roll, [roll chance+0.5%] in third roll)

[pearl pond]

@west osprey Has your question been resolved?

[eager jewel]

wait ur preparing for jee??

[placid geyser]

Yes

[eager jewel]

oh then why do u have undergrad math role

[placid geyser]

Idk what it means

I just kept it

[eager jewel]

undergrad is what u take up after 12th

when are u going to write jee

[placid geyser]

Oh

[eager jewel]

2027?

[placid geyser]

Yes

[placid geyser]

Then what am I supposed to select?

[eager jewel]

pre university

[placid geyser]

I thought undergrad meant something like before graduation...

Wait wait wait

Makes sense

Ok lol

Ig I had pre university before but idk why it felt like it should be the next one

So I changed it

[eager jewel]

ohh ok xd

[west osprey]

Going to sleep

[worthy temple]

i am also preparing for jee advance rn

[west osprey]

.

[pearl pond]

@west osprey Has your question been resolved?

[pearl pond]

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[pearl pond]

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[hushed leaf]

hey

[hushed leaf]

does this not apply the modification rule?

since e^-2x are both present

[pearl pond]

@hushed leaf Has your question been resolved?

[hushed leaf]

help please

[pearl pond]

@hushed leaf Has your question been resolved?

[pearl pond]

@hushed leaf Has your question been resolved?

[pearl pond]

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[frozen field]

I cant do radicals for my life.

[frozen field]

Even the most simple stuff its just like, not registering for me.

Could be a √5

3√6+4√6=

Still couldnt solve

I need some help

[celest cedar]

3a + 4a = ?

[frozen field]

My stupid ahh guesses 7a-

I am a bit lost

[celest cedar]

correct!

[frozen field]

Oh

[celest cedar]

Consider root 6 as a

[frozen field]

Oh..

Thats

Simple

What if its a different radical, lets say

[celest cedar]

Yes, sometimes u need to simplify

[frozen field]

2√4+2√7

[celest cedar]

U can't that's like a and b

Different

[frozen field]

Oh right

[celest cedar]

But u can factorise

2 (√4+√7)

[frozen field]

So the answer would be 4 (√11)?

[spare lark]

<@&268886789983436800>

[frozen field]

Huh

[celest cedar]

$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2}$

Dont click on the link

[frozen field]

Ik

Grabify

Prob

[jolly parrot]

SLANDER

[celest cedar]

That's a simplification

[frozen field]

Thats usefull

[celest cedar]

Another thing,

$\sqrt{5} + \sqrt{4} \neq \sqrt{9}$

[jolly parrot]

SLANDER

[celest cedar]

U can't add different roots

[frozen field]

Right

[celest cedar]

But u can multiplie them

Or divide

Consider $\sqrt{4}$ as a and $\sqrt{5}$ as b

[jolly parrot]

SLANDER

[frozen field]

Right

Seems simple when explained

[celest cedar]

It's simple

U will use it a lot later

$\sqrt{5 + 4} \neq \sqrt{5} + \sqrt{4}$

[jolly parrot]

SLANDER

[frozen field]

√9?

[celest cedar]

$\sqrt{5+4} = 3$ and $\sqrt{5} + \sqrt{4} = 4.23\cdots$

[jolly parrot]

SLANDER

[celest cedar]

Yes

[frozen field]

Wait 3-

[celest cedar]

3 or - 3

But that's if u have variable

Like x = root 3

[frozen field]

Right

Makes...sense

[celest cedar]

Any more questions?

Fractions?

Exponents?

[frozen field]

Yes thatd be good, fractions

[celest cedar]

$\frac{x}{x + 2} \neq \frac{x}{x} + \frac{x}{2}$

[jolly parrot]

SLANDER

[frozen field]

https://tenor.com/view/daeth-funi-periflight-dies-from-gif-22212023

[celest cedar]

You cannot split the denominator.

[frozen field]

Oh god

Right, cant split the denominator.

[celest cedar]

$\frac{4}{5 + 3} \neq \frac45 + \frac43$

[jolly parrot]

SLANDER

[celest cedar]

Try to calcul it

You will find different values.

[frozen field]

It seems so simple but like..

Isnt.

[celest cedar]

8/4 = 2

Right?

[frozen field]

Right

[celest cedar]

4 = 2+2

8/2 + 8/2 = 4 + 4 = 8

So: 8/4 /=/ 8/2 + 8/2

[frozen field]

Right

[celest cedar]

That's it

[frozen field]

I am surprised it took me 30 secs to comprehend that

Shouldbe prob been less

[celest cedar]

$\frac {x + 1}{x} = \frac{x}{x} + \frac{1}{x}$

[jolly parrot]

SLANDER

[celest cedar]

Take ur time

Lets change that x

[frozen field]

Yep..

[celest cedar]

$\frac {4 + 1}{2} = \frac{4}{2} + \frac{1}{2}$

[jolly parrot]

SLANDER

[celest cedar]

4/2 = 2 and 1/2 = 0.5
So: 2 + 0.5 = 2.5

And 5/2 = 2.5

That's True!

[frozen field]

I really hope i get the hang of this, ima just keep practicing

Youve actually been help.

Thank you

[celest cedar]

Ur wlc

!done

[pearl pond]

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

[frozen field]

.close

[pearl pond]

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[pearl pond]

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[versed mica]

<@&268886789983436800>

[pearl pond]

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[eager jewel]

was not able to make much progress

[rustic tendon]

hmm

I think you're gonna have to list all subsets that add up to 45

[eager jewel]

that is exactly the problem i had

at first i did n(n-1)/2 hoping the sum of first 10 natural numbers would be 45

but nope

[edgy stone]

it would be easier to start from 55 and then remove subsets that add up to 10, i think

slightly

but is there an actually nice way...

[eager jewel]

yeah?

[rustic tendon]

yeah I was gonna suggest that

So find the number of subsets that add up to 10, and then your answer will be the sum of $(-1)^k \prod_{k \in S_i} k$

[jolly parrot]

dyxn

[eager jewel]

uh

?

[rustic tendon]

bad notation

the highest power of x is 55 here

and we need 10 less than that

the way we get 10 less is by picking the constant term instead of the actual power

agreed?

[eager jewel]

yes

[rustic tendon]

so we need to reduce by 10, find the indices that add up to 10, and pick their constant terms

[eager jewel]

by constant term do u mean coefficient?

[rustic tendon]

{10}
{1, 9}, {2, 8}, {3, 7}, {4,6}
{1, 2, 7}, {1, 3, 6}, {2, 3, 5}
{1, 2, 3, 4}

[rustic tendon]

the constant term in each parenthetical

the -i basically

[eager jewel]

oh ok let me try this

[eager jewel]

yeah i got the answer using this

but i am a bit unclear about what we did exactly

[eager jewel]

we started with x^55 and we chose the -i term instead of the power in all these cases?

[rustic tendon]

yeah basically

we worked down instead of up

[eager jewel]

ohh okay thanks a lot man

this is a new concept to me

[rustic tendon]

you should also be asleep now

[eager jewel]

XD

my sleep schedules is F'ed man

i sleep at 5:30 and wake up at 11:30

[rustic tendon]

unhealthy but I do the same

[eager jewel]

XD ur also indian?

[rustic tendon]

yes

[eager jewel]

which city

[rustic tendon]

i'm at bits in goa rn

[eager jewel]

WOAHHHH

i have a friend at bits goa

[rustic tendon]

that's nice

everyone does for some reason

[edgy stone]

there is also (1, 4, 5), i think

[eager jewel]

yeah counted that

coeff = 2

[eager jewel]

thank you^^

[eager jewel]

how is bits? i hope ill get in their as well

[rustic tendon]

it's lovely

:D

[eager jewel]

so college life is not too stressful/studious right?

[rustic tendon]

depends 🫠 I really should study more

[eager jewel]

dawg u need to study more?

[rustic tendon]

I tend to do only math and computers slack on everything else

[rustic tendon]

you still need to study

but at least it's at my own pace

[eager jewel]

oh u got cs?

[rustic tendon]

fuck cs

i'm doing math and computing

far superior

[eager jewel]

ohhh

im aiming for electrical

[rustic tendon]

don't come to bits goa then

EEE and to some extent ENI is pretty fucked

[eager jewel]

oh man

[rustic tendon]

ECE is alright

[eager jewel]

what about the pilani campus? would u say goa is better?

[rustic tendon]

although next semester onwards there's a new BE programme called electronics and computers or something

fusion

[eager jewel]

OOH

that is great

[rustic tendon]

pilani is too far from my domicile city, i wouldn't consider going there

but i have friends there

[eager jewel]

oh ive heard it is kind of cut off

middle of the desert

[rustic tendon]

it is

also they're in a staggering amount of debt

[eager jewel]

oof

[rustic tendon]

so their fests and stuff suffer

[eager jewel]

how are they in debt

isnt it a private college

[rustic tendon]

yeah imagine

their student welfare division owes over a crore afaik

goa has like 3 departments just to ensure that we aren't in debt

[eager jewel]

ugh

how were placements this year

at goa

[rustic tendon]

i don't know tbh

[eager jewel]

i heard bits has good placement %age

well anyway

i better get back to the questions

[rustic tendon]

good placements and good salaries

[pearl pond]

@eager jewel Has your question been resolved?

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[pearl pond]

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

[eager jewel]

added the three eqns which makes rhs = 0

but that did not help

so ig 1

[dense jasper]

Hint: Recall that $$a^{\log_b (c)}=c^{\log_b (a)}$$

[jolly parrot]

Civil Service Pigeon

[eager jewel]

okay but how would i use that

there are no powers

(in the 3 eqns given)

[dense jasper]

I mean

You want xyz

So solving for x, y, z isn’t unreasonable

[eager jewel]

right

could u give me the next step?

[dense jasper]

Try working with what I gave you so far

That’s all you need anyway

[eager jewel]

abbe yaar

ok fine

[rustic tendon]

yeah i think it's better to just isolate x y and z and multiply them together and see what happens

[eager jewel]

oh thats what he meant

[rustic tendon]

$xyz = 3^{\log(7/11)}7^{\log(11/3)}11^{\log(3/7)}$

[jolly parrot]

dyxn

[eager jewel]

ohhhhhhhhhh

[rustic tendon]

you can interchange the argument and the base of the exponent

[eager jewel]

got it

love u bro

.close

[pearl pond]

Channel closed

Closed by @eager jewel

Use .reopen if this was a mistake.

[eager jewel]

.reopen

[pearl pond]

✅

[rustic tendon]

💀

factorize

(a + b)(a^2 + b^2 -ab)

a + b is 11

[eager jewel]

came in my test btw 😭

[rustic tendon]

11(a^2 + b^2 - ab - 1) + 33ab

hmm

11(a^2 + b^2 + 2ab - 1)

11( 11^2 - 1) =1,320

so all you need to find is the log

mb

edited to fix

there's probably something Im missing

[eager jewel]

uh what did u do here exactly?

[rustic tendon]

first favtorize a^3 + b^3

[dense jasper]

The sums are equal (reindex one of the sums by doing r -> 12-r)

[rustic tendon]

yeah makes sense

[dense jasper]

I’ll let you do the explaining

👋

[rustic tendon]

so you have (a + b)(a^2 + b^2 -ab)

[eager jewel]

yeah
i got a^2 + b^2 - ab -11 + 33 ab

[rustic tendon]

11(a^2 + b^2 - ab)

[rustic tendon]

since a + b = 11

[eager jewel]

oh shit

i took a+b = 1

;/

[rustic tendon]

right so that part is sorted

[eager jewel]

yeah

[rustic tendon]

now as civil service pigeon said the two sums are equal

c and d that is

[eager jewel]

how are they equal?

[jolly parrot]

dyxn

[rustic tendon]

write it out term by term and apply this

[eager jewel]

oh okay

[rustic tendon]

so you have log (1/1) =0

At least I think it's meant to be a fraction in the argument

kind of looks like an exponent and a base 💀

[eager jewel]

yeah thats what i thought

[rustic tendon]

but log_1 is undefined so

[eager jewel]

are u sure about this part?

[rustic tendon]

hmm

let's run it back

[eager jewel]

yeah cause answer is not matching

[rustic tendon]

11(a^2 + b^2 -ab) - 121 + 33ab
11(a^2 + b^2 + 2ab) - 121
11(11)^2 - 121 =1,210

yeah I made a mistake

11(a + b) = 121 not 11

[eager jewel]

oh okay yeah

and i think it is an exponent and a base

so that log term should come out to 1

[rustic tendon]

oh it's just 1

yeah mb for some dumb reason I thought the sum was 1

[eager jewel]

okay so our answer is 1211

yeah it matches

thats crazy the question wasnt that hard

[rustic tendon]

they usually aren't

they're a deterrent for the feint hearted

[eager jewel]

im still a bit confused about the sums being equal

[eager jewel]

come on would you try attempting the question upon seeing summation cot ^3 ?

[rustic tendon]

$\tan \frac \pi{24} = \cot \frac{11\pi}{24}$

[eager jewel]

OH

[jolly parrot]

dyxn

[eager jewel]

nvm got it

yeah

[rustic tendon]

yes 100%

[eager jewel]

;/

[rustic tendon]

the ones that look the hardest are the easiest

[eager jewel]

yeah i thought that

i went to an exam

[rustic tendon]

at least stuff like this

[eager jewel]

saw a really hard q

and thought this must be ez

and it turns out IT WAS HARD

so never did that again

[rustic tendon]

jebaited

[eager jewel]

;//

.reopen

.close

[pearl pond]

Channel closed

Closed by @eager jewel

Use .reopen if this was a mistake.

[eager jewel]

.reopen

[pearl pond]

✅

[eager jewel]

not really able to understand q

[dense jasper]

What specifically don’t you understand?

[eager jewel]

p(s) denotes set of subsets

[dense jasper]

Ex. If we had the set {1,3,5}

Then P(S) would be $${{}, {1}, {3}, {5}, {1,3}, {1,5}, {3,5}, {1,3,5}}$$

[jolly parrot]

Civil Service Pigeon

[dense jasper]

This is known as the power set of S btw

[rustic tendon]

notice that by the construction of a power set, an element is either there or not there in a subset

so can you guess how many times each element would show up in the total sum

[dense jasper]

^^

[rustic tendon]

first off, how many subsets does a power set generate?

[eager jewel]

2^11 subsets

[rustic tendon]

yeah

[rustic tendon]

btw you could probably just count here and notice the pattern

[rustic tendon]

this is importsnt btw

there's a 50/50 chance that an element is in a randomly selected subset or not

[eager jewel]

wait

[eager jewel]

would it be 2^10?

[rustic tendon]

yeah

so it's just 2^(10)(1 + 3 + 5 + ... + 21) which is 2^(10)*11^2

[eager jewel]

oh so u just multiply the summation of the whole set by 2^10

so the answer is 121

thanks man

do you have any tips for me studying wise

struggling with a lot many of these questions

[rustic tendon]

don't be intimidated by these

in many cases reducing the problem size will help

like that previous trig summation question

instead of starting with 11, start with 2

here too, reduce the size of the set down to {1, 3, 5}

it becomes easier to solve, and then when you know how to do it move on to these ones

[eager jewel]

oh alright

thank you

[pearl pond]

@eager jewel Has your question been resolved?

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[autumn marsh]

hello I was wondering if I could see if my proof is correct for this question please?

[autumn marsh]

here is my proof handwritten

[median rock]

yeah its correct

but what if (2k+1)^2 - 1 = 2

then it won't be divisible by 4

[autumn marsh]

good to know thank you

[median rock]

You can do it like that

You can explain more thk if u want

[autumn marsh]

From what you proof says it seems like you expanded (2k+1)^2 and got 4k^2+4k+1 and found that in order for this to be divisible by 4 you subtracted by 1 giving b=4 for the congruency statement and then from the def of congruency statement 4|(4k^2+4k+1)-1=4|(4(k^2+k) where k^2 +k is an integer and by def of divisibility the case for odds is true

Am i on the right track?

Was me not expanding the (2k+1)^2 the problem or am I still neglecting the case where (2k+1)^2-1< 4 ?

[autumn marsh]

wouldn't that mean that 2k+1 would not be an integer then? because this would mean that (2k+1)^2 would equal 3 and (2k+1) in this case would be sqrt(3). Now that I think about it, would that mean that k would have to exclude zero for this to work?

[median rock]

oh yeah true I forgot about that

no k can be 0 since n in IZ

[median rock]

maybe that would work then

but I think you gotta explain why (2k+1)^2 -1 is divisible by 4

[median rock]

which you said here so its good

[autumn marsh]

sounds great thank you for your help 🙂

[median rock]

no problem

[autumn marsh]

Sorry about this. But I just have 1 more quesiton please? The homework that I am doing is asking for an outline for an alternative method in doing this proof. My professor hinted that there was a way of doing this without splitting it into cases. I was thinking about doing an arguement revolving around consecutive integers and the fact that 2 consecutive integers have opposite parity. Do you think that approaching the proof from this angle is feasible?

[median rock]

can you show how

and the question includes cases how can u solve it without using those cases the question gave you

[autumn marsh]

I have no idea other than that 😂

tbh. That's just what he said. I appreciate that he wants us to think about different approaches in proving it but I still have no clue how to do this without involving cases into the strategy.

I guess this part is in the "reflection part" of our assignment so I hope he doesn't dock me points for saying some bs. I'll see if there's something that is missing and try and expand on my original thoughts.

[pearl pond]

@autumn marsh Has your question been resolved?

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[shadow stag]

$\to$

[jolly parrot]

lpieleanu

[shadow stag]

wtf

$\to should be the right arrow thingy???

wait why did my color change

[fair creek]

april fools

[shadow stag]

the $\to thing or the color change thing

[fair creek]

to thing

[versed mica]

no?

it was always like this wdym?

[shadow stag]

huh are you sure

[fair creek]

gaslighting is crazy

[versed mica]

yea

[shadow stag]

i've used $\to before (not with texit tho) and its always been a right arrow

[versed mica]

uhh no

[fair creek]

https://tenor.com/view/how-it-feels-when-you-meme-nanami-jjk-gif-10683277372535996893

[indigo pewter]

💀

[shadow stag]

texit pulling an april fools joke is wild

[versed mica]

$\to \ni$

[jolly parrot]

knief

[versed mica]

$\to \cdots$

[jolly parrot]

knief

[fair creek]

💀

[fringe robin]

is that thing riemann integrable...?

[fair creek]

<@&286206848099549185>

[fringe robin]

why did you ping Helpers

[fair creek]

who's gonna help you then 😔

[fringe robin]

I'm not the one needing help

I just don't think that that thing is riemann integrable

[fair creek]

help the guy then 😔

[near wharf]

T_T

[versed mica]

$\rotatebox{90}{$\to$}$

[shadow stag]

so the function is $f: [0,1] \to \mathbb{R}$

[jolly parrot]

lpieleanu

knief

[fair creek]

😔 can @near wharf get some help ong stop being nuisances

[fringe robin]

why are you mini modding

[versed mica]

$\vdots \ \rotatebox{90}{$\to$}$

[jolly parrot]

knief

[versed mica]

fr

[fringe robin]

where did you get this from

and this is continuous almost nowhere so can't be Riemann integrable

[near wharf]

lecture notes hahaha

[fringe robin]

no way

are you at Nottingham Trent or something

Can you show the whole text?

[versed mica]

y’all are in the same class

[fringe robin]

like not the bit you cut out

preferably the whole page

[near wharf]

man im not lying to you

its example 5. i can show g is,integrable and gof is not

[fringe robin]

yeah I think I'm wrong

lemme try work out why

[plush bramble]

this is incorrect

[fringe robin]

not bounded right?

[plush bramble]

https://math.stackexchange.com/questions/500796/need-example-a-riemann-integrable-function-is-not-continuous

https://en.wikipedia.org/wiki/Thomae's_function

[near wharf]

homies name is riemann im sure he got this

[versed mica]

reincarnation

[pearl pond]

@near wharf Has your question been resolved?

[lime hollow]

@near wharf

[pearl pond]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[peak prawn]

can someone show hand working out of how this was done

[vital crescent]

which line number are you confused with?

[peak prawn]

uhh ghoing from line 2 to line 3

[vital crescent]

well z^2+2z+1 is (z+1)^2, and 4 is -(2i)^2

so well z^2+2z+1+4 is (z+1)^2 -(2i)^2

does that clear things up?

[peak prawn]

ohh right

and then difference of two squares

(z+1)^2 - (2i)^2

a = z + 1

a^2 - b^2 = (a+b)(a-b)

therefore

(z+1 - 2i)(z+1+2i)

okay thank u so much

[vital crescent]

precisely!

np

[peak prawn]

.close

[pearl pond]

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[pearl pond]

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[cold tapir]

.close

[pearl pond]

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as this action is irreversible, and this channel may abruptly lock.

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[heavy hill]

can someone help me do d, f and g?

i dont really understand how to do it

[tulip matrix]

hmm

so when does the particle would pass through the rorigin

do yk?

[tulip matrix]

lol

[lilac jackal]

did u not try anything yet

[terse tartan]

g(x) is velocity.

Thus it would pass through the origin when there is no displacement.

Acceleration would be 0 when the first derivative of velocity is 0 or when the second derivative of displacement is 0.

displacement being s(t)

[tulip matrix]

Ye he will have to equate the integral to 0

[terse tartan]

t=0 ?

[tulip matrix]

no lol

wait 1 sec

mb

s(t)=0 right cuz at that time pos = 0

[terse tartan]

No I think it's t=6

Because the areas of the triangles are the same but one is negative and other positive. Canceling out for the integral to equal 0.

[pearl pond]

@heavy hill Has your question been resolved?

[terse tartan]

I meant x=6 not t=6

[past perch]

for d we know that since s(t) = integral of g(x) with no constant, the particle STARTS at the origin since the integral from 0 to 0 would be 0

so basically the question is asking when does it reach the origin after leaving the first time

to understand d it would help if you understand F first

so let's do that

BELOW the x axis the velocity is negative meaning movement in a negative direction. let's assume negative means left from the origin point.
now even though the graph is going up, the movement is still left. this is a weird concept to understand but basically for every value on the graph see the y axis value. if the value is positive, then it is moving right, if it is negative it is moving left.

if we know the particles instantaneous velocity we can find it's direction of motion, left or right

now as for towards or away, that brings in a relative frame of reference to the origin

it's no longer just left or right

imagine youre the particle

you start moving with a negative velocity

you start moving left from the place you started

[pearl pond]

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[past perch]

you're moving AWAY from where you started