help-23

[gritty lotus]

ahhhh

that makes sense now

you pulled out the 48 in such a way that k is left

and from there u use the summation rules

so for the one next to 48/n

its a n*k

wait no

its n * some variable so we use the formula n(n+1)/2 right

so then do we just swap k for n?

cause the correct answer has no k in it

i got this from my profs sollutions

and he completely gets rid of k

[icy lance]

i think youre fixating too much on the n outside the sum and its confusing you, its just a number

just think of it as a constant you pulled out

[gritty lotus]

right

so why do we have all ns in the solution?

[icy lance]

because the general formulae are in terms of n, i agree with what you said here to a degree, it would just then be 48/n * n(n+1)/2 which is what you see in the answer

[gritty lotus]

ah ok makes sense

i think maybe if they used a different variable it woulda been a bit more clearer

but that explains alot thanks!

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[wraith prism]

I tried to solve it last night and here are my replies. #help-26 message

[wraith prism]

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[bright turtle]

how do i do this

[light shoal]

,rotate

[bright turtle]

what do i do

[safe radish]

@bright turtle Has your question been resolved?

[lean thorn]

hi there just follow the numbered instructions

it shows you how to solve them above

[bright turtle]

what

[worthy hemlock]

Just follow the given steps

For the first problem, the first step says, "write the proportion", did you write out the proportion?

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[lean thorn]

assuming you're not trolling, what are you confused about?

[edgy walrus]

ok im trolling ill delete messages and stop im sorry

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[pastel verge]

assumption was right

[edgy walrus]

it was

i will never do it again

i swear

[pastel verge]

then assumption was wrong

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[whole forge]

Am tutoring someone and was asked to help for this. Just to check that I am not missing anything. You have to leave the answer in terms of either the initial radius,r(0) or volume v(0) right? Not possible to find an exact solution

[stray socket]

You need to set up a differential

[whole forge]

So what I did was, let V be volume of sphere, S be surface area of sphere

dV/dt=4πr^2(dr/dt)
dS/dt=8πr(dr/dt)

I don't see any way of continuing this without an initial value of r

[quasi bison]

you're gonna need to leave the answer in terms of r yes

[whole forge]

Okay that's all thank you

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[prisma epoch]

Answer for 46, how did we get it?

[drifting elk]

x^3 - 3x^2 - 7x + 21 = 
x^2 (x - 3) - 7 (x - 3) =
(x^2 - 7)(x - 3) =
(x - sqrt(7))(x + sqrt(7))(x - 3)

and then just substitute

[prisma epoch]

Substitute what?

[drifting elk]

the zeroes found by factorization

[prisma epoch]

Okay got it

Thanks

[prisma epoch]

Also any idea how 48 is done?

[prisma epoch]

Correct option is a) 1/2^128

[vestal pulsar]

its a proof

actually

[prisma epoch]

What? Sorry I don’t understand

[drifting elk]

(sqrt(x))^(1/16) = 1/16

[prisma epoch]

How we get that sqrt x is power to 1/16

Since it is a infinite series of power

[drifting elk]

well, you just raise sqrt(x) to the power of the whole left side, which is equal to 1/16

[prisma epoch]

Why?

[vestal pulsar]

can we take √x as 2

like assuming that

[drifting elk]

because sqrt(x) ^ (sqrt(x) ^ (sqrt(x) ^ ...)) is the same as sqrt(x) ^ (sqrt(x) ^ ...)

[vestal pulsar]

yea like basically we replace that

[drifting elk]

you can't actually always use this technique, sometimes the thing might not converge at all, but since you are expected to choose one of the answers, we don't need to think about it too much

[vestal pulsar]

anyways to prove it

?

[prisma epoch]

Aren’t those two things the same so where does 1/16 come?

[drifting elk]

yes they are, and they both equal 1/16

but then you can also rewrite the first as sqrt(x) ^ (1/16)

because the second one is 1/16

and so is the first one, thus sqrt(x) ^ (1/16) = 1/16

[prisma epoch]

How is the second one 1/16

[drifting elk]

because the first one is

and they are equal

it's just what's stated in the problem

[prisma epoch]

So shouldn’t it be 1/16^1/16……

[drifting elk]

no

[prisma epoch]

Like if you would have to write an explanation for this in the exam how would you frame it so that the professor understands how you concluded that?

You say that sqrt(x)= 1/16?

[drifting elk]

let's denote the whole thing as y, so y = sqrt(x) ^ (sqrt(x) ^ (sqrt(x) ^ ...)) = 1/16
note that y = sqrt(x) ^ y

and since y = 1/16, 1/16 = sqrt(x) ^ (1/16)

[prisma epoch]

Okay so we get sqrt(x)^y = 1/16

[drifting elk]

yes, with y = 1/16

so just solve for x

[prisma epoch]

Okay so how did we assume that the 1/16=y. I understand that sqrt(x)^y = 1/16 how do we find y from this?

[drifting elk]

just by definition, here

we defined y as the left-hand side of the equation

obviously it equals to the right-hand side as well

[prisma epoch]

Okay I got it so we get sqrt(x)^1/16 = 1/16 how do we solve for x from here?

We get x^1/32 = 1/16

[drifting elk]

yes, then just raise both sides to the power of 32

to eliminate the ^(1/32) part

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[glacial lodge]

no

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[glacial lodge]

<@&286206848099549185>

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[broken kiln]

How would I solve this using integrals?
An object moves in a straight line for 5 seconds
I need to get s(t) so distance traveled in function of time, from 0s to 5s
And i know a(t) = t+1

[broken kiln]

I know a few formulas like s(t) = int(v(t) * dt))

But not sure how to get the a(t) to v(t)

Would i use v(t)= v0 + a*t ?

[quick marsh]

Mhmm

When is that equation for velocity valid?

All the time?

[broken kiln]

Uh no clue, my question doesn't say that so I'll guess it's all the time yeah

[quick marsh]

Can I see the question?

[broken kiln]

It's in a different language sadly

[quick marsh]

What's the context? Physics class? For fun? Held at gunpoint and asked to solve questions?

[broken kiln]

Calculus - studying for a test in a few days

[quick marsh]

Ok, was there a chapter on kinematics?

[broken kiln]

And my book only lists answers not method of getting there

[quick marsh]

Usually there's a short blurb

[broken kiln]

Yeah

[quick marsh]

Did it talk about how acceleration being the derivative of velocity?

and velocity being the derivative of position?

[broken kiln]

It was written in such a complicated way but i do remember that vaguely yeah

[quick marsh]

Ok

So if acceleration is not constant, you can't use $v(t)=v_0+a*t

[broken kiln]

Oh yeah true

[quick marsh]

, $v(t)=v_0+a*

huh, I don't know how to use the latex bot

So if acceleration is the derivative of velocity, and you know a function for acceleration, how can you find the velocity?

[broken kiln]

Derivative of that?

No wait

Uh what's the inverse of a derivative

[quick marsh]

Hint: you mentioned it in your opening message

[broken kiln]

Integration?

[quick marsh]

Yep

[broken kiln]

So I integrate my acceleration formula?

[quick marsh]

Yes, and that will get you what?

[broken kiln]

(x^3 / 3) + x + c

[quick marsh]

I meant more generally, not the specific formula

Btw, everything should be in time

[broken kiln]

Oh yeah forgot

Uh would be integral with range t0 to t1 of ( t^2 + 1)dx

*dt

[quick marsh]

Maybe, but before you do the integral, you have to know what it means

Let's summarize the given information: An object moves in a straight line for 5 seconds
I need to get s(t) so distance traveled in function of time, from 0s to 5s
And i know a(t) = t+1

We want s(t)

We have a(t)

We know the object moves for 5 seconds

before you do any computation, have a plan to get what you want from what you have

[broken kiln]

I'd say integrate it to get v(t) and then integrate it again to get to s(t)

[quick marsh]

Yes, that's a good plan

$(v(t)=\int_{0}^{5} (t+1)dt)$

[broken kiln]

So that'd be (t^2+1 / 2+1) + x

[flat frigate]

alll

[quick marsh]

No

It is quadratic, but there should be no x

[broken kiln]

Yeah sorry meant t

[quick marsh]

Do you want me to check your corrected answer?

[broken kiln]

Sure

[quick marsh]

(t^2+0.5+1) + t is incorrect, if that's what you meant

There might be a typo though

[broken kiln]

What i have rn is
$(s(t)=\int_{0}^{5} ( ((t^3)/3) + t * dt)$

[flat frigate]

JoJoCa

[broken kiln]

Well that could've gone better

[quick marsh]

Mhmm, did you evaluate part of the integral already but leave it in the integrand?

[broken kiln]

Is evaluating filling in the 0 and 5?

[quick marsh]

It's "doing" the integral

[broken kiln]

Oh yeah I got the result from evaluating a(t), which would be v(t) and filled that in in s(t) formula

[quick marsh]

Ok, there's been a mistake in the integration of a(t), if a(t) = t+1

s(t) should be cubic, v(t) should be quadratic, and a(t) is linear

[broken kiln]

Oops I messed up i thought it was t2 + 1

Yeah in that case it's v(t) = t^2 / 2 + t

[quick marsh]

Yes

If you know that v(t=0)=0

That has to be given in the problem

If not, you can add a constant of integration and give a general answer

[broken kiln]

It only says that s(0) = 0 so I'll assume v is also 0, since the exercises seem to go for a specific answer

So from there I'll evaluate s(t) and then I'm basically there, just filling in 0 and 5 and getting the difference

[quick marsh]

Yes

Although I suspect that whoever wrote this question has made a mistake

With two integrations, you get two constants of integration, or degrees of freedom

[broken kiln]

That's possible, it's a pretty bad book tbh, so convoluted and not clear

Thanks a ton for the help, that made it more clear than my book ever could

[quick marsh]

np

.close

^you have t type this

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[flat oar]

what is a connected planar figure

[flat oar]

and how can you turn this into a function:
"Number of distinct connected planar figures that can be formed from n 1 X 2 rectangles"

[devout shale]

https://mathworld.wolfram.com/PlanarConnectedGraph.html#:~:text=A planar connected graph is,A003094%3B Steinbach 1990%2C p.

this what you are talking about?

[flat oar]

connected just because all the points are connected one way or another or because the edges are connected?

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[flat oar]

bleh

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[crude star]

stuck for case 2

[crude star]

can i get a hint

[still charm]

Hint:

0 <= (a-b)²

[crude star]

mhm I think I got it

let me show u

[still charm]

Then:
0<= a² - 2ab + b²
4ab <= a² + 2ab + b²
4ab <= (a+b)²
4ab/(a+b)² <= 1
4(ab)²/(a+b)² <= ab
4(ab)²/(a²+2ab+b²) <= ab
4/(a² + 2/(ab) + b²) <= ab
4/(1/a + 1/b)² <= ab
2/(1/a + 1/b) <= sqrt(ab)

[crude star]

I should add that if a, b > 0 in the beginning

but ye there

I was just being an idiot

[crude star]

Dam I woulda never thought of this

[still charm]

Damn

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[mint veldt]

I'm not sure what the u sub would be here

[marsh walrus]

think about the power rule

[mint veldt]

well, I thought x^4 would work

cause the deriv would be 4x^3

[marsh walrus]

rewrite everything as a power

[mint veldt]

there's a x^3 there which is nice

[marsh walrus]

do you see what i mean

[mint veldt]

rewrite everything?

no I don't

[marsh walrus]

like dont write $\frac{e^\sfrac1x}{x}$

write $e^{x^{-1}}x^{-1}$

[flat frigate]

jan Niku

jan Niku
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[marsh walrus]

get rid of all the fractions, use powers instead

[mint veldt]

ohhhhhh

so

you wrote e^1/x * 1/x -> e^x^-1 * x^-1
because 1/n -> n^-1

right?

[marsh walrus]

yea

[mint veldt]

alright

[marsh walrus]

do the same thing, but for your problem

[mint veldt]

okay

I'll see what I can do from there

hmmm

u = x^-4 and du = -4x^-3

I can do du / -4 = x^-3 dx

I'm not too sure if this is working

[crude bear]

Dude

You have x^{-4}

And x^{-3} above Euler's constant

What is the derivative of x^{-3}

[mint veldt]

-3x^-4

[crude bear]

So?

[mint veldt]

.close

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[lavish remnant]

Do you know how to express that with an equation(s)?

[lean otter]

thats what im having trouble with

[devout shale]

take it a step at a time

[lavish remnant]

can you show what you haved tried so far?

[devout shale]

leo is 5 years older than pat

can you model that as an equation?

[lean otter]

L=P+5

?

[devout shale]

sure

in 10 years

what does that look like

[lean otter]

no idea

[devout shale]

well, if L is an amount of years

and P+5 is an amount of years

after 10 more years, what does that equation look like

[lean otter]

add 10 to both?

[devout shale]

mhm

[lean otter]

so 10+l. and p+5+10, p+15?

[devout shale]

write it out completely

[lean otter]

L+10 = P+15

[devout shale]

alright

from the beginning equation

L=P+5

what is pat's present age?

P=?

[lean otter]

im gonna be honest, i have no idea

[devout shale]

Solve L=P+5 for P by itself

[lean otter]

P=L-5

idk

?

[devout shale]

yes

so, pat's present age

is P=L-5

[lean otter]

yeh

[devout shale]

and in ten years, the equation looks like L+10 = P+15

now

L+10, should be equal to double pats present age

right?

[lean otter]

yes

do u just sub it in now

[devout shale]

sorry, I have been taking you down a slightly bad path. Let me rethink how we should do this for a second

[lean otter]

oh ok

[devout shale]

I'll give you better instructions in just a minute

[lean otter]

nah its alg

take ur time

[devout shale]

Okay

We have two bits of info here

Leo is 5 years older than Pat's present age

in 10 years, Leo will be twice Pat's present age

So, like you said earlier we model the first one as

L=P+5

How can we model the second one?

L = Leo's present age, P=Pat's present age

[lean otter]

l=2p?

[devout shale]

not quite

Is leo's present age equal twice pat's present age?

[lean otter]

no

[devout shale]

or is leo's present age, plus 10 years, equal to double pat's present age

[lean otter]

this one

[devout shale]

so write it out like that instead

[lean otter]

L+10 = P

in ten years wont leo be double pats age currently ?

[devout shale]

yes that is what I meant to say

so rewrite that equation again

[lean otter]

10+L=2P?

[devout shale]

Yes

okay so now you have two equations

L=P+5

and L+10=2P

now you can solve for their present ages

[lean otter]

so subsitution?

[devout shale]

I'd subtract the top equation from the bottom one

probably easier

[lean otter]

oh fair enough

[devout shale]

(and then substitute once you solve for P doing that)

Sorry I misled you a bit, I got a little wrapped up in the wording and trying to explain it simply, but it is simpler than it even looked lol!

[lean otter]

no its okay dw about it

ty for ur help i appreciate it

[devout shale]

Yeah no problem

[lean otter]

have a good day

[devout shale]

you too!

[lean otter]

.close

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[sly igloo]

hi, can anyone check if my answers are correct?

[sly igloo]

16. x-3 17. -y+3 18.-z+5 19. 2-5a 20. 3b^4+2b^2+5 21. -b +4a+7ab 22. -2+8a^2b 23. 3x^2+x-5 24. 5x^2-3x+2 25. -2x^2+6x-3

[thin bridge]

aren't you given an answer key

||but yes, those do seem to be correct||

[sly igloo]

nope, not yet

[sly igloo]

oh alr, thank you!

.close

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[cedar cloak]

i think its = -2-5, 3

[split ether]

lambda is equal to -2.5 or 3

[cedar cloak]

thanks

.close

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[bright dirge]

hi

[bright dirge]

does anyone know
why
52 (mod 53) = -1

actually im doin rabin miller test for number 53 to check it is prime or not

[obtuse jackal]

52 = 53 - 1

[bright dirge]

so if any one know
52 modulo 53 is -1 how is that possible

i read some comments on the yt video they said it is something realted to addtive inverse

[bright dirge]

after that?

[obtuse jackal]

Hence 52 = -1 mod 53

[bright dirge]

how

sorry i dont understand

[obtuse jackal]

Look at the definition of modulo

[empty gyro]

What is definition of mod

[bright dirge]

ya i know that

[obtuse jackal]

a = b mod n iff n | b - a
53 | 52 - (-1)

[bright dirge]

wait what lol

ya ya

this :_)
acc. i was thinking how remainder can be negative

[obtuse jackal]

It causes no problem whatsoever

Things being -1 mod n can prove pretty useful depending on what you're doing

But since 52 in [0, 53[, the principal value would be 52 mod 53

But it's totally correct to say it's -1 mod 53

[empty gyro]

52^100 mod 53 is way easier to do as (-1)^100 mod 53

[obtuse jackal]

For example

[bright dirge]

hm okay thanks for the help

do i need to close this channel or bot will do it

?

[obtuse jackal]

You can type .close

The bot would wait a given amount of time, ping you to ask if you've been answered, leave it open if you react no, close if you react yes or if you don't react in 15 minutes

[bright dirge]

oh okay

thanks

.close

[safe radish]

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[lean otter]

How do I do this?

[brave wolf]

next time post it as image

[quasi bison]

(but DON'T delete your original post)

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[uneven veldt]

Ok, Can you send your working

!status

[safe radish]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

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[balmy sky]

im not able to figure it out

can someone help please?

[lean otter]

I see a pattern

Do you see any patterns?

[thin bridge]

consider splitting the squares into a 3 by 3 grid

[clear blade]

i thought it was simpler than that

2 3 2 3, horizontal vertical horizontal vertical

leaves only one answer

[balmy sky]

i did but it doesnt fit for the next term

[balmy sky]

i already did that. cant think further

[thin bridge]

what did you think the pattern was

in reference to

i did but it doesnt fit for the next term

[balmy sky]

the alternate boxes. place the sticks opposite and then shift them right by 1

[thin bridge]

wdym by shift them right by 1

[balmy sky]

if we make a 3x3 grid

[thin bridge]

how is that even applying from
box 1 → box 2

[balmy sky]

then the two sticks get shifted right if we change our perspective

same with fig 2 and fig 4

[thin bridge]

not sure what you mean, can you draw out you mean

[balmy sky]

yes give me a min

[thin bridge]

box 1 → box 2
box 2 → box 3
box 3 → box 4

for each of them

[balmy sky]

1)Shift by 1 to the right box
2) Place them in the opposite box

i drew it wrong sorry

[thin bridge]

that looks like you're considering two separate sequences

1 → 3
and 2 → 4

instead of
1 → 2 → 3 → 4

[balmy sky]

are you saying that fig 1 and fig 3 are in pattern

and fig 2 and fig 4

[thin bridge]

you could speculate something that happens between them, but with this few images, isn't enough to deduce what should come next doingthat

this is presented as a single sequence

[thin bridge]

that's what you're doing

[balmy sky]

yes there are possibilites

[balmy sky]

yeah sorry i misinterpreted your above message

[thin bridge]

describe what you observe happening between box 1 and box 2

three aspects to focus on:
number of sticks
horizontal or vertical sticks
movement / location

[balmy sky]

the number of sticks is alternating between 2 and 3

horz vert horz vert

1 2 3
4 5 6
7 8 9
if I number the boxes like these

then the movement is like
4 → 7
7 → 9

9 → 2

[thin bridge]

draw arrows going from boxes
1→2→3→4
and see you if you observe a pattern on how much the sticks are moving

[balmy sky]

ohhhh

1 box movement

then 2

then 3

then it should be 4

[clear blade]

👏

[balmy sky]

the number of sticks should be 2

movement is anti clockwise

Thank you all for your help

I have another question

can I ask it here?

[clear blade]

yeah

[balmy sky]

had an exam today

I did prove this but not sure if it is correct or not

I got that there will atleast be 6 perfect cubes among the 51 numbers

and at max there can be 10

Can someone confirm please

[clear blade]

how did you get that

[balmy sky]

there are 5 primes uptil 11

we can make a number n by using either 1, 2 or 3 distinct factors

[flat frigate]

tushar

[balmy sky]

yes

did the same

in case 1 I chose 1 out of the 5 factors and got 5

the power will range from 0 to 2022

so 5 n in case 1

in case 2, there will be 10 ways of choosing

[clear blade]

and the number of factors of such a number is $(a_1+1)(a_2+1)(a_3+1)(a_4+1)(a_5+1)$

[flat frigate]

tushar

[balmy sky]

i did figure that out during the exam

[clear blade]

so you want to show that if you have 51 distinct tuples $(a_1,a_2,a_4,a_4,a_5)$ that satisfy $$(a_1+1)(a_2+1)(a_3+1)(a_4+1)(a_5+1) = 2023,$$ then some tuple in the list has all $a_i$ divisible by 3

[balmy sky]

so in case two the powers can range from either (0 to 6 and 0 to 289) or *0 to 16 and 0 to 118)

[flat frigate]

tushar

[balmy sky]

yeah could have approached it this way

but i approached it in some other way

[safe radish]

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[wide crescent]

Is this correct ?

[quasi bison]

yes

[wide crescent]

Okie ty

.close

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[twin hamlet]

Help pls: 0 =<a1 =<a2=<……=<an=<1 Prove: a1 + a2^2 + …… + an^n >= na1a2….an

[pseudo scroll]

Maybe some AM-GM stuff

[twin hamlet]

I think not

[obtuse jackal]

not convinced because of the varying powers. Got no clue though. Maybe Jensen on a very specific function, but I don't really believe in it either. Cauchy schwarz is maybe a possibility, not sure either

[twin hamlet]

Mb induction

[obtuse jackal]

Oh yes

Works very well

[twin hamlet]

But I don't understand how to make a transition to this inequality.

[obtuse jackal]

It works well for n = 1

[twin hamlet]

Yes, it's a base

[obtuse jackal]

Take the ineq. for a fixed n, add (a_n+1)^(n+1) to the previous ineq

[twin hamlet]

I did it

But I don't understand what's next.

[obtuse jackal]

use the fact an+1 >= every other ak

So (an+1)^(n+1) >= a1 a2 ... an+1

Also use the fact an+1 <= 1

Then you can say it's greater than the desired product

[twin hamlet]

That’s not correct

0 =< a1 =< a2 =< …. =<an =< 1

[obtuse jackal]

Yes but when you choose an+1

[obtuse jackal]

It has to verify this property too

But for n+1 values

Otherwise it doesn't fall under the hypotheses

[twin hamlet]

I didn't understand

[obtuse jackal]

Start writing the proof. You should understand when you state what a1, ..., an+1 must verify

[twin hamlet]

.close

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[keen pebble]

^So

[keen pebble]

I got an not mathematical question directly

Its more like in opinion question

On how you study math the best way

Like ive been trying to study like math in diffrent ways

But i just not seem to improve

[karmic hedge]

Like school math?

[keen pebble]

Yea

Like

Ive been practicing

Doing the theory

Trying to really understand the algorithm behind certain things

But when i got exams its like it doesnt even matter what ive done

[earnest wagon]

I don't know the best way but I can tell you the way I study math

[peak estuary]

what are your problems during the exams

[earnest wagon]

Consistently writting notes, maintaining notes, revising notes, asking and practicing questions

[keen pebble]

Like the level of complexicity

Like when i do like practice i always do like the things that are in book

But then when exams coming

Its like holy god

[peak estuary]

well then get different practice questions?

[keen pebble]

Like more difficult ones?

Like rn i got rotationbodys

Idk how you call it in englisch

Like when you have a function and you rotate it around x or y axis

and then you can calculate the volume or whatever you want

[peak estuary]

if you are struggling because the questions on the exam are harder than the one you practice with, then yes get harder questions to practice with

[keen pebble]

Alright

Ill try

[safe radish]

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[scenic badge]

0=-16t^2+32t+2

How do you solve with every method? (Quadratic formula, factoring, completing the square. Also sorry if my english is bad, it wasnt my first launguge)

[jaunty goblet]

I hate when the quadratic has first term negative, multiply by -1 please

[scenic badge]

uh

sure??

[jaunty goblet]

Yes

[scenic badge]

0=16t^2-32t-2

[jaunty goblet]

Perfect a=16, b=-32, c=-2, x = (-b +- √(b²-4ac))/2a

[scenic badge]

oh

how about completing the square?

and factoring

[jaunty goblet]

16t²-32t-2=0
for completing the square, make the first term a perfect square, which it is (4t)²
hence it can be written as (4t)²-2(4t)(4) + 4² - 4² -2 (add and subtract four squared)
This equals (4t-4)²-18=0

[scenic badge]

oh

wait

can you not factor 0=-16t^2+32t+2

or

[jaunty goblet]

Yes you can

[pseudo scroll]

(you can divide by 2)

[scenic badge]

oh

wait about like actual factoring like x^2+2x+1=(x+1)(x+1)

can you not do that with 0=-16t^2+32t+2

[jaunty goblet]

You can, you would have to factor out -ve sign and then factorise what's left within the brackets

f(x) = -16x²+32x+2
= -(16x²-32x-2) and factor the brackets

[scenic badge]

oh so then

-(16x²-32x-2)
= -2(8x^2-16x-1)

is that it?

[jaunty goblet]

yea

Then factorise more

[scenic badge]

wait how

show me pls

[jaunty goblet]

Wait does it have irrational solutions? Then we would have to factor out the other way

[scenic badge]

i think it does

[jaunty goblet]

Oh okay then find the roots using quadratic formula, say they're p and q
then a polynomial ax²+bx+c with roots p and q can be factorised as a(x-p)(x-q)

[scenic badge]

oh

so hold on

-(16x²-32x-2)
a=16 b=-32 c=-2

solve

and then find out the roots

[jaunty goblet]

Yea, then the factorisation is -16(x-p)(x-q)

[scenic badge]

i see thx

[jaunty goblet]

k

[scenic badge]

.close

[safe radish]

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[hardy lion]

welcome back :D

[serene kraken]

i have two questions

[hardy lion]

Thhis one looks awful

[serene kraken]

do i send the second

[hardy lion]

Sure

[serene kraken]

it is

[hardy lion]

I dont think i can figure this one out

[hardy lion]

Looks like you started a new section with sequences

[lean otter]

This is like Cicada 3301 but bad

[serene kraken]

okay do i send the third maybe its easy

[hardy lion]

Sure

[hardy lion]

Beetle 2201

[lean otter]

(actually a moment but we can pretend)

[hardy lion]

I was better at this last night lol

[lean otter]

I feel like this is the type of question where if someone were to ask me "Why do you even bother with these?" I'd jokingly reply "I'm in it for the money." to hide the fact that I'm just a nerd

[hardy lion]

There are good questions, and then theres this book

[serene kraken]

this type of question will get me into university

[lean otter]

So you are in it for the money, in a sense...

[hardy lion]

Ive got nothing

[serene kraken]

thats okay

[empty gyro]

The fact that this book doesn't explain why the answers are what they are tells me this is an awful prep book

[serene kraken]

all books like this

i mean the books we have

[empty gyro]

"We"?

[serene kraken]

"we" in turkey

so no one has an idea in that questions

[empty gyro]

I hope you're spending a lot of time in the actual math section of your study too

You never ask actual math questions, so I'm assuming you know those 100% perfect

[serene kraken]

for us this is the actual math questions

i hate it too

but i have nothing to do

[hardy lion]

The test is 30 maths and geometry questions and 50 "general ability" questions

I love how geometry is separate like it isnt math

[serene kraken]

that's kinda right

every university has like different count of questions

[hardy lion]

Oh

You have to take one per university?

Do they cost money?

[serene kraken]

yes but not that much

[hardy lion]

Oh ok

[serene kraken]

i can take how many i want

and chose the highest number

[hardy lion]

Oh so its like the SAT kinda

[serene kraken]

it is we have sat too

[empty gyro]

But with worse problems

Does it have to be turkey?

I have a friend from turkey. I'll ask him about this

[serene kraken]

bout the question?

[hardy lion]

A few of us were checking out the one from istanbul

They seem less abstract

[serene kraken]

this exam just for the people who came from out side the turkey

[empty gyro]

What's the name of the entrance test again?

[serene kraken]

yos

YÖS exam

[empty gyro]

My friend wasn't helpful, sorry

[safe radish]

@serene kraken Has your question been resolved?

[serene kraken]

i dont know man

let me close it and come back later

[safe radish]

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[tawdry yacht]

When does infinity / infinity equals 0 in limits?

[viral loom]

When denominator grows faster

[twilit spindle]

something like $\lim_{x\to\infty}\frac{x}{e^x}$? where both top and bottom tend to infinity but the limit evals to 0?

[viral loom]

sorry

[flat frigate]

XxMrFancyu2xX

[viral loom]

I missread

[tawdry yacht]

Yeah

[viral loom]

I corrected it

[tawdry yacht]

Oh so thats how

Cus i just knew infinity / infinity was undetermined so this fucked with my head when i saw it in class

[twilit spindle]

indeterminate* 🤓

[viral loom]

It's like that when you don't know with your eyes who grows faster

[tawdry yacht]

ahaha mb

[viral loom]

but if u have something like x/x^2 you know x^2 grows faster

[tawdry yacht]

Yeah for sure

Is there somewhere on the web where i can see which things grow faster

like a log compared to exponentials

and so on

[twilit spindle]

https://en.wikipedia.org/wiki/Big_O_notation

[solar pike]

This is actually the little o notation

[viral loom]

log_a(x) are the slowers

[tawdry yacht]

Thank u!

[solar pike]

If lim f(x)/g(x) = 0 then we say that f(x)= o(g(x))

[viral loom]

logatirmic, radicals, powers, exponential

[twilit spindle]

factorials 👀

[viral loom]

😄

[tawdry yacht]

What about something like e^x compared to radical of x

[twilit spindle]

fun challenge prove x! grows faster than any b^x

[twilit spindle]

wdym?

[tawdry yacht]

which one grows faster

Cause i saw it in my homework once

[twilit spindle]

exponentials ALWAYS grow faster than any polynomial

[tawdry yacht]

Oh okay

[twilit spindle]

for sufficiently large x

[viral loom]

yes

[twilit spindle]

if base is greater than one

cause 0.75^x does the opposite of growing... lmao

[tawdry yacht]

makes much more sense now im just getting the hang of limits rn

Ooo this is great

gonna print it on my wall when i do hw

thanks!!

[viral loom]

lol

[twilit spindle]

lol yw man

[tawdry yacht]

.close

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[alpine pebble]

idk what this even means

[green bane]

wdym

[alpine pebble]

i dont know what it means

idk what to look for

[twilit spindle]

do you know what line/point symmetry is?

[alpine pebble]

no

[merry sleet]

line symmetry: there is a line such that each point on one side of the line can be matched to point at the same place on the other side of the line

point simmetry, same but the mirroring has to pass through a point

[alpine pebble]

can you draw them i dont fully understand

i fell like all of them have that

[merry sleet]

first is line symmetry and second is point symmetry

[alpine pebble]

so if there cut in half up and down there the same and if the cut diagonally there the same?

[merry sleet]

no

the line can be any line

and for point symmetry

the thing is that there is a point (C in that case)

such that for each point on the figure

if you draw a line from the point through C

and continue it for the same distance

theres another point

at the end

look on the right

start from A

draw a line through C

then continue for the same distance

A' is there

for exemple a circle has point symmetry

with the point being its center

[alpine pebble]

ok

[merry sleet]

and line symmetry,

for any point A

draw a perpendicular line to the line of symmetry

continue for the same distance

A' is there

[alpine pebble]

im sorry i still dont get can we go in a call and u show me

.close

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[unique valley]

Why is it when I apply the shifting property of delta I end up with a different answer?

[safe radish]

@unique valley Has your question been resolved?

[plucky elk]

Show your different answer

[safe radish]

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[unique valley]

.reopen

[safe radish]

✅

[unique valley]

Which is based off this result

[safe radish]

@unique valley Has your question been resolved?

[plucky elk]

That's not cosh, that's cosine

But also you didn't do change of variables correctly

Your answer should depend on the sign of a

[plucky elk]

To put your integral in this form, you need to do aw+b = a(w+b/a) and x = a(w+b/a). So when you calculate dx, you may pick up a minus sign

[safe radish]

@unique valley Has your question been resolved?

[unique valley]

I don’t understand the need for this? How is it not in the correct form.

Why is a change of variable necessary?

In my attempt I did not do any change of variables, I don’t understand why it’s necessary?

[plucky elk]

Because the formula you're referring to use isn't in the form of your problem

[plucky elk]

There's no constant being multiplied by x here

[unique valley]

I see I’ve made an assumption of how the delta function works thanks for the help

[safe radish]

@unique valley Has your question been resolved?

[safe radish]

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[swift skiff]

does someone know how I would solve this problem

Put the conic section into Graphing Form: y^2+14y−2x+59=0

[queen parcel]

What is graphing form?

[swift skiff]

I think like standard form

I am used to completing the square for both variables but x isnt squared so I dont know how I would do this

[queen parcel]

I think this would be a parabola instead of a conic section then

[swift skiff]

Ok but how would I solve for it, I thought quadratic equation only had 1 variable.

.close

[safe radish]

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[upbeat swan]

If i drink a beer with 4% alcohol, do i get drunk slower than if i were to drink a beer with 4% alcohol but bigger?

[upbeat swan]

Does the smaller contain more alcohol/ml?

Or are they the same

[quasi bison]

i mean the whole purpose of stating alcohol content as a percentage by volume is that you ingest it at the SAME rate whether you drink it from small bottles or straight from the barrel...

[upbeat swan]

So if i drink more it doesn't mean more alcohol?

If i drink 1 beer with 4% and another guy drinks 3 beers with 4%, he doesn't get more drunk than me?

[still charm]

Huh?

You can just compare the absolute amount of alcohol ingested

A beer is 12 oz

[upbeat swan]

Ok and

[still charm]

So a 4% ABV beer is 0.48 oz of pure alcohol

And 3 of them would be 1.44 oz of pure alcohol

[lean otter]

Depends whether you drink the same volume of beer at the same rate in both cases

[upbeat swan]

If its a bigger beer then the volume is different

[lean otter]

Yes, but do you drink the same volume at the same rate despite that?

[still charm]

Yeah but it takes longer to drink a bigger beer

[lean otter]

Since the percentages of alcohol are the same you can just ignore the size of the bottle and focus on how much you drink in a day

[upbeat swan]

I guess it takes longer...

[quasi bison]

ew american units

[lean otter]

Okay so would you say that you drink at the same rate regardless of the size of the bottle?

[quasi bison]

how much is 12 oz in real units again?

an ounce is like 30 ml right

so 360 ml ...?

[lean otter]

,w 12 oz to ml

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Labyrinth#3979

[quasi bison]

i guess that's the american equivalent of a 0.33 can

[lean otter]

@upbeat swan That's all we need to know

[upbeat swan]

Idk

You tell me

Im talking about real life

So it takes longer to drink a bigger beer ig

[lean otter]

I tell you at which rate you drink beer depending on the size of your beer?

[lean otter]

I guess if you look at a single can yes but wouldn't you still drink just as frequently over a day?

Or would you adjust to the bigger beer size by drinking it less frequently?

[upbeat swan]

Does it matter

[lean otter]

Yes, obviously how much beer you drink affects how drunk you get

[upbeat swan]

You drink i bigger beer in the same time you drink a small one

[lean otter]

You're talking about me? I don't drink beer

Look if you drink the whole thing no matter which size you pick then the bigger one makes you drunk faster

[upbeat swan]

Not about you🤣

About the question

[lean otter]

English be like

[upbeat swan]

The situation

[still charm]

Beer is American

[lean otter]

Germans reading this:

[quasi bison]

look what you made me do @still charm

what you said was so cringe i was compelled to spend a super react on you

[lean otter]

@upbeat swan Does that answer your question?
If so, you can close this channel by typing .close

[still charm]

Try a Yuengling sometime it's pretty good

[upbeat swan]

If i drink a 600 ml beer with 3%, it's not the same as 3 200ml beers with 3%?

[lean otter]

Bless you

[lean otter]

Do you drink as much beer in a day when you buy a 3200ml beer?

[upbeat swan]

I dont understand

You drink it at the same rate

I mean it takes the same time

To drink a small and a big one

[lean otter]

Wait really?

@upbeat swan Okay so like, consider a scenario where you have a habit of buying 600ml beer and one where you have a habit of buying 3200ml beer
And in both scenarios you measure how much beer you drink by volume on average every day over a long period
Do you think the result would be different in the 2 scenarios?

[upbeat swan]

If it doesnt take the same time to drink the 2 beers, then the result wouldn't be different

[lean otter]

Am I overthinking this hold up my brain just rebooted

This is a basic question why am I having a stroke over it

[upbeat swan]

Cuz a smaller beer seems more concentrated

But i dont think it is

[lean otter]

That's not the case

[upbeat swan]

Cuz it's still 4%

No matter what ml

[lean otter]

A 3200ml beer with 4% is just a 600ml beer with 4% but bigger

It's just as concentrated as the small one

[upbeat swan]

A bigger beer contains more alcohol?

[lean otter]

Well yeah because it's bigger

[upbeat swan]

That's not what Ann said

[lean otter]

If the alcohol percentage is the same then the amount of alcohol is proportional to the beer size

[still charm]

The size of the cans themselves doesn't matter at all, just how much you drink in a sitting

[lean otter]

Hence the concentration doesn't change

[lean otter]

Yes yes exactly what I was thinking (although I focused on how much you drink in a day which is different and I'm now realising that's not what matters)

[upbeat swan]

So if i drink 200ml out of a 400ml beer bottle with 4%, it's the same ammount of alcohol as it was if i were to only drink a 200ml in the same ammount of time

[lean otter]

Seems to me like she said exactly what we're saying

Same rate, same concentration

[lean otter]

Yes

Assuming the 200ml bottle also has a 4% concentration

[upbeat swan]

If a 400ml beer has 4% and i drink 200ml, do i get 4% out of the 200?

[lean otter]

Yep, 4% of 200ml is what you get

[upbeat swan]

But which gets me drunk quicker

[lean otter]

Just like what Gamer said, it depends how much you drink in a sitting in both scenarios

[upbeat swan]

I drink a 400 and a 200 with 4% each in the same time in one sitting

Which gets me drunk faster

[lean otter]

The 400ml one because you drank more alcohol

More alcohol in one sitting and same concentration => More drunk

[upbeat swan]

Ok thanks

[lean otter]

@upbeat swan .close

[upbeat swan]

Why are you so eager to close

[lean otter]

I dunno it do be like that around here

Unless you have more questions of course

[upbeat swan]

Well it's a bad habit

[lean otter]

Should've told the whole server yo

Can't believe we've been closing our help channels once they're done being used for this long

[upbeat swan]

It's annoying to tell me repeatedly

To close

[lean otter]

I'm sorry about that

[upbeat swan]

No worries

Thx for the help

Cheers

.close

[safe radish]

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[frosty granite]

bit lost on where to start

[frosty granite]

yeah i expanded if thats what ur saying

[uneven veldt]

yeah, expand and multiply by 4 to the numerator and the denominator

[frosty granite]

thx

.close

[safe radish]

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Remember:
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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[lean otter]

Can someone please explain why t+2 was subbed into the rp1

[severe ruin]

Exactly the red circled text

2 seconds after they are launched

You want to find their collision point

[lean otter]

I still don’t get why it’s subbed into the rp1

How does it give collision point

[severe ruin]

Actually good question

What happens when you subtract from the input variable?

The graph

[lean otter]

What do you mean?

[severe ruin]

Like y = x^2 versus y = (x-h)^2

Which direction does the graph move

[lean otter]

Towards the right by h units

[severe ruin]

Right

So since it's x+2 or in this case t+2 the graph moves right by -2 units which means it moves left

Which gives you that the graph of the first vector is projected 2 sec before p2

Its a lil counterintuitive but you can try graphing on desmos to see for yourself

[lean otter]

Ohhhh okay

[lean otter]

So basically the whole purpose of substituting t+2 is so they ‘start’ at the same time

And then the collision point can be found by equating x of p1 and p2

[severe ruin]

Not exactly, it's to account for that they don't start at the same time

[severe ruin]

Right

[lean otter]

Yeah moving the graph so it accounts for it

[severe ruin]

Mhm mhm

[lean otter]

Thank you, much appreciated

.close

[safe radish]

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[raw cedar]

Just got a math test tomorrow on linear equations.

Just not sure on how to simplify this and find the value of x

[hazy elbow]

subtract a number on both sides

such that the variable (here x) is left in either LHS or RHS only

[raw cedar]

would we always take the x as the variable and keep the 7 there as the coefficient?

[hazy elbow]

Yes

Variable is a term which can change its value

7 can not change its value (i.e. it can not equal to 8)

but x can

[raw cedar]

ok so the next step would be like 7x - x = x + 30 - x?

[hazy elbow]

Yes

Now you can simplify

[raw cedar]

so the answer would now be 6x = 30 and then would we divide both sides by 6?

[hazy elbow]

Yes

[raw cedar]

so x = 5?

[hazy elbow]

We want only the variable to remain in either of LHS or RHS

[hazy elbow]

Correct

[raw cedar]

thank you

.close

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[lean otter]

hey ik its an easy q but i nee dto find the volume and i keep getting it wrong

[lean otter]

this is what im doing:
(0.4x1.2) / 2 times 0.2 times by four (to geth all four triangular prism volumes = 0.192
for the rectangular prism: 1.6x0.4x1.2=0.768
now to subtract the cylinder part: 0.4^2 x pi x 0.4 divided by two= 0.1005
0.192+0.768= 0.96
0.96-0.1005= 0.86
and thats wrong so im not sure

[hazy elbow]

you sure 0.8 is the diameter of the circle and not radius?

[lean otter]

i tried it both ways but i still didnt get the right answer

[hazy elbow]

You have the answer with you?

[lean otter]

the correct answer is 0.94

[hazy elbow]

Yes

so 0.8 is radius

[lean otter]

ohh ok sorry my bad

thank you

[hazy elbow]

Volume of this dent is equal to area of semicircle* thickness

[lean otter]

oh okk

thank you so much

[stark flame]

I need help

Graphs

[hazy elbow]

#❓how-to-get-help

[stark flame]

Oh

My bad

[lean otter]

.close

[safe radish]

Channel closed

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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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[elder sparrow]

[(sin a - cosec a)^(2)] + [(cos a - sec a)^(2)] = tan^(2) a + cot^(2) a - 1