help-27

[hardy marlin]

.close

[devout snow]

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[violet wind]

And you said you weren't a math person

[hardy marlin]

I'm not. I'm just on the spectrum and have a weird brain

If i wrote out my process how I got to the solution your brain would melt

[violet wind]

Real 😭

[devout snow]

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[zinc siren]

I need help doing b)

[zinc siren]

It's a combinatoris problem, what I've done is try to count how many ways can the people be arranged when A and B are together

[uncut crow]

good idea

any progress on that?

[zinc siren]

I came up with 8x6!x2!/4 because you can place the couple in 8 possible places 4 edges and 4 sides, and also you can rearrange them in 2! ways

then the other people can be arranged in 6! ways

[uncut crow]

,calc 8*6!*2!/4

[woven radish]

Result:

2880

[uncut crow]

,calc 2*6!

[woven radish]

Result:

1440

[zinc siren]

but shouldn't it be the same as if I take them as the same object and count the number of linear arranges and divide it by the number of rotations?

[uncut crow]

hm well rotations aren't as nice as they are in circular tables here

[uncut crow]

i agree with your answer here just btw

[zinc siren]

I'm trying to figure out why 7!/4 doesn't work

[alpine python]

why 7! ?

[zinc siren]

put them as the same object

[uncut crow]

i think he is just treating AB as one thing for now and not counting rotations as equivalent yet

[zinc siren]

so that they're together

[alpine python]

oh

[zinc siren]

you can permutate them in 7! ways

[uncut crow]

what about the permuting AB factor?

[alpine python]

yeah you should multiply by 2 but it doesn't fix it

[uncut crow]

yea

[alpine python]

what i'm wondering is, i think this doesn't count arrangements where the pair crosses the boundary

[zinc siren]

the 7! way?

[alpine python]

yeah

[zinc siren]

whut

explain pls

[alpine python]

wait i may have jumped the gun, i got excited when the numbers matched

[zinc siren]

oh

[alpine python]

but yeah i'm still thinking that you're not counting arrangements where the pair crosses the boundary

[zinc siren]

u agree with this one tho?

[alpine python]

it seems right

it probably makes more sense like this

there are 2*6! arrangements where the pair crosses the boundary. account for rotations at the end

[zinc siren]

why 2x6!

[alpine python]

because the location of the pair is determined

then choose an arrangement of the 6 remaining people

the pair can also swap, so multiply by 2

[zinc siren]

oh right

and 2x7! is the number of arrangements where the pair doesn't cross the boundary?

[alpine python]

yeah

[zinc siren]

why doesn't it cross the boundary in this case

[alpine python]

say you have seven objects A, B, C, D, E, F, P
P represents the pair

say the members of the pair are x and y

give me an arrangement of the seven objects that represents this:
x A B C D E F y

if i were to ask for A B x y C D E F you could say A B P C D E F

[zinc siren]

oh alright

ty

I got it now

.close

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[devout snow]

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[vivid estuary]

can someone point out my misunderstanding but please don’t give me the proof,

Suppose A subset of X is compact and B subset of A is closed then B is compact

[vivid estuary]

Why can it not be that Simce A is compact

nvm i see

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[blissful comet]

can someone confirm answers pls

[hollow ice]

erm what answer? show yours or at least describe your idea so theres something to confirm

(preferably show your work rather than just the simple final numbers)

this is not correct. redraw the circuit for this specific part where the caacitor is uncharged, and use the consequences of that to simplify the circuit

[blissful comet]

huh how

isnt r1 and r3

parallel

[hollow ice]

well, the uncharged capacitor is perfect insulator, so its same as there being no wire

so the whole combo of r1 and r2 together is in parallel with the whole combo of r3 and r4

[blissful comet]

is b wrong too

[hollow ice]

yes

[blissful comet]

omg what do i do now

i m so confused

[hollow ice]

coz you took it as insulator there, whereas it behaves as a wire in that part

[uncut crow]

decent handwriting

[blissful comet]

thanks but i m cooked

[hollow ice]

wait, lemme confirm it tho maybe im the one confused

[blissful comet]

how will u confirm it

@hollow ice bro

[hollow ice]

I just needed to write the current-voltage relation there lol

[blissful comet]

i cant find whats wrong

[hollow ice]

Fully charged cap is insulator, so no wire there. uncharged is conductor, so behaves as a wire

[blissful comet]

but now i m more unsure

[hollow ice]

so yea, your b is correct

[blissful comet]

a ?

[hollow ice]

but a still remains wrong

[blissful comet]

how

bro

the branch splits

check the diagran

omg bro

u ghosted

[hollow ice]

chill dude, lemme work it out

I think I did mess it up a ton 😭

yea you are right, mb

[blissful comet]

are u sure

[hollow ice]

you got it dude 💯

[blissful comet]

i m confused

i m paranoid now

[hollow ice]

nah, its mb. I read it wrong

sorry

[blissful comet]

oh okay

[devout snow]

@blissful comet Has your question been resolved?

[devout snow]

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[devout snow]

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[jade wraith]

im not sure how to find the antiderivative of e ^x ^2

[winter torrent]

you can't

try a different choice for u

[jade wraith]

it stays like that right

oh

ok so since i couldnt find antidertivative if this happens again i should also look for a dif U right

so u is x^2 - 6x

[winter torrent]

also a few things:

• that x^2 - 6x is all in the exponent; I think you misread?
• it's important that when you do a u-substitution, all traces of the former variable (x) are removed before you continue

they cannot be mixed

[jade wraith]

i got -[e^72 - e^40]

but it checked answer key and im missing a 1/2

on ther outside

where is that frio

nvm

x-3 over 2x-6

is 1 half

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[devout snow]

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[devout snow]

@sonic kiln Has your question been resolved?

[devout snow]

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[night rune]

regarding the second question, isnt this extrapolation ?

we cant assume anything about the trend for values that arent in the range

why is there a value to be chosen here

<@&286206848099549185>

[signal ruin]

Kyudo

I am here to help too

Generating response...

[night rune]

is this AI?

[signal ruin]

No I am a helper

Generating answer..

[night rune]

oh okay

[signal ruin]

Greater than 85°F a temperature of 91 degrees Fahrenheit would correspond

[night rune]

.

[night rune]

but this is my question

[signal ruin]

Well 91 Fahrenheit is a corresponding Fahrenheit of 81¹

[night rune]

i dont follow

the only explanation i have is that the question starts with a hypothetical if

otherwise, we cannot use the equation since x has constraints

does this make sense?

[rough trellis]

it would be 93

the equation of the line is given

[night rune]

how did you find that answer

[rough trellis]

$y = 0.1 x - 3.3$

[woven radish]

pasta 🍝

[rough trellis]

in the last line of the first paragraph

just put $y = 6$ and solve for $x$

[woven radish]

pasta 🍝

[night rune]

but this gives a value of x that isnt in the constraint

[rough trellis]

since $6$ is the differential for which we need to find the temperature

[woven radish]

pasta 🍝

[rough trellis]

yeah but they have asked that if the best fit line was extended beyond $85$ so it is extrapolation

[woven radish]

pasta 🍝

[night rune]

alright, so my guess was right

its the "if" part that makes it sound

[rough trellis]

yup

[night rune]

thanks pasta

[rough trellis]

anytime

[night rune]

.close

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[devout snow]

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[mental folio]

uughi feel. kind of stupid because i dont remember how to work with the limit definition,, can i have some help?

[dull parrot]

Notice that sin(x)/x is an even function

Oh wait

Nvm you did that already

Do you know Feynman's integration trick?

[rough trellis]

I was gonna say take fourier transform

[runic prawn]

@mental folio

[rough trellis]

because the fourier transform of rect signal is sinc

[tall comet]

this can be solved using laplace transform, no?

[rough trellis]

fourier transform

and then pick the one with frequency zero

[tall comet]

idk about that but we can solve this using laplace transform

ℒ(sin(t)/t) for s = 0 if im not wrong (i could be)

[rough trellis]

Consider $f(t) = 1$ $\forall \ -1 < t < 1$ and $f(t) = 0$ otherwise. The fourier transform of this signal will be $\frac{2 \mathrm{sin} \omega}{\omega}$.

[woven radish]

pasta 🍝

[dull parrot]

Yeah that works

It would be pi/2

[rough trellis]

Thus, taking inverse fourier transform, $f(0) = \frac{1}{2 \pi} \int \limits_{- \infty}^{\infty} \frac{2 \mathrm{sin}(\omega)}{\omega} d \omega$ from which we get value of the integral as $\pi$

[woven radish]

pasta 🍝

[rough trellis]

it would be $\pi$

[woven radish]

pasta 🍝

[tall comet]

Laplace transform integral runs from 0 to inf so it would be pi/2 but the question had -inf to inf and its an even function so pi/2 * 2

[rough trellis]

yeah true

I did with fourier transform

[idle dune]

What’s Fourier transform

Signals right

[rough trellis]

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

[rough trellis]

yeah

[devout snow]

@mental folio Has your question been resolved?

[idle dune]

i should know this im an electrical engineer

damn i suck

[rough trellis]

m an ee too

[idle dune]

wtf fr?

[rough trellis]

yeah who else knows fourier transform bruh

[idle dune]

aye add me big bro

do u know about asic analog design

[rough trellis]

I work in controls bruh

like very hard core

[idle dune]

oooo

[devout snow]

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[signal ruin]

Help me

[pearl sapphire]

guys

how to be good at the redaction

[sand pumice]

just send ur q

[sand pumice]

!occupied also better to send specific problems u r struggling with

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[signal ruin]

i have smth hard by $\int^{1}_{0} 8 dx \times 7$

[woven radish]

Noah

[sand pumice]

what have you tried

[pearl sapphire]

what

[signal ruin]

I tried thinking its 15

[sand pumice]

this channel has been claimed by somebody else, try smth like #help-23, also it is better to send specific problems on the topic you're struggling with

[junior mauve]

this channel is currently in use by a user. see #❓how-to-get-help for instructions on getting your own channel

[sand pumice]

how come

[signal ruin]

Pls help me

[junior mauve]

I don't think responding to a helper asking you "how come" (that is, asking you to explain your thinking) with "pls help me" would be the best response

[rain summit]

graph for $y = 8$ is just a straight line at $y = 8$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

so the area under the graph is just a rectangle

[signal ruin]

Oh

$\rectangle$?

[woven radish]

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

[junior mauve]

?

[signal ruin]

?

[rain summit]

lemme graph it in desmos for ya

[signal ruin]

Ty

[rain summit]

this is the graph

the red part is your graph $y = 8$ which is in your integral

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

and the blue part is the area under your graph

[signal ruin]

So the uppercage is ʸ?

[rain summit]

wdym?

[signal ruin]

Or ᵍ

Like replacing 8 by y

[rain summit]

idk

take a look at the graph

[signal ruin]

looking

[rain summit]

the blue part is the area shaded at x = 0 -> 1

and the area of that is your integral

notice that this is just a rectangle with width of 1 and height of 8

someone correct me if im wrong

because integration is defined by the area under the graph

[junior mauve]

can't correct if I don't even know what OP is talking about

[signal ruin]

Finished looking

[rain summit]

this integral basically

[junior mauve]

after looking at OP's history of writing integrals I am not confident I get what the integral is

and OP seems to vehemently not post pictures of his questions for... some reason

[signal ruin]

Ph

Oh

What is the answer

[fluid stag]

!noans

[devout snow]

The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.

[signal ruin]

On

Oh

I forgot that….

[rain summit]

read this

[signal ruin]

Okay

The blue part is the area. Shaded at $*x = 0 \to 1$

[woven radish]

Noah

[signal ruin]

Thanks 🙏🏻

[devout snow]

@signal ruin Has your question been resolved?

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[signal ruin]

Yes

.close

[devout snow]

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[karmic moon]

Help please, I'm not sure if i did this well u.u

[rain summit]

,rccw

[rain summit]

this is so blurry

[karmic moon]

srry

that better¿

[polar chasm]

|3x^2 - 1| - 4 = 7

[karmic moon]

.o.

[rain summit]

,w abs(3x^2 - 1) - 4 = 7

[woven radish]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Feb 20, 2026, 5:25 PM

[polar chasm]

is that what you are solving?

[rain summit]

did you learn complex numbers yet?

[karmic moon]

It's the next section on the book O.o

[signal ginkgo]

you know sqrt(4) is 2 right

[rain summit]

🤯

so you're not allowed to use complex number yet 🔥

[karmic moon]

yes¿

[rain summit]

so simplify

[signal ginkgo]

so why not have it as +-2

instead of + - sqrt(4)

[rain summit]

how about $3x^2 = -10$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

do you think this is valid in reals?

[karmic moon]

no

[rain summit]

so instead of saying $x = \pm\sqrt{\frac{-10}{3}}$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

you could say that $3x^2 = -10$ is impossible to happen

[woven radish]

1 divided by 0 equals Infinity

[karmic moon]

Yes

So at the end, ±2 are the only two real answers right

[rain summit]

yes

[karmic moon]

Ok tnks

.close

[devout snow]

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[karmic moon]

.reopen

[devout snow]

✅ Original question: #help-27 message

[karmic moon]

srry

And if i get to this?

[burnt saffron]

Okay so here's the thing

Mod fn returns +ve values

You can't really go ±11, as that result itself is +ve

Basically if the inner value is -ve, the value outside mod gets a -ve sign to compensate and allow for a +ve result and prove equality

[burnt saffron]

But yes, the verification is valid

[karmic moon]

¿what is +ve?

[burnt saffron]

Positive

[karmic moon]

ok tnks

.close

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[devout snow]

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[short hare]

.@strange scroll claim this

.send the question here

[strange scroll]

Can someone explain to me why there is 0.5 here and not 1

[void fox]

0.5 is where?

[short hare]

I dont think its 0.5

but why do you think it should be 1?

[icy sail]

Is the slope 2 or am I tripping

[strange scroll]

Sorry wrong picture

[short hare]

yes

so why do you think its 1?

[icy sail]

Bro the formula for the slope is delta y/ delta x

Take any two points and apply this formula, it will give you half

[strange scroll]

Ok thank you because we only had 1 to the right in class until now now I understand that too

I first thought 1, but when counting you see: 2 to the right and 1 up, so 0.5

[devout snow]

@strange scroll Has your question been resolved?

[devout snow]

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[void fox]

Didn't you ask this already and got an answer

Or you abandoned your channel

[rain summit]

!status

[devout snow]

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

@sage ibex Has your question been resolved?

[devout snow]

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[karmic basalt]

how to know the expo form of -1-i*sqrt2 +i

[karmic basalt]

im lost

[jade oak]

You want to express this in the form $re^{i\theta}$ right?

[woven radish]

Max Coy

[karmic basalt]

yeah exactl

i thought of seperting them like re^.. and r'e^... and then merging them using euler's formula

but im lost

[jade oak]

Do you know what r and theta represent here?

[karmic basalt]

yes i do

module and argument

[mystic scarab]

And do you know how they are related with real and imaginary part?

[karmic basalt]

i didnt understand the question

[mystic scarab]

Do you know what real and imaginary part are?

[karmic basalt]

yeahh

[karmic basalt]

ah yes i do

[mystic scarab]

Such as r = √(x² + y²)

[karmic basalt]

yeah i do know them

[mystic scarab]

And tan(θ) = y/x

(I used x and y for real and imaginary part, resp.)

[karmic basalt]

wouldnt treating -1+i and sqrt(2)*i seperatly be easier

[karmic basalt]

no its arctanx

[tall comet]

isnt it |y/x|?

[mystic scarab]

Nope. The exponential (Euler) form doesn't work well with addition of complex numbers

[karmic basalt]

wait mb

[mystic scarab]

Mmhh no

[tall comet]

the arguement depends where the complex number is located right like pi - theta for 2nd quad, theta - pi for third

[icy sail]

Should be (-π,π] or I am mistaken?

[tall comet]

idk i was taught like arg(z)= theta = arctan(|y/x|) and we use pi - theta or theta - pi or -theta if the number is located in 2nd 3rd or 4th quadrant respectively

[mystic scarab]

I guess it depends on the convention used, but typically it's that interval, yes

[tall comet]

wait i think yes it is this interval

[mystic scarab]

This seems to be an overcomplication (by your teacher/book)

[icy sail]

I get what he is talking about

[mystic scarab]

Yeah mebtoo now

[tall comet]

ig so maybe it was just to explain so that the arguement isnt beyond the interval

[mystic scarab]

Yeah probably that's the reason

[icy sail]

You take the absolute and get the angle with calculator and use some formulas depending on the quad but I forgot

[devout snow]

@karmic basalt Has your question been resolved?

[devout snow]

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[timid tendon]

i have no clue where to start icl

[restive river]

someone anyone just solve this question for maeeeeee

[timid tendon]

cheers pal channels already taken

[graceful cosmos]

"gradient of the curve" is just another way to say "slope of the tangent line"

(Where the gradient of the curve at A is the slope of the tangent line at A)

[timid tendon]

so its basically dy/dx ?

y/x sorry

so just 6.6 / 16.4?

[graceful cosmos]

We want the slope of that blue tangent line. In order to get it, we need two points on it. Then, we plug those two points into the slope formula

[timid tendon]

how would one do that im not familliar with the slope formula

atleast not the name\

[graceful cosmos]

Like, m = (y2 - y1) / (x2 - x1)

[timid tendon]

so would i take the coordinates of these 2 points and plug it into that?

[graceful cosmos]

Yes! But, I suggest using points that are on the grid lines. Like, (3,1) is a point on this line

[timid tendon]

oh so i can take any points on the tangent?

i thought it was where the tangent cuts off

[devout snow]

@timid tendon Has your question been resolved?

[lunar harbor]

yes

because the gradient of a line is always the same

[timid tendon]

gotcha

ty

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[atomic halo]

Im having problem with a question. When I do it the standard way I get an answer for this problem but when I try to relate the displacement between the trains the solution does not exist or it is wrong.

The question is: Red and Green Trains A red train travelling at 72
km/h and a green train travelling at 144 km/h are
headed toward one another along a straight, level
track. When they are 950 m apart, each engineer sees
the other’s train and applies the brakes. The brakes
slow each train at 1.0 m/s2
. Is there a collision? If so,
what is the speed of each train at impact? If not, what
is the separation between the trains when they stop?

[atomic halo]

The answer is yes there is collision and impact velocity is 10m/s and 0m/s respectively

I’m not sure why when I do it this other way it does not work

[green crypt]

do you understand why they collide?

[atomic halo]

How do you mean

[atomic halo]

I had a mistake in this picture
|d1 - d2| = 0 but even so the answer is no solution

Or no real solution

<@&286206848099549185>

[uneven coral]

have you found the point where they collide?

[atomic halo]

The time?

[uneven coral]

no I meant the distance they travel to the point of collision?

[atomic halo]

Yes sorry

200m for the first one

750m for the second

[uneven coral]

why didn't you use $v^2 = u^2 - 2as$

[woven radish]

doctorstrangejr

[uneven coral]

finding out time seems like a headache for this if you have s @atomic halo

[atomic halo]

I did it this way already

I wanted to see if the other way would work

But it’s not working

[uneven coral]

well time would be a headache, let me see

wait shouldn't deltad1 + deltad2 = 950?

@atomic halo

[atomic halo]

Yeah

It should

Or their magnitudes

|d1| + |d2| = 950

[uneven coral]

yes

does that help?

[atomic halo]

I tried that

I think it still gave the same no sol

[green crypt]

I think your condition for the displacement is anamoly

Do you know what time they collide?

I think d1 + d2 = 950

[atomic halo]

Yeah i think so too

But i tried this one

It still doesnt work

[green crypt]

I have some ideas but its really late for me

[devout snow]

@atomic halo Has your question been resolved?

[devout snow]

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[viscid root]

how do i find the equation of this curve (the lower part)?
this is a set of triangles with all centroids at y = 0 and rotation in radians equal to the x coordinate of the centroid

[viscid root]

t goes from -pi/3 to 0

a little brighter

[versed juniper]

can i ask what its for

[devout snow]

@viscid root Has your question been resolved?

[viscid root]

shitpost where i need to render a million of these triangles

but that's infeasible + the result is going to be a solid green shape

so i'm going to render the envelope, which i need the equation for

[bronze void]

it looks really cool, in this in Desmos ?

[viscid root]

yeah

[bronze void]

would it be possible to send the link for it? for some reason its not letting me input it

[viscid root]

https://www.desmos.com/calculator/8tznqfqkco here

[devout snow]

@viscid root Has your question been resolved?

[devout snow]

@viscid root Has your question been resolved?

[devout snow]

@viscid root Has your question been resolved?

[devout snow]

@viscid root Has your question been resolved?

[ocean quest]

To me it looks like some transformation of |sinx|

I can't get that to work

could be a piecewise of -cosh(x) functions?

[weak cloak]

Is this college maths?

[tawny pewter]

meh early college imo

https://en.wikipedia.org/wiki/Envelope_(mathematics)

when the two condition at the end of this screenshot are respected simultaneously for some (x,y), it's on the envelope

to get that F(t,x,y) you need the implicit equation of the curve family

in your case that's a bunch of lines specified by two endpoint of the triangle, so you will need 3 family of curves, one for each side

you can use $F(t,x,y)=m(t)x+b(t)-y=0$, where $m(t)=\frac{y_2(t)-y_1(t)}{x_2(t)-x_1(t)}$, $(x_1(t),y_1(t))$ and $(x_2(t),y_2(t))$ are two vertex for one side of the triangle

[woven radish]

pola_touche

[tawny pewter]

Then you isolate b(t) by using one of the point on the triangle. It can be done but imo the computation is kinda hard, you need to simplify as you go or else computing the partial derivative will be annoying

Alternatively you can use this other way to write an implicit equation for a line passing by two points :

$F(t,x,y)=x(y_1(t)-y_2(t))-y(x_1(t)-x_2(t)) + (x_1(t)y_2(t)-x_2(t)y_1(t))=0$

[woven radish]

pola_touche

[tawny pewter]

you compute $$a(t) = y_1(t)-y_2(t) , b(t) = x_2(t)-x_1(t), c(t) = x_1(t)y_2(t)-x_2(t)y_1(t)$$

and then for a given t you have a linear system that can be solved with let's say cramer's rule for x(t), and y(t):

[woven radish]

pola_touche

[tawny pewter]

$$F(t,x,y)=a(t)x+b(t)y+c(t)=0, \pdv{F}{t}(t,x,y) = a'(t)x+b'(t)y+c'(t)=0$$

[woven radish]

pola_touche

[tawny pewter]

imo that second way is simpler, generalize better, and I think it's implementable in Desmos

[tawny pewter]

https://www.desmos.com/calculator/1uslqzjxxv

[devout snow]

@viscid root Has your question been resolved?

[viscid root]

oh wow

this is very useful

thank you!!

.close

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[tawdry notch]

Which one of two solutions is wrong? I checked it twice and it was still c=24

[supple knot]

,calc sqrt(596)

[woven radish]

Result:

24.413111231467

[tawdry notch]

Oh, well then mine is correct, thanks

.close

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[umbral cradle]

for this question, do I just integrate the arctan or is there any other way? because we didnt really learn integral of arctan

[green crypt]

Integrating by parts works no?

[umbral cradle]

ohhh i guess yes

thank you haha

[green crypt]

You're very welcome

Would you be kind enough to give me 5 stars?

I don't know if IBP works btw

I'm in class right now, so that's just an assumption

[glossy dew]

you can also use the fact that arctan(x) is an odd function and \\$\int_{-a}^ag(x) \text{d}x=\int_{-a}^ag(-x)\text{d}x$

[green crypt]

You're so cool blurple_galaxy

You're my helper

[glossy dew]

am i?

[green crypt]

You are

Wait lemme check if u have the helper tag rq

You do

Good job

[glossy dew]

our helper

[alpine python]

is there some principal value nonsense if you do that?

cause you have two limits

[glossy dew]

nope

arctan(-x) = -arctan(x)

[sand dove]

But does it make sense talking about integral of a function which doesn't converge

g is not integrable on R

[alpine python]

oh yeah

[glossy dew]

oh 🤔

[green crypt]

Exactly what I thought

[alpine python]

you need to require the limits to approach infinity at the same rate, then it's ok

[sand dove]

Which would be the "symmetric integral"

but the regular integral is divergent

[umbral cradle]

Uhm

Sorry to interrupt you guys but

Am i doing this wrong

Ignore some notation issuess with the lim

[sand dove]

first, -(-...) = +...

so it's -R^2/2 + R^2/2

[sand dove]

second, we talked about this

the symmetric integral is 0, because the way you computed it needs to approach the upper and lower bound at the same rate

[sand dove]

but a simple test to figure out if an integral over R is divergent is to check the potential limits at +-infinity

If the function does have a limit there and isn't 0, the integral diverges

[umbral cradle]

i understand this but

i dont get the part after

[sand dove]

which one

[umbral cradle]

this part

[sand dove]

this?

[solemn hatch]

You forgot to differentiate arctan on line 4

[sand dove]

Just like for an infinite series to converge

If you keep adding big enough quantities, you can never hope for it to settle on a convergent value

[devout snow]

@umbral cradle Has your question been resolved?

[devout snow]

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[glossy rover]

what is 1+1?

[river pond]

that can be quite a tricky problem depending on the mathematical understanding one has

[void fox]

2

Don't post troll questions

[glossy rover]

are you sure?

[glossy rover]

it isnt

[river pond]

But please don't use these help channels to troll, as they are probably needed by others who need help.

[void fox]

Yes

[glossy rover]

yeah, i thought it was 1+1=3 because i thought there was a one in the +

thanks for clarifying this

[river pond]

oh ofc you did...

[river pond]

np happy to help

[devout snow]

@glossy rover Has your question been resolved?

[devout snow]

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[short aspen]

does anyone know how they got -8 root 21 + 12

[short aspen]

nvm

.close

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[frail aurora]

help

[frail aurora]

i cant solve this one smh

[trail eagle]

Is there any context to this question?

[frail aurora]

nope my teacher said uhh use substituion

[sand pumice]

first thought is u=ln(x+1)

[frail aurora]

yea i did but

what to do with the x-1

[sand pumice]

that should be e^u -2, but this seems nasty

[frail aurora]

yea idk anymore

i think the problem is wrong or am i jus dumb

i cant find a way to cancel the x-1

[frozen aurora]

this looks nasty

indefinite too??

[frail aurora]

yuh

only number 14 left bruh im so confused

[sand pumice]

yeah wolfram alpha gave a non elementary antiderivative

[marsh trail]

Probably a typo , the denominator should have x+1 ig?

[trail eagle]

Considering how relatively simple the substitutions are for the other exercises, it's 100% a typo

[frail aurora]

.close

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[untold wigeon]

(root400÷5)×(root144÷3)+root81​×16−(root225÷9)

[untold wigeon]

how to do this one?

sir

[minor crypt]

This one?

[runic prawn]

calculator

[untold wigeon]

yea i forgot to add root sir

[minor crypt]

Nah

Dont use calc

[untold wigeon]

k sir

[minor crypt]

First learn the squares of numbers up to 15

225 is square of 15

And 9 is square of 3

[untold wigeon]

wha how

[minor crypt]

So if you root them it is 15/3

[untold wigeon]

so fast?

[minor crypt]

I know them by heart

[untold wigeon]

what is squares?

[minor crypt]

Its not that hard

[untold wigeon]

umm ok

[untold wigeon]

really?

like what do i have to do

what r squares

[minor crypt]

When a number is multiplied by itself, it is said to be squared

[untold wigeon]

like 17x17

[minor crypt]

What grade r u in, so i can teach u better

[untold wigeon]

18x18

5x5

[minor crypt]

Yes

[untold wigeon]

oh

[minor crypt]

Yes 25

[untold wigeon]

5

[minor crypt]

Ok

[nimble dragon]

You…

Anyways go on

[minor crypt]

You see Root reverses this square process

Root(25) = 5

[untold wigeon]

wait r u fromt that channel?

[minor crypt]

Root(81) = 9

[untold wigeon]

oh yea right

[nimble dragon]

I’m not the “bad guy” bro

[untold wigeon]

damn thats ez ]

[nimble dragon]

Don’t have PTSD over it 🙏

[untold wigeon]

but u all laughed at me

pls wait

[nimble dragon]

I didn’t bro

Anyways continue

[fluid stag]

since when did the majority of that channel laugh at you though? it was only that one user

but yeah, continue

[untold wigeon]

yea yea

sir what about 400

[minor crypt]

Ill write a list of squares just have a glance at them
1 square is 1
2 square is 4
3 is 9
4 is 16
5 is 25
6 is 36
7 is 49
8 is 64
9 is 81
10 is 100
11 is 121
12 is 144
13 is 169
14 is 196
15 is 225

[untold wigeon]

200x200

400

[minor crypt]

20 square

[untold wigeon]

?

[untold wigeon]

what

[minor crypt]

20 x 20

[untold wigeon]

lemme screenshot it thx sir

[elfin pecan]

can sm girl help me

[gusty sparrow]

you allowed on discord?

[elfin pecan]

@sonic isle

[untold wigeon]

oh yea right

[untold wigeon]

um well am here for study and gaming so yea

[minor crypt]

Atleast he is using it for homework lmao

[untold wigeon]

yea

[nimble dragon]

???

[gusty sparrow]

haha ik, i didn't mean in this specific case 👍

[fluid stag]

!occupied, please use another channel.

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[untold wigeon]

sir wait lemme solve and show it to u

[green crypt]

can anyone do the latex magic thing?

[minor crypt]

Stop calling me sir bru its weird

[untold wigeon]

what do you mean

[nimble dragon]

It’s almost condescending lmao

[untold wigeon]

ok wat

[minor crypt]

Nvm

Its alr

[nimble dragon]

Say less

[green crypt]

thanks

[nimble dragon]

$\dfrac{\sqrt{400}}{5} \times \dfrac{\sqrt {144}}{3} + \sqrt{81 \times 16}-\sqrt{\dfrac{225}{9}}$

[minor crypt]

Answer should be 395 i think

I think 81 didnt have root

[woven radish]

robin.dabanc_

[nimble dragon]

It probably does cus 9^2 uk

[minor crypt]

No i meant

Sorry

16 didnt have root

[fluid stag]

4^2 mate.

[minor crypt]

Yea but

[gusty sparrow]

he was talking about the original question

[minor crypt]

Ok maybe

[nimble dragon]

Are fifth graders expected to know 9x16 or 9x4 better

[minor crypt]

9x4 prob

[untold wigeon]

root 400 is 20,root144 is 12, root 81 is 9,root 16 is 4,root 225 is 15,root 9 is 3

i got this first

[minor crypt]

So the answer should be 35

Thats seems like a good answer

[untold wigeon]

no ig i 16+36-5

which is 47

[minor crypt]

Wut

[untold wigeon]

yea

[minor crypt]

1 min

[untold wigeon]

sir chech it once

[minor crypt]

Oh yea mb

I cant even do 5th grade math

Ur right

I did it in my head

[untold wigeon]

lets go yea

[minor crypt]

Goodjob @untold wigeon

[untold wigeon]

k come to chill

arigato sensai @minor crypt

bye

.close

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[neon wagon]

yo for the c) i just gotta plug in a=2 then find the inflection points and then plug it into the first derivative and then make a tangent out of that?

[supple knot]

yes

[neon wagon]

okay thank god ty

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[obsidian nebula]

this is for a level

[pastel pasture]

sub x = 1/u

[supple knot]

a level is probably region specific

[obsidian nebula]

UK

[polar chasm]

or just "plug in"

[supple knot]

you mean intro calculus?

[polar chasm]

is there a direction btw

[polar chasm]

from right / from left?

[supple knot]

does -0 mean 0 from the left?

[obsidian nebula]

yes

[supple knot]

0^- is the notation for that

[obsidian nebula]

oh okay

oh got it

thanks

.close

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[terse ravine]

Yo bro help with my very hard homework x + 0
X = boobs

[worthy raft]

Seems right to me

[uncut crow]

i know someone who can help

<@&268886789983436800>

[worthy raft]

???

[winter patrol]

.close

[devout snow]

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[faint zinc]

You got swooped, try again in another open help channel

(sorry)

[true wing]

Kk

[devout snow]

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[ebon surge]

hi, im having trouble with this. i've tried using the double angle formula, product-to-sum etc. but i always get a negative discriminant in the quadratic formula. i suspect there might be a typo, but im not 100% sure.

[green crypt]

Are you trying to prove they're equal?

[ebon surge]

i need to solve for x

[green crypt]

I see

Try rewriting the right hand side in terms of cos2x?

[ebon surge]

so if i did it right i get cos2x + 2cos^2x at the right side

[green crypt]

cos2x = 2cos^2x - 1

See you can take a 2 common from the left side and divide it on the right side yea?

[ebon surge]

ok ok

[green crypt]

So you get 2cos^2x - 1/2

[green crypt]

Now we need -1

So we can write it was 2cos^2x - 1 + 1/2 yea?

[ebon surge]

is not cos^2x - 1/2?

cos(2x) - 1/2*

no wait

im lost

[green crypt]

Look at the right side

Its 4cos^2(x) - 1

When you divide it by 2 (which you took common from the left side)

You get 2cos^2(x) -1/2

[ebon surge]

ohhh okay

but what do i do with the cos4x?

[green crypt]

We can use the sum to product

Hmmm

Oh wait cos4x is just 2cos^2(2x) - 1

So after getting everything in terms of cos2x we can make a quadratic

[ebon surge]

so i get cos2x = -1/3

when i write it like that

no

mb

if it were 4cos^2(2x) on the right side it wouldve made sense

hey i got it, i rewrote the right side as 2(2cos^2(x)-1) + 1 which is 2cos2x so i get a quadratic after turning 4cos^2x-1 into 2(cos^2(2x)-1)

thanks!

.close

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[coral forum]

Can i say that u = 3 + sin x in order to solve this integral $\int\frac{2\cos(x)}{3 +\sin(x)}$

[versed juniper]

yes

[woven radish]

dream

[coral forum]

Okie

.close

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[coral forum]

Is $\int\cos^2(x)\cdot\sin(x) dx = -\cos^3(x) -2 \int\cos^2(x)\cdot\sin(x) dx$?

[drifting sierra]

No

[trail eagle]

Don't think so. How did you get that?

Yes

+C somewhere

but yes

[coral forum]

Okai

[woven radish]

dream

[inland carbon]

nvm

[brave plaza]

no

[trail eagle]

I mean

They'll need a + C at some point

[coral forum]

But can i integrate further?

[trail eagle]

It doesn't really matter when. I was just pointing it out

[brave plaza]

it does

[trail eagle]

Well if you do it this way, you could just bring the integral you have on the RHS to the left.

[trail eagle]

It doesn't. If anything they'd have a trailing coefficient in front of C, which is absorbed. I was just mentioning it to stress it.

[trail eagle]

You'll get $3I = -\cos^3(x)$

[coral forum]

Ohhh

[woven radish]

Azyrashacorki

[coral forum]

I forgot i could do that

[trail eagle]

But do note that you could've done it using u-sub instead of IBP

[coral forum]

Now i got this

$3\int\cos^2(x)\cdot\sin(x) dx = -\cos^3(x)$

[woven radish]

dream

[brave plaza]

yes, you are right my bad

[coral forum]

Maybe i can bring -cos^3(x) to LHS

[trail eagle]

Well you’re done now

You can just divide by 3

[coral forum]

Ohh really

I thought i needed to integrate again

But you are right

The answer is just (-cos^3(x))/3 + C

[trail eagle]

When you do IBP like that and you get the same thing you started with you can just “solve” for your antiderivative directly like this

[coral forum]

Ohh okai

I think i understand

Thanks a lot for the help!

[devout snow]

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[kindred mauve]

can someone check this answer

because i think its incorrect

[wicked turtle]

where's the (2+j)^2 coming from

[kindred mauve]

i dont know

[wicked turtle]

should just be 2+j no?

[kindred mauve]

thats why i think its wrong

[wicked turtle]

,w 1/(2+i)

[woven radish]

Failed to get a response from Wolfram Alpha.
If the problem persists, please contact support.

Feb 24, 2026, 12:07 AM

[wicked turtle]

bruh

hmm, the final answer is right

the intermediate step is wrong, the (2+j)^2 should just be 2+j

[kindred mauve]

its saying this is the answer for 3a

[wicked turtle]

wait, aren't they doing b here?

[kindred mauve]

and this for 3b

[wicked turtle]

yea so for (b) it's right, with an incorrect intermediate step

[kindred mauve]

i thought so ill re do that

[wicked turtle]

the answer for (a) is right too

[kindred mauve]

so this working is wrong

[wicked turtle]

why would 1/z equal (2+j)^2

z = 1/(2+j), so 1/z is just 2+j

if you change that to just 2+j then everything is right

they got the right final answer somehow

[kindred mauve]

so it would be: 2-j/5 - 2+j

[wicked turtle]

- (2+j), use brackets

and (2-j)/5, not 2-j/5

here i'll typeset it

$$z - \frac{1}{z} = \frac{2-j}{5} - (2+j)$$

[woven radish]

Bungo

[kindred mauve]

okay ty

i got it

[wicked turtle]

yw

[kindred mauve]

.close

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[supple knot]

<@&268886789983436800>

[delicate dust]

please dont use help channels for this

[devout snow]

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[wind rapids]

Good morning everyone! Pls help us in physics🥹

[versed juniper]

what is q and p

[wind rapids]

q is the distance of image
P is distance of object

From a mirror

[versed juniper]

M?

[wind rapids]

Magnification

[versed juniper]

t isnt time!?

[wind rapids]

T is time hehe

[hollow ice]

start from the basic relation between p, q and f

if you even call the focal length as f

[cloud plover]

So 1/f = 1/p + 1/q?

[hollow ice]

yes, but its better to let OP do this, coz its their problem

[wind rapids]

@cloud plover and i are classmates hehe

[hollow ice]

[wind rapids]

Is this correct?🥹

[hollow ice]

yea, looks right

except this should be 1/f instead of 1/p

[wind rapids]

Thank you!

How to explain?🥹

[hollow ice]

wdym?

[wind rapids]

How to explain the process?😅

[hollow ice]

like what? that velocity is derivative of position?

[wind rapids]

The whole process in general, why dq/dt = -M² dp/dt

[hollow ice]

coz you have some relation between the positions of object and image, and that constrains the effect of miniscule changes in position of object on changes of positions of the image

[wind rapids]

Ohhhh okay I get it noww

[hollow ice]

[wind rapids]

Thank you!

How about a mathematical explanation 😅

[devout snow]

@wind rapids Has your question been resolved?

[devout snow]

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[fickle moon]

whats the fastest way to do this question?? i did it like this but it felt very inefficient

[winter prairie]

Hmm... I solved it in 2 min
May I tell you my method?

I think you have done the same thing

@fickle moon

[fickle moon]

let me hear it

[winter prairie]

Umm ok

So Our top right corner is clear

That's 7

Cuz 56 and 21 have only one common prime number

Similarly, the box R2C3 is also clear that's going to be 5 as 135 and 160 have one common prime factor which is 5

Right?

?

[fickle moon]

yeah thats basically how i did it

i hate those types of questions

[winter prairie]

Oooohh

I think these are only ways to solve

The only thing is that you increase your speed

[fickle moon]

theres most likely more but yeah, i suppose

waterloo math contest in 2 days

[winter prairie]

Ohh

[devout snow]

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[hollow warren]

My question is on a youtube tutorial for a topic in this case is quadratic simultaneous equation he has 5x^2 - 4x-33=0 he used the quadratic formula but multiplied the 5 by 33 which gave 165 in the examplw but dont you have to do 5 x -33 when doing the quadratic formula

[granite island]

can you explain it a bit more clear plz i dont rly understand sorry

[supple knot]

,tex .quadratic formula

[woven radish]

riemann

[hollow warren]

this

[granite island]

which step do you not understand

[hollow warren]

when he multiplied the 5 by 33 why isnt it -33 for the quadratic formula

[granite island]

he didnt use quadratic formula

also teh discriminant is b^2-4ac which would be 16-(45-33) which is 16+(4533)

[hollow warren]

oh fuck i just realised he used that triangle method

has to multiply and add to the same numbers

[granite island]

yes

anymore questions?

[hollow warren]

ye if he used the triangle method why isnt it 5 x -33

or do u just multiplty the number and ignore the symbol before it

[granite island]

like why it is 5x-11 instead of 5x-33?

[hollow warren]

ye and when he did 5 times 33 but not 5 times -33

[granite island]

probably because he was going to dd the sign later

[green crypt]

Good handwriting

[granite island]

lol

[hollow warren]

thanks for the help

.close

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