help-28

[void jay]

i find a>11

[void jay]

which is is correct

[merry seal]

isolate a in the first equation

[void jay]

a>11

[warped frost]

so what's exactly the issue?

[void jay]

whats the answer?

[warped frost]

if a must be greater than 11, which of those ranges of a fulfill what you found?

[void jay]

i picked a>15 , but that isnt correct

[warped frost]

well yea, a = 12 fulfills what you found but not a > 15

[merry seal]

I think you should choose a "wider" range

[void jay]

yeah thats where i am confused

[merry seal]

so if a is bigger than 11, then a must always be bigger than 8 too

[void jay]

how do i know if its asking for the father or the child constraint?

[warped frost]

test sample values

[void jay]

by father i mean one that encoumpases the child

[warped frost]

you know the constraint you found must be true

so which of those other constraints is necessarily also true?

[void jay]

do you have a visual explanatio for this in mind ?

my mind is still fixated on d

[warped frost]

I can't draw one atm, but you can convince yourself by drawing inequalities on a number line

[void jay]

to me a value of 9 would be wrong

thats why a>8 is not my choice

[warped frost]

but a = 9 doesn't fulfill what you found

why would that even be in consideration

the main constraint is the one you found

any test values must satisfy your constraint first

[void jay]

ahhh

i think i uderstand

thanks

[full forum]

@void jay Has your question been resolved?

Channel closed

Closed by @void jay

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[torn bane]

i’m confused on solving for the x 2nd particular solution

for undetermined coefficients, i just remember that you would guess yp =Acoswx+Bsinwx if f(x) is sinwx or coswx or sinwx+coswx

I got a hint that you cant just set v=lnt, v'=1/t and v''=-t^(-2) but im very confused

[autumn raptor]

Do u have a specific example?

[torn bane]

the specific example is in the picture i sent

[torn bane]

originally i just set it as this and solved xp2' and xp2''. In the picture i took i know i have v'=u'/t but that was from a hint

[somber pike]

Seems like you're forgetting the chain rule for the second derivative of x if I'm not mistaken?

[full forum]

@torn bane Has your question been resolved?

[torn bane]

i see

[full forum]

@torn bane Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[proven lynx]

can someone help me herepls

[proven lynx]

the c)

and d)

[full forum]

@proven lynx Has your question been resolved?

[proven lynx]

<@&286206848099549185> help?

[full forum]

@proven lynx Has your question been resolved?

Channel closed

Closed by @proven lynx

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[dry arch]

How do i explain this? I have a sequence a_n and I want the the indexes of every third term, and the bigger of the other two, so i can sum a function over those indexes

[dry arch]

Argmax almost works, but apparently it returns a set

It would be a problem if a2 = a3

[gritty rose]

bigger of the two what?

indices of every third term is just k = 3n

[dry arch]

Yeah

I mean

Say you have a1 a2 a3 a4...

If a2 is bigger than a3, include f(2) in the sum, otherwise include f(3)

Likewise for a5 and a6

[gritty rose]

what's f?

[dry arch]

f(i) = a_i + min (a_(i+1), a_(i+2))

Its for a competition problem, I can give more context if you want

[gritty rose]

yea i think you're better off just showing the original problem

[gritty rose]

this contradicts your previous sentence #help-28 message

[dry arch]

S1, S2 are not correct here.

Because sets dont hold duplicate elements

[dry arch]

The fact that f uses the min function is kind of unrelated

Oh I didn't mean to spoiler the image 😂

[full forum]

@dry arch Has your question been resolved?

[full forum]

@dry arch Has your question been resolved?

[full forum]

@dry arch Has your question been resolved?

[full forum]

@dry arch Has your question been resolved?

[dry arch]

.close

[full forum]

Channel closed

Closed by @dry arch

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[little night]

Hello can someone please help me prove it

[split hatch]

What do you think the group of symmetries is?

[little night]

I think they are the symmetry about the x axis and y axis and the rotation of 180degrees and there composition

[dry arch]

there's translation

[little night]

There are alot but I don't know how they will end up being 3

[split hatch]

One of these is redundant, can you see which one you should get rid of?

and also you're missing translation as Axe pointed out. Since the question requires that you provide reflections as generators, can you try to express translation as a combination of reflections (about some different axes)?

[dry arch]

it asks you to determine the symmetry set, so i think including all of those is good, even if they are redundant

[little night]

The problem is it says prove it i can think and write. Them but the proof is hard

[dry arch]

the problem has two parts

only one of those parts asks for a proof

for the first part, i think you should just describe the symmetry set, without proof

[little night]

symmetry set for this infinite diamond pattern consists of:
Translations: Shifting the pattern left or right by a specific unit length (the width of one diamond).
Horizontal Reflection: A reflection across the central axis running horizontally through the middle of all diamonds.
Vertical Reflections: Reflection axes that pass vertically through the center of each diamond and through the points where the diamonds touch.
180^{\circ} Rotations (Half-turns): Rotation points located at the center of each diamond and at the intersection points between diamonds.
now the second part is so har

[dry arch]

that's good

there are also glide reflections

[little night]

Yes but they are redundant

[dry arch]

i don't think so

[split hatch]

what is meant by glide reflections

[dry arch]

a reflection about the horizontal line, followed by a translation

[split hatch]

then it's redundant no?

in the way you describe

[dry arch]

i don't think so

for the first part, you should identify all symmetries

not just a generating set of symmetries

[split hatch]

you just described how to obtain it from the composition of existing symmetries

[split hatch]

Obviously you're not going to write down an infinite group

Unless you are Sisyphus

[dry arch]

no, but you can describe them

[split hatch]

It is common to describe a group in terms of generators and relations

[dry arch]

yes

[little night]

I usually try to make the model by a paper and then see how to solve but this problem says infinite pattern if its infinite then may be there are infinite symmetries how they end up being just three

[dry arch]

there are infinite symmetries, but they can be generated by three symmetries

you can make them from three "ingredients"

[dry arch]

so for the second part of the question, you should describe how each of these can be made from the three ingredients

[little night]

Ahhh i see now
Reflection 1 (R_1 - Horizontal): Let this be the horizontal line passing through the center of the pattern.
Reflection 2 (R_2 - Vertical): Let this be a vertical line passing through the center of one diamond.
Reflection 3 (R_3 - Vertical): Let this be a vertical line passing through the point where two diamonds meet (half a unit away from R_2).

[split hatch]

yes that is correct

[dry arch]

ye

so you should show how to get rotations, translations, and glide reflections from those

as well as the other reflections (about different lines)

[little night]

I got it Thank you two so much for your wonderful help🥰

[full forum]

@little night Has your question been resolved?

[little night]

Yes

[full forum]

Channel closed

Closed by @little night

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[twin wolf]

Not sure where to start

[onyx glen]

induction?

[twin wolf]

Oh

Yeah probably

.close

[full forum]

Channel closed

Closed by @twin wolf

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[steady forum]

gi

[full forum]

Please don't occupy multiple help channels.

[steady forum]

.close

[full forum]

Channel closed

Closed by @steady forum

Use .reopen if this was a mistake.

[spiral vigil]

be aware that this has not escaped our notice. please do not repeat this behaviour.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[summer creek]

how can i prove it?

[onyx glen]

step 0 would be to figure out wtf "affix" means in this context

what kind of old-ass complex numbers book are you using

[summer creek]

just normal university book?

i can DM you the pdf of it

affix mean vectex

no"?

[shell jetty]

In mathematics, particularly complex analysis, an affix is the point in the complex plane that corresponds to a given complex number (z=a+ib)

[glossy valve]

Japanese_SeiRyou

[shell jetty]

From google ai

Don't you need some previous part of the question to answer this?

What is O for example?

[onyx glen]

!noai

[full forum]

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

[onyx glen]

did you mistype "vertex"

okay so i guess the more familiar way to say it is that P, Q, R are the points representing the complex numbers z1, z2 and z1+z2

anyway can you tell me the defn of a parallelogram

[summer creek]

2 pair of parallel sides

[onyx glen]

that's more like it.

so how can you tell whether sides OP and QR are parallel or not

[whole lily]

@summer creek

[full forum]

@summer creek Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[summer creek]

.closd

.closd

.close

[turbid badge]

⁉️

[pseudo roost]

What

[foggy vapor]

this seems ok

but continue ur work

simplify

3 + 1 = 4 so i mean just write it as so

[pseudo roost]

Oh ok

Thanks

It seems won’t tho

Idk what to do

[hot herald]

what?

[pseudo roost]

It seems wrong

[hot herald]

which part seems wrong, show your updated work

[lunar bobcat]

well, 2^2=4 so…

u will be left with 3^2x=3^1/2

[pseudo roost]

Oh

Wait so the four cancel out?

[lunar bobcat]

yep

[pseudo roost]

I got 2x=1/2

[lunar bobcat]

now jst do like normal

[pseudo roost]

tysm mei

Guys should I use the k method for this

I don’t. Think I can factorize it

[wary condor]

is that 6.3 or 6 * 3

I think irts 6.3

otherwise it'd be a weird way to denote multiplication.

[pseudo roost]

6.3

[wary condor]

is it 6 multiplied by 3^x

or is it six point three as in the number

oh actually multiplication would make a lot more sense here

nevermind then.

[pseudo roost]

Yes

[halcyon sundial]

Hi , can ask you?

[wary condor]

!help

[full forum]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[wary condor]

روح افتح channel ثانيه

[pseudo roost]

Can I do this

[white badge]

hint: consider making this into a quadratic.

[pseudo roost]

What’s Tht pls

So the k method?

[wary condor]

I mean yeah you didnt do anything wrong

refer to what nicople is saying

[white badge]

I'm not sure what method it is called for you, but see that you have 3^2x and 3^x, and a constant term.

[pseudo roost]

Yes

[white badge]

by the power rule of exponents, realize that you can write 3^2x as (3^x)^2, and now you have (3^x)^2, 3^x, and some constant.

[pseudo roost]

👏

[white badge]

and then you can do as you would a regular quadratic.

[pseudo roost]

But wait

How

Yeah I don’t understand

[white badge]

can you rewrite the equation such that all terms are on one side, and rewrite 3^2x as (3^x)^2?

[pseudo roost]

Ok

[white badge]

do nothing more than that, by the way. just stop there first, and then we can proceed step by step.

[white badge]

excellent!
now, let u = 3^x for clarity.
rewrite the quadratic to be a quadratic in u, and solve the quadratic for u using whichever method you prefer.

(you may skip the substitution step; if you do, then you are solving the quadratic for 3^x. the idea remains the same.)

[pseudo roost]

Like this?

[white badge]

yes! in this case, solve the quadratic for k.

[pseudo roost]

Tysm

Question pls

When do Ik when to do this

Ik a lot of ways that are different but I get confused on who’s one to. Use

[brittle sun]

Usually you just look for patterns

"oh this thing is the square of this other thing involving the same variable"

"maybe I can quadratic this"

-# sorry for the intrusion Nicole

[white badge]

no, please do! I'm just a newcomer.

[brittle sun]

-# Speedrun green asap smh

[white badge]

well, normally if I see {number}^(nx) and {same number}^(2nx), and the rest are constants, that's a sign to bring out the quadratic.

[pseudo roost]

Wdym by this please

[pseudo roost]

Oh ok ok

Lemmenot this

[white badge]

here's an example:
$6^{6x} + 5 \cdot 6^{3x} - 6^2$

[pseudo roost]

Oki noted

[glossy valve]

Nicole

[white badge]

this can also be reduced to a quadratic, but this time in 6^{3x}.

[pseudo roost]

Oh

And the quake makes it the beginning of a quadratic

Wait then what’s a trinimial

Idk the terms for anything, I just know what they are💔

[white badge]

a trinomial is any polynomial with three terms.

it does not have to be a quadratic.

$x^3 - x + 3$ is a trinomial.

[glossy valve]

Nicole

[white badge]

but it is not a quadratic - note the x^3.

[pseudo roost]

So square is quadratic

Anything above is trinimialk

[white badge]

you can remember trinomials as triples (tri- = 3, -nomial = terms).

[pseudo roost]

Oh ok ok

[white badge]

no, a trinomial has strictly three terms.

[pseudo roost]

Triple

[white badge]

it has nothing to do with the degree of the trinomial.

[pseudo roost]

No I mean the square thing

[white badge]

$x^6 + x^4 - 2$ is also a trinomial, but it is not a quadratic, nor is it a cubic.

[glossy valve]

Nicole

[pseudo roost]

Now I’m confused

Quadratic also has three terms

[white badge]

yes, but in a quadratic, the highest degree is 2, as in $x^2 + x + 1$. you will never find anything higher than a 2 as a power of the variable in a quadratic.

[glossy valve]

Nicole

[brittle sun]

Not necessarily, x² + x is also a quadratic

[white badge]

terms like quadratic, cubic, quartic, etc. refer to the degree of a polynomial - that is, the largest exponent of the variable present in the polynomial.

terms like binomial, trinomial, etc. on the other hand refer to the number of terms in the polynomial, which is a separate concept from its degree.

[onyx glen]

up to 3 terms, not necessarily exactly 3

[pseudo roost]

Oh ok

How

Uh like how do I do the k part now pls

[white badge]

now, what was k?

[pseudo roost]

3 or -9

[white badge]

no, as in what did you use k as a substitute for?

hint: you wrote it to the left.

[pseudo roost]

3^x

[halcyon sundial]

K=-9 canceled

[pseudo roost]

Oh why though pls

[white badge]

right. now, since k = 3^x, we now have 3^x = 3, and 3^x = -9.

[halcyon sundial]

If x belong to real number

[onyx glen]

this ^2 shouldn't have been there. k is just 3^x and not (3^x)^2 after all.

[onyx glen]

"cancel" is the wrong word

[white badge]

solve for x in both cases.

you will find that one of the cases is indeed impossible, as alluded to by the other user.

[pseudo roost]

Oh so we don use the k^2

[pseudo roost]

Ic tysm everyone

[pseudo roost]

Oh ok ok

Ty

You guys are so smart

[onyx glen]

there is no "k^2" to "use" anymore.

you got 2 values for k; there is no reason to raise one of them ^2.

[pseudo roost]

Oh hhhhhh

[white badge]

you're already at the end goal. squaring does not help us.

[pseudo roost]

That make sense

I think her said something about not being able to prime base a negative number

So k=1

[white badge]

do you mean x = 1?

[white badge]

this is a bit inaccurate (and confusing) as stated.

[pseudo roost]

Yes

[pseudo roost]

My teacher

Ik k isn’t the -o9 but I can’t explain

[white badge]

what you cannot have is a positive base leading to a negative number for any exponent x.

try graphing y = {some positive number}^x and look at the graph (if you have learnt about graphing already).

you can do it in Desmos or Geogebra (or your favourite graphing tool).

[pseudo roost]

Idk both

[white badge]

ah, then here is an example.

notice that no matter how negative x gets, the graph never quite goes below the x-axis.
it is impossible to get 3^x, or any positive number raised to any real exponent, to be negative.
this will become more relevant once you learn about logarithms, but it is also relevant in this question as it tells you that you should reject one of the solutions.

[pseudo roost]

Oh ok

Can I ask for help again

[white badge]

<@&268886789983436800>

[white badge]

is the first line the original question as written?

[pseudo roost]

Yes

I wrote into the questions part w th least question u he
Led me w

So I’m doing this one on the back

[white badge]

I would recommend rewriting that 2^(-1) as 1/2.
then, try rewriting (2^x)^(-3) as a fraction using the rule of negative exponents as well.

[pseudo roost]

Oh

Oki

I think I can take the 1/2 to factorize

But that wouldn’t make sense

[white badge]

I would recommend not doing that, as it would complicate things.

there is another thing you can do once you have rewritten things as I've suggested.

[delicate torrent]

when you got $A - B = 0$, then that means $A = B$

[glossy valve]

1 divided by 0 equals Infinity

[delicate torrent]

try to see what you can do knowing this

[pseudo roost]

Take term 2 to the other side?

[white badge]

I'll let Infinity take over the guide, and stand back.

[pseudo roost]

Oh oki

[delicate torrent]

-# im in a middle of an online class 😭

[full forum]

@pseudo roost Has your question been resolved?

[delicate torrent]

anyways

[delicate torrent]

try using this @pseudo roost

[pseudo roost]

Ik

[delicate torrent]

after you did that, you should be able to notice there's a common base on both sides here after you simplify the powers

[delicate torrent]

ping me when you need help or you're done with what i said

[full forum]

@pseudo roost Has your question been resolved?

[pseudo roost]

oki

[white badge]

please remember to react to this bot prompt!

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[waxen obsidian]

Is there anything wrong with what i wrote?

[waxen obsidian]

,rcw

[torpid surge]

what's the original function

[whole lily]

probably $y = \ln\left(\cos\left(e^{x}\right)\right)$

[glossy valve]

Roy

[near kelp]

Yeah my best guess too

[whole lily]

@waxen obsidian

[full forum]

@waxen obsidian Has your question been resolved?

[waxen obsidian]

No

I just need to know if the 2nd line is a correct simplification of the 1st linr

[whole lily]

your spacing is a bit awkward and also you should include brackets

[waxen obsidian]

Is ln for log? Then you're correct

[waxen obsidian]

Add brackets where

?

[whole lily]

$$\frac{dy}{dx}=\frac{-\sin\left(e^{x}\right)\cdot e^{x}}{\cos\left(e^{x}\right)}$$
$$\frac{dy}{dx}=-\tan\left(e^{x}\right)\cdot e^{x}$$

[glossy valve]

Roy

[waxen obsidian]

Just wanted to know if it was accurate to add the minus on tan instead of
doing
-e^² • tan^e^x

[whole lily]

??

[waxen obsidian]

Oh ok so on the angles, got it thanks

[waxen obsidian]

Basically what i wrote just flip it and putting the minus on e^x instead

hey...

.close

[full forum]

Channel closed

Closed by @waxen obsidian

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[still current]

just wanted to clarify something i need to determine the 0 if it exists

[still current]

0 = -4.25(e)^(x+7) + 4.25

-4.25 = -4.25(e)^(x+7)

1 = (e)^(x+7)

log 1 = (x+7)log e

0 = (x + 7)log e

[stiff musk]

use brackets

[still current]

0/log e = x + 7

[stiff musk]

(x+7) log e

[stiff musk]

so far so good

[still current]

log e = x + 7

?

[stiff musk]

log e is nonzero

0 / nonzero = ?

[bleak osprey]

Just log both sides

No

[still current]

is log e the actual log e or is it just a variable

[bleak osprey]

I mean ln both sides

Since its e

[stiff musk]

or just use the known value of log e (assuming natural log)

[still current]

i dont know how to use ln

[bleak osprey]

It's the same

[hot herald]

just another log

[stiff musk]

even if you don't know how to use it, all you need to know is that log e is nonzero (regardless of what log base you use)

[glossy valve]

scoob

[stiff musk]

^ so do the division on the LHS correctly, the result is not log e

[still current]

its 0

[stiff musk]

therefore x = ?

[still current]

x = -7

[stiff musk]

yep!

[still current]

what if it was log b

so 0/log b

[stiff musk]

0 / log b is also 0

0 over any nonzero number is 0

[still current]

oh alr

[bleak osprey]

Just put all your questions here

[still current]

got it thanks

[still current]

alright lol

[stiff musk]

for future reference, ln e = 1

that's why the natural log is nice when working with e^stuff

[still current]

determine the all-in-one solution of each equation

3(2/5)^(x+1) -4 =< 14,75

3(2/5)^(x+1) =< 18,75

(2/5)^(x+1) =< 6,25

[bleak osprey]

And what do you do after

[still current]

hm

[bleak osprey]

Hint: ln

[still current]

not sure

[bleak osprey]

Or log

You can do it

[stiff musk]

log (of any base) is monotonically increasing, so if a <= b then log a <= log b

that's why you can apply it here

[still current]

what if i do (x+1) log 2/5

[bleak osprey]

Also the other side too

Yep that's correct

What's next

[still current]

(x+1) log 2/5 =< log 6,25

[bleak osprey]

Then

[still current]

divide by log 2/5

wait no

[bleak osprey]

Yes

Divide both sides

[still current]

oh alr

gives -2

[stiff musk]

be very careful though

is log 2/5 positive or negative?

[bleak osprey]

Then

[still current]

positive

[stiff musk]

almost

it is in fact negative

[still current]

oh yeah

it ids

what does that mean

[stiff musk]

so what does that mean for the inequality

[still current]

it gets switched

[stiff musk]

yep!

[still current]

=

[bleak osprey]

Be careful with signs

[still current]

so how can i know exactly like what makes it get switched

like here it was log 2/5

[bleak osprey]

The sign

[stiff musk]

log 1 is 0

log of anything bigger than 1 is positive

log of anything smaller than 1 (but still positive) is negative

log of zero or negative numbers don't exist

[still current]

alright i see

x >= -3

so as soon as i added log 2/5 into the equation

we switch the equality

?

[stiff musk]

as soon as you divide both sides by log 2/5

[still current]

oh alright

[stiff musk]

because multiplying or dividing both sides of an inequality by a negative number flips the inequality

[still current]

oh yeah true

gotcha ok

what does it mean if a question asks me to determine the signe of each function

f(x) = 4^(x+3) - 16

what does it mean by determine the signe?

[stiff musk]

probably they mean what values of make it positive and what values of x make it negative?

do you have a screenshot or an example you can show?

[still current]

well the example (equation) is this

[still current]

its in french

[stiff musk]

sry i meant like worked out example (not necessarily this particular function)

[stiff musk]

that's ok

[still current]

wait

ik now

[hot herald]

you could also post the original French as some people (not me) understand it

[still current]

it means like for example when u find x = ?

it means the fonction f is positive in ]-infinite,-1] and negative in [-1,infinite[

thats what it means

[stiff musk]

yea that's what i was guessing it meant

good

[still current]

but idk how to do that

[stiff musk]

it basically amounts to solving 4^(x+3) - 16 > 0

(to get the x values that make it positive)

and you can do that similarly to how you did the last one

[still current]

alright ima try

x = -1

[stiff musk]

how did you arrive at that?

btw your answer should be an interval, not just a single x

[still current]

0 = 4^(x+3) - 16

[stiff musk]

this is an inequality, not an equation

[still current]

thats the part idk how to do

then 16 = 4^(x+3)

[stiff musk]

well you're right that you get = 0 when x = -1

[still current]

4^2 = 4^(x+3)

2 = x +3

-1 = x

[stiff musk]

one easy thing to do is to plug in an x value greater than -1 and see if the result is positive or negative

[still current]

what does that do

like if the result if positive or negative

[stiff musk]

well you know the function crosses y=0 at x = -1 and nowhere else

so it has to maintain the same sign for all x to the right of -1

and all x to the left of -1

so to find out which sign, just plug in a number in each interval

like plug in x=0 to see if it's positive in the interval (-1, infinity)

if you don't like doing it that way, then just solve the inequality as an inequality instead of changing it to =

[still current]

plug in 0 in f(x) = 4^(x+2) - 16

the x

f(x) = 48

[still current]

@stiff musk

[stiff musk]

wait how did we get 4^(x+2)

wasn't it x+3

but yea assuming that was a typo, you're correct

so f(x) is positive when x > -1

and you can check, it's negative when x < -1

[still current]

oh sorry yeah

x+3

so does that mean positive interval ]-infinite, -1[

[stiff musk]

is x=0 in that interval?

[still current]

it isnt

[stiff musk]

so that's the interval where f is negative, not positive

[still current]

oh

so its [0,infinite[

positive

[stiff musk]

you sure about the left endpoint?

[still current]

like that?

[stiff musk]

no the numerical value

are you sure it's 0?

[still current]

uh yeah

ohhh

wait no

]-1, infinite[

[stiff musk]

yep!

that is correct

[still current]

alr ty

.close

[full forum]

Channel closed

Closed by @still current

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[rancid flame]

Unsure how to solve this?

I got x = 7.46 or x= 0.54

[gritty rose]

!show

[full forum]

Show your work, and if possible, explain where you are stuck.

[rancid flame]

This is my working so far

So, since we’re trying to figure out a parallel to 6x -5, I tried using 6x - 11

Since the kx has to be the same for two lines to be parallel

[sudden condor]

This is correct

[sudden condor]

I don’t know where this came from

[rancid flame]

As the two are parallel, I just picked 6x - 11 randomly

To start out with

[torpid surge]

you can differentiate it

and equate it to 6

[sudden condor]

Randomly is not a pretty good reason to solve it

[rancid flame]

Ok I got 4

For that

[torpid surge]

yes 2x-2 = 6

[sudden condor]

Going great

[torpid surge]

you can find y value

by putting 4 into the quadratic

[rancid flame]

Y is 1

[torpid surge]

equating it wouldn't work here

[rancid flame]

?

[torpid surge]

because they said the curve's tangent is parallel to the linee

they didn't say the line is the tangent

[torpid surge]

yeah pretty sure that's right

[rancid flame]

Ok so what was the reasoning behind this?

As in why = 6?

[torpid surge]

they said at what point

is the curve's tangent

parallel to that line

for the tangent to be parallel they should have the same slope right?

[rancid flame]

Oh, because kx = 6x

[torpid surge]

so you can say the tangent will hav a slope of 6; dy/dx = 6

[rancid flame]

Ok ic

Thanks for the help

[torpid surge]

np

what does ^ mean

as a reaction

[verbal crater]

That people concur with you

[torpid surge]

oh ok thanks

[full forum]

@rancid flame Has your question been resolved?

Channel closed

Closed by @rancid flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hardy ravine]

Can someone explain the red arrow step to me?

[bright bronze]

,w sin(0.449 radian)

[glossy valve]

Results provided by WolframAlpha

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

Requested by bacter10fr4g

[bright bronze]

They just found the principle angle for that corresponding sine value

[hardy ravine]

Ah I get it now, appreciate it :>>>

[full forum]

@hardy ravine Has your question been resolved?

[robust slate]

!done

[full forum]

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

[robust slate]

.solved

[full forum]

Channel closed

Closed by @robust slate

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[summer depot]

The original drawing is the right

The left is mine with the auxiliary construction and hypothesis and thesis

[serene hazel]

please close your other help thread or this

you dont need to spam it twice

#1464815892121784340 message

[summer depot]

Oh ok

A'B' is the reflection of AB through O

[charred carbon]

No offense but can you type the hypothesis out, I tried to understand them but couldn't , the handwriting is a bit hard to read

[summer depot]

Ok

No worries

Hypothesis: 1. AD is perpendicular to AB, 2. BC is perpendicular to AB. 3. AD ll BC. Auxiliary Construction: It draws the segment DC, and it draws the segment A'B' through O as the reflection of the segment AB. Thesis: Prove that ABCD is a rectangle.

[charred carbon]

if ABCD is a rectangle, reflection of A and B wrt O would be C and D, right? Or am I being dumb

AD//BC is not even a hypothesis, you can deduce that from 1 and 2

[summer depot]

Well that's correct

The part of AD ll BC

I deduce it. Before

But i don't undertsand your first point

Also the thesis is to prove that ABCD is a rectangle

We only can prove that AA'BB' is a rectangle because of there 4 parallel sides and 4 rectangles angles

[summer depot]

Sorry but what is wrt?

[charred carbon]

Yes, because that's the only thing you can

[charred carbon]

With respect to

[summer depot]

Oh ok

[charred carbon]

There aren't enough info to show ABCD is a rectangle

[summer depot]

Oh ok.

Then can you help me to proof that triangle ABD = triangle ABC?

With the same hypothesis

Without auxiliary construction

Only that the thesis changes

[charred carbon]

😭 that doesn't have to be true either, if ABD=ABC then ABCD would be a rectangle

[summer depot]

Yeah but without the auxiliary construction

Only with the original drawing

Which is this one

[charred carbon]

Idk what info are in this drawing, is this figure for scale?

AD=BC?

[summer depot]

Yeah is the original problem

The same hypothesis

But the thesis is to prove the triangle ABC equal or congruent to triangle ABC

[charred carbon]

Then nah, not enough info to show DAB=CBA either

[summer depot]

Wait wait

But if i do the same hypothesis plus the auxiliary construction then I can say the triangle ABD is equal or congruent to triangle ABC no?

[charred carbon]

No , it doesn't give you any more info

[summer depot]

Nop

.close

[full forum]

Channel closed

Closed by @summer depot

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[strange dove]

am i doing 6a correctly?? i got an explanation from someone a few hours ago but i feel like it can still be simplified?

[torpid surge]

,rotate

[torpid surge]

,rotate

[torpid surge]

,rotate

[brittle sun]

You can just use the arrows, or use ,rccw

[torpid surge]

sorry

[brittle sun]

No worries

[torpid surge]

4x^2 - 5 is not equal to (2x-5)^2

[strange dove]

oh srry i shouldve taken a better photo

[torpid surge]

you simplified the denominator

of the first fraction

to (2x-5)^2

but that's not the same as 4x^2 - 25

[strange dove]

oh

[torpid surge]

you can still simplify it using identities though

[strange dove]

wait how do i simplify 4x^2 - 25 then-

[strange dove]

oo okok

[torpid surge]

try using the a^2 - b^2 identity

[strange dove]

okayy

[torpid surge]

simplify the quadratic on top too

i think they'll cancel out

[strange dove]

does it equal to (4x - 5)(4x + 5)

or is it (2x - 5)(2x + 5)

[torpid surge]

the second

because when you multiply 2x * 2x you get 4x^2

[strange dove]

ohh ok

[strange dove]

wait this might take me a while

ok so i got (-4x + 3) (2x - 5)/(2x - 5) (2x + 5)

i can cross 2x - 5 from both sides so that leaves

(-4x + 3)/(2x + 5)

[torpid surge]

yes

and you can now subtract the other fraction

[strange dove]

dont i hv to multiply the two rightmost fractions first-

before subtracting

[torpid surge]

you already did that here

[strange dove]

OH

okok i get it

tysm!!

is that the final answer or can it be simplified further

i tried making the denominators the same earlier but it js made the equation more confusing

[torpid surge]

you can

make the denominator and numerator quadratics

into one fraction

but that'll be very tedious

[strange dove]

aaaa okok

[delicate torrent]

Just try, what if they simplify nicely actually

[torpid surge]

hmm yeah maybe

[strange dove]

is this fully simplified?

aaeeaeaae

[strange dove]

i highly doubt it, my teacher usually puts random numbers so

[full forum]

@strange dove Has your question been resolved?

[full forum]

@strange dove Has your question been resolved?

[strange dove]

.close

[full forum]

Channel closed

Closed by @strange dove

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[crimson kernel]

Let 𝐺 be a simple graph with 9 vertices and suppose that the sum of all degrees is at least 27. Then 𝐺 has a vertex of degree at least 4.

[woeful horizon]

hello

[crimson kernel]

Hi

[woeful horizon]

oh nvm, uhhh not what ive learnt

sry bruh

[crimson kernel]

alr

[woeful horizon]

ill let the helpers know

[queen gull]

If every vertex has degree at most 3, then the sum of all degrees is at most 27

[onyx glen]

you don't need to know any graph theory actually

this is straight up pigeonhole

well ok no actually you do need to know a bit of graph theory

namely that the degree sum can't be exactly 27 (why?)

[crimson kernel]

oh yea

the sum must be even

cus its twice the amount of edges

[whole lily]

ding ding ding

[crimson kernel]

Yea I know that but I was just wondering how to put it in a valid proof

I tried proving by contradiction

[onyx glen]

do you know the handshake lemma

$\sum_{v \in V} \deg(v) = 2|E|$

[glossy valve]

Ann

[full forum]

@crimson kernel Has your question been resolved?

Channel closed

Closed by @crimson kernel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[flint crane]

I dont know how to prove divergence theorem as a special case of the generalized stokes theorem, im stuck at this step and i dont know how to turn it into the integral of F.n dS

[full forum]

@flint crane Has your question been resolved?

[full forum]

@flint crane Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[autumn token]

how ro go from

[full forum]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[autumn token]

to

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[cedar flint]

Can someone please help

[robust slate]

bashing

[full forum]

Show your work, and if possible, explain where you are stuck.

[cedar flint]

?

[robust slate]

this is just annoying algebra soup

hence I call it bashing lol

[cedar flint]

b=a+3 and c=a+12 and a+3=ar and a+12=ar^2

d=ar^3

[astral sinew]

The worst part is having to express it as a mixed number. That's insane

[robust slate]

Personally, I'd go for ||isolating r||

[cedar flint]

r=(a+3)/a

[robust slate]

mhm

what's another easy way you can get r?

you may find it helpful to ||think back to the definition||

actually doing this from the start prob would've been easier lol

but not by much tbf

[cedar flint]

r is the common ratio of the numbers so c/b= r

so (a+12)/(a+3)=r

[robust slate]

yeah

[cedar flint]

ok thanks i got the answer

81/2

.close

[full forum]

Channel closed

Closed by @cedar flint

Use .reopen if this was a mistake.

[robust slate]

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[novel stratus]

Any hint how to start?

[prime pier]

,rccw

[brittle sun]

That's gonna be ugly

First instinct is some trig sub

[bronze solar]

yes

[bronze solar]

same but then which trig ratio

[fair flower]

YIKES.

ok ill leave it to @brittle sun

[novel stratus]

Also for reference

[bronze solar]

are you sure you wrote down the question correctly?

[onyx glen]

step 0 would be to write your fraction bars longer so they don't look like they're shrivelled up

[brittle sun]

My guess is sec

[novel stratus]

It was smth like this

I reduced it to this

[brittle sun]

Cuz then you get a tan from the du and from sqrt(u^2-1) which cancel out

,rccw

[bronze solar]

gosh show the original question

[novel stratus]

Third

[brittle sun]

,rccw

[brittle sun]

God yeah it's gonna be ugly as fuck

[novel stratus]

Absolutely

Fun fact : I have solved it because I have marked it like that

It means it was absolutely shitty question

[brittle sun]

Honestly if you have options I'd differentiate those

Although the options are equally ugly

[novel stratus]

I m able to get the ln|.......| part correctly

Idk about other tho

[novel stratus]

Fr

[brittle sun]

This is the kinda shit they make you do in jee

[novel stratus]

Yes

Those heartless bastards🗣🗣🗣

[bronze solar]

i think you substitutr (tan²x-1) or (cot²x-1) for soemthing

[brittle sun]

I'm gonna peace out, best wishes

Just gonna link this ig

https://www.integral-calculator.com/

[novel stratus]

Is there like no general way of solving 1/[(Quadratic)(sqrt(quadratic))]

[bronze solar]

there are, this is just hideous.

[novel stratus]

[fair flower]

goodness

i tried solving this

i quit as soon as i saw trig

[bronze solar]

what even is the worth of solving questions such as these

[novel stratus]

I think I got it

[bronze solar]

how did you do it

[novel stratus]

Imma solve it a little more

To make sure I m correct

Ok so

@bronze solar you here?

[bronze solar]

yes

[novel stratus]

So in this

u=cotx

Then du = -csc²xdx

Then it simplifies to

-dx/sqrt(cot²x-1)

Not change cotx to cos/sin

Taking lcm and taking sin out

It becomes -sinx dx/sqrt(cos²x-sin²x)

Then changing sin²x to 1-cos²x

Then taking cosx=t

[bronze solar]

im out

[novel stratus]

Fair enough

Nvm I m out too bro

Answer isn't matching

[full forum]

@novel stratus Has your question been resolved?

Channel closed

Closed by @novel stratus

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[torn jolt]

Hello, i'm in 7th grade and taking algebra 1 honors

[torn jolt]

i have midterms soon

[fair flower]

hello

[torn jolt]

and i'm studying for that

i forgot how to solve absolute variable equations, with absolute value terms on both sides

?

[fair flower]

like lets say |x+3| = |2x-5|?

[torn jolt]

yeah, something like that

[fair flower]

there are 4 cases for these types

LHS neg RHS pos
LHS neg RHS neg
LHS pos RHS neg
LHS pos RHS pos

you have to solve for all 4

[torn jolt]

what does that mean?

whats a LHS and RHS?

[fair flower]

lhs is left hand side

[torn jolt]

oh

[white badge]

left/right-hand side.

[fair flower]

aka left side of the equal sign

[torn jolt]

okay

so how do i solve it?

[fair flower]

solve for all 4 cases

[torn jolt]

okay

thanks

[fair flower]

btw by LHS neg i mean like

you know how when u have an absolute value in a function

for example

|x+3| = 5

[torn jolt]

yeah

[fair flower]

you can do

x+3 = -5 or x+3 = 5

[torn jolt]

i know that

[fair flower]

same case here

[torn jolt]

thats how i always solve them

[fair flower]

just to clear up some confusion

thats why there are 4 cases

due to both left and right hand sides having both positive and negative counterparts

[torn jolt]

okay

thanks a lot

[fair flower]

yw

can someone close this channel

OP doesnt need any further help

[void nova]

.close

[full forum]

Channel closed

Closed by @void nova

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[static verge]

hi

[static verge]

i got first part, but how do i do second part

what do i need to integratre

integrate

[robust slate]

In the future, please make the first message you send the actual question since that's what the bot pins. \ \
Recall that the arc length of $f$ on the interval $[a,b]$ is given by
$$L=\int^{b}_{a} \sqrt{1+\left(\dv{y}{x}\right)^2} \dd{x}.$$

[glossy valve]

Civil Service Pigeon

[static verge]

mb

[static verge]

ohh

i forgot that rule lol thank you

[robust slate]

[void nova]

Rather than a rule, it's simply the formula for the arc length 😉

[static verge]

Lol

.close

[full forum]

Channel closed

Closed by @static verge

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[sturdy oriole]

Hi there, can anyone help?)

[full forum]

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

@sturdy oriole Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wanton mortar]

I have a question about two postulates in geometry, known as the Parallel Postualte and Perpendicular Postulate.
Why, as said in the Parallel postulate is there exactly one line through any point not on the given line, which creates two parallel lines? Is that line always parallel? Why can't it not be parallel? Why not just a point even? I thought that two points determine a line.
Also, as said in the Perpendicular postulate, why is there exactly one line through any point not on a line, thus creating perpendicular lines? Is the line associated with the point not on the given line always perpendicular? If so, why can't it not be perpendicular?

[umbral dome]

there are lots and lots of lines through a point which is not on the original line. but only one of those lines is parallel to the original, and only one is perpendicular to the original. all the parallel and perpendicular postulates say is that those particular parallel and perpendicular lines exist

it doesn't say that you can't possibly draw any other line that isn't parallel or perpendicular

[full forum]

@wanton mortar Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[cedar flint]

help please

[cedar flint]

stars and bars question

[gritty rose]

<@&268886789983436800> spam

[rare dock]

any ideas?

[full forum]

@cedar flint Has your question been resolved?

[cedar flint]

complementary counting?

[rare dock]

what would that be like?

well just fyi i do not think that is a good idea

[cedar flint]

i think make cases for where x_3+x_4=6,12, or 18 cause that's when x1,x2 are able to be even

[rare dock]

good idea

i might like to reframe the question as the number of nonnegative integer solutions to $$2(x_1 + x_2) + 3(x_3 + x_4) = 20$$

[glossy valve]

generating function shill

[rare dock]

then you can count

1. how many solutions (x_3,x_4) there are to x_3 + x_4 = 0, then how many solutions (x_1,x_2) there are to 2(x_1 + x_2) + 0 = 20, equivalently x_2 + x_2 = 10 (and multiply these values together)
2. how many solutions (x_3,x_4) there are to x_3 + x_4 = 2, then how many solutions (x_1,x_2) there are to 2(x_1 + x_2) + 6 = 20
   and so on

there will only be 4 of these cases so it won't be too bad

,w 1/(1-x^2)^2 * 1/(1-x^3)^2 series expansion

,w 1/(1-x^2)^2 * 1/(1-x^3)^2 series expansion at x = 0. give many terms

[glossy valve]

Results provided by WolframAlpha

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

Requested by slayyla

[rare dock]

fuck you

,w 1/(1-x^2)^2 * 1/(1-x^3)^2 series expansion at x = 0

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar flint]

.reopen

[full forum]

✅ Original question: #help-28 message

[cedar flint]

sorry i had to do something

[rare dock]

tis ok

[cedar flint]

i think i can try to solve it from here

[rare dock]

let me know what you get

[cedar flint]

74?

[rare dock]

as per the generating function that is correct

the generating function does not lie

[cedar flint]

oh ok thanks for helping

.close

[full forum]

Channel closed

Closed by @cedar flint

Use .reopen if this was a mistake.

[gritty rose]

Amazing layla

[rare dock]

thank you

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[autumn token]

how did they do this

[whole lily]

$$\csc\left(x\right)=\frac{1}{\sin\left(x\right)}$$
$$\sec\left(x\right)=\frac{1}{\cos\left(x\right)}$$

[glossy valve]

Roy

[autumn token]

oh bruh thats literaly it

thx

.close

[full forum]

Channel closed

Closed by @autumn token

Use .reopen if this was a mistake.

[whole lily]

You know google is always a good first place to ask for these things, if you don't know about the reciprocal trig functions

[autumn token]

no i do, i thought they did like (costheta + isintheta) /sinthetacostheta and then canccelled it

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[elder hinge]

hi can someone explain how 3n+7 is simplified to n/2*6?

[elder hinge]

just no overcomplications please

[fast peak]

the 7 is still there

just in the next factor

and 3n=6n/2

[elder hinge]

ok thank you

.close

.close

[full forum]

Channel closed

Closed by @elder hinge

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[pliant fractal]

help

[pliant fractal]

theres no x arpproaching a value what do i do?

[minor crater]

huh?

is that the full question

!xy

[full forum]

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

[minor crater]

yeah it makes no sense without the values there

[pliant fractal]

yes