help-28

[full forum]

Channel closed

Closed by @spice grail

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.

[full birch]

how can I depict a curve/bend in a space? what's the key, dragon scroll to knowing about 3 dimensional weirds (like curved spaces).
where should I begin my intuition after imagining a 3 dimensional graph in my head

[tame cradle]

look if you think of it

any 3d curve or bend is a surface so like you can maybe try to think of as a dependent coordinate's relation with indepenedent coordiantes like z=f(x,y)

for eg z^2=x^2+y^2

,w plot z^2=x^2+y^2

[glossy valve]

Results provided by WolframAlpha

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

Requested by oppailol.

[full birch]

but isn't this just regular 3 dimensional objects?

[tame cradle]

could you like clarify more what you want to delve in

[full birch]

what does it mean for the space itself to be bended? how do you depict the bend if the bend bends the actual graph instead of an object

[full birch]

yeah one sec

[tame cradle]

how i understand now you are referring to how space bends due to gravitational effects and you are interested in that right?

like how to imagine curves and bends in 3d space

[full birch]

if you see the image, you can see that it's a typical 3 dimensional graph

[tame cradle]

yes

[full birch]

imaginary lines but yes the usual space

[full birch]

but

[tame cradle]

yes

[full birch]

what does it mean if the actual lines there (that are parallel to each other and evenly spaced)
sort of bend/curve

not an object inside it

[tame cradle]

it means that the space itself has bent like the actual 3d graph in which we map objects

you could say that the space takes a geometry in that case

look the space itself takes a geometry

[tame cradle]

dependent on the distance and strength of the gravitational field or effect

[full birch]

hmmm but it really doesn't come to intuition

[tame cradle]

look consider 3d space mapped on a 2d surface as a blanket

[full birch]

u can see an example of a bend here (this one's really neat and evenly spaced but)

[tame cradle]

lets say if you drop a ball on it

the blanket bends due to the weight

[full birch]

hmmm

[tame cradle]

i am like trying to give a intution consider spacetime as a fabric or blanket

and say earth is a ball

due to gravitational effects it bends the space around it

look we consider cause we observe the effects okay

like due to black holes time dilation or shifting but i know its hard to imagine

[full birch]

a few major things don't make sense here, if I just imagine empty space vacuum and 3 dimensional graph, and a particle going in it, I really don't understand how 3 dimensional space can actually be bent or curved; like what happens to the empty space that's generated/deleted when the shift from natural 3d graph to the bent area happens

[full birch]

And, how would you even measure what happens to the particle as it touches/goes to/through the space.
I don't think I have any set intuition to understand how regular 3 dimensional objects behave in curved spaces inside the same 3d world

like isn't it impossible to think that? does the particle expand and occupy all the curved area or does it

[tame cradle]

there is no empty space it just the fabric or space stretches accordingly lets say a black hole is moving while the space around it has a specific geometry as the black hole moves to another position the space restores it static or normal geometry basically like the fabric is streched no extra space is created

[full birch]

how would you even know or equate something

[tame cradle]

its an analogy

[tame cradle]

look i feel the geometry of spacetime has relation with einstein equations and we derive using that

[full birch]

oh wait that's true

[tame cradle]

i dont have exact knowledge

[full birch]

3 dimensional space comes back hmm

[tame cradle]

yes

there is no evident extra space

its an analogy

[full birch]

wait but

[tame cradle]

it is for understanding okay its not like i pushed in blanket so extra space is created space takes a geometry

look this space time curvature fits well with the effects we observe

look one more thing understand like this take a black hole for example how does a 2d looking hole has a horizon and a singularity due to the shear mass and gravity the space time breaks its pushed to infinity through the horizon to singularity

look i may not be 100 percent correct in the above context but you can understand gravity gives geometry to space time around it just that

[full birch]

hmmmm

[limpid quail]

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

watch the last part

[tame cradle]

good

cya

[full birch]

alr thanks

[full forum]

@full birch 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.

[torn jolt]

Great channel. Vsauce also also has a decent vid to help visualize: https://youtube.com/clip/Ugkx4NnQT43f9pquIiPNztPP-Ai3u_IqTCO9?si=zgsw_ELb0W5F5TSF

[full forum]

@torn jolt Has your question been resolved?

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.

[granite girder]

Hallloo

[red scaffold]

do you have a question?

[granite girder]

I did

But i now solved it

So im good

[red scaffold]

you can close the channel in that case :3

hope you do good on your assignment, good luck!!

[gritty rose]

.close

[full forum]

Channel closed

Closed by @gritty rose

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.

[jaunty iris]

200000 s / 86400 s

why cant we get an useful answer to this question when thinking of division ONLY as

"how many numerator-units per 1 denominator-unit"
since it will give us the answer :
2.3148 numerator-seconds per 1 denominator-second.
which seems useless here

so again If we ONLY allow ourselves to think of division as “how many numerator-units per 1 denominator-unit,” can we figure out how many days are in 200,000 s ?

[rough tundra]

if I recall didn't riemann already help you with this question?

[fickle adder]

im not sure what that restriction implies.

[hot kraken]

The way I see it, I don't think so.

[fickle adder]

if Alice lives in a world where 2.3148 seconds pass for every second in Bobs world (where seconds are 1:1) then after a day passes in Bobs world, 2.3148 days pass in Alices.

[jaunty iris]

I dont think so, at least I dont remember

[hot kraken]

If we follow your self-imposed restriction, wouldn't this lead to a unitless ratio?

[rough tundra]

my bad, it wasn't riemann

[jaunty iris]

we got mixed up in dimensional analysis and other stuff that was not my question, so I thought of a better way to ask the same question that was clearer

[rough tundra]

but in any case it isn't 200000s / 86400s, it's 200000s / (86400s/d), right?

[fickle adder]

i think the question is flawed because it asks about converting between two units but also assumes that you cannot have a conversion ratio between these two units

[jaunty iris]

okay sure lets do this

what does this tell us 20a / 4a

[fickle adder]

that in order to go from 4a to 20a you must multiply by 5

[rough tundra]

5, but it's dimensionless, assuming a is some unit

[jaunty iris]

okay can we figure out how many sets of 4a are in 20a by ONLY thinking of division as
"how many numerator-units per 1 denominator-unit"

[fickle adder]

yes, 5

you said seconds to days, thats not the same question

[jaunty iris]

tell me how you figured that out by using STRICTLY this definition of division
"how many numerator-units per 1 denominator-unit"

[fickle adder]

thats like asking "how many sets of 4a are in b" using only 20a/4a

[rough tundra]

then I suppose 5a per a? for each a in 4a, we have 5a which would give 20a and keep the proportion

[fickle adder]

theres nothing restrictive about this in this context at all

its just normal division

[jaunty iris]

you are dancing around the question for some reason

can you just tell me what you did in you head when doing 20a / 4a while also only using the "how many numerator-units per 1 denominator-unit" definition of division

[fickle adder]

are we assuming mathematics doesnt exist in this hypothetical universe ??

4a + 4a + 4a + 4a + 4a = 20a

20/1 = 20, so you can say 20 is " 20 per 1 " in some abstract unitless sense

[jaunty iris]

that is repeated addition/subtraction
or "how many times the denominator goes into the numerator"
the whole point of this question is to strictly avoid that definition of division

[fickle adder]

so we dont care about the units

[jaunty iris]

and to figure out the answer to the question without using it

[jaunty iris]

this is exactly what I was thinking

[rough tundra]

I still think you're question is flawed, go back to 200000s / (86400s/d), the answer is ~2.3148days... it's a single unit, the way I see it it's nonsensical to ask about "2.31days per..." what??

[fickle adder]

what does "how many times does something go into something else" even mean if you dont have subtraction or addition

it is literally how many times can you add it to itself until you get the thing

[jaunty iris]

lets not go back to seconds, since its constantly moving the topic to something else
20a / 4a is just an better thing to focus on

[fickle adder]

but its a different question so i wonder why you ask the first one to begin with

it is fundamentally not the same question, because one converts between units and the other doesnt

the only reason the first "doesnt make sense" is because you talk about days without ever establishing what the ratio between days and seconds is

[jaunty iris]

sure, thats why 20a / 4a is better

[fickle adder]

so your question is "why do we say division is how many times the denominator goes into the numerator if that is (allegedly) not enough to provide an answer"

[jaunty iris]

no my question that there's 2 correct ways to think of division
"how many times does something go into something else" / repeated addition / repeated subtraction
and
"how many numerator-units per 1 denominator-unit"

and each definition should be able to give us the answer to the same question

so how can we figure out the answer to
how many sets of 4a are in 20a by ONLY thinking of division as "how many numerator-units per 1 denominator-unit"

[fickle adder]

but those are the same sentence.. this feels like a linguistics question. try rigorously defining what you mean by "goes into" without referring to addition or subtraction

[jaunty iris]

it would be pretty hard to be more precise than this, I guess I can try to draw something like this

but it would prob not help if the original question didnt make sense

[jaunty iris]

but this to me seems much clearer

pretend like it says 5 instead of 4

[fickle adder]

that is repeated addition/subtraction

you are only able to tell what cut of that bar to make because you know the answer

replace 20 with y and 4 with x

now draw a bar that is Y wide and one that is X wide

in order to figure out the ratio you need to stack X bars together until they meet or exceed the Y bar

that is repeated addition

[jaunty iris]

you are using the same methods, but you are thinking of the answers differently between the two methods

[fickle adder]

so you want to arrive at the same answer using the same methods... thats doing the same thing. it doesnt matter how you look at the answer, you asked about the process, how we can go from 20/4 or Y/X to 5 or some Z. the intermediate steps, the "methods", are the subject here.

[jaunty iris]

do you see that you kinda get 2 different answers

[fickle adder]

i honestly dont know what the red notes are meant to mean.

for the record, "5 per 1s" is wrong unless its 20 s / 4 s^2

[jaunty iris]

does this make more sense on how we think of "per" definition

so this tells us that theres 5s "in" or "for" every 1s

[fickle adder]

do you not see what you are doing here ?

are you saying this isnt repeated addition/subtraction?

[jaunty iris]

I do, but im telling you that we can think of it in a different way, and that way would make more sense depending on the scenario

this way does not really make sense, since it tells us that theres 5s "in" or "for" every 1s
which is not really useful when we want to figure out how many times 4s fit into 20s

but when we think of it this way:

it makes more sense, even tho its the EXACT same thing

its just kinda annoying that I have to switch between these 2 sometimes for an answer to make sense

[jaunty iris]

if I were to ask you how much a there are per a

you would be forced to think of it this way now

so you are constantly flipping between the two

[fickle adder]

i think i see what you are trying to say but i still dont agree.

if im right, i think the best way to phrase your thought in the future though, is that you can represent it as either 5s / 1s or just 5.

i think the 5s / 1s interpretation makes perfect sense. i gave an example earlier.

5s / 1s = 5 because division by 1 and the seconds in both the numerator and denominator cancel. 5 is a scalar, so that if A/B = 5, then B goes into A "5 times", while 5s / 1s is a relationship that says "for every 1s that passes in X frame, 5s passes in Y frame"

[jaunty iris]

yeah but

1. if you are using more complicated units it can def get confusing or not make sense
2. I think that you are still 100% forced to flip between these 2 definitions of division to get an answer, depending on the question

[fickle adder]

i think the only application i see for this is pedagogy to like, school children though. i dont think anyone working with "complicated units" needs to clarify the interpretation of their answer like this.

[jaunty iris]

if you want to visualize what you are doing you would have to flip between them tho

200000s / 86400s

you can visualize chunk of 86400s going into 200000s

but if you tried to use "per" visualization it will not make sense, so you would have to flip back to "going in" definition

you would get how many seconds are there per every second like here

useless info

[fickle adder]

the per visualization does make sense

[fickle adder]

.

its just seconds in one frame per second in another

[jaunty iris]

that is a very indirect answer, idk if with that information we can even get to the answer that 86400s goes into 200000s 2.3148 times

[fickle adder]

we dont get to the answer with the interpretation we've literally been over that

its the answer itself

[jaunty iris]

I dont get what that means

[fickle adder]

we already have the 2.3148. what do you need to "get"

the computational process of the answer does not change, interpretation is irrelevant

we're just talking about how you look at the answer

[jaunty iris]

we "got" the information that in every 1s we get 2.3148 s (when using the "per" way of thinking)

how does that help us find the answer to how many times a chunk of 86400s goes into 200000s

I kinda can visualize it now tbf after drawing these 2 pictures, but its still not 100% there

we can say that every unit of the denominator is 2.3148 s smaller

and stuff like that

but if you know any other "better" way to visualize it let me know

[jaunty iris]

this is prob the best way to get the the answer to both questions

"how many numerator seconds are there per denominator seconds "
and
"how many times does a chunk of denominator seconds fit into the numerator seconds"

[jaunty iris]

just by picturing this one way of thinking if you head

[fickle adder]

the answer is implied. its 2.3148. because the units are the same

[jaunty iris]

without having to flip flop between this one too sometimes

[jaunty iris]

ye I think this is it I will prob think ab this a little bit more but I can now answer both questions by just visualizing one single method and not having to flip flop between the other

which will make stuff like this a lot simpler / faster

I can type lol

thanks for the help 👍
this makes it a lot clearer

[full forum]

@jaunty iris Has your question been resolved?

Channel closed

Closed by @jaunty iris

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.

[spring vigil]

i wrote

(T ^ F) V NOT (F V T)

would that be wrong?

[somber pike]

is that not the same as the answer given in the screenshot?

or is that your answer

[spring vigil]

this one is

[spring vigil]

this one is the correct

ik its an or (T V F) but im confused because of the NOT outside of

not (T V F)

i can switch them fine?

[sterile surge]

hi does anyone know how to solve this

[somber pike]

open a new help channel

[full forum]

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).

[sterile surge]

OH SORRY

[somber pike]

wym by switching

[spring vigil]

the t or f

[somber pike]

oh yeah

[spring vigil]

even if theres the not

[somber pike]

its the same

yep

[spring vigil]

also

its equivalent to f

how i did my soln is

-F V T ^ F
_ F VF eqiuvalent to F

[somber pike]

You're asking if your solution is also equivalent to false?

[spring vigil]

yeaaa

[somber pike]

You can easily check yourself

What does True and False give?

[spring vigil]

false

[somber pike]

What does not(true or false) give?

[spring vigil]

yea thats what i did

[somber pike]

Is that statement true or false?

[spring vigil]

false or false is false

[somber pike]

Yep

[spring vigil]

yuhhh

🙏

[somber pike]

Any other questions?

[spring vigil]

yes

im about to watch a vid on boolean algebra

but is this something we could work on together>

?

[somber pike]

This question?

I have to go in a bit so can't help with much

But i'm sure there's other people who can help you

[spring vigil]

ok np thanks alot

[somber pike]

you're welcome

[spring vigil]

ill just watch a vid

[somber pike]

alright if you have any questions just ask here and i'm sure you'll get help

[spring vigil]

.close

[full forum]

Channel closed

Closed by @spring vigil

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.

[torn jolt]

WAIT

.close

[full forum]

Channel closed

Closed by @lime pasture

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.

[proper sun]

Alright, so i changed the order of integration and you get 2 different double integrals, the only issue is one is too difficult to solve anyways. The guided solution shows that we just used 0 to 3 for dy and 0 to y^2 for dx which is confusing since they intersect no? If you tell GPT to do the former it gets the same answer as when you generalise for 0 to 3.

[proper sun]

Im wondering why do they yeild the same answer if we are integrating for different areas then? heres a desmos graph for reference

[brisk obsidian]

You're not integrating different areas. The boundaries on the integral define the Region that is being integrated.

[proper sun]

Right, so why does the integral that includes the "extra chunk" is equal to the one that doesn't include it

[brisk obsidian]

What "extra chunk" do you mean?

[proper sun]

Sending image

Internet is bad sry

[brisk obsidian]

That's not in the defined Region.

Although, you could technically use that in a solution.

[proper sun]

Yes it's not, but even though if you integrate everythng including the extra chunk it gives the same solution why

[brisk obsidian]

It won't. Where did you see that?

[proper sun]

Well initially I couldn't compute the tough integral I sent in my image so I asked chat gpt to do it for me and used that answer, when I submitted I checked the guided solution it had used the integral from 0 to 3 with respect to y yet still got the same answer

[brisk obsidian]

This is your bounded region.

[proper sun]

Yes

[brisk obsidian]

This is your work?

[proper sun]

Yes

[brisk obsidian]

And what did AI show you to do?

[proper sun]

That aswell, it's just the one on the right is really hard to do

Try doing it
3 / (12 + y^3)

Actually don't it will probably take too much time and not that they will expect us to integrate that

[brisk obsidian]

Perhaps break it down using partial fractions.

[proper sun]

not sure i understand quite much

[brisk obsidian]

Do you under the point it is trying to make?

[proper sun]

Nah I don't really understand what it's saying

[brisk obsidian]

What they did here looks incorrect.

[full forum]

@proper sun Has your question been resolved?

[brisk obsidian]

The integration I showed is incorrect so that entire explanation is invalid.

[proper sun]

I mean its saying that yes it did a mistake there but that the overall point is still correct

If instead of the 3's you make it into 5's you get different answers according to gpt, which I've tested and seems to be correct? Eh it's really weird I doubt I'll see it in the exam. I'll investigate it further when I'm done with exams

Thanks tho @brisk obsidian

.close

[full forum]

Channel closed

Closed by @proper sun

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.

[tribal dome]

I need help with my project

[gritty rose]

Yikes 25 pages

[tribal dome]

Yeah ik it’s a lot

Just thought I’d give it a shot

But I’d appreciate help if your willing to offer

[gritty rose]

How much of the final project is your grade

[tribal dome]

20%

Why?

Ballright

[empty blaze]

Where exactly are you stuck?

[tribal dome]

I just need like a start to the project to get me going

[empty blaze]

I didn't really get what the project is about.

[tribal dome]

Welcome to my life

Well verison a is the one I’m on

If that helps there is version b and there’s version a

[gritty rose]

Yea pictures of screen ain't easy to read

[empty blaze]

k start with slide 1

[gritty rose]

You should summarize in your own words what you need help with

[empty blaze]

you're supposed to make a frequency distribution right?

[tribal dome]

Yes

[empty blaze]

kk start with that

do you know how to make it?

[tribal dome]

Kinda doesn’t excel have a feature?

[empty blaze]

it said do your own work and its supposed to be original

so you can use excel but try to keep all calculations by hand or max by a calculator

[tribal dome]

.close

[full forum]

Channel closed

Closed by @tribal dome

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.

[sacred yarrow]

So for the first one, I can't come up with an approach other than brute forcing it

is there any approach to do this?

[gritty rose]

Find one solution then permutation

[sacred yarrow]

1 1 1 9

4!/3! = 4

but how would that help?

[languid junco]

ever heard of stars and bars?

[gritty rose]

Oh they don't have to be distinct

[sacred yarrow]

no, lemme google it rq

oh wow, that's much easier lmao

I assume the answer should be
11C3, right?

and for B I just need to find the value from 1 to 11

tysm

.close

[full forum]

Channel closed

Closed by @sacred yarrow

Use .reopen if this was a mistake.

[gritty rose]

Nah https://brilliant.org/wiki/integer-equations-star-and-bars/

[sacred yarrow]

.reopen

[full forum]

✅ Original question: #help-28 message

[sacred yarrow]

bruh, hell yeah 15 spaces to pick

.close

[full forum]

Channel closed

Closed by @sacred yarrow

Use .reopen if this was a mistake.

[sacred yarrow]

ty for that

[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.

[vestal kindle]

is my step correct to find the derivative of this equation?

[dry arch]

the second line is y, not y'

[vestal kindle]

oh yea, i 'll get rid of that

[dry arch]

you haven't done the derivative yet, right?

you're rewriting y

[vestal kindle]

yes

i havent

[dry arch]

rewriting ln(e^x + e^-x) as ln(e^x) + ln(e^-x) is an error

[vestal kindle]

oh unles they are multiply with each other then i add them right

[dry arch]

yeah ln(a*b) is ln(a) + ln(b)

[vestal kindle]

is that too much parenthesis lol

i forgot the derivative sign on the left again

ok i added

how do i find the derivative of ln(e^x - e^-x ) ..

[dry arch]

you should use the chain rule

it tells you that the derivative of ln(e^x - e^-x) is
1/(e^x - e^-x) times the derivative of e^x - e^-x

oh those should be +'s instead of -'s

[vestal kindle]

ok this is correct

[dry arch]

looks good other than these missing parentheses

[vestal kindle]

oh ok i'll add them

[dry arch]

btw these are hyperbolic trig functions
you just showed that d/dx 3 ln cosh x = 3 tanh x

[vestal kindle]

hmm what is that

is there trig in this function lol, or maybe wrong channel 😄

[dry arch]

you're in the right channel don't worry

[vestal kindle]

sorry, i dont understund the previous one the trig one ^^

[dry arch]

don't worry about it

you finished the problem already

[vestal kindle]

oh ok ty for helping

.close

[full forum]

Channel closed

Closed by @vestal kindle

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.

[foggy vapor]

if a function $f\in L^2(\vb R)$ has compact support, why is it impossible for its Fourier transform $f$ to vanish on \emph{any} interval of non-zero length?

[maiden vapor]

Recall a basic theorem from Complex Analysis:
If an entire function vanishes on any open interval (or any open set), then it must vanish everywhere.

A compactly supported function has a Fourier transform that is infinitely harmonic, i.e., analytic and highly smooth. Analytic functions have strong rigidity: if they are zero anywhere on a chunk of the real line, they are zero everywhere indeed.

[foggy vapor]

[maiden vapor]

Compact support ==> \hat f is entire

[foggy vapor]

ok i gotchu gang

wagwan

[maiden vapor]

wagwan mandem

[foggy vapor]

skrrt skrrt

.close

[full forum]

Channel closed

Closed by @foggy vapor

Use .reopen if this was a mistake.

[maiden vapor]

💀

[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.

[left moon]

Based on the series, tell whether it is geometric or arithmetic
Find d or r
Find sum of first 15 terms

[left moon]

Did I do this wrong

[warped frost]

this step is fishy

[left moon]

Oh

OH

oops

Lemme fix it

[keen vector]

mfw 15/2 = 30

[left moon]

Okay the final answer is 285/4

[warped frost]

correct

[left moon]

Lol I multiplied by 2 for some reason idk I saw my teacher multiply like that on a similar problem

[warped frost]

depends on how the fractions are

[left moon]

Oh

How so

[warped frost]

$\frac{\left (\frac{a}{b} \right)}{c}$ is not the same as $\frac{a}{\left (\frac{b}{c} \right)}$

[glossy valve]

Hanako(x, y); ∂(fox)/∂x

[warped frost]

the first one results in $\frac{a}{bc}$, but the second results in $\frac{ac}{b}$

[glossy valve]

Hanako(x, y); ∂(fox)/∂x

[warped frost]

maybe you faced one of these instead

[left moon]

It was like this

[warped frost]

oh

$x \left( \frac{y}{-1} \right) = x \left( -\frac{y}{1} \right) = x (-1) (y) = -x(y) = -xy$

[glossy valve]

Hanako(x, y); ∂(fox)/∂x

[warped frost]

it's kinda multiplying? but also the denominator is 1 anyway. I prefer to think of it like this though

if the denominator is not -1, you can still do roughly the same steps to get the negative sign out: \
$x \left( \frac{y}{-z} \right) = x \left( -\frac{y}{z} \right) = x (-1) \left( \frac{y}{z} \right) = -x \left( \frac{y}{z} \right)$

[glossy valve]

Hanako(x, y); ∂(fox)/∂x

[warped frost]

but that's all that's happening here

[left moon]

Ohhh

Okay that makes sense

Thank you so much

[warped frost]

nps, glad to help

[left moon]

.close

[full forum]

Channel closed

Closed by @left moon

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.

[left moon]

Is this work correct?

Instructions:
Based on the summation notation, tell whether it is geometric or arithmetic
Find d or r
Find sum of first 15 terms

[sturdy valve]

huh

but in ur summation notation u have put from n=0 to n=infinity?

[left moon]

Yeah that’s how the problem was given in the textbook

[full forum]

@left moon Has your question been resolved?

[full forum]

@left moon Has your question been resolved?

[sour shore]

yes

[left moon]

thank you

[full forum]

Channel closed

Closed by @left moon

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.

[torpid perch]

how to solve sin = -11/10

[slate violet]

that's not possible for real values of theta

$\sin \theta \in [-1, 1]$

[glossy valve]

south

[torpid perch]

ok perfect

.solved

[full forum]

Channel closed

Closed by @torpid perch

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.

[mental pewter]

i want to dive more into these questions:
in the first limit, why we have to multiply (ax+b) with (x-2)
in the second limit, why we have to conjugate (like a²-b²)

[slate violet]

recall if the limit to infinity is not one of 0, -infinity, or +infinity, then the degree of the numerator and the denominator is the same

so actually there's another way to do the first limit

$\frac{x^2 + x}{x - 2} \approx \frac{x^2}{x} \to \infty$, so $a = -1$ (you want the $x$ term to cancel out)

[glossy valve]

south

[twin wolf]

south w the clutch

[mental pewter]

ohhhhhhh

[slate violet]

again for the second limit, there is another way

$\lim \sqrt{4x^2 - 3x + 1} = \lim (ax + b)$ and now square both sides

[glossy valve]

south

[mental pewter]

we can square limit? new to me

[slate violet]

well, square the functions inside the limit

then you want the coefficients of x^2 and x on both sides to match

||so that means you should complete the square of the quadratic||

[mental pewter]

🤯🤯🤯

[slate violet]

the idea is that $\sqrt{(ax + b)^2 + c} - (ax + b) = (ax + b) \left(\sqrt{1 + \frac{c}{(ax + b)^2}} - 1 \right) \to 0$

[glossy valve]

south

[slate violet]

you can use the approximation $\sqrt{1 + u} \approx 1 + \frac{u}{2}$ for $u \approx 0$

[glossy valve]

south

[mental pewter]

really, why we have this

[neon silo]

You can see why by squaring both sides

[twin wolf]

wow physicist

[mental pewter]

1+u=1+u²/4+u

hmmm ohhhhhhh

i see it now

appreciate you guys a lot

.close

[full forum]

Channel closed

Closed by @mental pewter

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.

[silent dove]

Given segments of length 9 and 12, how do I construct a segment of length 20, using both lines

[hot kraken]

Can you elaborate on this more? Just so I can be sure we're on the same page

[silent dove]

I have a compass and a straight edge

No ruler nor protractor

[burnt grotto]

Eh?

[hot kraken]

Hold on. I'm confused on what you're trying to ask for help on.

Is it how to draw them?

[burnt grotto]

Practical construction kinda thing

[silent dove]

No. How do I get to length 20 given segments of length 9 and 12. I'm supposed to use both, and not just divide them and multiply them

[burnt grotto]

how do you divide and multiply lines 💀

[silent dove]

I can't just split the 9 into 9 sections and copy it 20 times

[burnt grotto]

I was thinking of angling up the 12 cm line

but that clearly doesn’t make sense

[hot kraken]

I'm confused here

[silent dove]

I can still bisect the lines tho. I probably have to make a shape or something. Idk what's going on 😭

[hot kraken]

Perhaps euclidian construction?

[burnt grotto]

Smth like that

[silent dove]

Lately we've been making triangles with midlines for proportionality to get the lines but idk how to do that with these numbers

What's euclidean construction?

[burnt grotto]

mid point theorem?

Thales theorem?

[cloud creek]

Male it a triangle with 90 degrees

[burnt grotto]

I don’t get what the question is

[burnt grotto]

no ruler up for use

[silent dove]

What do I do with that?

[burnt grotto]

you can raise an angle

[silent dove]

I can still use a compass and a straight edge to make a right angle

[unreal wren]

You get a line with length 15

[burnt grotto]

they don’t have it

[silent dove]

How do you know???

[cloud creek]

You get a side of 15 and divide that by 3

[unreal wren]

Pythagoras (sorry typoed)

[burnt grotto]

that doesn’t help

[cloud creek]

Pythogoream theorem

[silent dove]

Ok

[cloud creek]

Yes it does

I think

[burnt grotto]

they only have a straight edge not a ruler

[silent dove]

Is there any way to get like exactly 20?

A straight edge lets me draw straight lines

[burnt grotto]

I have no clue ngl

[bright bronze]

why not? thats absolutely possible with a compass and a straight edge

[silent dove]

Because my teacher is annoying and said no

He wants us to find some creative solution that gets us to like exactly 20 or something idek. Like, he doesn't specify but he'll take points off

I hate my math teacher

[burnt grotto]

he seem unreasonable Al

[silent dove]

I guess I'll just do the right triangle and hope he accepts it 😭

[winter rune]

||i think you are supposed to use 9 and 12 to easily multpily by 4/3 and 15 = 12+12-9|| idk how to motivate this

[silent dove]

Wait that's genius

The 15 to 20 gives me a 3:4 ratio

And so does 9 to 12

[burnt grotto]

that would be the best method if you also had a protractor to your disposal

But you don’t

[silent dove]

I can still use a compass to draw the perpendicular.

[burnt grotto]

yeahh

[twilit leaf]

ABC right angle at B with AB=9 and BC=12 (AC=15) with angle bisector at C splits AB into 5 and 4

[burnt grotto]

but you don’t know how high it must be raised to

since you don’t have a ruler

[twilit leaf]

then double the 5 and then double the 10

[unreal wren]

Use the compass?

[silent dove]

Ok tysm I think I know how to do this now! Imma close this 😁

.close

[full forum]

Channel closed

Closed by @silent dove

Use .reopen if this was a mistake.

[slate violet]

genius

[twilit leaf]

oh you dont even have to do this, just copy the segment of 5 onto the line with 15

[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.

[manic bramble]

Hello. Can I have some help rearranging the left (yellow) side into the right (blue) side?

[leaden ermine]

I would just expand the terms and make use of sin^2+cos^2=1 as well

[pseudo cape]

Most of it is just the terms becoming zero because of the orthogonalities

I don't think there is any sin^2 + cos^2 = 1 involved

[leaden ermine]

oh ya

[full forum]

@manic bramble Has your question been resolved?

[manic bramble]

.close

[full forum]

Channel closed

Closed by @manic bramble

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.

[thorny cloak]

can someone plz explain how on earth they got that in green for the norm squared of the time derivative of r(t)

i got this so far when computing it

[full forum]

@thorny cloak Has your question been resolved?

[full forum]

@thorny cloak Has your question been resolved?

[full forum]

@thorny cloak 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.

[cold sail]

i have no idea how they determined that the infinite sum of the measures of B'_k is < eps

[full forum]

@cold sail Has your question been resolved?

[full forum]

@cold sail Has your question been resolved?

[full forum]

@cold sail Has your question been resolved?

[full forum]

@cold sail Has your question been resolved?

[silk vine]

Are you asking why the series converges?

[cold sail]

yes

im not sure where it came from

[full forum]

@cold sail 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]

ki dont get this question, like what is Q1 and Q2

[slate violet]

$Q_1 (x)$ and $Q_2 (x)$ are polynomials

[glossy valve]

south

[slate violet]

but it doesn't matter what exactly they are

your aim is to sub some values of x in to get the remainders (R and 2R)

[autumn token]

Ok yea

and the number we sub is -2?

[slate violet]

yes

oh yeah both of them have (x + 2)

[full forum]

@autumn token Has your question been resolved?

[autumn token]

wha tdo i do

from there

[slate violet]

if you sub x = -2 into both equations

you will get two simultaneous equations involving a, R

[autumn token]

i subbed it in

but wht is it = to

equal to

[autumn token]

ok so i subbe nto first and got -45 -2a

is -45 the R value

[slate violet]

yep, that's the correct left-hand side

now how about the right-hand side, $(-2 + 2) Q_1 (-2) + R$?

[autumn token]

it would js be R?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[autumn token]

.reopen

[full forum]

✅ Original question: #help-28 message

[autumn token]

i still dont get what Q1 is this notation odesnt look correct at all

[knotty grail]

you could say they are quotient polynomials

[glossy valve]

south

[slate violet]

woops, corrected

I didn't sub in x = -2 into Q1(x) before, yep

but anyways you should get the idea

[slate violet]

the idea is that polynomial long division / synthetic division will let us find the quotient

but the remainder theorem allows us to skip finding the quotient

it's like if I want to divide 1234567892 by 10

I don't need to know the quotient is 123456789

I just look at the last digit which is 2, so the remainder of the division is 2

[autumn token]

how do you move forward with "a" thouhg

ok so rn im stuck at

so i have first equation is -45 -2a

second equation is 4a-50

i have no idea what to do now

[slate violet]

can you simplify this for me? @autumn token

[autumn token]

R?

[slate violet]

yep!

so your first equation is -45 - 2a = R

[autumn token]

ohh i think i kinda get it

so can i view Q1(x) like the same as f(x)

[slate violet]

whatever helps you, sure

[autumn token]

no i mean like would it be wrong to

[slate violet]

I actually don't know what you mean by this

[autumn token]

like yk how a normal funuction is f(x)

ok i tihnk its fine i kinda get it tysm

.close

[full forum]

Channel closed

Closed by @autumn token

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.

[brisk minnow]

Why do we need the dummy variables?

[brisk minnow]

I don’t get why textbooks have them written asw dummy variables

Like what’s the intuition behind it?

[keen vector]

do u understand the notation $\int_a^b f$

[glossy valve]

sheaf of markov chains

[brisk minnow]

Well yea f(b) - f(a)

[keen vector]

no

[brisk minnow]

I mean

F(b) - F(a)

Where F is defined to be that

[keen vector]

what

[keen vector]

do u understand this?

[brisk minnow]

Definite integral?

[keen vector]

what i wrote

💀

[keen vector]

yes it's a definite integral

[brisk minnow]

Yea? We’re integrating f from a to b

[keen vector]

alright

so f is a function with 1 input

f: R -> R

in definite integrals ur integrating the function

ur not integrating f(x), but rather just f

u follow?

[brisk minnow]

Not quite no 😭

wdym by

[brisk minnow]

^

[keen vector]

it takes 1 number as input

[brisk minnow]

yea so how does that come into definite integrals?

[keen vector]

like f(0) not f(0,1)

[brisk minnow]

oh I see alright

[keen vector]

ur integrating it

[brisk minnow]

Alright so regardless of whatever ever the limit, it takes 1 input ?

[keen vector]

what limit

for the definite integral?

[brisk minnow]

b or a

Yea

[keen vector]

yes

u define f first

then let a,b be numbers

$\int_a^b f = \int_a^b f(x) \dd{x}$

[glossy valve]

sheaf of markov chains

[keen vector]

the rhs is just new notation

[brisk minnow]

Oh that’s what a dummy variables does

?

[keen vector]

don't ask dumb questions

[brisk minnow]

💀

No I’m genuinely confused where ur try a go w this

[keen vector]

so here i could write the lhs as $\int_{x_0}^{x(t)} \frac{1}{\xi}$

[glossy valve]

sheaf of markov chains

[keen vector]

? im explaining the notation to u

[brisk minnow]

Alright

[keen vector]

1/xi is a function

does that answer ur question

u don't need dummy variables

[brisk minnow]

Hm wait lemme try digest this

[keen vector]

on the rhs u could say x is a dummy variable

[brisk minnow]

So what’s their use in having them?

Just for formality?

[keen vector]

no actually informality

to simplify notation basically

so u don't need to keep defining new functions

[brisk minnow]

So we could’ve just left it like this?

[keen vector]

yes

[brisk minnow]

Ah I see

[keen vector]

but in other cases it's not so simple

and dummy variables simplify the notation

[brisk minnow]

Oh alr

[keen vector]

like if u have a multivar func and ur only integrating wrt 1 variable

[brisk minnow]

Then its useful to have a variable involved

[keen vector]

bro needs that validation

[brisk minnow]

I’m not a bro

[keen vector]

mb

[brisk minnow]

Nah I’m joking

Love

.close

[full forum]

Channel closed

Closed by @brisk minnow

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.

[narrow mica]

This is very embarrassing but

[narrow mica]

I am not sure if I understand what mutually exclusive means

Idk how I got 90% on a level maths and somehow got away with not understanding it properly 😭

But yeah

[marsh vault]

Two statements are "mutually exclusive" if they can't both be true at the same time.

[narrow mica]

Wait is it

No that doesn’t feel right

At least for combinatorics

[marsh vault]

That is, if you know one is true, the other has to be false -- so one excludes the other, and vice versa.

Do you have a particular context in mind where that explanation won't fit?

[narrow mica]

Like you have to multiply two mutually exclusive combinations together

[marsh vault]

Huh, something must be garbled there.

[narrow mica]

I did a interview question today and it was the number of ways you can go from the top corner to bottom corner of a 7x5 grid

Assuming you can only go right and down

And considering you had to go through one other point

And basically I considered when you from the top corner to the one point and the number of combinations for that

And then from that one point to the bottom right point and the number of combinations for that

And I added them together and my friend said I can’t do that I multiply them because they are mutually exclusive

But again I’m not sure if I fully understand because

[narrow mica]

In this case does that mean we’re saying we can only get one point to the bottom right or the bottom right to the one point

Idk if that makes sense

[marsh vault]

Hmm, do you say you're counting "paths that start by going right" and "paths that start by going down" separately?

In that case I would understand your friend's objection as saying that "the first move goes right" and "the first move goes down" cannot be true about the same path.

[narrow mica]

That’s what I did kind of yeah

[narrow mica]

OHHH

So basically all of the path never crosses the other path

Kind of

Yeah ok

That makes sense

I understand now

[marsh vault]

So the "mutually exclusive" comes in when you have counted possibilities in two bins where each solution falls in one bin or the other, but never in both (that is, the two bins are mutually exclusive), then you should add the numbers rather than multiply them.

(By the way, the easier way to solve that original problem is to say that no matter which we you go, you'll be taking 10 steps in total, of which 6 go right and 4 go down -- and the path is completely determined once you've decided which 6 of the steps are "right". So there are (10 choose 6) ways to make those choices).

[restive geyser]

This line isn't even quite right - you multiply values (vague, btw) when events are independent, not mutually exclusive

[full forum]

@narrow mica Has your question been resolved?

[narrow mica]

Ohhhhhhh

Yeah that’s what I thought

So my friend made a mistake?

[restive geyser]

Possibly

Mutually exclusive events, with probabilities for instance, generally are added up

[marsh vault]

Oh, I didn't even notice it was the friend who had it backwards. 🙃 Sorry!

[restive geyser]

RTFQ, Tropo

[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.

[full forum]

Please don't occupy multiple help 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.

[gritty flax]

<@&268886789983436800>

Oh faster than ping

[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.

[frozen cipher]

I need help to verify if I'm right

[frozen cipher]

[(24x^4y^7)/2 = 2^-1(24x^4y^7)] = 12x^4y^7

If for example:

1/2^3
2•2•2=8
1/8=0.125

Then
2^-3=1/2^3
Because:
(1/2)•(1/2)•(1/2)=0.125

I can do another example:
1/5^2
5•5=25
1/25=0.04

5^-2=1/5^2
Because:
(1/5)•(1/5)=0.04

If I'm right pls tell me cuz I'm trying to manage to know why it work

[hoary ember]

are you asking if this is correct?

[frozen cipher]

Yeah and if 2^-3=
(1/2)•(1/2)•(1/2) is valid

[hoary ember]

yes to both of them

$a^{-m}=\frac{1}{a^m}$

[glossy valve]

ihave<skissue>

[hoary ember]

so here, $2^{-3}=\frac{1}{2^3}=\frac{1}{8}$

[glossy valve]

ihave<skissue>

[frozen cipher]

Ty idk if I was supposed to learn that myself at 15 but yeah i think it kinda logic

[hoary ember]

15 should be the age to learn this

[frozen cipher]

Alr thx but my teacher told me that I was supposed to learn it only in this way tho:
1/2^3=1/8=0.125

I think I proved him wrong

Finally

Well how we close I think I'm all good

[full forum]

@frozen cipher Has your question been resolved?

Channel closed

Closed by @frozen cipher

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.

[reef mural]

Can anyone elaborate the magic behind cos(42,99) =0,547

[reef mural]

Like is that the ratio between b/c?

Sides

[full forum]

@reef mural Has your question been resolved?

[reef mural]

Wow..

No one is bothered to help

Racist server

[gritty rose]

uh idk <@&268886789983436800>

[arctic wedge]

Please be patient, our helpers are just volunteers and you’re not entitled to help. You asked a very vague question that’s pretty hard to answer, there no magic, that’s just what cos is.

We take any accusations of discrimination seriously here, but there doesn’t seem to be any, so please don’t claim this without reason, even as a joke.

[rotund pebble]

cos is the the length of the adjacent side to the angle over the length of the hypotenuse so there's no magic

[full forum]

@reef mural Has your question been resolved?

[reef mural]

chill…

[reef mural]

Can you visualize it?

[remote cradle]

What are you asking?

Do you want to visualize cos function properly?

There is a method to do so
Draw a circle and a right angled triangle inside.

Take the angle from center and vary it

[reef mural]

Cos(50°) is?

[remote cradle]

Like this

[remote cradle]

You can find out the approx range

To find exact value, use calculator or log table

Is your doubt resolved?

[reef mural]

It doesn’t make sense

Fucking

It isn’t even half of circle

What does 1/2 indicate?

@remote cradle

[remote cradle]

It is half circle

Here watch this:

https://youtube.com/shorts/3yT1ndjaoVE?si=fgYYbCEKkuOk3Hzc

[reef mural]

That is trash explanation

I don’t understand

[remote cradle]

@reef mural Ok so what exactly do you want to know?

How to find values of cos?

Or how cos function works?

[reef mural]

No

Like

Yes

[remote cradle]

?

So the cosine is a function which takes in an angle as input and gives output in range of -1,1

[steel nest]

Maybe this would help https://www.mathsisfun.com/sine-cosine-tangent.html

you have to give us a picture of your triangle if you use a,b,c for the side lengths

[remote cradle]

The output is decided by first forming a right angled triangle with angle equal to input angle and then taking ratio of base and hypotanse

[reef mural]

Why

When do you use cotg?

[remote cradle]

Itz a function, it does what itz defined to do

[remote cradle]

What's that?

[restive geyser]

Cotangent

@reef mural fyi "tan" is generally more commonplace than "tg" in Anglophone areas

[reef mural]

My bad it’s ctg

[reef mural]

It’s not

[restive geyser]

https://math.stackexchange.com/questions/179881/best-way-to-denote-some-trigonometric-functions-tg-vs-tan-ctg-vs-cot#:~:text=2-,2,lot of people use tg.

I know how to cite my shit

[remote cradle]

OO ok

I write it as cot

[restive geyser]

"tg" is generally more common in Eastern Europe fyi

[remote cradle]

sin, cos, tan, cot, sec and cosec

[restive geyser]

Regarding your original question... I mean it's not rly "magical"

That's just from the definition (well, one of many) of the cosine

Namely, that, if you have a right-angled triangle with another angle of measure 42.99°, the adjacent side and the hypoteneuse form a ratio of about 0.547

... Not that that's actually right lol

Because you're in RADIANS why

[restive geyser]

Essentially you take this method of extending the trig functions beyond angles that you can draw, to allow for any real input

Then (and at a university level and higher you default this input to be in radians, essentially) you plug 42.99 in as the input

There's not much "magic" to elaborate besides this

[reef mural]

TanGes.

Not that hard

And when do you use ctg

It’s like… skipped

[restive geyser]

tf is your point even, now.

[reef mural]

You guys clearly lack pedagogical features.

Literally every person on this server.

You guys are not the first.

[remote cradle]

Counter question, when do u use tan?

[restive geyser]

Brilliant argument; wanna try giving evidence and explaining yourself? Else you're only talking to a mirror here.

[reef mural]

Clearly at a/b

[reef mural]

And you’re talking back now?

[restive geyser]

Well, as the person who didn't open the help channel i.e. NOT the requester for help, I've every right to, if what you've been saying is counter to any productive discussion.

[remote cradle]

Then cot at b/a

[remote cradle]

The thing is actually that yr concepts are not clear

[next cedar]

you know, OP, you should probably consider not being an ass to people who devote their time to helping you for free.
if you don't like their explanations you could just ask questions about them, or do your own research.
plus, if you dislike their pedagogy, why not say how you want things to explain instead of this pointless callout?
not every means of explanation work for everyone, and I think you agree, but nothing stops helpers from trying to adapt to your method of understanding.

[remote cradle]

And you are not sure what question to ask in the first place

[remote cradle]

He's not sure what he's asking ig
His concept is not clear

[next cedar]

I'm not addressing the quality of his question.

[remote cradle]

Well whatever
I really don't care
I just like helping u know

[reef mural]

I give up

[next cedar]

it's good that you don't, but that was for OP, not you, so there's that.

[reef mural]

You guys are so maniacal

.close

[full forum]

Channel closed

Closed by @reef mural

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.

[twilit leaf]

.is this how you talk to all your teachers

[brittle sun]

. This channel became available quickly. Looks like even Bot was waiting for it to be over

[reef mural]

Honestly I disregard my math teacher

[twilit leaf]

ok have fun

[reef mural]

Adios

[last slate]

Holaaa

Alguien que hable español?

[brittle sun]

.close

[full forum]

Channel closed

Closed by @brittle sun

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.

[north gust]

I have this worksheet, I understand the basics on how to do it I just can't find out which method to use

[north gust]

is tehre a trick

or something taht can help

i understand when to use difference of squared or cube group or factor

but its mainly trhe first step

especially on number 11 i had to look up how to start it

[stone meteor]

uh

just like

factor out the gcd's of certain parts

and make common terms in parentheses

and combine or something

[full forum]

@north gust Has your question been resolved?

[north gust]

uh

ok

[full forum]

Channel closed

Closed by @north gust

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.

[delicate jacinth]

how does the answer key fit into the formula?

[onyx glen]

you could think of it as a trapezoid rule with one (1) trapezoid

i.e. n=1 and so there are only the first and last terms in the sum, with nothing in between

that's if you are going to insist upon shoehorning the trapezoid rule in at all, when in fact the area under f(x) is a very literal trapezoid

[delicate jacinth]

how do we know n = 1

[onyx glen]

girl it is literally just one big trapezoid

[delicate jacinth]

ok didnt know n was the number of trapezoids...

[onyx glen]

n is in fact the number of trapezoids.

[delicate jacinth]

thanks

.close

[full forum]

Channel closed

Closed by @delicate jacinth

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.

[idle osprey]

So far the function I have is 340sin(120(pi)t) and wo=240pi
av I got 680/pi
But I'm stuck on the integral with the limits of 0 to 1/240
sin(120(pi)t)cos(k240(pi)tdt

[idle osprey]

I tried integration by parts but it does not seem the best

[slate glacier]

Can you write the integral down somewhere and then send it

[idle osprey]

I got sin(k(pi)t)/240k(pi)-1/(480k^2pi)

this is the answer key

[full forum]

@idle osprey Has your question been resolved?

[full forum]

@idle osprey Has your question been resolved?

Channel closed

Closed by @idle osprey

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.

[fallen jolt]

i need some help from ye engineerin folks with this question

[fallen jolt]

this ones about thevenin

i already removed the load to start off

i got the total resistance and current source

and now i gotta figure out how i should find VTH

My progress

i dunno if i got it right

its cuz this load usually appears at the right side of the circuit, now its in the middle

like if i already removed RL then it becomes a series circuit

oh right there was another voltage source

got rid of it by short circuiting tho

[foggy vapor]

Your steps are very convoluted

[fallen jolt]

ik its confusing

[foggy vapor]

Just do standard nodal/mesh analysis?

Mesh analysis is good here because there is one loop

Your objective is to find the voltage between the two resistors

[fallen jolt]

i could do kirchoff yeah

seems easier that way

[foggy vapor]

Yes

[full forum]

@fallen jolt Has your question been resolved?

Channel closed

Closed by @fallen jolt

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.

[gray magnet]

So we are looking at a function of the form f(x)=P(x)/Q(x) where P(x) and Q(x) are quadratic polynomials, and both P(x)>0 and Q(x)>0 for all real (x), leading coefficients of both quadratic are >0, domain=R, co-domain=R
So f(x)>0 for all x∈R, so teb range of f is contained in (0,∞), which means f is not onto R, because ut never takes negative values or 0

As input is R but range is only positive

So can we say that the f(x) is not injective by pigeonhole principle

[rare dock]

what is your argument, in a little more detail?

[gray magnet]

What part
I mean what am I expected to explain in more detail?

[rare dock]

i agree with everything you said but i’m not sure about saying f is not injective from them

[gray magnet]

Like f(x) is many-one function

[rare dock]

yea

there are injective functions whose image is contained in (0, \infty)

so what’s special about these ones you’re working with

like you haven’t really mentioned anything else about this class of functions and that property alone isn’t enough

[gray magnet]

I'm asking for general

Discriminant is always -ve

[rare dock]

i don’t think we’re on the same page

[onyx glen]

So can we say that the f(x) is not injective by pigeonhole principle

can you state what you understand by "pigeonhole principle"? @gray magnet

and i will tell you exactly why it deos not apply

[rare dock]

also @onyx glen hi

[onyx glen]

hello layla

ok let's see whether OP shows signs of life again cause he's offline atm

[gray magnet]

.close

[full forum]

Channel closed

Closed by @gray magnet

Use .reopen if this was a mistake.

[rare dock]

[onyx glen]

@gray magnet it's kind of rude to slam the door like that

if you dont need help then at least say "nvm i got it" or "nvm i see my mistake"

[gray magnet]

Ohk ty
And also sorry again

I mean one of my friend told me that he is explaining it to me
So i closed and he explaining it to me rn
Btw he is also a beast like you guys he is also from top universities like you, from MIT

[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.

[olive dock]

on my school Chromebook rn but dose anyone know alg 1?

[full forum]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question!

[onyx glen]

if you have a question then send your question lol

[olive dock]

im failing rn with like a 61 but I'd like help instead of using ai

[onyx glen]

aight so. these help channels are for getting help with specific math problems/questions

if you want study advice or looking for a study buddy or whatever that's for #study-discussion

[full forum]

@olive dock 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.

[signal solar]

no idea why it just stays on 2/3

[queen crater]

"it"?

a_n does not "stay on" 2/3

[coral torrent]

try the ratio test for convergence

[signal solar]

it would approach 0

[signal solar]

i dont understand the 2/1 2/2 2/3 2/3 2/3 2/3

[coral torrent]

yes

since that's less than 1, the series would converge

[signal solar]

but the way they solve it is confusing to me

[coral torrent]

is the image not your working?

[signal solar]

no

sorry i shouldve said i dont understand the solution

i understand using a ratio test n! grows faster than (-2)^n so it approaches 0

i dont know what they did there

[queen crater]

Every term n > 3 is less than 2/3

[signal solar]

ah

[queen crater]

Sorry that's wrong