help-28

[worn matrix]

!show

[full forum]

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

[torn jolt]

RS/20 = 80/40

[hybrid nexus]

it shud be 40/(40+80)

coz its the whole side

[torn jolt]

yes

[hybrid nexus]

not only that part

[torn jolt]

is it cause it's one triangle split into 2?

[hybrid nexus]

kinda

[worn matrix]

just know that we are applying similarty critieras in triangle OPQ and ORS

[torn jolt]

oh okay i see

thanks guys!

.close

[full forum]

Channel closed

Closed by @restive jungle

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[royal raptor]

Hi, I would like some help with complex analysis

• Some details on Rouche's thm, and
• A question which I think is about uniqueness thm in particular

[royal raptor]

I'd like to first ask about Rouche's about the number of roots \
if $|f(z)| < |g(z)|$ for $z$ on a circle $C$, then we know the number of roots of $f+g$ in $C$ equals the number of roots of $g$ in $C$. \
Say $g$ has 1 distinct root of order 5 in $C$. Will $f+g$ have 1 or 5 roots in $C$?

[glossy valve]

Lemonsity

[devout valley]

(you may want to ask this in #real-complex-analysis as well, if you haven't)

[royal raptor]

Thank you very much for the tip, I have but it got buried, so I figure it might be better to ask with a dedicated thread here

[devout valley]

Ahh I see, yea you can ask here too, sometimes the advanced channels get buried and asking in these channels, sometimes people help out

[royal raptor]

yup, a bit luck based

Hmm, I dug up Lang's Complex Analysis, and it seems to suggest that multiplicity have to be accounted

the example from Lang compared it with a function 5z^3

and then specifically mentioned that "you have to count multiplicity"

[devout valley]

Was about to say that my notes derive Rouche from the Zero Counting Theorem, where [before they introduce them] you count the roots with their multiplicity

[royal raptor]

mine seems to be the same too

then that has to be the answer then

is your notes the "integration over f'/f"

[devout valley]

Yea something like that, they basically show that the integral of (f + g)'/(f + g) is the same as the integral of f'/f at the last point

[royal raptor]

I see, our notes sounds very similar

Then it is solved

(In terms of server rule, should I open a different help channel for a different complex analysis problem?)

[devout valley]

Well you can if you want, generally better as someone else might pick it up! (not sure if I'll be able to answer much other than reading my notes, kinda tired, though I will try take a look )

[royal raptor]

If you are tired, then you should get some rest

Thanks for the confirmation and help

I will start a new channel

.close

[full forum]

Channel closed

Closed by @royal raptor

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[graceful yoke]

I am having trouble interpreting the stokes theorem

[graceful yoke]

It states that the flux of the curl of a field is equal to the field integrated over the boundary

But the word "boundary" is really ambigious. For example, if we consider a sphere which some electric field E, then I can take the flux of its curl and if stokes is correct it should be the same as integrating the field over the spheres boundary

But what exactly is supposed to be the boundary here?

The term boundary implies some sort of one dimensional path, I imagine it to be some sort of thin thread wrapping around a surface, basically what would be called as a perimeter

But it makes no sense to talk about the perimeter of a 3d object

How exactly do I imagine stokes theorem visually?

[split swift]

the sphere doesn't have a boundary because it's a closed surface, so the integral is zero

you can also view this by splitting the sphere into two hemispheres

then the boundaries form circles, but they are oriented in opposite directions

so applying stokes to both surfaces then combining them cancels them out, which also yields zero

normally, you apply stokes to non-closed surfaces (your intuition about a boundary being a path is correct, your example just happens to not have such a boundary)

[full forum]

@graceful yoke Has your question been resolved?

[graceful yoke]

So is it always the case that the flux of curl will always be zero for a closed object?

And about cutting the sphere into two halves, doesn't the cancellation only occur because of the symmetry of the sphere? If I take some asymmetric object, can it still be proven that the flux of the curl will be zero?

[umbral dome]

it's true in general that the flux of a curl field across a closed surface is 0. the main thing is that if you split it then the boundary of each curve will be the same but with the opposite direction (since it only depends on the shape of the boundary, not the shape of the surface)

you can also prove it with the divergence theorem (along with the fact that the divergence of a curl field is 0)

[split swift]

the cancellation occurs because the two boundaries will be where you slice the closed surface in half

and the orientations will necessarily be opposite in that case

[graceful yoke]

Another thing, if I take a hollow cone and then make a cut at the bottom of the cone such that the cross section is perpendicular to the height ofthe cone, then the cone now has two circles with different radius, which circle here will be the boundary now?

Also thanks for the insights, I really appreciate them

[split swift]

I don't work with integrals/manifolds much but I believe the boundary has to be at least connected and piecewise smooth

so your case of an annulus does not meet the hypotheses of stokes

let me check something

ah, okay

so you can basically do a similar thing to the sphere

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[split swift]

where you "close" one of the holes

.reopen

[full forum]

✅

[split swift]

and apply stokes to the resulting surface, and subtract that away from the total

[graceful yoke]

Damn that closing one of the holes is a really clever idea, it does bring the problem of how we close it though, but I can sort of intuitively see it working

[split swift]

it doesn't really matter how you do it, because the boundary of the resulting surface is just the other part of the boundary we had in the first place

so if your boundary is a union A U B, close B and apply stokes to a surface with boundary A

then apply stokes to the surface you closed B with

and it doesn't matter what that surface is, since you know it has boundary B

[graceful yoke]

Yes, the boundary doesn't change, but the surface area does change, which might change the flux

[split swift]

and stokes says that this isn't the case

stokes precisely says that the surface doesn't matter, only the boundary

[graceful yoke]

Yeah I get it better now, thank you very much for the help 🙂

Thanks to @umbral dome too for the explaination

.close

[full forum]

Channel closed

Closed by @graceful yoke

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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]

Part b how do I find the first quartile

[full forum]

@twin wolf 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[tired sedge]

How <BAC can be 90°

Or my drawing is incorrect

[fossil river]

Your drawing seems correct. There seems to be an issue with question

[full forum]

@tired sedge Has your question been resolved?

[tired sedge]

Okkkk

.close

[full forum]

Channel closed

Closed by @tired sedge

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[ancient wyvern]

for this

is there a simpler way

then doing compelte teh square

then doing u sub twice to convert it in 1/(1+x^2) form

i feel like thats way too long

[fathom saddle]

It's a very long question sadly

[ancient wyvern]

the part that pisses me off

is that this is 1 part of a larger integral

and i felt like i was doing it so wrong

cause theres no way this is right

[fathom saddle]

I think you can get away with a complex factorization if you know your stuff, but that's a big ask

[ancient wyvern]

this is the original

question

[fathom saddle]

Yep that's pain.

[ancient wyvern]

so if theres a shortcut that doesnt create that monstrosity pls tell

[granite torrent]

this is alrd fairly simple isn't it?

u don't need to formally do u-sub

[ancient wyvern]

yeah but its 3 steps seperated from another integral

how then?

[granite torrent]

once u have 1/((x + 1/2)^2 + 3/4) u can immediately integrate using arctan formula

[ancient wyvern]

i dont know the formula

i only know 1/(1+x^2) = arctan

oh

is that how teh calculator did it

[fathom saddle]

You can step into it with a good u-sub

But that's another step yeah

[ancient wyvern]

how does this work

if it isnt x

and it isnt 1

do u have it in a +b form

at

[fathom saddle]

Try the u-sub:
3/4 (x + 1/2)² = u²

[ancient wyvern]

ok

[fathom saddle]

Or, really, try it from
√[3/4] (x + 1/2) = u

[ancient wyvern]

imt rying toher one

[fathom saddle]

But I hope the logic is clear on how I got this

[ancient wyvern]

yeah

[buoyant pewter]

and it is very fast , if you calculate good

[ancient wyvern]

im doing the bx+c part

[buoyant pewter]

ok very well

[ancient wyvern]

ok yeah tihs is way easier

got it

is sqrt(3)arctan(sqrt(3/4)(x+1/2)) correct

i dont know if this is equivalant

[ancient wyvern]

close enough

[full forum]

@ancient wyvern Has your question been resolved?

Channel closed

Closed by @ancient wyvern

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[abstract hearth]

what does the last line of the question say?

i cant read it properly;

[hoary surge]

A customer survey indicates that for each $1.20 decrease in price, sales will increase by 6 pails of paint

[abstract hearth]

alr gimme 1 sec to solve

[hoary surge]

ok

[abstract hearth]

ok im not entirely sure what its asking but * ** i tihnk ** *its c

[hoary surge]

we're looking for r(x) = x*p(x)

[abstract hearth]

right then i think its d but im really tired so i wouldnt trust me rn but i think its that

sorry

[hoary surge]

what do u mean by d

it isnt multiple choice btw

[abstract hearth]

i honestly dont know man

[hoary surge]

u have to solve all of them

[abstract hearth]

im just being stupid and dumb

[hoary surge]

alr 😂

[abstract hearth]

sorry

almost 36 hrs awake lmao

[full forum]

@hoary surge Has your question been resolved?

[hoary surge]

<@&286206848099549185>

[full forum]

@hoary surge Has your question been resolved?

[full forum]

@hoary surge Has your question been resolved?

[torn jolt]

hello

@hoary surge can i try?

is this economics qn?

thats out of my league bro

but i can try to think from a maths perspective

[hoary surge]

Yes

[torn jolt]

lol

i know functions but no dice abt eco

the first one is a linear function right?

can you help me a bit here

what price function is asked?

like if you elaborate

a bit

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[sly solstice]

quick help please

[sly solstice]

how to do this

from h/2(E + 2M)

since i did 0.5 * (1 + 1/1.5 + 2(1/1.25)) = 1.6333

please @ me reply so i see

howd u do this one, desperate exam tmr 💀, how come int4,2(9x+15)/(x-1)(x-3) = 3int(4,2(3x+5)/(x-2)(x+3)
how does the 2/x-1 relate to this at all

Please answer all, I'll come back and read them so Ty 🙂

Plz

[full forum]

@sly solstice Has your question been resolved?

[main trellis]

we arent allowed to straight up give you answers

[main trellis]

trapezium rule just apply the formula

[main trellis]

looked at what they've given you and what they are asking you to find

can you see any similarities?

maybe multiplying by something

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[vivid berry]

how i do dis

[vivid berry]

idk where to start

[neon geyser]

do you know pigeonhole principle?

[vivid berry]

hmm

kind of?

i know that

i rmb my teacher saying

for n people, there is n-1 handshakes

[vivid berry]

the pigeon hole is the boxes and the crayons are the pigeons?

[full forum]

@vivid berry 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 badger]

so far this is my attempt for the question, please let me know if I am doing it right (context: renewal processes)

[full forum]

@proven badger Has your question been resolved?

[full forum]

@proven badger Has your question been resolved?

[fathom saddle]

ye

[proven badger]

update: 340 was marked as incorrect 😦

[full forum]

@proven badger 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hollow summit]

for trig substitution here

how do we transform this into x

like x^2-a^2 but theres a 16

[sacred sparrow]

well you could factor out the 16

or you can incorporate it into the ²

since 4² = 16

16x² = (4x)²

which then lets you do tan sub

@hollow summit

[hollow summit]

yes ill try to do that

[brisk obsidian]

Don't complicate things. Change 16x^2 to 9u^2 if that's your goal.

[hollow summit]

is x 3sec dx 3sectan

[hollow summit]

yeah thats what i did

[full forum]

@hollow summit 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[cunning ravine]

Can someone explain set classes to me? I’m having a little trouble getting the concept

[wild sleet]

what's that

[cunning ravine]

Not entirely sure myself

Here is the footnote from Apostol’s book explaining them. I sorta understand the operations on them, but not the classes themselves. Would their sets not just be subsets of the class?

[wild sleet]

,rccw

[full forum]

@cunning ravine Has your question been resolved?

[full forum]

@cunning ravine Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cunning ravine]

.reopen

[full forum]

✅

[full forum]

@cunning ravine 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[loud hull]

For 58, would this be as simple as 4 * 4 (4 aces in each deck) or would I need to find the probability of getting an ace from both deck?

[deft tulip]

the first, it's not asking about probability just the number of hands

[loud hull]

thank you!

.close

[full forum]

Channel closed

Closed by @loud hull

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[stiff wagon]

Could anyone help with this?

[simple totem]

what are you struggling with

[stiff wagon]

honestly just wanted someone to check if am on right track

[simple totem]

then send your work

[stiff wagon]

Thoughts?

[simple totem]

i dont know what most of these groups are, but i think you have the right idea

[full forum]

@stiff wagon 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[knotty musk]

A set of 12 different types of fruit are sitting on a table. In how many ways can you select at least two of he fruit to eat.

[summer chasm]

you can use formula for choosing r from n objects

nCr = n! / r!(n-r)!

so it'll be 12C2 + 12C3 + 12C4 + ... + 12C11 + 12C12

[wild sleet]

yeah

slow but correct

[knotty musk]

Is there any faster way

[glad hound]

Are you doing this by hand or with a calculator?

[knotty musk]

Calculator

rn im doing it on calculator but

on test im not sure cuz there might be a non calc portion

[glad hound]

Doing factorials by hand sucks.. but you'll have scratch paper, so...

[wild sleet]

it's technically can be solved without calc or paper

if you know 2¹² = 4096

[glad hound]

When you start your test, do a quick data dump of your factorials, up to.. whatever you think you might encounter.. 12 or 15 or so

[summer chasm]

21

[sage stream]

Just find complement

[glad hound]

I mean.. taking factorial much past 10, by hand?

[full forum]

@knotty musk Has your question been resolved?

[knotty musk]

Oh wait ur right 2^12 is gonna work

Thanks

[full forum]

Channel closed

Closed by @knotty musk

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[quaint bolt]

can someone help me find the surface area for this

[full forum]

@quaint bolt Has your question been resolved?

[quaint bolt]

<@&286206848099549185>

.close

[full forum]

Channel closed

Closed by @quaint bolt

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[silk lake]

How do I tell the things below to be in mathematical notation or whatever you call it
M and/or n is a positive odd integer

[vapid scarab]

u mean like

set builder form?

[rare dock]

the exact language you could use depends on the context

[vapid scarab]

tho what im talking abt is just 2n+1 where n belongs to whole numbers

thats what he means probably

by mathematical notation

[rare dock]

the prose kinda depends on if M and n have already been introduced and their purpose

and if you’re trying to say at least one of them is a positive odd integer, they should already have been introduced

so then i would like to know what they were introduced as

before i give any suggestions

[full forum]

@silk lake 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 agate]

In △ABC, AB = 3, BC = 6, CA = 5, AD is the bisector, E is the midpoint of the segment BD s, i I is the center of the inscribed circle. If IE ∩ AC = {F}, find out the value of the ratio CF/ FA

[full forum]

@sacred agate Has your question been resolved?

[sacred agate]

<@&286206848099549185>

[full forum]

@sacred agate Has your question been resolved?

[sacred agate]

<@&286206848099549185>

[full forum]

@sacred agate Has your question been resolved?

[sacred agate]

<@&286206848099549185>

[full forum]

@sacred agate Has your question been resolved?

[sacred agate]

<@&286206848099549185>

[elder trellis]

hey

i take it that this is geometry-related

[full forum]

@sacred agate Has your question been resolved?

[open zinc]

That’s a fun problem

!status

[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

[glossy valve]

ItzJezze

[old condor]

!done

[full forum]

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

[open zinc]

I don’t think your cf definition is correct

[sacred agate]

What do you mean?

[open zinc]

Cf is on ac not bc, so cf ≠ bc - ec

[jade garnet]

Now I see it, thanks for pointing it out! So I'm guessing that, without additional information about the exact location of ( F ) on ( AC ), we cannot determine ( CF ) and ( FA ) precisely?

[open zinc]

No you can

[sacred agate]

...how?

[sacred agate]

And also, I really appreciate your efforts. Thanks a lot man

[jade garnet]

Huh, I don’t get it. Would you care to demonstrate?

[open zinc]

You can use law of cos and the lengths of AB, BD, and BE to fully identify ABI, and use the interior angles to find m<BIE with that and ACI, find FIA and solve FC/FA

[full forum]

@sacred agate Has your question been resolved?

[sacred agate]

I think that works? Although I'd rather have a synthetic solve rather than an algebric one

[sacred agate]

.c.ose

.close

[full forum]

Channel closed

Closed by @sacred agate

Use .reopen if this was a mistake.

[serene hazel]

smh the gpt response

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hard eagle]

hello can anyone solve this?

[hybrid nexus]

assume point C to be h,k

find relation between h and k using area of triangle formula

and then find centroid p, in terms of h and k

[hard eagle]

didnt understand this step

if possible can you solve and show so i understand?

[full forum]

@hard eagle Has your question been resolved?

[full forum]

@hard eagle 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[pale otter]

Hey I ned to confirm a few things about cross products

[pale otter]

so If I have two vectors A and B,
A = <bi, cj, dk>
B = <fi, gj, hk>
(I'm reserving a and e for the real component of a quaternion)
Well I guess that should be the first thing: the i, j, and k in our vectros reference the i, j, and k in quaternions, right?

as in if we pared off the real component from a quaternion to make it a 3d vector, the math would be the same right?

ij=k
ji=-k
ijk = -1
i^2=j^2=k^2 = -1
and all that?

[full forum]

@pale otter Has your question been resolved?

[pale otter]

no

[full forum]

@pale otter Has your question been resolved?

[pale otter]

no

[torn jolt]

Wsg guys. I'm tryna get the correct answer to this question but I don't get it. It says I have to find the area of this figure. Can anyone help me by chance?

<@&286206848099549185>

[coral fjord]

D

[torn jolt]

How?

[coral fjord]

there are two rectangles

one with 9x8

and 6x25

[torn jolt]

Ohh I get it now

Thx @coral fjord @shadow burrow

[full forum]

@pale otter Has your question been resolved?

[pale otter]

no but i'll give up the channel ig

[full forum]

Channel closed

Closed by @pale otter

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 kestrel]

9 distinct balls are to be distirbuted in 4 boxes: B1, B2, B3, B4
what is the probability that B3 contains exactly 3 balls?

[autumn kestrel]

my first approach is to think of it as a multinomial expansion:
(B1+B2+B3+B4)^9
and find all the terms that have (b3)^3

however, multinomial theorem has been removed from the course and I'm doing an old question, so I have no idea how to find the sum of the required coefficients

[steel cove]

theres an easy way to think about it. If B3 has 3 balls, then theres 6 balls to be distributed across B1, B2, and B3

Find how many possibilities there are for this, and subtract it from the total number of possibilities

[autumn kestrel]

oh yeah, we can find the number of ways by which we can distribute 6 balls among b1, b2 and b3 and subtract it from the total possibilities?

oki

[wise karma]

6*

[autumn kestrel]

6 mb

[steel cove]

yep

this is a moderately difficult problem but since ur in a combinatorics course I assume you'll be able to do it pretty easily

[autumn kestrel]

oh am not in a course, am in grade 12th

[wise karma]

this may need beggars method tho.. there might be some other way too

[autumn kestrel]

there prolly is

alrighty, i got my answer, thanks!

.close

[full forum]

Channel closed

Closed by @autumn kestrel

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[oak otter]

How do I start number 19

[acoustic forum]

What is the anti derivative of 3x

Oh you don’t even need to solve

Ok what does the graph of 3x look like

Just a line going upwards from the origin right

[oak otter]

It’s( 3x^2)/2

But how does that tell me the shape of the object

[acoustic forum]

that would tell you area

From there you find the difference between plugging in 1 and 0 for x

But it looks like your book doesn’t even make you find the area

It just wants the shape

[acoustic forum]

This is that

The area under the curve, which in this case is just a line, will just be a triangle

[oak otter]

Oh I get it now

Thanks

[acoustic forum]

🙏

[oak otter]

.close

[full forum]

Channel closed

Closed by @oak otter

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[tiny drum]

help

[runic portal]

!status

[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

[tiny drum]

i dont know where to begin

[runic portal]

well you know that it's a circle, so the radius must be the same throughout

[tiny drum]

yep

[runic portal]

can you find something with that information?

[tiny drum]

no

[runic portal]

LMFAO

what is triangle AOC

[tiny drum]

obtuse angled triangled

[runic portal]

hmm

well it is but

that's not gonna help us here

[tiny drum]

do i need to construct a quad

quadlitateral

[runic portal]

nope

not at all

remmeber what i said about the radius

[tiny drum]

but how will that tell me angles

[runic portal]

should i tell you what the triangle is

[tiny drum]

yes

wait

scalene

i mean

isoceles

[runic portal]

YEAHH

you got it

and what's the property of an isoceles triangle

[tiny drum]

two sides equal and one unqeual

30?

shouod the sum be equal to 180?

[runic portal]

yes

[tiny drum]

40

[runic portal]

the interior angles of a triangle should always add upto 180

[runic portal]

correct

[tiny drum]

this not even in my syllabus why they give this 🥺💔

[runic portal]

now how do you find ACD

remmeber that's not the answer hahaha

[tiny drum]

o

im not sure

[pallid roost]

exercise name ?

[tiny drum]

angle in a segment of a circle i think

[runic portal]

do you think you could use the properties of parallel lines?

[tiny drum]

i dont think so

[runic portal]

well you know that a straight line would have an angle of 180 degrees right

so angle of AB = 180

and you know a part of it, AOC = 100

so COB would be?

[tiny drum]

80

[runic portal]

yeah

now can you do something with that information

(use how AB and DC are parallel lines)

[tiny drum]

so 40 is the answer?

i mean

60

[runic portal]

nooOOO you got it correct the first time hahhhaha

[tiny drum]

but if one of the angle of side AB is 80 degree then opposite to it will also be 80 degree..then triangle aoc angle is 40 so the other would be 60 cus 80+40+60=180 which is a straight lines angle???????

[runic portal]

why would the opposite side also be 80 degrees?

[tiny drum]

its a transverse lone

line

which bisects

[runic portal]

if you're refering to adjacent angles

that is

[tiny drum]

the other parallel line

[runic portal]

oh you're talking about the opposite interior angles?

[tiny drum]

no

exterior

[runic portal]

this x?

[tiny drum]

yep

[runic portal]

a straight line has an angle 180 degree

[tiny drum]

ye

[runic portal]

so 100 + x = 180

[tiny drum]

ye

[runic portal]

and x = 80 correct

[tiny drum]

yea

[runic portal]

and this is true because opposite interior angles are equal

[tiny drum]

no the other side

oh

but then

[runic portal]

haha it's opposite

[tiny drum]

isnt the other x 40

[runic portal]

it would be wrong to say that it's the same side anyways - it looks different just by the raw eyes

[runic portal]

hmm look at the diagram again

[tiny drum]

ok then

80 + 40 = 120 but that option isnt there 😭😭

[runic portal]

why would you add it?

see

[tiny drum]

because of the angle C

a part of obtuse angle and the line

makes angle c

[runic portal]

the sides that are parallel are AB and DC, so the opposite interior angle rule would apply for angles DCO and BOC

[tiny drum]

yeah i got it but im confused whether it will be 40+80 or just 80

i used the theorem in my previous grade but i dont remember it anymore and i gotta apply another property

[runic portal]

well what you did before to get 40 is you got angle ACO right?

and you want to find angle ACD

this is a better diagram with all the values we got till now

we need to find angle ACD, which i marked with a question mark here

how would you go about doing that

[tiny drum]

yeah i know algebra

acd will be 40 because boc is 80 and its half would be 40

[runic portal]

YESS

you got it

well done 💪 💪

[tiny drum]

all this sh for 1 mark 😭😭😭

thanks so much

[runic portal]

NAHH 1 MARK

[runic portal]

haha npnpnp 🙏

[full forum]

@tiny drum 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[grand carbon]

so i am learning complex analysis, and we learn about CR equations

[grand carbon]

to know at what points is a complex function f differentaible.

for example, solving CR equations, i get x = iy, since x,y must be real, thus the only solution is (0,0)

complex function f is differentiable only at (0,0)

if i get something like y = mx, then f is differnetiable on that straight line only. cool

but suppose f is analytic in some region, how would the answer when i solve the CR look like?

[fast peak]

I have no clue how you jump from CR equations to x=iy

what function are you even considering

[grand carbon]

that's the end of me solving cr from a past year paper

i might be wrong of course, but for now, i know that, if i did not make mistakes in manipulation, then i believe that is the answer (0,0) for where f is differentiable.

and since that is a point, not an open region where f is differentiable everywhere inside, f is not analytic.

i have not found an example, to give me intuition, of the "form"? the end result of CR will take, if f is actually analytic

like if i get y = p(x), then f is differentiable along a line of points. but is still not analytic

so how would it look, if f is analytic

[deft tulip]

@quaint prawn CA doubts for you to solve

[quaint prawn]

the answer to what?

!original

[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.

[grand carbon]

alright, gimme abit

[grand carbon]

hope you don't mind the ping. was searching through pc

so the real part we can is u(x,y), imaginary part is iv(x,y)

so x,y are real numbers

part a...what i eventually got was
partial derivative u/dy = - partial v/dx
lead me to x = iy

(the du/dx = dv/dy gives me a polynomial? of powers of x, y and multiples of both but no constants)

since x, y must be real, the only solution is x = y = iy = 0

so f(z) is differentiable only at (0,0)

then comes part b

which suppose my answer to a is correct, then f is not analytic because its differentiable....in a closed? region(exact point)

honestly, i don't know what to write besides this argument. is there a more "mathy" way to make the case?

then since we are on the topic, suppose a function g(z) is actually analytic in a region. when solving the CR equation, how would it look like? any examples?

[grand carbon]

this is my questions.

[full forum]

@grand carbon Has your question been resolved?

[quaint prawn]

What?

[grand carbon]

me solving part a

[quaint prawn]

Your solution makes no sense

f(z)=u(x,y)+ i*v(x,y)
is real differentiable everywhere u(x,y) and v(x,y) are differentiable

[grand carbon]

so i just do individual tests for differentiability?

isn't the CR equations meant to check for differentiability of f?

[quaint prawn]

it's asking you if it is real differentiable

[grand carbon]

i am sorry, i don't follow.

i am supposed to test for differentiability of u and v separately?

[slow canopy]

Yes and take the intersection of where they are differentiable

[quaint prawn]

That is what part (a) is asking for

[slow canopy]

But are we sure that "Differentiable" here means real differentiable? I suppose it would have to, otherwise the answer to the second part would be the same

[fathom saddle]

It's hard to know what exactly you're getting and doing from that write up. It would be much more handy if you had your work available.

Assuming you're correct that the CR equations are only satisfied at (0,0), then indeed the function is complex differentiable only there

[quaint prawn]

CR being satisfied doesn't imply holomorphic, but also (0,0) is the only point where there should be any doubt if it is differentiable

complex or not

so the solution makes 0 sense

everywhere else it is the sum / product / quotient of holomorphic functions

[slow canopy]

it does if satisfies CR on like an open ball though right

[quaint prawn]

I believe so

[fathom saddle]

So yeah, logic is good. (0,0) is the only point, assuming the work was correct.

[quaint prawn]

the only point where it might not be differentiable

definitely not the only point where it is

[fathom saddle]

Well I haven't seen the work so I can't be sure

[quaint prawn]

the function is posted tho

[grand carbon]

to test for real differentiability of bivalue(?) functions u and v

i take partial derivatives and compare?
i have never done it for real at least

[fathom saddle]

I'm assuming their conclusion is correct

[quaint prawn]

You don't know how to check if a real-valued function is differentiable?

[fathom saddle]

If you ran the CR equations and got a different result, I'm glad you checked!

[slow canopy]

How about you assume you can't divide by 0?

[grand carbon]

test lim g'(x) = lim g'(x)

not sure how to test generally,
but at a point, c, take limit as x approaches c from left vs limit as x approaches c from right

[quaint prawn]

What

[slow canopy]

⁉️

[quaint prawn]

I think you need to do a lot of review on your calculus before coming back to complex analysis. Checking if a complex function is analytic or holomorphic will require you to know and understand how to differentiate real-valued functions of several variables

As for part (a), like I said earlier if you wanted to continue working on it, write f(z)=u(x,y)+i v(x,y)

then check if u, v are real-differentiable

if you're not sure how to do that then you need to review some stuff

[waxen summit]

wait how would you do this in R2?

there’s no left nor right

[fathom saddle]

@slow canopy
Of course! Thank you for reminding the people nearby. I think you reacted to me by accident.

[slow canopy]

Just dont want you to keep confusing him by "confirming" that the only place the function is real-differentiable is at the origin (which is not even in the domain)

[fathom saddle]

Ah wait, I see your concern now Austin

Like I said, didn't check the work. Took the result and confirmed the logic, given it's true.

[grand carbon]

closest i can think of is differentiating f(z), where its nicely written in z

lim(h to 0) f(z+h) - f(z)
simplify, then change z to x + iy,

then compare lim(h to 0) lim(ih to 0) (...) vs lim(ih to 0) lim(h to 0) (...)

if they contradict, f'(z) does not exist

[quaint prawn]

We are not talking about f(z)

[fathom saddle]

Indeed, (0,0) is not in the domain. The function doesn't exist there, much less have a derivative there

[quaint prawn]

Remember part (a) is asking if it is real-differentiable

So you rewrite it into the form I provided above a few times

and check if u(x,y) and v(x,y) are differentiable

[fathom saddle]

This is the part that confused me though. Part a) is not asking that?

[quaint prawn]

as functions of two real variables

[grand carbon]

i was answering pikachu's question above

not the one posted

[quaint prawn]

I think it is, like, f(z)=u(x,y)+iv(x,y) is differentiable as a function of real variables, otherwise it'd say holomorphic, and part (b) would be pointless

if it isn't asking that then part (a) and part (b) are the same question

[fathom saddle]

Indeed I don't see how b) would give 4 points

But a) gives 16

[grand carbon]

as far as the course syllabus goes

a function can be complex differentiable but not analytic

analytic requires it being differentiable in an open connected region

[fathom saddle]

But yeah I can't say for certain

[quaint prawn]

Part (b) would be instantly solved by solving part (a)

you would find from part (a) the region(s) where the function is holomorphic

if it is only at a point (or nowhere) then it isn't analytic anywhere

otherwise, it's analytic in the entire region of holomorphicity

I don't think the question is that clear

I think it's time we ask a better sir @stiff musk

[grand carbon]

yeap.

which was my original question. how would a region(valid) look like?

a point/s would mean there are exact solutions? implies not analytic

a line? would be y = some function of x? also still not analytic

nowhere would be no solution?

though thank you for the headsup regarding my part a. i am looking at it again, or well, googling/reading stuff

[full forum]

@grand carbon Has your question been resolved?

[full forum]

@grand carbon Has your question been resolved?

[stiff musk]

what is your doubt?

[quaint prawn]

What is your interpretation of the helpees doubt?

I took it to be asking if it was real differentiable

But we’re unsure

[stiff musk]

the pinned original doubt was unclear
is this the actual doubt?

i guess it could mean complex differentiable

but who knows

the doubtee must ask his sir

[quaint prawn]

I think this is the actual doubt yes

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[tepid glen]

It would be difficult to calculate ln(10^123456) via brute force, but manipulating the equation a bit gives 123456 * ln(10), which is much easier to compute. Is there a special name for when an equation gets simplified so no extremely large/small values come up in calculation?

[alpine vigil]

not sure if this is exactly the term but perhaps preconditioning?

it definitely falls under some kind of numerical method for computers though

[wild sleet]

that's solving

no name

[full forum]

@tepid glen 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[worldly surge]

right?

[golden cape]

a) is true if A and B commute which is not always the case

b) nothing changes

[worldly surge]

so no

[worldly surge]

wym?

rows match collumns

it should work

[golden cape]

also the reason you gave for a is wrong

to multiply two matrices their inner dimensions must match

they don't need to have the same columns and rows

[steel cove]

the reason we can derive A^2-B^2=(A+B)(A-B) is because the second one expands to A^2-AB+BA-B^2 which is normally A^2-B^2

[worldly surge]

ones rows must match anothers collumns..

[golden cape]

yes

[steel cove]

there is an implicit assumption that they can be multiplied

[golden cape]

matrix multiplication is usually not commutative so AB != BA

[steel cove]

note that this doesnt work bc of what cygntauri said

[golden cape]

doesn't matter if they are square or not

[worldly surge]

hows a true

[golden cape]

its not

[steel cove]

its not

[worldly surge]

^

[steel cove]

Thats b

[worldly surge]

if sizes are the same

[steel cove]

Which also happens to be false

[worldly surge]

you can

[steel cove]

Sizes being the same doesnt mean they commute

[worldly surge]

its a square

[steel cove]

Try
1 3
8 1

Times

4 9
12 8

Just random numbers i made up

Multiply them and you see its not communatice

[golden cape]

the conclusion we came to on the first question generalizes to whatever matrix multiplication

[steel cove]

Communative*

[golden cape]

2nd question is just a special case

[steel cove]

Yep, so not communative

[worldly surge]

so b is

[steel cove]

False

Bc mm is not communative

Commutative*

[steel cove]

Understand?

[worldly surge]

no

[steel cove]

Ok

So do you get why the (a+b)(a-b) formula relies on commutativity

[worldly surge]

ye

ohhhhhhhh

i see

AB != BA

ok

now i gotta give 2x2 matrices that make 3 of these true

[golden cape]

actually your reason for a isnt completely wrong

since we don't know anything about A and B we don't even know if their dimensions agree

so thats an additional reason

[steel cove]

One 2x2 to satisfy 3 at once

Or 3 2x2s

[worldly surge]

either or

[worldly surge]

ye

[steel cove]

Well 1 is easy

[worldly surge]

how

oh #1

ye

[steel cove]

2 is slightly harder

[worldly surge]

gimme a sec

[golden cape]

for 2 you can do

1 0
0 0

with

0 0
1 0

and for 3 you can reuse one of the two

[worldly surge]

2 3 7 1 27 + 36=32 2 + 9=11
5 6 6 3 35 + 36=71 5 + 18=23

[golden cape]

you can use these for example 1 too

[worldly surge]

``
1 0 0 0 10 + 01=0 10 + 00=0

0 0 1 0 00 + 01=0 00 + 00=0``

[golden cape]

https://matrixcalc.org

[worldly surge]

you cant

^2 isnt 0

for both

[golden cape]

just this

mb

[worldly surge]

oh ye

[full forum]

@worldly surge Has your question been resolved?

Channel closed

Closed by @worldly surge

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[vale cipher]

hi im confused why it says determine the equation ? like determine what and why (also im confused how f(x) is related to the second equation

[full forum]

@vale cipher Has your question been resolved?

[quartz zenith]

i believe determine here implies multiple (x-3) and (x+1)

[quartz zenith]

the second equation actually applies the function f, by subbing x+2 into the function

hope that makes sense

[vale cipher]

uh

[vale cipher]

ya i dont get this

[quartz zenith]

what does f(x) mean at all?

[vale cipher]

but fx = (x-3)(x+1)

[quartz zenith]

f(x) is basically saying "input value x into function f"

and what comes after the = sign is what will be done to that x

so in f(x+2), you are replacing every x you see with x+2

[vale cipher]

so isnt it = (x+2) - 3 (x+2) + 1

[full forum]

@vale cipher Has your question been resolved?

[worldly tapir]

Yeah but better way is to write ((x+2)-3) ((x+2)+1), don’t forget the brackets

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[grand carbon]

the syllabus, as far as the lecturer taught, for this chapter and the way they are tested, to my knowledge, is about CR equations yeah
but i will try using the real differentiable method of components by austin.

but my original question is how will the solutions to CR look if f is analytic.

attached is a picture of an in class example. f is differentiable at these 4 points. f is not analytic

so how will the CR equations look if f(different from example) is analytic. like is there a pattern/form/structure?

we know that if we get specfic values, then f is differentiable only at these points, i.e not analytic.

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

if i have f(x) defined as to include $\int f(x)$ and $e^(\int\int f(x))$ is it possible to determine $\int\int f(x)$? (technically it is the integral minus some infisimential quantity) also i dont rlly need help actually solving it, once ik the method i can prob do it

[glossy valve]

speedydelete

[fast peak]

what do you mean with "include"

[torn jolt]

its basically a giant complicated quadratic/linear (i forget) equation that is defined in terms of those 2 parts

[fast peak]

it would be better if you just gave all context

[full forum]

@torn jolt 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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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 goblet]

how do i solve c)? i know that L_R=(40n-25)/n and R_R=(40n+25)/n from b)

[full forum]

@sacred goblet Has your question been resolved?

[sacred goblet]

<@&286206848099549185>

[torn jolt]

Hello. I'm trying to find the answer to these 2 questions but I can't figure it out. Can anyone help me figure it out by chance. Have a great day/night

<@&286206848099549185>

[full forum]

@sacred goblet Has your question been resolved?

[sacred goblet]

first question is 9in and second question is 75in

[torn jolt]

How??

I get the 5th question but I don't get the 4th one

[sacred goblet]

you have 4 equal sides (since its a square). so u know that 4*length of each side = 3feet or 36in.

then divide 36/4=9

[torn jolt]

Ohh ok I get it

Ty @sacred goblet

[sacred goblet]

np

[sacred goblet]

.close

[full forum]

Channel closed

Closed by @sacred goblet

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[storm tusk]

The following subvector spaces U1, U2 of the vector space IR2 are given:
U1 = span((-2,8)), U2 = span((2,1),(1,3))

Is the following statement true or false? Explain your statement precisely.
”The amounts {(1,−4)} represents a proof system of U1 ∩ U2.”

So I´m not sure how I can solve this, I don't know what U1 ∩ U2 is, maybe {(0,0)}? And if yes, how should I then proof that it doesn't or does represent a proof system?

[thin flint]

U1 intersect U2 is all vectors in R^2 that can be written as both a linear combination of the vectors in U2 and U1

which you have been given

[full forum]

@storm tusk Has your question been resolved?

[storm tusk]

okay so then I have to proof if (1,-4) is a linear combination of the vectors U2 and U1?

[thin flint]

i'm not sure i know what proof system is but any vector in U1 intersection U2 is both a linear combination of the vectors in U1 and one of those in U2

you can construct that by just saying

any (x, y) where (x, y) = t (-2, 8) and (x, y) = s (2, 1) + r (1, 3)

that is U1 intersect U2

[storm tusk]

hmm okay aaah it' so weird for me right now

i think a proof system is a set of vectors that can build a vector space

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[thin flint]

.reopen

[full forum]

✅

[storm tusk]

nevermind its only a set of vectors

maybe the term generating system says more to you?

[thin flint]

as in the set of vectors that span the space?

[storm tusk]

yea, I think so, now I have to proof if it represents a proof system of U1 ∩ U2

so (-2,8) is a linear combination of (1,-4)

but is ((2,1),(1,3)) a linear combination?

if not, then maybe it is not a proof system

[full forum]

@storm tusk Has your question been resolved?

[thin flint]

other way around

1, -4 has to be a linear combination of the set that spans U1 and of the set that spans U2

not other way around

[storm tusk]

oh okay how can I write that
maybe

x * 1 + y * -4 = ?

and then I turn them into equations

[thin flint]

well linear combination means

(x, y) = s (2, 1) + r (1, 3)

[storm tusk]

oh

so x needs to be 1 and y -4

[thin flint]

if you want to find out if a vector is a linear combination of these then you put in x and y of the vector

and find out if it gives you values for s and r

if it isn't

it will give you some error

something like 1 = 2

[storm tusk]

ooooh okay

[thin flint]

or /0

[storm tusk]

thank you, this sounds good

[thin flint]

something that says it is not possible

[storm tusk]

.close

[full forum]

Channel closed

Closed by @storm tusk

Use .reopen if this was a mistake.

[storm tusk]

.reopen

[full forum]

✅

[storm tusk]

okay I have now these equations:

2s + r = 1
s + 3r = -4

is this correct?

s = -0,15
r = 9/7

but it doesn't give the vector (1,-4)

i feel like the given statement is wrong but I got a s and r

s = 7/5, r = -9/5

[thin flint]

that's the correct one

i got that too

[storm tusk]

oooh okay

[thin flint]

wait

[storm tusk]

so I can say {(1,-4)} is a proof system of U1 ∩ U2

[thin flint]

i just noticed

[storm tusk]

oh

[thin flint]

dummy me

(2, 1) and (1,3) span R^2

[storm tusk]

okay that means hm.. {(1,-4)} spans also IR2 i think

[thin flint]

no because you have U1

not just U2

[storm tusk]

oh so we have to have another equation?

[thin flint]

no since U1 = R^2

U1 interset U2 = U2

sorry

U2 = R62

R^2

and U1 intersect U2 = U1

since U1 is a subspace of U2

and since the intersection of U1 and U2 = U1 it means any vector that spans U1 spans the intersection

[storm tusk]

oh does it mean any linear combination of U1 is also possible with U1 intersect U2?

so U1 = U1 intersection U2

[thin flint]

i cannot believe i did not see that sooner

smh

right so if you want to prove that 1, -4 spans U1 intersect U2

you only have to prove it spans U1

because the intersection is equal to U1

[storm tusk]

(1,-4) * -2 = (-2,8) so it spans U1?

[thin flint]

yeah

basically

[storm tusk]

okay thank you for helping me!

.close

[full forum]

Channel closed

Closed by @storm tusk

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[wraith river]

Can someone explain why it's 45-45t

i get that 45-45(1) = 0 but

Why do we want it to be 0

[sacred yarrow]

Have you found its function?

[wraith river]

No whats the function ?

[sacred yarrow]

For example, like the function that tells in 3 second, A moves 3 meters

[wraith river]

Idk how to set that up

[sacred yarrow]

I see

How many kilometers does the former train moves after a minute?

[wraith river]

One minute

It goes one km

[sacred yarrow]

yes

[wraith river]

yeah

[lime ether]

so you should create a function that relates the distance between the two trains

and then solve for a minimum

[wraith river]

so I do the distance formula

[full forum]

@wraith river Has your question been resolved?

Channel closed

Closed by @wraith river

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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]

Can someone draw a representation of a right triangle, a calc like: height / hypotenuse?

[steel cove]

what

i can draw a right triangle

oh you mean trig functions visualized?

i actually has a desmos graph for this

[steel cove]

.

[torn jolt]

Can i see it?

[steel cove]

https://www.desmos.com/calculator/jldf79msrk

sin is opposite/hypotenuse

cos is adjacent over hypotenuse

tan is opposite over adjacent

secant is hypotenuse over adjacent

csc is hypotenuse over opposite

cot is adjacent over opposite

[torn jolt]

But like

Isn't cos the base and sin the thing that goes with the height?

Wait whaaat?...

Okay

So

In this example

Where is our theta?

My drawing was this

Green = Hypotenuse
Blue = Height
Red = Cos

I just wanted to understand what we get when we divide height by hipotenuse

That's it

[steel cove]

our theta starts when you cross the positive y line

and it keep increasing clockwise

and the cool thing about the unit circle definition of trig functions

is that they can go into the negatives

and they are defined past 90 degrees

[steel cove]

sin(theta)

where theta is red green meeting angle

[grim skiff]

Blue = Height Red = Cos
You don't want to memorize it like this, because the trig functions are defined based on where the angle is located

[torn jolt]

Ohhh

So sin and cos can also change?

[grim skiff]

If theta was here, then the red is the adjacent side, and the blue is the opposite side in perspective of theta

And cos is defined as adjacent over hypotenuse, while sine is defined as opposite over hypotenuse

[torn jolt]

Ohh

OHHH

[grim skiff]

If theta was here, then red is opposite and blue is adjacent

[torn jolt]

So cos and sin are together with angle?

I know about opp and adj

Okay

So...

With cos we can get the angle with the hypotenuse and the height

No

We get the hypotenuse and the height with the angle?

Yes!?

[grim skiff]

It depends on where theta is located

[torn jolt]

What if it is on the red line?

[grim skiff]

This one?

[torn jolt]

Yeah

[steel cove]

https://www.desmos.com/calculator/pnsnhdhlhe i made an easier to understand version

with only 2 of the

functions

theta is the middle angle

kind of

sort of

[grim skiff]

If you wanted to find the value of the angle, use what you know. You have two given values, the one in blue and the one in green. In perspective of theta, is the blue side opposite, adjacent, or hypotenuse?

[torn jolt]

So from origin to a point?

[torn jolt]

Adjacent

[grim skiff]

No

[torn jolt]

Wait what?

[grim skiff]

This image here

[torn jolt]

Yeah, the adjacent and the hypotenuse

[steel cove]

the black orange angle

[torn jolt]

The opposite being blue

[grim skiff]

Is the blue side opposite or adjacent or the hypotenuse from theta?

[torn jolt]

Opposite

Ohh

I read it wrong before

[grim skiff]

What about the green side?

[torn jolt]

Hypotenuse

And the other one adjacent

[grim skiff]

We don't care about the red side because you don't know the value of it

You only focus with what you know

You know the value of the blue side and the green side only

Since you just said that the blue side is opposite from theta and the green is the hypotenuse, what trig ratio can you use?

[torn jolt]

I can use the soh

?

[grim skiff]

Yes

[torn jolt]

Yeah okay... Lemme think a bit

But then we like

Just calc opp / hyp, or we use like, sin(opp / hyp)?

Oh no

Because sin(opp/hyp) would be an angle that is opp/hyp

Ahh

So, 15/17 ~= 0,882

We got the other one

[grim skiff]

Do you know the concept of inverse trig functions?

[torn jolt]

I know tan, atan and atan2 only..

[grim skiff]

This is wrong

If you wanted to find the red side, you didn't need to do trig

It's a right triangle

Do you recall the famous equation used for right triangles?

[torn jolt]

17² + 15² = x

[grim skiff]

Not quite that

[torn jolt]

x²

No?

[grim skiff]

What's the equation in general?

[torn jolt]

Equation of what? Which equation?

[grim skiff]

.

[torn jolt]

C² = A² + B²?