help-23

[lavish rivet]

so in this case we put the 3 to the right to solve

[vagrant ice]

yes, we add 3 to both sides
5x/2 - 3 + 3 = 7/2 + 3

[lavish rivet]

sweet, thanks!

Have a great day/night!

.close

[safe radish]

Channel closed

Closed by @lavish rivet

Use .reopen if this was a mistake.

[lavish rivet]

.reopen

[safe radish]

✅

[lavish rivet]

How would I go about solving 5a/3-a=2/3?
I cant seem to get the right answer

[hybrid silo]

Suppose that a=3a/3

And find 5a/3 -3a/3

[lavish rivet]

so it would be 2a/3 = 2/3?

[hybrid silo]

Yeah

[lavish rivet]

Great, thanks for the help!

have a great day/night!

.close

[safe radish]

Channel closed

Closed by @lavish rivet

Use .reopen if this was a mistake.

[safe radish]

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.

[desert pasture]

Prove that $\gcd(a,b) = a \alpha + b \beta$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[desert pasture]

I was thinking of using the well ordering principal here

[solar hazel]

[desert pasture]

Consider the set ${a\alpha + b\beta >0 : a,\alpha, b, \beta \in \Z}$

[indigo bay]

why not use euclid's algorithm

😄

[solar hazel]

what does this mean

[desert pasture]

set of numbers of this form

[desert pasture]

Hmm, doesn;'t that required the extended algorithm>

[solar hazel]

this is just Z

[solar hazel]

also i was replying to this message

[desert pasture]

Not the entirety of $\Z$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[solar hazel]

then what you were trying to write and what you wrote are different

[flat frigate]

Mr bean is not $\R \setminus \Q$

[solar hazel]

well now it's just the set of positive integers

[desert pasture]

At the very least this has an element $|a|$

[solar hazel]

and doesn't parse very well for me

[flat frigate]

Mr bean is not $\R \setminus \Q$

[solar hazel]

do you mean $a$ and $b$ are fixed integers and you want to consider the set ${a\alpha+b\beta: \alpha,\beta\in\bZ}$

[desert pasture]

yeah

[flat frigate]

generating function courtesan

[desert pasture]

or on second thoughts , I know $gcd(a,b) \mid a \land gcd(a,b) \mid b \implies \gcd(a,b) \mid \alpha a + \beta b$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[indigo bay]

@desert pasture

[flat frigate]

>> 20 & 0b111
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[indigo bay]

can I give you a hint

[desert pasture]

yeah

Can't use the extended division algo though

[indigo bay]

so consider the set ax+by with x,y in Z

[desert pasture]

and a,b fixed

[indigo bay]

mhm

and take the intersection with N

I think this set cannot be empty

[desert pasture]

yes, so assuming a<b, it has a least element $|a|$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[indigo bay]

I mean even without assumption

a and b are natural numbers no?

[desert pasture]

(a,b) \in \Z

[indigo bay]

no no x,y in Z

a,b fixed in N

don't we consider gcd to be defined on natural numbers?

[desert pasture]

no, on $\Z$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[indigo bay]

okay then I guess this works

but it has a least element

idk if it has to necessarily be |a|

but my idea for proof doesn't rely on that

let's say it is d = ax + by

now I guess every common factor of a and b also divides d

so we just need to show that d | a and d | b@desert pasture

[flat frigate]

>> 20 & 0b111
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[indigo bay]

word

I think using the divison algorithm

and it's straight forward from here to show d = gcd(a,b)

[desert pasture]

hmm

[indigo bay]

a = dq + r for some q,r with 0 <= r < d

[desert pasture]

yeah

one min

I'm not fully convinced

this just proves that $d \mid ax+by$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[desert pasture]

where $d=gcd(a,b)$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[indigo bay]

well I'm showing

from here

that d | a and d | b

trust trust

follow along a little and you will see

a = dq + r for some q,r with 0 <= r < d

r = a(1-qx) + b(-qy)

this is done by subbing in d = ax+by

but since 1-qx \in Z and -qy \in Z

[desert pasture]

hmm, yeah

[indigo bay]

but hmmm

p sure this implies r= 0

because we chose d to be the minimum

[desert pasture]

oh yeah

right

[indigo bay]

but that means

d | a

[desert pasture]

and similarly we can show $d \mid b$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[indigo bay]

mhm

and then we are done

[desert pasture]

I see

[indigo bay]

math is cool again

yay

[desert pasture]

So just to sumarise

we know that $ { a\alpha+ b \beta > 0 : a,b,\alpha, \beta \in \Z }$ We now let $d$ be the smallest element in the set . So we now know let $d = a \alpha + b\beta $.

[flat frigate]

Mr bean is not $\R \setminus \Q$

[desert pasture]

I know try to show $d \mid a\land d \mid b$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[desert pasture]

$a = dq+r ; 0 \leq r < d$

[flat frigate]

Mr bean is not $\R \setminus \Q$

[desert pasture]

how did you get qy?

[indigo bay]

d = ax + by

no?

we get like

a = (ax+by)q + r

a = aqx + bqy + r

r = a - aqx -bqy

@desert pasture

[flat frigate]

>> 20 & 0b111
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[desert pasture]

hmm

one minute

I'm really sorry, ENT is my weak point

wait what

how

[indigo bay]

hmm

which step

[desert pasture]

This

[indigo bay]

oh a = dq + r

and we know that d = ax + by

[desert pasture]

Ah yes

my abd

• bad

got it

thanks

.close

[safe radish]

Channel closed

Closed by @desert pasture

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.

[nocturne condor]

hi

[nocturne condor]

how did the sign in the denominator change

or is my teacher wrong?

[light shoal]

looks wrong

[nocturne condor]

so it should be positive right??!!!

[light shoal]

i would expect to see 1 + 2(1)(1) in the denom yea

[nocturne condor]

alright thanks

.close

[safe radish]

Channel closed

Closed by @nocturne condor

Use .reopen if this was a mistake.

[safe radish]

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.

[polar fjord]

Laura runs a food bank. On Monday she gave away 1/4 of her stock of flour. On Tuesday she gave away 1/3 of what was left from Monday. On Wednesday she gave away 1/2 of what was left from Tuesday. If she started with 1000 pounds of flour, how much was left by the end of Wednesday?

can someone explain me the question?

[brave wolf]

explain the question itself or explain how to solve it?

[safe radish]

@polar fjord Has your question been resolved?

[polar fjord]

can i know both?

English is my second language

[safe radish]

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.

[modern bloom]

Do the global extrema occur if f'(x)=0?

[light shoal]

depends

[brave wolf]

No

not in general

[peak estuary]

|x|

[light shoal]

if f is differentiable everywhere on the real line then the global extrema will occur at a point where f'(x) = 0, but there can be other points with f'(x) = 0 that are not global extrema

[brave wolf]

and also it's not iff

f'(x) = 0 isn't sufficient to conclude that x is a global extrema

[light shoal]

if the domain is bounded, the global extrema can occur at an endpoint even if f'(x) is nonzero

[brave wolf]

it can be a saddle point or a local extrema

[median vigil]

extrema can occur at

• f'(x) = 0
• f not differentiable
• endpoints of domain

[modern bloom]

Can extrema be boundary point? Is boundary point = endpoints of the domain?

[light shoal]

yes, say for example f(x) = x on the domain [1,2]

global min is at x=1, global max at x=2

[modern bloom]

If x0 is the extrema and f'(x0) exists, then f'(x0) may be equal to 0 or may not?

[light shoal]

f'(x0) will be zero unless you're considering the one-sided derivatives at the endpoints of the domain

[modern bloom]

I mean like if the domain is restricted, not the whole real line

@light shoal

[light shoal]

yea what i said above holds whether the domain is restricted or not
if the (two-sided) derivative exists at x0 and there is an extremum at x0, then f'(x0) = 0

[modern bloom]

could you give a concrete example that one side derivative which isn't 0?

[lean otter]

at 0 in sqrt x

[modern bloom]

Wait isn't the derivative still 0 at 0?

[lean otter]

no it tends to inf

[modern bloom]

Oooh right

Thx!

.close

[safe radish]

Channel closed

Closed by @modern bloom

Use .reopen if this was a mistake.

[safe radish]

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.

[vapid hull]

Can someone explain this simplification process?

[bitter vector]

first step multiply 3/2 to top and bottom

second step multiply top and bottom by sqaure root 2

[vapid hull]

How is 2 sqroot2 x -2/3 = 3 sqroot2

sorry 3-2*

3/2*

Ohh

Nvm ty

.close

[safe radish]

Channel closed

Closed by @vapid hull

Use .reopen if this was a mistake.

[safe radish]

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.

[light crater]

please help with how to get from step 1 to step 2

[primal parcel]

;

.close

[gray dirge]

Does πr mean π*r?

[strange surge]

yes

[gray dirge]

Thanks

[winged wing]

I have no idea. How to approach this qns.!

[rich elm]

ask desmos

no one knows what that is

bots broken rn sadly

[winged wing]

I am not getting it. This server is in a glitch ig

[pine horizon]

$\frac{df(x)}{dg(x)} = \frac{f'(x)}{g'(x)}$

[flat frigate]

Astar777

Nethuja-Gunawardane

[fiery vine]

Is this possible to graph in a Cartesian plane?

[glass panther]

yeah, as long as you get the values for x and y, you can plot that

[fiery vine]

I get imaginary numbers
Like 4i and 2i

[glass panther]

ohhh

[fiery vine]

Is this an exponential equation?

[glass panther]

i thought that was quadratic equation

[rich elm]

is it not a quadratic

y^2-4x=0

[fiery vine]

do you think this makes a parabola?

[glass panther]

you cant plot imaginary numbers in a Cartesian coordinates

[rich elm]

well not a 'function' per say

[rich elm]

yes u can

argand

oh

[glass panther]

i mean in Cartesian

[rich elm]

its a quadratic relation in y instead of x

yes

[feral talon]

am i supposed to ask questions here?

[rich elm]

the easiest way to think about it is x=1/4y^2

[ripe tide]

i think its bugged

[rich elm]

the bot is currently broken

it started breaking down 30mins ago i think

[feral talon]

alright

[rich elm]

so the channels are a bit messy right now

[glass panther]

ik

[fiery vine]

Save me bots

[rich elm]

this doesnt really involve imaginary numbers tho

what you are graphing at least

think of it as an inverse relation of 4y=x^2 if you are really struggling

[feral talon]

what year are you in windy?

[glass panther]

3rd year high school

[feral talon]

Oh okay

Thought you were 4th year

[harsh sage]

is this channel occupied

[glass panther]

why?

[feral talon]

Nothing, just assumed it

[lean otter]

hello

where do i get help

[glass panther]

oh

[glass panther]

bots are bugged i think

[vivid hedge]

is my proof fine?

[lean otter]

HELP!

[vivid hedge]

its occupied

[feral talon]

i haven't seen this yet

[lean otter]

ok?

[feral talon]

What lesson is that now?

Ah imean topic

[lean otter]

how does log4 8 work

[fiery vine]

Answer is 4 but no idea how the calculator got it

[feral talon]

what year are u in?

[lean otter]

10

im in japan obviously (bc of language)

[feral talon]

Yeah i know

[lilac sun]

How do u evaluate the limit of (1+1/x)^x algebraically

[upbeat sparrow]

HEY

[modest harbor]

Let Ω ⊂ R^2 be the open subset in the first quadrant bounded by y = 0, y = x, xy = 1 and x^2 − y^2 = 1. Evaluate the integral (x^2+y^2) dA using the change of variables u = xy , v = x^2 − y^2.

How to solve this problem

I have tried to express x^2+y^2 in terms of u and v

[upbeat sparrow]

why are the bots b roken

[lilac sun]

Lmao

[modest harbor]

hi

testing

wtf

[hard crest]

i think something about discord might be slightly broken?

but yes the channel bot is broken currently

[upbeat sparrow]

Gg

[past hearth]

Is this chain of logic correct

fn converges pointwise to f

If it were to converge uniformly then it would converge uniformly to f as well

[past hearth]

<@&286206848099549185>

[serene aspen]

if i do infinity * 0 why is it undefined? wouldnt it be 0

oh

huh isn thtis available

its broken?

[ripe tide]

yup

[glass ether]

Can't see shit

[tender stirrup]

Hello there

[glass ether]

Oh bot working agaib

[tender stirrup]

Oh wait was this occupied?

Sorry

.close

[safe radish]

Channel closed

Closed by @tender stirrup

Use .reopen if this was a mistake.

[safe radish]

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.

[soft matrix]

i don't quite get what you are trying to ask bc radius of curvature for any curvilinear trajectory is defined as radius of the circle made at that instant

[rich elm]

ik this isn't correlated to this one but did u ever find your n-th derivative aerlier

i couldn't figure it out after an hour tbh

it was up to x^20 right

wait

is there a reason they write tanpi/4

i feel like thats meant to be a hint somehow

oh not

[soft matrix]

ic mb

[rich elm]

ok im goofy af, my fault

[flat frigate]

Scoria

Scoria

[safe radish]

@modern bloom Has your question been resolved?

Channel closed

Closed by @modern bloom

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.

[mossy ridge]

There an n bags and in the i'th bag(i€[0,n]) there are i black blacks and 2 white balls. If he keeps picking up 2 balls from every bag find the probability that he gets the 2 white balls(from 1 individual bag) from atleast 1 bag

[safe radish]

@mossy ridge Has your question been resolved?

[safe radish]

@mossy ridge Has your question been resolved?

[safe radish]

@mossy ridge Has your question been resolved?

[safe radish]

@mossy ridge Has your question been resolved?

[turbid raven]

@mossy ridge what have you tried?

!status

[safe radish]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I 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

[safe radish]

@mossy ridge Has your question been resolved?

[safe radish]

Channel closed

Closed by @mossy ridge

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.

[spring dagger]

What is the expected value of the product of 2 card draws from a deck that has six cards 1-6 without replacement? Compare the expected value with the product of 2 dice rolls.

I managed to solve it very manually but I'm wondering if theres a faster way or intuition especially for the second one that doesnt involve having to calculate everything out

[safe radish]

@spring dagger Has your question been resolved?

[spring dagger]

https://stats.stackexchange.com/questions/586385/sample-two-numbers-from-1-to-10-maximize-the-expected-product

finding very similar questins

.close

[safe radish]

Channel closed

Closed by @spring dagger

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.

[fierce mortar]

hi

[fierce mortar]

@safe radish

[safe radish]

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

[fierce mortar]

!commands

!command

!status

[safe radish]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I 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

[fierce mortar]

1

😭

[safe radish]

@fierce mortar Has your question been resolved?

[safe radish]

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.

[regal ore]

So I was asked to solve this integral from one of my friends who is in Calculus

[regal ore]

$f(x)=\int_{\frac{1}{2}x\pi}^{16sin(\pi x)}(25cos(\frac{9t^x}{2t^2x^{sin(t\pi)}}))dt$

[flat frigate]

Toast

[regal ore]

I did complete a Calculus course, but my memory is a bit foggy due to me focusing on other parts of my life

How would I go into simplifying this integral?

[plucky elk]

Plug into Wolfram alpha

[regal ore]

okay thanks

.close

[safe radish]

Channel closed

Closed by @regal ore

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

part b

still learning how to do epsilon delta properly 😄

but is this okay ?

[lean otter]

"Assuming that the limit exists at (0,0) we have L as 0.
To prove, by epsilon delta"

[lean otter]

Hence proved,(for every epsilon there exists a delta for which [f(x,y)-f(0,0)] < epsilon) limit exists at (0,0) and is equal to 0

<@&286206848099549185>

.close

[safe radish]

Channel closed

Closed by @hidden lily

Use .reopen if this was a mistake.

[safe radish]

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.

[fringe heath]

anyone here?

[safe radish]

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

@fringe heath Has your question been resolved?

[covert yoke]

No one here but us chickens

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[magic wadi]

i'm trying to solve this integral, i've tried changing the order of integration into both the yz, zy, xz, and zx plane but i can't seem to get rid of the cos(2z^2) integral is there a good approach to solve this

[magic wadi]

or is there an elegant way to solve cos(2z^2) integral

[safe radish]

@magic wadi Has your question been resolved?

Channel closed

Closed by @magic wadi

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.

[long shore]

So -2log(x) = log(x^-2) right? But desmos shows different graphs, is this because of the domain of the function changing as we convert it?

[long shore]

,tex $ log(x^{n}) = n \cdot log(x)$

[flat frigate]

suds

[median vigil]

strictly speaking if n is even then
log(x^n) = n log|x|

[long shore]

how come desmos shows different graphs?

[median vigil]

because log(x^-2) = -2 log|x| which has a larger domain than -2 log(x)

[long shore]

ah because x cannot be negative (for the basic log(x))/cant cross the asymptote but log|x| gives the mirrored version for the values across the asymptote

i dont think I will have an even valued power in the exam because we haven't covered this but if i got log(x^-2) which graph would i draw?

because that log rule is kinda fake then

because they teach is as log(x^n) = n log(x) which isn't true

[median vigil]

well if you don't care about preserving domain then it's true in all cases. the only additional case is in adding the absolute value when n is even

they really should teach that explicitly, though

[frozen marlin]

\log

[flat frigate]

ren

[safe radish]

@long shore Has your question been resolved?

[long shore]

oh well, its my last school exam ever, ill just keep it in mind for the future

.close

[safe radish]

Channel closed

Closed by @long shore

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.

[vapid hull]

Help me, I found the derivative what to do next, help me complete this problem

[vapid hull]

Work so far

[flat frigate]

krypton

[vapid hull]

Where does the y go?

Why does it become yy0/b^2

[wispy monolith]

Where did you get this?

[safe radish]

@vapid hull Has your question been resolved?

[safe radish]

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.

[timber depot]

How to solve this without approximation?

[safe radish]

@timber depot Has your question been resolved?

[timber depot]

No

[lean otter]

Hi

I would recommend making the bases the same

[timber depot]

yea i got log5(30)^2 - log5(150) * log5(6)

then (1+log5(6))^2 - ((2+log5(6)) * log5(6))

and now im stuck

if i use (a+b)^2
(log5(6))^2 + 2log5(6) + 1 - ((2+log5(6)) * log5(6))

ok I got it

.close

[safe radish]

Channel closed

Closed by @timber depot

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.

[glass ether]

How do I factorize (4y+12y²-3)⁵

[vagrant ice]

try (4y ......)(3y ...... )

hmmmm

[glass ether]

Or is it not possible

[vagrant ice]

that quadratic looks unfactorisable

[glass ether]

Ok thanks

[vagrant ice]

,w roots 12y^2 + 4y - 3

[flat frigate]

Results provided by WolframAlpha

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

Requested by sooouth.

[glass ether]

.close

[safe radish]

Channel closed

Closed by @glass ether

Use .reopen if this was a mistake.

[vagrant ice]

it is factorable in the irrational numbers

at least the discriminant wasn't negative

[safe radish]

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.

[obsidian vine]

need help, im so stuck

[flat frigate]

ren

[obsidian vine]

yes

but still i dont get the expression

pls help <@&286206848099549185>

[safe radish]

@obsidian vine Has your question been resolved?

[desert belfry]

There is no addition or subtraction in the original expression. You're supposed to multiply the brackets in the third expression, not do whatever happened there.

[safe radish]

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.

[woven zodiac]

help its off center

[woven zodiac]

do i have to redo the whole thing

[junior heron]

its offcenter because of the constants you added to the functions so yeah you have to rewrite

if you want it to be centered in the origin you can't add constants to the functions that pass through the center

[woven zodiac]

😦

.close

[safe radish]

Channel closed

Closed by @woven zodiac

Use .reopen if this was a mistake.

[covert yoke]

@woven zodiac add a +a to all of the lines

Then add a slider for a, and adjust it up and down until you get it where you want it

[safe radish]

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.

[magic patio]

is my answer wrong if so how to do it

[safe radish]

@magic patio Has your question been resolved?

[safe radish]

@magic patio Has your question been resolved?

[valid olive]

Can you show your calculations

[magic patio]

Yes wait

r = 2 ((5000/2500)^1/20-1)

500/2500 = 2

(2)^1/20 = 1.03526

1.03526 -1 = 0.03526

0.03526 x 2

0.07052 @valid olive

7.05

[magic patio]

<@&286206848099549185>

[valid olive]

Try writing 7

[valid olive]

Because this is correct

[magic patio]

just 7?

is 7.05 correct?

[valid olive]

Is 7.05 not correct ?

[magic patio]

no im just asking if 7.05 correct or not

[valid olive]

So you yourself don't know the answer

It's correct then

[magic patio]

oh okay thank u

.close

[safe radish]

Channel closed

Closed by @magic patio

Use .reopen if this was a mistake.

[safe radish]

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.

[coral dagger]

Why do we use the sum of cubes formula on one, but just double down on the factoring on the first 1

[agile vigil]

Well the first one isn’t a difference of cubes

Remember the first step is to factor out gcf

[coral dagger]

Ohhh because da 9 yeah?

Ohhh okay I see, I see

[obsidian oracle]

it's best to factor out common factors immediately, plus x^3 - 9x isn't really a difference/sum of cubes

[coral dagger]

Ty

[agile vigil]

Yeah remember to factor out gcf first in this case would be the x

[obsidian oracle]

it's because of the x mostly

[agile vigil]

Then making it a difference it squares

[coral dagger]

Ty ty

[coral dagger]

Yeah, you can look at it like dat too

.solved

[safe radish]

Channel closed

Closed by @coral dagger

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

.

[nova shore]

I know it’s physics, but still am I right in this? a is the gradient, so by calculating the tendency line trough liniear regression we get and then can determine R.

[plucky elk]

not really enough context to help you

if you're doing linear regression, what's your data and what are you trying to solve for

[safe radish]

@nova shore Has your question been resolved?

[nova shore]

We lover a constant resistor into some water and connect to power supply and measure different levels of current and the temperature change of the water. As the resistor gets hotter so does the water. We we want to determine the resistance of the resistor through the following:

It’s Joules Law where we combine the formulas:

HeatEnergy=Current^2•Resistance•time and HeatEnergy=m_v(massOfWater)•c_v(specificHeatCapacityWater)•TemperatureIncrease

And we want to solve for R(Resistance) which we can do once we have measured a number og TemperatureIncreases for each Current^2. So TemperatureIncrease as a function of Current^2. From these two sizes we plit a linear regression line which gives us a gradient which I call “a”. Since TemperatureIncrease is on the y-axis and Current^2 is on the x-axis then a= TemperatureIncrease/Current^2

And so we can calculate the Resistance using the gradient a: R=a•(m_v•c_v)/t

[nova shore]

^

[safe radish]

@nova shore Has your question been resolved?

[safe radish]

@nova shore Has your question been resolved?

[safe radish]

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.

[little sable]

could someone check this answer for me please? Im not sure if this answer is correct cause my textbook gets stuff wrong relatively often and I'm looking at my work and everything looks right

[icy lance]

,w expand 5(x+4)(x-2)^3

[flat frigate]

Results provided by WolframAlpha

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

Requested by aldrnari_

[little sable]

No way

so I was right?

[icy lance]

no

you wrote the wrong sign on the 160

in your equation its +
in reality it was -

[little sable]

it says in the problem that f(0) should be equal to 160

[icy lance]

im aware

but you have a sign issue

i was looking at the wrong term for it though

[little sable]

where'd I first write it wrong? I can't find it

[icy lance]

the issue is the x^4 coefficient

everything else in your work is fine

[icy lance]

as in this is all fine

[icy lance]

this isnt

[little sable]

The digital image is the textbook answer

They tricked me

[icy lance]

,w factorise 5x^4+10x^3+60x^2-200x+160

[flat frigate]

Results provided by WolframAlpha

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

Requested by aldrnari_

[icy lance]

,w factorise -5x^4+10x^3+60x^2-200x+160

[flat frigate]

Results provided by WolframAlpha

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

Requested by aldrnari_

[icy lance]

the digital answer doesnt hold up

[little sable]

!! thank you sm

[icy lance]

has a sign issue

[little sable]

textbook does this a lot so if im wrong but cant figure out why i always double check to make sure its not a wrong answer in the book

[icy lance]

does unfortunately happen

[little sable]

i usually dont mind but with word problems i cant just throw them into symbolab or w/e to check them

[safe radish]

@little sable Has your question been resolved?

Channel closed

Closed by @little sable

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.

[gentle tendon]

i know we're probably supposed to do ax^2 + sin x = pi

and 2x - c = pi

but im not sure where to go from there

[cloud warren]

in order for the function to be differentiable everywhere the derivative of f(π) must exist

[gentle tendon]

yep

[cloud warren]

f(π) is equal to a* π^2

[gentle tendon]

huh

since differentialibility implies continuity wouldnt we have to solve for ax^2 + sin x = pi first

[cloud warren]

why do they have to equal π?

[gentle tendon]

for continuity

both of the equations

[cloud warren]

when you talk about continuity you only care about the limits being equal

and the equal limit being equal to the real value

[gentle tendon]

oh huh

[gentle tendon]

wait so how did u get this

where did π^2 come from

[cloud warren]

you take the side of f(x) where π belongs to

so you take f(x) = ax^2 + sinx and just replace x=π

[gentle tendon]

oh wait i see

yeah

okay so

u do the same for the second equation too

right

[cloud warren]

then you take the limits

and you have to say that they are equal

the limits around π

[gentle tendon]

lim x -> π (aπ^2) = lim x->π (2π - c)

?

i think

[cloud warren]

you forgot sinx but sinπ is equal to 0 so it doesnt really matter

but yes this is what you have to do

finally you have an equation aπ^2 -2π + c = 0

and you find the perfect much from the multiple choices

[gentle tendon]

so just plug it in

[cloud warren]

you mean sinx?

[gentle tendon]

no like plug in the answer choices

into that equation

[cloud warren]

actually since you are given some choices you have to find the one that fits

[gentle tendon]

that takes so long 😭

ty for the help though

.close

[safe radish]

Channel closed

Closed by @gentle tendon

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.

[waxen carbon]

Hi, do you understand how to do it?

[safe radish]

@obsidian vine Has your question been resolved?

[obsidian vine]

nope 😢

<@&286206848099549185>

[plucky elk]

...

isn't this the same problem you had before

don't you have like a whole page of work

[obsidian vine]

i dont get what u meant with the exponent thing of
making 2^2

[plucky elk]

just show the work again

[plucky elk]

,rotate

[plucky elk]

do you know how to "combine like terms"

like $a^m b^n a^r = a^{m+r} b^n$

[obsidian vine]

yes

[flat frigate]

riemann

[plucky elk]

yea do that with 2 and x as the bases

[obsidian vine]

so like for example in the numerator (-2x^6/35-22/35)?

@plucky elk

[plucky elk]

don't know where -22/35 came from

,tex .exp rules

[flat frigate]

riemann

[plucky elk]

review those again and apply them

[obsidian vine]

-66/70

[plucky elk]

the base of a doesn't combine with base b

[obsidian vine]

oh so i add -2^6/35 + 2^9/35?

[plucky elk]

you add the exponents

right side

you're multiplying the two terms 2^m * 2^r

[obsidian vine]

but -2 and 2 arent the same right so ill multiply it? @plucky elk

[plucky elk]

-2 = (-1) * 2

https://www.mathsisfun.com/operation-order-pemdas.html

-2^m = (-1) * 2^m

[obsidian vine]

,rotate

[obsidian vine]

@plucky elk

[plucky elk]

you can keep going

[obsidian vine]

what abt the negative 1? does it stay there? or do i multiply it to the numerate at the end?

[plucky elk]

-1 stays

[obsidian vine]

@plucky elk

[plucky elk]

oh the -1 should have also been raised to the 6th power earlier

[obsidian vine]

so it becomes a positive right?

[plucky elk]

yes

[safe radish]

@obsidian vine Has your question been resolved?

[waxen carbon]

do u still need hlep

[safe radish]

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.

[quaint aspen]

Pls i dont know wht indid wrong

[quaint aspen]

Supposed to find the particular solution

[safe radish]

@quaint aspen Has your question been resolved?

[quaint aspen]

<@&286206848099549185>

[placid pulsar]

I think you're good, you just need to find B right?

[quaint aspen]

ye but wont b be 0

you

yo

@placid pulsar

[placid pulsar]

The coefficient of e^5t is 0, you need to collect coefficients on the left

There are two terms on the left with e^5t (and no other t)

[quaint aspen]

ok thx you soo much many god bless you

.close

[safe radish]

Channel closed

Closed by @quaint aspen

Use .reopen if this was a mistake.

[safe radish]

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.

[twilit mauve]

can someone please help me with this?

[safe radish]

@twilit mauve Has your question been resolved?

[compact herald]

do you know the general equation of a straight line?

[twilit mauve]

no not really

[compact herald]

okay

so its

$$ y = mx + c $$

[flat frigate]

seren

[compact herald]

now you have 5 values given

lets take two of them

(3,6) and (4,4)

you can see that those are points that are on the graph, right

the dotted ones

[twilit mauve]

yes

[compact herald]

so (x,y) = (3,6)

so x = 3 and y = 6

[compact herald]

plug that in into this equation

you get

$$ 6 = 3m + c $$

makes sense?

[twilit mauve]

kind of

[flat frigate]

seren

[compact herald]

okay

now plug in the other equation

(x,y) = (4,4)

so you get

$$ 4 = 4m + c $$

[flat frigate]

seren

[compact herald]

you have 2 equations and 2 variables, you can solve m and c here

with those you have your final equation

[twilit mauve]

i still dont understand im sorry

.close

[safe radish]

Channel closed

Closed by @twilit mauve

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.

[dusky ridge]

Does anyone know how i can determine what elementary operations are needed to get from A to B ?

[dusky ridge]

been looking at it for an hour now

: /

.close

[safe radish]

Channel closed

Closed by @dusky ridge

Use .reopen if this was a mistake.

[safe radish]

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.

[fickle rapids]

how to do c?

[safe radish]

@fickle rapids Has your question been resolved?

[fickle rapids]

<@&286206848099549185>

[fickle rapids]

<@&286206848099549185>

[safe radish]

@fickle rapids Has your question been resolved?

[safe radish]

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.

[rotund anvil]

me and my friend are reviewing before a test, and we've been stuck on this question. its:
can we please get some help? we end up getting 2 different answers for M so we're really confused

[severe pond]

if it has those factors what are its zeros

🤔

[weary socket]

Hi, im also working on this problem with @rotund anvil right now

i have no idea

30 works for f(2) but 45 works for f(1/3)

[rotund anvil]

zeros are at x = 1/3, x = 2

We know we have to sub in the zeroes into the function and then isolate for m but we end up with 30 and 45

[weary socket]

knief please

come back

please

please man i need this

i need this so bad

[severe pond]

hi

my bad

[weary socket]

god bless you

i dond understand

[severe pond]

indeed

so let x = those values

for f(x)

to find m

because 0 = …

[weary socket]

we made f(2) and f(1/3) equal to each other

and solved for m algebraicly but

for f(2) when m is 30 its 0

but for f(1//3) when m is 45 its 0

[severe pond]

$f(x) = 18x^3 + mx^2 - 11x - 2$

[flat frigate]

knief

[weary socket]

wizardly

[severe pond]

$f(2) = 144 + 4m - 22 - 2$

[flat frigate]

knief

[severe pond]

120 + 4m = 0

m = -30

[weary socket]

yeah but then it does not work for f(1/3)

its not zero

[severe pond]

lets see

[weary socket]

im so perplexed

can m be more than one thing for either f(2) or f(1/3)?

becasue x is constant in both of those and m is the only changing value, so if 30 and 45 are both respectively correct

then is this just a flawed question?

knief i need you

[severe pond]

ok i think we should try a different approach i guess

we can try building the polynomial maybe

(3x-1)(-2x+4) = -6x^2 + 12x + 2x - 4 = -6x^2 + 14x - 4

what am i missing??

if those are factors then both values should satisfy the equation f(x) = 0

[rotund anvil]

so is it just not possible?

[weary socket]

yeah thats what i was thinking

this is just not solveable

question was written wrong

we're not givven anything else btw, its just that

[severe pond]

yea i’m just confused because why would it be posed as if it were

did i do the arithmetic wrong?

[weary socket]

nope, and im almost sure that it can not be anything than 30 or 45 for either of the factors

[rotund anvil]

^

[weary socket]

nothing else works

[severe pond]

nah m is definitely -30 for f(2)

[weary socket]

-30?

[severe pond]

and it’s 45 for f(1/3)

[severe pond]

yea

[rotund anvil]

144 -22 -2 + 4m

[weary socket]

ohhh yeah

[rotund anvil]

120 + 4m
m = -120/4 = -30

but its still different values for m

thank you for laying us to rest knief, we have been stuck on this question for too long

[severe pond]

yea unless i’m stupid this is just inconsistent

factors are definitely p(x) = (something)(another thing)(another thing)…

[weary socket]

this is two hours of my life i will never get back

i thank you knief

[rotund anvil]

tysm knief

[weary socket]

you ended the suffering

[severe pond]

you’re welcome

i guess

[weary socket]

god bless

[rotund anvil]

.close

[safe radish]

Channel closed

Closed by @rotund anvil

Use .reopen if this was a mistake.

[safe radish]

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.

[arctic canopy]

what do i do now

if the sum starts at n=1 isnt it undefined?

<@&286206848099549185>

[safe radish]

@arctic canopy Has your question been resolved?

[arctic canopy]

<@&286206848099549185>

come on bruh

im like 1/5 in questions being answered

[safe radish]

@arctic canopy Has your question been resolved?

[rich elm]

yeah it is undefined

i think its a mistake

[arctic canopy]

i still dont really understand the next step tho

[rich elm]

i mean the quesiton is asking you to show convergence, not really find the summation value ig

so maybe start with the next integer with 2

[arctic canopy]

it says to find the partial sum formula tho

[rich elm]

u can split the summation

in particular

i recommend u to write out a few terms and even better if the word 'telescoping' means anything to you

intent here is to try to 'cancel' out some fractions

[arctic canopy]

yeah ik its supposed to telescope but i dont get how to show that

i just plug in values from 2 and up?

[rich elm]

can u think of a way to stagnate the terms

looking at the fraction denominator

we have (n-1), n, (n+1)

lets try to stagnate the summation of each term so that the denominator is equal

[arctic canopy]

wait wdym of each term

treat them as separate sums?

[rich elm]

you know how u can write $\sum (a + b + c)$ as $\sum a + \sum b + \sum c$

[flat frigate]

Dootud

[arctic canopy]

yes

[rich elm]

try that

[arctic canopy]

do i move the constants out

[rich elm]

you can

i find it easier with the constants outside

[arctic canopy]

wait what am i even doing

listing terms out from each summation?

[rich elm]

just maybe the first 2 term

and see if you recognise how we can simplify the summation

here, i will write something out to help with

[arctic canopy]

i mean i see the terms are 'shifted'

[rich elm]

yes yes

ok thats really good

can you try to apply a 'phase' shift here?

[arctic canopy]

what

[rich elm]

like for example

we want our $\sum$ terms to line up with where they start right?

[flat frigate]

Dootud

[rich elm]

can you try to apply a transformation idea here to let that happen?

if this idea is foreign, i will try my best to explain it

if not, just try that

[arctic canopy]

i dont get it

[rich elm]

hmm ok how about this

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[arctic canopy]

.reopen

[safe radish]

✅

[arctic canopy]

?

[rich elm]

$\sum_{n=3}^{\infty} \frac{1}{n-1} = \sum_{n=2}^{\infty} \frac{1}{n}$ does this seem reasonable?

oh oops

[flat frigate]

Dootud

[rich elm]

we 'phased' by replacing n-1 with n

they end up representing the same thing

we still have 1/2 + 1/3 + ...

[arctic canopy]

but they start at different values

is that like

ok

[rich elm]

yes im aware but they represent the same thing dont they?

[arctic canopy]

yeah

[rich elm]

can u try to apply that concept for what we have here

i will do one for you, and you try for the other

$\sum_{n=2}^{\infty}\frac{1}{n}=\frac{1}{2} + \sum_{n=3}^{\infty}\frac{1}{n} = \frac{1}{2}+\sum_{n=2}^{\infty}\frac{1}{n+1}$

[flat frigate]

Dootud

[arctic canopy]

so now i do the n-1?

[rich elm]

yes

[arctic canopy]

isnt it just that

[rich elm]

whilst that is a correct shift, can i suggest that you try to phase it towards the denominator of $\frac{1}{n+1}$

[flat frigate]

Dootud

[rich elm]

like i had done here

[arctic canopy]

oh

[rich elm]

we start at n=2 for the summation

but yes its fine

just write out a +1 since n=2 is where we start

using everything we have now, can u try to rewrite your original sums

[arctic canopy]

i thought we just did rewrite

so that its 'in terms of' the n+1

[rich elm]

$\sum_{n=2}^{\infty}\frac{1}{n}=\frac{1}{2} + \sum_{n=3}^{\infty}\frac{1}{n} = \frac{1}{2}+\sum_{n=2}^{\infty}\frac{1}{n+1}$

oh sorry formation is messed up

give me a sec

[flat frigate]

Dootud

[rich elm]

and also now $\sum_{n=2}^{\infty}\frac{1}{n-1}=\frac{1}{1}+\frac{1}{2}+\sum_{n=4}^{\infty}\frac{1}{n-1}\=\frac{1}{1}+\frac{1}{2}+\sum_{n=2}^{\infty}\frac{1}{n+1}$

[arctic canopy]

yes

[flat frigate]

Dootud

[rich elm]

lets sub everything back into our expression we have

so substitute what we have into

$\frac{1}{2}\sum_{n=2}^{\infty}\frac{1}{n+1}+\frac{1}{2}\sum_{n=2}^{\infty}\frac{1}{n-1}-\sum_{n=2}^{\infty}\frac{1}{n}$

[flat frigate]

Dootud

[arctic canopy]

now do i distribute the 1/2 and the negative

[rich elm]

yeah

it should come out pretty nicely

should expect the summation terms to cancel out in the process

[arctic canopy]

i think i messed up then

wait no

hold up

1/4

[arctic canopy]

so going back to the original question, what did i just do

[rich elm]

yeah dats right

[arctic canopy]

what was the nth partial sum formula

and what is the 1/4

[rich elm]

nth partial sum formula can be found in a few ways

sometimes u can just write out what happens if we are summing to n =2, n = 3 etc.

[rich elm]

1/4 is what the entire summation equals to

or essentially, the summation converges to 1/4

this in its own way shows convergence as you proved as you keep summing, u arrive at 1/4

[arctic canopy]

so 1/4 is Sn

and then technically youd take that limit

to get the sum?

but it just stays 1/4

[rich elm]

1/4th is the sum as you take limit of the summation towards infinite

what we did is technically correct only for n approaching infinite

otherwise we need to change the upper bound of our summation

$\sum_{n=2}^{\infty}\frac{1}{n}=\frac{1}{2} + \sum_{n=3}^{\infty}\frac{1}{n} = \frac{1}{2}+\sum_{n=2}^{\infty}\frac{1}{n+1}$

[flat frigate]

Dootud

[rich elm]

notice how we are summing towards infinite

thats the 'limit' part of it

in reality if we are summing to an actual fixed number

it would look like

$\sum_{n=2}^{k}\frac{1}{n}=\frac{1}{2} + \sum_{n=3}^{k}\frac{1}{n} = \frac{1}{2}+\sum_{n=2}^{k-1}\frac{1}{n+1}$

[flat frigate]

Dootud

[arctic canopy]

so 1/4 is not the nth partial sum?

[rich elm]

1/4th is the total sum of the series

[arctic canopy]

wait yeah ok

[rich elm]

if there exists a fixed sum for the series

that means it has to converge

otherwise it would go towards infinite

[arctic canopy]

so do i have an nth partial sum in my work

bc we were taught that taking the limit of that gives the sum of a series

[rich elm]

yeah technically we did the same thing

ok so we can go back to before we subbed everything back

and just write your expression out as such

its pretty much a same process

i just crunched the algebra if you really wanted an explicit n-th partial sum

$\frac{n^{2}+n-2}{4n(n+1)}$ is what you would get if u didn't apply the phase transformation

[flat frigate]

Dootud

[rich elm]

and just did the nth partial sum formula from there

evaluating the limit for n approaching infinite indeed gives u 1/4 as well

[arctic canopy]

how did u get this

thats more what we learned

[rich elm]

so we just use partial fractions

and write out a few terms to try to find the pattern

using ur partial fraction expression

so write out what summation from 2 to 2 might look like, or from n=2 to 3, and then n=2 to 4 until u notice a pattern

[arctic canopy]

i tried that early on but apparently didnt figure it out

[rich elm]

it is the same principle as we did before but just more based on patter nrecognition in my opinion

the way we did it above is more fool-proof in that it always works

im not very good at explaining how i pick up the patterns for nth partial sum, i just kinda see it from practise ig?

sorry

[arctic canopy]

i mean theres a pattern

[rich elm]

should see the some of the term cancels out every few iterations

for this one, it becomes more obvious the more terms you write out

although it becomes a bit tedious

[arctic canopy]

i see absolutely nothing cancelling

the first term can have odd denominators so how would those ever cancel

[rich elm]

u might find it more evident if u dont expand out the 1/2

and write out a few more terms

[arctic canopy]

yeah this is making no sense

i cant see a pattern

thanks for helping tho

much appreciated

.close

[safe radish]

Channel closed

Closed by @arctic canopy

Use .reopen if this was a mistake.

[safe radish]

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.

[ocean tapir]

how do i graph arg((z-2)/z) = pi/2?

[safe radish]

@ocean tapir Has your question been resolved?

[ocean tapir]

<@&286206848099549185>

[safe radish]

@ocean tapir Has your question been resolved?

[snow robin]

you try to write both z and z-2 in polar form

and then ignore the number in front of the exponent and take the angle = pi/2

[snow robin]

actually nvm i looked more into it and holy shit is adding complex numbers in argument a messy process

[safe radish]

@ocean tapir Has your question been resolved?

[vagrant ice]

HOW WAS EXT 2??

[safe radish]

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.

[exotic charm]

What’s a way of showing a group isn’t cyclic other than checking every element

[safe radish]

@exotic charm Has your question been resolved?

[obsidian oracle]

Take a cyclic group of order n and any p > 1 prime, then the group has exactly p-1 elements of order p if p|n. (and 0 elements of order p otherwise but that's the case for any group)

so if for example you find a group of order 6 with two or more elements of order 2...

[obsidian oracle]

In general taking any d > 1 with d|n, you have at most d-1 elements of order d for a cyclic group

[safe radish]

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.

[cursive kraken]

is it possible to split 1/(a+b)
into 2 fractions?

[safe radish]

Please don't occupy multiple help channels.

[versed isle]

@cursive kraken close a channnel

[versed isle]

yes it is

[cursive kraken]

how can i do so?

[cursive kraken]

mb someone hijacked my original channel

[versed isle]

multiply denominator and numerator with a-b