help-10

[kindred mural]

thank you

.close

[obtuse pebble]

Channel closed

Closed by @kindred mural

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[vocal verge]

Idk whr to start

[obtuse pebble]

@vocal verge Has your question been resolved?

[vocal verge]

.close

[obtuse pebble]

Channel closed

Closed by @vocal verge

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[inner basin]

how is this made?

[inner basin]

i cant grasp this approach... why is 16 denominator of 15?

[timid silo]

can you see what they did to 16x^2 to become x^2

[inner basin]

no.. sadly. also how did -32x become -2x did they kinda take a common here?

[timid silo]

they just divided the entire equation by 16

[inner basin]

ahhh

also can i ask another question?

[timid silo]

sure

[inner basin]

1$ was 320peso and he had some x dollars which resulted in some y1 pesos
Now dollar is 275 peso and he had a y2 pesos. the loss is 31,500 pesos, how many dollars he had

i am unable to comprehend this tbh

[timid silo]

!original

[obtuse pebble]

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.

[inner basin]

this is the original....

i am just trying to make sense of it

[timid silo]

post a pic/screenshot not your text

[inner basin]

1$ = 320 peso
now
1$ = 275 peso

He had x dollar and loss is 31,500 peso how many dollar he had

[timid silo]

forget it, anyways any ideas?

[inner basin]

like what....

[timid silo]

on how to tackle this, what have you tried

[inner basin]

some guy said in class to be something 699$

i dont know how he approached

or smth

like this?

by dividing loss with the loss in the dollar?

[timid silo]

loss is 31,500 the amount he lost after ?

that wording

okay

initially he had 320x then after the exchange rate changed he gets 275x and apparently lost 31500

can you write this in an equation for me

[timid silo]

just subtract 370x from 275x

[inner basin]

yess and by this way he got 31,500

370x - 275x = 31500

[timid silo]

yh

i think thats correct

[inner basin]

95x = 31500

331.579$

thanks!

[timid silo]

320*

[timid silo]

[obtuse pebble]

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

@inner basin Has your question been resolved?

Channel closed

Closed by @inner basin

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[ripe shard]

how do i find the number of 5 digit whole numbers that are divisible by 3

[ripe shard]

all i know is that a number is divisible by three if the sum of the digits are divisble by three

how do i sovle this using perms and coms

[obtuse pebble]

@ripe shard Has your question been resolved?

[drifting wraith]

there's no good way

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[drifting wraith]

.reopen

combinatorially, there's an easy way of another kind

[obtuse pebble]

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.

[timid silo]

hi

[timid silo]

What is this symbol called? What is it used for? How and where can i learn it best?

[cinder lintel]

Its used for summation

Its a sigma

[timid silo]

owkie

[remote lava]

sigma
it means summation

go to yt

n learn

[timid silo]

Owkie @remote lava thanks

[remote lava]

npnp

[timid silo]

Sigma notation for sums? is it the right term for it?

https://www.youtube.com/watch?v=5jwXThH6fg4&ab_channel=KhanAcademy

[remote lava]

yes

yes

[little flint]

yes

[timid silo]

Thanks

.close

[obtuse pebble]

Channel closed

Closed by @reef cairn

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[crude dawn]

heyy

[crude dawn]

how to calculate this

bcus icant just split them and make infinity -infinity right

[timid silo]

there is the obvious way using conjugates and all

but also

,align
\lim_{n\to\infty} \s{n+1} - \s n &= \lim_{n\to\infty} \s{n+1 \c b {-1}} -\s n \ &=\lim_{n\to\infty} \s n -\s n \ &=0

[barren walrus]

1. a) Show by induction that (VEN): 5">1+4n
   b) Deduce that (n € N): 2303+1 <5"

[timid silo]

subtracting by -1 does not affect the convergence behaviour of the limit as it is approaching infinity

[crude dawn]

oo thanks

but it would be right way too

??

oi forgot about the limes

but u know the way...

[fossil crag]

I have never gagged this much in my life 😂

[fossil crag]

this is the only right way yes

[crude dawn]

amazing thx

.close

[obtuse pebble]

Channel closed

Closed by @crude dawn

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.

[digital sorrel]

is this prove correct?

[digital sorrel]

i think it is wrong, but i dunno where

i think it is common sides not given??

but anything except that one

[fossil crag]

why is AB = DC and AC = BD? It might be correct but "prop of quadrilateral" is insufficient

[digital sorrel]

hmm

oh i think two angle are given

can i use a.a.s

[digital sorrel]

what is it then 🤔

<@&286206848099549185>

[wintry swift]

it can be anything else. it is just given that it is a quadrilateral, which can be anything with four corners and four edges.

start with the angles in the the triangles ABC and DBC. what do you know about them?

[obtuse pebble]

@digital sorrel Has your question been resolved?

[digital sorrel]

the angles given?

[wintry swift]

what do YOU know?

[digital sorrel]

🤔abe = edc?

[wintry swift]

you should not ask me, write down, what you do know. (hint: read what is given).

[wintry swift]

what is given about the angle at A in the triangle ABC?
what is given about the angle at C in the triangle ABC?

@digital sorrel

[digital sorrel]

they equals the other one?

[wintry swift]

which other one?

ok, bye.

[obtuse pebble]

@digital sorrel Has your question been resolved?

[obtuse pebble]

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.

[wanton kraken]

need help applying induction to this

[wanton kraken]

so, I've used the first step for n=1

hopefully I'm right

I've gotten sin^2(x) in the end

second step is assuming this is true for some n>/=1

I hope I'm right here

and the third step is just idk what to do for n+1

[little fjord]

you have to use doubled angle formula.

[wanton kraken]

you mean sin(2x)

orr

idk what you mean

can be applied anywhere

[little fjord]

sin2x= 2 sinx*cosx

[wanton kraken]

yes, I know

what's your point

[little fjord]

sin(nx)=2sin(nx/2)cos(nx/2)

[wanton kraken]

I'm still very lost

I have no clue what you're talking about what-so-ever

please, read what I've written already

let me ping helpers at this point

<@&286206848099549185>

[little fjord]

uh...

when k is "n", it is true..we assume...

and then

when k = n+ 1 , if it is true, the rule is true

[wanton kraken]

so step 2 is assuming n=k ?

[little fjord]

no

sorry

yep

[wanton kraken]

what about the first step

n=1 ?

[little fjord]

of course, you did?

[wanton kraken]

I've gotten sin^2(x)

that's true?

[little fjord]

see above again

[wanton kraken]

idk

is it true or not

I mean

did I do right

[obtuse pebble]

@wanton kraken Has your question been resolved?

[wanton kraken]

<@&286206848099549185>

[obtuse pebble]

@wanton kraken Has your question been resolved?

[unreal musk]

Use (one of) the cos double angle formulas: you should see it being true from there

Put n=1 into the RHS and after some rearranging, you should get sin^2(x)

[wanton kraken]

for this?

I can directly apply it?

[unreal musk]

Well this is more for the inductive step and what you’d want

Were you asking about your base case or the induction step(s)?

[wanton kraken]

idk tbf am I correct so far?

I askd for the third step

[unreal musk]

Well second/third step is basically assuming that the formula holds for some n, you want to show that it holds for the next integer, (n+1)

[unreal musk]

Using the truth of this for n

[unreal musk]

You want to show that you can get $\sum_{k=1}^{n+1} \sin^2(kx)$ to be this

[warm shale]

@unreal musk

[unreal musk]

But of course you need to show that the formula is true for some base case (here n=1) for the inductive step to be of any use: that is, replacing $n$ with 1, you want to convince yourself (and me) that $\sin^2(x) = \frac12 - \frac{\cos(2x) \sin(x)}{2\sin(x)}$

[warm shale]

@unreal musk

[wanton kraken]

yup, done that

[unreal musk]

Cool, as long as you have, then the inductive step is as per here: show you can do this assuming the formula for the sum, up until n, is true

[wanton kraken]

well there is kx in the original

sin^2(kx)

which makes me sceptical of what I'm doing

maybe k=n?

🤔

[unreal musk]

Well basically for each integer from 1 to the top limit of the sum, replace k with that integer

Of course, if from the sum $\sum_{k=1}^{n+1} \sin^2(kx)$ you can make the sum $\sum_{k=1}^{n} \sin^2(kx)$ appear, you should be at least a bit happier…

[warm shale]

@unreal musk

[wanton kraken]

so that's alright, yes?

[unreal musk]

You assumed the value of the latter ofc

[wanton kraken]

my base n=1 is correct

[unreal musk]

Yes it’s fine, as per above, true e.g. as a result of double angle

[wanton kraken]

oh ok

[obtuse pebble]

@wanton kraken Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[spice chasm]

Find $\int_0^{\infty} x²e^{-x²}dx$ given the fact that $\int_0^{\infty} e^{-x²}dx=\frac{\sqrt{π}}{2}$.

[warm shale]

Jash

[atomic hornet]

integration by parts twice ?

[spice chasm]

but you can’t integrate e^-x²

[atomic hornet]

it gives you the integral

root pi / 2

[timid silo]

you can't find an antiderivative

you can find some definite integrals of it

[atomic hornet]

ye

[spice chasm]

so u=x²

dv=e^-x² dx

[atomic hornet]

yeah

[spice chasm]

v=∫e^-x²dx

$x²\biggr|_{0}^{∞} \int_0^∞ e^{-x²}dx$

[atomic hornet]

[warm shale]

Jash

[spice chasm]

wait

can’t i split up x²e^-x² to x*xe^-x²

since xe^-x² is easy to integrate

and x is easy to differentiate

u get $\left(-\frac{x}{2}e^{-x²}+\frac{1}{2}\int e^{-x²}dx\right)\biggr|_{0}^{∞}$

@atomic hornet

[warm shale]

Jash

[spice chasm]

,w does ∫e^(-x²)dx=-x/2 e^(-x²)+1/2 ∫e^(-x²)dx

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by jashxdlol

[spice chasm]

bruh

ty anyway

.close

[obtuse pebble]

Channel closed

Closed by @spice chasm

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.

[timid silo]

I can’t find the inverse function of this can someone help ?

[tardy epoch]

!show

[obtuse pebble]

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

[timid silo]

Okay hold on

[tardy epoch]

?

[timid silo]

Not sure if u will understand it’s kinda a mess

I just noticed that I forgot in the 7 line it’s x^2

But I still can’t solve it

[tardy epoch]

at this step, you can divide by 2, then square again

[timid silo]

What I apply the square two times ?

[tardy epoch]

you didn't need to

if you had just solved for sqrt(1-y^2) the first time

[timid silo]

Well I got y^2(x^4y^2-1)= x^4+1 after factorising

So I still have nothing

Can I use delta ? Like solve it like

[tardy epoch]

set u = y^2 then quadratic formula on u

[timid silo]

Alright

Im kinda stuck at finding the a b and c tho

I won’t use the factorised form ?

[tardy epoch]

you don't have to

,tex .quadratic formula

[warm shale]

riemann

[tardy epoch]

except x = y^2 = u in your case

[timid silo]

So basically I have xy^4-y^2-x^4-1

So i will have sqrtroot at y^2

If I put u=y^2 u see what I mean

No wait

Well basically it’s not working this way

[timid silo]

Ah maybe badd

I thought u said u=y^4

Lol

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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.

[rose arrow]

how do i find the focus of a parabola, this is what i have so far and its been reformatted as (x+4)^2 = 12(y+6)

[rose arrow]

.close

[obtuse pebble]

Channel closed

Closed by @rose arrow

Use .reopen if this was a mistake.

[rose arrow]

figure dit out

[obtuse pebble]

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.

[shadow lava]

does skew symmetric matrix require 0's on the diagonal?

[shadow lava]

I think it does require 0's on the diagonal, but I am just wondering why

because the regular symmetric matrix does not require 0's on the diagonal

[polar fossil]

what's the definition of skew symmetric?

[shadow lava]

A= -A^T

[polar fossil]

can you use that to prove that the diagonal must be symmetric? try it with a 2x2 matrix first

that the diagonal must be 0*

[shadow lava]

but for symmetric it is can have any number on the diagonal

[shadow lava]

wdym by prove it?

I thought we are just changing signs

everything stays the same because transpose is equal

but diagonal is basically empty (all 0's)

[polar fossil]

i mean, write an argument that starts with "given an arbitrary matrix A, such that A is skew-symmetric" and ends with "all of A's elements on the main diagonal are 0"

[obtuse pebble]

@shadow lava Has your question been resolved?

Channel closed

Closed by @shadow lava

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.

[strong fern]

How to do this

[obtuse pebble]

@strong fern Has your question been resolved?

[obtuse pebble]

@strong fern Has your question been resolved?

[obtuse pebble]

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.

[blazing kestrel]

Hello I need help with solving a fairly simple equation

[blazing kestrel]

I get -2 as a solution but that doesn't fit when I reenter the values

Idk if I can undo the absolute value like that

[obtuse pebble]

@blazing kestrel Has your question been resolved?

[blazing kestrel]

<@&286206848099549185>

[obtuse pebble]

@blazing kestrel Has your question been resolved?

[obtuse pebble]

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.

[waxen portal]

i have 8 points and am looking to create an equation with them

[waxen portal]

the points are (3, 2/3), (4, 1/3), (5, 1/12), (6, -1/12), (7, -3/16), (8, -1/4), (9, -55/192), (10, -59/192)

when plotted, they look like this:

from my knucklehead alg2 knowledge, that looks like the graph of y=2^(-x+3)-1/3

when i plot my estimate, it shares the first point, but none others, along with some points above it

i am genuinely lost at how to find this equation, <@&286206848099549185>

[brave bramble]

Is this for class? Or are these points just from something

[waxen portal]

this is outside of class

[brave bramble]

Okay so this could really be anything. Have you tried a regression with excel?

[waxen portal]

i have not, that is a great idea

a lnreg from my ti84 shot out y=1.46-0.81*lnx

i feel like there should be an actual equation, rather than an estimate, though

im getting these numbers from non-random sources

[obtuse pebble]

@waxen portal Has your question been resolved?

[waxen portal]

this equation has the right shape

[waxen portal]

oh my god, i miscalculated the x-value for every point by +3

thanks for the help lol

.close

[obtuse pebble]

Channel closed

Closed by @waxen portal

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.

[sonic kiln]

I'm having trouble understanding this question and what Carlo means

[obtuse pebble]

@sonic kiln Has your question been resolved?

[sonic kiln]

@languid sage

[obtuse pebble]

@sonic kiln Has your question been resolved?

[obtuse pebble]

@sonic kiln Has your question been resolved?

Channel closed

Closed by @sonic kiln

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.

[quick basin]

ik that x+5 is the divisor and 7 is the remainder

but how do i find the 2 polynomials in general

[brave bramble]

Can you get everything over that (x + 5)?

[quick basin]

no

its written in quotient + (remainder/divisor) form

[brave bramble]

You can get everything over that (x + 5).

Just gotta add the terms together as fractions

[quick basin]

ik but thats unnecessary

bc its asking for the 2 polynomials

that multiply to it

its supposed to be found using very simple logic but i just cant figure it out

[brave bramble]

If you get everything over that (x + 5), you'll have a polynomial as a numerator, and (x + 5) as a denominator

Which are your two polynomials

[quick basin]

so the answer is (5x^2+3x+19)(x+5)?

[brave bramble]

• 7

Yes, that's the numerator

If we divide that by x + 5, we get back the question

[quick basin]

okay thanks for the help

i get it now

.close

[obtuse pebble]

Channel closed

Closed by @quick basin

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.

[obtuse pebble]

Please don't occupy multiple help channels.

[midnight narwhal]

could sm1 help me here

for b 22

[little ember]

hi

[midnight narwhal]

Hi

[obtuse pebble]

@midnight narwhal Has your question been resolved?

[obtuse pebble]

@midnight narwhal Has your question been resolved?

[obtuse pebble]

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.

[spare fable]

How do I carry over the circled part of the algebra legally

[spare fable]

<@&286206848099549185>

I have a new question

[daring rock]

the circled part was already on the right hand side, it's everything else that moved

[spare fable]

How do I rearrange this

[spare fable]

I need to carry it over to the left but I figured it out

[spare fable]

This is my new question

[daring rock]

ok

[daring rock]

is there any more context?

it's hard to tell exactly what you're trying to do here

[spare fable]

How do I rearrange it so that 1 isn’t over it

[daring rock]

Well, you could make a common denominator on the bottom

if you can combine everything in those bottom brackets into one function

then, you can just say

$\frac{1}{\frac{a}{b}} = \frac{b}{a}$

[warm shale]

tatpoj

[spare fable]

Ooh

So Yn/b?

[daring rock]

well, you have to turn the whole denominator into one fraction first

so you have to make a common denominator between $y_n$ and $\Psi(a_n+c_2)$

[warm shale]

tatpoj

[daring rock]

?

[spare fable]

Do I just combine them then

[daring rock]

These symbols are kind of all over the place lol, where did this problem even come from?

[spare fable]

It’s an Economics question but my issue is doing fractions

I keep messing up on basic fraction rules

[spare fable]

I’d say think of all the symbols as just letter algebra

Someone is trying to explain it to me but he’s confusing me

Do you know where I can find more fraction rules @daring rock

[daring rock]

I bet you already know them for the most part, if you know how to do things like $\frac{1}{2} +\frac{2}{3}$

[warm shale]

tatpoj

[spare fable]

Yeah

But stuff like carrying over, fraction in denominator, algebra fraction

Fraction multiplied by a single algebra and carrying it over

Confusing

[spare fable]

Yeah

[obtuse pebble]

@spare fable Has your question been resolved?

Channel closed

Closed by @spare fable

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[primal aurora]

Hi, I have a doubt about this exercise.

A block of ice of mass m = 2g is allowed to slide, starting from rest, from the edge of a semi-spherical container of radius r = 22cm without friction.
How much work does the force of gravity do on the ice block from point A to point B?

I then calculated the mechanical energy of the block at point A.

At point B, only the kinetic energy would be worth since in my opinion the object is moving with some velocity.

ΔE_{AB} = k - U_k = m g r - 1/2 m v^2

however, comparing the solutions, for some reason the mechanical energy at point B is placed zero. am I wrong to consider a kinetic energy at point B?

[primal aurora]

This is mine

This is the solution

[hollow schooner]

why not try by only gravitational potential energy

At point B the gravitational potential energy = 0

And at a whatever u got

Work done = Ub - Ua

and at point B all that potential energyy turned into kinetic

[primal aurora]

You're right, I hadn't thought of that! 😃

[hollow schooner]

Aight goodluck pal

[primal aurora]

ty very much! 😃

.close

[obtuse pebble]

Channel closed

Closed by @primal aurora

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.

[placid forge]

12. c)

[placid forge]

a) is geometric

b) is arithmetic

but c is neither?

how am i supposed to find the answer without just using the pattern

3+7+13

difference of 4 then 6

does it go 8, 10, 12, 14?

like of course i can do that, but it doesn’t make much sense considering this exercise is ‘Geometric Series’

[placid forge]

this wouldn’t even work as the answer is apparently 2146

i don’t know how to get that

[fickle oracle]

whats ur question

a or b or c

[placid forge]

.

c

a and b are easy

[fickle oracle]

well hint:
use a and b in order to solve c

[placid forge]

just add a and b?

[fickle oracle]

u need to use a and b

what do u think?

🙂

[placid forge]

i mean it gets the answer 😂

[fickle oracle]

yup

good luck

[placid forge]

i do think this is a dumb question tho

[placid forge]

thanks for the help :)

.close

[obtuse pebble]

Channel closed

Closed by @placid forge

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.

[graceful marten]

Hia

[graceful marten]

I dont get the second step :>

do they make 1 = sin^2 + cos^2

But that wouldnt get c^2 / c^2 + s^2

._.

[fickle oracle]

which step?

[graceful marten]

Blue 2

[fickle oracle]

well multiply by (cosx)^2

and thats it i guess?

like:

1 / (1 + (sinx)^2 / (cosx)^2) * (cosx)^2

[graceful marten]

Oh they want it in terms of cos only

Is the question

[graceful marten]

Ill have a look

[fickle oracle]

ye just mutiply by (cosx)^2

and u will (cosx)^2

[graceful marten]

okie

Ty freind

[fickle oracle]

ur welcome

[graceful marten]

.close

[obtuse pebble]

Channel closed

Closed by @graceful marten

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.

[fickle oracle]

tbh i dont know all the signs here because they are differnet from place to place

[royal basin]

with all due respect if you cannot help you always have the choice to not say anything

[fickle oracle]

aight

sorry

[kind hawk]

try a few examples first

examples always help you in figuring out whats going on

yes. that doesnt mean that examples hurt

[royal basin]

^

[kind hawk]

for your understanding

before you can prove something you should understand it

grab a set M

any set

grab some subsets X,Y of M

compute the operations

then some other sets X,Y

etc

where are you getting 4 9 and 12 from

why

for the operation "symmetric difference"

yes under the operation symmetric difference

where did the 2 go

I mean in P(M)

yes

you have to show that $(X \Delta Y ) \Delta Z = X \Delta ( Y\Delta Z)$ for all subsets $X,Y,Z\subseteq M$

[warm shale]

Denascite

[kind hawk]

you have to show that there exists some subset $E\subseteq M$ which is the identity. aka $X\Delta E = E\Delta X = X$ for all $X\subseteq M$

[warm shale]

Denascite

[kind hawk]

and you have to show that for every subset $X\subseteq M$ there exists a subset $Y\subseteq M$ such that $X\Delta Y = Y\Delta X=E$ for the specific subset $E$ from the step before

[warm shale]

Denascite

[kind hawk]

and with that I have to go

[obtuse pebble]

Channel closed

Closed by @daring olive

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[old ivy]

Have a question not too sure about it, how would I find the magnitude of a bezier curve?

[royal basin]

wdym by magnitude of a curve?

[timid silo]

arc length?

[old ivy]

just the length of the bezier curve basically

[timid silo]

okay so arc length

[old ivy]

yeah

[timid silo]

https://math.stackexchange.com/questions/12186/arc-length-of-bézier-curves

have a look into this. The procedure seems complex though

[obtuse pebble]

@old ivy Has your question been resolved?

[obtuse pebble]

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 aspen]

hi i was just asking for a hint on this question

i'm confused on how i shud get started but i know i need to use holders inequality in some way

[obtuse pebble]

@tepid aspen Has your question been resolved?

[vale linden]

try to calculate its derivative (about the variable p)

[tepid aspen]

idk if its differentiable tho

[tepid aspen]

wait wdym by this?

i think i have to fit holders inequality somewhere

[vale linden]

wait I might have done some mistake
wait a sec

OK my bad

[twilit prairie]

I’d suggest looking at Jensen’s inequality

Because |x|^p is convex

[tepid aspen]

wait how do u know its convex

[twilit prairie]

I made it slightly more clear

|f(x)|^p need not be convex

[vale linden]

Its derivative to $p$ is $(\int_0^1|f|^pdx)^{1/p-1}(\frac{1}{p}\frac{d}{dp}\int_0^1|f|^pdx+\int_0^1|f|^pdx\ln(\int_0^1|f|^pdx)\frac{-1}{p^2})$

[warm shale]

CollinGao-Original

[peak vessel]

For $q\geq p$, Holder gives
$$\left(\int |f|^q\right)^{p/q}=\left(\int (|f|^{p})^{q/p}\right)^{p/q}\left(\int 1^{(q/p)'}\right)^{1/(q/p)'}\geq \int |f|^p $$
then take $p$-th roots.

[warm shale]

grobmez

[twilit prairie]

Grobmez gives the answer </3

[vale linden]

$=||f||_p^{1-p}(\frac{1}{p}\int_0^1\ln(|f|)|f|^pdx-\frac{1}{p^2}||f||_p^p\ln(||f||_p^p))$

[warm shale]

CollinGao-Original

[tepid aspen]

wait can u explain to me why this is relevant please?

[vale linden]

$=\frac{1}{p}||f||_p^{1-p}(\int_0^1\ln(|f|)|f|^pdx-||f||_p^p\ln(||f||_p))$

[warm shale]

CollinGao-Original

[vale linden]

Now the inequality is in the bracket, need to prove that it's positive

[tepid aspen]

also doesn't 1/p + 1/q have to = 1 for holders

[peak vessel]

I am not applying Holder using the pair (p,q). I am applying Holder using the pair ((q/p),(q/p)').

Where ' denotes the Holder dual of the number q/p which is >= 1.

[tepid aspen]

im think im not too sure on what a holder dual is.
so are you saying (q/p) + (q/p)' = 1? but in that case i dont see how q/p can be > 1

[peak vessel]

Firstly, q/p is >= 1 becase q >= p.

Secondly, the Holder dual of a number r in [1,inf] is the unique number s in [1,inf] with 1/r + 1/s = 1.

[tepid aspen]

ah

i see

[peak vessel]

explicitly, r'=r/(r-1)

[twilit prairie]

It’s relevant to the application of Jensen’s inequality, which was just the method I suggested, but it looks similar to Gomez’s solution with Hölder in the end

[tepid aspen]

ah ok i see

thanks

i think i need to just stare at it for about like half an hour

[twilit prairie]

Yeah, ultimately, the (1)^(q/p)’ is holding significant weight in his argument

But I’ll let you see why

[tepid aspen]

oh

hmm ok i dont just dont understand where

$\left( \int_0^1 (\mid f \mid )^q \right)^\frac{p}{q}$ is justified

[warm shale]

qing dynasty

[tepid aspen]

we want to say that this is equal to

$| f |^q$ yes?

[warm shale]

qing dynasty

[tepid aspen]

ah

hence take p roots

[tepid aspen]

ah so this is how we got the holder in

it's the most magical 1 i've seen lmao

[twilit prairie]

Yeah, so in #advanced-analysis I mentioned this only works for probability measures, but what that kinda means is “objects with length 1”

So the 1 is magical and works here because…? (What interval are you integrating over?)

[tepid aspen]

yeee

0,1

and then int 0,1 1 = 1

damnnn so thats what prob measures refers to

[twilit prairie]

Roughly, this gets generalized heavily in a measure theory/probability course

But you might have seen that probability of events can be seen in terms of integrals of objects that integrate to 1 over the entire space

[tepid aspen]

i see i see

thank u all <3

[obtuse pebble]

@tepid aspen Has your question been resolved?

Channel closed

Closed by @tepid aspen

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.

[split estuary]

hi, how to go abouts this?

[split estuary]

<@&286206848099549185>

[timid silo]

Hi!

Get Tokyo and Washington's rug production data

[split estuary]

hi : )

So tokoyos production data is 29%

Washington is at 25%

[timid silo]

Yes but you have to calculate some stuff first

Hold on. let me check it for you

[obtuse pebble]

@split estuary Has your question been resolved?

[split estuary]

okayyy

[timid silo]

I got the answer now

Sorry kind of busy

Tokyo - 1958 number of rugs: 1958 x 92 euro x 365 days = 65749640 euros --> 65749640 x 0.29 operating cost = 19067395.6

Washington - 1569 -- 52687020 euros in a year x 0.25 -- 13171755

Difference; 19067395.6 - 13171755 = 5895640.60

Hope this helps!

@split estuary

[split estuary]

thank u so much, that was heplful!

[obtuse pebble]

@split estuary Has your question been resolved?

[split estuary]

@timid silo could u help me with another question?

[timid silo]

Sure thing, hit me up!

[obtuse pebble]

@split estuary Has your question been resolved?

[obtuse pebble]

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.

[lament dagger]

Can u tell me the equation or root so I can check my ans

[crude coral]

what u mean?

[lament dagger]

I want to check if my answer is correct

This is a quadratic equation question

So if I can get the equation or root (value of x)I can check

[rich plume]

well, it is better to show us your answer

[lament dagger]

4

Is my ans

X^2-4x equation

[rich plume]

show your work so as to get 4 as a root

[lament dagger]

It's a mess lemme write it again

[rich plume]

a minus sign should be there instead of that plus

[lament dagger]

Oh man

Mb

Thank you

@rich plume can u help me with this

[rich plume]

sum of first 1 term= 1st term itself

sum of first 2 terms=1st term+2nd term

make use of these

[lament dagger]

D=15??

[rich plume]

no

what do you get as first and second terms of the AP?

[lament dagger]

9,24

[rich plume]

no

you get a_1=9

and you should get a_1+a_2=24

[lament dagger]

D=6 I was writing s2 as a2

[rich plume]

yes

d=6

and a=9

so, just write the general term

as a+(n-1)d

[obtuse pebble]

@lament dagger Has your question been resolved?

Channel closed

Closed by @lament 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.

[dark fossil]

What is meant by "three (projective) lines that meet in this way"?

[dark fossil]

Is it supposed to mean that I should find three lines such that the intersection of say the first two lies in L1 intersect L2? And likewise for the others?

This is my current attempt:

[obtuse pebble]

@dark fossil Has your question been resolved?

[dark fossil]

<@&286206848099549185>

[obtuse pebble]

@dark fossil Has your question been resolved?

[obtuse pebble]

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.

[mortal yew]

hey

[alpine bison]

hey

[mortal yew]

is this true or false

[latent walrus]

true

[mortal yew]

demonstration pls

[latent walrus]

try multiplying by the conjugate of the denominator

[mortal yew]

i did

it didnt come out

or i must have not noticed it

imma try redoing it sec

[alpine bison]

if you set $x=z^2$ the the limit becomes $\lim_{z\to \sqrt 3}\frac{\sqrt{z^4-5}-2}{z-\sqrt 3}$ that seems the derivative of $\sqrt{z^4-5}$ at $z=\sqrt 3$

[warm shale]

everg

[latent walrus]

doing l'hopitals seems pretty quick

[mortal yew]

thx but idk what derivatives are

[latent walrus]

oh

[alpine bison]

you are actually doing a derivative

[mortal yew]

my best bet is to multiply by the conjugate

[latent walrus]

ikik

[alpine bison]

AZ0's bet

[mortal yew]

i did it with the conjugate tho

it didnt come up

anyone ?

[alpine bison]

mh...

[mortal yew]

can u try multiplying for urself

maybe it works for u

[high lily]

show work

[lone dagger]

For compact two-dimensional surfaces without boundaries, if each loop can be continuously compressed to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré Conjecture, proven by Grigori Perelmán, states that the same is true for three-dimensional spaces.

Someone to solve it

[mortal yew]

its on paper

[high lily]

take a pic

[mortal yew]

my phone dont have discord

[high lily]

reproduce your work on something like paint

[mortal yew]

wait actually

[alpine bison]

you ll be warned you unless you show your work

[high lily]

write it up in math using latex if you know it, or use something like desmos

to write it up

[mortal yew]

i get warned?

[mortal yew]

sec ill try to send the paper

ok here

[high lily]

use conjugates for the initial denominator component as well

[alpine bison]

I think its done

[mortal yew]

i treid that

actually sec

[alpine bison]

$x^2-5-4=x^2-9=(x-3)(x+3)=(\sqrt x-\sqrt 3)(\sqrt x+\sqrt 3)(x+3)$

[warm shale]

everg

[mortal yew]

let me try that

even tho i already tried it

[mortal yew]

omg it fucking worked

ur the best dude

i had the (x-3)(x+3) idea at first but thought developing it wont work

i spent 25 mins over this dumb prob 🥲

[alpine bison]

no... AZ0 has said the best advice

[mortal yew]

ye thx everyone

[alpine bison]

you are improving, its normal 🙂

[mortal yew]

yes

[obtuse pebble]

@mortal yew Has your question been resolved?

Channel closed

Closed by @mortal yew

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.

[ember oar]

Where do I begin to sketch this on a graph?

[ember oar]

t=30 btw

This one is the accurate one ignore the function above

Oh wait nvm

.close

[obtuse pebble]

Channel closed

Closed by @ember oar

Use .reopen if this was a mistake.

[obtuse pebble]

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 willow]

question for flux through a surface

[coral willow]

For r > 0, we denote by Wr = (-r, r) × (-r, r) × (-r, r) the open cube with center at 0 and side length 2r, where the sides of the cube are parallel to the axes of R^3. We use N to represent the outward unit normal vector field on ∂Wr (the boundary of Wr). The flux through the cube W2 is given as 4π (you can verify this).

It is also advantageous to use Wr,R to designate the (open) cube shell with center at 0, inner side length of 2r, and outer side length of 2R with R > r, i.e., Wr,R = WR \ Wr.

vektor field is this:

this is the question given: Calculate the flux through the cube W4 using Gauss's Divergence Theorem.
Hint: Consider the cube shell W2,4.

2 and 4 are the lengths for r and R

MY question: why do we have to use the shell of a cube to find the flux through the surface? Dont we normally just use a 2d surface?

(Also note divergence = 0)

<@&286206848099549185>

[obtuse pebble]

@coral willow Has your question been resolved?

[obtuse pebble]

@coral willow Has your question been resolved?

[obtuse pebble]

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.

[winged ibex]

can someone help me how this is derived?

[winged ibex]

!status

[obtuse pebble]

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

[pseudo swift]

yea?

[winged ibex]

1

[pseudo swift]

aight well you know what the step function does

[winged ibex]

yup

[pseudo swift]

let's start from the left, and try to build the function piece by piece

[winged ibex]

aight

like before 0?

[pseudo swift]

so before t = -1 nothing happens

at t = -1, the voltage goes up suddenly by 3V

[winged ibex]

3u(t+1)

[pseudo swift]

yeah it is a step, taken in isolation

so nothing happens between -1 and 0

now at t=0, we gain 9-3 = 6V

[winged ibex]

so 6u(t)

[pseudo swift]

yup

[winged ibex]

okay thats clear

[pseudo swift]

do that at each step

and you got the whole function

[winged ibex]

ah okay

ty!

.close

[pseudo swift]

i'm curious what the b) is now

[obtuse pebble]

Channel closed

Closed by @winged ibex

Use .reopen if this was a mistake.

[winged ibex]

.reopen

completely diffrent lol

[obtuse pebble]

✅

[pseudo swift]

ah okey

well

.close

[obtuse pebble]

Channel closed

Closed by @pseudo swift

Use .reopen if this was a mistake.

[winged ibex]

its this if your curious

oh bruh

[pseudo swift]

lol very diff

[winged ibex]

.close

.close

bot is broken lol

[pseudo swift]

i already closed

[obtuse pebble]

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 crag]

help

[tepid crag]

idk how to do this one

[latent walrus]

did you do some working to get that 500? If so please do show

[tepid crag]

👌 one sec

i’ll be hiney

i used chat gpt

[latent walrus]

well well well

[tepid crag]

but only cause then i copy down the work then understand it

and now because it got it wronf

i’m confused

but i’m learning thro chatgpt when it gets it correct

[latent walrus]

chat gpt will rarely be helpful with maths and even then it just gets lucky

do you know how to differentiate something like 5^x

[tepid crag]

it’s helped me like 60% of the time

differentiate means like all the formulas right?

chain rule, product rules

[latent walrus]

yeah i guess

do you know how to go about it?

[tepid crag]

not from the question no

chain rule

[latent walrus]

you can express $5^{x}$ like so:
$$5^{x}=e^{xln(5)}$$ For example

[warm shale]

AℤØ

[tepid crag]

damn we using ln now

[latent walrus]

kinda necessary

[tepid crag]

ok ok

let me write that down

[latent walrus]

do you know how to differentiate something in the form:
$$e^{f(x)}$$

[warm shale]

AℤØ

[tepid crag]

no

[latent walrus]

this is why you shouldnt rely on external things when doing questions, you dont learn how to actually do them

[latent walrus]

youd need to use the chain rule

[tepid crag]

oh yeah

so like

uv=u’v+uv’

[latent walrus]

thats the product rule, not the chain rule

[tepid crag]

wtf

my bad it’s this

i be getting confusdd

[latent walrus]

yeah pretty much
so whats the derivative of e^{f(x)}

[tepid crag]

okie

this is what i’ve got

is it wrong

[latent walrus]

well, in the scope of what i asked, yeah

do you want to jump back to the main question rather than going through the components?

[tepid crag]

let’s go thro the component cause i’ve been solving it one way only and it’s bad

[latent walrus]

alright, suppose we abstract down to this slightly simpler system

whats the derivative of this

using the chain rule

[tepid crag]

i’m

okay let me worried it doen

write

[latent walrus]

might help to establish this first

[tepid crag]

i’m ngl idk what ur asking for

like differenitate that but hoe

how

[latent walrus]

just in generic terms
using the chain rule what do you get by differentiating e^{f(x)}

[tepid crag]

like (e(f^x) times (f)

[latent walrus]

not quite, if i have $y=e^{f(x)}$ I can let:
$u=f(x)$, so i have $y=e^u$
$$\frac{du}{dx}=f'(x)$$
$$\frac{dy}{du}=e^u$$
So then
$$\frac{dy}{dx}=f'(x)\cdot e^{f(x)}$$ By the chain rule

[warm shale]

AℤØ

[tepid crag]

oh yeah

that makes sense

[latent walrus]

so thats what we're working with in general terms

[tepid crag]

yeah

[latent walrus]

try apply that to this

[latent walrus]

youve jumped back to the original question again

[tepid crag]

oh 💀

[latent walrus]

and its still not right

[latent walrus]

differentiate e^{xln(5)}

[tepid crag]

so instead of 5^u i wrote that?

write

[latent walrus]

sure and u=xln(5)

wait

no

you have e^u and u=xln(5)

[tepid crag]

yeah

okay

so like this?

[latent walrus]

sorry, im back
but no

youre just mixing and matching stuff now

why is there a 2x+2

whats the derivative of xln(5)

[obtuse pebble]

@tepid crag Has your question been resolved?

[tepid crag]

oh yeah

😭

wait 10 mor mine

mins

imma get back to this

[obtuse pebble]

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.

[open forge]

Are these right?

[obtuse pebble]

@open forge Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[timid silo]

for c dont we also have to add u1

[obtuse pebble]

@timid silo Has your question been resolved?

[empty cypress]

what is u1

oh it is like a bit unclear how the ball starts

the wording makes me think you wouldnt add the initial drop height but it could go either way

[obtuse pebble]

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.

[fair abyss]

Help please?

[daring sorrel]

Just choose any 3 numbers

They will most likely work

[fair abyss]

It must be relevant to sets

This is a discrete maths/finite maths question

[obtuse pebble]

@fair abyss Has your question been resolved?

[daring rock]

try setting B as the empty set

[obtuse pebble]

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.

[hidden edge]

complete the following sentence: “as the population n goes up by being scaled by a factor of s, the margin of error will be divided by ________”

[timid silo]

So let's say the the population n gets scaled up by a factor s. What would happen to the margin of error?

[hidden edge]

it would get smaller

[timid silo]

Yes

[hidden edge]

because the bigger your sample the lower the chance it isnt representative

but im not sure by how much relative to s

[timid silo]

So we have to devide the margin of error by something to make it smaller right?

[hidden edge]

yeah

[timid silo]

Do you know the square root law in statistics?

[hidden edge]

i do not but i think this is what the WS im doing is trying to get me to understand

it mentions squaring in one of the steps earlier but i cant make the connection i think it wants me to

[timid silo]

The square root law states that when the size of a sample or population is multiplied or divided by a certain factor, the standard deviation (and consequently, the margin of error) is multiplied or divided by the square root of that factor. In other words, if you increase the size of your population or sample, the variability (standard deviation) decreases, and to account for this reduced variability, you divide the margin of error by the square root of the scaling factor ( s ). This adjustment ensures that the margin of error accurately reflects the increased precision resulting from the larger population size.

So pretty much you just devide by sqrt(s)

[hidden edge]

awesome you put it out very clearly thank you so much!!

i wish they would just explain these kinds of things on the worksheets, it’s a little hard to infer yourself just by looking at data

[timid silo]

Happy to help

Also write .close if you don't have any more questions.

[obtuse pebble]

@hidden edge Has your question been resolved?

[obtuse pebble]

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.

[tawdry vigil]

How do we work this out?

[tawdry vigil]

The correct answer is B

[sinful plover]

do you know how to calculate surface area of rectangular prism?

[versed pier]

omg bestie

this is like the bc calculus

[tawdry vigil]

Yeah

[tawdry vigil]

Bc calculus?

[versed pier]

dwdw

[tawdry vigil]

Ok

[sinful plover]

then assume side length as x and then write an equation using surface area of rectangular prism. Surface area is already given as K

[tawdry vigil]

I got K = 180x + 2x^2

Is that correct?

I also got the second equation but I wasn't sure how to proceed from there

Oh nvm I think I got it

.close

[obtuse pebble]

Channel closed

Closed by @tawdry vigil

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.

[grave thorn]

Hello, I'm having an issue with this optimization problem because I got an answer of 14.5 and 0.5 for my x and y respectively, but it doesn't seem right because 7.5 for both X and Y would likely be larger in the conditions the problem has set

[errant lark]

!show

[obtuse pebble]

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

[grave thorn]

I'm not even sure if i set it up correctly to a point either

[errant lark]

P is not x+y^2.

P is xy^2.

[grave thorn]

OH

[errant lark]

It's product.

[grave thorn]

I JUST REALIZED

im so sorry

[errant lark]

It's okay.

[grave thorn]

would it be possible to check my answer with you when I finish it again?

[errant lark]

Yes

[grave thorn]

So i get to here now, but it still doesnt seem right

[errant lark]

Well, you differentiated wrong.

In f'g + fg', you forgot the f in fg' term.

[grave thorn]

I see that now

Give me a moment

So i get to here after this revision

I feel like in this case however I should have solved for y in order to get the smaller number, because if x is 5, it would not work out

after getting to this answer I mean

then when i do the same process for y, i then get 10 which would throw off the original way that I have it written

.close

[obtuse pebble]

Channel closed

Closed by @grave thorn

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[quasi cosmos]

Hi all, how do you perform the partial fraction here in part (ii)?

[obtuse pebble]

@quasi cosmos Has your question been resolved?

[tranquil arch]

,w Apart[x^3/((x^2 + a^2) (x^2 + b^2))]

[warm shale]

Results provided by WolframAlpha

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

Requested by qiu_shui

[obtuse pebble]

@quasi cosmos Has your question been resolved?

Channel closed

Closed by @quasi cosmos

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.

[foggy vortex]

so i have an equation of an ellipse with one of the foci at the origin, which is $\frac{a\left(1-z\right)}{1-z\cos\left(\theta\right)}$ where $z$ is the eccentricity. the issue is the fact that $a$ seems to be the distance from the origin to one of the ends of the ellipse, whilst $b$ is something else and i can't seem to understand that. Wikipedia states that $a$ and $b$ should be the semimajor and minor axes, which works fine in the normal equation where the ellipse is centered around the origin - but stops working here

[warm shale]

oof2win2