help-38

[hallow wren]

What do you need?

[topaz pasture]

^^

[hallow wren]

You want someone to do the math for you then?

[topaz pasture]

brother

can you read 2-3 lines of me typing?

please

I'm saying, i've tried, and it doesnt add up.

[hallow wren]

can you show what you have tried...?

[topaz pasture]

my god

[topaz pasture]

...

[hallow wren]

is that your math?

[topaz pasture]

YES

The whole point of math help, is for someone to come help, when you're stuck with something, or need help.

[hallow wren]

I don't know how cylinders work, but can I please recommend that you do your math with a pen and paper.

[topaz pasture]

I don't either.

We have been given a formula

[hallow wren]

Did you find the volume of the pipe?

[topaz pasture]

Yes.

Well

[hallow wren]

is V up there volume?

[topaz pasture]

It's not the correct volume

[topaz pasture]

Yes!

This is the formula

This is what the formula describes.

I have a copper pipe, and simply want to fill in the formula with the data that i have.

[hallow wren]

I'm having difficulty seeing what is your work and what is a part of the original question

[topaz pasture]

Alright alright.

[hallow wren]

since it's all text it's very hard for me to see what might potentially be your error

[topaz pasture]

You're right you're right 1 sec

This is as simple as i can explain it

[hallow wren]

sec I'm finishing my own prob

[topaz pasture]

Now my calculations:

find*

I inserted the volume and density

And we get 17 kg

The answer is 4,24 kg

I am wondering; where the snickers, am I making a mistake?

[topaz pasture]

You done yet?

<@&286206848099549185>

[hallow wren]

8600kg/m3 seems wrong

no?

[topaz pasture]

It says it in the question.

or maybe...

Nope.

I tried it with this, but didn't work,

I have clearly misunderstood something here, or the question is wrong.

[hallow wren]

All I can think of bro sorry, but it was also the first thing I saw

But a copper pipe can't have a density of 8600kg/m3 unless I am misunderstanding something

[topaz pasture]

when you make math questions, you can make certain values simpler.

as long as you use that given value in your calculation.

[hallow wren]

or wait

it can

I am misunmderstanding something

[topaz pasture]

Don't worry, i am confused too.

I've tried everything

[hallow wren]

8.6 ton per m3 of a metal is totally possible

idk what I was thinking

sounded heavier in my head

[topaz pasture]

I'm gonna ask my prof then.

.close

[trim jolt]

Channel closed

Closed by @topaz pasture

Use .reopen if this was a mistake.

[hallow wren]

why did you put in 2.8 for h?

nvm haha

[trim jolt]

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.

[iron glacier]

a) is asking to prove that the area of this traingle is the (function thats written)

b) is asking for the domain of the previous function

c) this is an optimization problem that Im not asking about (no problems here)

[iron glacier]

I have a problem with the second question about the domain, How do I find it? My teacher in the video lesson solved it by saying that since one of the angles is pi/4, and a triangle has a sum of 180 deg. It means that the domain is 0≤theta≤135

what i dont get is how can (0≤theta) like how can that angle be equal to zero, shouldnt it just be (0<theta)

Also he solved this question (c) without any work as stated above. So how do i find the domain for something like this?

[marble wharf]

well it cant be equal to 135 degrees either

[iron glacier]

oh yes i forgot to say that

so it should be 0<theta<135 right?

[marble wharf]

yes

[iron glacier]

but how do i solve the domain? I get how the teacher solved it but i want to see how it can be done with pen and paper and not just by logic

[marble wharf]

what

[iron glacier]

question (c) asks to find the domain of the previous function (the A=.......) and im asking how to find the domain of it

the teacher just said that since its a triangle and it has a sum of 180 deg and one of the angles is 45 then...... you get it. but I want to know how to solve it with steps and not with logic as i said

[marble wharf]

that makes no sense

your teacher made steps to get there

0<theta is clear. and theta+45<180

therefore 0<theta<135

[iron glacier]

wait, so you know how if i have sqrt(x^(2)-4) then i can find the domain by equalling whats inside to zero? so why cant i do the same with the function above, i did that and got no where.

what if i got a question to find the domain of a diffirent function that doesnt have to do with any triangles

it seems im wrong but idk where

[marble wharf]

without the triangle context, the function has as domain all of the real axis

[iron glacier]

so there arent any set steps to finding the domain of a function

[marble wharf]

well you need to check where the individual pieces are defined

sin and cos are defined everywhere

sqrt is only defined for >=0

[iron glacier]

ah so since its defined in the triangle then i have to play by its rules

and the info given to me inside

[marble wharf]

yes

[iron glacier]

I misundertood domains and thought that it was just equalling the function to zero and seeing how it turns out haha

thanks man

[marble wharf]

the domain is which values of the variable you can plug in so that the expression makes sense

for sqrts that means you are only allowed to plug in something that results in something >=0 in the root

and here that means only 0<theta<135 is sensible because of the triangle context

[iron glacier]

got it, so the domain is diffirent because of the context its in

just like how if a square root is in the denominator that it also cant be zero

[marble wharf]

yes

[iron glacier]

thanks for the help man

.close

[trim jolt]

Channel closed

Closed by @iron glacier

Use .reopen if this was a mistake.

[trim jolt]

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.

[willow compass]

lol

[willow compass]

@willow compass

[sage harness]

<@&268886789983436800> troll?

[fair bison]

Do you have a math question?

[trim jolt]

@willow compass Has your question been resolved?

[trim jolt]

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.

Channel closed

Closed by @delicate lance

Use .reopen if this was a mistake.

[trim jolt]

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.

[delicate lance]

how do you get the discriminant of x ?

[austere cedar]

We can get the discriminant of
x² + 4ax + (4b - 16)

[delicate lance]

Howd u get to that step?

[tranquil widget]

rearranging

[trim jolt]

@delicate lance Has your question been resolved?

[delicate lance]

ohh ok so the discriminant is 16a^2 - 4(1)(4) ?

[tranquil widget]

how did you get c = 4?

[delicate lance]

oh is it 4b-16 ?

I thought it would just be the coefficient of b

[tranquil widget]

a is the coefficient of x^2 which is 1 here

b is coeff of x which is 4a

whats left over has no x^some power term

so its the constant term

so thats why you take the whole 4b-16 as the constant term (c) here

[delicate lance]

oh okk

16a^2 -4(1)(4b-16)

[tranquil widget]

yes

[delicate lance]

16a^2 - 16b + 64

[tranquil widget]

yes

[delicate lance]

how come they got this?

oh because its factorable

wiat

wait

[trim jolt]

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.

[trim jolt]

@delicate lance Has your question been resolved?

[trim jolt]

Channel closed

Closed by @delicate lance

Use .reopen if this was a mistake.

[trim jolt]

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.

[mellow abyss]

i only have one attempt left, and i dont quite understand this concept. all i know is that the wronskian for 3 is 18t^2, so the two functions should be linearly independent?

[trim jolt]

@mellow abyss Has your question been resolved?

[mellow abyss]

I guess for wronskian method, all values of t need to be zero for it to be linearly dependent. so for f(t) = t and g(t) = |t|, this would not hold true as the derivative of |t| is t/|t|, where t cannot equal zero? (nvm it's cause with how |t| is a piecewise, you cannot make it the same as t

[trim jolt]

@mellow abyss Has your question been resolved?

Channel closed

Closed by @mellow abyss

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.

[outer nexus]

Could anyone give me a clue how to solve this?

[wraith hinge]

shaded area ?

[outer nexus]

Yeah

[wraith hinge]

ok so if you can say that all the angles are 90 deg somehow

then it would be rectangle

shaded area = rect area - two sectors area

[outer nexus]

Its a trapezoid tho

[wraith hinge]

aqr and brq already are 90 deg

[wraith hinge]

how do you know ?

[outer nexus]

Both circle have a different radius

[wraith hinge]

yeah ig that would not work for qab and rba

[outer nexus]

Ab would be 8, but idk where to go from there

[wraith hinge]

ofc

[outer nexus]

All i need is aqc and rbc area, but i dont know what is the angle of a and b

There is where i get stump

[wraith hinge]

we gotta use the triangle

hmm use properties of triangle

aq is parallel to br

there is some property by which we can get relation in sides i dont remember it

if corresponding angles of two
triangles are equal, then they are known as
equiangular triangles. A famous Greek
mathematician Thales gave an important truth relating
to two equiangular triangles which is as follows:
The ratio of any two corresponding sides in
two equiangular triangles is always the same.
It is believed that he had used a result called
the Basic Proportionality Theorem (now known as
the Thales Theorem) for the same.

Basic Proportionality Theorem

[outer nexus]

If use it before

I guess it could work

[wraith hinge]

try it

[outer nexus]

If im not mistaken, you could use it to get the area of a triangle aswell

[wraith hinge]

yeah ig

[outer nexus]

Idk, but im thinking about using it on a circle

Idk if it would work tho

[wraith hinge]

tbh i dont remember these stuff now i learnt this when i was kid ( i still am a kid ) but you would get somewhere using properties of triangles ,if not this then some other one prob

[outer nexus]

Now im just stuck, but good idea tho

Ill work on it later, perhaps others would have a great idea

[trim jolt]

@outer nexus Has your question been resolved?

[trim jolt]

@outer nexus Has your question been resolved?

[velvet aurora]

Your question solved bruhh?

[trim jolt]

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.

[wraith hinge]

root 2 (1.4..)+ root 2 = 2.4..(acc to the online and my calc) so like, the calc only adds like till the ones? or does the infinity gets added too

[tepid hamlet]

? root 2 + root 2 = 2.82...
how are you getting 2.4 something there

calculators just compute to some small number of finite decimal places, there are algorithms that allow you to compute stuff like square roots to within a known error, so like for example if you know the error is less than 0.0001 then you know you are accurate to 3 decimal places etc.

[wraith hinge]

i just checked again, and now im getting 1.84..

on my calc

[wraith hinge]

yeah online its 2.84

[tepid hamlet]

you probably aren't clearing your calculator and adding stuff to previous results, i don't know what you're doing but it's user error 😛

[wraith hinge]

..

[wraith hinge]

um isnt that 4 decimal places

[wraith hinge]

hm

aigh

.close

[trim jolt]

Channel closed

Closed by @hasty skiff

Use .reopen if this was a mistake.

[trim jolt]

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.

[lost minnow]

can somebody explain this:

[lost minnow]

idk understand this ref angle

thanks in advance

[delicate belfry]

The common ones, sin, cos, tan, is discovered by opposite, adjacent, and hypotenuse.

[lost minnow]

?

like what is the ref angle for and how to get it

bruh

<@&286206848099549185>

[delicate belfry]

What exactly are you confused with?

[lost minnow]

The ref angle

how to make one

and how to use it

[delicate belfry]

That's roughly. cos (theta) = x, sin (theta) = y. Those are found by remembering cos(90deg) = 0, sin (90deg) = 1, and cos(0) = 1, sin (0) = 0.

[lost minnow]

what

[delicate belfry]

x^2 + y^2 = 1^2, is a function as a circle, also as the pytagoras theorem, in tigonometry.

[lost minnow]

what

I get that

but how to derive r

for lets say 220 degrees

WAIT

I get it

I am so sry

thanks man

have a good one

.close

[trim jolt]

Channel closed

Closed by @lost minnow

Use .reopen if this was a mistake.

[trim jolt]

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.

[onyx dove]

how does the left hand side become the right?

im brain farting so hard

[devout drift]

They factored out the (k+1) term that was common $ab + bc= b(a+c)$

[onyx dove]

so b would be k+1

[solid kiln]

ColdTee

[devout drift]

Yep

[onyx dove]

wouldn’t it be like k^2 + k then

idk why my brain doesn’t understand this 😭

[devout drift]

Write it down

What you can't understand

And show me

[devout drift]

This is also true

But you have distributed it

Rather than factor it

Let's not play with variables take an example with numbers

$2(1 + 2) + 3(1 + 2)$

[solid kiln]

ColdTee

[devout drift]

$(2+3)(1+2)$

[solid kiln]

ColdTee

[devout drift]

Which is the SAME

Or if you wanna do $2 + 4 + 3 + 6$

[solid kiln]

ColdTee

[devout drift]

They all will give the same result

[onyx dove]

PHHH

OH

I SEE THE LOGHT

TY

[trim jolt]

@onyx dove Has your question been resolved?

[trim jolt]

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.

[random hawk]

pls help me

[lapis star]

Find the total number of possibilites

and

just see which a pair of numbers 1 each from each set which are a multiple of 3

[trim jolt]

@random hawk Has your question been resolved?

[trim jolt]

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.

[tropic turtle]

hi

[tropic turtle]

was just wondering

is it true that the area of a triangle, given that it has two x and y intercepts and then the other, origin as the 3 vertices

the area is 1/2 of the product of the x and y intercept?

its present in this solution here

and i was just wondering where he got that from

tho i satisfied my problem already

<@&286206848099549185>

Ok

Is it from the shoelace method

Ok

thax

.close

[trim jolt]

Channel closed

Closed by @tropic turtle

Use .reopen if this was a mistake.

[trim jolt]

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 lichen]

Hello, I was wondering what the order of operation on sets is? (for example R x Q u N, would i perform the cartesian product first or union?)

[velvet bolt]

You go from left to right

[shrewd ridge]

nobody knows

[timber lichen]

two contradicting answers, what am I supposed to do? is it not usually defined and you just go left to right?

[shrewd ridge]

only one order gives you a set that's one type of thing

that's how you deicde in this case

one choice would make sense

[trim jolt]

@timber lichen Has your question been resolved?

Channel closed

Closed by @timber lichen

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 tinsel]

how would u find this

[dusky tinsel]

where equaiton is 5 + 2cos(30t)

average rate of change?

but theres... varying gradients

wait

[delicate belfry]

$\frac{\Delta y}{\Delta x}$

[solid kiln]

Good

[dusky tinsel]

i got it nvm

.close

[trim jolt]

Channel closed

Closed by @dusky tinsel

Use .reopen if this was a mistake.

[trim jolt]

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.

[novel jay]

the example problem has an interval that the actual questions dont

[novel jay]

how do i find the jnterval?

wait is the interval just what the graph shows

lmao it is

.close

[trim jolt]

Channel closed

Closed by @novel jay

Use .reopen if this was a mistake.

[trim jolt]

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.

[rough goblet]

how can i find the value of this summation: (just give a small hint)

[solid kiln]

ren

[vagrant prism]

taylor/maclaurin series for ln(...)

[rough goblet]

clueless ren noises

[vagrant prism]

i honestly googled this lol

[rough goblet]

LMAO

[vagrant prism]

it looked familiar

next hint?

[rough goblet]

hmm

nah im good for now

[vagrant prism]

okay

[rough goblet]

imma try to figure it out maybe?

[vagrant prism]

good luck

[rough goblet]

thinks

wait before you go

is it related to riemann sums??

[vagrant prism]

uh

[rough goblet]

by any chance

[vagrant prism]

no(?)

[rough goblet]

xD

it's alright, thanks anyway

that's probably a huge hint in itself

[vagrant prism]

if you are asking about integrals then i don't think so

[rough goblet]

no i mean riemann sums

as in lim n -> inf 1/n etc etc

[vagrant prism]

yeah no

[rough goblet]

i believe it's this

$$\lim_{n\to\infty} \frac{1}{n}\sum_{m=1}^{\left(b-a\right)n}f\left(a+\frac{m}{n}\right)$$

[solid kiln]

ren

[rough goblet]

or something like that

[vagrant prism]

no, wrong direction

[rough goblet]

??

oh i see

okay

[vagrant prism]

sorry man

[rough goblet]

thanks anyway

[vagrant prism]

look it up

[rough goblet]

nah bro thanks

[rough goblet]

alr, thank you!

imma leave this open JIC

[tepid hamlet]

i think that's an alternating series though isn't it? so how would you make it fit this? 🤔
can you give any stronger hints with spoiler tags maybe if ren doesn't want them, since now I'm curious about this problem too 😄

@vagrant prism

[vagrant prism]

||so negating that will give the series he has, with x=0.5||

[rough goblet]

AAAAA

I SAW THE IMAGE

okay

thank god i didn't remember it

[vagrant prism]

lol

[rough goblet]

how

[vagrant prism]

||this can be derived from the ln(1**+**x) maclaurin series where the sign alternates, but putting -x will make the sign constant||

[rough goblet]

alternating how??

[tepid hamlet]

ahh oh brilliant,|| i kept thinking with 1/2^x so i kept trying to get a negative exponent somehow, didn't occur to me to also just use 1-x instead of 1+x, that's neat||

[rough goblet]

i swear all the messages are just black boxes for me now xD

[vagrant prism]

lol

[rough goblet]

i have no idea if they're hints or u guys are messing with me

[vagrant prism]

discussing the solution essentially

need another hint?

[rough goblet]

nah thanks im good

[tepid hamlet]

i dunno how you'd solve this problem other than kinda "knowing" what some various functions' maclaurin series look like and then coming up with one that fits this problem

[rough goblet]

i mean

this is where i got it

do NOT ask how i ended up here
it's a long and painful story

[vagrant prism]

we memorized them for school so i thought this looked familiar

[rough goblet]

we didn't

[vagrant prism]

🫡

[rough goblet]

only very few

[tepid hamlet]

I guess "give your answer in terms of natural log" is a decent hint of what to consider the maclaurin series of 😄

[rough goblet]

i mean yes
but i didn't know it existed

D:

[tepid hamlet]

do you know how you'd come up with it if you didn't like have it memorized?

[rough goblet]

no

and i'm going to figure out how

because i haven't searched it up yet, and i won't

[tepid hamlet]

you know what a maclaurin series is though right?

[rough goblet]

this ^ is basically my philosophy in maths

[rough goblet]

yes ik taylor series

not very well though, i might add

but eh
shrugs
we'll get there

artemetra disappeared
sad i liked his cuttlefish

[tepid hamlet]

me only being able to remember sin^2+cos^2 = 1 and having to derive every other trig identity from that every time i need to use one : (

[vagrant prism]

i am here

[rough goblet]

YAY

[rough goblet]

fr bro, same

actually nah i remember most things

but i derive more things

like i remember earlier i derived the formula for the volume of a sphere on my own using limits and stuff

i didn't get why 4pi/3 r^3 worked so i did it lmao

[tepid hamlet]

so easiest is to consider maclaurin series (when x = 0) vs taylor series for some other x value, but since ln(x) is undefined at 0, what do you think you could do instead?

[rough goblet]

x+1?

[vagrant prism]

yep

[rough goblet]

idk

will figure it out

i gtg eat dinner in like 3 seconds

[tepid hamlet]

that's actually exactly correct though

😄

[rough goblet]

xD

[rough goblet]

yooooooo

https://tenor.com/view/harvey-specter-happy-friends-best-gif-25907214

[tepid hamlet]

so yeah just start doing derivatives of ln(x+1) and filling in the maclaurin series

[rough goblet]

i feel the need to remind you that i still don't know what it is lmao

anyway, i gtg

imma leave this open!

@vagrant prism @tepid hamlet thank you so much

could i (possibly) notify you if i make any developments

[vagrant prism]

yes

[rough goblet]

yay

ty

gb for now

oh soosh is back

[tepid hamlet]

i'm also trying to review series so im gonna go get stuck on some other problem

[rough goblet]

okay

[tepid hamlet]

in the meantime

[rough goblet]

?

oh ok

bye

[tepid hamlet]

@vagrant prism actually while ren is eating, can i ask if you have any insight into this and hijack his channel 😛
question is, determine if this is absolutely convergent, conditionally convergent, or divergent, this problem was frustrating me yesterday

[vagrant prism]

i gotta be honest: i have never studied either real analysis or sums or stuff like that formally lol

so i am not an expert

[vagrant prism]

looks not fun tho

i think the hint is one of the options: "conditionally convergent"

if you can show that you can split this sum into two sums in two different ways and arrive at different results, you'll have a conditionally convergent sum

[tepid hamlet]

(only considering positive version for 1/n since i'm pretty sure its absolutely convergent),
my only thought i've had more recently is that maybe you could write this as being bounded by the sum of two 1/n^2 sums, then obviously the terms that are not perfect squares up to n would be bounded by one of those sums since they are the same but missing some, and the square ones would be bounded by another

[vagrant prism]

and your definition of c_n is good for that

[vagrant prism]

(only considering positive version for 1/n since i'm pretty sure its absolutely convergent),
wait wait wait

sum of 1/n is divergent

oh nvm i see the argument

oh

if it is a perfect square, you can reindex

let k^2 = n

[vagrant prism]

can you show your working?

i feel like i am arriving at the same thing

[tepid hamlet]

i'm having trouble putting it into a coherent argument, i can sorta see it in my head if you know what i mean lol

but yeah like with reindexing as you say

[vagrant prism]

$\sum_{n=1}^{+\infty} c_n = \sum_{n=1}^{+\infty} \frac{1}{n^2} - \sum_{n\text{ is a perfect square}}^{+\infty} \frac{1}{n^2} - \sum_{k=1}^{\infty} \frac{1}{k}$

sooooooo

[solid kiln]

artemetra

[vagrant prism]

soooooooooo

$\sum{n=1}^{+\infty} c_n = \sum{n=1}^{+\infty} \frac{1}{n^2} - \sum{k=1}^{\infty} \left[\frac{1}{k^2} \frac{1}{k}\right]$

[solid kiln]

artemetra

[vagrant prism]

shit

lol

[tepid hamlet]

so like the sum(1/n^2) + (1/n^2) is convergent right
that means that it adds up to some limit L and we can make L - (partial sum(1/n^2) + partial sum(1/n^2)) < epsilon for any epsilon give N sufficiently large. But bump N up to the next higher perfect square so that N = M^2 and it still fulfills the epsilon thingy
now break up the problem's sum into
sum(1/n thingys) + sum(1/n^2) thingys,
the one on the right is smaller than the sum of (1/n^2)
and the one on the left is smaller than the sum of another 1/n^2
if n > M
so that must mean the series has an upper bound, which means it must also have a least upper bound which is the sum
or something like that

[vagrant prism]

$\sum_{n=1}^{+\infty} c_n = \sum_{n=1}^{+\infty} \frac{1}{n^2} - \sum_{k=1}^{+\infty} \left[\frac{1}{k^2}+\frac{1}{k}\right]$

[solid kiln]

artemetra

[vagrant prism]

give me a sec to digest

[vagrant prism]

oof, the second term is divergent

[tepid hamlet]

but you don't have like the same amount of those you know what i mean :p

theres only sqrt(n) of them ultimately

[vagrant prism]

it's to infinity bro

[tepid hamlet]

i'm just having trouble putting that into proper math

lol

[vagrant prism]

not sure where you got the sum(1/n^2) + (1/n^2) part in the very beginning

[tepid hamlet]

just something convergent to work as an upper bound

[vagrant prism]

yeah makes sense

[tepid hamlet]

well btw according to the book it really is absolutely convergent

[vagrant prism]

OOOH i see the mistake

[tepid hamlet]

i dunno if this is the right way to think about it, but i sort of think that as n-> inf then the "harmonic-looking" terms are going to be spaced further and further apart too

[vagrant prism]

$\sum{n=1}^{+\infty} c_n = \sum{n=1}^{+\infty} \frac{1}{n^2} - \sum_{k=1}^{+\infty} \left[\frac{1}{k^4}+\frac{1}{k^2}\right]$

[solid kiln]

artemetra

[vagrant prism]

it's like this

fuck

$\sum_{n=1}^{+\infty} c_n = \sum_{n=1}^{+\infty} \frac{1}{n^2} - \sum_{k=1}^{+\infty} \left[\frac{1}{k^4}+\frac{1}{k^2}\right]$

[solid kiln]

artemetra

[vagrant prism]

yes

yes it is convergent

[tepid hamlet]

trying to understand this

[vagrant prism]

absolutely too

[vagrant prism]

basically, the left term is just 1/n^2
then, i subtract all the 1/n^2 where n is a perfect square* and add -1/n when n is a perfect square

and i let n=k^2

[rough goblet]

ok am back

[tepid hamlet]

is k^2 = n?

[rough goblet]

OMG U HIJACKED MY CHANNEL?

[vagrant prism]

yes

[rough goblet]

sed

is fine, continue idm

[tepid hamlet]

well cause i wanted to keep it open for you...obviously...

[vagrant prism]

*it's so that all i have left in the left sum is 1/n^2 where n is not a perfect square

because i took out all of those that are perfect squares

[rough goblet]

fr fr
go on, idrm. imma be a bit from now anyway

[vagrant prism]

larg brian 🧠

[rough goblet]

confused ren noises
u guys go on

[tepid hamlet]

yeah i think that works, that's neat! thank you!

[vagrant prism]

no problem :D

[tepid hamlet]

this problem was bugging my brain since yesterday, whew

[rough goblet]

ok i just saw the problem
this is my take

split it into two sums each with index k

set one to -1/k

and one to 1/k^2 + 1/k

then sum from k = 1 to infty

or smth llike that

shrugs

[tepid hamlet]

that's kinda along the lines of what artemetra did

[vagrant prism]

that's kinda what i did yeah lol

[rough goblet]

oh

i just saw k^2

that's it lmfao

anyway, go on

imma b around half an hour

[tepid hamlet]

but not 1/k 😛

i'm all done i think : )

[rough goblet]

(guess)

i did it mentally

btw @tepid hamlet @vagrant prism can u like delay a channel's closing?

because i gtg do smth and i don't want this to close

well

ig not?

sighs

ok

[vagrant prism]

uh

.close

[trim jolt]

Channel closed

Closed by @vagrant prism

Use .reopen if this was a mistake.

[vagrant prism]

.reopen

[trim jolt]

✅

[rough goblet]

...

[vagrant prism]

this should delay it?

[rough goblet]

wait HWAT

[vagrant prism]

lol

[rough goblet]

U CAN DO THAT?!

HEH?!

WHAT-

[vagrant prism]

helpful rights

[rough goblet]

ISN'T THIS LIKE MY CHANNEL????

[vagrant prism]

i think

[rough goblet]

oh

i see

well, we'll see

i'll ping ya and soosh (if permissible by you) if smth happens

hm

ok back

that took a lot less time than i expected

yooo arte's here

anyway, imma try to figure the taylor series out

without any idea of whatever the frick im doing

:D

thinks furiously

continues to think

@vagrant prism @tepid hamlet sorry for the ping, but i'm clueless

[vagrant prism]

unspoiler the image

[rough goblet]

which one

you forgot soosh hijacked the channel

xD

like can you guide me to the derivation/summation/thing

[vagrant prism]

this

[rough goblet]

OKAY that's the series

i was hoping for a hint

[vagrant prism]

lol ig

[rough goblet]

@tepid hamlet by the way relating to ur emoji idm

nah dw i didnt see it properly

[tepid hamlet]

so for the maclaurin series it starts off with f(0) then the next term is f'(0) x

then f''(0)x^2/2! etc.

you can build it with that

[rough goblet]

hang on, one second

some rando from the server DMed me

[tepid hamlet]

do you want a good way to remember that logically?

[rough goblet]

asking for help

[tepid hamlet]

the maclaurin formula

[rough goblet]

no idea who he is

i don't remember it lmfao

give me a sec, soosh

sorry, am back

anyway could you (possibly) help me derive it??

soosh disappears in a puff of smoke

[tepid hamlet]

i dunno about derive, but to remember it:

think about taking the n'th derivative of the maclaurin series and then evaluating it at 0

so if you just plug 0 into that, all the terms with x factors will disappear and you just get f(0) right?

if you take the derivative though, the first term poofs away, and you're left with f'(0) then a bunch of other terms with x's, if you plug in 0 in that you get f'(0), so you get the derivative at 0 after derivating term by term

and you can keep taking derivatives and seeing how only the nth term will be leftover whenever you apply the nth derivative and plug in 0 and give you f^(n)(0)

[rough goblet]

hm

i have no idea how or why that works

[tepid hamlet]

i think it's easy to remember the formula once you see the logic of all the factorials canceling out with the powers as you take derivatvies

[rough goblet]

i don't use a formula unless i understand it

my god, i just confused "remember" with "understand"

i should really go sleep--it's 9 PM here

[vagrant prism]

where in asia are you, exactly?

lol

[rough goblet]

India

u?

[vagrant prism]

ah

[tepid hamlet]

it's going on 8am here :p

[vagrant prism]

sweden

[rough goblet]

dam

oh nice

never been there

i might go this summer

[tepid hamlet]

i'm in western US

[rough goblet]

oh that's pretty cool too

[tepid hamlet]

quite an international pow-wow

[vagrant prism]

https://tenor.com/view/wake-up-sgt-hulka-stripes-gif-22955830

[rough goblet]

tbh

i don't see anything relating to taylor series

sighs

thinks

to be honest, i should probably do this tmw...

[rough goblet]

AAAAAAAA

NO

THE ANSWER

I MUST SHIELD MY EYES

[vagrant prism]

!noans

[trim jolt]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[vagrant prism]

pls

[rough goblet]

im typing with my eyes closed rn

edit: bookmark

if possible could you spoiler that

i cant tell if what im typing is even making sense to u guys rn

us it?

[tepid hamlet]

just use the formula even though you don't understand it

[rough goblet]

guys

[blissful bison]

you spent too much time on it

[rough goblet]

im openin gmy eyes

[tepid hamlet]

https://tenor.com/view/star-wars-darth-sidious-dark-side-do-it-gif-16332079

[rough goblet]

can u like spoiler that joanna

[vagrant prism]

be not afraid

[rough goblet]

AAAAAAAAA

SHE DIDN'T SPOILER IT

WHY

[vagrant prism]

broski chill

[rough goblet]

;-;

this isn't HW

i was doing it for fun

i didn't wanna know the answer :(

[vagrant prism]

you don't seem to be having fun tho lol

[rough goblet]

i am lmfao

[blissful bison]

forgive me, you shud write, do not write all answer 🙂

[rough goblet]

im just too tired to find anything new

[tepid hamlet]

he wants to derive the whole theory of taylor series from scratch or something without learning about it : (

[rough goblet]

??

[rough goblet]

no not really

[tepid hamlet]

slight exaggeration

[rough goblet]

fr fr

"slight"

"derive the whole theory of taylor series from scratch"
slight exaggeration indeed

[blissful bison]

i thought you really needed this solution, sorry

[rough goblet]

anyway @vagrant prism @tepid hamlet and joanna luckily that was only part of the problem so i actually have smth to do
and yes i am having fun--i just can't think of anything since i've been doing questions like this since morning

[rough goblet]

all good idm

it's alright

imma call it a night y'all

joanna, arte, soosh, ty all sm for the help

[blissful bison]

if you like i can paste here some analoogus problems for you to practise,

[rough goblet]

could you DM them to me??

if possible

[blissful bison]

ok

[rough goblet]

thank you

.close

[trim jolt]

Channel closed

Closed by @rough goblet

Use .reopen if this was a mistake.

[tepid hamlet]

can you post them here though

im curious too : (

[rough goblet]

xD

@tepid hamlet one second

@tepid hamlet here

@tepid hamlet there are more
yes there are MORE somehow

wait no

[tepid hamlet]

bookmark (now i can search boomark in search thingy : )

[rough goblet]

that's it

[rough goblet]

?

[tepid hamlet]

to find it later, and thanks thats more than enough

[rough goblet]

bookmark?

OH

i se

smort

[tepid hamlet]

.close

[rough goblet]

...

it's closed

lmfao

[trim jolt]

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.

[kind spire]

https://tenor.com/view/homelander-the-boys-gif-26162796

[kind spire]

my first time here im stuck on a physics question bc i forgot basic algebra

wait what

anyways

here is the question and explanation given by the book. what im specifically confused about in the explanation is how they've gone from [A -B]^2 to (Ax-Bx)2=(Ay-By)2 in steps 1 and 2

[nova spire]

it's a +, not an equal

and the 2s next to that should be at the exponent

[kind spire]

so its just a textbook mistake?

[nova spire]

yep

$(A_x-B_x)^2+(A_y-B_y)^2 = ...$

[solid kiln]

rafilou2003

[kind spire]

oh then i get everything thanks

[rough goblet]

discord.gg/physics

[kind spire]

rightt thank u

[rough goblet]

np

!done

[trim jolt]

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

[kind spire]

.close

[trim jolt]

Channel closed

Closed by @kind spire

Use .reopen if this was a mistake.

[trim jolt]

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.

[sudden basalt]

help me

[tepid hamlet]

!original

[trim jolt]

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.

[tepid hamlet]

there's gotta be more than that

[tepid hamlet]

can you just screenshot the ENTIRE thing?

including instructions etc.?

[sudden basalt]

i know how to do the first 2

not the 3rd one

[vagrant prism]

okay so it's just h

it's just substitution

plus you already got f(a) and f(a+h)

[tepid hamlet]

if you did the first two, now you just subtract the first from the 2nd, and divide all by h, it builds on itself

[sudden basalt]

lemmi try and see what i get cuz i got it wrong the last 2 tries of similar questions

[tepid hamlet]

and simplify, some stuff will cancel out

[sudden basalt]

i did an oopsie so this is the new problem

[tepid hamlet]

so start by finding f(a+h) and f(a) then post them here

[tepid hamlet]

now when you do the third part of the problem it will be helpful to foil the (a+h)^2 in f(a+h) because some stuff will cancel out: for example the first term of the foiled version is 6a^2 and that will cancel out with the 6a^2 from the f(a)

[sudden basalt]

?

like turn (a+h)^2 into (a+h)(a+h)?

[tepid hamlet]

yeah so if we write f(a+h) as: -4+6(a^2+2ah+h^2) =-4+6a^2+12ah+6h^2

[sudden basalt]

do i distribute before i do the exponent?

[tepid hamlet]

now f(a+h) - f(a) = (-4+6a^2+12ah+6h^2) - (-4+6a^2)
and you see how the -4 and 6a^2 cancel out between them when you distribute the negative to the second paranthesis

[tepid hamlet]

no

foil first then distribute 6

[sudden basalt]

ok

(-4+6a^2 +12ah+6h^2)/h

?

[tepid hamlet]

^

[sudden basalt]

(6a-6a^2-12ah-6h^2)/h

?

[tepid hamlet]

did you read the message above?

[sudden basalt]

its confusing

[tepid hamlet]

that paranthesis you calculated is f(a+h) right? so now subtract f(a) from it

[sudden basalt]

ok

[tepid hamlet]

i'm just writing the same thing you did: f(a+h) but then also subtracted f(a)

(so top of the fraction of the 3rd part of the problem, we can divide by h after we subtract)

[sudden basalt]

(6a^2 -6a +12ah+6h^2)/h

thats what i got when i minused

[tepid hamlet]

well something went wrong

ok so

f(a+h) = (-4+6a^2-12ah-6h^2)

f(a) = -4+6a^2
so far so good yeah?

[sudden basalt]

yes

[tepid hamlet]

now we just subtract them:

f(a+h) - f(a) = (-4+6a^2-12ah-6h^2) - (-4+6a^2)

i'm gonna distribute that negative to the 2nd parenthesis:

(-4+6a^2-12ah-6h^2)+(4 - 6a^2)

[sudden basalt]

is it just 12ah+6h^2 /h?

[tepid hamlet]

now you see the first two terms in either parenthesis just completely cancel out? and you're left with:

yes that

(12ah+6h^2)/h to be precise

[sudden basalt]

12a+6h?

[tepid hamlet]

if h is nonzero

otherwise we can't divide by 0 right

[sudden basalt]

yeah

[tepid hamlet]

so not sure what this problem wants you to assume, they're obviously hinting at definition of derivative, which is as limit of h approaches 0, in which case you can divide by 0 since for the limit h is not actually equal to 0, but uh yeah since they didn't mention h is nonzero in the problem statement not sure what to think

[sudden basalt]

should i check if 12a+6h is correct?

[tepid hamlet]

^ i would just try this as the answer

personally that seems more technically correct to me

[sudden basalt]

yay its correct

thank you :)

[tepid hamlet]

sure, make sure to practice your algebra skills a lot right now

calc will eat you up otherwise

this isn't a class to coast in from lesson to lesson since it really builds on itself and youre gonna be expected to be fluent in basic algebra, and trig

[sudden basalt]

this class is college algebra

[tepid hamlet]

ohh lol, i see, i guess i was assuming it's calculus because it looked like derivative definition intro, but i guess it's also just average of a function between x = a and x = a+h, never mind :p

[sudden basalt]

the unit is called polynomial functions

its unit 6 of 10 in the class

[tepid hamlet]

gotcha

!done

[trim jolt]

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

[sudden basalt]

.close

[trim jolt]

Channel closed

Closed by @sudden basalt

Use .reopen if this was a mistake.

[trim jolt]

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.

[cobalt sandal]

wondering if anyone knows how to use desmos 3D graphing calculator to make models

[neon dirge]

3d models?

for what purpose

[wraith hinge]

#computing-software is more suitable id imagine

[neon dirge]

CAD / meshes / dotclouds have lots of software

desmos certainly isn't good at letting one export defined shapes

[cobalt sandal]

im trying to graph this shape for my calc class, its the lesson about volumes with cross sections

[cobalt sandal]

oh, ill try that too, thanks

[neon dirge]

yea for that you can use it

works like with regular function expressions

and there's tons of tutorials online

[cobalt sandal]

oh I'll look at the tutorials then, thanks

[trim jolt]

@cobalt sandal Has your question been resolved?

Channel closed

Closed by @cobalt sandal

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.

[limber carbon]

I would like to get this problem done just to help launch my grade up more in my Intro to Diff Eq class. I've attempted this question 2 times and I have no idea how the key is the answer that it is?

[worldly wing]

!status

[trim jolt]

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

[limber carbon]

1

[worldly wing]

can you separate the variables here?

okay yeah nvm

you can't

this doesn't seem like an intro to diff. equation class question...

have you been taught bernoulli DEs?

[limber carbon]

I have but I have a hard time wrapping my head around how they work. If you want I can show you my work from previous attempts?

[worldly wing]

yeah

pls show

[limber carbon]

Ok give me a sec.

Hopefully its readable.

For the y' - 4y = xy^3 problem. I thought the first thing would be is to get x by itself.

[worldly wing]

yeah that works

[limber carbon]

Then I'm lost on what to do next.

[worldly wing]

well, the same thing

substitute u=y^(-2)

[limber carbon]

So now we are taking the integral of our fraction. I'm assuming that the y next to the 4y goes away and our y^3 goes down to y^2?

[worldly wing]

yeah

you'll have C1 u'+C2 u=x

[limber carbon]

So then taking the derivative of u we get -2y^-1?

[worldly wing]

no

[limber carbon]

-2/x^3?

[worldly wing]

x? or y?

[limber carbon]

y I don't know why I said x

So I know when you have 1/u for an integral you get ln|u| + C. What should I do if I have that y'-4 in the numerator? I need to practice my Integral Calc.

[worldly wing]

what do you mean?

can you show me?

[limber carbon]

So when we get to that integration step of (y'-4)/u?

What should I do next?

[worldly wing]

no

that's wrong

split the fraction first

[worldly wing]

the y only cancels out from the second term, not from the y' term

[limber carbon]

So its still y^2. Ok.

At least under the y'

On the right track?

[limber carbon]

This feels wrong

<@&286206848099549185>

.close

[trim jolt]

Channel closed

Closed by @limber carbon

Use .reopen if this was a mistake.

[trim jolt]

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.

[junior plover]

hello

[junior plover]

I have a very quick and easy question

if im trying to prove that (1/3)k(k+1)(k+2)+(k+1)(k+2) = (1/3)(k+1)(k+2)(k+3)

can I just factor out the (k+2), cancel it, and then end up with (1/3)

.lose

.close

[trim jolt]

Channel closed

Closed by @junior plover

Use .reopen if this was a mistake.

[trim jolt]

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.

[fiery nest]

Problem is at the top

[fiery nest]

Find the value of C that makes this equation work

I don’t know how to get anything that wouldn’t just diverge

[kind axle]

can anyone answer 3 rad 864

[fiery nest]

?

[fiery nest]

Wrong channel lmao

[kind axle]

what channel is that for

[fiery nest]

An open help channel

[trim jolt]

@fiery nest Has your question been resolved?

[trim jolt]

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.

[delicate lance]

2/4 😠

[austere cedar]

,w maximum of 8x/(2xx + 18)

[solid kiln]

Results provided by WolframAlpha

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

Requested by kaynex

[austere cedar]

So you found the t-value of the maximum correctly

But why did you go on to evaluate v(0)?

[delicate lance]

because I couldnt find t so i panicked

I think thats the reason i lost 2 marks because of stupid thinking

[austere cedar]

You did. It's 3.

[delicate lance]

no that was after the quiz my friend showed me how to do it and they worte on the quiz

I put the answer as 0.4 bc i couldnt find t

Do u think i shouldve lost 2 marks for that

[austere cedar]

I'm sorry I'm here to help with math questions haha

[delicate lance]

Lolol ok np

[trim jolt]

Channel closed

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

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.

[halcyon onyx]

may someone explain why ur able to just do the underlined part

[marble wharf]

basically the same as 2 dx/dt = d/dt (2x)

[halcyon onyx]

ye but i dont see how that's the same

C^-1 is a matrix?

[marble wharf]

you could try an example

pick your favourite 2x2 matrix

and a function x

and then compute both sides

[halcyon onyx]

lemme c

[trim jolt]

@halcyon onyx Has your question been resolved?

[trim jolt]

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.

[solemn jolt]

This is simple critical point w/ second partial derivative question. I don't understand why my selection is wrong?

Transcript: Suppose we have these second partial derivatives: fxx(x,y) = 2(y+ 1), fyy(x,y) = 2, fxy(x,y) = 2x.
Now suppose we have these points: (0,0), (sqrt(2), -1), (-sqrt(2), -1).

Which of these points is a saddlepoint (there could be multiple), and which is a local maximum or a local minimum? None of these could be correct btw.

[solemn jolt]

This is all that's needed, i followed it and I'm getting B still. Idk what's wrong here!?!

[trim jolt]

@solemn jolt Has your question been resolved?

Channel closed

Closed by @solemn jolt

Use .reopen if this was a mistake.

[solemn jolt]

Scantron error, my answer was right

[trim jolt]

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.

[rapid raptor]

Someone know the answer?

[nimble stone]

i do, but do you

[rapid raptor]

D right

[nimble stone]

something like that

[rapid raptor]

.close

[trim jolt]

Channel closed

Closed by @rapid raptor

Use .reopen if this was a mistake.

[trim jolt]

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 halo]

The smallest positive integer having the remainders 2,3 and 6, when divided by 3,5 and 11 respectively lies in between what numbers?

How to solve this

[lusty delta]

is this part of a multiple choice question

(asking since that prompt doesn't make much sense on its own)

[quick halo]

It is

41-50 61-70 81-90 and 91-100

<@&286206848099549185>

[trim jolt]

@quick halo Has your question been resolved?

[quick halo]

No it has not

[quick halo]

<@&286206848099549185>

[quick halo]

.close

[trim jolt]

Channel closed

Closed by @quick halo

Use .reopen if this was a mistake.

[trim jolt]

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.

[bright patrol]

Hi there! I'm having trouble solving an Arc Length (Integral) problem.

Here's where I'm stuck at! (2nd image: "Attempt 2")

[bright patrol]

$$
\begin{aligned}
&y=\sqrt{x-x^2}+\arcsin(\sqrt{x}) \
&y'=\frac{d}{dx}\biggr[(x-x^2)^{1/2}+\arcsin(\sqrt{x})\biggr] \
&y'=\frac1{2}(x-x^2)^{-1/2}\cdot\frac{d}{dx}\biggr[(x-x^2)+\arcsin\sqrt{x}\biggr] \
&y'=\frac1{2(x-x^2)^{1/2}}\cdot(1-2x)+\frac1{\sqrt{1-x}}\cdot\frac{d}{dx}\sqrt{x} \
&y'=\frac1{2(x-x^2)^{1/2}}\cdot(1-2x)+\frac1{\sqrt{1-x}}\cdot\frac1{2}x^{-1/2} \
&y'=\frac{1-2x}{2(x-x^2)^{1/2}}+\frac1{2x^{1/2}\sqrt{1-x}} \
&\int_0^1\sqrt{1+y'^2}:dx \
&\int_0^1\sqrt{1+\biggr(\frac{1-2x}{2(x-x^2)^{1/2}}+\frac1{2x^{1/2}\sqrt{1-x}}\biggr)^2}
\end{aligned}
$$

[solid kiln]

AWACS Sky Eye

[bright patrol]

<@&286206848099549185>

[trim jolt]

@bright patrol Has your question been resolved?

[bright patrol]

<@&286206848099549185>

[edgy willow]

that's right, it's just there's a gigantic simplification for the bottom fractions that makes it nice

like the denominators are actually just the same if you factor out a sqrt(x)

[bright patrol]

is there any other things to watch out for or to try? i don't know if i'll get a question like this on my exam

[edgy willow]

ummm not much to learn here except that the expression should greatly simplify if you're going to have to do an integral of sqrt(1+...^2)

like here it reduces to 1/x or something

[bright patrol]

cheers, man.

.close

[trim jolt]

Channel closed

Closed by @bright patrol

Use .reopen if this was a mistake.

[trim jolt]

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.

[heavy elbow]

i have no idea how to set up 34

[heavy elbow]

24*

[trim jolt]

@heavy elbow Has your question been resolved?

[trim jolt]

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.

[full fossil]

this is quite a general question, but I don't understand how log restrictions work

[full fossil]

more specifically: why can't the base be negative, 0, or 1

[gritty gyro]

0 to the power of anything is undefined, 1 to the power of anything is 1 and cannot be defined for any value not equal to 1

[full fossil]

wait 0 to the power of let's say 2 isn't 0?

i thought it was only undefined for negative exponents & 0

why does the fact that it can't be defined for any value not equal to 1 make it a restriction (sorry about the poor wording)

also, my math teacher said you can't have an exponential function with a negative base, but I don't see why not?

[ionic pendant]

(-2)^x where x is not an integer leads into the rabbit hole of complex numbers, which is outside the scope of the class

[full fossil]

I would be interested in learning about it if possible, can you provide any resources?

[ionic pendant]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/a/intro-to-complex-numbers

[full fossil]

thanks (: is there anything specifically about complex logarithms?

I tried looking at the wikipedia article but was immensely confused

I definitely just lack a lot of background knowledge, but negative bases are still possible right? just not taught at the high school level

[ionic pendant]

when you start considering fractional powers of complex numbers, then there are many different ``valid'' roots. you know how $x^2 = 2$ has two solutions $+\sqrt{2}$ and $-\sqrt{2}$, whereas $x^3 = 2$ `only' has solution $x = \sqrt[3]{2}$. But when you consider complex solutions, it actually has 3, and the pattern continues like that. so there are 3 different (valid) complex numbers that can be considered $(-2)^{1/3}$, so there become some weird difficulties of ``choosing which one", which translates into logarithms with multiple outputs. By the time you get into complex number logarithms, you usually only consider the natural (base $e$) logarithm, since any other logarithm can be changed into that with the change-of-base formula

[solid kiln]

cloud

[full fossil]

thank you so much - also, is it ok for them to have multiple outputs? would it still be considered a logarithmic function?

[ionic pendant]

traditionally functions only have 1 output, which is why functions like roots and logarithms for complex numbers becomes weird, since they're not functions in that sense anymore

[full fossil]

okok

[ionic pendant]

they're sometimes called "multivalued functions", although it's a bit confusing terminology wise (since we usually define a function based on the fact that it only has one output value)

[full fossil]

i see

regarding base 1 and 0, do we not use it just because its not useful? or because you'd end up with multiple outputs? or something to do with it not obeying the laws, which a classmate of mine mentioned

[ionic pendant]

with logarithms, we know that [ \log_2 (16) = 4 ] conveys the same information as [ 2^4 = 16]. but since [1^x] can only output one value, the only sensible input to $\log_1$ would be $1$, and a function with only 1 input (and infinitely many possible outputs) isn't very useful. To take a different approach, we know the log base change formula: [ \log_2 (x) = \frac{\log_{10}(x)}{\log_{10}(2)} ] But for every base, since for any number $a^0 = 1$, it means that [ \log 1 = 0 ] so to try and use $\log_1$ via that formula would result in dividing by 0

[solid kiln]

cloud

[ionic pendant]

for log base 0, we run into the same difficulty where 0 to any power is itself, and using the log base change formula doesn't work either, since log(0) is not defined for any base (you can't take any number to a power and make it 0 if that number isn't 0)

[full fossil]

i see

[full fossil]

got it

sorry to bother you again

but there's this one question on our workbook where the answer doesn't make much sense to me

the answer is D, which is fairly reasonable

but I was wondering why if they're using log base restrictions (x > 0), why they included x = 1