help-10

[shrewd egret]

☠

[crisp cradle]

adj = 5.6/tan 55

put on calc

then there u got it

round it off also

dont forget

[shrewd egret]

Idk what the f am I doing

[crisp cradle]

uh oh

ill calculate it

[shrewd egret]

Plsss I'm sorry for my stupid ass

I'm only a major in Economy

[crisp cradle]

3.9211 = 4

[shrewd egret]

TYSM

[crisp cradle]

hehe you're welcome!

[shrewd egret]

Me relieve that I finished it and realized I have many more to do

[crisp cradle]

HAHAHAHA

[shrewd egret]

[crisp cradle]

6 shud be same thing as earlier

[shrewd egret]

It's a tangent?

[crisp cradle]

wait hold up

can u draw it

[shrewd egret]

What number

6?

[crisp cradle]

yeap

u askin that one right

[shrewd egret]

Hol up

I hope I ain't taking much of your time lmao

[crisp cradle]

its oki

[shrewd egret]

Really appreciate your help

[crisp cradle]

im free rn

[shrewd egret]

Blurry goddayum

[crisp cradle]

ahh

use sin then

soh

looking for hyp

[shrewd egret]

Longest side?

Hol up

[crisp cradle]

isntit

🤨

im confuse oso

[shrewd egret]

What in the Albert Einstein am I doing

[crisp cradle]

ehh

[shrewd egret]

What now

[crisp cradle]

yeah

thats correct

[shrewd egret]

I am confused as you are

Lmao

[crisp cradle]

no gud brain not braining

[shrewd egret]

Even my calculator is wondering wtf is this guy doing

[crisp cradle]

HAHAHAHAHA

[shrewd egret]

Wait

Do I need to round this off or na

[crisp cradle]

qs said to round off

[shrewd egret]

It says in the question round off to a whole number

[crisp cradle]

😭😭😭

[shrewd egret]

Deadass

[crisp cradle]

THEN YES LAAA

omaiii

😭😭😭

[shrewd egret]

My brain is not braining in 12am

[crisp cradle]

as if my brain is

haiya

[shrewd egret]

I'm a disgrace to my asianese culture

Zesty alr

Now onto number 8

[crisp cradle]

🤣

my brain cant process the words

can u draw HAHAHA

😭

[viral ridge]

how much is 2+2?????????

[crisp cradle]

4

thats so random

[shrewd egret]

Most sane discord member

Alrighty

[shrewd egret]

Not saying that I can't but a Lil bit

[crisp cradle]

draw diagram qs 8 bro

[shrewd egret]

Why is all of my pictures sideways

Like this?

[crisp cradle]

me dunno bro

u very sure thats the diagram ah

[shrewd egret]

Im very sure of my existence my guy

[crisp cradle]

HAHAHAHA

try solve lah

soh cah toa

which one

u think

qs want the height

height = opposite

we have hypo

[shrewd egret]

Sine?

Soh*

WAYT

Is it soh?

Since its finding the hypo

[crisp cradle]

finding opposite lah wym hypo

hypo alr given

but yes sine

go calculate

round of nearest hundredths

[shrewd egret]

Otw coacj

[crisp cradle]

[crisp cradle]

ek

soh
sin 53= opp/27

opp= 27sin53

🤨🤨🤨🤨

why divide

[shrewd egret]

Wayt

DID I DO IT WRONG

[crisp cradle]

basically make opposite the subject

i cross multiply it

[crisp cradle]

so i got this

27 × sin(53)

[shrewd egret]

Oh you multiplied it?

[crisp cradle]

im so sleepy already bro😭😭

[shrewd egret]

Wayt lemme

[crisp cradle]

yes bro

[shrewd egret]

Coffee

[crisp cradle]

its alr 12:58

coffee not working

[shrewd egret]

Wayt

Philippines?

Lemme guess

[crisp cradle]

naur

oi do hw

stop guessin

[shrewd egret]

21

27 x sin(53) is 21?

[crisp cradle]

is it

[shrewd egret]

It says on my calc

Even I don't trust my calcu

[crisp cradle]

21.5631

[shrewd egret]

21.5 to be exact

[crisp cradle]

then u round off

nearest hundredth

which is 21.56

oki bro next faster

draw diagram

[shrewd egret]

Okay wayt

It's finding the angle basically

[crisp cradle]

use soh cah toa

[shrewd egret]

Toa?

[crisp cradle]

yeap

[shrewd egret]

Alrighty

[crisp cradle]

angle - theta so

tan theta = opp/adj

[shrewd egret]

Theta?

[crisp cradle]

uhh theta is the angle

can be tan x

[shrewd egret]

Oh

[crisp cradle]

label it anything u want

and then theta = tan^-1 (opp/adj)

[shrewd egret]

Hol up am I doing it right

[crisp cradle]

ah okii

then thats the ans

degree right ?

[shrewd egret]

My brain is now successfully brajnjng

[crisp cradle]

if degree round of to 1 decimal place

[shrewd egret]

30.9?

[crisp cradle]

nope

31.0°

cuz 6 is big, then 9+1 which 10 already so cannot

[shrewd egret]

My dumbass

[crisp cradle]

🤣

[shrewd egret]

Bro a 6th grader can be smarter than me

[crisp cradle]

mhm true

[shrewd egret]

LAST ONE BABY

[crisp cradle]

yes

draw

[shrewd egret]

.

Toa?

[crisp cradle]

where diagram

[shrewd egret]

It's finding the angle again

[crisp cradle]

u hv hyp n opp

soh

[shrewd egret]

Oh soh

Just like 9 before?

[crisp cradle]

mhm

[shrewd egret]

Wait a sec

Ye it's good

No need to round it off

Why is there 2 answers btw

@crisp cradle heres the ans btw

[crisp cradle]

sleepy

[shrewd egret]

Bro ti's the last one

Is it 155?

[crisp cradle]

hmmwhat qs

wait

[shrewd egret]

What qs

That's the last one lol

[crisp cradle]

angle

the angle should be below 90°

[shrewd egret]

24.6?

[crisp cradle]

hm

[shrewd egret]

Alrighty

[crisp cradle]

yes

[shrewd egret]

We can go bye bye sleep now

[crisp cradle]

oki byebye

[shrewd egret]

THANKS FOR THE HELP BTW

[crisp cradle]

wilkam ^^

[shrewd egret]

I understand the lessonalot now

Nytie

[crisp cradle]

good job

night

[obtuse pebble]

@shrewd egret Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[autumn kiln]

Can someone please help me with part 3

[autumn kiln]

I’ve sent a pic of my workings so far

[obtuse pebble]

@autumn kiln Has your question been resolved?

[autumn kiln]

<@&286206848099549185>

[obtuse pebble]

@autumn kiln Has your question been resolved?

[obtuse pebble]

@autumn kiln Has your question been resolved?

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[fathom flicker]

I have a question about this, because I am watching a lecture that goes over a proof of this

and instead of doing the method above, they do something more roundabout and I am wondering why they might be doing that

[warm shale]

AustinU

AustinU

AustinU

AustinU

[fathom flicker]

and then they finally conclude from that, that q<2
but why not just do it the way that I did? I don't see anything wrong with it..

for the equality q^2<4, taking the square root of both sides implies that |q|<2, not strictly q<2, but the set already restricts q>0, so |q|=q. If I had to write that out, I could. Would that then make mine fine? Or is there anything wrong with it as is?

[unreal musk]

I mean as you're assuming q>0 I would think that it was fine (as square [roots] are increasing (for positive inputs), unless there's something clear I'm missing out on

[forest sinew]

same

[fathom flicker]

the elements of the set E are ${q\in Q: q>0$ $q^{2}<2}$

so it is not an assumption that q>0

right?

[warm shale]

AustinU

[dark stirrup]

You mean an upper bound in R?

[fathom flicker]

just any upper bound, not a supremum

an upper bound in Q

but not a supremum in Q because there isn't one

which is what I am getting to

[dark stirrup]

Then there is none

[fathom flicker]

yeah 2 is an upper bound

[dark stirrup]

Oh

Nvm

[fathom flicker]

it just isn't the least upper bound

[dark stirrup]

Right

I'm

[fathom flicker]

I just can't see a reason why the professor did the proof in the way I wrote above, like its really confusing me

seems easy/fair enough to do it my way, and if need be to include the part about since q>0 |q|=q yadda-yadda

still less steps

[dark stirrup]

Maybe there's some property about increasing that hasn't been proven yet

These analysis proofs are tricky because you have to be very careful with easy assumptions

Why not ask your prof?

[unreal musk]

Hmmm I mean there are times where I've seen something explained in the most roundabout way when there's a significantly easier way to explain it, but then in some other cases there is a good reason to

[fathom flicker]

because it's just an online course, I'm still not in school

I'm just perusing

[unreal musk]

Is there like a comment feature or anything there, or not?

[fathom flicker]

I could send the timestamp/lecture if you want, but I don't see anything significant about it

https://youtu.be/mlPLLXHZ8_U?t=700

[dark stirrup]

Ok

If I had to guess...

You don't have access to the property $0<a<b\implies 0<\sqrt{a}<\sqrt{b}$ yet.

[fathom flicker]

maybe not wanting to make use of absolute values yet? or something

[warm shale]

SWR

[dark stirrup]

That's my guess

[fathom flicker]

hmm

We have not proven that yet

[unreal musk]

[or that it's easier to not have to explain that by doing it that way]

[fathom flicker]

so if that means I don't have access

then that'd be it

[dark stirrup]

I'm not sure how trivial it is to prove

"Obvious" things are hard to prove, especially with inequalities

[fathom flicker]

agreed

Okay. Fair enough then

[dark stirrup]

But yeah, I would water that is the reason, your professor avoids using square root

[fathom flicker]

I guess that makes sense because like

you could just say since

q^2 < 2 then q<sqrt(2) and be done

if you were allowed square roots

but sqrt(2) isn't in Q so I guess ehhh

but

I see what you mean

[dark stirrup]

Ehhh indeed

Real analysis is one of those funny classes

All the obvious things from calculus now need to be proven

[fathom flicker]

I feel like all of the things from calculus were not so obvious to me

but the formulas were easy enough to learn

assuming much much less easy to prove

[dark stirrup]

I had a really good calculus teacher

He wouldn't let me goof off

[fathom flicker]

I don't take it for real until 2 years though I think because next year I'm just taking like a weird course with a weird name, idk how to describe it. Not calculus but not analysis either

[dark stirrup]

What's the name?

Topology?

[fathom flicker]

Honors Advanced Calculus (but again, it's not really calculus at all) it comes after calc1-3 and multivariable calc

in it's description it says it covers the content of: intro to proofs, intro to real analysis, fundamental concepts of analysis, complex analysis, and two other course codes that I can't find what they used to be

so I just decided my best bet would be to study some analysis beforehand

[dark stirrup]

Yeah sounds like a bridge to analysis

Complex anal is fun

[fathom flicker]

I've heard that before

well thanks for the help, and ty chartbit

.close

[obtuse pebble]

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[crude plover]

why is f"(-0.5) < 0

[warm canopy]

what does the second derivative tell you about a function

[obtuse pebble]

@crude plover Has your question been resolved?

[crude plover]

concave up or down

intercepts represent point of inflection

[warm canopy]

then you now know why f''(-0.5) < 0

[obtuse pebble]

@crude plover Has your question been resolved?

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[misty jetty]

find the angle next to 140 using supplmetray angles. then find 1 using 112 and the angle u just found using supplemetary angle rule

[tepid goblet]

Please notice that two lines are just opposite vectors, so, they form 180º. Keep that in mind

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

@timid silo Has your question been resolved?

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[timid silo]

Why do we not know x_2^k is bounded but we do know x_1^k is?

[warm canopy]

Why do you think we don't know x_2^k is bounded?

[timid silo]

im not sure

maybe because its not the first term?

[warm canopy]

No I mean

We do know its bounded

And i don't know why you think we don't

[timid silo]

then why do we take $x_2^{(k_j)}$ instead of just $x_2^{(k)}$ as the bounded sequence to take a convergent subsequence

[warm shale]

! matthewzz

[timid silo]

I remember my professor said its important to keep taking subsequences and im not sure as to why

[warm canopy]

Because otherwise you won't have x_i^(k_m) -> x_i for all i

If you just take a random convergent subsequence of each x_i^k then you have no way to "glue them together" to make a convergent subsequence x^(k_m)

[obtuse pebble]

@timid silo Has your question been resolved?

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[timid silo]

.reopen

[obtuse pebble]

✅

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

im confused by thi

why does he take the subseq $x_2^{(k_{j_{l}})}$?

[warm shale]

! matthewzz

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

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[normal perch]

How would I start this?

[jolly ginkgo]

what are the factors of polynomial if the zeros are given?

[normal perch]

Then I divide into two categories then multiply iver?

Then multiply the two again for one big number

Then combine like terms

[jolly ginkgo]

into categories

?

[normal perch]

Like this

,rotate

[jolly ginkgo]

yes

[normal perch]

Great

What about a question like this

[jolly ginkgo]

you know vertex form of quadratic equation?

[normal perch]

I probably do if it was set out but just saying to do it I couldn’t atm

[jolly ginkgo]

anyway you can do it in other way too

[normal perch]

Like, for the question how would I star

Start

[jolly ginkgo]

A quadratic equation is of the form $y=ax^2+bx+c$ and it's derivative is $y=2ax+b$ you can input the values of given points to get value of $a,b,c$

[warm shale]

fäf

[normal perch]

Uh

This is how my teacher did it but I didn’t understand how to follow

.close

[obtuse pebble]

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

how do i do this?

[willow fractal]

i keep trying this but am off

[storm scaffold]

Show your work

[willow fractal]

ill try to take a picture of a more organized step by step process of what i did

[storm scaffold]

Yes

[willow fractal]

give me a few min

[storm scaffold]

Ok

[willow fractal]

Here it is

sob

[obtuse pebble]

@willow fractal Has your question been resolved?

[willow fractal]

NO

IM CRYING BOT

[storm scaffold]

• distri utes

Minus distributes

[jolly ginkgo]

pls don't cry

I'll feel bad

[willow fractal]

wait a minute

still doesnt get the right answer

aguhga

[jolly ginkgo]

[storm scaffold]

Part of the process was that

[willow fractal]

mmmm thonking

OH WAIT

I GOT IT

OMG

THANK YOU

.clse

[storm scaffold]

Uh

[willow fractal]

.close

[obtuse pebble]

Channel closed

Closed by @willow fractal

Use .reopen if this was a mistake.

[storm scaffold]

What was it

Nvm

[willow fractal]

i forgot to factor -2xy - y^2

and get the y out

[obtuse pebble]

Available help channel!

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Remember:
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[obtuse pebble]

@distant flame Has your question been resolved?

[distant flame]

<@&286206848099549185>

[royal basin]

!show

[obtuse pebble]

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

[distant flame]

ya let me show u my work

i solve itttttttttt just right now

[knotty gulch]

yeah

you are correct

[obtuse pebble]

@distant flame Has your question been resolved?

[obtuse pebble]

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[uneven night]

Can someone help me solve this?

[dire valley]

x=rcos(theta)
and y=rsin(theta)

[uneven night]

yeah i got that but what is my boundaries?

i got r is between 0 and square root(2) but what is my bound for phi

[dire valley]

a circle ring

[uneven night]

so between 0 and 2pi?

[dire valley]

1<=r<=2 and 0<=theta<=2pi

[uneven night]

thanks so much

it makes sense

[dire valley]

oh sorry that sq2

[uneven night]

yeah i got that

but how do i integrate

or which do i integrate first

Is this correct?

[kind hawk]

for double integrals you can integrate them in either order

(in most cases, by fubini)

[uneven night]

Oh okay

[uneven night]

but i'm i doing right @kind hawk

i mean should it be now partial integration?

[kind hawk]

well the lower bound for r is false

it is also a good idea to write down for which variable these bounds are

$\int_{\theta=0}^{2\pi} \int_{r=1}^{\sqrt2} \ldots dr d\theta$

for example

[warm shale]

Denascite

[uneven night]

yes my bad

[kind hawk]

I'm also not sure what you wrote before the r^2 inside the ln?

[uneven night]

but how do i move on now since i have product of two r

its 2

[kind hawk]

why

[uneven night]

r^2+r^2=2r^2?

[kind hawk]

on a circle, x^2+y^2=r^2, not x^2+y^2=2r^2

well but its not r^2+r^2

its r^2 cos^2+r^2 sin^2 = r^2(cos^2+sin^2)=r^2

you can try ibp but there is something else that works better here

[uneven night]

ofc i agree, my bad also

[uneven night]

what is better here

[kind hawk]

there are only 2 usual integration techniques

so take a guess

[uneven night]

when we have ln we can do something with 1

maybe?

hmmmm

or no i don't really know

[kind hawk]

what are the big 2 integration techniques

[uneven night]

IBP and maybe SUB

[kind hawk]

u-sub, yes

[uneven night]

try to sub 1+r^2?

[kind hawk]

yes

what do you get

[uneven night]

well i will get du/2r

and the r will cancel out

thanks so much

[kind hawk]

yes

[uneven night]

you r best

[kind hawk]

dont give out solutions

[dire valley]

oh sorry

[kind hawk]

also better to do a proper u-sub instead of using stuff like dr^2 which is just confusing to people

[uneven night]

I got this

Should I integrate this with dphi?

i get wrong answer for some reason? @kind hawk

the real answer should be pi(ln27/4-1)

[kind hawk]

lets not forget log laws

[uneven night]

ln3-ln2 is ln3/2

but it dosen't change anything

[kind hawk]

you cant just combine these

you have a factor before the ln(3)

[uneven night]

3/2

but is 3/2Ln 3-Ln2-1/2 is correct

so now i should use ln laws?

[kind hawk]

try to use ln laws to simplify this as much as possible

and hopefully end up with the other solution

[uneven night]

ln3^3/2?

i don't really know how to simplify 3/2ln3-ln2-1/2'

[kind hawk]

thats the first step. keep going

[uneven night]

and now Ln3^3/2divide by2 -1/2

Like this

[kind hawk]

yes

and lets not forget about the 2pi in front

[uneven night]

You mean I should integrate now in 2pi and 0

[kind hawk]

no thats not what I said

your expression was 2pi(....)

you conveniently forget about that 2pi

[uneven night]

Yea ofc that’s because I integrated on the 0 and 2 PI

But yeah it get like you say

[kind hawk]

jesus that 2 is unreadable

that's an n

[uneven night]

Hahahaha

Sorry

[kind hawk]

now also pull that 2 inside the log

[uneven night]

Like this?

[kind hawk]

no you forgot some brackets

[uneven night]

Omg almost right

[uneven night]

Wait what

Ohhh

It should be outside the whole

Thanks so much @kind hawk

This was really hard question

I wouldn’t do that without you

[kind hawk]

well the last part was just some basics

that you should probably revisit

[uneven night]

That’s right

[uneven night]

I will do it

Thanks again!

.close

[obtuse pebble]

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[eager star]

help

[eager star]

with B and D

omg im actually dumb

nevermind

.close

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[uneven night]

can somone help me to find the bounds?

[obtuse pebble]

@uneven night Has your question been resolved?

[thick gyro]

i saw that you wanted to convert it to polar

[uneven night]

How did u find that ??

[thick gyro]

my head, but you can also use desmos

[uneven night]

But I will not have Desmos if I will approach this question In a test so I wonder how did you think?

I wanna learn to see it in my head also

[thick gyro]

well i drew the lines x -x and circle with radius 1

i know that everything is contained within the radius

so

[uneven night]

Ofc now it make sense

[uneven night]

So x is blue line and -x is the green line?

@thick gyro

[thick gyro]

well yes

its colour coded on the left

[obtuse pebble]

@uneven night Has your question been resolved?

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[timid silo]

in y = mx + c , "c" is a y-intercept but why are we specifically taking y intercept as a constant..... why not x-intercept?

[sage geode]

There is a form including the x intercept

[timid silo]

what form?

[ruby path]

It's just a lot more convenient

Because this form preserves the slope, and can also easily be written as a function

[sage geode]

y = a(x - b)

a is slope and b is x intercept

[timid silo]

ooohhhh

thx for clarifying my stupid doubt 💀

.close

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[exotic oak]

If I'm doing the function study and I find that the limit of the function with x going to + and - infinity both make + infinity, then in theory there should be no oblique assistants

[high lily]

where are you getting that idea

[sage geode]

What's an oblique assistant?

[teal turret]

oblique asymptote

[high lily]

lol i didn't even look at that last word,

assumed it was going to be asymptote since it started with a and the preceeding word was oblique

[teal turret]

oblique asymptote happens when numerator degree - denominator degree = 1

[exotic oak]

So if i don't have a denominator it can't be a oblique asymptote

I'm sorry for my english

[sage geode]

Rational functions are not the only functions having oblique asymptotes

[sage geode]

Take something like |x| + 1/x I guess

[exotic oak]

If i have lim x -> +ininity of | x + sinx | = +infinity and with -infinity = +infinity, it's impossible we could have an oblique asymptote?

[sage geode]

Yeah

[sage geode]

But consider this

[exotic oak]

Thank you very much!

Hmh i see

Thanks!

.close

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[timid silo]

so i was in middle of finding normal form of eq and i am getting two different values for theta.... or did i make a mistake somewhere?

[gleaming ridge]

Since trig functions are periodic there will be infinitely many solutions in fact unless you restrict the domain

[timid silo]

ohh so the sign is telling me where the line is standing... is that how it works?

[gleaming ridge]

If both sin and cos are positive then you're in 1st quadrant, both negative means 3rd quadrant. Only sin positive is 2nd and only cos positive is 4th.

[timid silo]

ok

thx

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[tulip anvil]

How do you integrate (x^2).(x^3 +9)^1/2?

[haughty coyote]

u-sub

[tulip anvil]

Oh yeah im dumb

Mb

.close

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[haughty coyote]

When sometihng looks complicated, always try to set u = that
It works out fairly often

Especially when it's the inside of a function

[obtuse pebble]

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[frozen acorn]

hi

[frozen acorn]

how do i solve this?

[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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[half crown]

u charlie

[tropic dagger]

Hey Emp do you still need help?

[obtuse pebble]

@frozen acorn Has your question been resolved?

[obtuse pebble]

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[proven zealot]

can anyone explain why the infinity part will be gone

[wooden cipher]

x^(-theta)=(1/x)^theta

What happens when you plug in infinity?

[proven zealot]

ahhh

[obtuse pebble]

@proven zealot Has your question been resolved?

[brazen nacelle]

X^-inf = 0 then 0 multiply the rest = 0 then - - will be positive

[obtuse pebble]

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[normal perch]

,rotate

[normal perch]

So I understood 90% of this but when making the equations on the right side I’m not sure why it’s x^2 and then -x on bottom

I just wanted to see if anyone could explain why that’s made

[teal turret]

Are u wondering about the degree or the coefficients

[normal perch]

These ones

[teal turret]

Well those were the results after the synthetic division, can u elaborate as to what ur actually confused about? Do u think it shd be something else?

[normal perch]

I understand the x^3 the -8x and -12 but idk how it got x^2

From the -9x^2

@teal turret

[obtuse pebble]

@normal perch Has your question been resolved?

[obtuse pebble]

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[static oar]

hi i need help with venn diagrams

[static oar]

so i have a problem but one of the sides of the venn diagram is missing

the problem is the following

60 pcs have been inspected

23 have a hard drive error only

18 have both a hard drive and short circuit error

the questions im being asked are

how many pcs have a short circuit error only

and how many have no errors at all

[half crown]

u there @static oar

[static oar]

ys

[half crown]

okay

so just answer my question for this one okay

23 have hard drive error only, and 18 have both hard and short circuit error right

so how many people have hard problem?

[static oar]

how many ppl have short circuit

and how many have none

[half crown]

answer my question thomas

[static oar]

how many ppl have hard problem

well that is 41

23 + 81

[half crown]

okay good, so how many people don't have hard-drive problem then

[static oar]

idk

60 - 41 is 19, but how that 19 is distributed is unknown

maybe the 19 computers dont have any problems

maybe 4 have a short circuit and 15 are good

[half crown]

so 19 people are either from short circuit only or none right?

[static oar]

yes

[half crown]

hmm, let me think for a sec

[static oar]

kk

[half crown]

are u sure this is the full question?

[static oar]

yes

that is it

ive been stuck on it for 2 hours

"They found that the failures are due to defects in the hard drive and defects in the motherboard. There are 18 computers that have both faults and 23 only on the motherboard. 60 computers were reviewed"

this is literally wat i have

[half crown]

do u have answer i think short ciruit only is 1?

[static oar]

hmm whys that

[half crown]

do u have answer thou?

[static oar]

no

thats y im asking

[half crown]

well let's see here
assuming this assumption is correct

Short circuit error only = (Total inspected - No errors - Hard drive error only - Short circuit and hard drive error) - (Short circuit and hard drive error)

Short circuit error only = (60 - No errors - 23 - 18) - 18

No errors = Total inspected - Hard drive error only - Short circuit error only - Short circuit and hard drive error

No errors = 60 - 23 - ((60 - No errors - 23 - 18) - 18) - 18

Short circuit + no-error = 19

short ciruit = 19 - no error

can we find no-error out of the last equation?

[static oar]

idk

there has t be a way according to the problem

but it makes no sense to me

[half crown]

which satetement does not make sense to you tell me

[static oar]

well were never told the other side

were never told how many computers have no error

so how can we get the short circuit side

[half crown]

short ciruit only = 60(all) - 23(hard drive only) - 18(both) - none

[static oar]

how do u find the none tho?

u dont know none

[half crown]

I think i can solve it but I will solve it tmrw it's night 11 in the evening. uh can u dm me the question right now?

[static oar]

ok

[half crown]

but we know their sum is 19 😛 do other question for now

[static oar]

yes, and?

we dont know how its split

[half crown]

their is only one varaiable x if we really think about it

i assume it can be solve using subtitution method but whatever for now

[obtuse pebble]

@static oar Has your question been resolved?

[static oar]

no

[obtuse pebble]

@static oar Has your question been resolved?

[static oar]

not yet mr robot

[obtuse pebble]

@static oar Has your question been resolved?

[static oar]

No

[obtuse pebble]

@static oar Has your question been resolved?

[timid silo]

Equation please

[static oar]

@timid silo

[obtuse pebble]

@static oar Has your question been resolved?

[static oar]

No

[obtuse pebble]

@static oar Has your question been resolved?

[static oar]

No

[obtuse pebble]

@static oar Has your question been resolved?

[crimson berry]

draw a diagram

[violet vine]

Are u sure it's possible

Cuz the answer ranges from 0,19 where 18 is a subset of the 23+18
To 19,0 where all devices have errors

[static oar]

I did

[static oar]

Idk

[crimson berry]

Then... show the diagram

[civic socket]

,tex .original

[warm shale]

Akira

[obtuse pebble]

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[obtuse pebble]

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[plain pumice]

so i need some help understanding how this works i got this question då means when and it says the answer is 1

[twin sapphire]

you dont know how absolute value works?

[plain pumice]

i dont

[twin sapphire]

ok so its simple

|a| = a if a is positive

|a| = -a if a is negative

so calculate whats inside

and apply this rule to get the answer

[plain pumice]

alright let my small brain try here 5 - 6 = -1? OH WAIT I GOT IT

so if lets say the answer is -1 on the result

then its the negative of that which is just 1

but if the answer was 1 from the question it remains 1

my brain will just take this as
postive equals postive
negative equals positive
is that correct?

or did i manage to confuse myself into the wrong dimension

got it thank you i understand absolute values now

.close

[obtuse pebble]

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[modest falcon]

I need to calculate the derivative of this thing. My plan was to solve the integral first and then derive. But I cannot solve the integral. Can someone help me with?

[modest falcon]

and I should also calculate this one in the same task

[twin sapphire]

start with the obvious u = cos(x) maybe?

or something along those lines

unless you know some derivative theorems for integrals

[modest falcon]

I tried starting with the weierstrass thing t = tan(x/2). But I didnt really came along. It was a mess super quick

[twin sapphire]

do you know any derivative theorem?

under the integral?

[modest falcon]

No

at least i dont think i do

[twin sapphire]

you would know

it should be its own chapter in a real analysis course

but then indeed this looks undoable in a reasonable amount of time

by just finding a primitive

[modest falcon]

Well, last lecture I was sick, we talked about some partial derivatives ways. I assume this is what you mean

[tardy epoch]

You just change the order of differentiation and integration

[modest falcon]

but it's not that I really understood it

[tardy epoch]

d/da of the integrand

[twin sapphire]

its only applicable under certain circumstances though which you have to verify before doing it

[modest falcon]

So, technically I derive by x and integrate with a (or the other way around=

Well, I need to study this first

[twin sapphire]

yes

essentially three conditions

the function must be integrable

differentiable

with regards to another variable

and the derivative must be dominated

by an integrable function

[modest falcon]

ye well, I am just watching some stuff and reading some stuff about it and then will try to solve it

[obtuse pebble]

@modest falcon Has your question been resolved?

[modest falcon]

Well, I found a way to solve the derivative now. I think at least. It's a solution that I had to look up for a lot. But overall I get what I did here. Technically, I just derived the inner part first and then integrated. Which should work since the function only is given in (-1,1). x is not pi/2 which is stated above.

[modest falcon]

Can someone help me with the integral then? I am not really making progress with that one.

[tardy epoch]

Show your derivative of the integrand

[tardy epoch]

.

[modest falcon]

The second substitution came actually from the calculator but it seemed to work out

[tardy epoch]

,w int 1/(1+a * cos(x)) dx

[warm shale]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tardy epoch]

You did the right substitution t=tan(x/2)

[modest falcon]

And the rest? Is it okay?

well, I'm going to get some sleep now. Will try to see if I can calculate the integral itself tomorrow. Shouldn't be too complicated right. Idk if I need to close this channel or not, but if so feel free to do so

[tardy epoch]

You should close

Just look in your history later

[obtuse pebble]

@modest falcon Has your question been resolved?

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[worldly narwhal]

i need help

[worldly narwhal]

on geometric sequences

algebra 2

if they give me 2 _ 2/9

how would i find the term (underscore) in the middle

[grizzled shore]

What do you know about geometric sequences

[worldly narwhal]

the formula

[grizzled shore]

Not the formula

What is special about a geometric sequence

[worldly narwhal]

first term (multiplier)^x-1

only multiplying

arithmetic is adding

[grizzled shore]

So a geometric sequence is where consecutive numbers are…?

[worldly narwhal]

you’re

yes

[grizzled shore]

How are they different

[worldly narwhal]

like

2 4 6 8

constant multiplier

and arithmetic is constant adder

[grizzled shore]

Right

So we know from 2 to _

We multiply by something

[worldly narwhal]

yes

u gotta

go to a diff channel

for that

[grizzled shore]

Let’s call this _ x

[worldly narwhal]

okay

[grizzled shore]

And let’s call the scaling factor k

We know 2 * k = x

[worldly narwhal]

yes

[grizzled shore]

Ok what else do we know?

Is there a connection between x and 2/9?

[worldly narwhal]

yes

there’s a constant multiplier

needed

to get that middle term

[grizzled shore]

What’s the constant multiplier?

[worldly narwhal]

2/9 divided by 2

?

[grizzled shore]

Nah

[worldly narwhal]

oh

[grizzled shore]

.

[worldly narwhal]

well

i think that’s where i’m going wrong

would it be like

2 times x^2 = 2/9

[grizzled shore]

Not quite

[worldly narwhal]

then sqrt it?

after divine

g

[grizzled shore]

For a geometric sequence, $ a_1, a_2, a_3\$
$\frac{a_3}{a_2}=\frac{a_2}{a_1}=k$

[warm shale]

Frosst

[grizzled shore]

This works for all geometric sequences because that’s how they are defined

[worldly narwhal]

oh ok

[grizzled shore]

If this didn’t work they wouldn’t be a geometric sequence

[worldly narwhal]

would it be 1/9 / x = x/2 then

[grizzled shore]

Where did you get 1/9

[worldly narwhal]

nvm

it’s 2/9

[grizzled shore]

For a geometric sequence, $ 2, x, 2/9\$
$\frac{2/9}{x}=\frac{x}{2}=k$

[warm shale]

Frosst

[grizzled shore]

I’ve just replaced a₁, a₂ and a₃ with the 3 you gave me

[worldly narwhal]

yup

so you get 2/9 = x^2

right

[grizzled shore]

Do you think you can solve for x?(the k doesn’t matter here)

[grizzled shore]

Not quite

[worldly narwhal]

would i need to get rid of fractions

[grizzled shore]

$\frac{2/9}{x}=\frac{x}{2}$

[warm shale]

Frosst

[worldly narwhal]

yuh

[grizzled shore]

$\frac{2/9}{x}\times x=\frac{x}{2} \times x$

[warm shale]

Frosst

[grizzled shore]

$2/9=\frac{x^2}{2}$

[warm shale]

Frosst

[worldly narwhal]

yeah

you did x times x

[grizzled shore]

That’s not the same as 2/9 = x²

[grizzled shore]

.

[worldly narwhal]

can i not cross multiply

bc of the equal sign

[grizzled shore]

What are you multiplying both sides by

[worldly narwhal]

just cross multiplying

to get 2/9 and x^2

[grizzled shore]

Cross multiplication is a shorthand

What you’re really doing is multiplying both sides by something

[grizzled shore]

What are you multiplying from here

[worldly narwhal]

ohh

isn’t it 2/3

[obtuse pebble]

@worldly narwhal Has your question been resolved?

[timid silo]

Hello could someone help me with a cross country gas estimation? I’m about to leave tomorrow morning and just need help from someone whose good at math to verify if I have the cost correct on gas thanks

[gilded needle]

this channel is in use - you can open your own: #❓how-to-get-help

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[tardy epoch]

What don't you get

[dim copper]

all of it lmao

[astral ivy]

Such a dumb question

They’re asking you if you know Pascal’s Identity

https://en.m.wikipedia.org/wiki/Pascal's_rule

[dim copper]

I mean, I'm looking at pascal's identity

from my textbook

[astral ivy]

Ye

[dim copper]

but I don't see how this applies

[astral ivy]

Set m = n + 1

Now change all the n expressions to be in terms of m

What happens?

[dim copper]

ok, one sec, lemme work this out on paper

[tardy epoch]

Do you understand it

[dim copper]

not in the slightest

[astral ivy]

Oh shit u got honorable? Nice

[dim copper]

XD

[astral ivy]

Have you seen Pascal’s triangle

[dim copper]

yeah

[astral ivy]

It’s like that

Do you know what Pascal’s triangle does though

Like what it’s for

[dim copper]

not really

[astral ivy]

Oh

It’s for what happens when you expand out something like (x + y)^5

[astral ivy]

The numbers in the 5th row of the triangle correspond to the coefficients

Yep there it is

[dim copper]

that's what my textbook says about it

[astral ivy]

Yeah

Wait

Do you know the binomial theorem?

[dim copper]

yes

[astral ivy]

(Do you understand it?)

[dim copper]

yes

[astral ivy]

Ok

[jolly ginkgo]

how can't you?

[dim copper]

reasons

[astral ivy]

So Pascal’s triangle is interesting because you get the next row by adding the top two terms

Do you know how to construct Pascal’s triangle?

[dim copper]

ooh, okay

uhm, I'm looking at the triangle

it looks like you use the formula for combinations

[astral ivy]

See the blue part? You get 21 by adding 15 and 6

[dim copper]

(n choose r)

weird

but yeah

[astral ivy]

I know right

It’s unexpected

So basically

[astral ivy]

This formula is saying that algebraically

[dim copper]

I see the pattern, yeah

[astral ivy]

It’s saying the n+1,k coefficient is found by adding the previous two

[dim copper]

oooooh

[astral ivy]

So basically encoding that interesting behavior

Does that make sense?

[dim copper]

yes

[astral ivy]

Anyway just take this and rewrite it with M := n + 1 instead

See what happens

[dim copper]

oooh, okay

wait, where did M come from

[astral ivy]

I’m just inventing it

[astral ivy]

So you see how it connects to the question better

They just (literally) rewrote the formula but change it from n+1 to n, and from n to n-1, etc

[dim copper]

huh, okay

[astral ivy]

Shit I gotta go

GL

[dim copper]

lol thx

[obtuse pebble]

@dim copper Has your question been resolved?

[obtuse pebble]

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[wanton dagger]

How am I supposed to do question 20. ?