help-10

[cloud spear]

We didnt learn that yet

[azure glacier]

you just keep doing it over and over

[cloud spear]

how though

[azure glacier]

here ill write it out

[short spruce]

$\dv{x}f(g(h(x)))=f'(g(h(x)))\cdot g'(h(x)) \cdot h'(x)$

[warm shale]

a disappointing son

[azure glacier]

this is so true

[cloud spear]

Tysm

So x^2 is g, sin(5t) is h, and 5t is x?

Wait how do I solve that without the derivative of f'(g(h(x))) when that is what we are solving for

Are the derivatives of trigs not real rules?

Zero reason this is wrong

Oh right fucking product rule

HOW

I DID THE PRODUCT RULE

Nah I am being dumb]

[scenic sundial]

maybe it wants you to simplify it

[cloud spear]

I did hte product rule wrong

But how is H''(theta)=-theta sin(theta+ 2 cos (theta)

Where the fuck does the 2 come from

Is theta not a variable?

[obtuse pebble]

@cloud spear Has your question been resolved?

[obtuse pebble]

@cloud spear Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wide sparrow]

if f(x) = 3x+1 and g(x)=2x+5 and (fog)(x) =28 can you find me the x

[sand portal]

what have you tried?

[wide sparrow]

Is it possible it is 1 ?

[sand portal]

You'll have to show your work

[wide sparrow]

So

I did

f(g(x))

and

Then

f(2x+5) = 28

And

3(2x+5)+1

Then

6x+15+1

[sand portal]

Yeah this is fine you seem to have it

[wide sparrow]

6x+16

[sand portal]

Now solve for x

[wide sparrow]

Then idk

[sand portal]

you want to isolate x on one side

[wide sparrow]

Yes

[wide sparrow]

That x in front of the 6

[sand portal]

Well you have to move the 16 to the other side first

[wide sparrow]

I think it’s 1 or 2

[sand portal]

Notice that 6x+16=28 doesn't work with x=1: 6(1)+16=23 not 28

however yeah 2 works

Although do you understand how to arrive at x=2

[wide sparrow]

Ok I think it’s 2 then

[sand portal]

.

[wide sparrow]

Why it’s 23 there

Oh wait

Nvm

Ok thanks for helping then

.close

[obtuse pebble]

Channel closed

Closed by @wide sparrow

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.

[surreal moth]

for question 2e

i did all of it

and got the asnwer

of Zc = -5/3-10/3 i

but idk how to get the radius

i thought if i sub back into circle equation then it will be same as (-5/3)^2 + (-10/3)^2

then ill square root it to find the radius

however its the answer was different

nvm

i

im dumb

dumb

got it

[tardy epoch]

👏

[surreal moth]

i just sub back into the other equation and get R^2

then r

[tardy epoch]

Yea the center of the circle is not a point on the circle. Feel free to .close

[surreal moth]

.closd

.close

[obtuse pebble]

Channel closed

Closed by @surreal moth

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.

[rocky sierra]

I need some help with this question

[rocky sierra]

im just really cofused on this one

[mental solstice]

wait @tardy epoch does this look familiar?

[rocky sierra]

well no one was replying for awile

so i did not know what to do

im just new here

[mental solstice]

you wait until someone comes by to help

i'll start by asking the same question

what did you try?

[tardy epoch]

😂

[rocky sierra]

well i tried to add them and divid them to the people they are

but that did not work out

so than i did not know what to do

[mental solstice]

well, it's a rate question after all

i like to think of it in terms of "how much work can a person get done in a day?"

so for example if antony can do the job in 4 days

how much of the job does he finish in one day?

[obtuse pebble]

@rocky sierra Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tepid blade]

If the sum of the binomial coefficients in the development of the binomial (ax + 1 / √x) ^ n is 512, then find the summand that does not contain x.

if someone can help me with that it would be of much help

[obtuse pebble]

@tepid blade Has your question been resolved?

[tardy epoch]

The sum of binomial coefficients is always a power of 2

That tells you what n is. Now the hard part is counting all the constant terms

Ah ok. You get a constant term if you multiply x by 1/sqrt (x) twice in the expansion.

[tepid blade]

.close

[obtuse pebble]

Channel closed

Closed by @tepid blade

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fervent finch]

Simplifying Radical Expression by Rationalizing the Denominator

[fervent finch]

thats the lesson

uhhh not sure what formula to use

[prisma sky]

times r2 to the top and bottom

[fervent finch]

whats r 2

*r2

[sullen solar]

root 2

[prisma sky]

root 2

[sullen solar]

square root of 2

[fervent finch]

hhmm

[sullen solar]

please wrferf

[prisma sky]

ye and then the denominator becomes 2

[sullen solar]

shut up

[prisma sky]

and the top becomes 8 times root 2

[fervent finch]

hmm

i don't get it

[undone axle]

lets start with the basics

do you know how to multiply things

[fervent finch]

yes mostly

[undone axle]

do you know what a square root is

[fervent finch]

yes

[undone axle]

ok

[sullen solar]

do you know what rationalisation is

[fervent finch]

no

[sullen solar]

ok

so rationalising

[fervent finch]

pretty sure they haven't taught us

[undone axle]

so if i have the square root of 2 times square root of 2

what does that give

[fervent finch]

not sure

[sullen solar]

is when you try to get root of a square root in the denominator

[fervent finch]

never encountered that

[sullen solar]

nah ur trolling

[fervent finch]

nah fr

[prisma sky]

STOP

[sullen solar]

bro

im sorry

[fervent finch]

what

[undone axle]

can u tell me what you think a square root is?

[prisma sky]

ok so when you have a root 2 and you times it with a root 2 you get 2

[fervent finch]

when you multiply a number by itself you get like number

[sullen solar]

yeah

so square root is just reverse of that

[timid silo]

rationalizing is multiplying the thing with a ratio which equals 1/1 = a/a so that the denominator becomes a rational

[fervent finch]

so what does that mean

[timid silo]

$\frac{8}{\sqrt{2}}$

[warm shale]

SKJJ

[timid silo]

what could you multiply the denominator with so it becomes a rational?

[fervent finch]

not sure

[timid silo]

what if you just multiply it by root(2)

what happens then?

[undone axle]

$\frac{8}{\sqrt{2}}=\frac{8\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=4\sqrt{2}$

[warm shale]

horiseun

[fervent finch]

you get 2?

[timid silo]

yes

and to make that a valid operation

[fervent finch]

yes

[timid silo]

you have to make sure you dont change the value of the whole expression

[fervent finch]

meaning

[timid silo]

to do that, you have to multiply it by a ratio

which makes it so that the denominator is 2 (or root(2) * root(2))

and the numerator also changes by the same factor

that is, numerator is also multiplied by root(2)

[sullen solar]

UR A GIFT

[fervent finch]

i see

[timid silo]

since root(2)/root(2) = 1

multiplying the equation with root(2)/root(2) makes it a valid operation

[fervent finch]

so you also have to multiply root 2 on the numerator since we also did it in the denaminator/?

[timid silo]

which helps us to remove the division by a irrational number which is tedious

[fervent finch]

*denominator

[timid silo]

and turn it into a multiplication operation

[timid silo]

yes

precisely this

[timid silo]

.

similarly, if the question said

[fervent finch]

what would it come out as then

[timid silo]

$\frac{8}{\sqrt{3}}$

[warm shale]

SKJJ

[timid silo]

what could you multiply this with so the denominator becomes a rational?

[fervent finch]

root 3?

[timid silo]

yes

[timid silo]

and so the overall ratio you multiply this expression is? (hint: it should equal to 1)

[fervent finch]

what does overall ratio mean

[timid silo]

i mean

just the ratio

[fervent finch]

root 3?

[timid silo]

you multiply the numerator and the denominator with root(3)

yes

and the ratio of both the root(3)'s is?

[fervent finch]

what do you mean by ratio

[timid silo]

$\frac{\sqrt{3}{\sqrt{3}} = \frac{1}{1}$

nvm

i mean

root(3)/root(3)

[fervent finch]

yes

[wheat palm]

RATIO

[fervent finch]

how did it become 1/1

[timid silo]

bruh

you multiply the numerator

and the denominator

both by root(3)

[fervent finch]

yea but

[timid silo]

which essentially means

[fervent finch]

8 times root 3 is 1?

[timid silo]

no

root(3)/root(3) is 1

[fervent finch]

what happend to the 8

[timid silo]

that isnt in the discussion as of now

root(3)/root(3) = 1 right

[fervent finch]

yea

[timid silo]

now, if i multiply something by 1

it will equal the same thing it was before

[fervent finch]

yes

[timid silo]

so you can multiply 8/root(3) by root(3)/root(3)

and what will it give you?

[fervent finch]

hmm

[timid silo]

$\frac{8}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}$

[warm shale]

SKJJ

[fervent finch]

how would I multiply it

[timid silo]

like you do normally

...

[fervent finch]

uhhh give me a moment

[timid silo]

you multiply the numerator by root(3) and it becomes?

[fervent finch]

I may or may not have forgotten how to multiply

[timid silo]

yes

$a*a = a^2$

[warm shale]

SKJJ

[timid silo]

this is what a square is

$\sqrt{a}*\sqrt{a} = a = \sqrt{a}^2$

[warm shale]

SKJJ

[fervent finch]

root 3?

[timid silo]

numerator bro

8 * root(3)

[fervent finch]

is there any formula for that or do I just have to multiply

[timid silo]

you dont have to multiply a irrational by a rational and make it a single thing

you can leave it like $8\sqrt{3}$

[warm shale]

SKJJ

[fervent finch]

hmm

ohh

does it work like that

[timid silo]

yes

[fervent finch]

i see

[timid silo]

you cant multiply 8 with 1.72727248203678730624 completely

[fervent finch]

what

[timid silo]

i mean

thats just root(3)

[fervent finch]

i see

but on the simpler version

[timid silo]

how would you go about multiplying 8 with 1.71498038609346

you wont do that right?

[fervent finch]

yea

[timid silo]

so we just leave it like that

so the entire thing becomes

$\frac{8\sqrt{3}}{3}$

[warm shale]

SKJJ

[timid silo]

im afraid you're gonna have to repeat 4th grade

[fervent finch]

where did the 3 at the bottom come from?

[timid silo]

$\sqrt{3}*\sqrt{3} = 3$

im 15 too

[fervent finch]

ahh

huh

[warm shale]

SKJJ

[fervent finch]

ohh because you also multiply the top?

[timid silo]

okay whatever

[timid silo]

yes

[fervent finch]

with root 3?

alr got iot

[timid silo]

see

lets make it simpler

or lets not

[fervent finch]

simpler pls

[timid silo]

it will just become more complicated lol

[fervent finch]

what

[timid silo]

i thought lets turn it into a equation

[fervent finch]

wait where were we

[timid silo]

but then you guys will just become confused

okay lemme just go to the beginning

[warm shale]

SKJJ

[fervent finch]

yes

[timid silo]

how will you do that?

[fervent finch]

wym

ohhh

you multiply root 2

in numerator

and denominator

[timid silo]

yes

and next

[fervent finch]

it becomes

8

how doi type iot

8root2/2

[timid silo]

just write root(x)

[fervent finch]

right?

[timid silo]

yes

and you can divide the 8 by 2

[fervent finch]

yey

4

[timid silo]

and hence it becomes

[fervent finch]

omg

4root2

omg

[timid silo]

good

[fervent finch]

its that simple?

[timid silo]

yes

now

[warm shale]

SKJJ

[timid silo]

just solve this and you should be good

for now*

[fervent finch]

hmm

but 8 isnt divisible by 3 tho

[timid silo]

you just have to rationalize the denominator*

if there are any radical/sqrt signs, or something not divisible leave it like that

just make it so the denominator doesnt have a irrational number

[prisma sky]

so rationalizing means getting rid of the root sign at the bottom

[fervent finch]

so its

8root3/3

[timid silo]

yes

[prisma sky]

yep

[fervent finch]

so thats the answer?

[timid silo]

are you asking?

[timid silo]

yes it is

[fervent finch]

ooooo I see

i get it now thx

[timid silo]

would you want to try a harder problem?

[fervent finch]

uhhh maybe not?

cause I have another question

[timid silo]

i think you should try this

but

if you dont know how to do it

its fine

[fervent finch]

sure ig if its still related to the lesson

[timid silo]

Q) Rationalize the denominator of: $\frac{(a + b)^2}{\sqrt{a + b}}$

[warm shale]

SKJJ

[fervent finch]

oh...

what does that mean

they haven't thought me any of that LOL

[timid silo]

alright then you can skip it

[fervent finch]

so can I ask my other question?

[timid silo]

yes

[fervent finch]

its abt this

[timid silo]

okay

first

break that down

why are there like 5, 9 year olds in this chat bro

[fervent finch]

nah fuck that

[primal bear]

3r10/14

[fervent finch]

like how

[timid silo]

okay

you know that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

[warm shale]

SKJJ

[fervent finch]

oh yes yes

so thaats cuberoot 5/ cuberoot 4?

[timid silo]

thats a cube root

so the same goes for it

[fervent finch]

?

[timid silo]

yes

[fervent finch]

oooo

oke

whats the next step

[timid silo]

$\frac{5^{1/3}}{2^{2/3}}$

[fervent finch]

yes

i only reached till there

what

why is it 2^2

[timid silo]

2^2 = 2*2 = 4

[fervent finch]

but why tho

cant it just be 4

[timid silo]

i would write it like

[fervent finch]

or does it need to be like that

what?

[warm shale]

SKJJ

[timid silo]

@fervent finch what does the answer expect from you?

like

[fervent finch]

our lesson is rationalizing denominator

[timid silo]

ohh

then its

see

[fervent finch]

see?

[timid silo]

$\frac{\sqrt[3]{5}}{\sqrt[3]{4}} = \frac{\sqrt[3]{5}*\sqrt[3]{2}}{2}$

[fervent finch]

yes yes

i only got up to there

np

have a good day

nooo did @timid silo

dissapear

[warm shale]

SKJJ

[fervent finch]

oh nvm

[long lodge]

Off topic

[fervent finch]

why is it cube root 2 on top?

[timid silo]

i multiplied the denominator by cuberoot(2)

and it became 2

[fervent finch]

but isnt it cube root 4 on the bottom

[timid silo]

this should be the answer

[timid silo]

its cube root 4 = cube root 2^2

you just need to get in another 2 in the cube root to turn it into cube root 2^3 = 2

and so i multiplied the denominator by cuberoot(2)

[fervent finch]

uhh alr

[timid silo]

<@&268886789983436800> these guys are trolling from like 15 minutes

[fervent finch]

whats next

[timid silo]

thats the answer i suppose

or it could be

[timid silo]

yeah

this

[fervent finch]

this is what comes out in the answer key

but how tho

[timid silo]

listen

[fervent finch]

yes

[timid silo]

they most likely meant cuberoot 10

you are asking for help in an occupied channel

[fervent finch]

ahhh

[timid silo]

then shit talking

[fervent finch]

yea i think

[timid silo]

with other trolls

[balmy mortar]

<@&268886789983436800> ^ Trolls (and check deleted msg logs in this channel)

[timid silo]

$\sqrt[3]{5}\sqrt[3]{2} = \sqrt[3]{52}$

[fervent finch]

guessing its cuberoot 5 x cube root 2

thats why

[balmy mortar]

can u fripping stop spamming other peoples help channels

[fervent finch]

it became cuberoot 10/2?

[warm shale]

SKJJ

[fervent finch]

yess

[timid silo]

bruh just go to some other help channel

alright im out

[fervent finch]

i got 13 mins left

can u help me with one last one?

[timid silo]

@fervent finch your question done?

[fervent finch]

please?

[timid silo]

alrigth

[fervent finch]

just one last

[timid silo]

sure

[balmy mortar]

open a new channel

[balmy mortar]

and close this one

[fervent finch]

oh is that

do i close this

[timid silo]

.close if you got the question

[fervent finch]

ok ill ask it in another ticket

ill ping u there

.closer

[timid silo]

i mena

[fervent finch]

.close

[timid silo]

no

[obtuse pebble]

Channel closed

Closed by @fervent finch

Use .reopen if this was a mistake.

[timid silo]

wait

[fervent finch]

.reopen

[obtuse pebble]

✅

[fervent finch]

wut

[timid silo]

he was asking the other guys

[ocean topaz]

they were banned

[fervent finch]

oh

[timid silo]

nice

[fervent finch]

sooo

can u help with this one

[timid silo]

first multiply the denomintor and numerator by cuberoot 36

and see what happens

let me know too

[fervent finch]

wait

6?

[timid silo]

and numerator becomes?

[fervent finch]

wdym 36

[timid silo]

thats 6^2

[fervent finch]

ohh

cuberoot 9 x cuberoot 6

[timid silo]

what does the numerator become then?

[timid silo]

no

you working?

[fervent finch]

wdym

[timid silo]

the denominator becomes 6

the numerator becomes?

[fervent finch]

yes

[timid silo]

?

[fervent finch]

is it not this?

[timid silo]

nope

[fervent finch]

which part did I go wrong on

[timid silo]

you multiplied the denominator and numerator by cuberoot (36)

not cuberoot(6)

[fervent finch]

so it would be

cuberoot 9 by cuberoot 36?

[timid silo]

yes

now you can take one of the cuberoot(3) from cuberoot(36) and multiply it with cuberoot(9)

[fervent finch]

so that would be

cuberoot 324??

*?

[timid silo]

i mean

yeah but

cuberoot(27) = 3

cuberoot(12) = cuberoot(12)

[fervent finch]

27?

what

[timid silo]

yes

[fervent finch]

where you getting the numbers from

[timid silo]

cuberoot(9)*cuberoot(3) = cuberoot(9*3) = cuberoot(27)

[fervent finch]

i see

but where you get 3 from

[timid silo]

cuberoot(36) = cuberoot(12*3) = cuberoot(12)*cuberoot(3)

[fervent finch]

i see

[timid silo]

you got theasnwer?

[fervent finch]

what would the answer be

[timid silo]

what do you think

[fervent finch]

im not sure also

[timid silo]

but what do you think

[fervent finch]

whats on my paper rn is cuberoot 9 x cuberoot 12 x3 over 6

from there where do i go

[timid silo]

cuberoot(9)*cuberoot(3)*cuberoot(12)

simplify this

[fervent finch]

how do you simplify again

whats the formula

[timid silo]

no formula

cuberoot(9*3) = ?

[fervent finch]

27

cuberoot 27

[timid silo]

and that is?

[fervent finch]

what do you mean

[timid silo]

cuberoot(27) equals?

[fervent finch]

3

right?

[timid silo]

and your question is solved

3*cuberoot(12)/6 = cuberoot(12)/2

[fervent finch]

so3 cubretoor

yea

answer key shows this

how did 6 become 2 btw?

[timid silo]

its

3*cuberoot(12)/6 = 3/6 * cuberoot(12)

)

[fervent finch]

huh

[timid silo]

.close this channel please

[fervent finch]

ayo?

[timid silo]

i think your problem has been solved

[fervent finch]

i dont get it

[fervent finch]

this part

[timid silo]

$\frac{3*\sqrt[3]{12}}{6} = \frac{3}{6} \sqrt[3]{12} = \frac{1}{2}\sqrt[3]{12}$

[fervent finch]

yes

from there

ohh

[warm shale]

SKJJ

[fervent finch]

wait where did it go

[timid silo]

its there wdym

[fervent finch]

so in the answer key

the one above

thats cuberoot 12?

[timid silo]

yes

[fervent finch]

and thats why 2 is on the bottom

[timid silo]

yes

[fervent finch]

ok wait

give me 2 mins

lemme just copy it on my notebook

thanks man @timid silo

[timid silo]

its alright

[fervent finch]

I shall close the channel

.close

[obtuse pebble]

Channel closed

Closed by @fervent finch

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

Help?

[timid silo]

What do you need to find? Where are you stuck at?

[timid silo]

e

[timid silo]

Grade

How big is C

So you need to find angle C right?

YH

Do you know what is the sum of all the angles in a triangle?

Nvm

?

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @wild carbon

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.

[noble hemlock]

can someone help me solve this? im a bit lost and this is my first time doing this in this discord so yea

[timid silo]

This isn't a test or a quiz right

[noble hemlock]

its a review

i have the answers

[timid silo]

Alright

[noble hemlock]

or the ans keyf u need it too

[timid silo]

Do you know the epsilon delta definition of limits?

[noble hemlock]

uhhh no its really foggy for me

its a kinda

i know epsilon means that

[timid silo]

Alright let me write down the definition for ya and explain it as well e

[raven spire]

Limits though, do you need them?

[noble hemlock]

the value is either +0.1 or -0.1 in this case

right?

[timid silo]

Wait oh

[timid silo]

I think we don't

[timid silo]

Yes our epsilon is 0.1

[noble hemlock]

i know we need epsilon im pretty sure but idk about delta

but can u go over what delta is

just to be safe

cuz the teacher kinda speedran this when she was teaching and left my brain in shambles

.-.

[timid silo]

Delta+2 is just the value of f(epsilon)

[noble hemlock]

so in this case f(0.1)

[timid silo]

No

[noble hemlock]

oop

[timid silo]

f(4+0.1)

We're approaching to 4 on x axis right

[noble hemlock]

uhhhhhh

[timid silo]

See

[noble hemlock]

yes

from both sides

right?

[timid silo]

Where is this

the distance between 4 and that question mark is epsilon

[noble hemlock]

ohhhhhhhhhhhh

ok ok ok i see

wait

but isnt epsilon also

the distance between the top 2

like sandwiching the 2

[timid silo]

Top 2 like.
.?

[noble hemlock]

with the 2 in between

[timid silo]

That's delta

[noble hemlock]

ok ok ok

[timid silo]

The distance from 2 to question mark on y axis

Is delta

[noble hemlock]

so delta is y and epsilon is x

[timid silo]

Yes kind of

[noble hemlock]

ok i got it

so now we know that weve established that where do we go

[timid silo]

So we need to find delta

[noble hemlock]

alright cool

[timid silo]

We now know delta is tje distance thing on the y axis

[noble hemlock]

wait

question

[timid silo]

Sure ask

[noble hemlock]

isnt delta just 4.1 and 3.9

since it gives us epsilon at 0.1

[timid silo]

Well not exactly

epsilon and delta aren't always same

[noble hemlock]

oh sorry typo

isnt epsilon just 4.1

and 3.9

**

[timid silo]

Epsilon is the distance

4+epsilon is 4.1

[noble hemlock]

ohhh ok

so we have epsilon figured out

how do we figure out delta

[timid silo]

Yes for that

Look at this

$\abs{f(x) - 2} < \epsilon$

[warm shale]

Pencil

[timid silo]

Epsilon is already given

[noble hemlock]

that splits into 2 right

[timid silo]

0.1

[timid silo]

No

[noble hemlock]

oh?

[raven spire]

Does this help?

[noble hemlock]

wait

[timid silo]

That's absolute value

[noble hemlock]

do we substitute 0.1

for epsilon ?

[timid silo]

Nono wait

[timid silo]

That's delta

[raven spire]

|f(x) - f(4)| < epsilon

[timid silo]

Yeah

[raven spire]

the difference in height < epsilon.. wdym

[timid silo]

Okay the whole time i thought epsilon was delta and delta was epsilon

I'm such an idiot

[noble hemlock]

wait

so whats happening .-.

[timid silo]

@noble hemlock look at this

[noble hemlock]

mhm

[timid silo]

Epsilon is the difference in height

And delta is on the x axis

[noble hemlock]

between intercepts of the blue line?

[timid silo]

From 4 to ?

[noble hemlock]

ok wait

[timid silo]

Yes

[noble hemlock]

so is epsilon always on the y axis

[timid silo]

Yes

[noble hemlock]

and delta always on x axis?

ok gotcha

[timid silo]

I told the other way round 🤦‍♂️

[noble hemlock]

lol all good

[timid silo]

Alright

[timid silo]

So look at this

[noble hemlock]

so the difference in interception points

is epsilon

[timid silo]

Yeah difference in height basically of |f(x) - f(4)|

[noble hemlock]

awesome so where do we go from here

[timid silo]

So $\abs{\sqrt(x) - 2} < \epsilon$

[warm shale]

Pencil

[noble hemlock]

where did u get that from?

[timid silo]

It's given in the question

[noble hemlock]

did u just sub

[timid silo]

See this

[noble hemlock]

yeah

i gotcha

[timid silo]

Wait we need to find delta right

[noble hemlock]

so do we split the abs value into positive and negfative now

yeah

[timid silo]

Let's not make this complicated

[noble hemlock]

cuz we have epsilon

mhm

[timid silo]

See we know our epsilon

0.1

[noble hemlock]

yeah

[timid silo]

Our value the f(x) is approaching

2

[noble hemlock]

wait

[timid silo]

Our 2+epsilon is 2.1 right

[noble hemlock]

how do u kjnow our f(x) value is approaching 2

[timid silo]

It's marked 2 there

On y axis

[noble hemlock]

but the blue line

goes past 2

like it crosses through it no?

[timid silo]

(4,2)

At x=4

y=2

[noble hemlock]

oh ok so our line is headed there right?

[timid silo]

y=sqrt(x) right

Yes

[noble hemlock]

ok got it

then why did the line not end there

why did it have to overshoot by so much?

[timid silo]

So see we have 2.1

[noble hemlock]

mhm

i got that part

[timid silo]

It's just a graph, we're checking what happens to f(x) if x is (approaching) 4

But focus on this

[noble hemlock]

oh ok

mhm

so we haev 2.1

[timid silo]

2-epsilon is 1.9 right

[noble hemlock]

yeah so we have 2.1 and 1.9

cool

[timid silo]

Now

Let's take 2.1 as our y

So 2.1 = sqrt(x)

[noble hemlock]

mhm

[timid silo]

x = (2.1)^2

Find it out

[noble hemlock]

4.41

[timid silo]

Yes

It will be this

[noble hemlock]

wait

wait a minute

correct me if im wrong

[timid silo]

Sure

[noble hemlock]

then do i just do 1.9^2

and thats my second delta

and then i just find the difference

[timid silo]

Not delta

[noble hemlock]

between those 2

[timid silo]

Your second bound

Yeah

[noble hemlock]

wait so then

[timid silo]

Which 2

[noble hemlock]

1.9^2 is 3.61

[timid silo]

Yeah

4 is between 3.61 and 4.41

[noble hemlock]

so then I do 4.41 - 3.61

[timid silo]

Noo

See

[noble hemlock]

mhm

[timid silo]

This distance is delta

The left circle

[noble hemlock]

why is it the left and not the right?

[timid silo]

The distance between 4 and ?

Even on right it's delta

[noble hemlock]

so why cant we just do 4.41 - 3.61 /2

[timid silo]

We're finding the distance delta from 4 till 3.61 or 4.41

The distance

[noble hemlock]

oh so

4 - 3.61

[timid silo]

Yeah

[noble hemlock]

and 4.41 - 4

[timid silo]

Yes

[noble hemlock]

or | 4 - 4.41|

[timid silo]

Also yes

[noble hemlock]

so then its .39 and .41

[timid silo]

Both can be our delta

It's better to choose the smaller one

But both 0.39 and 0.41 are fine

[noble hemlock]

why is it better to choose the smaller one?

just curious?

[timid silo]

I saw it in a video

Wait see

[noble hemlock]

uh huh

[timid silo]

If we choose delta 0.41

From 4 we need to add or subtract 0.41

In this case it's fine

[noble hemlock]

right

[timid silo]

Sometimes for bigger delta, it may cause to cross the bounds for the given function

Like here if we choose delta as 5 for suppose

[noble hemlock]

ohhhh

but the smaller one is always in bound right

ok

[timid silo]

4-5 =-1

Yes

[noble hemlock]

cool so just a quick finalrecap

epsilon is always on y

delta is always on x

[timid silo]

Yes

[noble hemlock]

correct?

[timid silo]

Yes

[noble hemlock]

ok cool

i understand it all now!

Thank you so much for your help!

[timid silo]

Np ^^

[noble hemlock]

I really appreciate it you saved my life on this!

do I just close the room now so others can use it or?

[timid silo]

Lol don't mention it ^^

Sure

[noble hemlock]

ok! thanks again!

!close

[timid silo]

And @raven spire lol thx for making me understand epsilon is the difference in height XD

[balmy mortar]

https://media.discordapp.net/attachments/576430342974734385/937776839471022080/321445119171756033.png

This alternative definition of continuity might be more intuitive to visualize 👀

It says the image of that interval (what everything within delta of a maps to)

must be contained in the interval on the right

For limit instead of continuity, there is a hole at x = a

in the original (a - delta, a + delta)

And you replace f(a) with L

$$(\forall\varepsilon\in\bR^+)(\exists\delta\in\bR^+)f((a-\delta, a+\delta) - {a})\subseteq(L-\varepsilon, L+\varepsilon)$$

[warm shale]

Shuri2060

[balmy mortar]

(Interval notation representing a set, not coordinates)

[obtuse pebble]

@noble hemlock Has your question been resolved?

Channel closed

Closed by @noble hemlock

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.

[zinc pulsar]

How do I find X?

[raven spire]

You mean you're trying to solve $x^3 - 4x = 0$

[warm shale]

Ansh

[raven spire]

?

[zinc pulsar]

Nope

[raven spire]

then!?

[zinc pulsar]

I'm trying to solve 0=x^3-4x

[raven spire]

$0 = x^3 - 4x$?

[warm shale]

Ansh

[zinc pulsar]

Yep

It's not quadratic

[raven spire]

but you can factorize?

[zinc pulsar]

How?

<@&286206848099549185>

UhhH

The question is
"Find the co-ordinates of the points when the curve y=x^3-4x crosses the x-axis"

[obtuse pebble]

@zinc pulsar Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[zinc pulsar]

Bruh

.reopen

[obtuse pebble]

✅

[zinc pulsar]

.close

[obtuse pebble]

Channel closed

Closed by @zinc pulsar

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.

[deep wing]

Consider a car traveling along a straight road. Suppose that its velocity (in mi/hr) at any time
‘t’ (t > 0), is given by the function v(t) = 2t + 20. Find the distance travelled by the car after 3 hrs if it starts from rest.

Is my solution here correct?

[deep wing]

$$\begin{align*} \
& \int_{0}^{3} 2t+20t dt \
&= \bigg[t^2+20\bigg]_0^3 \
&= (3(3+20))-(0(0+20)) \
&= 69
\end{align*}
$$

[warm shale]

orelyus
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[little scarab]

shouldn't your first equal sign be t^2 + 20t not t^2 + 20

your final ans looks correct though

[deep wing]

oh yeah my bad

[deep wing]

alright thanks!

.close

[obtuse pebble]

Channel closed

Closed by @deep wing

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[grand obsidian]

why in my book it explained that 74+118+104 =296, and thats the answer for it, is there a rule for it?

[obtuse pebble]

@grand obsidian Has your question been resolved?

[grand obsidian]

<@&286206848099549185>

[obtuse pebble]

@grand obsidian Has your question been resolved?

[worthy comet]

bad book explanation:) The correct answer is 224°. You might know that the inner angles of a n-polygon sum up to (n-2) * 180°, i.e. the inner angles of a pentagon sum up to 3 * 180°=540°. You can easily get the inner angles at S,T and Q. For P, you use the parallel lines and then the above formula gives you the inner angle at R. Finally the outer angle is 360° - the inner angle

[grand obsidian]

aight

thanksss

[obtuse pebble]

@grand obsidian Has your question been resolved?

[timid silo]

Can someone explain me what Maijer G-functions are and how they work?

<@&286206848099549185>

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brittle swan]

i’m learning about improper integrals

and there’s this thing called principle value

what’s its use?

<@&286206848099549185>

[brave bramble]

If you ignore the analytic rules of what an integral should follow, but retain the algebraic rules, you can get answers for integrals that are otherwise impossible. This is called the Cauchy Principal value

,w integral of 1/x between -1 and 1

[brittle swan]

so what’s it used for lol

[warm shale]

Results provided by WolframAlpha

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

Requested by Kaynex#7520

[brittle swan]

this has to do with integrability?

like algebraically obtaining values over non integrable intervals

[brave bramble]

Ye.

[brittle swan]

..?

[brave bramble]

I'm pretty sure it can be used for approximating useful integrals, I remember screwing with it a bit in complex analysis

[brittle swan]

???

complex analysis?

[brave bramble]

Yeye. Integration over the complex plane

[brittle swan]

sweet jesus

[brave bramble]

It's actually a pretty friendly course kek

[brittle swan]

so it’s used in complex analysis for whatever reason?

[brave bramble]

But yeah I don't know if there's a ton of uses to it. It's just interesting to see how a "kind of" integral behaves.

[obtuse pebble]

@brittle swan Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[last bone]

help please

[obtuse pebble]

@last bone Has your question been resolved?

[obtuse pebble]

@last bone Has your question been resolved?

[obtuse pebble]

@last bone Has your question been resolved?

Channel closed

Closed by @last bone

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Please don't occupy multiple help channels.

[stray ridge]

<@&286206848099549185>

[balmy mortar]

we're not here to do your entire paper for you.

[stray ridge]

i just wanted to check a few answers

[balmy mortar]

Then ask directly

and also chill on the channel spam

[stray ridge]

Ok, please can you help me with number 20

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

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.

[umbral oasis]

how would u integrate this

[balmy mortar]

Differentiate it, perhaps that will give you a clue for the antiderivative

[misty terrace]

substitute u=-x/4 and use the fact that du = -1/4 dx

[umbral oasis]

ty

ngl im stuck on the whole problem

this is the full question

This what I got

[misty terrace]

Let $u \coloneqq -\frac{x}{4}$ such that $\mathrm du = -\frac{1}{4} \mathrm dx$. Then
\[
\int 5e^{-x/4} \mathrm dx = 5 \int e^u \cdot -4 \mathrm du = -20e^u = -20^{-x/4}.
\]

oops

[warm shale]

Lance

[umbral oasis]

ohh\

that integral rlly messed me up

ty

.close

[obtuse pebble]

Channel closed

Closed by @umbral oasis

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.

[inland spoke]

Hi

[inland spoke]

the key says this

but I got 3pi/4

idk how they got that

did i miss something?

[hazy marlin]

interesting..

it looks like you're correct actually

[hazy marlin]

this is wrong

sec-1(sqrt(2))=-pi/4

[obtuse pebble]

@inland spoke Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

yo if my answer is -1.11111111111 and so on is it stil right or will i have to make it into a whole number

[wicked ice]

You can express it as -1.1 repeating or - 10/9

[quartz pecan]

you can round it to the nearest hundreths

[timid silo]

ok thanks just wanted to clarify because i was anxious if I was still gonna get it right

.close

[obtuse pebble]

Channel closed

Closed by @haughty crypt

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dusk osprey]

did i mess up anywhere?

please @ me

[obtuse pebble]

@dusk osprey Has your question been resolved?

[dusk osprey]

<@&286206848099549185>

[little scarab]

it seems correct to me but you should probably mention what rule you used on each step @dusk osprey

[dusk osprey]

alright thanks

[obtuse pebble]

@dusk osprey Has your question been resolved?

[raven spire]

You could've skipped steps 2, 3, 4 and directly arrived at step 5 if you went the conventional way

[dusk osprey]

conventional way?

[raven spire]

$p \to (q\lor r) \iff \neg p \lor (q \lor r)$

[warm shale]

Ansh

[dusk osprey]

ahh

i applied the wrong law

at first

[raven spire]

yup

[dusk osprey]

are you really familiar with discrete math?

[raven spire]

just some basic hs logic

$p \to (q\lor r) \iff \neg p \lor (q \lor r)$ \
$(\neg p \lor q) \lor r \iff \neg(p \land \neg q) \lor r$\
$\iff [(p \land \neg q)] \to r$

[warm shale]

Ansh