help-19

[faint knot]

this way is different because it uses product limit rule instead

these rules let you rigorously remove "easy" portions from the outside

here, I split apart e^(-2x) into two limits that I already know the limit of

now if we want to do 5 - e^(-2x)/2 properly,

,,\lim_{x\to\infty}\left(5-\frac{e^{-2x}}2\right)

[clever fjord]

mtt

[faint knot]

we know the limit of e^(-2x) is 0, so we are expecting to eventually get to that stage

[faint knot]

the first rule we use is limit subtraction rule

@shrewd trellis tell me, what does that rule look like? you were taught this in school

[shrewd trellis]

Binomials

[faint knot]

unfortunately the limit subtraction rule doesnt involve any binomials inside of it

read the words limit, subtraction, and rule carefully

what would this rule be about?

[shrewd trellis]

What’s the best method

[faint knot]

h, please answer the question

it looks like you dont want to do this the rigorous way anymore

[shrewd trellis]

Im reading but some parts confused me

[modest nacelle]

Just, what is the limit subtraction rule?

I think I gave you already the formula.

[faint knot]

there arent very many to twist those words around, you can read it directly

its a rule about?

[shrewd trellis]

Memorise limits you already know wdym

[faint knot]

in case you didnt notice, Im walking you through various examples of how this way usually works

that means I dont expect you to fully know how that way works yet

[shrewd trellis]

Oh ok

[faint knot]

given Im teaching you that way right now, you noticed that, right?

yes or no

[shrewd trellis]

I didn’t notice it because I never learnt it until u mentioned it

[modest nacelle]

Huh? It's not there in your textbook?

[faint knot]

what about the context clues?

[shrewd trellis]

no

[faint knot]

it makes sense to leave it out until you get more experience in algebra

usually graphing and the similar get the job done easy enough

the context clues is I tell you "theres one way we can do this" then I walk you through a method

presumably that method Im walking you through is that way we can do this

since you missed those clues, Ill have to be more direct about this

the limit we're solving today is $\lim_{x\to\infty}5-\frac{e^{-2x}}2$

[modest nacelle]

It's the first corollary

[clever fjord]

mtt

[faint knot]

now to do this, we can use a set of rules that can split apart this limit into smaller bits

an example is the limit subtraction rule, which is in fact
a rule about subtracting limits

[faint knot]

now youll notice here we currently have one limit, the limit subtraction rule lets us split this into two limits

the limit subtraction rule says: $\lim f(x)-g(x)=(\lim f(x))-(\lim g(x))$

[clever fjord]

mtt

[modest nacelle]

You need to check that each limit is defined, though.

[faint knot]

thats asking for a bit much right now

[faint knot]

we can use the limit subtraction rule on here to get:

,,\lim_{x\to\infty}5-\frac{e^{-2x}}2=\lim_{x\to\infty}5-\lim_{x\to\infty}\frac{e^{-2x}}2

[clever fjord]

mtt

[faint knot]

@shrewd trellis can you recognize that the limit subtraction rule has been used here?

and to be clear, this is a yes or no question, I only need a yes or a no

[shrewd trellis]

I never heard of a limit subtraction rule

[shrewd trellis]

But I recognise this form

[faint knot]

h, thats why Im telling you what the rule is

so when you read the words "limit subtraction rule"

did it occur to you that it should be a rule about subtracting limits?

you werent able to answer this last time I asked

[shrewd trellis]

Yes

[faint knot]

you shouldve said so

now with $\lim_{x\to\infty}5-\lim_{x\to\infty}\frac{e^{-2x}}2$, we can try and break apart the right limit into two limits

[clever fjord]

mtt

[faint knot]

this would be using the limit division rule, or the limit quotient rule, either name works

this time I want you to use context clues to guess what this rule ought to do on the right limit $\lim_{x\to\infty}\frac{e^{-2x}}2$

[clever fjord]

mtt

[faint knot]

what would the limit look like after the rule is used?

[odd edge]

@shrewd trellis Has your question been resolved?

[odd edge]

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[fallen jolt]

<@&286206848099549185>

[twin plover]

1 cubic meter is 10^6 cubic cm

[fallen jolt]

Okay

So

[twin plover]

Density is the same

[fallen jolt]

1 cubic meter has 4060000 gm

1 cubic meter will have ?

[twin plover]

Cubic cm

[fallen jolt]

Yeah cm *

[twin plover]

Just multiply by 10^-6

[fallen jolt]

Why

[twin plover]

Density=Mass/Volume

[fallen jolt]

Ohh

[twin plover]

And it's the same

[fallen jolt]

Okay got it

So it’s 4.06 gm

Right ?

[twin plover]

Yeah

[fallen jolt]

Okay

Thanks

.close

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[odd edge]

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[young jungle]

I don't understand what I am doing wrong, first I applied chain rule to the top portion, then I applied the quotient rule to get that answer

[modest nacelle]

I think you're on the right track. It's just not the simplest solution

[young jungle]

Ohh, we typically don't have to simplify it so I kept on getting this problem wrong

I'll try simplifying

[modest nacelle]

Wait a minute.

[young jungle]

I multiplied the 1/2

[modest nacelle]

I forgot the half, sorry.

[young jungle]

Is this a formating error or am I applying something wrong

Also decided to do #10 later since it's a whole lot (gonna focus on other problems first)

[modest nacelle]

,rcw

[modest nacelle]

What is the derivative of $sin^4(x)$?

[clever fjord]

Xwtek

[young jungle]

OH

CHAIN RULE

😭😭

Wait I use the chain rule right...?

[modest nacelle]

You need to apply chain rule twice here

The first chain rule is correct, but to differentiate $g$, you need another chain rule.

[clever fjord]

Xwtek

[young jungle]

4cos^3(x) * sin(x)?

[modest nacelle]

Nope.

[young jungle]

Oh

4sin^3(x) * cos(x)?

[warped glacier]

yep

now put it all together

also note that you should be using t, not x

[young jungle]

Yeah lol

[young jungle]

Thankfully the application my homework uses doesn't allow the wrong symbol 😭😭

[warped glacier]

lol

[young jungle]

Can I get some more help with this, idk where to start with it

[modest nacelle]

You mean on simplifying it?

[young jungle]

Yeah

Do I just make sure square roots aren't being divided or something?

[modest nacelle]

You can start by the fact that $\sqrt{4x^2+8x^4} = \frac{4x^2+8x^4}{\sqrt{4x^2+8x^4}}$

[clever fjord]

Xwtek

[young jungle]

Okay, I'll try with that

[warped glacier]

that's correct, the derivative of $\sqrt{4x^2 + 8x^4}$ is $\frac{1}{2 \sqrt{4x^2 + 8x^4}} \cdot (8x + 32x^3)$

[clever fjord]

south

[young jungle]

gonna close the channel now, thank you for the help

.close

[odd edge]

Channel closed

Closed by @young jungle

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[warped glacier]

oh wait

[warped glacier]

come back

[odd edge]

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[dim sentinel]

I might be dumb or js paranoid but does

[dim sentinel]

Does point A count as inside the circle?

Or just on the circle

I was js stupid sorry

.close

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[dim sentinel]

Me back

[dim sentinel]

Need value of x

And the apparent near and far arc value

Uhm

[warped glacier]

isn't that just 216 + 2x + x = 360

or is (2x) the question number? yeah (2x) being the question number makes more sense

[odd edge]

@dim sentinel Has your question been resolved?

[dim sentinel]

Oh sorry

I forgot the tab

[dim sentinel]

Yes

Holy

I was too dumb

Didn't know that

[warped glacier]

oh wait that's not correct

(2x) is the question number

yeah it's terrible formatting

[dim sentinel]

No

We just need the value of x

If it's the question number the 2 is smaller

I mean wait

Imma prove u right

[warped glacier]

the problem is that the answer you get this way doesn't agree with the proper method

[dim sentinel]

Oh yeah

Js tried it

I have 50 degree angle tho

[warped glacier]

does the previous question have (2w)?

[dim sentinel]

This is the only question that involves 2(x)

[warped glacier]

weird

[warped glacier]

I know but do you see (2w) anywhere?

[dim sentinel]

(2x)*

[warped glacier]

or (2u)

[dim sentinel]

The other questions are just easier

[dim sentinel]

No

[warped glacier]

ok, weird

[dim sentinel]

Ik

[warped glacier]

yeah maybe they really wanted you to do 216 + 2x + x = 360 then

[dim sentinel]

The value of x disagree with the given tho

[warped glacier]

yeah it's a broken diagram

[dim sentinel]

Yea

[warped glacier]

using 2 different methods you get 2 different values of x

[dim sentinel]

There's no answer that can satisfy the question?

[warped glacier]

I told you, the question is broken

there's no single correct answer for x

[dim sentinel]

I have other questions u mind helping with it too

Pretty please

[warped glacier]

sure

[dim sentinel]

Wait

The diagram

If angle ABC=38 What is arcAC,angleADC and angleAXC

Im confused on how do i approach it

Cuz

Other than the measurement od angle ABC there's no more

[warped glacier]

ah, you need to know that the tangent is perpendicular to the radius

so draw the radii XA and XC

then you know both of those angles are 90

[odd edge]

Channel closed

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[warped glacier]

.reopen

[odd edge]

✅ Original question: #help-19 message

[dim sentinel]

Like this sire?

[warped glacier]

yep!

then you know that angles BAX and BCX must both be 90

[dim sentinel]

Yes

Since it looks like square

[small pond]

Sorry to hijack, no because the property always holds true

It has been experimentally established that the angle between a tangent and a radius is always 90 degrees

Don't go by looks

[dim sentinel]

Uh sorry

[small pond]

Remember this logic

[warped glacier]

no, it's not by experiment, although you can certainly draw a bunch of circles and measure it with a protactor yourself

you can convince yourself that way yes

but it's determined by geometric proof

[small pond]

I thought it was experimentally established

My bad

I am sorry

[warped glacier]

maths is never experimentally established

only the sciences are

[dim sentinel]

So uh

[small pond]

I gotta check that proof later

[warped glacier]

yeah it's online

[dim sentinel]

Uhm what's next?

[warped glacier]

then what's the total of the angles in any quadrilateral?

[dim sentinel]

360?

So 180-38=Angle AXC?

[warped glacier]

yep

[warped glacier]

yep!

right, and then by definition, minor arc AC = angle AXC (since X is the centre)

okay, we need to switch tracks completely to find angle ADC

[dim sentinel]

Uhm okay

[warped glacier]

this is another circle theorem

[dim sentinel]

Yes

[warped glacier]

yes, so do you agree that the angles z and z are equal?

you have an isosceles triangle cause the radiuses are equal

and for any isosceles triangle, the base angles are equal

[dim sentinel]

So base angles is equal to each other and same to the radius?

[warped glacier]

yes, radiuses are equal, so base angles are equal

[dim sentinel]

Uhm angle ABC is 38 degree

[warped glacier]

yes and also we're on ADC

try not to spoil the answer subrat

I'm guiding them through why

[dim sentinel]

Yes

So now?

[small pond]

angle ADC

[dim sentinel]

Yes

[warped glacier]

yes so y and y are also equal, ok now moving on

in the biggest triangle, what is the sum of all the angles?

it's 180 I know, but how about in terms of z and y?

[warped glacier]

.

[dim sentinel]

Uhm

So big okay

z+y+(z+y)?

Oh im lagging

Internet is bad

[dim sentinel]

Is this right?

[warped glacier]

yep!

so z + y + z + y = 180

[dim sentinel]

Yes

[warped glacier]

what must z + y be then?

[dim sentinel]

In terms of my problem?

Or just 2x+2y?

[warped glacier]

yeah, it relates to your problem

cause z + y is the angle on the circumference of the circle, given you have the diameter

so if you find z + y, that's the answer to ADC

wait, hold on

[dim sentinel]

Uhm why

[warped glacier]

I think I might have used the wrong circle theorem with you

sorry

yeah like how is D even defined

D could be anywhere

[dim sentinel]

Yes

[warped glacier]

yeah the question is broken for angle ADC

[dim sentinel]

Ik

I can't do anything with js one measurement

[warped glacier]

but I bet they are going to ask you this in future questions

[dim sentinel]

Btw

[warped glacier]

yeah

[dim sentinel]

Are u sure this is correct?

[warped glacier]

anyways, they're going to get you to use this in future questions

[warped glacier]

yes that's correct, 360 - 90 - 90 - 38

[dim sentinel]

I have one question with needing that but diff given

Is arc AC=48 what is arcADC,angleABC and angleAXC

360-48=arc ADC

Right

[dim sentinel]

Uhm

[warped glacier]

can you close and reopen this channel?

I'm helping someone else

[dim sentinel]

Oh alright

.close

[odd edge]

Channel closed

Closed by @dim sentinel

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[dim sentinel]

.reopen

[odd edge]

✅ Original question: #help-19 message

[dim sentinel]

Im still here

[honest quest]

Do you have a specific question

[dim sentinel]

.

Here

[odd edge]

@dim sentinel Has your question been resolved?

[dim sentinel]

.close

[odd edge]

Channel closed

Closed by @dim sentinel

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[odd edge]

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[north smelt]

idk what im doing wrong man so what i did was write
S= the sum given
then subtract 7 from each term and divide by 10 so
(S-7(n+1))/10=1+18+188+......
then subtract S from this to get n+1- Last term of original which is n+1-7-10^(n+1)-8(10+.......10^n) then just used gp sum formula

[waxen talon]

dang

notice this for me

from 17 -> 187, you times 10 and add 17

from 187 -> 1887, you times 10 and add 17

[north smelt]

yeah i saw that pattern too

[waxen talon]

so basically

[north smelt]

i got the answer that way too

[balmy wharf]

18.... n 8's 7 = (n + 1) 1's * 17

[north smelt]

but i dont know whats wrong with my soln 🙏

[waxen talon]

🙏

[north smelt]

u are just saying 17 x 1 + 17 x11 + 17 x 111 right

[balmy wharf]

🙏

[waxen talon]

🙏

oh god dang

[north smelt]

🙏

[waxen talon]

121 actually 🤓

[north smelt]

no

its just adding a 1 wdym

[waxen talon]

okay so $17 \cdot 11^{n-1}$ is the general formula right?

[clever fjord]

1 divided by 0 equals Infinity

[north smelt]

no

what

[waxen talon]

11^2 is 121

[north smelt]

what are you on bro

[waxen talon]

oh wait no

🙏

[north smelt]

try satisfying that for just n=3 lmao

im right

trust me

[waxen talon]

sorry

[north smelt]

i did it that way already

yeah no worries

mainly trying to find issues with my approach

[waxen talon]

so it's just a bunch of 1s

[north smelt]

yuh

take 17/9 common

and u get the 10^x-1 thing repeating so well yeah that is easy

[waxen talon]

to get 11, you do $\frac{10^2 - 1}{9}$

[clever fjord]

1 divided by 0 equals Infinity

[waxen talon]

to get 111, you do $\frac{10^3 - 1}{9}$

[clever fjord]

1 divided by 0 equals Infinity

[balmy wharf]

yea

[waxen talon]

try this one ig

to get a number with $n$ 1s, you do $\frac{10^n - 1}{9}$

[clever fjord]

1 divided by 0 equals Infinity

[north smelt]

my brother i already wrote it as 17/9 (9+99+999+...........) then wrote that as 17/9 *(10+10^+......10^(n+1)-(n+1)) already

and DID get the answer with that

[waxen talon]

alr alr

[north smelt]

can you try it by my way

:?

subtract 7 from each then divide by 10

[waxen talon]

did you use the sigma function?

[north smelt]

then subtract original sequence from the one i got

well

its summing so yeah i guess ?

not really tho

i didnt write a general term so like

[waxen talon]

well

[north smelt]

original thing is
17+187+1887+........
subtract 7 and divide by 10 gives
1+18+188+1888 subtracting from original gives
1+1+1+1+1......... n+1 times and negative of last term from original

[waxen talon]

since you got a $\frac{17}{9}$ as a factor and the question says about $\frac{17}{a^2}$, then maybe $a = \pm 3$

[clever fjord]

1 divided by 0 equals Infinity

[north smelt]

nah

when u do left side

u get another 9S

so a is 9

and that is correct as i got the same from the other method too

im getting the constant term wrong

😔

[waxen talon]

wait

[north smelt]

nevermind i found my mistake

accidentally wrote 80/9*10 =80/9

⚡

thanks for th ehelp

[waxen talon]

💀

no

[north smelt]

.close

[odd edge]

Channel closed

Closed by @north smelt

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[waxen talon]

problem

[north smelt]

bro i got a headache for like the last 30 mins cuz of that pmo

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[pallid apex]

Pls help

[pallid apex]

What integration method should I use?

[keen cipher]

Heyy

So

[tall ivy]

What in the world

[keen cipher]

Try substitution

Focusing on

[pallid apex]

Help pls

[keen cipher]

(u = \log(\sin x))

[clever fjord]

YZYBlueBoy22

[keen cipher]

Try substitution method

[tall ivy]

Dude went from trolling to asking - level questions

<@&268886789983436800>

[pallid apex]

<@&268886789983436800>

[hard drum]

<@&268886789983436800>

[pallid apex]

?

💡

I i derive

$\ln(sin(x))^{arctan(sin(x))}$

[clever fjord]

Richard Mullin

[pallid apex]

Uuu

Easy

[keen cipher]

What happened

[tall ivy]

scam

[pallid apex]

.close

[odd edge]

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[tall ivy]

Also <@&268886789983436800> this guy made a troll post earlier, and is now asking this question which I don't think is serious

[pallid apex]

I take this from a video

Lol

[tropic remnant]

I'm personally giving the benefit of the doubt here

but thanks, keeping an eye out

[keen cipher]

Bro really went from trolling to asking

[meager juniper]

he's got a note that he's been warned for this before, actually

[wooden python]

uhh rip bozo?

[meager juniper]

@pallid apex I think it's time to take a bit of a break.

[stoic cloud]

So many different colors in this channel… not that im against diversity

[pallid apex]

Wait

[tall ivy]

Just seemed kinda sus

[meager juniper]

magically delicious

[stoic cloud]

dude,

[tall ivy]

Oh brother

[stoic cloud]

holy bragging

[tall ivy]

do forgive me for my ignorance, how silly of me

[tropic remnant]

I'm going to close this channel now since there is no help question. Please move discussion elsewhere

.close

[odd edge]

Channel closed

Closed by @tropic remnant

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[tall ivy]

Thanks mate

[stoic cloud]

Thank you.

[keen cipher]

Bro?

[tall ivy]

Okay move to discussions guys

[keen cipher]

Yes

Okay Henry 🙏

[odd edge]

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[wide drift]

It says its surjective, but I dont get how

Surjectivity is like this right

[ember oak]

What's missing for it to not be surjective?

[wide drift]

How can infinity be mapped to with just (0, 1]

[tall ivy]

Well you want to know logically?

[ember oak]

Wdym?

[wide drift]

Yeye just the reasoning behind it

[tall ivy]

Well, what is 1/0.00000000000........00001?

[wide drift]

We have to map to infinity no?

[ember oak]

No

[wide drift]

Oh

I see

How

Its possible

haha

[tall ivy]

It's fine man

[wide drift]

Thank you! That answers my question

❤️

.close

[odd edge]

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[wide drift]

.reopen

[odd edge]

✅ Original question: #help-19 message

[wide drift]

Apparently this one is surjective too? I dont see how either

How can [3, 4] map to all real numbers

[wooden python]

uhh are you talking about sur or in

[wide drift]

OH

Okok

[wooden python]

cause that one definitely ain't sur

[tall ivy]

Yeahhhh

[wide drift]

I see how haha

My bad again

Thanks!

❤️

.close

[odd edge]

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[tall ivy]

You're fine man

[odd edge]

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[lavish mesa]

So we have previously learnt that the Borel sets on R are the sets in the sigma algebra generated by $${[a, b): a,b \in \mathbb{R} }$$

[clever fjord]

astral

[lavish mesa]

Is the approach therefore to try and manipulate the intervals of form $$(-\infty, b)$$ into something that can be expressed as the unions of the form $$[a,b)$$ and their complements and intersects?

[clever fjord]

astral

[low locust]

show that the intervals (-infty,b) are generated by [a,b) and show that [a,b) are generated by (-infty,b)

then they generate the same sigma algebra

[lavish mesa]

so [b, a) generates [b, infty) because that is a countable union of {[b, a)} as a tends towards towards infinity. The complement of [b, infty) is (-infty, b). So [b, a) generates (-infty, b)

Is something like this correct for the forward approach?

[low locust]

yes that works

(there is an easier way)

[lavish mesa]

what is the easier way

[low locust]

b->-infty

[lavish mesa]

ohh

.close

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[amber schooner]

good attempt

[odd edge]

@dusk nova Has your question been resolved?

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[analog reef]

Hi I’m using this method with 3 digit times tables but I seem to mess up a lot

632x681 has me stumped not sure why 1 digit and 2 digits were easy

I noticed with 1x you start on 2 rods and everything else seems to jump to the 3 rods

[brazen hare]

is that an abacus

[analog reef]

Yep

Nvm I figured it out but it annoys me that 1x tables in 3 digits is 2 rods from the digit being multiplied and everything is 3

What is happening there?

[odd edge]

@analog reef Has your question been resolved?

[analog reef]

Well since I don’t understand the theory I’m just telling myself 1 digit numbers have magical 0’s with them filling in the “3rd rod”, and it’s working. Still I hope someone can explain it to me

[near forge]

hi

[odd edge]

@analog reef Has your question been resolved?

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[river tapir]

how do i do this

[river tapir]

i forgot completely what to do

radicals are my favorite type of math cause theyre mad simple

i hate you for sending calc

[hard viper]

No helpers, it seems

[pure ice]

not sure what the problem is

is this an integrand?

[tall ivy]

Yeah can't really do anything here

is it an integral or differential?

[pure ice]

in both cases power rule

[river tapir]

ts the problem

[hard viper]

power rule?

[pure ice]

as in, if u are taking its derivative or integral

[river tapir]

wait i think im stupid

[pure ice]

but the problem statement is not given

[river tapir]

its already simplified

...

[pure ice]

oh lol

[river tapir]

oml

[pure ice]

is it just algebraic simplification?

yeah ur done haha

[river tapir]

yea

[pure ice]

QED

[hard viper]

Can you show me the power rule

[pure ice]

sure

[hard viper]

@pure ice

[river tapir]

.close

[odd edge]

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[river tapir]

.reopen

[odd edge]

✅ Original question: #help-19 message

[river tapir]

mb

how do i change it from me to someone else

?

[pure ice]

d/dt [t^n] = nt^{n-1}, so d/dt [(2t)^{1/2}] = (2t)^{-1/2}, same thing for the other one but with -2/3 in the exponent

[pastel steeple]

you just close it the bot will do it

[river tapir]

.close

[odd edge]

Channel closed

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[hard viper]

Oh this is called the power rule

It also has a limit edition

lim of (x^n - a^n)/(x - a), at x = a

[pure ice]

all "rules" of calc can be traced back to the limit defs

or, as I prefer, the sequence limit definition

[hard viper]

Sequence limit definition

[odd edge]

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[unreal pasture]

hello im just confused on how to do this

[lavish jackal]

!status

[odd edge]

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

[unreal pasture]

1

[lavish jackal]

start factoring out the denominator

[unreal pasture]

thats what i got stuck at im rlly bad at factoring

[lavish jackal]

have u done factoring before

[unreal pasture]

yea

wait im slow let me try it

[lavish jackal]

alright take ur time

[unreal pasture]

would itr be x - 3 x +2

i mean x + 3 x-2

[lavish jackal]

dont forget the brackets

[unreal pasture]

ok i put that then the x-2 cancles

[lavish jackal]

yup

[unreal pasture]

so how do i find the hole again

[lavish jackal]

u need to use simplified function which is 1/(x+3)

when x = 2

[unreal pasture]

so 5

2,5

[lavish jackal]

not quite

2 is correct but the y coordinate is not

[unreal pasture]

it would be 1/ 2 + 3 right

[lavish jackal]

it will be 1/5 bc 2+3 gives 5

[unreal pasture]

this may be dumb but why is the one there didnt the numerator cancle out

[lavish jackal]

since u cancelled x-2

u can just leave it like this

it will have 1

[unreal pasture]

ok i see

so no slant

domanin cant equal -3

vertical = -3

[lavish jackal]

u forgot x=2

[lavish jackal]

this is correct

[unreal pasture]

i did

[lavish jackal]

what do u have now

[unreal pasture]

sorry my laptop died one sec

[lavish jackal]

np

[unreal pasture]

x

-3

y 3

[lavish jackal]

x=-3

[unreal pasture]

yes

[lavish jackal]

what are ur x and y intercepts?

[unreal pasture]

x = -3 y = 3

[lavish jackal]

wut

for finding x u need to set y = 0

[unreal pasture]

maybe pre ccalc isnt for me

[lavish jackal]

and for y do the opposite

[unreal pasture]

so 0 = x+3

[lavish jackal]

for x u need to take the numerator

which is x-2=0

[unreal pasture]

ohh so use the eqaution before it cancled

[lavish jackal]

ya

[unreal pasture]

ok ty

[lavish jackal]

yw

[unreal pasture]

so would x = 2

[lavish jackal]

close

[unreal pasture]

-2

[lavish jackal]

we already know x=2 is a hole so no x intercept

[unreal pasture]

ohh

[lavish jackal]

for y-intercept make sure u use the whole function

,, f(x) = \frac{x - 2}{x^2 + x - 6}

[clever fjord]

Aκιρɑ

[lavish jackal]

set x = 0 and solve for y

[unreal pasture]

-2 /1

[proud totem]

Simplifying all that would make it easier

[lavish jackal]

try again

,, f(0) = \frac{0 - 2}{0^2 + 0 - 6}

[clever fjord]

Aκιρɑ

[unreal pasture]

-2/6

[lavish jackal]

u can still simplify it

divide by 2

[unreal pasture]

1/3

[lavish jackal]

sorry -2 not 2 lol

but 1/3 is correct

[proud totem]

-2/-6

U have 0-0-6

[unreal pasture]

ur right

so it would become 1/3 tho bc they r both negative

[lavish jackal]

yes

[unreal pasture]

alr ty

but

how would i grpah this

[lavish jackal]

use the key points that u found

domian, va, intercepts etc..

i gtg now and @proud totem can continue helping ya

[unreal pasture]

ok thank you lots

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[outer wadi]

how are they getting the isomorphism

[outer wadi]

hmm

is there some theorem about it being cylic allowing them to say its isomorphic

hmm I do know if one group is not cyclic and the other is then there is no isomorphism

here we have both are cyclic but that desont guarentee theres an isomorphism right

[zinc glacier]

the isomorphism is a bijection of powers of the generators

[outer wadi]

o ok

[zinc glacier]

cyclic groups of the same order are isomorphic

[outer wadi]

oh really?

hmm maybe I missed that theorem

[zinc glacier]

proof by lack of counterexample >_>

but yeah i think you can make the case the isomorphism is a^k -> b^k where a is a gen of G1 and b is a gen of G2

[outer wadi]

ok that makes sense thanks

.close

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[calm whale]

Algebra 2 absolute values

[calm whale]

i dont understand how to do any of this basically i know it but i need a refresh

[odd edge]

@calm whale Has your question been resolved?

[jaunty minnow]

This is my first time doing this so bare with me, but I'll try my best.

Ok for question 4

What graph is it? @calm whale

[solar galleon]

go for it

[calm whale]

inverted V shape i think?

[jaunty minnow]

Correct

What function do we call this?

[calm whale]

absolute value

[jaunty minnow]

Correct

Since its flipped upside down what do we call that?

[calm whale]

reflection

[jaunty minnow]

No the function

What do we call the function when its flipped upside down

[calm whale]

dont we say reflection over the x axis

idk

what is it

[jaunty minnow]

Negative absolute value

[calm whale]

ohhh

[jaunty minnow]

$-|x| $

Damn its not working

you understand tho I think

So

that gives us two pieces of information

We have an absolute value function and its pointing down so its a negative value

Now

What do we know about the domain in an absolute value function?

[calm whale]

its real numbers or negative infinite,infinite

[jaunty minnow]

Correct

So your domain is that

Does this make sense?

[calm whale]

yes

what abt the vertex

[jaunty minnow]

Ok lets talk about that

Lets say we have this graph on the origin

(0,0)

How many steps horizontally are moving to get to where the two lines intersect?

(steps = whats the value of x where the lines intersect)

[calm whale]

the line is not on x axis so isnt that just 0

or is it -3

[jaunty minnow]

Its this

[jaunty minnow]

Your thinking of the x-intercept

Ur being asked the vertex

Does -3 make sense why?

[calm whale]

yes yes

[jaunty minnow]

Okok

Now lets find the y value of the vertex

How many verticalsteps does it take to get to where the two lines intersect?

[calm whale]

5?

[jaunty minnow]

Correct

So what is your vertex?

[calm whale]

(-3,5)

[jaunty minnow]

correct

[calm whale]

also

is the range (negative infinite,5)

[jaunty minnow]

Correct

[calm whale]

and then

[jaunty minnow]

What else would this be?

[jaunty minnow]

And this?

[calm whale]

infinites?

[jaunty minnow]

Nope

Think what we called them

“Movements”

[calm whale]

hmm

shift ?

[jaunty minnow]

Correct

-3 will be your horizontal shift

[calm whale]

left 3

[jaunty minnow]

and 5 will be your vertical shift

[jaunty minnow]

Correct

[calm whale]

so now dilation

[jaunty minnow]

Yes

Let me look this up really quick because I didn't do dilation in alegbra 2, I did it in geometry lol

Let me see if its the same

[jaunty minnow]

Are they asking if there is a dilation or the value?

[calm whale]

wait not to jump to another topic but the other pages i sent i did them but i dont understand like this graphing one is kinda the easier part so

[calm whale]

if there is

[jaunty minnow]

Well then the answer will be yes I believe

Do you understand why?

[jaunty minnow]

the intervals?

[calm whale]

i need to ask my teacher about this one but kind of yeah

[calm whale]

solving and checking the absolute values

[jaunty minnow]

I can explain a little bit

Just for general understanding

[calm whale]

okay

[jaunty minnow]

So

Do you see how the graph is pointed down

and both lines are moving constantly down with equally opposite slopes?

Pretty much

the dilation is shown because the lines are moving infinitely apart with out moving from the vertex.

In simple terms

It doesn't change shape and the angles are congruent

[calm whale]

hmmm

[jaunty minnow]

I gotta get to my Calculus stuff in help 5 lol

[calm whale]

okay okay

i get it

[jaunty minnow]

Cool cool

[calm whale]

you can get to other channels i get it now thank you other stuff i sent i also get them kinda ill just ask my teacher

she gives us review time anyways

thank you so much

[jaunty minnow]

Ofc

Glad to help

[warped grove]

please don't advertise your help channel in other channels, it's against the rules

[mild bay]

ok

[jaunty minnow]

could I get university math role?

Idk why I'm still pre university

[warped grove]

you can choose yours in id:customize

[odd edge]

@calm whale Has your question been resolved?

[odd edge]

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[tired temple]

help

[tired temple]

1.The Philippine eagle is one of the largest and rarest birds in the world. Its powerful wings spread to about 2.4 m. What is the measurement of its wingspan in feet?

2.A metric ton, abbreviated as “t”, is a unit of measurement used for large masses such as those of cars, planes or heavy construction equipment. The weight of a compact excavator is 1.893 t. If 1 t = 1000 kg, what is the weight of the compact excavator in kilograms?

3.A kilogram of carrots costs 60 pesos. How much does 750 g of carrots cost?

[warped glacier]

what have you tried?

[tired temple]

nvm i finally solved it

[warped glacier]

cool, if you're done type .close

[tired temple]

.close

[odd edge]

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[junior hearth]

Guys

[atomic hornet]

yes?

What are you looking for?

[unkempt lichen]

do you have a question?

[junior hearth]

Hi

Yes

Not rly a question

More like i need help to study

[unkempt lichen]

we'll need you to be a little more specific please.

[junior hearth]

Well i have a study guide

That goes over what i need to learn

Could maybe someone help me with studying it or like some material or ai

[unkempt lichen]

well, we don't encourage AI for studying purposes here

as for helping with studying, that's too broad a question for a help channel, unless you can break down what you're having trouble with

general study questions can be asked in #study-discussion

[junior hearth]

Ok

[amber schooner]

[junior hearth]

I am lowk dumb

Test s tmrw i did not study

But she dont make it easy

It’s mostly word problems

[amber schooner]

try khan academy

ask for problem sets from your teacher

[unkempt lichen]

on top of Khan, use Math is Fun to bolster intuition

[junior hearth]

She is lazy i asked abt any study materials like ixl or smthing but she just says look at the hw

I reviewed the hw

It’s easy

But the test is way harder

[amber schooner]

if it’s easy then what are you stressed about

did you do the homework without using AI?

[junior hearth]

Ye

Why

[amber schooner]

because you asked us about using ai

[junior hearth]

Ok i only use it for studying sometimes

[amber schooner]

and if you are finding the tests harder than the homeworks to such an extent that you’re really struggling on the tests then perhaps you don’t understand the homeworks as well as you think you do

what’s 2/7 + 8/15

[junior hearth]

I did countless hw questions even i asked ai for tougher ones get them all right

But she just makes her stuff so complicated

I just dont know what to do

[amber schooner]

^

[junior hearth]

Mb im back

What that

U want me to solve?

Umm

6/105?

86*

[amber schooner]

yea

[junior hearth]

Brb

[unkempt lichen]

wait. so you do use AI for help on homework sometimes?

[junior hearth]

Sry im back

No

Just to create questions

So I can practice

[amber schooner]

can you define rational numbers?

[junior hearth]

I think any number reprinted as p/q

Here q cannot be 0

[amber schooner]

where p and q are…

[junior hearth]

Where*

[unkempt lichen]

where p and q are what?

[junior hearth]

Oh im dumb

[unkempt lichen]

that's what knief is asking

[junior hearth]

U number the can be a fraction

Or ratio

[unkempt lichen]

nonono

[junior hearth]

Of 2 integers

[unkempt lichen]

there we go

[junior hearth]

Where demoninator is not equal to 0

[unkempt lichen]

we were looking for the word integers

[junior hearth]

Sry guys 😅 I’m a little dumb

[unkempt lichen]

let's not use that label, alright?

[junior hearth]

Ok

[unkempt lichen]

so, do you have examples of these so-called "impossible" questions from your teacher?

I'd really like to see them

[junior hearth]

Well no

And they are not impossible

[unkempt lichen]

then how do you know they are "impossible"

well I use "impossible" in quotes for a reason

[junior hearth]

I’m just (censored) yk

[unkempt lichen]

because you made them out to be incredibly difficult

[junior hearth]

Dum

For me

At least

[unkempt lichen]

that's why we were hoping you could share at least one such problem so we can see where your weaknesses lie and maybe help you remedy it

cuz as it stands, we don't really know how else to help you

it's like we are your doctors but all you told us was that you're sick and nothing else

[junior hearth]

I keep asking for the results but as I said she is lazy i asked every day for a week and yet still i dont have the results (what i got wrong)

[unkempt lichen]

let's put the results aside

let's talk about the questions

[junior hearth]

Ye

She gave the score

But i cant see the questions

[unkempt lichen]

and not the question paper?

[junior hearth]

It’s online

Ogle forms

[unkempt lichen]

then do you remember anything about any of the questions?

[junior hearth]

Google*

No but what i have is this

[unkempt lichen]

you've shown this already

[junior hearth]

Ye

[unkempt lichen]

again, this is too vague. you have not stated your issue specifically beyond the fact that your teacher sets hard questions.

we don't know what you're struggling with.
we don't know what you're weak in.
we don't know if the problems are unreasonably hard.

[junior hearth]

It ok i don’t wanna be a waste of time im kinda dum anyways ima see what i can study and tell u my score tmrw

Have a gn

Or gm

It good evening

Or what i learnt in Spanish

[amber schooner]

i mean can you do everything on the list

[junior hearth]

Buenas

Mostly

Just need to memorize

[amber schooner]

which ones cant you do

maybe the PEMDAS?

word problems?

[junior hearth]

Mostly i get confused with rational irattional numbers and types of numbers

[amber schooner]

has she given any examples of irrational numbers

[junior hearth]

Yes as i said i will try my best to study and i thank you for your help but i want to see if i can study by myself and get a good grade i want to be independent

Bye guys

Ty again

[amber schooner]

interesting

have a nice night sir

[junior hearth]

U too

Bye

[unkempt lichen]

.close (by OP agreement)

[odd edge]

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[shrewd trellis]

is this correct?

[amber schooner]

its ln?

[shrewd trellis]

yes

[amber schooner]

this is wrong

[shrewd trellis]

i was differentiating ln

[amber schooner]

a few mistakes here

first, you seem to only be differentiating (x + 1)/(x - 1)
second, you differentiated this wrong (look at line 5 where you do x - 1 - (x + 1) = x - 2)

x - 1 - (x + 1) = -2

not x - 2

to differentiate this it might help to split it into two logs

[shrewd trellis]

I don’t get this

[amber schooner]

the function is ln((x - 1)/(x + 1)) not just (x - 1)/(x + 1)

or do you mean the second part where you subtracted wrong

[shrewd trellis]

we need to use this law right

[amber schooner]

the first one

or use log rules and use the second one

🤷‍♂️

[shrewd trellis]

derivative at the top, function at the bottom

how would we use

[amber schooner]

$\ln\left(\frac{a}{b}\right) = \ln a - \ln b$

[shrewd trellis]

the log law

[clever fjord]

knief

[shrewd trellis]

yea

And then

[amber schooner]

then use the derivative of a sum

[shrewd trellis]

of a sum?

isnt it

subtraction

[amber schooner]

a difference is a sum

same shit

[shrewd trellis]

alr

got it thank you knief

.close

[odd edge]

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Closed by @shrewd trellis

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[amber schooner]

nice

[unkempt lichen]

<@&268886789983436800>

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[solar marsh]

im confused why u cant take away the selections that hvae 2C2O 1C1O and no C and O

[wooden python]

the way you say it now it sounds like you can

did you get the wrong answer doing so?

[solar marsh]

yea

[wooden python]

show work?

maybe the issue lies somewhere else.

[solar marsh]

so i did 9C4 which is 126

take away 1 (2C2O)

[wooden python]

it's not 9C4 for the total is it tho

[solar marsh]

how come

[wooden python]

bc of the repetitions

and there isn't any easy way to account for it

i think maybe you have to do it additively