help-43

[raw dawn]

😭

[dusty harbor]

must be a nice hs

[raw dawn]

like there’s the normal kids in precalc then the accelerated kids in calc ab and then the accel accel kids in calc bc and then there’s me in diff eq 😭

[raw dawn]

It’s eh

We don’t have phys e&m

Which sucks

But the teacher is balls anyway

[dusty harbor]

yeah i was in calc ab and bc, loved the teacher

even convinced me i like math

[raw dawn]

I self studied bc 🫩

Got a 4 😿

[dusty harbor]

thats still good

not enough for credit tho

[raw dawn]

yea bruh at one of the universities I’m applying to they’re taking my calc 1 and 4 credit but not 2 and 3

😭😭

Ts is acc insane

[dusty harbor]

i got a 4 too and had to retake calc 2

[raw dawn]

Yea smh

Only at cc’s

[dusty harbor]

you in the states ?

[raw dawn]

Which is where I took 3 and 4

[raw dawn]

NY

[dusty harbor]

oh nice

you going to in state school?

for uni

[raw dawn]

Depends on price for oos

I’m applying to a few in state tho yea

[dusty harbor]

goodluck for oos

[raw dawn]

😭

[dusty harbor]

i stayed in state bc 😩

im broke

[raw dawn]

lmao

I got a good fund

[dusty harbor]

do you know what you wanna major in?

[raw dawn]

But not enough for oos top school

[raw dawn]

Mech e aero e double major or mech e aerospace specialization if they don’t have aero as a specific major

[dusty harbor]

you tryna go to embry riddle??

[raw dawn]

but in the back of my mind there’s always math major

[dusty harbor]

why

[raw dawn]

what

[raw dawn]

Would be fun

I js wouldn’t wanna do finance tho

[dusty harbor]

oh thats one of the top aero schools

[raw dawn]

So I’d have to be like a teacher

[raw dawn]

I ain’t that good

My stats mid

Gpa kid

Mid

Sat buns

Ec’s buns

[dusty harbor]

embry students are annoying

[raw dawn]

rigor my only good thing 😭

I’m applying to

One sec lemme get the list

Cornell u
Clarkson u
Purdue u
Rpi
Rit
Binghamton
Stony brook
U at B
U at Del
Uiuc
U Maryland
Umich
Ucsd

Clarkson is one of the major in state ones

Bc they give a ton of money

[dusty harbor]

mostly new england area

[raw dawn]

So is rpi but they don’t give that much

[dusty harbor]

all nice schools

[raw dawn]

I’m right near rpi

[dusty harbor]

which is your top?

[raw dawn]

Like 20 mins away

[raw dawn]

Mainly js whoever is cheapest

[dusty harbor]

makes sense

[raw dawn]

like if Clarkson is 30k and rpi is 30k I’ll go rpi

But if like clarkson is 30k and uiuc is 35k I’ll go uiuc prolly

[dusty harbor]

have you seen the tuitions ?

[raw dawn]

I’ve seen like without aid and scholarships but not like what I’ll get

I don’t think I’ll know that til after acceptance

[dusty harbor]

ah gotcha

i wish you luck

[raw dawn]

Thanks

[dusty harbor]

not that youd seem to need it bashshshs

[raw dawn]

I’m not that smart

I’m only like good at math 😭

English I’m horrid at

Same for history

[dusty harbor]

luckily you dont really have to take english or history

[raw dawn]

I took apush and ap world and somehow managed to pull of a 3

[raw dawn]

Gen Ed’s but yea nothing beyond that

[dusty harbor]

im glad i did all my gen ed's dual enrolled

now i just gotta focus on my cores

🙏

history no more

[raw dawn]

I’m so fried freshman year

I’m gonna have a bunch of gen Ed’s

[dusty harbor]

just make sure you take your prereqs as electives and yada yada

but yeah freshman - sophmore year are usually buns

[compact pewter]

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[flint wing]

i dont get it im looking at the equivalences here but i dont understand how they turned (pvq) -> r into the circled thing

[slate sand]

Did you try a truth table

And how have you define the -> symbol

[flint wing]

doesnt that just give me T or F values how will that help me achieve the expression i circled

[slate sand]

Look at the truth table for A -> B

And how one might construct that using nots and ors

[cursive harbor]

This is the more important question here

[upper shore]

I think they want you to do
p \rightarrow q == -p \lor q

[flint wing]

idk if thats the definition ur looking for

[cursive harbor]

Now construct the table of ¬p ∨ q next to this

[flint wing]

its TFTT?

[cursive harbor]

Yes

Which is the same as p → q

Meaning that the two are equivalent and you can substitute

[flint wing]

ohhhhhh

ok that makes sense

thanks 👍

.close

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• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
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[mystic crater]

i didnt get the mark scheme for this q

is part b 161 sec

[compact pewter]

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[sacred crystal]

Sigh...

Help

[blazing reef]

which one do you need help with?

[compact pewter]

@sacred crystal Has your question been resolved?

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[sacred crystal]

Everything..

[lusty elk]

what have you tried, and how did it go

[blazing reef]

a quick tip would be to convert all the numbers into exponential forms

[sacred crystal]

Ye

[sacred crystal]

Can U show me how the first one

I did it

[viscid shard]

which one do you still need help with?

[sacred crystal]

I'm doing the whole thing it's a hw...

I couldn't do 2 n 3 on ex 1

and 1 I'm not sure of it

[sacred crystal]

it's a big hw 💔

[viscid shard]

since you said you're not sure about q1, I presume you've tried something? could you please show your work?

[sacred crystal]

Excuse me for my bad handwriting

I prob did nonsense

[blazing reef]

you made a mistake with your exponents

[viscid shard]

so in the second step you kinda massacred the exponents in the denominator

[karmic stirrup]

-# yet they still got the right answer..?

[viscid shard]

then in the third step your numerator decided that its friends in the denom were having quite a lot of fun down there and decide to jump the exponent gun too

[viscid shard]

was that very surprising lol
plenty of cases of people using "illegal" methods but still coming to the right answer by chance or by some God-ordained miracle

whether that'd be given credit or not, though, kinda depends on the examiner

[sacred crystal]

oh

[sacred crystal]

What

[blazing reef]

wtf they got lucky as hell

[karmic stirrup]

or maybe they're using some method we dont recognize...

[viscid shard]

in short, you killed the denom in the second step and the numerator in the third

[sacred crystal]

I'm a genius

Trust

[sacred crystal]

What's denom

[viscid shard]

sure. good luck with the rest of the problems!

[blazing reef]

You made two mistakes but it kind of balanced out lol

with your fourth root of 2

[sacred crystal]

can you show me how it would've been correct

[viscid shard]

how about we walk you through then

[blazing reef]

$32^{1/4} = 2^{5/4}$

[boreal girder]

Katrro

[blazing reef]

this is something you missed

[sacred crystal]

what

[blazing reef]

on the top of the fraction

[sacred crystal]

Why's 32 have exponent

[karmic stirrup]

oh!

[blazing reef]

that's what square root and stuff is

[blazing reef]

yeah

$\sqrt[4]{32} = 32^{1/4}$

[boreal girder]

Katrro

[sacred crystal]

Oh

I don't think the teacer taught us that

teacher

So he prob won't accept the answer

[karmic stirrup]

okay

[toxic cipher]

honestly for these types of problems just write out everything in terms of prime factors and simplify it using exponent rules until you're done

[karmic stirrup]

explain what you did here then

[sacred crystal]

Well

The 32

Changed to

Wait a minute

[karmic stirrup]

do you know how to do this?

[toxic cipher]

why?

[sacred crystal]

I tried

[karmic stirrup]

i was asking them-

not you 😭

[viscid shard]

you tagged the wrong person

or rather you replied to the wrong person

[karmic stirrup]

my baddd

[sacred crystal]

I'm a he guys

anyways

2^4 x 2 is 32

I subbed it

With the 32

and then

The exponent 4 for the 2

Removed the radical

And itself

So 2x2

[blazing reef]

that's a mistake

[karmic stirrup]

?

[karmic stirrup]

.

[sacred crystal]

How

they cancel each other

Exponent 4 and rad index 4

[blazing reef]

$\sqrt[4]{2^4 * 2} = 2* \sqrt[4]{2}$

[sacred crystal]

They're both same nb

[boreal girder]

Katrro

[sacred crystal]

Oh

Hmm

Wait what

Where'd the exponent go

[blazing reef]

wdym

[sacred crystal]

The exponent 4

For the 2

Under the rad

[blazing reef]

I cancelled it out

[sacred crystal]

OH I SEE

[viscid shard]

when you take the fourth root of something to the fourth power, by definition they cancel

[sacred crystal]

ikik I got confused for a sec

[viscid shard]

just like how taking the square root of a squared term cancels the square

[sacred crystal]

So I should do this

Or other way to answer

Gr 10 lv

[blazing reef]

you should probably do this

and now we can work on the denominator

[sacred crystal]

Are the denominators correct

[blazing reef]

you almost had it but you did the same mistake from before

[sacred crystal]

Oh no

Oh

Is it the 162

[blazing reef]

yea

[sacred crystal]

One sec

How should

I do it

[blazing reef]

you should figure out what 162 reduces to

[viscid shard]

hint: prime factorize the number

[sacred crystal]

Hm

[blazing reef]

you got it

[sacred crystal]

Sec

[karmic stirrup]

there you go!!!

awesome

23 left!

[sacred crystal]

Thanks

[sacred crystal]

😭

[karmic stirrup]

honestly I'd start crying If i had to simplify all those expressions- yeah good luck hadi!

[sacred crystal]

My math teacher

One of a kind

[blazing reef]

just remember that they can be written as powers of prime numbers

[sacred crystal]

Katrro

[blazing reef]

and you'll be fine

[sacred crystal]

am I correct

[blazing reef]

yeah

[sacred crystal]

How now

[karmic stirrup]

you were correct before correcting your mistakes 😭

[blazing reef]

now you can cancel them down

yeah... you're mistake was basically turning the fourth root of 2 into 2

which is why you got it right

[sacred crystal]

Oh...?

I'm confused now

[karmic stirrup]

yeah the 2's still canceled out smoothly

[karmic stirrup]

nevermind!

continue.

[sacred crystal]

I GOT IT

2/45

IM A GENIUS

Thanks guyz

Correct?

These in ex 2

Uhhh I'm in 4 now

I can't find 25 in exponent

Like exponent 5

[karmic stirrup]

For 1 yeah looks correct,
2, I'd specify and say no real solutions to impress my teacher
3...

[sacred crystal]

Isn't it

Correct

Multiplied both side by minus

[blazing reef]

it is right

[sacred crystal]

ye

[karmic stirrup]

?

[karmic stirrup]

how?

x=-5?

[sacred crystal]

Ye

guys help in 4 pls 😭

[blazing reef]

it's right but there are more solutions

[sacred crystal]

I can't find 25 exponential form

[karmic stirrup]

how is negative 5 a solution 😭

plug it in

[sacred crystal]

It is bro

[karmic stirrup]

well... i dont think you know about logs

[sacred crystal]

What's logs

[blazing reef]

$(-(-5)-3)^4 = (2)^4 = 16$

[karmic stirrup]

OH

[boreal girder]

Katrro

[karmic stirrup]

wait the power is 4

i thought it was 2 mb

[blazing reef]

but he technically deleted a solution

[sacred crystal]

hm

[karmic stirrup]

when you take the root of an even number, always consider +-

wrong reply again

[sacred crystal]

Wait Ur right

[karmic stirrup]

which applys for every even exponent

[sacred crystal]

He did somt like this in class

[karmic stirrup]

do you wanna know why we do that tho?

[sacred crystal]

X can be both positive or negative

[karmic stirrup]

yeah! its x times itself and anything times it self, negative or positive, will always result in a positive output

[sacred crystal]

So wwe do both

[karmic stirrup]

as for this...

[blazing reef]

wait

[karmic stirrup]

yes, both are possible solutions

[sacred crystal]

Can we help me in 4

😭

[blazing reef]

you haven't finished q3 tho

[blazing reef]

you deleted one of the answers

[sacred crystal]

Ye Im writing t

I got it

[blazing reef]

you got the second solution?

[sacred crystal]

I wrote it

[karmic stirrup]

actually that spoils it

[sacred crystal]

He didn't teach

Us that

so he won't accept it

[karmic stirrup]

he didnt teach you this?????

i think it's ever that or logs which- you didnt learn im certain

[karmic stirrup]

do you know how you're supposed to

solve 4

without using exponent properties or logs 😭

[blazing reef]

you have to use them

I don't think it simplifies nicely

$x = \sqrt[5]{25} - 3$

[boreal girder]

Katrro

[sacred crystal]

I'll skip it

[karmic stirrup]

yeah if that's not the final answer then I'm guessing there are no ways to solve it

[karmic stirrup]

oh okay.

ill be here for the next 10 minutes then ill start studying

alright next question

[sacred crystal]

Lemme see

[blazing reef]

lmao i'm helping him instead of studying rn

[karmic stirrup]

same 😭 anything to escape arabic and chemistry

[sacred crystal]

I'm Arab too wowi

[sacred crystal]

Thanks I appreciate it 😭

[blazing reef]

that's right

[karmic stirrup]

اه عشان كده اسمك هادي

[karmic stirrup]

perfect

[sacred crystal]

Ye

6 is scary

[sacred crystal]

Egyptian?

[karmic stirrup]

yes

[karmic stirrup]

are you sureee

suree

that he wont accept this

bc seriously 6 and 4 cant be solved without them

atleast not nicely

[sacred crystal]

I've been there

[karmic stirrup]

terrible place dont come again

[sacred crystal]

it was fun

[viscid shard]

now I wonder if OP is from MY

[sacred crystal]

I went for 4 fays

Days

[sacred crystal]

What

[viscid shard]

nvm then

[karmic stirrup]

هادي

[sacred crystal]

eh

[karmic stirrup]

انت متاءكد ان المستر بتاعك مش هيرضي ب ده؟

[sacred crystal]

Yes

He didn't mention it today

[karmic stirrup]

3ashan raqam setta miesh hatet7l men8erhom

[sacred crystal]

Oh

[sacred crystal]

I went to sharm l sheikh

Hmm

I guess I'll skip this too

Wait actually

Hmm

I'll skip it

😭

[karmic stirrup]

wait do you know what imaginary numbers are

[sacred crystal]

Sorry

[karmic stirrup]

اعداد تخيليه

[sacred crystal]

Example

Give

[karmic stirrup]

x^2 = -1

x= i , -i

[blazing reef]

he definitely doesn't know

he's just learning exponents

[sacred crystal]

I'm in grade 10 guys

😭

[karmic stirrup]

HOW IS HE SUPPOSED TO SOLVE 8

[blazing reef]

lol

[sacred crystal]

Lemme solve 7 first

Hold up

[karmic stirrup]

is his teacher a maniac or smth

[sacred crystal]

He is

[blazing reef]

true I guess he can just say no real solutions

[sacred crystal]

he once made the fat guy do 30 push ups

[karmic stirrup]

oh that works too

[sacred crystal]

anyways

Nb 7

[karmic stirrup]

for 7, remember! consider both +-

[karmic stirrup]

سنه كام؟

[blazing reef]

and also remember that x can have multiple solutions..

[karmic stirrup]

what

[sacred crystal]

I'm 15 years old

[sacred crystal]

Does his work

[blazing reef]

you forgot to cancel out the negative sign on the right side

[sacred crystal]

Why would I cancel

It

[blazing reef]

because both sides are negative

[sacred crystal]

what

[karmic stirrup]

bc... -x =-y so x=y. genuinely makes everything so much simpler

[sacred crystal]

I expanded on left

[serene coral]

don't

[blazing reef]

oh you expanded it wrong

[karmic stirrup]

divide by -1

both sides

[sacred crystal]

Oh

[karmic stirrup]

then try again

[karmic stirrup]

oh did you- no. you cant shove a - inside an even root.

[sacred crystal]

WAIT

[karmic stirrup]

unless- imaginary numbers but no, you didnt get there yete

[sacred crystal]

NO SOLUTION

[serene coral]

why would you expand an eighth degree equation tho

[karmic stirrup]

?

[serene coral]

?

[blazing reef]

there is solutions

[sacred crystal]

Even nb exponent

Can't equal negative

[karmic stirrup]

السالب هيطير مع السالب و هيبقي

(-x+5)^8 = 2

[serene coral]

you've forgotten when you cancel the negative?

[sacred crystal]

What

[serene coral]

there are negative signs on both sides, aren't they?

[sacred crystal]

Ohh

so

I divide by -1

[karmic stirrup]

i def didnt say that

[serene coral]

if it works, it works

[karmic stirrup]

in both languages ❤️

no im not complaining its funny 🤩

[serene coral]

okay so now you should be able to solve the equation

[sacred crystal]

Sorry 😭

Guys am I too dumb or is this hard for my lvl

I think first option

[serene coral]

uhh what is the first line?

[blazing reef]

you're just learning it now

[serene coral]

but should be correct

[blazing reef]

if you practice more it'll get easier

[karmic stirrup]

correct

[karmic stirrup]

you're not dumb lmao everyone struggled with this

its also the basis of calculus, which is hte final boss of highschool.

[serene coral]

at some point or another, yes

i got introduced this way earlier

[sacred crystal]

Anyways

[sacred crystal]

Now what

How do I

Do the 2

it's too low of a nb

[serene coral]

just do it normally

[sacred crystal]

what does it convert to

[blazing reef]

you should just leave it as that

[serene coral]

move the 5 over

[sacred crystal]

Oh?

[storm dock]

Wouldn't it be |-x + 5|?

[karmic stirrup]

you would've done more if oyur teacher had common sense

[blazing reef]

leave the 2 i mean

[sacred crystal]

why would I absolute it if idk what x is

[serene coral]

it said find x tho, right?

[sacred crystal]

It said solve

[karmic stirrup]

they're saying that you forgot to consider -+ bc of the even root

[serene coral]

that's the same

[sacred crystal]

Ex 2 nb 7

[storm dock]

Yeah

[sacred crystal]

8 is impossible right

No real solution

[blazing reef]

ye

[serene coral]

but why ur teacher give such ugly solutions

[sacred crystal]

Same as 9 n 10

Tho

[blazing reef]

no

[sacred crystal]

he's a menace

9 ain't positive

[serene coral]

only even bases return positive results

[sacred crystal]

Right

So 10 is the impossible one

[blazing reef]

$\sqrt[5]{-1} = -1$

[boreal girder]

Katrro

[blazing reef]

so you can still do q9

[sacred crystal]

alr alr

[serene coral]

if 10 is (-70)^2 then it's still possible

[storm dock]

10 is not 70 x 70?

[blazing reef]

10 is no real solutions

[serene coral]

i fear for you when you get to the min max values of an equation

[sacred crystal]

9

[sacred crystal]

💔

[karmic stirrup]

look! they're learning proofs of real analysis while being in grade 10

wait a minute nvm

i didnt see the exponents

[serene coral]

uhh what is "proof of real analysis"?

[sacred crystal]

Correct?

[karmic stirrup]

real analysis is a college-level course and yeah it has proofs too

[sacred crystal]

I can't solve 12

[karmic stirrup]

yeah1

[blazing reef]

remember how to simplify the exponents?

from the very beginning of the channel

[sacred crystal]

Ohhh

Right

Sec

[serene coral]

so you have (x-1)^4 = 7^8 right?

simplify the ^4

[sacred crystal]

7^8 too big

Can't think 😭

[sacred crystal]

Thomas look

[serene coral]

have you learnt that x^(a*b) = (x^a)^b?

[karmic stirrup]

they werent taught how to do this btw)

[sacred crystal]

I'll skip...

[blazing reef]

don't skip it

[storm dock]

Wait cant you just do 8/4?

[blazing reef]

yes

[sacred crystal]

Oh

So

Uh

what

[blazing reef]

$\sqrt[4]{7^8} = 7^{8/4}$

[boreal girder]

Katrro

[karmic stirrup]

they weren't taught how to convert roots into exponents

[sacred crystal]

WAIT

[serene coral]

..damn

[sacred crystal]

WE WERE

IT WAS THE FIRST THIG WE TOOK

IM SORRY CAR

[karmic stirrup]

are you seirous

[sacred crystal]

I FORGOR ABT IT

7^2/1

Right

[karmic stirrup]

الي جوا علي الي برا

[karmic stirrup]

yes.

[sacred crystal]

Alr so

[karmic stirrup]

now i shall start studying

good luck hadi

the rest of the questions are easier

[sacred crystal]

49 right

[sacred crystal]

Thanks

[storm dock]

Yep the left side is 49

[sacred crystal]

X is 50

the other solution

X is -48

[blazing reef]

ye

[sacred crystal]

Ex 2 nb 2 is absolute value right

I change to absolute

I mean ex 3

[storm dock]

Yeah since they are even

Wait

For A no

Honestly idk

[sacred crystal]

I meant M

[storm dock]

Yes

For even numbers you do but you don't have to for odd ones

[sacred crystal]

Ah

I

Give up

[serene coral]

don't

there are plenty more harder problems down the line 🤣

[sacred crystal]

too late packed my shi up

thanks @storm dock @serene coral @blazing reef @karmic stirrup @viscid shard for help, you will definitely be asked for more help in the future by me, sorry 😭

[serene coral]

if you're done, then close the channel

[sacred crystal]

alrighty

[karmic stirrup]

you can ping me in your future channels

[sacred crystal]

I gotta swipe all way up?

[karmic stirrup]

no

just type .close

[sacred crystal]

I love you bro

ok

Bye guys

[storm dock]

Gl

[sacred crystal]

Thanks

.close

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[quasi halo]

In a volatile housing market, the overall value of a home can be modeled by V(x) = 415x2 – 4600x + 200000, where V represents the value of the home and x represents each year after 2020.

Part A: Find the vertex of V(x). Show all work.
Part B: Interpret what the vertex means in terms of the value of the home.

[random mica]

!status

[compact pewter]

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

[quasi halo]

4

[random mica]

Ok send your working

[gaunt pilot]

k

was this bout

wt ?

[quasi halo]

Part A: The x‑coordinate of the vertex is given by:
x = –b / 2a
Here a = 415, b = –4600.
x = –(–4600) / (2 × 415)
x = 4600 / 830
x ≈ 5.54
Now plug x back into V(x):
V(5.54) ≈ 415(5.54)² – 4600(5.54) + 200000
V(5.54) ≈ 187,253
Vertex ≈ (5.54 , 187,253)

Part B: - x = 5.54 means about 5½ years after 2020, which is mid‑2025.

• The vertex is the minimum point (since the parabola opens upward).
• So, the home’s value is predicted to drop to about $187,253 in mid‑2025, then begin to rise again afterward.

Final Answer:

• Vertex: (5.54 , 187,253)
• Meaning: The home reaches its lowest value of about $187,253 in mid‑2025, then increases in value after that.

[toxic cipher]

!occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[toxic cipher]

dont use a rounded value of x and of V(x), unless your teacher said before that it's accepted

otherwise, it's correct

[quasi halo]

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[next tusk]

A multiple choice test has 20 questions, with the answer for each allowing four options, A, B, C, and D. Devise a 2-tail test at the 10% significance level to show that a student’s mark was not the result of random guessing.

I put the formulae as shown in the screenshots, which generated the table also shown. Since this was a 2-tail test at the 10% significance level, I looked for cumulative chance < 0.05 and 1 - cumulative probability < 0.05 respectively, and got the result that I would suggest the answers were not selected at random if the student’s score was less than or equal to one, or greater than or equal to eight. However, the correct answer is <=1 or >8 correct.

I don’t get why eight would not be included in the critical range, since 1 - 0.959 < 0.05. Any help would be appreciated

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[next tusk]

<@&286206848099549185>

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[scarlet pebble]

Hi, can you explain Eulers formula? I’m getting into the zeta function

[kind crane]

https://brilliant.org/wiki/eulers-formula/

[scarlet pebble]

lol Riemann

[native shard]

that million dollars is yours bro

[scarlet pebble]

Come on you can’t type it for me 🥹

[scarlet pebble]

Wdym

[kind crane]

................

this person is not real

[scarlet pebble]

I don’t get the proof

What does the factorial

Have anything to do with it

[native shard]

you can't figure it out?

[kind crane]

start with calculus

shouldn't take you more than a couple minutes to learn taylor series:
https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

[scarlet pebble]

Buddy your just gatekeeping at this point

[native shard]

*you're

[scarlet pebble]

!done

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[steady swan]

can someone tell me why im only using positive values of x? (referring to "for all values x > 0")

[kind crane]

because the question is about x going to infinity

[steady swan]

ohh okay

soo if it was going to like 2 would it be like for all values of x < 2

[open girder]

Also, it’s helpful to state that for when you’re dividing by x+1

[kind crane]

no

limit exists if both one sided limits exist and are equal

[open girder]

This would make sense if you’re taking a one-sided limit, ie. going to 2 from the left

[mild sky]

also this would be x in some open interval round 2

[quartz oasis]

if it was going to 2 you could also assume x is positive, if that is what you meant to say

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[spark nymph]

1 sec

let me post work

I think that's how GNFA works, I make a new initial, and a new final state, with lambda transitions from the new initial to the old initial, and old final to new final, where the old final becomes non-final, and any labels are represented in terms of union if there are multiple symbols on any given transition

not 100% sure though

<@&286206848099549185>

[river portal]

Yeah, that's an equivalent GNFA, or you could just take the given NFA and call it that

Making new initial and start states is necessary when you are going to convert it into a regex

[spark nymph]

I see, so any NFA is a GNFA, but what I have is also fine (albeit unecessary)

[river portal]

Yes

[spark nymph]

alr cool, thanks for the help

.clolse

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[obtuse elk]

hello, im not sure which channel this falls under but this is not very urgent
how cooked am i if i cant perform ref/rref with getting the right solution? i understand row reduction and how to perform all the elementary row operations and whatnot, but i just lack the intuition on which like entry to eliminate or work on first if that makes sense?

[warm orchid]

Quite cooked, because in finite dimensional linear algebra, a lot of actual computation involves reducing matrices

Also the intuition there just comes from doing lots of practice problems and remembering the final form you want to get your matrix into (eliminating below the pivot and such)

[obtuse elk]

is it simply just practice

i’ve had this problem last year too when i took ab matrices briefly and i had the same problem

[warm orchid]

Yes

[obtuse elk]

😔😔

i understand

ty g

.close

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[clear marsh]

Im having alot of trouble finding the minimum value.

[near crown]

!show

[compact pewter]

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

[clear marsh]

So I've gotten to $\sqrt{\frac{2}{\lambda4}} = x = y= z$ and then I plugged in $\sqrt{\frac{2}{\lambda4}}$ for $x, y, z$ in the constraint and got $3\left(\frac{2}{\lambda4}\right)^2 = 5$ and simplied that to $\lambda = \pm\sqrt{\frac{3}{20}}$

[boreal girder]

డ్ర్యాగ్లొక్స్

[clear marsh]

If I plug in lambda back into x, y, and z, I get the maximum value, and I got a minimum value $-\frac{3}{2\sqrt{\frac{3}{20}}}$ but the website says it's wrong

[boreal girder]

డ్ర్యాగ్లొక్స్

[clear marsh]

I hope it makes sense, my written work may be sloppy, but I can post it if needed

nvm i got the answer

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[glass adder]

hello I am unaware of how to start with this problem :(

[viscid shard]

looks like an application of the squeeze theorem

[glass adder]

ahh i think youre right

we just went over that in our most recent lecture but not sure how to apply that to this problem :/

[viscid shard]

evaluate the limits of the other two functions

[glass adder]

do I apply the limits to the expression chain so it would be like 0 less than or equal to f(x) less than or equal to x^2

oh wait so f(x) would just be 0 then right

as x approaches 0

[viscid shard]

yes, because both LHS and RHS approach 0, and since f(x) is strictly in between the two functions, it must also tend to 0 as x -> 0

that's the squeeze theorem in a nutshell. if we have g(x) < f(x) < h(x) for an interval containing the limit point, then by this inequality chain, g(x) will squeeze f(x) from below, and h(x) from above

think of it as g(x) and h(x) being the curbs of a narrowing road

[glass adder]

I see i see,

but would x -> 1/2 be possible?

[viscid shard]

try it!

[glass adder]

im thinking it wouldnt because like

[viscid shard]

find the limits of the two functions at x = 1/2

[glass adder]

-x^4 would be -1/8 and x^2 would be 1/4

so thats quite a range between them

if the squeeze theorem is like they're hugging f(x) tho would f(x) be the average between them?

or like the middle?

wait my calculator lied

-1/16

[viscid shard]

nope

if the two limits are not the same, then your squeeze fails

not that the limit of f(x) doesn't exist, mind you, just that you can't use the squeeze theorem to do it

or at least not with these two functions

[glass adder]

AHH i see

[native shard]

if it does exist you can use the same bounds though

[glass adder]

so in order for the squeeze theorem to work the two other functions have to be approaching the same point

[native shard]

the squeeze theorem is a consequence of limits preserving order

if $f(x) \leq g(x)$ for some neighborhood around $x_0$ then $\lim_{x \to x_0} f(x) \leq \lim_{x \to x_0} g(x)$ provided these limits exist

[boreal girder]

knief

[native shard]

in the case of the squeeze theorem you just force the middle function to have a limit that is equal to the limit of the functions its squeezed between

[viscid shard]

quick question then, does this mean we can conclude that the limit just straight up DNE in OP's example?

[native shard]

for the 1/2 one?

no it might still exist

in the case of 0 it is forced to exist though

its just that we can't pinpoint a particular value that it might have if it does have a value at all

[viscid shard]

for the 1/2 one yes

[glass adder]

by force to exist you mean that because it is valid in the expression chain it exists

?

[viscid shard]

because I took "if it does exist you can use the same bounds" to mean that "since we used those bounds for 1/2 and the squeeze was inconclusive, thus the limit DNE"

[native shard]

well i can prove it for you if you'd like

[viscid canopy]

no it means that if the limit exists, the limit lies in the set [-1/16, 1/4]

[viscid shard]

ah ok, my bad

[native shard]

before i write out a proof, are you familiar with the epsilon-delta definition of the limit or should i not even waste my time

[glass adder]

I am familiar with it but not sure I have a 100% understanding, either way its ok you dont need to go that in depth its just a simple question on my homework :p

I appreciate the effort tho

[native shard]

here is the idea btw

[glass adder]

Looking at that in my notes rn

visualizing it like that def helps me understand it

alright I think I got it now

thank you guys!

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[upper bane]

<@&268886789983436800> another one of those message copying bots
(#help-43 message)

[sullen merlin]

.close

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[honest merlin]

can someone help please

I found magnitude r'(t) and didn't get 1

I got sqrt(1+4t)

now I tried taking integral from 0 to 5 of that and got 1/6 * (1+4x)^(3/2) + C

is this right? if so now what

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[west pulsar]

I have the drawing for one done but I need help figuring out what general equation I’d use for one

If someone could help me learn max/min problems it would be really cool of them!

[dusky nymph]

try introducing some variables for the height and width of the printed part

say x and y

what equation do they have to satisfy?

[compact pewter]

@west pulsar Has your question been resolved?

[west pulsar]

Ok so

Update

This is what I have

Is this right so far <@&286206848099549185> ?

And what’s the next step?

[kind viper]

ok so you've expressed h in terms of w, good

now simplify (w+2)(h+4) so that it's in terms of w only

will also suggest you expand it bc that will make your life easier

[west pulsar]

Wdym expand it though

What does that entail

[kind viper]

expand like open the brackets.

apply the distributive law

[west pulsar]

Ok ok one second

So I have

Wh= wh + 4w + 2h

Is that correct?

[kind viper]

Wh
what is this

did you mean WA maybe? based on what you've written earlier

also where is the 4*2

[west pulsar]

Width height

[kind viper]

mm

okay this notation is going to be really awkward.

so right now we've got $w$ and $h$ as the width and height of the printed material. i would use a single letter for the area of the entire sheet with margins included, say $A$ cause that's what we want to minimize.

[boreal girder]

Ann

[kind viper]

so you have $h = \frac{50}{w}$ and also $A = (w+2)(h+4)$

[boreal girder]

Ann

[kind viper]

expanding (as i told you) gives $$A = wh + 2h + 4w + 8$$ and this in turn becomes $$A = 2h + 4w + 58$$

[boreal girder]

Ann

[west pulsar]

But what do I do with this

[kind viper]

replace h with 50/w

now you have a function of one variable (w) that you want to minimize

[west pulsar]

Ok I got the rest of it, thanks for the help

.closed

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[next latch]

i dont really understand this part

the part when we have separate inequalities and then we somehow add them altogether

im lacking in knowledge about inequalities

id appreciate it if someone can explain step by step :)

[viscid shard]

if you have a number, say, a, that's less than another number, say, c, and have a second number b that's also less than c (such that a < c and b < c), then if you add a and b together, you will get a number that's less than adding c and c together
agreed?

[next latch]

yes agree

[viscid shard]

that's exactly what's going on here

[next latch]

once you simplified to just 3 numbers that made a lot more sense

thanks so much!

[viscid shard]

glad to help!

anything else? if nothing else, you may .close this channel

[next latch]

ok thanks!

.close

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[regal mortar]

Hello

[regal mortar]

Please an urgent need of someone good enough and having knowledge in battery design and sim software

[regal mortar]

I have a paper presentation at 30th oct please

[kind crane]

#old-network for EE server

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[mild prawn]

guys

[mild prawn]

how to find x here .. 50/3602pi*(6+x) + 2x+12=34.14

i dont know how to make x the subject here

[low sequoia]

$\frac{50}{360}\pi(6+x) + 2x+12 = 34.14$

[boreal girder]

MarcoMa210

[low sequoia]

expand that first parenthesis

[mild prawn]

how to?

[low sequoia]

distributive law

$a(b+c) = ab + ac$

[boreal girder]

MarcoMa210

[mild prawn]

...i havent learn that yet tbh..im on ordinary levels

is the answer 6+x

[low sequoia]

$\frac{50}{360}\pi(6+x) = \frac{50}{360}\pi \cdot 6 + \frac{50}{360}\pi x$

[bleak dock]

IGCSE?

[boreal girder]

MarcoMa210

[mild prawn]

yea

[bleak dock]

are you intimidated by the fraction and pi?

cause you really should have seen something like 2 (4 + a) = 8 + 2a before

[mild prawn]

by the entire thing tbh :/

[bleak dock]

it doesn't hurt to go step by step then

[toxic cipher]

Expand, bring all the terms with x to one side, factor out x, divide the other side by what you got in the prior step

[mild prawn]

ik that part...but then this question is soo idk

[bleak dock]

$\frac{50}{360}\pi \cdot 6 + \frac{50}{360}\pi x + 2x + 12 = 34.14$

[boreal girder]

south

[bleak dock]

,calc 50/360 pi * 6

[boreal girder]

Result:

2.6179938779915

[bleak dock]

that's just a constant

you can subtract both sides by 2.618, then subtract both sides again by 12

[mild prawn]

how did u get two 50/360 on both sides?

*on same side

@bleak dock

[bleak dock]

the distributive law

I guess if it helps, hopefully you agree that $a(6 + x) = a \cdot 6 + a \cdot x = 6a + 6x$

[boreal girder]

south

[bleak dock]

but then a can be anything

you can let $a = \frac{50}{360} \cdot 2 \pi$

now the key is, every time you see $a$, replace $a$ with $\frac{50}{360} \cdot 2 \pi$

so you replace a in a(6 + x)

you replace a in 6a + 6x

well, remember it's 6 * a + 6x, so you need the multiplication sign

[mild prawn]

alr so what would happen to that two in 2pir?

[bleak dock]

oh wait, so this is what you wrote

[boreal girder]

south

[mild prawn]

oh dang

[bleak dock]

okay I've made the correction

[mild prawn]

so 50/3602pi6 +50/3602pix??

[bleak dock]

Discord keeps swallowing your * so you need to put spaces

50/360 * 2pi * 6 + 50/360 * 2pi * x

that's correct

[mild prawn]

yay

[bleak dock]

,calc 50/360 * 2pi * 6

[boreal girder]

Result:

5.235987755983

[mild prawn]

afterwards what to do?

[bleak dock]

$\frac{50}{360} \cdot 2 \pi \cdot 6 + \frac{50}{360} \cdot 2 \pi x + 2x + 12 = 34.14$

[boreal girder]

south

[bleak dock]

subtract 5.235987 and then subtract 12 from both sides

[mild prawn]

50/360 * 2 * pi * x + 2 * x =16.904

now we subject x righ

so x ( 50/360 * 2 * pi + 2)=16.904

[bleak dock]

yep! that's correct

you're so close now

[mild prawn]

and then we divide the bracket part from 16.904

[bleak dock]

yeah

[mild prawn]

yay

[mild prawn]

ty!!

[bleak dock]

no worries!!

if you're done type .close

[mild prawn]

.close

[compact pewter]

Channel closed

Closed by @mild prawn

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

Send your question here to claim the channel.

Remember:
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[distant spoke]

I get it how least upper bound property implies cauchy completeness of R but I am not able to prove the other way that cauchy completeness implies least upper bound property for R

[short ferry]

try binary-searching for the supremum

do you know what i mean or should i explain it?

[distant spoke]

Binary searching?

[short ferry]

well, your goal is gonna be constructing a cauchy sequence which converges to the supremum

that's probably the most reasonable strategy

take some number a in the set, and some upper bound b. Look at the midpoint m, if its an upper bound, use b=m. If not, use a = m. Repeat

[distant spoke]

Yeah and most natural

[short ferry]

try examining the process above and use it to construct the cauchy seq

[distant spoke]

But we have a set and set of upper bounds

[distant spoke]

Ohhhhhhhhhhhhhh understandable 🥲🥲 ahh yessshh

[short ferry]

this "binary-searching" is pretty common btw, you will use it quite often in real analysis

in some form

[distant spoke]

Yeah I used it while proving that zero theorem.. intermediate value theorem ..

[short ferry]

yeah, thats exactly it

[distant spoke]

Thanksss buddyyyieee 😇

[short ferry]

np

[distant spoke]

.close

[compact pewter]

Channel closed

Closed by @distant spoke

Use .reopen if this was a mistake.

[compact pewter]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[vale perch]

for x = 2nπ/3 ± π/9 how to check number of solutions for x belongs to [0,π/2]

[vale perch]

What values of n to be put so that it satisfies interval of x

[winged dock]

I would start by the upper bounds and lower bounds

[vale perch]

n= 0,1,2,3,4,5,6,...... Till when

[livid orchid]

consider

$$0 \le \frac{2\pi}{3}n + \frac{\pi}{9} \le \frac{\pi}{2}$$

[vale perch]

as n is integer so ±

[boreal girder]

Rbit

[winged dock]

Cannot exceed 2 Right

[livid orchid]

and $$0 \le \frac{2\pi}{3}n - \frac{\pi}{9} \le \frac{\pi}{2}$$

[boreal girder]

Rbit

[vale perch]

Explain

[livid orchid]

this obviously yields only n=0, giving x= pi/9

[livid orchid]

and there is no integer after you isolate n

[vale perch]

Can I say other way that if n = 0 we left with ±π/9 and -π/9 is not acceptable in the given interval so for n= 0 we get x = π/9 and so n = 0 is one solution

[livid orchid]

yeh that's fine

[vale perch]

How can I be sure how many values of n should I take n= 0 is confirmed but n = 1,2,3,4 ??

[livid orchid]

using my method

solve the inequality

[vale perch]

0 <= n <= 11/12

[livid orchid]

no

-1/6 <= n <=7/12

[vale perch]

I am getting 1/6 <= n <= 11/12

[vale perch]

Okay I am getting

Now what next

[livid orchid]

well what's a possible n in that range

that's an integer

-1/6 <= n <=7/12

[livid orchid]

yes

for the other equation

1/6 <= n <= 11/12, in this interval, what integer values of n can it take

[vale perch]

N=1

[livid orchid]

no

[vale perch]

No integer possible

[livid orchid]

yes

[livid orchid]

how about this one

[vale perch]

0

[kind viper]

eh hold up

...wait, nevermind

no, hold up, something's definitely fishy

is this about solving cos(3x) = -1/2 except you closed the prev channel and opened a new one?

[vale perch]

Yes

[kind viper]

aight well first off,

!noclopen

[compact pewter]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[kind viper]

you just successfully cut away all the context and will make it hard to recover

anyway im gonna repeat the important points that i told you

you're solving cos(3x) = MINUS 1/2 only, not +1/2 yes?

confirm/deny.

[vale perch]

confirm

[kind viper]

then x = 2nπ/3 ± 2π/9

[vale perch]

Yes

[kind viper]

you were missing that two in your original post

so you have to solve the inequalities again and properly this time

you should get one value of n in each case

(this i tell you because i know how it actually plays out)

[vale perch]

One thing

Cos3x = -1/2
3x = 2npi ± pi/3
x = 2npi/3 ± pi/9

[kind viper]

no no bad. bad. bad.

Cos3x = -1/2
3x = 2npi ± pi/3

this step wrong

2pi/3 not 1pi/3.

cos(±1pi/3) = +1/2 not -1/2.

[vale perch]

Then I should freaking memorise unit circle

Nobody tell the logical way to get those values

[kind viper]

that's a good idea if you're smart about how much & what to memorize

you should at least know quadrants