help-27

[dire hinge]

When it says this in a question

What does it mean?

Like the < doesn't make sense and how would I mark the graph out like what

numbers

would go for what ticks

[mystic scarab]

Could you show the whole exercise?

[dire hinge]

Part b btw

[wind elbow]

it would just mean drawing the whole graph within those sections, if it had < instead it would mean to draw it up to 60 but not on 60 and same for the 0 side of itt

sorry if the wording is weirdd

[dire hinge]

Ok um

could u explain it based on this (this was the answer booklet)

how was I supposed to know

that those random inequatiles

[mystic scarab]

Random?

[dire hinge]

would lead to this? and hwo would I calculate the ticks and numbers per blah blah

[dire hinge]

sorry?

[mystic scarab]

You are given the bounds

[dire hinge]

oh as in

[mystic scarab]

Why random?

[dire hinge]

yeh the bounds

[mystic scarab]

You're overthinking a lot

[dire hinge]

im not sure it just seems strange when its written like that.

yeh maybe i am sorry

[wind elbow]

just as filler words inbetween i thinkk

[dire hinge]

0 ⩽ t ⩽ 60

[mystic scarab]

Yeah

[dire hinge]

and how do I get to the graph from that generally?

[mystic scarab]

Huh? You're saying that writing 0 ≤ t ≤ 60 is strange? 😱

[mystic scarab]

Well, it depends on the exercise 😅

[dire hinge]

I dont get itt mann 😭 but my main question is

yeh no nm

ur right i am overthinking it

k thanksss

.close

[devout snow]

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[devout snow]

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[dawn perch]

Im struggling with understanding the integration bounds, how exactly are they determined

[smoky gyro]

hello you must use the jacobian

[dawn perch]

No but how should I think about this visually

Like what would you say it means. I made the misconception of thinking I need to find the area bounded by the paraboloid/ellipsoid

[devout snow]

@dawn perch Has your question been resolved?

[void fox]

If you want to find the volume of K you would do ∭_K 1 dV

I don't think there's a super clear interpretation of what this integral "means"

Maybe you can think of it as computing the mass of an ellipsoid where the object's density at a point is given by the square of it's distance to the z axis

[devout snow]

@dawn perch Has your question been resolved?

[devout snow]

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[devout snow]

Please don't occupy multiple help channels.

[azure parrot]

Imma close this one, you can post the problem in your other tickt

.close

[devout snow]

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[restive river]

weird thoughts

[restive river]

lets consider this proof for √2 being irrational

lets assume the contrary such that p/q =√2

then p²=2q²

so q²|p²

[restive river]

p,q in Z, and gcd(p,q)=1 too htw

[rain summit]

yes

[rain summit]

so then this contradicts

[restive river]

gcd(p,q)=1 so gcd(p²,q²)=1 cuz no extra prime factors introduced, but q²|p² so gcd(p²,q²)≠1 unless and if q=1

[rain summit]

let me get this straight

[rain summit]

you just weakened your proof here

[restive river]

lets say q≠1 initially, its not hard to show √2 cant be an integer

[rain summit]

until here is already where it contradicts

[restive river]

well theres nothing wrong with it

[rain summit]

im not saying it's wrong, im just saying that you are weakening it

[restive river]

andd, how so

[rain summit]

look, $\gcd(p^2, q^2) = 1$ and $p^2 = 2q^2$

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

that already contradicts

[rain summit]

and if you're saying like this, then it would still leave a case of $q = 1$ for you to handle

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

or even $q = -1$ with your condition

[woven radish]

1 divided by 0 equals Infinity

[restive river]

it certainlt isnt hard to show √2 isnt an integer so p≠√2 in that case where q=1, which i already mentioned

[rain summit]

alright

okay okay

anyways

what's your question about?

you're only saying on how you proved that $\sqrt{2}$ is not a rational number

[woven radish]

1 divided by 0 equals Infinity

[restive river]

crosschecking on the proof

[rain summit]

i think it's fine here

it's not wrong too

and by using the method you used, you can actually prove that $\sqrt{k}$ is not a rational number if $k$ is not a square number

[woven radish]

1 divided by 0 equals Infinity

[restive river]

q²|p² does works nicely on these i noticed just now, lets say we wanna show forall a nth root of a is either

was js saying that

lets try on 4,

4=p/q

[rain summit]

$\frac{p}{q} = \sqrt{4}$

[woven radish]

1 divided by 0 equals Infinity

[restive river]

p=4q, q|p but their gcd is 1, do q=1 is forced, so p=4, and by initial assump p is an integer

[rain summit]

$\frac{p^2}{q^2} = 4$

[restive river]

yeah

[woven radish]

1 divided by 0 equals Infinity

[restive river]

works nicely

[rain summit]

$p^2 = 4q^2 = (2q)^2$

[woven radish]

1 divided by 0 equals Infinity

[restive river]

i was talking about 4 not √4, but what ever , works

would like to hear from other too if anyone's interested

[violet wind]

What's your question?

[rain summit]

he wanted to check his proof of proving $\sqrt{2}$ is irrational

[woven radish]

1 divided by 0 equals Infinity

[rain summit]

and wanted to expand on that

[restive river]

eh

[violet wind]

I mean it's slightly different

Usually you show 2 divides both p and q

[restive river]

just implying q²|p² looks just too good to be true even to me mysef so😭 well a bit more analysis and it was perfectly fine

[violet wind]

But if you prove √2 can't be an integer a different way it's fine

[tulip kettle]

whats the actual doubt??

[restive river]

with this its quite easy to expand to various root irrationality proof so, like nth root of a is always an integer or irrational

[restive river]

js proof checking

[violet wind]

It's quite easy already with the original proof

[restive river]

yea yea

guess lemme close, nothing much now

.close

[devout snow]

Channel closed

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[violet wind]

Ig it shows whenever a root of an integer is rational, it's an integer

[restive river]

yup

[violet wind]

Which is interesting. This can probably be applied to rings (at least UFDs)

[restive river]

i was doing that exact problem when this came up,

[devout snow]

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[night rune]

c?

[topaz beacon]

what happened to the x in 400x and why did you approximate

[night rune]

because its trivial

[topaz beacon]

its also trivial to notice that you dont get the right answer

[night rune]

i dont think its because of the approximation

also, what x are you talkig about?

it cancels out

[topaz beacon]

in the third line, you have 400 - 8x/100

that should be 400x - 8x/100

[night rune]

you are right about that

sorry

[topaz beacon]

anyway, as you said, the approximation is not really the problem

if you have something that is 5000 times x, what percent of x is that?

[night rune]

i would do: 5000x = ?/100 of x

if i solve for ? i get 500000

[topaz beacon]

yes

now we need what percent greater, so you would subtract 100%

[night rune]

sorry i dont follow

100% is 1?

[topaz beacon]

yes

you subtract the initial amount

if something is 8 times the amount of something else, it would be the initial amount plus 7 more

i.e. y=800% of x, or y=x+(700% of x more)

so y is 700% greater

[night rune]

ok hold on, i interpet what you are saying as: 8 compared to 1 ... is 800% of 1

and when it comes to "a factor of"

that should be +1 ?

[topaz beacon]

what

[night rune]

nvrm

give me a sec

so my issue is basically that i forgot to add a x100% ?

[pseudo basin]

is it just me or

10,000 percent of 500 percent of 20 percent less than x
does this have like, a shit-ton of ambiguity

[topaz beacon]

its a linguistic mess

[pseudo basin]

thought so

wb garlic btw

[topaz beacon]

heyo

[topaz beacon]

no, you need to subtract 100%

[night rune]

oh i was reffering to my solution sheet

[night rune]

so in your case : 500,000 -100% ?

[topaz beacon]

in your case, yes

[night rune]

alright i think i am set

thanks

[devout snow]

@night rune Has your question been resolved?

[devout snow]

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[narrow isle]

can anyone please help me understand why one changes to cubed and the other doesnt? im so confused 🥲

[devout snow]

@narrow isle Has your question been resolved?

[narrow isle]

<@&286206848099549185>

[dry oak]

Decision 🥀

[narrow isle]

its a purgatory…

[willow steppe]

yo

i can help ifyou want, u online tho

@narrow isle

[narrow isle]

YOO yes pleasee

[willow steppe]

aight bet

so like which question is confsin

[narrow isle]

basically i understand the formula

[willow steppe]

yeahh

[narrow isle]

u multiply the time by the order

[willow steppe]

time?

[narrow isle]

but in the first question it says its a squared order

[narrow isle]

ye

[willow steppe]

sry can i just ask which question you are referringto

[narrow isle]

this one

and

[willow steppe]

ok

[narrow isle]

this one

[willow steppe]

so like the dijkstras one

[narrow isle]

yep

[willow steppe]

ok wait ive used dijkstras like once i think 😭

[narrow isle]

lmaoo dw is calm

[willow steppe]

so like i neef the nodes and graph tho to solve

[narrow isle]

the question is unrelated to the order but i can pull it up

[willow steppe]

ok

[narrow isle]

onee sec

[willow steppe]

ok

[willow steppe]

ok dam

uhh

lemme take a look

[narrow isle]

okeee

[willow steppe]

lowkey i kinda forgot how to apply dude 😭 ✌️

[narrow isle]

LMAOOO real tbh

dw thanks for trying

[willow steppe]

i learned this once from my friend. If i can relearn i can dm ifyw

idk if thats weird or anythin

[narrow isle]

its up to u

[willow steppe]

i mean it looks like abcehj is the right answer, but idk the proof for it

like maybe just find the smallest numbers and stuf bro

:so

[narrow isle]

oh nah im fine for that part

its the order

[willow steppe]

😭 ok

[narrow isle]

mb mb lemme circle

[willow steppe]

order, i see

[willow steppe]

oh so its just 9000^2 *312/10000

so like 81*312 x 10^6/10^4

[narrow isle]

for this one its cubed but the squestion says squared

[willow steppe]

so like 2527200

oh wouldn;t the reason for B just be the formula n^2/time

[narrow isle]

but it’s apparently not correct

[willow steppe]

sry no nodes^2 times time not divided

wait its not crct

?

[narrow isle]

it cubes it insteadnof squaring

but then for the first one

is squared

[willow steppe]

yeah but for the 1st picture T = that so like calculating time idk

it says n(n^2)

idk

[narrow isle]

yeahh thats what i dont get

[willow steppe]

dawg what class is this for

[narrow isle]

if its done that for the first question it should do for second

[narrow isle]

further maths

edexcel

💔

[willow steppe]

yeah cyz they are both asking for time idk

💔

[narrow isle]

mock tmr

[willow steppe]

:sk

💀

dude

or gal idk

[narrow isle]

im gal

[willow steppe]

ok sry but still this is like cs stuff tho im bus at that 💀 💀

[narrow isle]

LMAOO dw is calm

ill just hope it doesnt come up tmr

[willow steppe]

yea i cant really help i just thought it was n(n^2) lowkey

idk bro

gl i guess ggs

[narrow isle]

hey if its the two of us mayhe that means no one knows and then the papers basically out of 73

[narrow isle]

thanks gang

[willow steppe]

ok yeah ig + what test is this for

?

[narrow isle]

js a mock exam

[willow steppe]

/73

oh i see

hopefully they don't ask about dikstra idk

ggs bro ttyl,hopefully someone smarter than me can help i gtg

[narrow isle]

thanks for trying gangg cyas

[fringe meadow]

First person I've ever seen doing decision A-Level further

[devout snow]

@narrow isle Has your question been resolved?

[devout snow]

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[sonic kelp]

yo is anyone up to explain abel summation?

[sonic kelp]

i don't quite understand it

[dry oak]

Neither do I

[timber pebble]

summation by parts

thats pretty fascinating

probably not what youre talking about though

[sonic kelp]

yes that

[timber pebble]

it seems really analogous to IBP

[sonic kelp]

yeah apparently it is

[timber pebble]

you know any finite difference stuff?

[frosty crescent]

so the intuition is just ibp, right

[timber pebble]

yea, i think so

i mean, you dont need much fd

[sonic kelp]

how do you derive it

[timber pebble]

just that $g_{k+1} - g_k$ is our discrete 'derivative'

[woven radish]

jan Niku

[sonic kelp]

hmm okay

[timber pebble]

similar to how you derive ibp

idk if youve ever done that

[sonic kelp]

you derive ibp from product rule

so how do you derive this

a reverse summation product rule?

[timber pebble]

i have a feeling if i write $\Delta (f_k g_k) = f_{k+1} \Delta g_k + g_{k+1} \Delta f_k$

[woven radish]

jan Niku

[timber pebble]

it seems not super familiar

but, try starting from here

@sonic kelp so lets say we sum from 0 to idk n

$\sum _{k=0}^n \Delta (f_k g_k) = \sum {k=0}^n f{k+1}\Delta g_k + \sum {k=0}^n g{k+1} \Delta f_k$

[woven radish]

jan Niku

[timber pebble]

we're actually already really, really close to our goal

notice anything about the LHS?

[sonic kelp]

is it just f_k+1 g_k+1 - f_0 g_0?

[timber pebble]

do you know what $\Delta$ means?\

[woven radish]

jan Niku

[sonic kelp]

f_k+1 g_k+1 - f_0 g_0?

[timber pebble]

yea

because a ton of the terms die

like for example $\sum _{k=0}^2 \Delta (f_kg_k) = f_1g_1 - f_0g_0 + f_2g_1 - f_1g_1 + f_3g_3 - f_2g_2$

[woven radish]

jan Niku

[sonic kelp]

yeah so all middle terms get telescoped

[timber pebble]

so, were basically there

maybe, just want to adjust our indeces a bit

but we have the result now, i think

so, derivation, pretty fast

just like its analogous to IBP the derivation follows more or less the same

[sonic kelp]

alright

thank you, Ill close the channel now

.close

[devout snow]

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[devout snow]

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[limber sequoia]

guys i need help with my hw problem

[frosty crescent]

ok

[limber sequoia]

here lemme show it

can u help me

i m struggling wit it

[frosty crescent]

ok gng

[limber sequoia]

help me

plz

[frosty crescent]

$1+1=1+0^+=(1+0)^+=1^+=2$

[woven radish]

nadat12

[frosty crescent]

.close

[limber sequoia]

i think bud over complicated it

[brittle inlet]

{∅,{∅}}

[frosty crescent]

no these are peano axioms

[brittle inlet]

There, that's the solution you were looking for

[frosty crescent]

gng just accept peano 😭😭😭

[vital edge]

<@&268886789983436800>

[frosty crescent]

are we serious rn

[brittle inlet]

🥀

[modest dagger]

Nope

[brittle inlet]

That didn't work twin, dw

[modest dagger]

You should stop trolling though.

[brittle inlet]

Fortunately

[frosty crescent]

lol it has a genuine answer

[modest dagger]

Doesn't make it a genuine question

[frosty crescent]

good point

for some reason i cant do .close

[brittle inlet]

.close

[devout snow]

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[austere saffron]

in the sequence 1111011011110110 (4 1s then a 0 then 2 1s then a 0 repeating), is there an index, k, such that all indecies k2^x is always 0. for example, lets way k=5, this would mean that 10, 20, 40, 80, and so on are also 0s

[austere saffron]

if there are multiple k s, what is its smallest value

[frosty crescent]

so $k2^x\equiv0,5\pmod8$?

[woven radish]

nadat12

[frosty crescent]

eventually $k2^x\equiv0\pmod8$, so $k\equiv0\pmod8$ is the only solution

[woven radish]

nadat12

[austere saffron]

oh, thank you!

that makes sense

.close

[devout snow]

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[devout snow]

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[lunar eagle]

i just want the energy equation

u dont have to solve it all the way

[thin basin]

What are going to be your initial and final moment?

[lunar eagle]

Honestly i just want to know the extension is the spring

When the cylinde ris displaced by x

[thin basin]

As it is small displacement

You can assume the spring is also displaced by x

[lunar eagle]

But

The book

Took 2x

[thin basin]

It says down by x

So along the incline that will be 2x

Lol

[lunar eagle]

?

[thin basin]

The angle is 30°

[lunar eagle]

No they meant x along the incline

Liek the center is pulled doen by x along incline

[thin basin]

Hmm

Are you familiar with rolling motion?

[lunar eagle]

Yes

[thin basin]

Maybe they mean that the top most point has double the velocity of CM

So displacement is also double

[lunar eagle]

Ye but im not sure if displacement

Also u can just say double

Im not quite sure

[thin basin]

Is small displacement so we can take such assumptions

[lunar eagle]

Then does that mean

If the spring qas say attached

To the bottom

Instead of top

If u displace the cylinder by x

There wont be any extension in it ??

[thin basin]

I guess

[lunar eagle]

That doesnt rly make sense tho

How does that work

[thin basin]

I would suggest that you ask your teacher

[lunar eagle]

Ye but next class is like monday

This shi gonan live in my head rrnt free

[thin basin]

Well because the bottom most point has zero velocity, it won't move

So no extension

However only valid for very small displacement
As in the next instant it will no longer be the bottom most point

[lunar eagle]

[devout snow]

@lunar eagle Has your question been resolved?

Channel closed

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[lunar eagle]

.reopen

[devout snow]

✅ Original question: #help-27 message

[queen hearth]

When the spring is attached to the bottom of the cylinded, the displacement will be 0 as long as the displacement x is less than the diameter of the cylinder

The spring will only move vertically and not horizontally wrt the incline

The vertical displacement can be neglected

[lunar eagle]

Ohh

Thank you

.close

[devout snow]

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[devout snow]

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[split dirge]

13 a

[split dirge]

13 a

I tried whatever I could

But I couldn’t

[rain summit]

Can you construct quadrilateral ABCD?

[split dirge]

I did

After that

[pseudo basin]

can you show your construction

[split dirge]

Ignore other lines

That was just me trying

[rain summit]

So how do you find the area of ABCD here?

[peak solar]

use this

[split dirge]

Well

[rain summit]

Danggg

[split dirge]

I’m using that

[rain summit]

I saw the arcs there

[split dirge]

Yes

Using a compass

[rain summit]

Is ABCD cyclic?

[split dirge]

Idk

[rain summit]

Well, check if ABCD is cyclic then

Construct BD and measure CAD and DCB

[split dirge]

Cad 28 deg

Dbc 30

[rain summit]

Dang it

[split dirge]

Dcb 83

It isn’t cyclic

Man

This question has been haunting me since 2 weeks

<@&286206848099549185>

[tulip kettle]

Yes?

[split dirge]

How to draw that fig

[tulip kettle]

Tell me where is the problem in it?

!show

[devout snow]

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

[split dirge]

I did

[split dirge]

.

I couldn’t draw the triangle

@tulip kettle

<@&286206848099549185>

Nevermind

[tulip kettle]

draw a triangle

[split dirge]

I did it

Thanks

[tulip kettle]

first find area

[tulip kettle]

okkk

[split dirge]

We don’t need it

The area and all

[tulip kettle]

👍

[split dirge]

It can simply be solved by keeping base as BC

.close

[devout snow]

Channel closed

Closed by @split dirge

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[tulip kettle]

base of tri.ABC???

[devout snow]

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[vital drift]

that paper looks like it survived world wwar 2

[upper schooner]

You don't have a question you need to ask, do you?

[fickle magnet]

Ig not

[upper schooner]

Yea, I'm closing this she can open another if she does

.close

[devout snow]

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[devout snow]

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[median yew]

Is this the correct fraction decomposition for the above fraction?

[obsidian stone]

split it up

[median yew]

what do you mean?

[fluid stag]

looks good since the two quadratic factors are irreducible

[median yew]

Thanks

just wanted to confirm

.close

[devout snow]

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[devout snow]

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[hexed holly]

Would someone please be able to help explain what the domain and range of a function is?? I am so lost - I feel like I missed a day somewhere they taught it.

[hexed holly]

im googling stuff but i really don't understand it

[misty crest]

send some questions

[hexed holly]

sure

okay so i understand kinda that basically the domain is just numbers that it can be to not be undefined/imaginary

so like for c x couldn't be 0 because then the denominator would be 0, right?

but like i don't actually understand what the domain is or what it represents

[hushed salmon]

Is this your first time dealing with the domain of a function or do you have experience with basic stuff like finding the domain of a linear or quadratic function?

[hexed holly]

If I do have experience, I don't remember it

Oh wait is domain just all the acceptable x-values?

And range is the acceptable y-values?

Ohhh mygod

okay i was freaking out

Thanks guys..........

[hushed salmon]

welp i had to stop typing out my 15 line explanation

but alright!

[hexed holly]

oh im so sorry

[hushed salmon]

as long as you got it

[hexed holly]

<33 thank you so much

!! ❤️ ❤️

.close

[devout snow]

Channel closed

Closed by @hexed holly

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[devout snow]

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[hexed holly]

Could someone help me with this question?

[hexed holly]

I'm a bit lost - can you add 4e^2x and 8e^x?

[toxic rain]

No u cannot

[hushed salmon]

I'd say you divide the entire equation by 4 first and then you get a quadratic equation.

a=e^x

[toxic rain]

To simplify u can take e^x as another variable t

Using power rule e^(2x) becomes t^2

[fluid stag]

when adding or subtracting, only terms with identical bases and exponents are considered like terms, for future reference.

[devout snow]

@hexed holly Has your question been resolved?

[hexed holly]

ahh okay

thanks guys

.close

[devout snow]

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[devout snow]

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[cinder minnow]

hi can anyone help me

[fluid stag]

!da2a, but.if it's that same question again I'll disengage again

[devout snow]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[cinder minnow]

now its areal problem

n is a pi

[pseudo basin]

and cos xVsinx?

[cinder minnow]

yeah

[pseudo basin]

can you post the original without the OCR?

[fluid stag]

can you disable translation and send another screenshot?

[cinder minnow]

it will be in the ukrainian

[faint zinc]

That's fine

[pseudo basin]

that looks like russian to me

ok so $f(x) = \cos(x) \sqrt{\sin(x)}$ is your function

[woven radish]

Ann

[pseudo basin]

in plain text, f(x) = cos(x) sqrt(sin(x))

any progress on this one?

[cinder minnow]

omg

will we just go in tg or ctg (x)

?

[pseudo basin]

i don't think so.

do you know how to find the min or max value of a function on an interval in general?

[cinder minnow]

test the function's value at all critical points inside the interval and at the endpoints
and
?The largest resulting value is the maximum, and the smallest is the minimum. ?

[pseudo basin]

ok and do you know how to find critical points?

[cinder minnow]

f'(x)=0?

[pseudo basin]

yeah. ok, and can you find the derivative of cos(x) sqrt(sin(x))?

[cinder minnow]

cos(x)=0

sin(x)=not =0

??

[pseudo basin]

can you find f'(x) or not

[cinder minnow]

maybe no

[pseudo basin]

btw we can continue in russian if that is more convenient for you. unfortunately i do not speak ukrainian

for your reference though, f'(x) is called "the derivative of f" in english

anyway... ok i guess let's try to figure out what you're missing

do you know how to find $(g \circ h)'$ if both $g'$ and $h'$ are known (and exist, obviously)?

(composition rule, or chain rule)

[woven radish]

Ann

[pseudo basin]

@cinder minnow

wait did op just fucking leave

yup OP fucking left

.close OP left

[devout snow]

Channel closed

Closed by @pseudo basin

Use .reopen if this was a mistake.

[fluid stag]

oh what

[pseudo basin]

i have no idea

well, i have one idea but it's a huge stretch. maybe he was a russophobe?

[devout snow]

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[devout snow]

Channel closed

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[ocean thicket]

function y=-x^2+8x-5 is defined in [0,9]
find biggest and smallest value of the function

[short hare]

what have you tried?

[sturdy fiber]

-# Okay time to learn how to be a proepr helper from this
Don't mind me 🙏

[ocean thicket]

I actually don't know where to start

[short hare]

interesting, well I can set you on a little bit of an ad hoc with you memorizing the steps

orrrrr we could discuss why the steps work beforehand

[ocean thicket]

yeah that would be awesome

[short hare]

amazing

[ocean thicket]

that would probably be too complicated

[short hare]

oh you meant-

[short hare]

not really! its just simple observation

[ocean thicket]

alr then why not

[short hare]

alright

let me draw something

very ugly function but it will do

by eyeing this graph, can you tell me where the minima(s) and maxima(s) appear?

[ocean thicket]

like their exact cords?

no

[short hare]

oh no, i just wanna make sure you know what a maxima and minima look like in the graph itself

[ocean thicket]

oh

yeah

[short hare]

ok perfect then

before continuing

are we finding local minimums/maximums or absolute ones?

we're gonna go over both concepts anyways, i just need to make sure of something before we go on

[ocean thicket]

local and absolutes

i think

[short hare]

great alright

do you know how local maximas/minimas look like?

let me graph another thing

ill ask you to

simply point out where they occur with a red dot or an arrow

[ocean thicket]

yeah

[short hare]

can you point them out here?

[ocean thicket]

yeah

1m

[short hare]

perfect!

observe something about each and every one of those black dots

something that is very special about them is, if you were to draw a straight line that is tangent to these points

do you notice something?

[ocean thicket]

all of their derativies equal 0

because their decline is 0

[short hare]

oh- great

amazing

[short hare]

and here

this black point

is also a local maxima for the previous function

anything special about it?

[ocean thicket]

I have no idea

[short hare]

hm thats okay

I can try to make things quick

what ive been trying to show you is a consistant pattern that all local/absolute minimas and maximas follow

which is, they're always critical points

[ocean thicket]

ohhh yeah

[short hare]

yeah! a critical point for a function is a point where...
the derivative of the function is 0 or undefined or doesnt exist

[ocean thicket]

I see

[short hare]

the derivative is 0 is equivalent to what you mentioned here.

the derivative is undefined if the line tangent to that point is vertical

or parallel to the y axis

[short hare]

like here

[ocean thicket]

so the maxima is always a critical point

[short hare]

indeed. both maximas and minimas whether absolute or local are always critical points

so if we wanted to find maximas and minimas for a function

we have to inspect and search for critical points first

again, a critical point for a function is a point wher
the derivate of the function is 0 or undefined

or doesnt exist but that really only happens with piecewise functions. if you know what that is

[ocean thicket]

I don't

[short hare]

but here's the thing, both maximas and minimas are critical points so even if you found all the critical points for a function, you wouldn't really be able to immediately tell which one is a minima and which one is a maxima

[ocean thicket]

you need to compare their y

[short hare]

well,

these two points are both maximas and its not because their y is positive or where they are relative to eachother

[short hare]

this is how we find ABSOLUTE minimas and maximas

with them having tio have the biggest/smallest y in the function

but for local maximas and minimas, they dont really need to follow that criteria

to get to the point, the way you would identify a point like a maxima is observe the function's behavior around it

[sturdy fiber]

-# Mohammad Ali and John Cena example 🤣🤣🤣

[short hare]

as i said, these two points are local maximas

the function behaves in a very specific manner before and after each one of them

[ocean thicket]

deritives positive before
negative after

[short hare]

PERFECT

[short hare]

and what about local minimas?

[ocean thicket]

negative before

postive after

[short hare]

and you're done!

so to sum what we're gonna do

first, all minimas and maximas are critical points and thus we first find critical points

second, we observe the sinage of the derivative before and after the point to figure out whether its a maxima or a minima

[short hare]

our function is

-x^2+8x-5

[ocean thicket]

so deritive

is -2x + 8

[short hare]

not quite

[ocean thicket]

oops

-2x*

[short hare]

indeed

[short hare]

alright so now that we have the derivative

a critical point is where the derivative is equal to 0 or undefined or doesn't exist (which is a thing for piecewise functions)

[ocean thicket]

yeah

[short hare]

mhm

[ocean thicket]

so we need to compare to 0

[short hare]

indeed

[ocean thicket]

0 = -2x+8

0 = -2(x-4)

x = 4

[short hare]

indeeed

but is that our only critical point?

check the other criteria

[ocean thicket]

i think we need to check the 0 one and the 9 one

[short hare]

9 one?

what is the "9 one"

[ocean thicket]

like it says its defined in [0, 9]
so the point where its x=9 and x=0

[short hare]

oh i was gonna explain that after a bit but

well- yeah

so

x=0 , x=9 and x=4 are your supposed critical points

[ocean thicket]

yeah

[short hare]

now here's the thing, because the function doesnt exist before x=0 and the function doesnt exist after x=9 you dont really have to check the derivative sign around them

so now, check the sign between x=0 and x=4

and then the sign between x=4 and x=9

[ocean thicket]

i do that using a table

[short hare]

yes.

do you know why x=0 and x=9 are also critical points tho?

[ocean thicket]

no

[short hare]

well lets think about it

[ocean thicket]

x=0
before: +
after: +
x = 4
before: +
after: -
x=9:
before: -
after: -

[short hare]

what makes a point critical?

[ocean thicket]

the deritives is 0

[short hare]

hmmm the way you tested the sign does tackle a very important question

[short hare]

that wasnt the only thing that would make a point critical

[ocean thicket]

i put the x in the deritive

[short hare]

I know I'm just gonna explain in a bit

lets get over with why x=0 and x=9 are considered critical points as well..

[short hare]

.

[ocean thicket]

if the deritive is undefined

which it is

[short hare]

not quite

the third case

being the derivative doesn't exist

[ocean thicket]

doesnt exist

[short hare]

indeed!

if you remember

at the start of calculuys

when you were learning about continuity

and derivatives with limits

one of hte main criterias for a derivative to exist at a certain point

was for the + limit to be equal to the - limit

[sturdy fiber]

Hm

Sorry to interrupt

(it's fine if you don't want to see this)

[ocean thicket]

wdym

i think i got the idea

[sturdy fiber]

We were taught defining a point to be differentiable by considering moving slopes

From both sides

[short hare]

well that's essentially the same thing!

[sturdy fiber]

I see

[short hare]

my wording mightve been a bit off here so exucse me

[short hare]

well for a point like x=0

if you try to calculate the left limit

you'd be surpised to find out that

the function doesnt exist before x=0

and thus the function cannot be differentiated at x=0

[sturdy fiber]

Yeah

[short hare]

thus the derivative doesnt exist.

@ocean thicket are you still here?

[ocean thicket]

yeah

i think i got the idea figured tho

[short hare]

even tho this is correct, i still got stuff to say about it

first, the function doesnt exist before x=0 and after x=9

you didnt have to check the sign.

[ocean thicket]

oh yeah

[short hare]

before 0 and after 9

[short hare]

and for x=4

it seems like you tested before and after twice?

or

wait no

you didnt

im so blind

[ocean thicket]

what

i didnt

lol

[short hare]

okay 😭

alright

[short hare]

so for x=4, what type of critical point is it?

before it was + and after it was -

that makes x=4 a?

[ocean thicket]

max

[short hare]

local maxima

[ocean thicket]

ohhhh yeahhh

[short hare]

that's one of your requirments

now we dont really determine "locality" for x=0 and x=9

because again, the function wasnt even doing anything before 0 and after 9

so how are you gonna test the sign before and after

[ocean thicket]

put the x in the deritive function

[short hare]

yes but you determine a max/min by observing the sign ( of the derivative) before and after the point

there is no "before" for 0

and there is no "after" for 9

[ocean thicket]

yeah

[short hare]

alright

now to determine absolute minimas nad absolute maximas

we do what you suggested at the very start

compare between the y's of the three critical points.

the smallest is the absolute minima nad the biggest is het absolute maxima!!!!!

[ocean thicket]

ohhhhhh

I see

[short hare]

make sure to sub into the original function and not the differentiated version

to check for the y's

[ocean thicket]

yeah yeah for sure

alr i probably have another question like this

so we can do it together

if its alright

[short hare]

of course

send after you're doing with this one!

[ocean thicket]

this one also has another sub-question in it

explain why the function y=7 cuts the function in 2 points

[short hare]

hm, what do you think we can do about this?

[ocean thicket]

probably sub 7 into the original question

[short hare]

well

[short hare]

this statement can be rephrased into soemthing very useful

[ocean thicket]

we can compare the 2 functions

[short hare]

"show that when y=7, the function has two solutions"

[ocean thicket]

yeah

[short hare]

what 2 functions?

[ocean thicket]

y=7 and the original function

and then we prove they cut at 2 points

[short hare]

oh yes. you want to find their points of itnersection which is exactly what you get when you solve them!

by the way.... i mightve not been checking your numerical results. im too lazy to grab a calculator.

[ocean thicket]

its correct dw

trust.

[short hare]

so i trust in you that you did amazingly well in the previous question

[ocean thicket]

ok so i just need to sub it in

[short hare]

sub in y=7 for the original function indeed.

[ocean thicket]

ok new question @short hare

@short hare x^3-15x^2+48x-3
[0,11]
Find biggest and smallest value

[short hare]

thats basically the same thing

do it yourself first 🤩

[ocean thicket]

oh nvm thats actually not a question in the exam prepartions

hold on

let me get another one

@short hare ok a whole new diff one
-3x^4+4x^3+12x^2-32<=0

[short hare]

what the fuck is that

[ocean thicket]

xd

[short hare]

yeah what do you wanna do with this

[sturdy fiber]

Im guessing you mean $-3x^4+4x^3+12x^2-32<=0$

[ocean thicket]

you need to prove it

[woven radish]

Itsuki

[sturdy fiber]

Grrr

[ocean thicket]

yeah

[sturdy fiber]

$-3x^4+4x^3+12x^2-32≤0$

[woven radish]

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

[short hare]

im not proving all that

wait for someone else to help

[ocean thicket]

wait how do u even start this

[sturdy fiber]

Hm

[short hare]

(sorry)

[sturdy fiber]

Tell me

[fluid basalt]

Prove that it's less than 0?

[sturdy fiber]

I'm free

Finding Maxima and minima again?

[ocean thicket]

no

[fluid basalt]

I assume real inputs

[ocean thicket]

you need to prove that

[fluid basalt]

What about it?

[sturdy fiber]

Huh?

[ocean thicket]

I don't know it says "prove these:"
and then this function

[sturdy fiber]

Ah i see what you mean

[sleek herald]

Help

[sturdy fiber]

I think they want the function f(x) to be proved that it is always ≤0

[ocean thicket]

yeah

[fluid basalt]

If you have to prove that the polynomial is always less than 0, find it's maximum value

If that's less than 0, then you're done

[sturdy fiber]

What happened? This chat is occupied, you can open your help channel by looking for available ones

[sleek herald]

Ok

[fluid basalt]

As for finding it's maximum value, find all the stationary points, determine their nature, and find their y values.

[ocean thicket]

okay

.close

[devout snow]

Channel closed

Closed by @ocean thicket

Use .reopen if this was a mistake.

[devout snow]

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[hearty nexus]

hello, this is a mirror and a bunch of rays coming from the right. im having trouble understanding why setting the distance traveled for each beam makes them reflect in such an angle that they all hit the same point

what guarantees they will all hit the same point, how is that even possible

its not intuitive or obvious to me, can someone please explain 🙏

[pseudo basin]

is that a parabolic mirror?

[hearty nexus]

yes

im watching this lecture and the guy says that setting these two segments (with the | mark) will ensure they all hit the same point after bouncing off the mirror

but that's what I don't understand

[pseudo basin]

do you know the analytic-geometry defn of a parabola

locus of a point equidistant from a directrix and focus

[hearty nexus]

no I don't know what any of that means

I can't figure it out without having to dig into these things?

[pseudo basin]

i dont think you can, no

[hearty nexus]

ah I see, then I can probably just accept this fact for now

thanks

[devout snow]

@hearty nexus Has your question been resolved?

Channel closed

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[icy flower]

Unsure how to get x ?

[untold ravine]

$4 \log x = (\log x)^2$ or $4 \log x = \log (x^2)$

[woven radish]

CherryMan

[icy flower]

this is the original question

[icy flower]

?

[untold ravine]

so just simplify this?

[icy flower]

i did the latter

How do i simplify?

normally I know you can divide both sides by x

but given its a logarithm i am not sure

[untold ravine]

do you know that a log(x) = log(x^a), and also log a - log b = log(a/b)

[icy flower]

that is not familiar to me

[untold ravine]

well there are some standard log rules

two of which i covered

another similar one is log a + log b = log(ab)

with these rules can you rewrite 2 lg x - 1/2 lg x^2

[icy flower]

anywas

anyways

4 log x = logx^2

[icy flower]

that would mean 2= 4 according to this?

[untold ravine]

i thought the question was to simplify 4 lg x - 1/2 lg x^2

not to solve an equality

or is it?

[icy flower]

this is correct

so we should use the latter rule then

[untold ravine]

well tell me what steps you get

[icy flower]

(well its 4 lgx - lgx ^2 firstly)

[untold ravine]

well how?

oh

alright go on

[icy flower]

ok so 4 lgx - lgx^2

if we use the latter rule

we get 4 log x/x^2?

[untold ravine]

we cant directly use the latter rule

if it was something like lg x - lg x^2 then that would be lg (x/x^2)

but we have a coefficient of 4 multiplied with lg x

using the former rule we can bring that into the lg and then use the latter

[icy flower]

so we do 4 log x = log x^4

i c

[untold ravine]

yes

[icy flower]

so we divide log x^4 nu log x^2

so the answer is log x^2?

[untold ravine]

yes

4 lg x - lg x^2 = lg x^2

[icy flower]

a snag:

the answer says its lg x

[untold ravine]

well that would be the simplification of the original question

2lg x - 1/2 lg x^2

can you simplify that using the rules

[icy flower]

2 lgx = lgx ^2

0.5 lgx^2 = lgx

lgx ^2 / lgx = lgx

[untold ravine]

yes

[icy flower]

ok, thanks for the help

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[south fable]

i cant find how to represent IG and IC in useful ways (geometry problem, less use of coordinates would be nice)

[south fable]

progress (?) i've made

[drifting sierra]

geometry problem
Post a diagram

[south fable]

Conditional diagram

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[empty heath]

is this wrong?

[empty heath]

wouldnt cancelling out one of the Ys on the left side make it

2y + 7 / 3

nvm

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[blazing gyro]

Can somrone tell me whatsthe right angle to use for this my answer sheet says it should be sin50 but i font get it

[vapid veldt]

what do you want to use the angle for?

what are you solving for?

[blazing gyro]

find the magnitude of tension

or smth

t1 and t2

[vapid veldt]

then you just need the 20° and 30° that they give you

[blazing gyro]

but if i use sine law dont i need to compare it with gravity x the weight of the sign

[vapid veldt]

are you solving for the horizontal or vertical components of tension?

[blazing gyro]

I have no clue im js solving for tension😭

[vapid veldt]

ok, the law of sines usually helps when you have 2 angles and their two opposing sides. if you know 3, you can solve the remaining

[blazing gyro]

yeah i have all angles

but im not sure waht to do now

[vapid veldt]

i think it will be much more useful if you draw a free body diagram

[blazing gyro]

i dont think i can i have to follow my teachers ways and thats more physics right

thsi si vectors math

💔