help-42

[ocean hornet]

Good, now i want you to split 2 as product of root 2

And apply that property from right hand side to left hand side

Log(ab) with base c = log(b) with base c + log(a) with base c

[heavy nimbus]

IT WORKED

Thank you both of you!!!!

[ocean hornet]

W

[heavy nimbus]

I just gotta know how to do it on the quiz now😭

Thanks again!

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[ocean hornet]

You look for common stuff, stuff that is common in both numbers and express in the shortest unit possible, like how all of the above could be turned into powers of root2

[heavy nimbus]

Got it!

Wait so i could've changed everything to 2 as well, except it would've take more steps?

[ocean hornet]

Yes, you could, even 4, or even 8

[heavy nimbus]

Ohhh okay I think I understand now

[ocean hornet]

But you would have to simpliffy/convert both rhs and lhs

We didnt touch Right hand sids above

[heavy nimbus]

Simplify as in get both sides to be the same numbers?

[ocean hornet]

But if we were to change it all to 2, we would have to change rhs as well

[heavy nimbus]

The common stuff thing

[ocean hornet]

Yes

[heavy nimbus]

Right

[ocean hornet]

Yes

[ocean hornet]

Making it lengthy

[heavy nimbus]

Bro I was literally tweaking, didn't know there was a shorter way💀

Oh also, I have this other question that I'm not sure how to do, if you could help me in that one as well, please?

[ocean hornet]

We could look at it

[heavy nimbus]

Number 13

[ocean hornet]

It is a square

You simplified it a little

But it still does not match with given option

[heavy nimbus]

Ye, apparently it's FOILing, but idk how to start

[ocean hornet]

I have a gut feeling that you should think of (a +b)²

[ocean hornet]

Does it ring a bell, or something like a little thought

[heavy nimbus]

Ye, the correct answer is D

But then how would I be able to turn that into (a + b)²?
Cause the only way I can think of is
(log x + log 2)²

[ocean hornet]

Yes, you thought right

And by applying the squaring identity, it will match with option D

[heavy nimbus]

Woahhh got the right answer!!!!

[ocean hornet]

Logarithm Majorly jave 7-8 properties, questions at first would mainly revolve around them

Division, sum, multiplication, base change, exponent

[calm coral]

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[gusty cliff]

Guys

I got x=28 and y=35

Is that correct?

[dull wagon]

yes

[gusty cliff]

Ok thank you 🙏

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[pine crow]

I have no clue where to start...

[calm coral]

Please don't occupy multiple help channels.

[pine crow]

I tried manipulating the numerator and tried to see if things cancelled but it didn't

work

<@&286206848099549185>

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[flat notch]

Given X~N(0,1) and Y~Bern(1,-1,1/2) and X ⊥ Y, how do we show Ye^X not ⊥ Y, can i simply say E[Ye^X] = E[Y]E[e^X] = 0, since X ⊥ Y. and then cov(Ye^X,Y) is some nonzero number from E[(Ye^X)*Y] - 0

[rigid kettle]

Im not sure what ur doing in the final sentence

My approach would be to use conditional probability with specific values of Y I think

[rigid kettle]

how do u know what E[(Ye^X)*Y] is

[rigid kettle]

oh are u simplifying this to E[e^X]

[spare beacon]

<@&268886789983436800>

[torpid brook]

(fyi: that message was a scam)

[spare beacon]

I would take E[Ye^XY] and try to apply Jensen's inequality to relate the expectation to the second moment

[calm coral]

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[tame crag]

for the diffeq y' = xy^3-xy

[tame crag]

I got two different solutions

using bernouli method I got y = (c/(e^(x^2)) - 1)^(-1/2)

and using seperable I got -ln(abs(y))-1/2ln(abs(y-1))-1/2ln(abs(y+1)) = 1/2x^2 + c

I need to show that the two solutions are equal

but, I'm not sure how, and I'm also not certain these are the right solutions in the first place

[drifting seal]

can you learn latex

did you mean

$y = \frac{c}{\sqrt{e^{x^2} - 1}}$

[potent lotus]

knief

[drifting seal]

or was it supposed to be ^(-1/2)

[tame crag]

c is included in the ^(-1/2)

so its more like 1/sqrt(c/(e^(x^2)-1))

[eternal shard]

i tried them on desmos, they don't seem to be equivalent

at best show your work

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✅

[tame crag]

.cloes

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[keen scroll]

I need help figuring out if this is correct. My gripe is when I checked photomath for example it showed me a different thing but in the end I got the same result. Even with that difference, is the way that I did it still correct or was that pure luck on my end?

[inner zealot]

https://tenor.com/view/mickey-mouse-wizard-cast-a-spell-magic-gif-8463641

Have you tried casting "Lumos" to give you more light?

[keen scroll]

Ahh I’m so sorry !!

Better ?

[inner zealot]

Yes.

[keen scroll]

Alright thank you 🙏

[limpid lagoon]

your way is correct

[keen scroll]

Perfect, thank you

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[tacit pewter]

yes

this

fun

[calm coral]

@tacit pewter Has your question been resolved?

[hardy shoal]

F_net=0

[tacit pewter]

bruh

yeah im toast

[summer bolt]

bro doing math under his blanket 🙏

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[misty pond]

A circle is inscribed in an isosceles trapezoid. The length of the side is 7 cm. Calculate the perimeter of the trapezoid. (i asked this question before but rn i’m rewriting a test and ran into a problem)

[misty pond]

so

wait

right we at this

[hardy shoal]

oh hell nah

[misty pond]

and the x seems to cancel out cuz 4x-4x

[misty pond]

[hardy shoal]

the lengh of what side

what is 7cm

[misty pond]

the sides 7cm

left and right

those

wait

[hardy shoal]

whot

[misty pond]

AB and CD

[hardy shoal]

There are 4 sides to thi sbih

[misty pond]

those are the same, 7cm

[hardy shoal]

aight

Well, it's definitely more than 14.

[misty pond]

yeah😭

[quiet swan]

yeah your calculation is right just sum them up

[misty pond]

but i get 4x-4x, is that supposed to happen

[quiet swan]

it cancels out

[misty pond]

is 28 the answer then..

[quiet swan]

so 28-4x+4x right?

[misty pond]

yeahh

[quiet swan]

yeah 28 is the answer

[misty pond]

oh so it’s really the answer?

[quiet swan]

your steps are fine

[hardy shoal]

A perfect number, some would say.

[misty pond]

ohhh okay thank uu

[misty pond]

tysm!!

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[blissful carbon]

How do I do this?

[blissful carbon]

Idk where to start

Actually i found where i can start

I can draw asymptotes when f(x) is 0

[undone shadow]

yep

[blissful carbon]

And then i can just estimate the points

and do 1/f(x)

?

[undone shadow]

if u have a calculator handy, you can manually subsitute the values

yeah

u can do that

[blissful carbon]

non calc :(((((((((((

Noo is there another way

idk what 1/3 is :sog

😭

ohh i dont need to

opk thanks guys

.clsoe

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[sacred anchor]

Hello, how can i solve this?

[sacred anchor]

basically asking for the maximum value of the integral where the maximum is taken “above” all the continuous functions…

for the record i don’t understand what above means in the native language either that’s just a direct translation

[grim blade]

since it’s a multiple choice question, you could consider the case when f is a polynomial and find the maximum possible value there

[sacred anchor]

yea i was thinking of that

and i suppose it should be “for” instead of “above”

that makes the question much clearer

thing is if i choose f(x)=x it’ll just be zero no matter what

so i suppose it wants me to find the function that has the said maximum or something?

[grim blade]

yes, so let f be a polynomial, like a + bx + cx^2 + dx^3, and then substitute in and complete the square or something

[sacred anchor]

oh okay mb now i get what you meant

[grim blade]

it wants you to find some function f such that the above integral expression is as big as you can make it

[sacred anchor]

i just thought a specific polynomial

okay thanks for the tip!

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[wet sable]

can you please help me in answering letter b? I have an upcoming boardwork about this one. Thank you!

[calm coral]

@wet sable Has your question been resolved?

[wet sable]

<@&286206848099549185>

[wet sable]

help

[calm coral]

@wet sable Has your question been resolved?

[wet sable]

<@&286206848099549185>

[keen scroll]

Quite literally 😭

[untold summit]

can you provide your definition of a limit point

[wet sable]

point where other points of the set keep getting closer and closer no matter how small of a “neighborhood” (like a tiny bubble) you draw around it, there will always be other points of the set inside that bubble.

[untold summit]

i mean, i meant from your textbook

what i want to know is is $A \subset L$ by your definition, because i wouldve treated it like that

[potent lotus]

Acman

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[iron apex]

for which one?

[upper sparrow]

inverse sin’s range is between -pi/2 and pi/2 inclusive, they tell you that as well

[acoustic creek]

,ask sin(-pi/6)

[potent lotus]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by hailinqs

[acoustic creek]

note the angle restrictions on arcsin/arccos/arctan

7pi/6 is in quad 3

are you familiar with the conversion $(x, y) = (r\cos{\theta}, r\sin{\theta})$

[potent lotus]

Hailinqs‽

[acoustic creek]

yes r is radius

[acoustic creek]

there's two points on the unit circle where y = -1/2

meaning there are two values of theta that make sinx = -1/2 true

but you need to omit the one in q3 to evaluate sin^-1(-1/2)

you should be familiar with ASTC, so just find values in each quadrant where sinx = 1/2

then choose the ones where sine is negative

then choose the one inside the domain restrictions

[acoustic creek]

that is, 30deg, 150deg, 210deg, and 330deg

yes, so you omit 30 and 150

its not

first thing you do is list out the angles where sin = 1/2

then chosoe the ones where its negative

then choose the one inside domain restrictions

-pi/6 is in q4

[acoustic creek]

in this case, its 330deg

but arcsin returns values in range of 90deg and -90deg

so u rewrite 330deg as -30deg

-pi/6 = 11pi/6 = 330deg

0 - pi/6 = -pi/6
2pi - pi/6 = 11pi/16

2pi = 0, so theyre equivalent angles

anyways i gtg

[calm coral]

@ionic venture Has your question been resolved?

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[crystal salmon]

I am a beginner at contour integration and would like to practice

[crystal salmon]

Can anyone give me questions, advice, tips?

Prefarably a beginner level question

[restive elk]

Get a book or utube

[crystal salmon]

i already tried you tube

pls

I tend to learn best with a human connection

idk why

[leaden thunder]

help channels are for questions/problems you've already tried, so not really for "working together"

if you have specific questions you're working on show them here. but otherwise you just need a real life study buddy

[crystal salmon]

ok

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[crystal salmon]

Sadly they don't make those nowdays, and also my only study buddy is in love with science not maths :(

.Reopen

.reopen

[limpid lagoon]

you can look up questions on youtube google, khanacademy, theres many websites where you can do that

[calm coral]

✅

[crystal salmon]

can someone explain the cauchy-goursat theorem

What is a holomorphic function

[leaden thunder]

https://en.wikipedia.org/wiki/Cauchy's_integral_theorem

[leaden thunder]

https://en.wikipedia.org/wiki/Holomorphic_function

[crystal salmon]

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[fresh ether]

I feel like the answers are really wrong can someone check this please

[remote mural]

I think your answer is false

[fresh ether]

yeah thats what I think too

[remote mural]

do u want to get f'(x)?

[fresh ether]

Yeah

[remote mural]

sin(20) is constant.. really?

[fresh ether]

Huh

[remote mural]

how old are u?

the result is.....

[fresh ether]

I dona get what you want

[remote mural]

10tsin(20)

where are u from...

[fresh ether]

? Whats this

[remote mural]

how old are u

[fresh ether]

also you cant see here x0 is 1,5

[fresh ether]

Why?

[remote mural]

i am very busy

see u again

[fresh ether]

ok?

[pale blade]

Can you explain what you're trying to do? Are you trying to get the derivative of 5sin(20)t^2 from the limit definition?

[fresh ether]

yeah im getting the derivativo of that function

And then the second one is the same but sin 40 instead

x0 is 1,5

[pale blade]

what do you mean by x0?

[fresh ether]

like the place I want to find the derivativo of

The x or t in this case

[pale blade]

Oh you want a specific value, lemme check

[fresh ether]

oki

[pale blade]

You did not simplify your limit enoguh, your infinity result is actually inf-inf, which is indeterminate

[fresh ether]

Ah okay let me try again then

[pale blade]

If i were you, I wouldnt plug in 5sin(20) into your calculator. leave it as 5sin(20), while keeping in mind that its a constant

[fresh ether]

ah okay

wdym a constant

like doesn’t change or ?

[pale blade]

yeah, 5sin(20) doesn't depend on h or t, right?

it sjust a number, like 2

[fresh ether]

yeah

oki let me do it again

like this right?

[pale blade]

yup!

[fresh ether]

oki

[pale blade]

once you seperate the fraction and plug in h=0 you'll get your numeric answer

[fresh ether]

what separating a fraction? I do maths in German 😭

[pale blade]

(a+b)/c = a/c+b/c

[fresh ether]

ah okay

Should I still remove the bottom h?

[pale blade]

Wait, there's actually a mistake.

[fresh ether]

😭

[pale blade]

Only in your last line, don't write 3.85 as a decimal, leave it in its original form

[fresh ether]

Okay

[pale blade]

do everything else the same way, you'll end up with two terms that cancel out

[fresh ether]

my calc doesn’t want to turn it into a fraction

[pale blade]

how did you end up getting it?

you multiplied 5sin(20)*1.5^2, right?

[fresh ether]

Yeah

[pale blade]

so do 5*1.5^2=11.25 and leave the sin(20)

giving you 11.25sin(20)

[fresh ether]

Ok

[pale blade]

generally its a bad idea to do operations involving trig functions until the very end, because they give ugly results

[fresh ether]

15sin(20) ?

[pale blade]

ja

[fresh ether]

ahhh okay ty for the tip

Yaaayyy

Now I have to do the second one ://

[pale blade]

its the exact same approach

[fresh ether]

thank you!

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[cunning crag]

Can someone help me with this: Find an equation of the circle which crossed the x-axis at the points (2,0) and (8,0) and touches the y-axis at the point (0,4).

[glad parrot]

Tried to draw it ?

[cunning crag]

i cant do that

I cant just plug stuff in

[eternal shard]

of course you can

[cunning crag]

ok show me how

[eternal shard]

you want to establish a relation

[glad parrot]

What do you know about the center

[eternal shard]

ok i will do an example so you can follow the lead

[glad parrot]

Ok i let u

[eternal shard]

(2,0) means (2-h)²+(0-k)² = r²

now do the rest with the other 2 points

and solve that system

[cunning crag]

i know that the center is in between points 8,0 and 2,0, therefore the center is 5 in the x axis, i dont know how to find the radius or the y value for this

[ancient thistle]

a tangent is perpendicular to the radius of the circle

[cunning crag]

Solving that system makes no sense, i will have three seperate variables in one equation, it doesnt help

[ancient thistle]

you can deduce the y-coordinate of the centre using that the circle is tangent to the y-axis at y=4

[eternal shard]

you will have 3 equations

which is the amount you need for 3 variables

[cunning crag]

Oh so your saying do simultaneous equations

[ancient thistle]

please don't

that path is painful

you already made the right argument for the x-coordinate of the centre

[cunning crag]

Coriolanus, what do with that information, i think what your saying is important

yeah i agree its painful

[ancient thistle]

draw a perpendicular line to the y-axis at the point of tangency

you will see what the y-coordinate of the centre must be

[cunning crag]

ok ill draw it and see give le a sex

Sec

sorry

ohhh thank you so much

I understand now

Thanks to everyone who helped

[calm coral]

@cunning crag Has your question been resolved?

[calm coral]

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[dreamy mirage]

Hey there, i got info something like this might be in my exam however i tried applying every method ive learned and cant solve it, AI is confusing me even more, how can i factor this

[chilly tangle]

first of all, you need to factor out the top expression

to start you need to multiply the first and last numbers to get -6, and then find two numbers that add together to get 5 and multiply to get -6

[dreamy mirage]

if you mean quadratic formula

[chilly tangle]

no

i domt

dont

[dreamy mirage]

ok but the way you started it didnt work for me i think

[radiant plinth]

Either complete the square or use quadratic formula

[dreamy mirage]

i tried something like that

[restive elk]

Do u know AC METHOD

[dreamy mirage]

i just end up with 2x^2+2x+3x-3 which goes to 2x(x+1) + 3(x-1) and you cant go anywhere from there

[dreamy mirage]

yes

[sonic snow]

that +6 not -6

[dreamy mirage]

doesnt apply here unless i made a very dumb mistake im sleepy

[sonic snow]

you need a product of -6

[restive elk]

Use that to factorize the numerator expression to product of two binomials

[dreamy mirage]

oh

[grave mango]

because u multiply the coefficient of x^2 by the constant

so the constant is actually -6

[dreamy mirage]

no i think this was it

[tawdry tapir]

Hii

[rotund linden]

Hi

[dreamy mirage]

yeah bro i know i sholdnt be using ai for math but it started talking about some polyminals and stuff so from there i just got brainf**ed

thanks i see now

shouldnt**

[tawdry tapir]

tips tips to understand integral calculus? :C

[dreamy mirage]

not in this channel

[sonic snow]

take your own help channel, this one is occupied

[dreamy mirage]

yup

give me 1 minute to try solving it on my own and ill close this channel, just incase i dont understand it yet 😄

[restive elk]

Find tw numbers say a and b such that

ab = 6 and a-b=5 (because c is negative)

And that's just 6 and 1

[sonic snow]

or we could do ab=-6 and a+b=5 assuming a and b are integers, its better cuz you dont have to different cases for each

[dreamy mirage]

isnt that just 2x^2+6x-x-3

cause then what do we do from there

[sonic snow]

take 2x common from first two terms

and -1 from 2nd rwo

[dreamy mirage]

uh im confused sorry

[restive elk]

Yesss

[dreamy mirage]

ok but from there... theres nothing to factorize..?

factor*

english not main language 💔

[restive elk]

Use the reverse distributive or taking the "common"

[restive elk]

Do u know a(b+c) = ab + ac

[dreamy mirage]

ok wait so i have x(2x-1) + 3(2x-1) i think i got it

then thats (2x-1) (x+3) which simplifies with the x+3

oh ok i solved it i think

thank you so much

[sonic snow]

gg

[dreamy mirage]

gg

10pm brain unbeatable

.close

[calm coral]

Channel closed

Closed by @dreamy mirage

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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

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

[ancient grotto]

Help

[true rover]

3

[ancient grotto]

Third picture is the one I need to answer, other 2 are given

[true rover]

So like

You gotta like take the square root

And multiply

[ancient grotto]

No trolling, please.

[true rover]

Shoot

[swift laurel]

ok so we have two things to keep track of:

• what does the magnitude look like as it goes in the circle
• what is the direction as it goes in a circle

[ancient grotto]

No clue

I just started this chapter today

[swift laurel]

well you can answer those separately

[ancient grotto]

Oh wait

I can just imagine v to be a unit vector

Right?

Then just let w move in a circle in that similar "direction" to v

[swift laurel]

something like that

[ancient grotto]

Cause I did an exercise in the book

Or rather, it was an example I was confused about which I decided to do

Yeah, there

My braincells are coming together now

:headache:

Ahaaa

I'm an idiot lol

$||\vec{x}||=||\vec{w}||||\vec{v}||\sin(\theta)$

[potent lotus]

;(

[ancient grotto]

Yeah this makes more sense now

.close

[calm coral]

Channel closed

Closed by @ancient grotto

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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

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

[river pike]

is my derivative done

[eternal shard]

you started wrong

[river pike]

oups

[eternal shard]

like yea you will need chain rule, but most importantly product rule

also dont forget the y' =

[river pike]

so my f is 6x^3?

[eternal shard]

yes

[river pike]

ok god I lost so much during my 1 week break

ok il go do product rule brb

[eternal shard]

now we are talking

[river pike]

oki il do the derivative left

Now i find the critical pts?

[eternal shard]

please use brackets like (-1)

then it's perfect

[river pike]

Ok

[eternal shard]

also

yes you would set y' =

equal to 0

and the best way to simplify it is try to factor

[river pike]

I see theres two “sections” but I have trouble factoring when its not just one “section” can you explain to me how to

[eternal shard]

ok!

in those 2 sections

do you see any common factors

start with 18x^2 and 6x^3

[river pike]

Section 1: 9 divides itself but can also divide 18

Section 2 I dont really see any

[eternal shard]

ok try to basically compare both sections

18x^2 and 6x^3 they sure have something common

[river pike]

They do have 9-x in common

[eternal shard]

yes!!

ok let's compare first (9-x)^4 and (9-x)^3

how often do they have it in common at most

[river pike]

1 time?

[eternal shard]

more

the power tells you it

[river pike]

Oh ok 4 and 3, i misunderstood

[eternal shard]

in section 1 you have (9-x) 4 times and in section 2 you have (9-x) 3 times

[river pike]

yes exactly

[eternal shard]

so in both you can take it away 3 times

so (9-x)^3

[river pike]

ya cause thats how the power rule thing works

you always take the lower power one

[eternal shard]

yes basicaly

now 18x^2 and 6x^3

[river pike]

x^2

[eternal shard]

yes

that actually suffices

to work with x^2(9-x)^3

[river pike]

I color coded it

[eternal shard]

also let's simplify first

what's 4 times (-1) times 6

[river pike]

-24

[eternal shard]

yes

so let's work with

,, y' = 18x^2(9-x)^4-24(9-x)^3x^3 = 0

[river pike]

ok il write it on my board 1 sec

ok im ready

[eternal shard]

ok now try to factor it

[river pike]

my tutor and I were doing this thing where we ship section to the other side

[eternal shard]

if you take away x^2(9-x)^3 in section 1, then whats left

[river pike]

for section 1, you would have 18 (1)^1?

[eternal shard]

uhm

what about the (9-x)^4 you took it away 3 times

[river pike]

so theres 1 left yes

and the 18

[eternal shard]

yes write it out

what's left

[river pike]

ok

[eternal shard]

here i mean

so we can work faster

[river pike]

ok

[eternal shard]

so what is it

like what remains

[eternal shard]

yes uhm yea

I would have added

[river pike]

y

prime

[eternal shard]

added the x^2(9-x)^3 what i am factoring

[river pike]

oh gotcha yes

[eternal shard]

the dots in the end represent whats left in section 2

[river pike]

oki

[eternal shard]

section 2 was 24(9-x)^3x^3

taking away x^2(9-x)^3 whats left

[river pike]

-24x?

[eternal shard]

yey

,, y' = x^2(9-x)^3 \cdot (18(9-x) - 24x ) = 0

[eternal shard]

that is now way easier to work with

because you apply now the zero product theorem

[river pike]

im not familiar with that term

can you give me an example

[eternal shard]

yes of course

it just tells you, yo if you have a product equal to 0 then at least one factor must be 0

that means

ab = 0 implies a = 0 or b = 0

works with infinite many factors

abc = 0 implies a = 0 or b = 0 or c = 0

which make it even simpler to get solutions

[river pike]

oh ok

[eternal shard]

because here you can see 3 factors

if i write it like

[river pike]

could you color the three

like differently

[eternal shard]

doesn the dot in between separate them?

[river pike]

oh nevermind its on my board

i forgot the dot

i see

[eternal shard]

ok nice!

what would be the first equation

[river pike]

x^2

[eternal shard]

try it

that's not an equation yet

x^2 equal to

[river pike]

0

[eternal shard]

yes!

x^2 = 0

now the next

[river pike]

(9-x)^3= 0

[eternal shard]

yes!

last one?

[river pike]

and the long long one

hahahaha

[eternal shard]

yes

[river pike]

18 to -24x

[eternal shard]

18(9-x)-24x = 0

and you solve all 3 now separately

that's way easier!

[river pike]

without the zero product theorem would it be what i did with my tutor?

putting one section on the other side

[eternal shard]

what did you do

[eternal shard]

you mean if you look at it like 3 sections?

[river pike]

example we had two section we would move one of them to the side with 0 and then solved

ya

[eternal shard]

yes that's exactly the zero product theorem

[river pike]

oh ok

[eternal shard]

should have told ya that :D

[river pike]

good to know then hahahaha

ok so when i put stuff =0

how do i solve when its not like a real number

like x^2

[eternal shard]

are you asking how to solve x^2 = 0

[river pike]

ya

[eternal shard]

oh

there many ways

x^2 is also just the product of x with itself

x * x = 0

[river pike]

the 0 doesnt mean x right

[eternal shard]

and then might as well apply the theorem again

you can also think of what number squared gets you 0

[river pike]

so in that case its 0

[eternal shard]

yes

that's like a trivial one

one might say

[river pike]

so thats our first critical point

[eternal shard]

yes!

now next (9-x)^3 = 0

can write it as (9-x) * (9-x) * (9-x) = 0 or some just apply the cube root on both sides

[river pike]

so this is like 9- what ^3 gives 0

[eternal shard]

yea

[river pike]

so basically the inside bubble needs to give 0

so 9

[eternal shard]

yes!

[river pike]

for the last one would we start with the 18

by sending it to the other side

[eternal shard]

let's first write down

18(9-x)-24x = 0

[river pike]

yesss im ready

[eternal shard]

what type of equation is that

linear, quadratic, cubic?

[river pike]

good question its not quad

maybe cubic

[eternal shard]

skull

[river pike]

linear I dont remember

[eternal shard]

linear yes

[river pike]

is linear a+b+c or wtv

[eternal shard]

because the highest power is 1

x^1

linear has the form ax+b

18(9-x)-24x = 0

if you expand you will see

[river pike]

ok

so with that knowledge at hand how does that help us

[eternal shard]

because then you can straight away expand and solve

since it's linear it's just algebra

rearranging

but before that

i would get rid of the big numbers

18 and 24 have a common number

[river pike]

would i distribute

[eternal shard]

yea but 18 * 9 is not so nice

18 and 24 have a common factor

[river pike]

6

[eternal shard]

yes

so we divide by 6 the equation because we are smart

3(9-x)-4x = 0

now distribute

much easier, right

[river pike]

yes but i have a question why are we allowed to do that move

why are we allowed to leave the 9 out

[eternal shard]

when you divide or multiply an equation by a number then you apply it to each summand

not each factor

it looks like

[river pike]

summand?

[eternal shard]

like a product has two factors

a sum has two summands

[river pike]

oh ok now i see it

[eternal shard]

maybe even on step too much

[eternal shard]

you apply the same operation on both sides one the whole expression

[river pike]

ok so now that I see what we have i distrubute the 3

[eternal shard]

and then you just know you can split the fraction between the + and -

yes

back to this
3(9-x)-4x = 0

[river pike]

oh i made a mistake

[eternal shard]

how?

[river pike]

it gives an ugly number

3.85

ish

[eternal shard]

just keep it as 27/7

[river pike]

good idea

[river pike]

ok so now i have my 3 points

[eternal shard]

your 3 critical values

now you need to classify them too

you can use the 2nd derivative test for example

[river pike]

what do they mean by classify

[eternal shard]

you look if your critical values is a local minimum or maximum

[river pike]

so i put my critical values on a line and test with inbetween numbers?

[eternal shard]

uhm

you wanna use the first derivative test?

you can do that too

[river pike]

idk

i cant differentiate either tests

[eternal shard]

what did your tutor taught you?

[river pike]

she had trouble explaining what the first derivative test was

and we didnt get around to the second

[eternal shard]

then let's stick to that

it's hard to transfer knowledge via keyboard

[river pike]

ya i understand hahahaha

ok let me erase my board

ok

il put them on a line

Now i choose values for the x marks the spot

(Is this first derivative test)

[eternal shard]

yes i see

you basically want to see if the monotony changes before and after the critical value

for example for a maximum

before you get to the maximum it's increasing (+) and afterwards decreasing (-)

[river pike]

Wow these are huge

[eternal shard]

both are positive

what does that mean

[river pike]

it goes down and then up and up

so the f(1) is max

[eternal shard]

it just goes up then at x = 0 it basically stops and then it keeps going up

[river pike]

f(-2) is min

[eternal shard]

nonono?????

[river pike]

ok rewind

[eternal shard]

your critical values are x = 0, x = 27/7 and x = 9

[river pike]

yes

[eternal shard]

this where you might have min/max

not 1 and -2 out of nowhere

[river pike]

oh ok i understand where you are at

so can we go back to what classification means

[eternal shard]

what do you understand by classification

[river pike]

it doesnt really make sense to me because it mentions min, max and stuff but like in a comma list

[eternal shard]

a critical value can be classified

put them in categories

it's can be a local max, local min or neither

classifying means for you to find out which it is

[river pike]

ok so 0 would be min

[eternal shard]

why?

[eternal shard]

what did you get

[river pike]

because the inbetween value before it waas -702 768

[eternal shard]

oh no

you used f(x)

not f'(x)

[river pike]

please elaborate lol

[eternal shard]

you have to use the derivative

not the function itself

[river pike]

oh so its not the og formula

[eternal shard]

no

[river pike]

oh gotcha

[eternal shard]

it's called first derivative test not og test lmao

[river pike]

YHAHAHAHHAA

[eternal shard]

my hair falling off

[river pike]

no please i cant loose my fav discord tutor

[eternal shard]

buy me new hair

[river pike]

il send you a wig

wait so is the first derivaitve the x^2(9-x)^3*(18(9-x)-24x

[eternal shard]

yes

what we factored

[river pike]

ok il get to work before you go bald

[eternal shard]

,, y' = x^2(9-x)^3 \cdot (18(9-x)-24x)

[river pike]

ok

[eternal shard]

i have seen this keyboard so often

i became jealous

[river pike]

Maybe il send you one

It even has a volume scroll thingy

[eternal shard]

did you use your og formula

[river pike]

NO

[eternal shard]

then why is the f not f'

[river pike]

i would never do that …

[eternal shard]

oh bruh i see

you forgot the prime

symbol

skll

[river pike]

Maybe

Potentially

[eternal shard]

ok but what are you showing me now, can you tell me now which are max/min/neither

[river pike]

Max would be between the 27/7 and 9

Min before 0

[eternal shard]

yea wrong

[river pike]

What dont i understand about this

[eternal shard]

you understood but got the numbers wrong lol

did you use a calculator?

[river pike]

Ya…

i even did them twice

[eternal shard]

use desmos

more handy

https://www.desmos.com/calculator/qqzhtxxwso

you can even just use a small error +-0.1

[river pike]

il just recalculate

too many parentheses

ok first one is 2363856

[eternal shard]

haha f'(-1)?

[river pike]

-2

[eternal shard]

let's see

,w (-2)^2(9-(-2))^3 * (18(9-(-2))-24(-2))

[river pike]

wait

[potent lotus]

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[river pike]

WAIT

i give up

whats wrong with me

lol

[eternal shard]

nothing

[river pike]

,w (1)^2(9-1)^3*(18(9-1)-24(-1)

[eternal shard]

that's usually what a computer should do

[potent lotus]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by mrb0808

[eternal shard]

lmao

still wrong

[river pike]

i can use discord too

HAHAHHAHA

[eternal shard]

,w (1)^2(9-(-1))^3*(18(9-(-1))-24(-1))

[potent lotus]

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Requested by adoniszgks

[river pike]

god i have like another 10 of them to do 😭

[eternal shard]

take a break

i already lost my hair

[river pike]

lets just finish this one

[eternal shard]

make sure you wont lose urs

[river pike]

can you put the last one into wolfgram

[eternal shard]

also

use smaller errors

[river pike]

,w 8^2(9-8)^3*{18(9-8)-24(8)}

[potent lotus]

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Requested by mrb0808

[river pike]

what do you mean by this

i think i wrote that one correctly

[eternal shard]

for example

lets do 27/7

take 27/7+0.1 and 27/7-0.1

,w f'(x)= x^2(9-x)^3 * (18(9-x)-24x) at x = 27/7-0.1

that was before

[potent lotus]

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Requested by adoniszgks

[eternal shard]

,w f'(x)= x^2(9-x)^3 * (18(9-x)-24x) at x = 27/7+0.1

[potent lotus]

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Requested by adoniszgks

[eternal shard]

now after

so it goes from increasing to decreasing (+ to -)

is that a min or max

[river pike]

min

wait

[eternal shard]

[river pike]

like on the graph the prof told us something about when you have two in between

so this would be max

cause it does a little triangle

[eternal shard]

yes up a hill you go first and then down

max

not min

next one

[river pike]

ok

[eternal shard]

9-0.1 and 9+0.1

,w f'(x)= x^2(9-x)^3 * (18(9-x)-24x) at x = 9-0.1

[potent lotus]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by adoniszgks

[eternal shard]

,w f'(x)= x^2(9-x)^3 * (18(9-x)-24x) at x = 9+0.1

[potent lotus]

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Requested by adoniszgks

[eternal shard]

- to + is?

[river pike]

so it goes down

then up

so min

[eternal shard]

yess

yes

ok lets write down

x=27/7 max
x=9 min

let's do 0 quickly

,w f'(x)= x^2(9-x)^3 * (18(9-x)-24x) at x = -0.1

[potent lotus]

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[eternal shard]

,w f'(x)= x^2(9-x)^3 * (18(9-x)-24x) at x = 0.1

[potent lotus]

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[river pike]

so this would be min

[eternal shard]

now i am curious how

what made you think that

[river pike]

cause it goes down and up

[eternal shard]

why does it go down

[eternal shard]

is 1252 something negative?

[eternal shard]

is this negative?

[river pike]

oh ok

its the neutral one

[eternal shard]

yea

goes up neutral goes up

so it's neither

x=9 min
x=27/7 max
x=0 neither

[river pike]

so thats how i classify them

[eternal shard]

yes

now my hair regrew

ty

[river pike]

basically like a chia pet

[eternal shard]

lmao

u funny

[river pike]

gotta laugh through the pain

[eternal shard]

my motto

[river pike]

i dont understand how webworks wants me to write it tho

i understand what we found

[eternal shard]

gotta love the easy software

so after reading (i am glad i can read)

it wants the order

min, max, neither

[river pike]

in that specific order

[eternal shard]

thats how i read it

and you must make sure it's the same order in both fields

[river pike]

webworks i hate you

[eternal shard]

x=9 min
x=27/7 max
x=0 neither

let's see if 9,27/7,0 is accepted

[eternal shard]

try it

[river pike]

anti

WE MADE IT

https://tenor.com/view/wedding-crasher-hro-gif-25636997

[eternal shard]

no it's all thanks to @upper sparrow

[river pike]

il harass you tomorrow, fav

i got 7 left

[eternal shard]

depends if i am avaiablable

[neon tundra]

Steps

[river pike]

[eternal shard]

blablabal

[neon tundra]

Steps

Where are the steps

[river pike]

i think you will

i just have a feeling

il water the chia pet

[eternal shard]

hope you are wrong 😄

[river pike]

math is exciting to you

youll be there

[eternal shard]

uhm

[river pike]

dont tell me you hate math

thats a lie

[eternal shard]

thats a liegroup

you dont even know what a lie group is

[river pike]

is that a math joke

[eternal shard]

ya

[river pike]

see

you do like math

[eternal shard]

no i basically make fun of it

i despise logic

does that make sense

[river pike]

oki il let you go do your scalp care, ive tortured you enough for today

[eternal shard]

you little

scalp care

[river pike]

YOU LITTLE WHAT

[eternal shard]

i'd say monkey because of your pfp

[river pike]

il send you some keratin in the mail

[eternal shard]

that is funny af

and random

[river pike]

are you a curious george fan

[eternal shard]

idk what means

[river pike]

its a show

a kids show

[eternal shard]

oh

[river pike]

i used to watch

[eternal shard]

LMOA

i see

[river pike]

HAHAHHAHA

[eternal shard]

merb

you like george

[river pike]

WHAT

I DO

[eternal shard]

https://tenor.com/view/donut-donuts-monkey-monkeys-man-gif-7052052860958630683

[river pike]

ok im off to have a banana or smth

[eternal shard]

ok see ya Merb (george)

[river pike]

have a great evening anti

.close

[calm coral]

Channel closed

Closed by @river pike

Use .reopen if this was a mistake.

[calm coral]

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[old epoch]

i kinda lost near the end of this proof. Specifically how does connectedness of gamma imply that there is at most one peak in the interval?

[old epoch]

like near the end of the proof

[glad plover]

they didn't really explain it but i think it's basically like, if it has two peaks in the interval, then it has to go all the way down to some negative number between them

by the nature of xsin(1/x)

or

something like that?

in a way that violates uniform continuity

[old epoch]

yeah, ig im kidna confused is

sppose we have two peaks

why must this imply that it crosses the x -axis?