help-19

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[raw jewel]

I could use some strategies for determining which kind of discontinuity tables are showing. for instance, this one:

[elfin zodiac]

What is your question?

[raw jewel]

I can tell it's not a jump discontinuity but i'm unsure where to go from here. It looks like a hole, but how can I be 100% certian whether it's not a vertical asymptote?

[nimble blaze]

you can't be certain from a table of values

and it could potentially be jump as well

[raw jewel]

Really? This is the question i'm being asked

[nimble blaze]

you can only assume the intentions of the question

It looks like a hole
explain what you think it looks like a hole

[raw jewel]

Because both ends are getting closer to the same y value

[nimble blaze]

yeh

[raw jewel]

so was the question just asking me for the best estimate?

If you can't be certain from a table of values

[nimble blaze]

yeh

the function could potentially shoot off somewhere else as you get even closer to 1

but based on the pattern, the question intends that you assume they'll get closer to a certain value

[raw jewel]

I see thank you so much!

.close

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[clever fjord]

riyobi

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[upper onyx]

@heady plover if the answer should hold in general which means it is not depending on p(x) then you could choose a concrete p(x), e.g. p(x) = 0 for all x.

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[heady plover]

Thank you!

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[robust pollen]

Quick help:
My tutor said there's a mistake in question 4b, can anyone tell me what's the mistake in 4b?

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[elfin bear]

what is this correct

[dense sonnet]

have you seen l'hopitals rule

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[signal sandal]

Does anyone know how to solve this integral (without using Fourier transform tricks, like the convolution thing) ?
x,y and lambda are considered as constants.

[signal sandal]

I'm guessing there would be some sort of trick by setting new variables but I don't see which one

I'd like to get a simpler expression from this, and I don't see anything when expanding the denominator and I also tried partial fractions decomposition but the algebra gets soo long and I felt like it wasn't that

[honest quest]

Have you considered using an integral calculator

[signal sandal]

well, the free version of Wolfram doesn't work for this

"Standard computation time exceeded..."

And I don't really know any integral calculator better than Wolfram, does anyone know one ?

[honest quest]

Maybe try sage then.

try https://www.integral-calculator.com/ if you haven't

[signal sandal]

ok thanks !

ok so the integral was actually this, without the square on the lamba at the numerator, though it doesn't change much.

And the calculator you gave me shows an awfully long antiderivative, then the definite integral simplifies like this

But it should be doable by a human in a couple of minutes because it was in an exam question (undergrad physics class)

If no one finds the trick then I'll just give up, thanks alot

[odd edge]

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[tough socket]

Wyd after this <@&286206848099549185> ?

[mystic saffron]

What u have to do in this question?

[tough socket]

Ques 11

[uneven osprey]

!15m

[odd edge]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[tough socket]

Read the ques?

[mystic saffron]

yes

[tough socket]

What?

[uneven osprey]

.

[tough socket]

Oh sry

[mystic saffron]

so basically when u have to find the range of y where it is in the form of quadratic/quadratic

there is a particular way of doing it

[tough socket]

I don't really know

[mystic saffron]

lemme tell u

[tough socket]

Prolly tho

[mystic saffron]

so basically u already it the first step, by cross mutiplying the denominator byy

now i want u find a quadratic in terms of x

where y is included

[tough socket]

How do I do that?,

[mystic saffron]

consider y as just a consant

[tough socket]

Ok

[mystic saffron]

take all coefficient of x^2 together and then x together and constant together

[tough socket]

Tell me what do I do after the last step?

[tough socket]

Yeah I did that alrd

[mystic saffron]

what do u get

[tough socket]

^

Also it's (y-1)x^2

-2(4y-1)x

+12y-1

So (y-1)x^2 -2(4y-1)x + 12y -1

[mystic saffron]

very good

now do u know what is the discriminant value of a quadratic

[tough socket]

Ye

B^2-4ac

[mystic saffron]

very good, now make the discriminant of this quadratic greater than equal to 0

[tough socket]

So [-2(4y-1)]^2 - (4)(y-1)(12y-1) >=0

[mystic saffron]

now simplify this and do u know how to solve an inequality?

[tough socket]

Yes

[mystic saffron]

okay should i tell u all the steps at one go??

[tough socket]

Oh so I'll get y belongs to smth to smth and that's the range?

But why do we take the discriminant tho?

[mystic saffron]

i dont know about that tho, probably because we have some x's range, then any quadratic with x will always give us root, and will never be imaginary

[mystic saffron]

but also there is one more thing

[tough socket]

Yes?

[mystic saffron]

even tho the discriminant is the final step, there is one last here

[tough socket]

What's that?

[mystic saffron]

u gotta make the coefficient of x^2 = 0, the value u get from there remove it from the range

[tough socket]

What?

[mystic saffron]

okay wait

after the discriminant step, u gotta make the coefficient of x^2 that u got right after cross multiplying it?

So (y-1)x^2 -2(4y-1)x + 12y -1

now for y=1, if u dont get a value of x, then u have to remove 1

from the final range

[tough socket]

Why do we do that?

[mystic saffron]

because we want out quadratic to remain quadratic, hence we need the coefficient to not be zero

hence we are removing the value of y

that will make it linear

i think thats the reasoning behind it

u want a summary i can give u that

[tough socket]

Ok so y belongs to (whatever range we get from inequality) - (value for y we get from the coefficient being 0)?

[mystic saffron]

correct, but coefficient being 0 only works, if u dont get a value of x

wait lemme make thismore clear

[tough socket]

Wait a min lemme solve

[mystic saffron]

y =1, x^2+2x+1=x^2-8x+12

[mystic saffron]

okay

[tough socket]

My answer is not matching any of the options tho

[mystic saffron]

can u show your working?

[mystic saffron]

what is discriminant here?

b^2-4ac

[tough socket]

@mystic saffron here

[tough socket]

No that's the final answer I got

[mystic saffron]

okay

what are the options??

[tough socket]

Here take a look

[mystic saffron]

wait, ithink there is acalculation error

[tough socket]

Where?

[mystic saffron]

i think inthe discriminant

i am getting 4y^2+21y

as the discriminant

[tough socket]

What?

Can you find out where I made the calc error?

[mystic saffron]

the pic is not very clear

and can u send it inhorizontal

try it again

[tough socket]

,rotate

[mystic saffron]

dude its upside down now

[tough socket]

Here @mystic saffron

[mystic saffron]

gimme sone time

ithink i saw it

the value of b is wrong

[tough socket]

b or b^2?

[mystic saffron]

b

like inb^2

[tough socket]

Yeah?

[mystic saffron]

yes

it should (-2-8y)^2

i think u did 2-8y, and forgot the -

[tough socket]

Why?

[mystic saffron]

u forgot

[tough socket]

It's 2x-8xy
You take -2x common it becomes
-2(4y-1)x

[mystic saffron]

i thinkthe equation is wrong then

[tough socket]

Uhm

[mystic saffron]

cause i got x^2(y-1) + x(-2-8y)+12y-1

this what i got

[tough socket]

Lemme see

Yess the eq is wrong

I did cross multiplication wrong

[tough socket]

It's this

[mystic saffron]

yeah

[mystic saffron]

yeah figured

now u will be able to solve

lemme know if u get the final answer

[tough socket]

Wait lemme do

[mystic saffron]

ok

i was waiting for u

[tough socket]

Yeah I got that one now

[mystic saffron]

okie

[tough socket]

Can you tell me how to do this one?

Q20.

[mystic saffron]

lets assume logx = a, then u have a quadratic in x

[tough socket]

Also is x+2 in the argument or is the 2 seperate?

[mystic saffron]

do u know the domain of x

[mystic saffron]

2 separated

[tough socket]

I left this ques in the exam cause I didn't know this initially

[tough socket]

Ic

[mystic saffron]

its fine

[tough socket]

How?

[mystic saffron]

if log x = a lets just assume

[tough socket]

It would be e = x^a hows that a quadratic?

[mystic saffron]

know hun listen

[tough socket]

Or 10 =x^a since we are using log base 10

[mystic saffron]

log x =a,then quadratic will a^2-a-2>0

[tough socket]

Ok

[tough socket]

How did you get this?

[mystic saffron]

log x = a, and (logx)^2=a^2

[tough socket]

Yes

[mystic saffron]

correct?

[tough socket]

Yes

[mystic saffron]

know u got a quadratic in a

"a"

[tough socket]

Howd you get a quadratic from this tho?

[mystic saffron]

substitute logx= a and logx)^2=a^2

in the question

[tough socket]

Wait a min lemme call my mom

[mystic saffron]

okay

[tough socket]

I meant my mother is calling

[mystic saffron]

alright its fine

[tough socket]

Yeah continue

[mystic saffron]

substitute logx= a and logx)^2=a^2
in the question

[tough socket]

In the ques?

[mystic saffron]

ugot this?

[mystic saffron]

yes

[tough socket]

Oh

So a^2 >= a +2

[mystic saffron]

yessss

and once u get that range

[tough socket]

Ohhh you meant we let logx = a to make the solution part /working easier

[mystic saffron]

u can substitute a back as logx to base 10

[tough socket]

And substitute the value in the end

[mystic saffron]

yupppp

[mystic saffron]

yesss boyyy

[tough socket]

Damn ic got it

I got more questions tho wait

[mystic saffron]

dude wait

i have a class rn

dm me the question

i will explain after this class, fine by u?

[tough socket]

When does it get over? It's fine by me

[mystic saffron]

probably in 1.5 hour

[tough socket]

.close

[odd edge]

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[tough socket]

I'll dm then

[mystic saffron]

okay

[clear parrot]

a^2 -a -2 > = 0

[tough socket]

Yes I got that ques now ik how to solve inequalities, thx for the initiative tho

[tough socket]

Thx for helping me through this

[clear parrot]

or u can solve with casio fx 570 :))

[tough socket]

It was on my test so I'd better learn to solve this myself tho 🥹

[clear parrot]

Are you not allowed to use a calculator?

[tough socket]

No

This is a high school test

Why would we be allowed to use a calculator in a high school test?

[odd edge]

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[idle tundra]

for the integral $\int \sec^2 (x) \tan(x) dx$ are there two equivelant solutions?

[clever fjord]

johnseymour20

[idle tundra]

$ln |\cos(x)| + \frac{1}{2} \sec^2(x)$ and $ln |\cos(x)| + \frac{1}{2} \tan^2(x)$ ?

[clever fjord]

johnseymour20

[idle tundra]

depending on the u substitution. either u = sec(x), where you get the first one. and u = tan(x) where you get the second one

[nimble blaze]

those don't look right

[idle tundra]

ah

I know the second one is correct, because it's in my answer booklet

but I used u = sec(x), which leads to the first one

[nimble blaze]

why is there ln|cos(x)| here

[mental lotus]

sec^2 = 1 + tan^2

so they differ by only a constant

[idle tundra]

tan(x) becomes ln|cos(x)

[nimble blaze]

you posted a different question

[idle tundra]

I was asking about the specific integral, the left one

\int tan(x) sec^2(x)

[idle tundra]

ah ok. and that's taken into account by C?

[nimble blaze]

that'd just be the $\frac12 \sec^2(x)$ or $\frac12 \tan^2(x)$, $\red{+c}$

[mental lotus]

yea. Since it is indefinite integral, it can have any function as a solution as long as the two functions differ by a const

[clever fjord]

ℝαμΩℕωⅤ

[idle tundra]

got it, thanks

.close

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[glossy lotus]

Why with x_1^2=x_2x_3 we know that the terms are in geometric progression?

[glossy lotus]

Ah nothing

r=1 srry

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[noble swallow]

Can someone explain me the anti symmetry of vectors

[noble swallow]

Why is area of vectors v and w minus of the area of vectors w and v

And what exactly does that minus mean

Also a visual example if possible

Please:c

[odd edge]

@noble swallow Has your question been resolved?

[noble swallow]

.close

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[pastel orbit]

#1260424130822541403 message

[summer cradle]

hi kepe

[pastel orbit]

hi Layla

.solved

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[pastel orbit]

@brittle beacon :Hiii:

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[main glen]

Is there any way to denote quotient in mathematical language? I'm trying to write a proof for the euclidean algorithm, but just writing q is the quotient of a and b doesn't really feel right, so is there like a symbol I could use to express that?

[fossil hawk]

c

[main glen]

could you elaborate a bit more?

[pastel dew]

$q\in \mathbb Z$ is such that $a=qb$

[clever fjord]

everg

[bitter lodge]

$a = b \left \lfloor \frac{a}{b} \right \rfloor + r$

[clever fjord]

Acman

[bitter lodge]

i.e. $q = \left \lfloor \frac{a}{b} \right \rfloor$

[clever fjord]

Acman

[bitter lodge]

this is called the floor function

floor(x) is the greatest integer <= x

[main glen]

ah, alright, thanks

i get it now

.close

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[jade flame]

How to do this?

[dense moth]

Hey

Divide numerator and deno with e^x

[ember oak]

!nosols

[odd edge]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[dense moth]

Sorry bro !

[jade flame]

Wdym by this?

[dense moth]

1/e^x tends to 0

So we can apply that

Express the function in terms of 1/e^x

[jade flame]

Still don’t know where this is going sry

[elfin zodiac]

Multiply by e^x numerator and denominator

[jade flame]

Ohk thanks now i know @elfin zodiac @dense moth

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[forest sky]

fun fact this function is called the hyperbolic cotangent

[jade flame]

Bruh

[odd edge]

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[honest abyss]

can someone please explain what rules they use when plugging in u to get du and all that etc

[uneven osprey]

substitution?

[honest abyss]

I can just set x in terms of u and plug it in🤦‍♂️

thanks

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[frank lion]

i have no idea whats wrong

[frank lion]

i've tried everything

[fossil hawk]

It should be [-6, -3) and why is the function increasing from 2 to 3?

[fossil hawk]

And it should be (-3, 2]u[5, 8]

[mental lotus]

[-3 is fine no?

[frank lion]

because it goes up from 2 to 3

[fossil hawk]

The function is increasing in the left and decreasing in the right so why will we include -3?

[fossil hawk]

Yea but it isn't defined between that interval

[mental lotus]

coz lhl is higher?

[fossil hawk]

Wait fck sorry mb

[frank lion]

[-6, 3) was incorrect

[fossil hawk]

And the other que
[-3, 2] u [5, 8]

[fossil hawk]

How @mental lotus wat do u think?

[frank lion]

that was also wrong

[fossil hawk]

dam

[frank lion]

i've tried everything

[mental lotus]

maybe coz the second half of the answer was wrong?

[fossil hawk]

? What's missing

[mental lotus]

No, he had that (2,3)

so something extra was there

that shouldnt have been

[fossil hawk]

U mean a typo

[mental lotus]

adding something extra is not typo, its just a mistake

[frank lion]

So what should the answer be?

[mental lotus]

increasing should be [-6,-3) and decreasing should be [-3, 2] U [5,8]

[frank lion]

Just tried, incorrect

[mental lotus]

then idk

[fossil hawk]

may be it's showing wrong since you are not answering all questions

[frank lion]

Nope, every other problem hasn't been like that.

[fossil hawk]

[-3,2] u (5, 8] try this

[frank lion]

I did

Incorrect

[mental lotus]

does it show you the solution? Maybe theirs is wrong? idk

[frank lion]

It does not show a solution.

[fossil hawk]

[-3, 2) u (5, 8]

[mental lotus]

well, [2,3] doesnt have f defined so it cant be constant

[fossil hawk]

Since the function isn't defined after 2

[frank lion]

Also incorrect

[mental lotus]

but can you try [3,5] for constant?

[frank lion]

This was wrong

[mental lotus]

that is most definitely the correct answer

[fossil hawk]

Gl

[frank lion]

It was what I wrote originally

[mental lotus]

ok, the answers are wrong then

[frank lion]

My answers or the software?

[mental lotus]

software

[frank lion]

Ahh

[mental lotus]

like theres no way [3,5] is not answer for constant domain

[fossil hawk]

Tru
Software knows something we don't bro is far ahead from us

[odd edge]

@frank lion Has your question been resolved?

[odd edge]

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[vital dirge]

how do i solve

[vital dirge]

sin(12x-18)=cos(10x+9)

whats 2x?

[odd edge]

@vital dirge Has your question been resolved?

[vital dirge]

.close

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[crimson bay]

Please help thanks

[crimson bay]

I tried to sub abc in for the 1s in the equation but didn't know how to go from there

[fluid tundra]

are you supposed to prove your result

[fluid tundra]

if so, just substitute c = 1/ab

[crimson bay]

Alright let me try it

thank you

[crimson bay]

sorry but what can i do afterwards?

[fluid tundra]

remove every nested fraction

so you in the middle term you have b/(b + (b/ab) + 1) multiply numerator and denominator by a

[crimson bay]

so for middle term i'd get ab / ab + 2?

wait sorry i mean ab + 1 + a

so i'll add it to first term

@fluid tundra in the end i got 2ax(b+ 1) / (a + ab + 1) + 2x(c+b+1) / ab

[fluid tundra]

you aren't supposed to have a c anywhere

[fluid tundra]

.

[crimson bay]

my bad

[crimson bay]

so i got 2ax(b+1) / (a + ab + 1) + 2x + 2ab^2x + 2ab / a^2b^2

[fluid tundra]

try again

[fluid tundra]

start from here

[crimson bay]

wdym

ok ill just redo it hang on

YOO I GOT IT

i got x = 1/2

@fluid tundra thank you so much

[fluid tundra]

welcome 🙂

[crimson bay]

.close

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[worldly dirge]

How do i do this with like chain rule?

[fringe bough]

Have you tried anything here yet?

You need to start by finding an equation that includes both r and h. Drawing a picture will probably help

The chain rule only comes in when you differentiate both sides of that equation (with respect to time) to get an equation relating dr/dt and dh/dt

@worldly dirge

[worldly dirge]

Im trying to find the equation but i never know like which one is which

[fringe bough]

Did you try drawing a picture? It can be a little hard to decipher just from the text

There is a right triangle involved, so you can use the pythagorean theorem to get the equation

[worldly dirge]

Would it just be like h^2 +w^2 = r^2?

[fringe bough]

sort of, but what is w?

[worldly dirge]

3

[fringe bough]

yeah

[worldly dirge]

Yeah

[fringe bough]

since w is constant, you can just use h^2 + 9 = r^2

That's the relationship you need between h and r

and then differentiate with respect to time (t) to get an equation relating dh/dt and dr/dt

since you're given dr/dt, and essentially you're asked to find dh/dt at a specific point in time

[worldly dirge]

Oh is it like dh/dr times dr/dt

[fringe bough]

Not quite

Just from h^2 + 9 = r^2

Can you differentiate both sides with respect to t?

d/dt both sides, in other words

This is where the chain rule comes in, but even if you're not sure how to use it, tell me what you think you're going to get when you take the derivative of both sides

[worldly dirge]

Im a bit lost i cant lie

[fringe bough]

No worries

Just take the first part, h^2

Do you know what the derivative of that would be?

[worldly dirge]

Differentiating with respect to time?

[fringe bough]

let's just say you're differentiating with respect to h for now

just $\frac{d}{dh}(h^2)$

[clever fjord]

tatpoj

[worldly dirge]

Just h^2

2h

[fringe bough]

2h yeah

but

if we're differentiating with respect to t, we need to treat h as a function of t (it's changing over time)

That's why we need to use the chain rule

so

$\frac{d}{dt} (h^2) = 2h \cdot \frac{dh}{dt}$

[clever fjord]

tatpoj

[fringe bough]

Using the chain rule, we differentiate with respect to h, then multiply by the derivative of h with respect to t

[worldly dirge]

Implicit diff?

[fringe bough]

Yes

Implicit differentiation is just applying the chain rule in this way

[worldly dirge]

What should i do after?

[fringe bough]

Can you differentiate both sides of the equation in this way?

both sides of h^2 + 9 = r^2 I mean

[worldly dirge]

Would it just be like 2h dh/dt = 2r dr/dt

[fringe bough]

Yeah, awesome!

Now, you want to solve for dh/dt, so you need values to plug in for h, r, and dr/dt

You're given enough information to know all three, but one is a bit more hidden than the others

[worldly dirge]

Oh wait i got it

U just sub in h and then rearrange

[fringe bough]

I'm not sure exactly what you mean, you need to sub in values for h, r, and dr/dt

but maybe you just went a slightly different route than me

[worldly dirge]

Like h = 5 r = like root 34 and then dr/dt is 12

[fringe bough]

dr/dt should be -12 (since the distance is decreasing)

But otherwise yeah you got it 👍

[worldly dirge]

Thank you very much

[fringe bough]

no problem 👍

[worldly dirge]

.close

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[paper cape]

Hello guys, why is this true? I don't understand how the thing in the brackets is simplified to $1 -\frac{1}{N}$.

[clever fjord]

Akkaman

[wild vault]

it isn't

well

[paper cape]

Am I missing something? 😂

[wild vault]

not on its own

there's a sum remember

[sharp oak]

Writing out that sum:
(1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4)...

[wild vault]

the thing is that there's the initial 1/(n-1) - 1/n, but then that's added to (1/n - 1/(n+1))

and so on

so the only terms u need are the final -1/N and the initial 1/(2-1) = 1/(1) = 1

@paper cape do u see

[paper cape]

I did that but it didn't help.

[sharp oak]

Hopefully there's some clear cancellations

[paper cape]

I'm thinking about this one, seems to make sense.

[paper cape]

Oh wow I completely forgot that we can't forget the brackets because of addition. 🥲

Thank you two. 🙂

[odd edge]

@paper cape Has your question been resolved?

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[junior ether]

why is my second code not working as intended

[odd edge]

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[terse mauve]

How do I do this

[odd edge]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@terse mauve Has your question been resolved?

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[prime cloud]

Three numbers form a geometric sequence. if 5 is added to the second term, then the resulting numbers will fconstitute an arithmetic sequence. If 22.5 is added to the third number, these numbers will again form a geometric sequence.

[prime cloud]

Find the original numbers

[vernal yacht]

!status

[odd edge]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[prime cloud]

x,y+5,z+5 i got this equation due to some help from someone yesterday, and i progressed it even further by substituting these equations in an arithmetic formula

so an=a1+(n-1)d, i got y=x+5

for z i got, z=x+45, but no idea where my steps is

[vernal yacht]

Look carefully, it says the first three numbers form a geometric sequence

[prime cloud]

yes, but the second term forms an arithmetic sequence

i got the end result i just need confirmation

because i feel like my steps are wrong

[vernal yacht]

alr, I thought those were your initial numbers

[prime cloud]

OH

[prime cloud]

no its just an equation someone came up with

[prime cloud]

were trying to find the original numbers

still*

[prime cloud]

anyways continuing

for z=x+2(22.5)

since it says "Adding to the third number" not multiplying i assumed it has to be an arithmetic sequence again

so with this, lets find x so, y=x+5 turns to -x=5-y to x=y-5 and z=x+45 to -x=45-z to x=z-45

x=x, 5-y=45-z

[prime cloud]

@vernal yacht do i continue with this?

<@&286206848099549185> i need hewlp

[mystic saffron]

yes?

[prime cloud]

how do i continue this

[mystic saffron]

Ah okay I see your problem

Hold on let me read your problem for a minute

Mhm I think you can express all the numbers in one var

[prime cloud]

how

[mystic saffron]

I'm training for AMC/AIME rn so this'll be a good exercise for me too @prime cloud

Suppose a is the first term

wait hold on

[prime cloud]

ight

[mystic saffron]

Let me get out of bed and actually get scrap paper lol

[prime cloud]

oh ight

[mystic saffron]

I was able to get 10b+25=22.5a, @prime cloud

But it's too late for me to continue

Maybe find another equation in terms of a and b and solve

[prime cloud]

i got 10 for a

[mystic saffron]

oh well then plug that in for b

[prime cloud]

and 15 for the second term

im trying to understand why is my third term 22.5 😭

15/10 = 3/2 is my ratio

[mystic saffron]

Yeah that doesn't make sense

It can't be 10

Maybe someone else can help you, I need to sleep

[prime cloud]

oh ok

ight have a nice rest

amd sleep well

and uh gl on aie

aime

<@&286206848099549185> i would like to gain some assistance

[upper onyx]

whats the (remaining) question?

[prime cloud]

this is my last stop

[prime cloud]

did i do it right or am i wrong at the beginning?

[upper onyx]

sorry, if you say "this is my last step" i do not have any clue since i do not know what the previous steps were.

anyway.

you have 3 numbers,

1. x, y, z they are part of a geometric series so there is some q such that y = qx and z = qz.
2. if you add to the second then the form an arithmetic series. -> (y+5)-x = z-(y-5) -> 2(x+z) = y+5
3. if you add 22.5 to the third then the form a geometric seqence again. -> there is some p such tthat y+5 = px and (y+5)p = z+22.5

[prime cloud]

ok we may start at the beginning

[prime cloud]

i believe that q represents r?

or am i wrong again

[upper onyx]

whatever r is.

[prime cloud]

wait i do not understand the formula y=qx and z=qz

[upper onyx]

z = qy, was typo.

[prime cloud]

in the geometric formula n=xr^(n-1), so if we say z=qy its a3=a2(r)^2?

[prime cloud]

or do we substitute for a3=a2 and a2=a1?

[upper onyx]

wtf is a1, a2, a3 now?

[prime cloud]

x,y,z in my equation

[upper onyx]

why should we use different notations?

[prime cloud]

no idea someone told me to

[prime cloud]

ok lets start solving i feel like we would be able to understand my weakness thru solving

so we have a1,a2+5,a3+22.5

ok

.close

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[keen plover]

Given the instructions on image 1 I must solve number 9 on image 2

I don't see any constants so how should I start with this?

Take note we haven't learned anything about D's

Our book doesn't mention it either

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@keen plover Has your question been resolved?

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@keen plover Has your question been resolved?

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[cerulean garden]

So say I have x+1 = 2, this is basically asking, at what value of x is this equation equals to 2

[cerulean garden]

right?

say I wanted to state something like, at all values of x this equation will equal to 2

for instance x*0 = 0

like (a+b)^2 = a^2+b^2+2ab

This isn't asking anything, this is telling us that for all values of a,b belonging to real numbers, this is true

so how do we write this?

[weary pelican]

there is no meaning in an equation equaling anything

a VALUE equals something

an equation sets two things EQUAL to each other

so "x+1 = 2" is the EQUATION that states "this quantity x+1 is equal to 2"

[cerulean garden]

yes

but say I wanted to tell someone that the qualtity x+1 is ALAWYS equal to 2 for all values of x, this ofc is not possible in this case, but say we take x*0 = 0

[weary pelican]

then this is a statement here

[cerulean garden]

Yes so how do we differentiate the two?

[weary pelican]

$\forall x \in \bR, x\times 0 = 0$

[clever fjord]

rafilou2003

[nimble blaze]

x+1 = 2, this is basically asking, at what value of x is this equation equals to 2
an equation by itself isn't actually asking anything
here its stating that
2 is 1 more than x

[cerulean garden]

I have seen some people use this symbol $\cong$

[clever fjord]

PianoDolphin

[cerulean garden]

wait no not this

The equals to with three lines

instead of 2

[weary pelican]

that's used for definition

or equality of statements

[cerulean garden]

so what is the difference between 3 lines equals to and two lines equals to

[weary pelican]

two lines equals to is equality of numbers and pretty much every object you can think of

(a+b)^2 = a^2 + 2ab + b^2

three lines or two lines preceded by : can refer to the FIRST time something is defined

for example, for $x > 0$, we DEFINE $ln(x) \equiv \int_1^x\frac 1t dt$

[clever fjord]

rafilou2003

[weary pelican]

or $ln(x) := \int_1^x\frac 1t dt$

[clever fjord]

rafilou2003

[cerulean garden]

ah

thank you

I was studying implicit differentiation, imma ask a lot of doubts

see ya again

thank you that cleared it tho

.close

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[coarse idol]

hi

[coarse idol]

what did i do wrong

[weary pelican]

is the premise even true?

take z1 = z2 = z3 for example...

I highly doubt 3*|z1|^2 = 0

[coarse idol]

that is my bad because i forgot to say z1 and z2 and z3 are diffrent points

[weary pelican]

ok

[coarse idol]

but i tried another numbers but it did not work

[weary pelican]

z2 = 2z1, z3 = 3z1

premise is false to begin with

is this the original problem exactly as stated to you?

[coarse idol]

yes its in persian and I translated it

here is the original

[weary pelican]

"on 1 line" are you sure there aren't MORE specifics about that line?

or the opposite is true

[coarse idol]

no nothing it just says on line

i even tried to solve it with all of them having same arg like theta

but did not work

[weary pelican]

well first of all it's not just any line

since you're taking a line that goes through the origin

[coarse idol]

so i should rewrite them like z2 = kz1 + j + si

like this?

[weary pelican]

uh, not exactly

z2 = z1 + k(j+si)

z3 = z1 + m(j+si)

but it still doesn't change the fact

that the premise is wrong

[coarse idol]

hmm

alright

thank you so much

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[mystic saffron]

$rotate

E, doesnt work

[weary pelican]

,rotate

[mystic saffron]

Anyways i did it like this

Then..

What am i supposed to expand and how?

[mystic saffron]

Tnx there

[swift rock]

Perform binomial expansion on left thing

[mystic saffron]

And then multiply it with (1-x)?

[swift rock]

U could do that but easier way would be to only. Multiply the thing that would give u x^7

[mystic saffron]

I see, i thought i had to do something like this

Wait lemme try

@swift rock is it right?

,rotate

[swift rock]

Seems alright

Hopefully the calculations are correct tho

[mystic saffron]

Hopefully

[mystic saffron]

Eh?

[swift rock]

Should be multiplied not add

Oh no nvm

I was thinking something else

[mystic saffron]

Lmao

[swift rock]

Yeah I got it

[mystic saffron]

So.. Ig, i should close the channel now?

[swift rock]

Yeah unless if u have more doubt

[mystic saffron]

Well, i dont have any doubt unless my answer is wrong

Can we solve the problem in another way?

[swift rock]

Not that I'm aware of

U can apply binomial expansion on A and B seperately

[mystic saffron]

Oh yeah..

[swift rock]

And multiply the terms that would give u x^7

[mystic saffron]

Hmm...

[swift rock]

(there will be more than 1 term with x^7 term so u will need to add them)

[mystic saffron]

But the answer, of course, will be the same?

[swift rock]

Should be

[mystic saffron]

Hmm.. I should better ask my teacher which way is better

And i think

.close

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[swift rock]

This way u did is faster

[mystic saffron]

Ik

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[dry birch]

what does the brackets beside every equation represent?

[mystic saffron]

where exactly ?

[steady tide]

seems like its clarification on where you got the equation

[sacred stirrup]

because your teacher (or whoever this notebook belongs to) used theorems/some reasoning/some information given in the question which have to be mentioned once you arrive at a result. apart from that, all i see is fantastic art lmao

[dry birch]

oh sorry i didnt see yall msgs i was in the toilet. So its like the explanation on why i wrote that certain equation?

ohh okay thanks now let me figure out how to close this

[sacred stirrup]

.close I think

[dry birch]

.close

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[pale lynx]

simplify this algebraic expression as much as possible.
2a^3b + ba^3. well i tried doing it and got 3a^3b +b but the answer is 3a^3b. can anyone explain where did the +b go?

[clever fjord]

MæthIsAlwaysRight

[tepid pelican]

So you got something like this?

if i add few parenthesis

[pale lynx]

it doesn't have any
Parentheses

[tepid pelican]

$2a^{3}b+a^{3}b$

[clever fjord]

MæthIsAlwaysRight

[tepid pelican]

sure, so we can work with this

What is 2 potatoes + potato?

[pale lynx]

3 potatoes

[tepid pelican]

and what is 2a^3b + a^3b?

[pale lynx]

3a^3

[tepid pelican]

where did the b go now?

you can treat a^3b like a potato

Here are the potatoes

[pale lynx]

oh

i never saw it this way

then its 3a^3b

[latent yew]

Yes

[pale lynx]

thanks

im good at math but sometimes i get stuck on the most stupidest things

[honest cobalt]

Brother, can you take a look at my channel?

[tepid pelican]

np, happens to all of us

[latent yew]

which one is urs

[latent yew]

Happens to all of us bro

[honest cobalt]

26

[mental lotus]

if only someone told that to the irish ppl back in the 1800s

[pale lynx]

im gonna close here now

.close

[odd edge]

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[odd edge]

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[modest flicker]

2+2

[dense moth]

It depends on the definition of '+' operator

Also the base of number system you re using

[modest flicker]

@everyone if x =2 .find the the value of y=x+10

[hot dome]

Why are you pinging everyone with this troll

[modest flicker]

i ma new

[hot dome]

Just ping helpers

[dense moth]

y = 2+ 10 = 12 Considering we re using base 10 number system and the general definition of +

[hot dome]

With a non-troll question

[uneven osprey]

After 15min*

[modest flicker]

thanks

[elfin zodiac]

Stop this now. For non-serious questions go to #chill

[hot dome]

The definition of the numbers themselves is also important
Like how do you even define the number 1

[elfin zodiac]

.close

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[dense moth]

"I mentioned base 10 number system "

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[timber patio]

guys, what's the range for the function:
f(x) = x^2 + 3 for -2 ≤ x ≤ 5

[timber patio]

my answer is -7 ≤ y ≤ 28

[dense moth]

Hey you see it's an increasing function for x> 0

[steep mantle]

find the minimum then find the maximum

[dense moth]

It's x² (which can't be negative) + 3(constant)

[mystic saffron]

do f(-2) and f(5)

[steep mantle]

wrong

[mystic saffron]

range will be f(-2) <= y <= f(5)

[dense moth]

f(0)

[mystic saffron]

wait how is it wrong

[dense moth]

Dino what's the least value of a square?

[timber patio]

why is it wrong tho? bcs i did this too

[uneven osprey]

it should be done piece-wise
like [-2,0]U[0,5]

[tepid pelican]

The function can (and will) look like this

[mystic saffron]

ok

[steep mantle]

f(-2) isnt the minimum, also even if it is you put it in wrong

[mystic saffron]

i really dont remember this anyway

[timber patio]

least value? what's that

[dense moth]

y = x²+3
So vertex of parabola at 0,3

[dense moth]

What is the least possible value for x²

Can it be negative?

I mean when you square something it becomes positive

(-3)² = 9 = 3²

[timber patio]

yees

[dense moth]

So what do you guess will be the least value of the square?

x²+3 , we can only assume the lowest value of x² to find the lowest value of the function

[timber patio]

wait how do i know this

[dense moth]

A square can never be negative, in real field

You ought to know this

[timber patio]

so (-3)^2 is not possible?

[dense moth]

Can you say a x² = -1

Is there any such x that satisfies the function?

[timber patio]

ohhh cannot

[dense moth]

So what's the least value , 0 right ?

[timber patio]

yess

[dense moth]

so what's the least value of , f(x) = x² +3?

[timber patio]

3

ooohhh

[dense moth]

And you know the square will keep increasing

So what the max value in the given range ?

[timber patio]

5

[dense moth]

Yeah so 5²+3

[timber patio]

ohhhh

[dense moth]

It says x can be 5

So f(x) = x²+3 max value = 28 in given range

So now you know how to do it !

[timber patio]

yesyes

wait

[dense moth]

Ofc

[timber patio]

i still don't understand about the square thingy

[dense moth]

Ok let me re- explain

Consider y = x²

[timber patio]

yes

[dense moth]

Can you make y negative?

[timber patio]

cannot

[dense moth]

By plugging different values in x ?

What do you see when you put large -ve numbers ?

[timber patio]

it will give positive y

[dense moth]

They all equal to the square of the positives

So x = ± 1 , ± 2 .... All

Just increases the value of y

What is the minimum value of y , you can achieve then?

[timber patio]

it's 0

[dense moth]

So do you understand now ?

[timber patio]

OHH yesss

[dense moth]

Wait

,w y = x² graph

[clever fjord]

Results provided by WolframAlpha

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

Requested by xor_11

[dense moth]

Can you visualise the lowest value of y ?

[timber patio]

yess

[dense moth]

The shape is called a parabola

You will learn about it later

Ok byee I gtg , I hope your doubts are addressed

[timber patio]

ohhh i understandd it now

[timber patio]

thank you soo muchh

thank youuu yalls @dense moth @mystic saffron @steep mantle @uneven osprey @tepid pelican

.close

[odd edge]

Channel closed

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[uneven osprey]

bro literally pinged all of them☠️

just to say thanks

overpowered move

[timber patio]

yes thanks guys

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[odd edge]

@mystic saffron Has your question been resolved?

[pale atlas]

You need to find X first
X is the sum of matrix multiply by their transpose from 1 to 6

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[mystic saffron]

Can somebody explain?

[nimble blaze]

the explanation is pretty much already there
which part of it do you have an issue with?

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@mystic saffron Has your question been resolved?

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[sterile wadi]

how tf

[elfin zodiac]

What is your concern?

[sterile wadi]

how

how can i solve this

[leaden karma]

are you confused by why the limit is not 99?

[sterile wadi]

i dont get what the question is saying

[leaden karma]

$$f(x)=\begin{cases}
x^2;\ x\ne 10\
99;\ x=10\end{cases}$$

[clever fjord]

kheerii

[dense moth]

At x = 10 , f(x) = x²-1

[leaden karma]

and you need to find the limit of this function at the value x=10

[sterile wadi]

oh it has a hole

[leaden karma]

yes indeed

[proper solstice]

f(10) = 99

this is trick question

it should be f(10) = 100

oh

no it should be 99

[leaden karma]

it's not a trick question at all

[sterile wadi]

OH

I GET IT NOW

I NEED TO FIND THE EQUATION ON LIKE WHY IT BECAME 99 RIHT

[leaden karma]

what?

what became 99

[sterile wadi]

wait

[sterile wadi]

can you explain this

why is it that

[leaden karma]

that's unnecessary

you don't need to write it like that

[leaden karma]

this is a perfectly valid function

you don't need to "complete it" or "find the equation which explains why the function is like this"

[sterile wadi]

oh so thats it?

[leaden karma]

that's what is given to you in the question

now the actual question is to find the LIMIT of this function as x tends to 10

[sterile wadi]

99?

oh wait

thats the f(10)

[leaden karma]

yes

but the limit doesn't necessarily have to agree with the value of the function

[sterile wadi]

yes yes

hold on

isnt the limit of a constant the constant itself

or is that not the theorem used here

[leaden karma]

but this is not a constant

try drawing a graph of the function

[leaden karma]

this function

particularly around x=10

[sterile wadi]

i really dont know how to find a limit with brackets like these

i will look up stuff

[odd edge]

@sterile wadi Has your question been resolved?

[odd edge]

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[hoary cape]

Any smart ideas to solve this?

[tepid pelican]

This looks painful

idt that any trick can make it significantly less painful

[clever fjord]

Result:

88

[hoary cape]

I know the brute force method, but it should be some easier ways.....lol

[uneven osprey]

I think I got some idea

[uneven osprey]

I've only checked 3 terms

[hoary cape]

https://tenor.com/view/pepe-popcorn-pepe-pepe-frog-frog-meme-pepe-gif-13771789960385103599

[small fulcrum]

AGP?

[hoary cape]

What is agp

[uneven osprey]

okay nvm

it was a something else

[uneven osprey]

The second order difference of the denominators are constant

that's a thing that might come handy

[small fulcrum]

how about trying to reverse engineer a smarter solution

[uneven osprey]

that's literally what's our GOAL

[tepid pelican]

im trying to do that

[small fulcrum]

brute force first, then find what a is, put it into the question, and try to find patterns

[tepid pelican]

this is what reverse engineering means

[small fulcrum]

\ye

[tepid pelican]

I got the prime factorizations

[small fulcrum]

3, 5 , 7 and 11 i believe are the prime factors(dk what the powers are)

[tepid pelican]

$\frac{x}{3\cdot7}+\frac{x}{7\cdot11}+\frac{x}{3\cdot5\cdot11}+\frac{x}{3\cdot5\cdot19}+\frac{x}{19\cdot23}+\frac{x}{3^{3}\cdot23}$

[clever fjord]

MæthIsAlwaysRight

[uneven osprey]

btw, is there a formula for sum of an Harmonic progression?

[tepid pelican]

hmm interesting, the sol is ||729 = 3^6||

[small fulcrum]

Pretty sure they arent in a HP though

(could be wrong)

but thats just what my gut says rn

[uneven osprey]

can't find any on the internet

[small fulcrum]

sadge

[tepid pelican]

I think I found the intended solution

[tepid pelican]

It's supposed to start like this

but now instead of adding the fractions all at once, we add them one by one

or rather two by two

idk

[clever fjord]

MæthIsAlwaysRight