help-13

[robust glen]

Also very unsure how to solve

[smoky idol]

Well, your first instinct was right, to transform 1/(1+x) into its series representation

but you don't need to do long division

@robust glen (sorry for ping, unsure if you left)

[cedar kiln]

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[daring flame]

i got +- 12 for this somehow

[cedar kiln]

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

[daring flame]

here’s my work

[obsidian coral]

,rotate

[obsidian coral]

Where did this equation come from?

[daring flame]

i dont know, was i supposed add then set it equals to 90

[obsidian coral]

Yes

[daring flame]

ahh

i have a question was algebra 2 or geometry harder for you

[obsidian coral]

Don't remember

[daring flame]

my teacher said geometry would be easier but so far i’m not believing her

would 10x - 8y + 16 = 90 be the correct formula

equation*

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[daring flame]

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[crimson sedge]

lim x-> 0^- |x|/x
is equal to lim x-> 0 -x/x

x is approching from the left side so we write |x| as -x
why dont we put negative x in denominator? x is approching from the left side(negative side)

[zenith sail]

if x is approaching 0 from the left, then x is negative

which is why we can replace |x| with -x.

since x is negative, -x is positive

[crimson sedge]

yeah i understand that
but why we dont do this in denominator(x)

[zenith sail]

because the denominator is simply x, not |x|

why would we change the denominator from the negative number x, to the positive number -x?

[crimson sedge]

okay, |x| is approchng from left side (negative side) so we write it as -x right?
but why we dont write x as -x, because its also approching from the negative side

[zenith sail]

The only reason we can do it for the absolute value is because when x is negative, |x| = -x

However it is not true that x = -x

for example consider the negative number: -2

|-2| = -(-2) = 2

but it is not true that -2 = -(-2) = 2

You're interpreting -x as a negative number, but that's not right

-x is positive when x is negative

[crimson sedge]

oof i am confused
I should learn more about it
thanks for helping

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[scarlet heron]

anyone help with c?

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[dawn pasture]

How do you do this using l hospital rule

[dim cipher]

Do you know what the derivative of g(x) and f(x) is given the graph?

[dawn pasture]

yes a parabola

[dim cipher]

Since lhopitals is just saying that f(x)/g(x) = f'(x)/g'(x) given lim -> a

And its asking you to find the sign

I would find the sign for the derivative of f'(x) and g'(x) as it approaches a

[dawn pasture]

how do I find that?

[dim cipher]

Lets say we are looking at f(x)

is the function increasing or decreasing as it approaches a?

[dawn pasture]

It’s decreasing

[dim cipher]

exactly

so we can just represent the derivative as negative

how about for g'(x)?

[dawn pasture]

It’s pos, so pos/ neg = negative?

[dim cipher]

yes

Right hand and left hand limit will be the same

[dawn pasture]

Ok wait that sounds right but my teacher showed his work differently, I’m gonna send you his work

[dim cipher]

Alright sounds good

[dawn pasture]

16

[dim cipher]

Awesome

[dawn pasture]

Do you know what he means?

[dim cipher]

yes

I will break it down in a moment

Its been a while since Ive done calc so I wanna make sure im giving you good information

[dawn pasture]

Ok thank you so much

[dim cipher]

Do you know what the second derivative of a function is?

[dawn pasture]

Yes

I just don’t know how to find it with what I was given

[dim cipher]

I see

So

What happens when you derive a function

Generally you are reducing its power

[dawn pasture]

Ok yes

[dim cipher]

Lets say this function is x^3

We get the derivative and that will be 3x^2

[dawn pasture]

Yes

[dim cipher]

The issue with that is... well if you plug in 0 its not negative or positive

So we derive again

6x

as the 3rd derivative

(we can do this because a is 0 and f'(x) is still 0 so lhopitals works again)

This runs into the same issue

plug in 0, which is a, and we get 0

So we derive once more

the derivative of 6x = 6

[dawn pasture]

Yes

Isn’t that Positive though?

[dim cipher]

Exactly

It will always be positive

[dawn pasture]

Wait but the answer says negative

[dim cipher]

Mhm

So now we have to do the same thing for g(x)

[dawn pasture]

OH

[dim cipher]

its still f(x)/g(x)

[dawn pasture]

Ok that makes a lot more sense

[dim cipher]

We can represent g(x) as -x^3

then you can probably see where you can go with that

Derive until you get a constant

[dawn pasture]

yes, tysm for your help I have a test tmrw and I was stressing!!

[dim cipher]

I believe in you, you got this

Remember that lhopitals only works though if the result for f(x)/g(x) = 0/0 or inf/inf

[dawn pasture]

Ok yes I’ll remember that tysm

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[jolly jay]

If I am trying to evaluate an infinite series, and I see that the expression inside is the product of two different series that do converge, can I split it up

[cedar kiln]

Please don't occupy multiple help channels.

[jolly jay]

I've closed the other one

[flint plinth]

can you paste a screenshot

[jolly jay]

I am at part (b) there

trying to evaluate that series

I know that (e^t)^x can be evaluated as a geometric series for |e^t| < 1

and the thing in parentheses is just two poisson random variables summed over their support sets

[flint plinth]

offhand i would think it would be useful to do
$$e^{tx}\lambda^x = (e^t \lambda)^x$$
and similarly for the other term

[wraith dagger]

Bungo

[jolly jay]

yeah that could also work

the sum of (e^t lambda)^x/x! would be the taylor series of e^(e^t lambda) right

[flint plinth]

then you can pull e^-lambda out since it doesn't depend on x

yes that's right

[jolly jay]

awesome, that's way better

thanks a ton

[flint plinth]

sure

[jolly jay]

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[lavish trout]

Need help solving activity 16 number 5. Much appreciated

[gusty forum]

uh, well that’s asking for a calculator or your teacher did a derp

[lavish trout]

Wdym?

[gusty forum]

you’re not going to get nice numbers so get a calculator

[lavish trout]

Alright

Yeah got it

Ok nvm imma solve this on my own

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[past sleet]

yo

[past sleet]

need help

exact value for q 35

not sure what it means

[echo falcon]

square root of 2 / 2

[past sleet]

how did you find that

could you explain

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[wooden geyser]

Please can someone explain to me how the Handshaking Lemma works in Graph Theory? I do not understand how to know when a Graph is allowed to exist.

[cedar kiln]

Please don't occupy multiple help channels.

[spice kraken]

the sum of degrees of vertices equal 2 times the number of edges

thus there are even number of odd degree vertices

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[prisma gull]

Please check the proof

@crimson delta

@crystal raptor

If you are free now, please check

My goal is to get better, so please point out every mistakes you see, i’ll take my time to review them.

[sage forge]

Looks almost exactly like the proof in our script

[prisma gull]

I didn’t mention the choice of N again

[tropic oxide]

can i criticize your handwriting a bit

[prisma gull]

sure

[tropic oxide]

these n's are supposed to be subscripts, yes?

[prisma gull]

yes,

[tropic oxide]

they don't look like subscripts the way you wrote them

subscripts should be (a) visibly below the letters they attach to, and (b) visibly smaller

[prisma gull]

Noted

[tropic oxide]

just as superscripts should also be smaller and visibly above where they attach to

[prisma gull]

sure

[tropic oxide]

also your epsilons are incorrectly written again

the proof itself seems fine to me

[prisma gull]

third last step there is a typo, it should be |a| instead of |b|

now, how should be my choice of N?

max{N1,N2}?

I require both inequalities to happen

[sage forge]

Oh, I thought they were t's 😂

[prisma gull]

mb

Thank you,

Thanks Ann, have a great day.

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[scarlet heron]

Do you know what rational means ?

[cedar kiln]

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.

[scarlet heron]

We’re not allowed to just tell u the answers

:)

[obsidian coral]

You just wait for someone to come and help you

No

You're taking a test?

<@&268886789983436800> Academic dishonesty

[summer nova]

LMAOOOO

i mean you are cheating on an exam

[obsidian coral]

You're cheating on a test

[olive hedge]

👍

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[pliant cairn]

from Serge Lang's Basic Mathematics

[pliant cairn]

I think I did a) correctly

but I don't understand how I would prove this with a disc

what is the difference?

[slate lintel]

disc is solid, circle is only the boundary

[pliant cairn]

sure, but what would that change when proving?

with the circle, I think I proved that the distance between O and P' is r

with the disc, should I prove that the distance between O and any point X between O and P', where d(O, X') is equal to d(O, X)?

where d(O, X) <= r

hold on, I've got this all wrong

I'll try again, sorry

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[zealous jungle]

Q1.Imagine that a logician puts four cards on the table in front of you. (Each card has a number on one side and a
letter on the other). On the uppermost faces, you can see E, K, 4, and 7. He claims that if a card has a vowel on one
side, then it has an even number on the other. How many cards do you have to turn over to check this? Explain
why, using reference to propositional logic.

Q2.Imagine that a logician puts four cards on the table in front of you. On the uppermost faces, you can see E, K, 4,
and 7. He claims that if a card has a vowel on one side, then it has an even number on the other. How many cards
do you have to turn over to check this?Explain why, using reference to propositional logic

Im confused about how the difference between these 2 statments affect the cards to be turned over.
the difference is in between the brackets in Q1

In Q1 my answer would be p->q / not q -> not p
SO i would have to turn over 2 cards: E and 7

I can't understand how the answer changes in Q2.
Should i just assume that -Each card has a number on one side and a
letter on the other- in my answer?

[cedar kiln]

@zealous jungle Has your question been resolved?

[fair geyser]

@zealous junglethat is the difference, you can't assume that

like your question doesn't make sense, if you assume it, there's no difference left

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[errant wasp]

was wondering if my proof was no rigourous enough

[errant wasp]

its for 4c

i said

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[crimson sedge]

What's the way of solving this without using heron's formula

[covert tangle]

Jenny goes to school by bus every day. When it is not raining, the probability that the bus is late is 3/20. When it is raining, the probability that the bus is late is 7/20. The probability that it rains on a particular day is 9/20. On one particular day the bus is late. Find the probability that it is not raining on that day.

[runic garnet]

@covert tangle #❓how-to-get-help

[runic garnet]

1/2 ab sin c = area

[crimson sedge]

wait

how

isn't that basex height

if we do that there would be extra unknown

[runic garnet]

Set up system of equations

What would it be for the first one

[crimson sedge]

What uh

[crimson sedge]

using this? Isn't area =1/2 base into height so base, and for height that would be root of (6-x)^2 -a^2

please correct me If i'm wrong 🥲

[runic garnet]

Use the given side lengths and area

In the first one, it doesn’t tell you a,b, or sin c

But u can still make the equation

4 = 1/2 (6b sin A)

5 = 1/2 (6b sin C)

x = 1/2 (6c sin D)
13 = 1/2 (6a sin D)

[crimson sedge]

Oh

[runic garnet]

U can keep making eqns like that until u have enough stuff u can cancel out with

[crimson sedge]

Right

i didn't think of area that way

I'm sorry 💀

[runic garnet]

u good

[crimson sedge]

yessir

thank u so much

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[stiff frost]

A rectangle has the area (12x+2)cm^2, now make a formula for the perimeter ( factorise expression) I literally don’t know what to do

[desert cedar]

Hello. Think of the formula for the area of a rectangle and try to reverse engineer the equation

Side A x side B = 12x + 2

The formula of the perimeter is:

Side a2 + side b2

[stiff frost]

Yeah

So 12x^2 + 4

[desert cedar]

You don’t distribute the square. In this case the square represent the unit of measurement

A line would just be cm
Area is cm^2
A cube with volume is cm^3

[stiff frost]

Ik

[desert cedar]

Split 12x + 2 into 6x + 1. I factored out a 2
6x* 1 = 24x + 4

[stiff frost]

Ah thank you

But it says the answer is (12x+6)cm

[desert cedar]

Omg I’m so sorry

[stiff frost]

It’s ok

I also don’t know so…💀

[desert cedar]

That’s because I read that as a square

[stiff frost]

No it’s rectangle lmao

So it’s b*h

Not x*x

So b and h are different so I don’t know how to solve it

[desert cedar]

I see why now

[shut tapir]

The product of l and b is 12x+2, factorise it and you will get two factors namely 2 and 6x+1. The perimeter will be the sum of the factora multiplied by two that is 12x+6

Option C

[desert cedar]

6x+1 + 6x +1 +2+2

[shut tapir]

Yes

[desert cedar]

Thank u ericsson

[shut tapir]

https://cdn.discordapp.com/emojis/759987154767052840.gif?v=1&size=64&quality=lossless

[desert cedar]

I’ll be more careful when I help people. Lesson learned

[stiff frost]

Hm how come

Oh 2(6x+1) +4

[desert cedar]

Factor out a 2 and you get 2(6x +1) for the volume of the rectangle.

Area

[stiff frost]

So 12x+6

[desert cedar]

Yes

[stiff frost]

Nice

Thank you for your help!

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[west mica]

how can i study trigonometry properly?
been trynna understand trigonometry for a decent amount of time, i think im pretty decent with the simplification but when it comes to questions with unit circle i literally cannot move my pancel, any tips or tricks?

[stable edge]

u might have more luck if u ask in #geometry-and-trigonometry btw

[west mica]

oh then let me put my question here, thanks

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[empty meadow]

is it possible to say \newline$\int\left({\sum_{n}(C_n\psi_n\right)^{}H\left(\sum_{n}(C_n\psi_n)\right)dx=\int\sum_{n}\sum_{n} c_n \cdot c_n (\psi^{} H \psi)dx$?\newline
where
psi is an energy eigenfunction and H is the hamiltonian?
and if so how could i get rid of the double sum? Would it be the same as just having one of them?

[empty meadow]

oh

[wraith dagger]

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

[dire geode]

...

What are C, psi, H, and sum and integral over

[gritty galleon]

i am fascinated and scared both at the sametime

[empty meadow]

C is the expansion coefficient, psi_n an energy eigenfunction
i have a wavefunction psi which is the sum of all c_n*psi_n
integral is from -inf to inf

[dire geode]

Oh there's C and c. What's the difference

[empty meadow]

oh sorry, those are the same

[empty meadow]

here the * isthe conjugate

[dire geode]

Yea you're leaving too much context out

[empty meadow]

im trying to prove this

[dire geode]

That would have been better from the start

[empty meadow]

sorry

[dire geode]

Did you write the expectation value of energy

[empty meadow]

yeah, thats the left of this when subbing the expression for psi

[dire geode]

Oh you meant little c_n

[empty meadow]

yeah

[dire geode]

You just use orthogonality of the eigenfunctions in the double sum

[empty meadow]

is that where if n=m you get 1?

[dire geode]

Google orthogonality if you don't know it

[empty meadow]

okie

[dire geode]

They're probably orthonormal even though it doesn't state it explicitly

The psi_n

[empty meadow]

would that leave me with the integral of sum (cn(cn) psi* H psi)?

i think i get it now, thank you 🙂

.close

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[feral creek]

how can i find tan27°36' when the only information i have are tan27°30' = 0.5206 and tan27°40' = 0.5243

[feral creek]

it is trig value from looking up at table thing

[cedar kiln]

@feral creek Has your question been resolved?

[crimson sedge]

Maybe

[feral creek]

not at all

😔

[cedar kiln]

@feral creek Has your question been resolved?

[feral creek]

do i just approximate normally

like find changes per minute arc

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[orchid summit]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[orchid summit]

ok

do u know what a denominator is

can u tell me what the denominators are

in this question

what's the least common multiple of 5 and6

[long sequoia]

30

[orchid summit]

@obsidian coral dude gives the answer everywhere

[long sequoia]

My bad yall

[orchid summit]

yep now u got ur lea at common denominator

now find ur numerators

nooo

what is 30/5

do u know how to add fractions with diff denominators?

nope

yes

that's correct

ur done?

ur answer is 30

as 30 is the denomination

no worries

cya

no lol

that's only for helpers to help explain

[cedar kiln]

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[placid chasm]

im working on a geometrical ruge goldberg machine but dont know where to start

[placid chasm]

is anybody out there

.@me if your helping i wont have discord open

nvm

/close

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[sinful mirage]

I have to solve the question at the top, but I'm really unsure about how I'm supposed to continue/ find the angle for this given problem.

Also I'm pretty unsure if what I wrote already is even correct in the first place

[blazing dune]

So what did you tried to use any trick in the final form to get the answer ?
@sinful mirage

Like using trig identities

Specifically

$$\sin(x) = \cos(\frac{\pi}{2}-x)$$

[wraith dagger]

Sherif Player

[sinful mirage]

I'll try it real quick

am I allowed to scrape the cosines on the left?

[blazing dune]

You can't treat them as you treat exponents

[sinful mirage]

I could try to graph that and check for an intersect (I think),
but I really wonder if there's a way to know/ approximate the answer without using a calculator

is there a way to simplify/ move on with solving this?

[dim gulch]

Are you supposed to solve for alpha without a calculator?

[sinful mirage]

I'm pretty sure not? The prof told us that it's gonna be a number for which we probably would need a calculator.
I just kinda wanna avoid using one, but I'm not sure if it's possible to solve this without one

at least I just don't know how

[dim gulch]

well you can approximate it using a series known as a taylor series expansion (basically a infinite series that the more terms you calculate the closer you get to cot x )

but the one for cot x is very annoying so

i would recommend you just use a calculator

[sinful mirage]

ait, with that I assume that's also the solution right? (aka this issue should be solved)

[dim gulch]

basically just use a calculator, if you really want to not use it use this to approximate

[sinful mirage]

ah I assume that's the taylor series expansion for cotx?

[dim gulch]

yeah for a few terms

[sinful mirage]

ait, thanks!

[dim gulch]

Np!

[sinful mirage]

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[fathom carbon]

does anyone know how to answer this question? "Ann and Bob shared 240 $ in the ratio 3:5. Ann gave a half of her share to colin. Bob gave a tenth of his share to colin. What fraction of the 204 dollards did colin recieve"

[desert cedar]

Write it out. ask yourself:
A)What’s 3/5 or 240
B)what’s 1/2 of What Ann has now
C) what’s 1/10 of what Bob has now
Add them together

Then they’re asking for a fraction of that whole amount

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[bronze briar]

given the plane 3x-7y+2z = 8, is the line
x = 3t + 2
y = -7t = 1
z = 2t -1
perpendicular to the plane?

[flint plinth]

do you have any thoughts about whether it's true or not?

[bronze briar]

so i saw this in a youtube video. I think it's false and that's why i came here

like wouldn't the vector < 3, -7, 2 > be parallel to the plane?

[flint plinth]

nope

perpendicular

[bronze briar]

what

so then what would a parallel line look like?

[flint plinth]

in general if you have a plane in the form
ax + by + c = d
then <a,b,c> is perpendicular to the plane

[flint plinth]

one way is to find two points in the plane and then find the line connecting them

[bronze briar]

oh okay, thank you so much

wait, but how would you tell if a vector (not residing on the plane) is parallel?

[flint plinth]

see if it's perpendicular to <3, -7, 2>

any vector parallel to the plane must be perpendicular to <3, -7, 2>

[bronze briar]

oh so i can just take the dot product and see if it's 0?

.close

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[verbal terrace]

Not able to calculate the direction angle of the vector BE (btw the location points are correct for B)

[verbal terrace]

Tried doing inverse tan for the points but gives a wrong answer

<@&286206848099549185>

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[verbal terrace]

Close

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[sonic sentinel]

hi can someone plz help me with this homework question?

[sonic sentinel]

ive done the Aroc and i got 24/4

but its incorrect

<@&286206848099549185>

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[compact sandal]

Can anyone help work consumer and amortized loans?

[quaint spear]

Which equations are for what? (Chemistry. I lost my attention during class😶)

[shut river]

First is mols I think

Second gives mols from mass and molar mass

[quaint spear]

Moles from particles?

[shut river]

Your M and m look very similar. This should be a lesson to take better notes. Formulas without units and explanation are useless to you later

Yes, mols from particles and Avogadro's number

[quaint spear]

What are the other 2?

[quaint spear]

Yeah ig

[shut river]

There are only two unique equations

I gave info on those

[quaint spear]

No you didn’t on the other 2?

[shut river]

I gave info on the unique equations

I.e my second was the second unique equation

2nd and 4th lines are just rearrangements

m is mass

M is molar mass

[quaint spear]

Oh. So the 3rd one is for calculating particles from mols? And the 4rth one is calculating mass from mols?

[shut river]

Yeah, sorta. Same info

[quaint spear]

Wiat, so are you sure? I have a test soon🥲

[quaint spear]

Ok thx

[shut river]

Dude, read your textbook

[quaint spear]

I dont have it

[shut river]

Google "chemistry libre" or mols definition

[quaint spear]

Regardless, they’re ineffective for me bc im dumb🥲

[quaint spear]

Yeah

[quaint spear]

Oops, srry made a mistake, i fixed the questionn

[cedar kiln]

@compact sandal Has your question been resolved?

[cedar kiln]

@compact sandal Has your question been resolved?

[potent quest]

where is point E?

[cedar kiln]

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[void sand]

!status

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
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6. None of the above

[void sand]

1

<@&286206848099549185>

.close

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[tulip patio]

Question #3

Am I not looking for the PV?

<@&286206848099549185>

[cedar kiln]

@tulip patio Has your question been resolved?

[verbal compass]

principle amount of investement means the amount that was invested

for simple intrest, each year (or whatever time period), the intrest gained is a fixed amount of the initial depost

in this case lets call the deposit D, the intrest rate x, and the time t

the intrest gained each year = i%*D
the total intrest gained = i%*D*t

so we know the intrest rate, we know the time and the intrest gained

so using the second eq we get -> 37.50 = 2.5%*D*9/12 (time = 9/12 years) we can find D

unless im completely wrong then idk

[cedar kiln]

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[mellow nimbus]

<@&286206848099549185>

[cedar kiln]

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.

[verbal compass]

ignore rhe first two, cut out lines

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[mellow nimbus]

thanks bro

[verbal compass]

no worries

sorry if my workings were shit i was acc js tryna figure it out too 😭

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[crude scroll]

Hmm ok. So I managed to prove 1.

But for 2, the indexing is a little weird.

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[crimson sedge]

why does desmos not show 0 as a solution?

[violet flume]

try just plotting the curve

its likely an issue with the domain of the function

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

hwo would I do that?

[violet flume]

remove the =0

[crimson sedge]

Perfect! thank you very much

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[cedar kiln]

Please don't occupy multiple help channels.

[obsidian coral]

Don't open multiple channels, you have #help-4 already

.close

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[honest bobcat]

can i have some help structuring this proof

[dry dirge]

well sqrt(1,000) is 1

so we will have sqrt(1.001)<1.5

which is the same as 1.001<2.25 which is true

idk why you should use that a^2-b^2 formula though

[honest bobcat]

i think i get it

you end up with

1 < 1/2 * (sqrt(1001) / sqrt(1000) + 1/2

sqrt(1001) / sqrt(1000) is > 1 s

rhs > 1/2 + 1/2 > 1 i guess

i got stuckj on this one too

as both sides are clearly positive youi can bring both sides power of 7

then i got sorta lost

[dry dirge]

7!=6!*7

[honest bobcat]

mhmm

I got to 7! > (6!) * (6!)^(1/6)

but then im lost

[lean sable]

Divide both sides by 6!

[tropic oxide]

$6!^{1/6} \overset?< 7$

[wraith dagger]

Ann

[lean sable]

Yes

6×5×4×3×2×1<6⁶

[dry dirge]

@tropic oxide ihave question to you i will post question now and plz answer

[tropic oxide]

no

[dry dirge]

why not

[tropic oxide]

i refuse on principle lmao

you're not entitled to my time and energy

[dry dirge]

ok

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[remote cedar]

i still cant figure out what they want me to write here

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[nocturne nexus]

what values were used to create 29.7

ive tried using the average rate of change of 3 and 4, 2 and 3, and i tried averaging out different velocities but i wasnt able to get 29.7

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[nocturne nexus]

.reopen

[cedar kiln]

✅

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[cedar kiln]

Channel closed

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[spice kraken]

find another channel

it's already closed

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[median bay]

How to use laplace's rule to solve this det

There seems to be a lot of smaller portions that could be solved with upper/lower triangle

4 big ones but idk how i can get em so to say

Oh btw it goes to 2n

<@&286206848099549185>

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[arctic eagle]

How do i apply implicit differantation

[jaunty mural]

step 1: apply the d/dx operator to both sides of the equation.

[arctic eagle]

Ok ill write down 1 sec

[jaunty mural]

please dont write 9's like g's

[arctic eagle]

k

[jaunty mural]

im going to assume all the steps to this point are correct

then you want to isolate dy/dx

and that process is the same as how you would isolate one variable in equations

You need to try eventually factor the two dy/dx together

[arctic eagle]

do u know if this correct?

it as in fact correct, expect y^5 --> y^6

.close

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[tropic oxide]

horizontal black bands

[solemn harbor]

can someone please explain why it not a vector space please

[solemn harbor]

what’s wrong with that?

[brittle lynx]

check zero vector

[tropic oxide]

for mine and everybody else's sake

[tropic oxide]

a subspace needs to be closed under addition

this W fails that

[solemn harbor]

oh i didn’t réalisé when taking it. sorry

won’t happen again

[solemn harbor]

vertical *

[tropic oxide]

🥖 ❓

[solemn harbor]

bread?

[tropic oxide]

are you french

(it's a baguette)

[solemn harbor]

no but i can speak a bit why?

[tropic oxide]

no i just wondered why your autocorrect put "réalisé"

[solemn harbor]

ohh thé ‘réalisé’ 😭

[tropic oxide]

and the thé

[solemn harbor]

yeh bc i learn french the keyboard autocorrect’s english words to french words sometimes and vice versa

[solemn harbor]

how’d does the 2 in the third component fail it?

[tropic oxide]

by not being 1

[solemn harbor]

o ok danke

.close

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[crimson sedge]

please help, is a AM-GM-HM problem but I dont get how to prove it

[south tundra]

Making common denominators and expanding could help

[crimson sedge]

yes i tried that

[south tundra]

Did you get that (1 + 1/x)(1 + 1/y) = 1 + 2/xy ?

[crimson sedge]

yes

i am slow typing

[south tundra]

Right, now you just need to justify that xy >= 1/4

Given x + y = 1

Try expressing xy in terms of x only

[crimson sedge]

I will try but the idea is to use the AM-GM-HM inequality

[south tundra]

Weird, z^2 >= 0 alone is sufficient

[crimson sedge]

mmmh i will try

could you solve it , I still dont get how, expressing it in terms of x seems to not work

or at least it doesn't make a big difference

<@&286206848099549185> I get a lot of expression but still I cant prove it

[crimson sedge]

ok so here its given x+y=1 then try finding x value which will be x=y-1
now just directly substitute in the second equation and find y value then just put ur values of x and y

the answer u will get

will automatically show

that its greater

[crimson sedge]

x+y is equal to 1

[crimson sedge]

yeah it was a typing error mb

oh

but general idea is this

after u get x=y-1

open the bracket down there

u will get 1+2/x+1/xy

wich is the second equation?

now substitute value of x everywhere

[crimson sedge]

second equation is in the question itself

cuz it is given it is greater than or equal to

so automatically u can use that

ur second equation is

(1+1/x)(1+1/y)=9

find the x and y values

then substitute in
(1+1/x)(1+1/y)>=9

and once u get smthn equal to 9 or greater than 9

u proved it

thats all

but x=y-1 ? isn't it?

yes

now all u have to do is just put x=y-1
in (1+1/x)(1+1/y)=9

and equate

i will try

yea

is the same y-1 and 1-y?

oh wait another mistake

x=1-y

not y-1

mb

xD

but yeah

concept wise im clear

abt how it will be solved

so i have to find y

after u find the correct value of y

come back to x=1-y

and find x

[crimson sedge]

then finally substitute in this

and ur answer must be greater than or equal to 9

and yes

u proved it

but how did you find "y"? if there is no equal sign in the hipotesis?

'cause if you make the entire expression equal to 9 it obviously is equal or greater to 9, but what if you make the expression equal to 5 for example?

[crimson sedge]

for that there is a different method

u have the concept of determiners

if thats the case

.close

[cedar kiln]

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[nocturne void]

Why is w not a linear combination ? It says reader can verify but I tried to work it out and I can’t see why it’s not

[tidal thunder]

!help

[cedar kiln]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[nocturne void]

Oh wait would u just get the r s t values and then input them in front of x y z and see if they add up to give w?

The thing that confuses me is it says “there is no solution” but I have solutions they just don’t satisfy the equation rx + sy + tz = w

[cedar kiln]

@nocturne void Has your question been resolved?

[cedar kiln]

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[slim shell]

Find the radius and central angle of a sector which has area 6𝑐𝑚2 and arc length of 5cm

[cedar kiln]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[slim shell]

I know how to normally find the area, perimeter and arc length

But idk wtf to do on that

Am I supposed to get to the feta thing on both sides?

[gritty galleon]

feta?

have u done any work?

[slim shell]

The circle with line in it

For an angle

[gritty galleon]

its called theta

[slim shell]

Ahh

I’ve tried couple times but I keep getting lost on what to do where

[gritty galleon]

show work if u done something

[slim shell]

I’ve tried getting both the area and arc length to equal the theta and then find the highest common factor but it don’t work

One sec

[gritty galleon]

,rcw

[slim shell]

It’s not full workings at all but I’ve tried so many different things hoping from one idea that could work to another

So I doubt any makes sense

[gritty galleon]

yeah makes little to no sense to me

sorry

[slim shell]

Gimme few minutes I’ll put it in order to show what I tried to do

5 minutes 🙏

[gritty galleon]

lamar you do know that $\theta = \frac{l}{r}$?

[wraith dagger]

ItzKraken

[slim shell]

What is l

[gritty galleon]

arc length

r is radius

[slim shell]

I’m

Um

Maybe idk give me a minute to do this working clearly

I get theta on the right hand side for both then put them together

[slim shell]

Then tried to find the highest common factor

[gritty galleon]

dont do that ❌

solve it

as a quadratic

[slim shell]

Got stuck when I got them equaling eachother and I did HCF as well for algebra recently so guessed I’d do it again

[gritty galleon]

u do know how to solve quadratic equations right?

[slim shell]

Farmers field way

That you use to factorise

[gritty galleon]

uh i do not know that

[slim shell]

One sec

[gritty galleon]

do you know quadratic formula?

[gritty galleon]

it might be called mid-term splitting

[slim shell]

Ehhh maybe again one sec

Something like 2X squared - 4X + 5

Otherwise no idea

[gritty galleon]

...

[wraith dagger]

ItzKraken

ItzKraken

[slim shell]

Yhyh

Zero trick

[gritty galleon]

u recognize these?

[gritty galleon]

trick..? its a formula but okay nvm

[slim shell]

My school ain’t do any of that but we did equations like that

[slim shell]

What my school called it

[gritty galleon]

so we have $\frac{2160}{\pi r^2} = \frac{900}{\pi r}$

[gritty galleon]

oh

[wraith dagger]

ItzKraken

[gritty galleon]

multiply both sides by pi*r^2

$2160 = \frac{900}{\pi r} \cdot \pi r^2$

[wraith dagger]

ItzKraken

[gritty galleon]

@slim shell u dont need quadratic formula (trick or whatever)

[gritty galleon]

@slim shell can u cancel the common things out here?

[slim shell]

900 x r

= 2160

[gritty galleon]

now divide both sides by 900

r = ?

[slim shell]

2.4

I’m actually a numpty

I tried doing so much extra shit

[gritty galleon]

no no its fine

[slim shell]

I can get theta easy from that myself

[gritty galleon]

nice

[slim shell]

Thanks for the help 👍

[gritty galleon]

do .close

[slim shell]

.close

[cedar kiln]

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[autumn current]

Hello, I have something weird i noticed

[autumn current]

so when I was looking at the integral of cosx/x

i tried dividing by it itself to get some kind of result(I wanted to see if something like the borwein integrals happened)

so i kept increasing

interestingly it becomes undefined at 3,7,8,9,10,14 but not 11,12,13

i dont see any apparent pattern

anyone have an idea?

<@&286206848099549185>

[tropic oxide]

feta is a type of cheese from Greece btw. the Greek letter θ is called theta, as said above

@autumn current all of these integrals have a (1/x)-like asymptote at 0 so it's questionable to speak of any of them

while f(x)/f(x/k) is periodic and so should not really have its integral over the entire real line converge either i don't think

[cedar kiln]

@autumn current Has your question been resolved?

[autumn current]

hmm

ok

[tropic oxide]

well ok no not all of them but like cos(x)/x specifically

[cedar kiln]

@autumn current Has your question been resolved?

[cedar kiln]

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[hazy grail]

2sqrt(x) + 2sqrt(y - 1) + 2sqrt(z -2) = x + y + z

[hazy grail]

Id like some help with this problem when I tried i got an absurdity of a result

[cedar kiln]

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

[long arrow]

what's the question asking

[silver parcel]

maybe solving it

[hazy grail]

Oh my bad prove that x = 1 y = 2 and z = 3

[silver parcel]

I think you have to use some inequalities to prove that x = y-1 = z-2 is necessary

then when you have this condition, it's just soliving 6sqrt(x) = 3x+3 and x = 1 is solution

leading to y = 2 and z = 3

[hazy grail]

Yeah i think so too, But how might i go about it, I'll see what i can do

[silver parcel]

inequalities of means may give the result

[hazy grail]

Of means?

[silver parcel]

the different averages

like (x+y)/2 > sqrt(xy)

because it's the IAG

or a clever use of Cauchy Schwarz, something along these lines

[hazy grail]

I didn't really study those is the problem

But theres like a million ways to solve one problem

[silver parcel]

first you can do changes of variables to get something nicer
let u = y-1 and v = z-2
your equation becomes 2(sqrt(x)+sqrt(u)+sqrt(v)) = x+u+v+3
then let a = sqrt(x), b = sqrt(u), c = sqrt(v),
you get 2(a+b+c) = a²+b²+c²+3

your problem is equivalent to solving this and then reversing the change of variables

[hazy grail]

Wait where did the 3 come from

[silver parcel]

x+y+z = x+u+1+v+2 = x+u+v+3

[hazy grail]

Oh nvm

Doesnt that mean u is just equal to y

Not u = y - 1?

[silver parcel]

hmm no

u = y-1

because I defined it like so

[hazy grail]

Yeah but then we added 1 + 2, shouldnt we substract- 3

[silver parcel]

x+y+z = x+(u+1)+(v+2) = x+u+v+3

[hazy grail]

Oh yeah nvm 💀

[silver parcel]

are x, y and z real numbers ?

[hazy grail]

Yeah they are

[silver parcel]

yeah that's still a pain to solve

[hazy grail]

On the last step shouldnt we square that 3 aswell (why am i asking about that 3 so much)

[silver parcel]

no, that's a change of variables

we set a = sqrt(x)

so x = a²

the 3 has nothing to do with it

[hazy grail]

Oh yeah mb how did i not see that

Yup solved it

Thanks a lot for the help

[silver parcel]

how did you solve it in the end ?

[hazy grail]

.close

[cedar kiln]

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[hazy grail]

Oh

I reversed the change of variables

[silver parcel]

no I mean, how did you solve 2(a+b+c) = a²+b²+c²+3

[hazy grail]

I got 3 identities (a-1)² + (b -1)² + (c - 1)² = 0

[cedar kiln]

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[hazy grail]

Since theyre all positive this means all of them are equal to 0

[silver parcel]

oh yeah nicely seen

[hazy grail]

Then I reversed the change of variables squared them and got the result

Yup thanks a lot

.close

[cedar kiln]

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[azure citrus]

quick set question. is {a,b,c} - {a,b,d} = {c, d}??

[foggy merlin]

is it a difference of sets ?

[azure citrus]

yes

[native heath]

it's just c

{c}

[azure citrus]

what happens to d

[foggy merlin]

hmm, so x in {a,b,c} but not in {a,b,d}
then its only {c}

[azure citrus]

ohh

[native heath]

do you know how it's defined

[azure citrus]

i’m trying to disprove this then. do i include the empty set

[azure citrus]

i do now! i get it

[native heath]

yayyy

[native heath]

this is powerset right?

[azure citrus]

yes

[native heath]

well

if you're disproving

you could just provide a counter example

[azure citrus]

so P(A) - P(B). Let A = {1,2} B = {2,3}

[native heath]

yeah

take pretty much any two sets

[azure citrus]

so P(A) = {empty set, {1}, {2}, {1.2}}

[native heath]

call the empty set $\phi$

[azure citrus]

okay

[wraith dagger]

Percy

[azure citrus]

so P(B) = {phi, {2}, {3}, {2,3}}

[native heath]

oh also

if you're writing it down

you could write it as $\phi$ or just {}

if you're speaking you call it the null set

[azure citrus]

mmk

[native heath]

(random but yes)

anyway yes proceed

[wraith dagger]

Percy

[azure citrus]

P(A) - P(B) in my example is just..

[native heath]

alrighty i have forgotten my latex

[native heath]

just {1}

[azure citrus]

what about {1,2}?

that is not in B

[native heath]

oh sorry

i thought you said P(A-B)

[native heath]

yes {1,2} is there

so is {1}

[azure citrus]

so p(a) - p(b) = {{1}, {1,2}}

[native heath]

pretty much yes

[azure citrus]

A - B is really just {1}?

[native heath]

yes

and its powerset would be-?

[azure citrus]

{phi, {1}}

[native heath]

yes

so

[azure citrus]

not equal. okay cool

[native heath]

there you go

[azure citrus]

thank you

[native heath]

counter example gotten

[azure citrus]

or not subsets

:p

[native heath]

yesyes you're welcome

[native heath]

I thinkkkkkk the subsets thing can be disproved without an example

like

P(A) would have a null set

so would P(B)

this implies that P(A) - P(B) def wouldn't have the null set

but P(A-B) would def always have a null set

since the null set is an element which belongs to P(A)-P(B) but def not to P(A-B), the former can never be a subset of the latter

But mentioning this approach is probably really just overkill full credit all stars lmao

[azure citrus]

ohh my god ur right

[native heath]

:p

[azure citrus]

do you understand unions and intersections ?

[native heath]

i believe i do xD