help-26

[scarlet meteor]

candidates

[ripe spoke]

?

[scarlet meteor]

i mean that question ha been written by non native human

[noble laurel]

a what

[ripe spoke]

Even then, regardless of the English, the aquarium is missing units

[scarlet meteor]

SAHAHAHA

[ripe spoke]

A non native human 👽

Regardless, point still stands, you start by finding volume @scarlet meteor

[scarlet meteor]

nah how can i close this room?

channel

[ripe spoke]

Use .close I think

[scarlet meteor]

/close

.close

[topaz sinew]

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[ripe spoke]

Yep

[scarlet meteor]

.solved

/solved

!solved

[topaz sinew]

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[verbal spear]

for part C, can someone please explain how they got 7 as the lower bound? i only got 37/4 > k idk how they did the other part or why they did it

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[chrome lantern]

k whats ur question

[misty niche]

i know that the first solution diverges, and the second has a limit that approaches 0

but I dont know what the solution for the second would be if it approaches 0

🙂

[chrome lantern]

k, it it is an infinite series, then there is a simple eq

Sum = first digit/(1-ratio)

here, it would be

9/1-(-3/4)

or 9/(1+3/4)

7/(7/4)

28/7

[misty niche]

first digit?

[chrome lantern]

and

4

yea

just sub n for 0

[misty niche]

oh i see

[chrome lantern]

thats only if it converges tho

[misty niche]

and ratio is the -4/3?

[chrome lantern]

yes

[misty niche]

oh i see

ahhh i tried that with another question that was like this and it wasn't right

[chrome lantern]

and i didnt check to see if it converges of diverges

so keep that in mind

[misty niche]

i dont oknw what i did wrong

okay, sounds good

[gritty birch]

!nosols

[topaz sinew]

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.

[chrome lantern]

im sorry

[misty niche]

i understand how to do it now, thanks

[chrome lantern]

kk

gl

[misty niche]

🙂

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[prisma onyx]

Can someone help me with b? I understand that the mode in general is the maximum of the distributions but I am unsure how to solve for this here.

[prisma onyx]

Can I use some gaussian property or something?

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[tall quiver]

Can someone see if I did this correctly with isolating a variable? I feel like I did it wrong because of the s variable

[dim pulsar]

Shouldn't it be (-r )+ (s/-4 pi r)

The 4pi cancels

[tall quiver]

oh ur right

gotcha

but is the s/ -4 pi r correct?

it looks so weird

[dim pulsar]

Yes

Ngl first step I would factor idk that's just me

S = (4 pi r)(k + r)

[tall quiver]

can u tell me how u would do it? im struggling in math and any better methods are appreciated

[dim pulsar]

Divide by 4 pi r

S/ 4 pi r = k + r

Subtract r

We have k = (s/4 pi r) - r

[tall quiver]

ohh

that makes a lot more sense

i learned abotu facotring but forogt it

[dim pulsar]

It doesnt matter as long as you get the same answer

Which ever one you like better / prefer

[tall quiver]

thank you! i had another similar problem to this one i worked out but since i have you here can i get you to see where i went wrong by chance?

its a simplifying problem and i solved it, but when i put it in the answer it said "correct but must be simplified" so im not sure what steps i need to take further

[dim pulsar]

Sure

Also

[tall quiver]

ok let me send a picture of it, one second.

[dim pulsar]

!da2a

[topaz sinew]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[tall quiver]

ok noted

[dim pulsar]

Ping me when u send picture

[tall quiver]

will do thx

so i feel like i did it in a way that made it way more complicated, but not sure what steps i shouldve done instead @dim pulsar

[dim pulsar]

Ok

B/ (1/4)

Is the same as 4b

[dim pulsar]

That's the way I would do it

I don't see any other way

The last simplification is

S = 4B/M) - K

[tall quiver]

for fractions, am i able to multiply it by itself to make it a whole number?

So in the problem I wrong: B / 1/4(m)

I would multiply the above fraction by 4/4 and get 4B/M, which is allowed right?

since i can multiply anything by 1?

[dim pulsar]

Well

B / 1/4 m

Is the same as

B/(M/4)

Dividing by a fraction is the same as multiplying by a reciprocal

M * 4/M

Oops

B * 4/m

4b/m

[tall quiver]

ah okay

gotcha

so the method i did for this problem wasnt the issue, it was just the simplyfying at the end

would i be able to factor to solve the problem?

probably not because its arleady factored out and i distributed..

.closed

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[oak grail]

Hi, in this paper ( https://www.sciencedirect.com/science/article/pii/S0950705122004282 ) i dont understand how the decomposition is done for "from-below BMF", can someone help me please?

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[oak grail]

<@&286206848099549185> 🥺 i hope i asked correctly

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[oak grail]

😦

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[modest burrow]

i believe the 'from-below' part is just in the specification of (A circ B) < I

but im not familiar with this, so that is just a guess from what i see here

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[gentle birch]

I am a little confused on how they got C=-1

can someone explain that for me?

[slate pebble]

expand the rhs of the equation and youre left with C * x on the RHS and -x on the LHS, the coefficients have to be equal

[gentle birch]

ok

still confused a lil lol

[slate pebble]

about the expansion? or the reason it works

[gentle birch]

both to be honest

[slate pebble]

convince yourself of what the expansion is on the right hand side of x^2-x+12 = A(x^2+3)+(Bx+C)x first

[gentle birch]

like is it just safe to assume that C would always = -1

[slate pebble]

it has to be

[gentle birch]

so that is a must

[slate pebble]

the solution is unique so the parameters will be I believe

[torpid sparrow]

Exactly in which step are you lost?

[gentle birch]

how they managed to get C=-1

[torpid sparrow]

Look at rhs

[slate pebble]

thats quite broad, is it convincing yourself of why it works or just the algebra causing issue

[torpid sparrow]

A/x + (Bx+C)/(x^2+3)

Add this and tell me what you get

[slate pebble]

I dont think they have issue with either A,B considering the original question

[gentle birch]

Ok but like take a look at this example though. If I set x=0 I get A=2, and equating coefficents of x^2=A+B gives me B=-1 and from what ur saying C would equal -1

[slate pebble]

which is correct?

[gentle birch]

Honestly I could convince myself that C would alway equal -1 but I gotta know at least how

or why

[slate pebble]

wait, I hope you dont assume that C is ALWAYS -1 in ALL questions

[torpid sparrow]

[gentle birch]

No no no no, Im just assuming that it would be -1 if I have a problem with A+Bx+C

[slate pebble]

again, you have to expand and then compare to understand why its -1 in both cases

[torpid sparrow]

Why don’t you get the values instead of assuming?

Expand the original

[torpid sparrow]

Do this

[slate pebble]

this is what I meant, dont assume just because its of this form that C is -1, its not. in both of these questions it just happens that is the solution

[gentle birch]

is this what u want @torpid sparrow

[torpid sparrow]

That is not correct

If i am reading correctly

X multiplies both, not only C

Also

Wasnt x^2+3?

[gentle birch]

X multiples to both what u mean, Bx+C is a function being multipled by (x) because we have x and x^2+3

[torpid sparrow]

You should get (A(x^2+3)+x(Bx+C))/(x(x^2+3))

Do you agree with this?

[gentle birch]

No? Cuz the book says this?

[torpid sparrow]

That is what i said

The book is doing several steps at once

I am showing you all the steps

So u dont get confused

[torpid sparrow]

If you add these

[torpid sparrow]

You get this

Now, from the left side we have

(x^2-x+12)/(x(x^2+3))

As yoi can see both denominators are equal

So we can say that the numeratos have to be equal too

So

x^2-x+12=A(x^2+3)+x(Bx+C)

Now you work on the right side

Expand that

Ax^2 + 3A + Bx^2 + Cx

Do you agree?

[gentle birch]

yea

[torpid sparrow]

If you are getting lost here you have to say

[gentle birch]

No so far Im good, usually I just do the cover up technique we learned and get that far

[torpid sparrow]

Ok now we gather in a way where we separate the x^2 the x and the other

[gentle birch]

k

[torpid sparrow]

Ok we keep working on rigjt side

We get then

x^2(A+B) +xC + 3A

Is that correct?

Ok so now we compare again the equations

[gentle birch]

yea

[torpid sparrow]

x^2 - x + 12 = x^2(A+B) +xC + 3A

I will write this in a different way so you can see better

x^2(1) - x(1) + 3(4) = x^2(A+B) +x(C) + 3(A)

Can you see the similarities?

[gentle birch]

yea

[torpid sparrow]

So A+B= to what

[gentle birch]

A+B= 1, C=-1, and 3=A

[torpid sparrow]

A=4

[gentle birch]

Yea A=4 my badd

[torpid sparrow]

So if A=4

B=-3

C=-1

[gentle birch]

yea

[torpid sparrow]

4/x + (-3x-1)/(x^2+3)

Can you see now from where we get C=-1?

[gentle birch]

yea

[torpid sparrow]

Great, do you have any other questions?

[gentle birch]

nah this pretty much answers my Q on where C=-1 came from

But I do have another question

If we see a problem with A/x +Bx+c/x^2+4 for example, can we just assume that C would always =-1 or would it be a good idea to just check it through what we did

cuz its a lot of steps

[torpid sparrow]

It is better to always do the process

When u are used to do it, it does takes 30 seconds to do

[gentle birch]

alright neat

thanks man

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[devout veldt]

when does long division not work?

[devout veldt]

I have x^4-2x^2+1 all over 1-x^2

would it work?

[wooden osprey]

you could use the fact that (1-x)(1+x)

and do 2 divisions with each term

[devout veldt]

would it be easier to just factor everything then?

[cursive patrol]

(why?)

[wooden osprey]

alternatively theres a method of synthetic division with any polynomial

[cursive patrol]

it is always possible to long divide two polynomials

there's no such thing as long division not "working"

[devout veldt]

so how would i synthetically divide that

also when i try long division and i get funky things like -2x^2-x^6

[wooden osprey]

refer to this

[devout veldt]

could i technically

rewrite it as -(x^2-1)

and then long divide with whats inside?

or is that not allowed

i did it

hooray

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[topaz sinew]

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[gaunt bear]

could someone help with this integral using the substitution x=3sinh(u)?

[gaunt bear]

i have an end result that is not the same as an answer i have been given

[loud oasis]

post the steps you took and the given solution

[gaunt bear]

the given solution is this

this is my working out that i stopped due to it being messy and seems like the wrong direction

[loud oasis]

you have a sqrt(9) = 3 from the square root and you should also get a 3 from the 3 cosh(u)

[gaunt bear]

however that isnt the glaring issue no?

i cant seem to get the first term of the given solution to match up with my second term on the paper

[loud oasis]

well you can use the hyperbolic version of the double-angle identity to get [ \sinh(2x) = 2 \sinh(x) \cosh(x) ]

[thorny flame]

cloud

[gaunt bear]

i will try that

that seems to be the solution thanks

!close

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[frigid cobalt]

i think referencing the properties of limits would be helpful

[burnt swift]

like?

[frigid cobalt]

these could be especially helpful in dealing with this problem

[burnt swift]

okay I know both of these

but . . .

3^n outgrows n

[frigid cobalt]

i think that

because this problem is complex, you might have to "split" the limit

[burnt swift]

I tried multiplying and dividing by the conjugate lol

mmm how should I go about solving this limit?

lowkey I am hardstuck

[frigid cobalt]

so let's look at what's inside the limit

you could express it as the difference of 2 functions: f(n) and g(n)

what would be f(n) and what would be g(n)?

[burnt swift]

aaaaaaaaaaaaaaaaa

f(x) =

g(x) =

bro help my ass out cmon

[normal tapir]

I would do a sandwich argument

[burnt swift]

with what

[normal tapir]

sqrt(9^n/n^2) - 3^n/n <= your thing <= sqrt( 9^n/(cn^2)) - 3^n/n

think that should work

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[worldly oriole]

Hi I js need someone to identify the interpretation of slope of regression line for this graph

[hasty verge]

wdym interpretation

as in "for each increase of 1 unit x, the y value is predicted to increase by 0.24"?

[worldly oriole]

I'm not sure cuz that's what it said on the slides

And ion get the first one too 😭

@hasty verge do yk what it means?

[hasty verge]

no sorry

[hasty verge]

this is what i'd assume but i cant be too sure

[worldly oriole]

Oh danggg

Do yk what to do for the residuals?

[worldly oriole]

Is there any chance you could ping someone to see if they know what it is?

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[molten forge]

Which quantity is bigger? A or B? 2 other possibilities are they are equal OR cannot be determined

[neon iron]

Try substitution

[molten forge]

I did and my answer is basically that B is always bigger

But I don't think its right

[ruby mural]

So you've to find which one of
(a+b+c)/3 and (b+c)/2 is bigger

Hmm

[molten forge]

The answer scheme says C. But I cannot prove it

[odd pagoda]

I think they typoed the question

I think they wanted to ask about average of a,b,c,d versus b,c

[modern rock]

agreed

[molten forge]

Okay so I was not going mad

[molten forge]

Yup I think so too now, thank you

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[rain sluice]

How do I do this

[ruby mural]

! status

[topaz sinew]

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

[ruby mural]

Get the trig terms on one side and a and b on the other

[rain sluice]

a/b = tanA

[ruby mural]

Yes

[rain sluice]

what do I do now

[ruby mural]

Using tanA, you can find sin and cos

Use either trig identities or a right triangle

[rain sluice]

is tan not sin / cos?

[ruby mural]

It is

[ruby mural]

But you need to use either of these two to find the exact values of sin and cos

[thorny remnant]

form a right angled triangle

with the information of tanA

with that u get the valueof sin and cos

[rain sluice]

thx

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[thorny remnant]

!status

[topaz sinew]

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

[hexed quartz]

for second part i dont know wbere to start

[thorny remnant]

u meanq10?

[hexed quartz]

yes

[thorny remnant]

best method to do these qs is to get the feel of the first few terms

there is usaly a pattern to it

[hexed quartz]

for a=1
first term is 1

second = 0

third = -1

fourth = -1

fifth =0

sixrh and seventh =1

[bright musk]

notice that the previous matrix is always embedded in the lower right corner of the next matrix

and also only the first two cofactor expansions matter

[hexed quartz]

yes i saw it

how do i use it

[bright musk]

so the determinant is always
the previous determinant - second cofactor expansion

the second cofactor expansion (circled in red) is just the previous matrix but the first column replaced with [1, 0, 0, 0, ....]

[hexed quartz]

okay

[bright musk]

how does this affect the cofactor expansion

[hexed quartz]

it would be like 1x(previous matrix )

[bright musk]

remember cofactor expansion is recursive

the matrix with the first column all 0 is singular

[hexed quartz]

i get this

[bright musk]

so the second cofactor expansion is just the matrix twice before

[hexed quartz]

but i was looking for some pattern. i though doing stufflikd fhis wont help upto term 2017

[hexed quartz]

twice before?

[bright musk]

yes

notice how the second cofactor expansion of the 5x5 matrix is just the 3x3 matrix

cuz everything else is just 0

[hexed quartz]

okY

[bright musk]

so we end up with this simple formula:
this determinant = previous determinant - previous previous determinant
D1 = 1
D2 = 0
D3 = 0 - 1 = -1
D4 = -1 - 0 = -1
D5 = -1 - (-1) = 0
D6 = 0 - (-1) = 1
D7 = 1 - 0 = 1

u see?

[hexed quartz]

ohh

so d8 will be 0

Dn = D(n-1) - D(n-2)

[bright musk]

yes

D8 is 0

[hexed quartz]

so now how we calculate the summation?

[bright musk]

well lets continue the pattern some more

D1 = 1
D2 = 0
D3 = 0 - 1 = -1
D4 = -1 - 0 = -1
D5 = -1 - (-1) = 0
D6 = 0 - (-1) = 1
D7 = 1 - 0 = 1
D8 = 1 - 1 = 0
D9 = 0 - 1 = -1
D10 = -1 - 0 = -1
D11 = -1 - -1 = 0
D12 = 0 - -1 = 1
D13 = 1 - 0 = 1
...

1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, ...

pretty easy pattern

[hexed quartz]

i see pairs

[bright musk]

they need us to calculate absolte value of these

so all the minuses become positive

1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, ...

if we ignore the first entry, its just 0, 1, 1 repeated

so from 2 to 2017 its 0, 1, 1 repeated

[hexed quartz]

i get it. i assume the sum will be 1345

[bright musk]

something like that

yeah

[hexed quartz]

1+(2/3*2016)

[bright musk]

it will be almost 2/3 of 2017

yeah

[hexed quartz]

thanks

u helped a lot

[bright musk]

do u have answer key?

i wanna see if i got it right

[hexed quartz]

no.

[bright musk]

well

best of luck

[hexed quartz]

i'll ask my group to check

thanks

how do i close?

.close

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[gleaming drum]

how do I indicate if a matrix is complete and if it contains a bridge

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[misty arch]

A biased coin is tossed 10 times. The results are 7 heads and 3 tails. Given these results, what is the probability that the coin is biased towards showing heads 80% of the time?

[misty arch]

<@&286206848099549185>

[vocal willow]

maybe word question so i dont have a stroke

[thorny remnant]

Don't ping if it's with in 15 min of posting the question

[misty arch]

sorry

[thorny remnant]

Np

[misty arch]

that is the best my english can do

[floral cloak]

why is the coin biased😭

[thorny remnant]

Use binomial distribution

[vocal willow]

^^^

yeah thats the only way i can think of?

[thorny remnant]

Let p=4/5

[long stirrup]

this can't be solved

[thorny remnant]

Why?

It can be solved

[misty arch]

so if biased coin's odds are 80% heads and it came up heads 7 times out of 10 . 10C7 (8/10)^7 (2/10)^3 this would give me how probabal is 7 times is out of ten can i do reverse and make it like 10C7 (x)^7 (1-x)^3 = 8/10?

[thorny remnant]

Nah ur method is right but executions is wrong

Simplify 8/10 and 2/10

Then slove it

[misty arch]

would this be correct?

≈20%

[topaz sinew]

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[thorny remnant]

Yes the value of y at x= 0.8 will be the answer

[misty arch]

thanks for help <3

.close

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[neon iron]

need some help

[neon iron]

if u = 2 + cotx

and du = -cosecx dx

-du would = cosecx dx right

[lunar tartan]

yo gang

ill help u

if u help me

[neon iron]

so if we applied this to cosec^2x / (2 + cotx)^3

nah help me rq lil gng

[lunar tartan]

im doing a twst

i need ur help

[neon iron]

what is it

[lunar tartan]

u dont understand

geomotry

😭

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

[plush tulip]

also don't cheat

[lunar tartan]

Ok

It was a joke

[neon iron]

ok can someone help me please

[lunar tartan]

Bro so u wont helpnme

Bruh

[neon iron]

i will

but you're not saying what it is

[lunar tartan]

Oh bet

Check dms

[neon iron]

ok

[lunar tartan]

Just a study guide fr

[prisma mesa]

cosec^2

[neon iron]

if u = 2 + cotx
and du = -cosecx dx
-du would = cosecx dx right

so if we applied this to cosec^2x / (2 + cotx)^3

what?

wtf is that

[prisma mesa]

what's the derivative of cotx?

[neon iron]

-cosecx

[prisma mesa]

You sure?

it's not

[neon iron]

💀 yeah just realized

im legally blind

[prisma mesa]

and if you do it properly, everything should cancel out nicely

almost everything

every trig term

[neon iron]

wait no

i was using cosec^2x

in my work

But I was getting an issue at the end

[prisma mesa]

What issue

[neon iron]

i was div by -2

and getting something else

[prisma mesa]

Why dividing by -2

[neon iron]

because -3 + 1 = -2

[prisma mesa]

hmm

[neon iron]

ill send a pic

[prisma mesa]

alright, that will be better

[neon iron]

if I have -1

in the u sub

when i integrate it's - u right

[prisma mesa]

What do you mean

du = - cosec^2(x) dx

so dx = -du/cosec^2(x)

[neon iron]

wait

can I not just do

-du = cosec^2x

but you still shouldn't get - a fucking half u^-2

this thing is pissing me off

[prisma mesa]

Sure you can

[prisma mesa]

why not?

[neon iron]

because you need to get 1/2(2+cotx)^-2 + c

not -1/2

i keep getting -1/2 im gonna break sometyhing

[prisma mesa]

After the substitution, you should get integral of

-1/u^3, then integrating this you should get 1/(2u^2)

I think this might be where you screwed up

integral of -1/u^3 is 1/(2u^2)

ill actually retype it in latex to make it more clear

if you need it

[thorny flame]

MethIsAlwaysRight

[prisma mesa]

@neon iron

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

bro

it should be fine the other way too

right

like

[prisma mesa]

anything that lead you to the correct result should be probably fine

[neon iron]

bro

its not -

where did you get

-1/u^3 from

oh wait

ur doing it liek that

ok so i was right the entire time from the start im actually so dumb

ok nvm

all I had to do was multiply by -1

💀

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[dense shore]

how to prove $\frac{\sec^3 x}{\tan^4 x} = \frac{\cos x}{\sin^4 x}$?

[thorny flame]

babario

[dense shore]

ah shit right

fk im stupid

.close

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[wintry hare]

https://discord.com/channels/268882317391429632/1021175428326633542

[wooden moon]

What is your question? Post it here.

[wintry hare]

I need to find a function f that satisfies the conditions in the image, and then "wrap it around the origin" as seem in this graph: https://www.desmos.com/calculator/wzuoowgndw for 12 periods

[topaz sinew]

@wintry hare Has your question been resolved?

[wintry hare]

<@&286206848099549185>

[topaz sinew]

@wintry hare Has your question been resolved?

[wintry hare]

<@&286206848099549185>

[wintry hare]

? hm

[bitter parcel]

Here is the updated plot showing the function ( f(x) ) with the specified values at each interval. The discrete points illustrate the function's behavior as defined in the provided conditions.

[thorny flame]

Eliana Cuomo

[wintry hare]

can it be a continuous and differentiable function as well?

maybe some type of fourier analysis

[bitter parcel]

To construct a continuous and differentiable function that approximates the given values, we can use a piecewise-defined function or smooth approximations like spline interpolation. Here, we will use spline interpolation to create a continuous and differentiable function.

[wintry hare]

are these chatgpt responses kek

[bitter parcel]

a continuous and differentiable function that approximates the given points using spline interpolation. The red dots represent the original points provided, and the smooth curve fits through these points while ensuring the function is continuous and differentiable.

[wintry hare]

can it not be piecewise nor a spline? preferably it should be a "nice" function like a sine wave sum

[bitter parcel]

Fourier series approx?

[wintry hare]

probably yeah

[wintry hare]

that fits exactly doesn't it?

what's the equation for that

https://chatgpt.com/share/908d6446-acfe-4d30-b20a-afd4b4079c8e here's what chatgpt says

<@&286206848099549185>

[bitter parcel]

Same u were questioning

[bitter parcel]

I can’t open chatgpt

[wintry hare]

which one again?

[bitter parcel]

Was this

[wintry hare]

can you extend that definition to the reals?

like the factorial is to the riemann zeta yk

define it in a way that has a defined value for all reals not just natural numbers

@bitter parcel any ideas?

[wintry hare]

maybe this could be one of the waves

it's satisfies the first condition f(n)=0

hm what's a wave that satisfies f(n+1/5)=1/4

<@&286206848099549185>

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[hardy vector]

https://youtu.be/HUnaZYkRZes?si=ObazGHA-eG295ScO

[hardy vector]

Why is there no work being done in this pulley system?

I thought the conservation of energy states that all non conservative forces do work

And tension is non conservative

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[sullen river]

!help

[topaz sinew]

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[sullen river]

i dont understand

where did they get the numbers

so the denominator is 1 + 5 for both cases x and y

where did they get 1 + 5 from

is it point A (1, 5)?

then for the top case x-coordinate they did 1 * -5 + 5 * 1

or is the denominator from the ratio

[cedar wagon]

ima try

[sullen river]

ah

i understand yakubros

[cedar wagon]

the hardest is from the substitution

[sullen river]

no

i get the formula

i dont understand the ratio tho

[cedar wagon]

this representation of the ratio would be more logical

[sullen river]

i see

so what is the ratio of this

is it 2:3

also

which one are your x1 x2 y1 y2

is the point c (x1, y1) is point a (x2, y2)

or is it vice versa

how are you suppose to tell

[cedar wagon]

in this one the vector is AC so the first coordonates are A(x1 ; y1) and second C( x2 ; y2) because you're calculating the ratio of AB to AC so the first one is A

[cedar wagon]

they want you to say where is the point B such as 3AB = AC

they give ya the ratio

[sullen river]

yes

they say the ratio is 1 : 3

but its always wrong

they give some ratio but thats not the actual ratio you take in for the calculation

its some other number

if it said it was 6 times as long that means the ratio is 1 : 5

not 6 : 1

so is the ratio 2 : 3

so is A(x1, y1) because its on top of the grid

its like on a higher y value than c

[cedar wagon]

no it's about the direction of the vector

going from A to C

[sullen river]

s

so

it goes from AB to AC

because AC is in the second position its (x1, y1)

is that what yore saying

right there

im gonna ask the ai

[cedar wagon]

when i talk about position, it's about coodinates of the points that composed the vectors not the coordinates of the vectors himself which are really different

[sullen river]

idk what vectors are sorry

ok

so the ratio was 1 : 2

you know how it says its 1 : 3 but apparently ur suppose to use 1 : 2 for the calculation

[cedar wagon]

in fact you'll have to use this reasonnement but the ratio is given so you don't have to substitute m and n

[sullen river]

well

the ratio is wrong

the problem always tells you that the ratio is like 2 : 3 for example but in reality your suppose to use 1 : 3 to calculate

[cedar wagon]

okay and then you multiply it by 2 or smthing ?

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[royal sky]

hello, i reached x (lnn+5)/ln((x+1)+5)) after ratio test and i am stuck

what does (lnn+5)/ln((x+1)+5)) beocme when n ---inf

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[sullen river]

wtf

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[desert pulsar]

How do I solve pls?

[desert pulsar]

Past question

[topaz sinew]

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

[desert pulsar]

I don’t know where to begin

[chilly walrus]

hint: angle BOD is twice of angle BAD

[desert pulsar]

So value of t is 2y?

[chilly walrus]

i haven't solved the problem completely so idk

but all i am saying is that BOD is 2t

[desert pulsar]

Yeah I saw that out

But I’m so lost

I’d like to see your solution

[topaz sinew]

@desert pulsar Has your question been resolved?

[desert pulsar]

@chilly walrus any luck?

[chilly walrus]

ooh, i got it

[chilly walrus]

construct a segment OC. then, OB=OC=r because it's a circle and BC=OB because it's a rhombus

hence, OBC is an equilateral triangle

hence, BOC is 60 degrees

same argument applies to triangle ODC

[desert pulsar]

Wdym construct a segment OC?

[chilly walrus]

so, BOD = BOC + DOC = 60 + 60 = 120 degrees

[chilly walrus]

just like do this

[chilly walrus]

hence, t is 120/2 = 60 degrees

which is the answer

the y was a distraction it seems

[desert pulsar]

OHHH

[chilly walrus]

y is ||30 degrees|| if you are curious

[chilly walrus]

yep

[desert pulsar]

Let me put this down

To fully understand

[chilly walrus]

it took me much longer than it should've lol

[desert pulsar]

Perhaps you know this too? @chilly walrus

[chilly walrus]

i do know this!

consider triangle OTQ. it is isosceles because OT = OQ

because it's isosceles, angle OTQ = OQT

recall that the sum of all angles in a triangle is 180 degrees

try solving for OQT now yourself

[desert pulsar]

62°

[chilly walrus]

correct

[desert pulsar]

Is it 90-62° now?

For TQP

[chilly walrus]

yep

[desert pulsar]

Woah

How’d I do that

[chilly walrus]

crazy right

[desert pulsar]

Not too sure about QTS tho

Any idea?

[chilly walrus]

am thinking

oh got it

[chilly walrus]

first, notice that SVT = OVQ

wait

nvm

forget that

[desert pulsar]

Oh

[chilly walrus]

see we have OTQ = 62 but i am not sure how to get OTS

[chilly walrus]

i think i got it

[chilly walrus]

this thought was correct

SVT = OVQ

[chilly walrus]

we can find OQV=180-56-109=15

again, draw OS

OSQ is isosceles

[desert pulsar]

Ohhh

[chilly walrus]

thus angle OSQ is also 15

[desert pulsar]

I’m lost here

[chilly walrus]

forget the OQS part, that wasn't relevant

[desert pulsar]

Why was 109 included?

[chilly walrus]

SVT and OVQ are congruent

so OVQ=SVT=109

[desert pulsar]

Ohh

So QTS is 86°

[chilly walrus]

wait how

[desert pulsar]

OQT = 62°

OQV = 15°

Subtracting

47

Then isn’t the other triangle isosceles

[chilly walrus]

the thing is

i don't think so

if it was isosceles the 109 angle would've been a 90 angle

so you can't really make a symmetry argument here

[chilly walrus]

having this

[chilly walrus]

i found this

[chilly walrus]

so we have that SVO is 180-109 = 71
so VOS is 180-71-15 = 94
so SOQ is 94+56 = 150

[chilly walrus]

and i don't know if you guys cover this theorem but QTS = 180-(SOQ/2)

so we get 180-150/2 = 105

[desert pulsar]

Never heard of that before

[chilly walrus]

which is the answer

[chilly walrus]

https://www.youtube.com/watch?v=53ueXQa8OEM

[desert pulsar]

Oh damn

Wait lemme look at this again

But

I appreciate your help really

You made it easy to understand

[chilly walrus]

thank you

i gtg now

glad i helped

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[uneven pagoda]

F is integrable on [a, b] implies that $\exist \lim_{n \to \infty} \sum_{i=1}^{n} f(x_{i}^{}) \Delta x \forall x_{i}^{} \in [x_{i-1}, x_{i}$, then does limit has to be all the same regardless what $x_{i}^{*}$ I've picked?

[uneven pagoda]

oh i mean [0, 1]

f is integrable on [0, 1] implies that $\exists \lim_{n \to \infty} \sum_{i=1}^{n} f(x{i}^{}) \Delta x \ \forall x_{i}^{} \in [x_{i-1}, x_{i}]$, then does limit has to be all the same regardless what $x_{i}^{*}$ I've picked?

[thorny flame]

io

[uneven pagoda]

.close

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[spare coral]

Hello, I am in trigonometry. Trig Graphing and Solving Unit. I am having trouble converting Sine equations into Cosine equations. We are not aloud calculators.

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[silver ridge]

Could someone help me find out the line of best fit using a number chart ? There are specific questions i could help on

[wary tulip]

[silver ridge]

alright

ill ping u when im done writing the question

The number of entrants in the Boston Marathon was recorded every 5 years since 1975. Use the line of best fir to predict the number of entrants in 2012

gonna post the chart now

Year: (1975,1980,1985,1990,2000,2005)

Entrants:(2395,5417,5594,9412,9416,17813,20453)

@wary tulip

[wary tulip]

and what does line of best fit mean here? least squares stuff?

[silver ridge]

I honestly dont know, the way they teach it is so complicated. what would it be in gr 9 ?

[wary tulip]

actually doing least squares stuff is beyond grade 9

but that’s what a “best fit calculator” does for example

[silver ridge]

soo

ig im not in luck

[wary tulip]

i’m not really sure what the question is looking for

[silver ridge]

Idk,ill ask schoolmates and find out, ill tell u if i do find out

thx tho

[wary tulip]

that’s ok i don’t care that much

[loud oasis]

they might just expect you to use a regression calculator

[topaz sinew]

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[mint stream]

can someone explain why you don't have to do 2 integrals from 1 to 2 and 2 to 3, subtracting the smaller function from the bigger one?

https://imgur.com/CNnWOWt

[mint stream]

this absolute value thing is how i thought the whole area under curve thing would work

but then it didnt work sometimes...

for example in this question

https://i.imgur.com/cu3Y1bn.png

here we integrate with respect to y but my question is the same

why isnt it valid to take the absolute value of the difference of the 2 functions in this case

but it is in the other one

oh wait no it is the same

just gotta not make a sign error taking abs value integral lol

.close

[topaz sinew]

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[wraith ruin]

Hi, I'm new here

[wraith ruin]

Heres my question:

I need to find a equation for this, which I came u with y^2=28x

Then I need to check if the height of the roof is at least 6m above the pool at all points, since the pool is 18m, each side is 9m from the origin, so I substitued y (which is width as i am using y^2=4ax) for 9. so 9^2=28x which =2.89, so it's less than 6m at the end points, is this correct so far?

then after that, I needed to come up with a new equation where it is at least 6m above the pool surface at all times, I came up with y^2=12x, substituting 9 again I got 6.75m, so it does meet the criteria now. But is this correct?

Thanks

<@&286206848099549185> thank you

Thank you

Does anyone have any idea?

[obsidian canyon]

I'm gonna try using vertex form

[topaz sinew]

@wraith ruin Has your question been resolved?

[wraith ruin]

NO

[obsidian canyon]

with the focus the form is (x-h)^2 = 4(-p)(y-k)

so this one comes out to x^2 = 4*(-7)(y-8.5)

do a little alebra here for a sec...

[wraith ruin]

np

[obsidian canyon]

For the original shape I'm getting x^2 = -28(y-8.5)

so y = -(1/28)x^2 + 8.5

Which at x = 9 is just under 6

[wraith ruin]

at x=9 I got 2.89

hm

[obsidian canyon]

You might be grabbing the wrong pieces for your inputs. Because your equation is kind of close. You got the 28x. But it should be 1/28x^2. Are you maybe directly inputting values into x and y?

[topaz sinew]

@wraith ruin Has your question been resolved?

[wraith ruin]

My equation is correct I checked with the teacher

I'm not sure about the rest

[topaz sinew]

@wraith ruin Has your question been resolved?

[obsidian canyon]

I see it now. You and I are just flipped horiz-vert so your equation is good.

I figure as long as your other equation meets the height requirement it should be good right?

[topaz sinew]

@wraith ruin Has your question been resolved?

[topaz sinew]

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[noble marsh]

What is happening here..?

[noble marsh]

I don't understand what's going on

[fiery badge]

Neeeeemmm

What part do you not understand?

Let's call the first limit L

L would be equal to e^ln(L)

so they computed ln(L)

Which came out to be 0

and then plugged it into L = e^ln(L)

which then makes

L = e^0 = 1

[noble marsh]

Why do we take the ln of this limit in the first place?

[fiery badge]

To solve it more easily

since we have that pesky 1/x in the exponent

err 1/n

by taking the ln we pull it out of the exponent

and then we L'Hospital it

[noble marsh]

Wait is there a rule like that?

you can remove the exponent by taking the ln?

[fiery badge]

ln(a^b) = b * ln(a)

ye

works for all logs, not just ln

[noble marsh]

Ooooh

[fiery badge]

but ln is convenient

[noble marsh]

I wouldn't have come up with that in the exams ngl

[fiery badge]

The whole point of why logs were invented was to handle exponents lol

[noble marsh]

so if i see exponents similar to this one in a p series excercise then i should consider taking the ln of it?

[fiery badge]

It's worth giving it a shot for sure

Doesn't always work, sometimes it makes things more complicated

But sometimes it works out nicely

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[noble marsh]

.close

[topaz sinew]

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[manic frigate]

I need help

[fiery badge]

,rcw

[manic frigate]

?

[fiery badge]

Wait, so you need to calculate e^-2 without a calculator to 4 digits?

[manic frigate]

I think so

[fiery badge]

Cursed, I'm fairly sure there's an algorithm for this, but it's still cursed

[manic frigate]

Oh can u recommend something I can learn about this

[fiery badge]

You must have learned it in your lessons if your teacher is asking for this

[glacial adder]

the way that i would do it probably wouldn’t fit in here

def should look back at your notes to see how your teacher does it

[manic frigate]

Ok bet

[topaz sinew]

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[late crypt]

Idk how to start

[torpid sparrow]

Can you rewrite in a format rhat can be read?

@late crypt

[craggy haven]

,rccw

[craggy haven]

partial fraction decomposition to start

[torpid sparrow]

Long division

Is not y^3?

[fiery badge]

no

just split it with ABC shenanigans

you know that?

[torpid sparrow]

Oh ok then yes, i thought it was y^3

[fiery badge]

Also take out -1 from the bottom fraction to simplify

those minuses will come back to haunt you

[late crypt]

Uhm

(Y-3)/((-y²-2y-2)(y-1))

[late crypt]

How can I use abc with this tho

[torpid sparrow]

Rewrite denom as -(y^2+2y+2)(y-1)

And take out - out of the integral

[late crypt]

K

[fiery badge]

Yeah, then to the ABC shenanigans

[late crypt]

Can u show please

[fiery badge]

https://www.mathcentre.ac.uk/resources/uploaded/mc-ty-partialfractions-2009-1.pdf

Like so

As an example

[late crypt]

Ok I try

[fiery badge]

I call this ABC shenanigans

but it's called partial fractions

[late crypt]

Ninjutsu yeah

[torpid sparrow]

Remember doing it with your original question

[late crypt]

Wdym

[torpid sparrow]

This was an example

[late crypt]

B=5

A=-1/3

C=1/3

[torpid sparrow]

Are u solving in your integral?

[late crypt]

Yes

[torpid sparrow]

Then show your work to say where did u make a mistake

[late crypt]

I made a mister?

Mistake

[torpid sparrow]

Yes