help-39

[stiff mauve]

i got it

.close

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[short orchid]

Guys, is the yellow highlighted integral supposed to represent the yellow coloured triangle in the graph?

[cobalt hinge]

Yes.

[short orchid]

but the yellow triangle is outside the curve, it is still possible to use the curve’s integral to find the area of that triangle?

even though its not within the curve

[cobalt hinge]

It is the subtracted area.

It is not exactly a triangle.

[short orchid]

uhmm

[short orchid]

i was wondering if the integration of the curve can be used to find the area outside the curve

[short orchid]

this solution is using equation of the curve to find area of yellow (which is outside the curve) right?

[cobalt hinge]

Yes.

[short orchid]

okaayy thank youuu

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[short orchid]

.reopen

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✅

[short orchid]

Wait so what’s the answer to this

[pearl pond]

@short orchid Has your question been resolved?

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[young orbit]

hey

[young orbit]

I need help on this

I rationalized bottom

but I didnt get correct answer

got 0

and answer is -3

[golden bramble]

show your work

[young orbit]

k

one sec

here

[golden bramble]

rearrange your numerator, try factoring some stuff out

[young orbit]

k

figured it out

.close

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[lusty galleon]

Ive been really confused on how to solve this one. I’m pretty sure my approach (using differentiation of some sort - I tried implicit) is the right one.

[pearl pond]

@lusty galleon Has your question been resolved?

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@lusty galleon Has your question been resolved?

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[burnt skiff]

can anybody help me simplify this ?

[fierce totem]

substitute x = 5^(2n) + 5^n

that should make it easier to manage

[burnt skiff]

i substituted 5^(2n) with x

i will try this way too

ok, that works much better

i complicated it too much in the first place

thank you

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[mild yarrow]

can anybody help me with a basic math concept

[mild yarrow]

so IDK I got stuck with a basic concept , like -7/-2 will be 7/2 and further if we calculate we will get quotient 3 and remainder as 1 , so by division method it will be like this 7 = 2x3 +1 , as both are same so , -7 should be equal to -2 x3 + 1 which is ofc not , I might be dumb here , or u dint get the question

[wheat elbow]

why should -7 equal -2 x 3 + 1?

[pearl pond]

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[lunar cliff]

I do not get this question

[mild yarrow]

Like it's so hard for me to explain 😭

[pearl pond]

@lunar cliff Has your question been resolved?

[lunar cliff]

<@&286206848099549185>

[hard fjord]

It is said that the cost is a linear function of time

[plush schooner]

So plumber A asks 140 dollars for 1 hour (which includes a one-time fee and the fee for 1 hour), for 4 hours, he asks 320 dollars (which includes a one-time fee and 4 times the hourly fee)

the difference in price is thus 3 times the hourly fee

So 320 - 140 = 180 = 3 times the fee

so the hourly fee is 60 dollars

[hard fjord]

For Quality Plumbing you can just read the slope and the one time fee.
For the other you can calculate the slope as (y_2-y_1)/x_2-x_1

[plush schooner]

And if you know that the hourly fee is 60 dollars, while the cost for 1 full hour is 140, then you know that the one-time fee is 140 - 60 = 80 dollars @lunar cliff

[lunar cliff]

oh

I get it now

Thank you

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[lunar cliff]

.reopen

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✅

[lunar cliff]

wait i still need help

never mind

I finished

.close

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[prime hill]

How do I answer number 2

which has the higher acceleration

[merry carbon]

,rccw

[merry carbon]

You basically have, "no, [the car] has the higher acceleration"

[pearl pond]

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[ebon belfry]

Hi, i want to understand the rightmost equality, i understand that the union of Bn and An are equal and since the Bn are disjoint we can use the definition of the probability of a union of Bn to say it's equal to the sum of the probabilities of Bn.
But not how both limits are equals

[ebon belfry]

It's the proof for

[pearl pond]

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[pearl pond]

@ebon belfry Has your question been resolved?

[ebon belfry]

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[stiff mauve]

1b

[stiff mauve]

im having troubles finding the second derivative of f(x,y) for my jachobi matrix

if i take the derivative with respect to y

but y is in absolute values so y is not differentiable no?

[pearl pond]

@stiff mauve Has your question been resolved?

[plush bramble]

Only when y=1

[stiff mauve]

How to differentiate it if y is not 1

[pearl pond]

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[edgy latch]

Translate: Given 3 positive real numbers a, b, c different from 1. The graph of the function y=log a(x), y = b^x, y=c^x is given in the figure below. Compare a b and c

[edgy latch]

I know that c is the smallest cuz the figure going down but both b and a are > 1 how do i compare b and a

[pearl pond]

@edgy latch Has your question been resolved?

[fierce totem]

quan sát log(a,x)

hàm nghịch biến thì a thế nào

[edgy latch]

0<a<1

[fierce totem]

à từ từ

hàm này đồng biến chứ

[edgy latch]

uk 2 hàm đồng biến

[fierce totem]

có mỗi c^x nghịch thôi dk

[edgy latch]

đugns r

[fierce totem]

thế là c<1

[edgy latch]

yes

có 2 cái kia đều đb nhưng 1 cái là mũ x 1 cái là log nên đang ko bt so sánh kiểu gì

[fierce totem]

còn b^x và log(a,x) thì ông sẽ vẽ đường y=b

[edgy latch]

rồi sao nữa v

[fierce totem]

từ từ

a^b > 1 chắc k cho đc cái j

bạn có thể vẽ thêm hàm log(b,x)

chắc là sẽ đc

hàm này đối xứng với y=b^x qua đường y=x

[edgy latch]

bên yt có mấy thầy làm cx được nma

hình của bài kiểu nó rõ ràng ra 1 2 3 với cả đồ thị xa nhau nên biết đc

chứ bài này của tôi nó hình đối xứng quá khó biết cnao lớn hơn

[fierce totem]

ủa

đáp án là C hay D

sao t vẽ ra C

[pearl pond]

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[fierce totem]

.reopen

[pearl pond]

✅

[fierce totem]

@edgy latch

[edgy latch]

ra D á

[fierce totem]

tf

[edgy latch]

hỏi cô cô bảo như này 😭

[fierce totem]

rõ ràng là C

b khoảng 3 còn a mới có hơn 2

[edgy latch]

chịuuuu

sáng cô tớ tính ra D

[fierce totem]

bảo cô check lại kĩ đi

[edgy latch]

uk tớ vẽ cx ra c là s nhỉ

[fierce totem]

là cô sai =))

[edgy latch]

=))

khả năng c r

vẽ nó to hơn 1 tí

[fierce totem]

đó

[silent trellis]

adma help

[fierce totem]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[edgy latch]

ok cảm ơn bro nhé

.close

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[calm wing]

this is the wikipedia article for Borel hierarchy

why is there a union and a substet if we have that a set is in delta iff it is in both sigma and pi

OH i didn't see the index

so from what i gathered, these two hold:
$$\mathbf{\Sigma}{\alpha}^{0} \cap \mathbf{\Pi}{\alpha}^{0} = \mathbf{\Delta}{\alpha}^{0}$$
and
$$\mathbf{\Sigma}{\alpha}^{0} \cup \mathbf{\Pi}{\alpha}^{0} \subseteq \mathbf{\Delta}{\alpha+1}^{0}$$

[jolly parrot]

artemetra

[calm wing]

is this correct?

[plush bramble]

maybe try #foundations

[calm wing]

ok

[calm wing]

yes #foundations message

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[split pulsar]

how do i calculate the end point of a object following a ballistic trajectory based on the angle we launch it at

[bitter lodge]

!original

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[warm copper]

Seems like a physics question but first off we'd have to know the force, and gravity

And air resistance if you take in that

[split pulsar]

there isnt an original problem just something that came to mind

[bitter lodge]

oh then nvm

[toxic lichen]

do you know ONLY the initial launch angle and NOTHING else?

[split pulsar]

earth gravity

[split pulsar]

i mean we could give an example

i just want to know how you would calculate it

[crystal lion]

Oh so thats why the solution is not pretty.

[toxic lichen]

you would need the initial velocity and position in order to calculate its path fully

for position, i suppose just the initial height off the ground would suffice

[split pulsar]

lets say it starts off at 0,0

[brave sluice]

use trig functions to get the initial vertical velocity

then v(t)=v_0-gt

for vertical velocity

integrate to get vertical position

[toxic lichen]

do not drop the brackets

[split pulsar]

🥺

sorry

[warm copper]

[split pulsar]

and what about horizontal

[brave sluice]

you can use another trig function

[split pulsar]

what would that be

[warm copper]

horizontal ie cos

[brave sluice]

initial vertical velocity is s*sin(theta) where v is the initial speed

[split pulsar]

lets say something launched from (0,0) at 9m/s at 60 degrees with 9.81 gravity

[brave sluice]

then initial vertical velocity is 9*sin(60)

[split pulsar]

ok

[split pulsar]

m/s?

[brave sluice]

yes

[split pulsar]

ok then we calculate how much time till it hits the ground

[brave sluice]

v(t)=v0-gt

y(t)=v0*t-gt^2 / 2

set to 0

[split pulsar]

yeah

[split pulsar]

why need that

[brave sluice]

only to derive y(t)

if you memorized y(t) you don't need it

[split pulsar]

yeah thats why i wondered

[split pulsar]

also Y0 but it dont matter because it starts at 0,0

[brave sluice]

y0

[split pulsar]

yeah mb

thx dude

.close

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[split pulsar]

wait but what is v0 here

[brave sluice]

s*sin(theta)

initial vertical velocity

[split pulsar]

not cos?

[brave sluice]

no

[split pulsar]

so whats the horizontal velocity

[brave sluice]

s*cos(theta)

[split pulsar]

oh ok

[brave sluice]

so once you solve for t, the answer will be st*cos(theta)

[split pulsar]

ill keep the room open cuz i might have more questions

[split pulsar]

yeah ik

[brave sluice]

@split pulsar i assumed theta is measured from the ground

[split pulsar]

yeah ofc

[split pulsar]

hey is it -sin(2theta)*v0^2/g

the final position

[brave sluice]

you should have a sqrt

sqrt is needed to solve the quadratic for t

and it doesn't simplify

[split pulsar]

how so

[split pulsar]

only 1 real answer

its 2

but t isnt 0

[brave sluice]

yeah there are two solutions and you want to choose the larger of the two

[split pulsar]

i think this is right

check it

[brave sluice]

oh

oh because you have x0 = 0

[split pulsar]

yeah

so is it right?

[brave sluice]

s not v0

i mean

ok what is v0?

[split pulsar]

the initial velocity

[brave sluice]

why do you have a negative sign?

is g negative?

[split pulsar]

cuz the gravity is supposed to be negative

[split pulsar]

yeah

[brave sluice]

ok

looks right

[split pulsar]

could u make something like this with starting position of something that isnt launched from (0,0)?

[brave sluice]

yes

[split pulsar]

you know what it is

[brave sluice]

https://www.desmos.com/calculator/u1mpmok3yk

[split pulsar]

thx

[brave sluice]

you have y(t)=v0*sin(theta)*t - gt^2 / 2 + y0
now you can solve for t with the quadratic formula

oh i used positive g there

[split pulsar]

wait u made this?

[brave sluice]

yeah

[split pulsar]

oh nice dude

rn?

[brave sluice]

ye

[split pulsar]

you're fast

yeah i think i understood, thanks for the help🙏

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[tranquil badger]

yo im just gonna ask like

[tranquil badger]

is there a better method than synthetic division?

cuz like this is insane

i know how to do it yet every time somehow something goes wrong or i have to scan like 5 different roots just to get one answer and then if i get a difficult root there isnt even an answer and i have to do it all over again

and then that was just the first two answers

not the other 3

hate polynomials smh

[crystal lion]

Not really

[brave sluice]

it's not so easy to find roots

[crystal lion]

At least not a popular method.

You shoule know polynomial division though

[brave sluice]

the cubic formula is more complex than the quadratic formula

the quartic formula is nuts

[tranquil badger]

NAHHHH

[brave sluice]

and there is no quintic or higher formula

[tranquil badger]

yeah i heard they proved it was like impossible i think

[brave sluice]

yes

[tranquil badger]

curious if an AI could make a quintic formula as itself

shrug

[brave sluice]

[tranquil badger]

alr ty

.close

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[tranquil badger]

pro

[brave sluice]

wat

[tranquil badger]

that was all i needed i just wanted to ask what other methods existed lol

[brave sluice]

there's methods to approximate roots

[tranquil badger]

alr

[crystal lion]

Also RRT

[pearl pond]

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[stiff mauve]

Can anyone elaborate on 2a and d

[stiff mauve]

is it readable

[plush bramble]

use the definition of total derivative at (0, 1)

[stiff mauve]

yeah

[plush bramble]

oh you mean elaborate the answers

[stiff mauve]

i understand to this point

but

can we do

epsilon delta proof

let epsilon larger than zero

and the norm be smaller than delta

this part

is it possible to set this smaller or equal to | y-1|

[plush bramble]

do you know the norm of what has to be smaller than delta?

$\norm{?} < \delta$

[jolly parrot]

riemann

[stiff mauve]

yeh

the sqrt of x^2 + (y-1)^2

[plush bramble]

yes

[stiff mauve]

but like x divided by the norm is smaller than 1

cant we just make the equation smaller or equal to |y-1| because of that

[plush bramble]

uhhh can you write out what inequality you mean

[plush bramble]

if you think that's true you have to prove it

[stiff mauve]

is the inequality correct

@plush bramble

[plush bramble]

i don't see any work justifying the inequalities

sooooo no?

[stiff mauve]

@plush bramble and this?

[plush bramble]

yea that works

you filled in the steps to justify this sentence

[stiff mauve]

oh is that what it says

i have another question about how to draw the area of a double integral @plush bramble

if u got time?

[plush bramble]

you should just ask in a new channel

[stiff mauve]

✅

.close

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[quaint pilot]

idk where to start

[versed mica]

jump

[strange fox]

thats

agressive

[crystal lion]

Draw a function such that f(-1) = -3 (make it continuous)

[versed mica]

brother

no

[strange fox]

lmao

[versed mica]

thats not continuous lmao

[crystal lion]

Then just delete it at -1 and put a circle on 1

[plush moss]

It's not continuous

[versed mica]

this yes

but continuous is not the word you want

[crystal lion]

I mean if you make it continuous you gurantee that lim as x -> -1 f(x) = - 3

[strange fox]

its the easiest way to draw it

idk why you guys are being so difficult

the man is right

[quaint pilot]

thanks

[versed mica]

brother you dont know what continuous means

[strange fox]

brother he aint using continuous to say that it is continuous, hes describing how to draw it

he legit says to erase the point after

[crystal lion]

$$\lim_{x \to a} f(x) = f(a)$$

[versed mica]

yawn

[jolly parrot]

casework

[open rivet]

no need ot make it so difficult guys

[quaint pilot]

.close

[pearl pond]

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[hasty edge]

Just do anything

[quaint pilot]

only 2 people gave a actual respone

[hasty edge]

I mean, it's kind of a general question. You're not going to get a specific answer.

[versed mica]

you're welcome sir

[open rivet]

there are infinitely many answers

[brave sluice]

well, i agree with casework's answer
you can start with a continuous function and then just modify that one point

the missing point is represented by an open circle

[pearl pond]

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[robust sentinel]

Hello, don't know how to get started with this question

it's asking to evaluate the determinant

[shrewd mist]

cofactor expansion about the first column

[robust sentinel]

how would i do that?

[shrewd mist]

how would you do cofactor expansion?

[robust sentinel]

yeah

[shrewd mist]

https://math.libretexts.org/Bookshelves/Linear_Algebra/Linear_Algebra_with_Applications_(Nicholson)/03%3A_Determinants_and_Diagonalization/3.01%3A_The_Cofactor_Expansion

[cobalt hinge]

It's a nice problem.

You could use the good ol' determinant method where you just take the top row values and do the "cross" method.

[shrewd mist]

Once you do cofactor expansion, recall that the determinant of a diagonal matrix is the product of all the diagonal elements (which will help you get the determinant of the minor of M(n,1))

[robust sentinel]

does the ... mean the previous element is repeated until the next one?

[shrewd mist]

yup, so 0, 0, ..., 1 means that it's all zeroes (n-1 times) and then a 1 at the end

[robust sentinel]

so first column is all zeroes until the last 1

[shrewd mist]

yep, that's why cofactor expansion along it is a good idea

[robust sentinel]

ahhh i see

lemme try

is it (-1)^n+1

[shrewd mist]

yeo

[robust sentinel]

well that was tricky

[shrewd mist]

thats the cofactor (and the final answer, since the determiant of the minor is just 1)

[robust sentinel]

i wouldn't have thought of that ever lol

[shrewd mist]

it comes with experience

[robust sentinel]

so i had to notice first column only had zeroes except for a 1 and that the minor of a_n1 was the identity matrix

is that the pattern

[shrewd mist]

Yep. I first noticed the diagonal of 1s so I looked to see if there was a way to turn that into a minor.

[robust sentinel]

i mean looking back it kinda makes sense

[shrewd mist]

Yeah, it'll come naturally once you do a couple problems like it.

[robust sentinel]

anyway thanks for the help!

appreciate it 🙏

[shrewd mist]

The slight abstraction with the ... and n makes it scary at first glance

np

[robust sentinel]

yeah didn't notice that at first lol

.close

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[runic aspen]

Doing this problem through Strong Induction. Prof specifically told us not to use any identities in our solution and to solve it using purely Strong Induction. Not sure where to go from the inductive step, any ideas?

[pearl pond]

@runic aspen Has your question been resolved?

[runic aspen]

<@&286206848099549185>

[marble sigil]

it's not going to be a usual induction style argument. see how you can multiply things by 13^2 and still have square numbers

[runic aspen]

yeah so i tried doing this

thought i was on to something

but just confused now lol

how would i resolve this

is my approach just entirely wrong

[marble sigil]

that works, just might have to adjust the wording once you realize what's happening

that proves P(k+1) from P(k-1), so you're almost done, just need enough base cases

[runic aspen]

ah so the (13a) and (13b) don't even matter because they are really just representations of a and b

i was thinking i had to do something further algebraically

would the 2 base cases just be n = 1 and n = k-1?

[marble sigil]

the base case can't have k in it

[runic aspen]

n - 1 ?

[marble sigil]

can't have any variables

like you need enough starting dominos to get the ball rolling

[runic aspen]

ah

[marble sigil]

so like make sure you can reach P(3), P(4), and stuff

[runic aspen]

so enough base cases to make it where we can show it works for a n-1

[runic aspen]

could you explain this further

do you mean basically just have enough base cases to where we can show n and n-1 holds

since if i just have n = 1 as the base case we don't show a n - 1 could also work

[marble sigil]

uhh so here's 2 ways of looking at it

from the start: 1 can be used to prove 3 with the inductive step, then 5, 7 etc. but that's not all n
from the back: in the inductive step proof, maybe k-1 isn't valid yet, like if you used this tep on P(2), k-1 would be 0

[runic aspen]

ahh i think i understand

we need enough information to be able to use the inductive step for any n >= 1

so would the base cases be n =1, 2, and 3?

[marble sigil]

just 1 and 2 is fine

1 covers all odds and 2 covers all evens

[terse tartan]

13^(k+1) = (13^k) * (13). 13 = 3^2 + 2^2 and 13^k = a^2 + b^2 by the proposition. The product is (3a)^2 + (3b)^2 +(2b)^2 + (2a) ^2 = 9(13^k)+4(13^k) = 13*(13^k) = 13^(k+1). Its probably very stupid what I just did. IDK why I posted this.

[runic aspen]

i see

[runic aspen]

but is this a correct way of thinking about it?

[marble sigil]

yea

just trying to avoid out of bounds errors

[runic aspen]

gotcha

[runic aspen]

seems like a overly complex way to solve it compared to what i did lol

[terse tartan]

It's rather cyclic so I thought it was an invalid attempt.

[runic aspen]

this look correct?

anything i missed

[marble sigil]

just this

[runic aspen]

wait why would that be 2

oh because k-1 has to be inside the interval

[marble sigil]

yea you're doing everything besides the base cases in that

[runic aspen]

ok yeah that makes sense

thank you very much

i appreciate it

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[brave sluice]

Let $\phi:G\to B$ be a one-to-one map from a group $\langle G,\rangle$ to a binary structure $\langle B,'\rangle$, which satisfies the homomorphism property $\phi(ab)=\phi(a)'\phi(b)$ for all $a,b\in G$. Then $\phi$ carries all the structural properties required to be a group onto the image $\phi[G]$, and $G\simeq \phi[G]$

[jolly parrot]

Axe

[brave sluice]

does this make sense

this proves phi[G] is a group and G is isomorphic to phi[G]

[pearl pond]

@brave sluice Has your question been resolved?

[pearl pond]

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[muted iris]

Determine the equations of both lines that are tangent to the graph of
f(x) = x^2 and pass through point (1, - 3).

[muted iris]

im confused how to approach this

ik f'(x) = 2x

but what do i do with that info

[frail temple]

since you have the derivative, you know the slope of the tangent lines

at a specific point, say a, the slope of the tangent is 2a

you also have the y coordinate

f(a)

you have the slope and a point

you can write the equation in point slope form

[muted iris]

2 is the slope of the tangent lines?

how come tho?

[flint zenith]

since f'(x) is 2x

and the x coordinate of the point you're trying to find the tangent line for is 1

f'(1) =2(1)

it tells you the slope of the tangent line at that point

[carmine void]

Yeah

Derivative just finds slope so you plug it in

[frail temple]

what I did was find point slope with arbitrary point a and then I got a quadratic which I just solved for a

might not be the best way but I got two equations from it

[muted iris]

but doesnt this just give the slope at point x = 1 of the function x^2? how does that give us the slope of the tangent?

[carmine void]

Do you know point slope form

[muted iris]

sorry im a bit new to derivatives

[carmine void]

Slope at x=1

[frail temple]

that is the slope of the tangent

at that point

[carmine void]

Tangent lines have the same slope throughout

[frail temple]

i mean tangent to the function

it's not the same everywhere

[carmine void]

Yeah it is for tangents

[frail temple]

no like for x^2 the tangent slope at x=1 and x=2 is different

[carmine void]

Like the tangent to x=1 will always have a slope of 2

[frail temple]

yes ofc

[feral leaf]

The derivative of the function represents the slope of the tangent line at a specific point

[carmine void]

Oh yeah

I didn't know what you meant

[frail temple]

*slope of the tangent line of a function

[carmine void]

It's okay

[carmine void]

Both are right

[frail temple]

more specific cause wording

[carmine void]

Tangent line is parallel to the slope of the point

[carmine void]

Okay just clarifying for him

[frail temple]

ok so do you understand what a derivative is

[carmine void]

You use the point given and the slope you solved for to plug into point slope

[frail temple]

yes exactly what I did

[muted iris]

so the slope at x = 1 for the function x^2 is equal to the slope of any tangent to the function that passes through x = 1?

[carmine void]

I mean for him 😭

[frail temple]

ya ik

[carmine void]

Yes, the slope at the point is always the same

The check marks 😭😭

[frail temple]

😭😭

[carmine void]

Ohhh you meant like we did it similar I read it in a sassy way 😔

[frail temple]

sorry 😭😭😭

[carmine void]

@flint zenith came just to put an x

[frail temple]

fr

[carmine void]

No my fault 😭

[flint zenith]

damn right I did

[obsidian plume]

whats happening here

[frail temple]

wait @muted iris do you understand

[muted iris]

yeah, thank all u guys

i really appreciate it

.close

[pearl pond]

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[frail temple]

yeah ofc!!

[obsidian plume]

yea

i helped

so much

[frail temple]

@flint zenith get out 😭😭

[pearl pond]

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[midnight haven]

how do the side lengths get the values ​​of a and $$a\sqrt{2}$$? Can someone help?

[jolly parrot]

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

[plush bramble]

https://slideplayer.com/15261030/92/images/slide_1.jpg

have you learned this triangle yet

[midnight haven]

oh right 😅

[midnight haven]

I learned but I didn't take into account that it could be a 45-45 triangle. I was expecting an answer at a different point.

thx

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[night hearth]

Hello

[night hearth]

How come the value for both is the same?

[toxic lichen]

cos(360° - t) = cos(t)

for any t

[spiral pivot]

Because cosine is an even function, and also periodic with a period of 360 degrees

[night hearth]

Oh okay, so anything below 360 will be the same?

[toxic lichen]

wording...

if you look at the unit circle, going from angle t to angle 360°-t means flipping yourself around the x-axis. the x coordinate stays the same while the y coordinate flips (thus sin(360°-t) = -sin(t) )

[night hearth]

oh right

These terms are very complex

[night hearth]

What do you mean by "t"

[toxic lichen]

the angle

you can replace all of those t's with the letter theta if you want

which terms do you think are complex tho?

[night hearth]

Everything, im abit stupid lmfao

From what I understand, so everything under 360 will be the same

[toxic lichen]

"everything under 360 will be the same" is...

well it's either meaningless or nonsensical or maybe i simply do not understand what you're trying to say.

[wide maple]

Have u learned abt cast rule?

[night hearth]

cast rule?

[wide maple]

You should watch this to clear ur concept

https://youtu.be/0eVPl3Idjtk?si=tVjX4hNykK4IlJhY

[night hearth]

Oh yeah I know exact trig values, ill watch this though

[night hearth]

I use the soh cah toa method for finding the trig angles

[pearl pond]

@night hearth Has your question been resolved?

[night hearth]

OH right

Now I sort of understand it

Ill try to illustrate and post on here

So if I was for example told to find sin270

So something like this?

That I made on paint

Would it equal -1 ?

[wide maple]

Sin 270?

[wide maple]

Yes

[night hearth]

yeah as an example

Right now I get it

and the same process for the other

[wide maple]

I suggest u look into cast rule, complementary, and supplementary relation too.

But if u understand the graph then ur fine for now ig

[night hearth]

I'll have a look

[wide maple]

I like the videos made by Dennis Davis on yt

They’re good

[night hearth]

I'll have a look tonight

Thanks for the help

[pearl pond]

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[shy spindle]

sorry i am a bit reta rded atm

[shy spindle]

so Say that {an} is decreasing and all values are between 5 and 8. Explain why the sequence will have a limit and what can you say about the value of this limit

[spiral pivot]

please don't r-slur

It's bounded and monotonic

you should have a theorem about that

[shy spindle]

ye i did know that

but uhm

A sequence and series are something different right

for series if i am rigth lim n to inf Sn = sum n=1 to inf an?

[spiral pivot]

the theorem I'm talking about applies to sequences

yes they are different

[shy spindle]

or is this also for sequences ?

[spiral pivot]

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

sorry for being short, I need to go AFK to pick up my wife, she just called. 😦 sorry

[shy spindle]

no worries!

family first!

[midnight basalt]

dam

bro is deffo professor

[shy spindle]

💀

so this sequence will be between 5<={an}<=7?

[plush bramble]

it says 8 here?

not sure why you wrote 7

[shy spindle]

aaah mb 8

5<=an<=8

but my TA said it can be 5 but how tho?

since the limit will go to 5 right? so it will never be 5?

[plush bramble]

no that's not what limit means

[shy spindle]

Hm?

[plush bramble]

oh depends on the definition of decreasing

could be $a_n > a_{n+1}$ or $a_n \ge a_{n+1}$

[jolly parrot]

riemann

[shy spindle]

aaaah

[plush bramble]

does your book have a definition

[shy spindle]

this is not from my book

this is from my professor

[plush bramble]

then notes from your class

[shy spindle]

ill check rq!

aaah in this case it is an>=a{n+1}

if it is strictly decreasing it would be an> an+1

so since it is only decreasing it would be 5<=an<=8 and if it was strictly decreasing it would be 5<an<=8?

[plush bramble]

maybe. changing the assumption would change the entire problem

[shy spindle]

aaah okay

but notation wise?

would it make sense or really depends on the question?

[plush bramble]

yes depends on the question

[shy spindle]

aah okay

could you maybe help with something else too?

I must determine the value of c but I think I did something wrong since wolfram says it will diverge for my values of c

if anyone could look at this would be nice

[plush bramble]

show what wolfram output

[cobalt hinge]

You should just have $\frac{(1+c)^{-2}}{1-\frac{1}{1+c}}=2$

[jolly parrot]

;(

[cobalt hinge]

That is true

[shy spindle]

aaah shit

i wrote down the following : sum n=0 to inf x^(n-1) = 1/(1-x)

but now i have -n

wait let me retry again

[cobalt hinge]

Ok

I thought there was some weird assumption in your working

[shy spindle]

yup :-; sadly

[open rivet]

im back 🙂

[shy spindle]

welcome back

[open rivet]

whats the progress so far?

[shy spindle]

i am working on it ;-;

it is late and my smartness is decreasing

[open rivet]

still at the library?

[shy spindle]

this must be wrong

since it is not the same as 😭

[open rivet]

is this a different question than from the pin?

[shy spindle]

eh ye

[cobalt hinge]

Yes.

[open rivet]

aha

[cobalt hinge]

Here.

[open rivet]

ah, here

[cobalt hinge]

Okay. Mind if I teach you a nice trick?

[shy spindle]

i would love that

[cobalt hinge]

You really only need (for infinite geometric series) to calculate the first term, then just find the ratio (which is fairly obvious here), then apply the formula. No need to reindex, adjust bounds, etc.

[shy spindle]

huh

so first term will be 1/(1+c)

what do you mean with ratio?

[cobalt hinge]

First time meaning?

[cobalt hinge]

Common ratio.

[shy spindle]

sorry changed it

[cobalt hinge]

Like in $\sum_{n=1}^{\infty}\frac{1}{2^n}$, the ratio is $\frac12$ and the first term is $\frac12$

[jolly parrot]

;(

[cobalt hinge]

I simply plugged in n=1 to find the first term.

[shy spindle]

so the ratio is (1+c) and the first term is 1/(1+c)²

[cobalt hinge]

Wait, nevermind. You forgot something important.

[shy spindle]

or is the ratio 1/(1+c) since it is minus n?

[cobalt hinge]

I’m lagging a lot, give me a second

Yes

[shy spindle]

aaah okay

[open rivet]

$\sum_{n=2}^\infty\left(\frac1{1+c}\right)^n$

[jolly parrot]

Bonk

[cobalt hinge]

Yeah

[shy spindle]

alright

and now?

[cobalt hinge]

Use formula

[shy spindle]

1/(1-(1/(1+c)) * 1/(1+c)² ?

[thick sphinx]

idk how to latex but formula is :

[a(1-r^n)]/(1-r)

[open rivet]

$\frac1{(1+c)^2}\frac1{1-\frac1{1+c}}$

[jolly parrot]

Bonk

[open rivet]

is this what you wrote?

[shy spindle]

alright

yup

[cobalt hinge]

And multiply distribute blah blah blah

The boring algebra

[shy spindle]

alright thank you

good night/day guys

.close

[pearl pond]

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[modern patio]

Hello, I'm not looking for help with a specific question but more looking for guidance on how to approach and breakdown calculus questions as well as problem solving strategies, id be happy to send examples of questions that ive struggled with, I can always get the answers but its taking me about 3x as long as it should (given length of exams)

[lime crest]

!show

[pearl pond]

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

[modern patio]

right yeah sorryh 2 seconds just need to look throuigh my note book to actually find my attempts

[lime crest]

Nice

[modern patio]

I did actually get them ones in the end so ill get one that I just did that I couldnt get

[modern patio]

you can kinda tell im not going into it with much strategy

[versed mica]

why are you doing product rule

that’s a -

not a *

[modern patio]

omfg yeah

im a dumbass

[versed mica]

try again

[modern patio]

I shall

cant believe I dint immediatly spot that

Alright yeah that pretty much instantly solved the problem with that one

Anyway do you guys have any tips on breaking down problems like these, I tend to always panic and rush in a little (as much as I try not to) and then end up making idiotic mistakes like that, I know practice is the main thing that helps but got an exam on it next week and also a bunch of assignments due soon so don't have alot of time to spend on only calculus

[versed mica]

do more of them

and don’t look at solutions if you haven’t solved it

there is no shortcut really

[modern patio]

Yeah I did kinda assume that but thought it might be worth asking anyway

Just gotta lock tf in I suppose

Thanks for the help anyway

[versed mica]

you’re welcome

[modern patio]

.close

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[chrome niche]

this is a regular nonagon, i need to find angle KIH

[lime crest]

Do you have an idea of the answer, without really proving it ?

[chrome niche]

the answer is 45 degrees

but i have no idea how to get that answer

[lime crest]

If I were to be an octagon, yea it would be that, but there it is a nonagon

The angle shown being 45° is not KIH, it is AIJ

[chrome niche]

KIH is 45 degrees

[feral sedge]

no it isn't

[chrome niche]

how do you know?

[lime crest]

It's about the geometry of the nonagon, what is an inside angle of a nonagon ?

[chrome niche]

140 degrees

[lime crest]

Indeed, so if you have the line (KA)

[chrome niche]

you dont know if K,I and A lie on the same line

[lime crest]

Aaaah okay

[chrome niche]

😐

[chrome niche]

how do you know that it isn't 45 degrees?

[errant fable]

there's no practical solution without using reverse proving

not worth going a lot into it imo

[chrome niche]

but i still need help

@vast sluice

[feral sedge]

i don't know if K, I, A aren't collinear

ok it's not 45

and it's just angle chasing

write in every angle value you can find and you'll get it

[pearl pond]

@chrome niche Has your question been resolved?

[chrome niche]

it is

[feral sedge]

[chrome niche]

what

<@&286206848099549185>

[feral sedge]

i already told you how to solve this

[chrome niche]

i wont get it

[chrome niche]

<@&286206848099549185>

[unique summit]

why is there a red circle?

[chrome niche]

its a circumcircle

of GIJ

[dapper kraken]

how do you construct K exactly?

[unique summit]

and ur only given is the 140degree angel of the nonagon?

[dapper kraken]

whats J?

[unique summit]

is this given or they found it?

[chrome niche]

AIJ is 45 degrees

[unique summit]

yo i found sum

oh i think i can solve it

give me a second

[chrome niche]

i think you cannot

[unique summit]

dont underestimate my math frfr

[spiral pivot]

Has it been noted yet that IHF and IKF are related by the inscribed angle theorem? If not, you might be able to find it using that

[dapper kraken]

ABCDEFGHI is a regular nonagon, J is on AH such that AIJ=45, the circumcircle of G,I,J is constructed and extensionnof FH intersects the circumcircle at K, find KIH

is the problem something like this

[chrome niche]

yeah

[spiral pivot]

!original please

[pearl pond]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[chrome niche]

this is the original

[spiral pivot]

There is no text?

How do you know you need to find KIH?

[unique summit]

@chrome niche

did most of it

u can find the rest now

[chrome niche]

i can't find the rest

and this is wrong

[unique summit]

tis is not wrong but ok

[chrome niche]

because thats the problem

i dont know how to find KIH

[chrome niche]

IAJ = 20 and not 17.5

[unique summit]

if a nonagon has an ngle of 140 degrees then this is right

[unique summit]

oh i took it as 140 not 145

mb

[unique summit]

then i guess ill solve the rest too

[chrome niche]

KHI = 60 and not 47.5

[unique summit]

nah wait

ye ye

i took wrong angle

[chrome niche]

"dont underestimate my math frfr"

[unique summit]

bro

[spiral pivot]

How was that communicated to you?

[unique summit]

this is basic math i promise u

[chrome niche]

i got the screenshot

[unique summit]

now gimme 5 minutes

[chrome niche]

and i need to find KIH

[spiral pivot]

There's no reason to mock someone for making a mistake. We are not mocking you for not being able to answer this question.

[chrome niche]

it was just a joke, everyone makes mistakes

[unique summit]

is the 45 degrees given or u found it?

[chrome niche]

i found it using geogebra

[spiral pivot]

Anyway, just checking, are you familiar with the inscribed angle theorem.

[chrome niche]

i am

[ebon cloak]

use this theorem

[dapper kraken]

can you just write whats given and what you found

[chrome niche]

please if you find the solution just write it because i tried everything

and don't tell me to find any more angles

[spiral pivot]

Ok, so as adobo works, here is an outline for how to find this angle:

0. Find IHG (using regular nonogon)
1. Find IHJ, GHF, etc (they are all the same angle, isoceles angle, 180 degrees in triangle)
2. Using 0 and 1 find JHF
3. Using inscribed angle theorem find FKI
4. Using 1 and 2 find KHI
5. Using 180 degrees in triangle find KIH

Oh it renumbered on me

[chrome niche]

how to find FKI

[spiral pivot]

Using the inscribed angle theorem

[unique summit]

@chrome niche have u taken trigonometry?

[spiral pivot]

I thought you said you were familiar

[unique summit]

like cos and sin

[spiral pivot]

You don't need trig at all

[unique summit]

its alot easier with trig

[spiral pivot]

No it is not

[unique summit]

yeah u can find side lengths

[chrome niche]

yeah but i don't see the solution

[spiral pivot]

You really don't need to

[chrome niche]

can you show how to find FKI

[spiral pivot]

Hmmm, sorry, actually I was running under the assumption that H is the center of the circle

But on second glance it is probably not

[chrome niche]

its not that easy

[unique summit]

if u want angel K there is an easier way to get it

[chrome niche]

i tried everything

[spiral pivot]

This is probably the way

[unique summit]

this is where i reached rn

[chrome niche]

inscribed angles, symmetry, finding all the angles, algebra

and nothing

its been 9 days

[unique summit]

9 DAYS ON THIS OOOF

okay okay

do u know trig? cuz im more familiar with trig and would make soving easier (for me)

[chrome niche]

i do

[unique summit]

pak

peak

gimme 2 minutes

oh

we dont have a single side

nvm

[ebon cloak]

i think i found a solution

[chrome niche]

"dont underestimate my math frfr"

[chrome niche]

i think you didn't but we'll see

[unique summit]

😮‍💨 unless u finished all engineering math u cant underestimate my math frfr

[chrome niche]

yeah, its so advanced that none of us can understand it

[unique summit]

its because we know nothing about IJ

[chrome niche]

https://tenor.com/view/bh187-spongebob-patrick-star-derp-duh-gif-21500098

this is me

and everyone who looked at the problem and couldnt find the solution

[ebon cloak]

i think that is it

i used this

[unique summit]

K isnt 30

[ebon cloak]

what is the value of k

[unique summit]

here

[chrome niche]

its not 80

its 75

[ebon cloak]

wait

whats the angle that you want?

[chrome niche]

KIH

[unique summit]

?

how

[ebon cloak]

kih is 40?

[chrome niche]

because KIH is 45 degrees

so IKH is 75

[ebon cloak]

kih has to be 40

no?

[unique summit]

the nano is 140

suplementary is 180\

how did u get 45?

[ebon cloak]

bruh

[chrome niche]

K, I and A are not collinear

[unique summit]

oh

[ebon cloak]

?

[chrome niche]

K, I and A dont lie on the same line

the angle is not 180

so KIH is definitely not 40 degrees

[unique summit]

how did u find K

[crystal lion]

Didnt we already go through this problem?

[chrome niche]

your solution seemed wrong

like how did you get 65 degrees

from what

[crystal lion]

From cyclic quads

[chrome niche]

can you show

[chrome niche]

and how did you get 65

[crystal lion]

So IJXK is cyclic quad

So $\angle IKX = 180 - 65$

[jolly parrot]

casework

[unique summit]

H isnt the center

[crystal lion]

Why would it matter

A cyclic quad means a quad inscribed in a circle

[chrome niche]

how did you get 65 degrees

[crystal lion]

Also you have KXGI is a isosceles trapezoid

So you have $\angle KIG = 180 - \angle XKI$

[jolly parrot]

casework

[chrome niche]

but you dont know XKI

[crystal lion]

[chrome niche]

how did you get that

[crystal lion]

Cyclic quads

[chrome niche]

how did you get 65 degrees

[crystal lion]

$\angle IJH = 65$

[jolly parrot]

casework

[unique summit]

hm

[unique summit]

i got an idea

is x perpendicular to H?

[crystal lion]

No reason to assume that

[unique summit]

oh wow

i got a genius ide

idea

[crystal lion]

I mean the problem is solved in that picture

[unique summit]

i dont get it 😭

i dont get where the 65 camefrom either

[crystal lion]

Do you know what cyclic quads are?

[unique summit]

ye

[crystal lion]

What 65?

The IJH or the KIG one

[unique summit]

65 of I

[crystal lion]

Of KIG?

[unique summit]

yes

[crystal lion]

Well because
$$\angle KIG = 180 - \angle XKI = 180 - (180 - \angle IJH)$$

[jolly parrot]

casework

[ebon cloak]

but theyre not opposite angles in quad

[crystal lion]

Its a trapezoid

[ebon cloak]

why?