help-13

[fast barn]

ye

it will be solved with that?

[tropic oxide]

ok then why did you even say any of it

were you trying to help or were you just messing around

[wintry monolith]

Do u know what a^2 - b^2 is

[floral flax]

ofc messing arnd bruv

[tropic oxide]

please don't call me "brother" or any variation of it.

[fast barn]

(a+b)(a-b)?

[floral flax]

ok dude

[wintry monolith]

Yes exactly

[tropic oxide]

... don't call me "dude" either.

i'm a girl.

[floral flax]

ah i didnt see

[tropic oxide]

and also if you were just messing around then you shouldn't have come into this help channel in the first place.

[floral flax]

srry

[floral flax]

why not

[wintry monolith]

If cosec^2 - cot^2 is 1 then cosec + cot= 1/cosec - cot

[tropic oxide]

these channels are where people get actual serious help

if you want to mess around -> #chill

[wintry monolith]

@fast barn

[floral flax]

aahhh okay

[fast barn]

hmm...

can send some paper work 😅

if possible

[wintry monolith]

Okay

[fast barn]

i'll go do a different question until then... ping me when you wrote that

[fast barn]

i get that much but how am i suppose to solve that... 😅

do i sqr both side to find the answer?

[wintry monolith]

No

If cosec + cot is 3/2

[fast barn]

OOOHHHHH
okokok

[wintry monolith]

Cosec - cot is 2/3

[fast barn]

wait

[wintry monolith]

Add them

[fast barn]

????

i still don't get it

[tropic oxide]

add these together

or actually better yet

treat this as a system of equations where your unknowns are csc(θ) and cot(θ)

x + y = 3/2
x - y = 2/3

find x and y

and then cos(θ) = cot(θ)*sin(θ) = cot(θ)/csc(θ) = x/y

[fast barn]

i am confused... if you can solve it a bit then that would be helpful...

@tropic oxide

[wintry monolith]

Add them

[fast barn]

hmm

[fast barn]

did i do some useless stuff here?

[wintry monolith]

No

Just add the equations

[fast barn]

ok

[tropic oxide]

yeah ok so there are two routes you can do through

but in both cases you have to apply the same idea of a system of linear equations

[fast barn]

things looks good at the same time bad

very bad

idk

[wintry monolith]

Bruh

If u add them

U will get 2cosec

Not cosec

[fast barn]

fguck

minor mistake made things bad

now where did i go wrong

ik it is... but WHERE

fuck me

this time i didn't ad

[wintry monolith]

Bro

Add them properly

[fast barn]

fuck yea i got it now

[wintry monolith]

[fast barn]

thanks but many things didn't get in my head @wintry monolith... like how
cosec+cot=3/2
cosec-cot=2/3

did'nt get in my head

[wintry monolith]

ask ur teacher

[fast barn]

ok

well thanks tho

[wintry monolith]

Or just use ur brain a little bit more

[fast barn]

hmm

well anyway... thanks a lot @wintry monolith and @tropic oxide

.close

[wintry monolith]

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[warm apex]

Hello just need a tip on whether i should primarily do math instinctively or should I understand more details about a topic?

[normal cipher]

depends on the topic

[twilit escarp]

You mean, prepare only for an exam or learn more of it by yourself ?

[warm apex]

because for example for precalc : Translation of Graphs uh y=x^2, y+2 = (x+1)^2

[warm apex]

yeah like that

[twilit escarp]

Depends if you find it interesting or not

Or if you have the willing to know more than what you already do

Or maybe the need to know more

[warm apex]

oh wow thats actually something ive been looking for

thy

[twilit escarp]

For some competitive exams that do take a turn with respect to the schools program

[warm apex]

alright ill focus on method of examining then research about it after once its done

[twilit escarp]

Sounds good

Hf !

[warm apex]

HOLD ON

im not done yet

[twilit escarp]

Yes?

[warm apex]

im in the middle of trying to copy this example by hand

wait no i need to picture it cuz of the graph

or do u know how to visualize it so i dont have to grab my phone

[twilit escarp]

Whats the function ?

We have tools in this server

[warm apex]

y=x^{2}

y+2=\left(x+1\right)^{2}

[twilit escarp]

,w graph y = x^2

[wraith dagger]

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[twilit escarp]

,w graph y+2 = (x+1)^2

[wraith dagger]

Results provided by WolframAlpha

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Requested by yakubros

[twilit escarp]

Am i correct on the functions

[warm apex]

yes

[twilit escarp]

Whats your question about it

[warm apex]

so like

h=h2-h1=-1-0=-1

oh wait no oh my god i just understood it

[twilit escarp]

Whats h

Oh ok

[warm apex]

uh h2=-1

i dont understand the further explanations

[twilit escarp]

So its like y = (x-h)² + smth ? Is that what you do ?

[warm apex]

no its just translating

like ex

h=h2-h1=-1-0=-1 is -1 unit left

[twilit escarp]

Got it

Would rather use x1 and x2 tho

[warm apex]

heres what i dont understand

[warm apex]

same 🥹

[twilit escarp]

So what do you use for the vertical?

[warm apex]

alright lets do that\

its y1=-2 an d y1=0

[twilit escarp]

So here you use y lmao

I see

Ok tell me the problem

[warm apex]

why does the translation units point to a point

sorry idk how to explain

wait

[twilit escarp]

Why does the translation is applying to every points ?

[warm apex]

ok i got the word

Why does the Unit Translations

point or LEAD to -1, -2

or basically just the 2nd function

what is the connection*

sorry took too long

[twilit escarp]

What are the operations to get the second function out of the first one ?

[warm apex]

i just used desmos and screenshot wont pop in my folders

,w graph y=x^2, y+2=(x+1)^2

[wraith dagger]

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[warm apex]

aw

[twilit escarp]

Wait you talking about the vectors that represent the translation ?

[warm apex]

what is a vector?

[twilit escarp]

Ok nvm

[warm apex]

like a point?

[twilit escarp]

Its an object that has a norm (length) and a direction

Often used to represent deplacement

[warm apex]

is that something similar to a triangle thing?

run and rise

[twilit escarp]

Can be seen as with the vectors relations

I gtg

But im sure someone will take over

[warm apex]

no its fine

i need to sleep

thx

.close

[cedar kiln]

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[cedar kiln]

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[proper turtle]

Plz help .. i have an exam after couple of days. How to solve this question

[vital jay]

!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 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

[proper turtle]

1

[vital jay]

Alright, well what do you know about circumscribed circles?

[proper turtle]

they are outside the triangles

they have something inside it

i guess they have this formula for eq. triangles = a/2root3

[vital jay]

Okay that's one formula, do you know of any others?

[vital jay]

I believe there's a more general version of this one

[proper turtle]

abc/4 area and 2Area/a+b+c

only thse 2

[vital jay]

https://math.libretexts.org/Bookshelves/Precalculus/Elementary_Trigonometry_(Corral)/02%3A_General_Triangles/2.05%3A_Circumscribed_and_Inscribed_Circles

This page lists some useful formulas

I believe 2R = a/sinA = b/sinB = c/sinC will do, though obviously those variables have different meanings on that webpage vs your worksheet

[proper turtle]

if u dont mind

plz can u sovle the 1st part

like how to approach it

[vital jay]

Okay, well this formula is basically saying "Take a side length and divide by the sin of the angle opposite to the side and you will get two times the radius"

a,b,c and A,B,C in the formula I gave are like the ones in this diagram

[proper turtle]

yah..

goccha an example

[vital jay]

In the triangle ADC, we know the angle at point A and the sidelength of DC

Or... No wait we have the angle at point D lol

[proper turtle]

angle 60 at D

[vital jay]

Well we can use that and the fact that the angle at point C is 90 to get the angle at A

[proper turtle]

yes angle A is 30

[vital jay]

Yeah! So we have DC is 1 and the opposite angle is 30

[vital jay]

This formula shows how to use those to get the radius

Do you think you can do that?

[proper turtle]

goochha let me try

if i mess up..shall i ping u again ?

[vital jay]

I'll keep the tab open don't worry

[proper turtle]

great 🙂 thanks. I'

[vital jay]

If I disappear feel free to tag me though, I do get distracted sometimes

[proper turtle]

hahha sure sure

@vital jay I'm stuck on the 2nd one..

we are only given half a length

[vital jay]

Can I ask what you got for (1)?

[proper turtle]

1

[vital jay]

Great :)

[proper turtle]

i was trying 2

but got stuck

we only know DC 1

[vital jay]

Well you have that AC = BC

Do you think you can find AC from the information you've got?

[proper turtle]

NO

[vital jay]

Well in the triangle ACD you have the angle at point D and the length of DC

Remember your sohcahtoa?

[proper turtle]

ahhh

tan 30 ?

[vital jay]

Yeah!

AC = 1*tan30

Do you think you know enough for (2) now? Or do you need some more hints

[proper turtle]

noi noi

let me try

thans

[vital jay]

👍

[proper turtle]

bro

is 2nd ans root2/2

@vital jay

i think i'm making a mistake somewhere

[vital jay]

I don't think it is ^^;

Can you show your work?

[proper turtle]

I'm on desktop

wait i'll try to

replicate

@vital jay

ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

i gocchhhaa

i'm so dumb

[vital jay]

Did you use the wrong angle in there? lol it's all good

I actually made a mistake myself where I was using 1/sqrt(3) instead of sqrt(3)

[proper turtle]

2r = a/sinA
i did not put a

[vital jay]

Ahh yep yep

[proper turtle]

yah... once a is there

it cancles the other root 3

and ans is root6 /2

:_) finally

[vital jay]

Ye that's what I got too :)

One thing of note, I'm not entirely sure if this is correct but it looks like it might be

[proper turtle]

actually these are previous year question papers

[vital jay]

If you have a right angle triangle, would the diameter of the circumscribed circle be the same as the hypotenuse?

After all, sin 90 = 1

[proper turtle]

i have no idea about this:_0

[vital jay]

Fair enough!

[proper turtle]

lets move to

3rd one

if u are not busy

[vital jay]

Yup!

[vital jay]

So looking back at this page, Theorem 2.10 or Theorem 2.11 looks like what we need

[proper turtle]

let me see

s is the area ?

[vital jay]

Maybe? I just filled in s = (1/2)(a + b + c)

[proper turtle]

its

heronz

formula

semi perimeter

goccha

[vital jay]

@proper turtle Just checking in, you still working away?

[proper turtle]

yah

i'm working on3

i

i'm confused

now i'm trying 2.19

approch

[vital jay]

Alright! 2.19 uses the formula from 2.11

[proper turtle]

yes

[vital jay]

What are your values for s,a,b,c?

[proper turtle]

root 3 root 3 and 1

for a b and c

according to the ques

[vital jay]

Shouldn't c be root 6?

[proper turtle]

ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

i made a mistake

[vital jay]

Assuming a = AC, b = BC, c = AB

All good!

[proper turtle]

yes..

root 3 root 3 and root 6

[vital jay]

How about s then?

Don't worry about simplifying too much

[proper turtle]

s is

(root 6 + 2 root 3)/2

[vital jay]

Yup!

Think you can get the answer now?

[proper turtle]

yah

already woeking on it

will be done in 1-3 mins

[vital jay]

👍

[proper turtle]

im stuck

again

🙂

[vital jay]

No problem

I think Theorem 2.10 is probably the easiest way to go about this

[proper turtle]

let me see

[vital jay]

After all, what is tan 45?

[proper turtle]

1

but angle is already 45

A angle

and if we diivde it half

wont it make more troublesome ?

[vital jay]

Yeah but look at the angle at C!

That one's 90, which we can divide by 2 to get to 45 :)

[proper turtle]

yah

dem

let me work on it

i'll notify u

[vital jay]

👍

[proper turtle]

LOL

what took me 1 page calculation

just ended in 3 lines

🅰️

🙂

[vital jay]

Lmao yeah, math is like that sometimes

So what'd you get?

[proper turtle]

{2root3 - root 6 }/2

[vital jay]

Yup same as me!

[proper turtle]

great

[vital jay]

Onto 4 then?

[proper turtle]

yep

lets go

[vital jay]

So for this one, I think a good place to start would be to start filling in facts about the triangle BDH

[proper turtle]

h is 90

[vital jay]

Yup!

[proper turtle]

b is 45

as for d

let me see

75

ahh

[vital jay]

d should be 45 as well?

[proper turtle]

fk

ys

[vital jay]

lol yeah all good

[proper turtle]

my mind does stupid tings

but why ae we moving to next traingle ?

[vital jay]

It's all good, you make some mistakes but you really do seem to grasp this material better than a lot of people I've helped

[proper turtle]

heheh somtimes i intelligent

most time i dumb

[vital jay]

Well if BDH is a 45,45,90 triangle, what does that tell us about the relationship between DH, BH, and BD?

[proper turtle]

its a right angles triangle

as well as

isoleses

i think this

🙂

[vital jay]

So DH = BH right?

[proper turtle]

yes

[vital jay]

So then what's the relationship between DH and BD?

[proper turtle]

they are equal ?

[vital jay]

I'm asking you this btw, because we know both BC and DC, so we can solve for BD

[proper turtle]

in lenght ?

[vital jay]

Not quite sadly

[proper turtle]

ohh

[vital jay]

Think of the pythagorean theorem

[proper turtle]

ahhhhhhh

goccha

pytha will give bh and DH

as they are same

[vital jay]

BD^2 = BH^2 + DH^2 right?

[proper turtle]

yes

we can take

BD2 = 2BH2

OR 2DH2

[vital jay]

Yeah!

[proper turtle]

so here we are trying to find... Sin DAH
= P/H

? right ?

from the triangle BHD we will get P

[vital jay]

I'm not quite sure what you mean ^^;

We're trying to get the length of DH right?

[proper turtle]

overall

for this..

sin is p/h

so P from above traingle

[vital jay]

Yeah I think so, if I'm understanding you right

But we shouldn't we finish up (4) first?

[proper turtle]

ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

i went to five

i didint see 4

[vital jay]

Ooooh lmao okay that explains it

[proper turtle]

sry

[vital jay]

No problem no problem

[proper turtle]

now onto 4

[vital jay]

Aaanyway, do you think you can solve for DH with what you've got here?

[proper turtle]

yah

let me do it

[vital jay]

👍

[proper turtle]

gococha

[vital jay]

Yeah!

Actually, is that a root 2 or root 3?

[proper turtle]

2

[vital jay]

Then yup!

[proper turtle]

great

[vital jay]

So then, you think you can use this for (5)?

[proper turtle]

yah

let me do it then

[vital jay]

👍

[proper turtle]

huhhhhhhhhhhhhhhhhhhh

i made a mistake or ans is too esy ?

is AD = 2

[vital jay]

Yeah AD = 2

So what does that say about sin(DAH)?

[proper turtle]

let me see

here

[vital jay]

Yup!

[proper turtle]

as for the last ans

its same

[vital jay]

Oh?

[proper turtle]

just

+ve sign

[vital jay]

Yeah, (root 6 + root 2)/4

How did you get there btw?

[proper turtle]

where ?

[vital jay]

How did you get that the answer was the same, just with a plus sign?

[proper turtle]

i solved it side by side..

we have ac

bc

we hav DH

and AD

pythagores

gives AH

[vital jay]

Great!

[proper turtle]

and cos is B/H

[vital jay]

So does this make you feel better about these sorts of questions?

[proper turtle]

yah

its feels awrsome

but the next question

if this comes in my exam

i

m

leving

it

[vital jay]

Lol

I think this really looks more complicated than it is

[proper turtle]

i dont even see it as question

[vital jay]

Well it's just saying match the lines with their equations

[proper turtle]

i just assume its a round ball on a plus sign.. and lots of thread hanging around it

then i leave the question

[vital jay]

Well it's certainly very cluttered

But I think (1) is the straight line that's sloped more upwards, (2) is the straight line sloped more flatly, (3) is the upwards hyperbola, (4) is the downwards hyperbola, and (5) is the circle

[proper turtle]

no parabla ?

parabola in this ?

[vital jay]

Oh yeah, (3) and (4) would be parabolas

I got my terminology mixed up ^^;

[proper turtle]

yah.. i was like .. hyperbola ;; how >>.

great man

thanks for helping

[vital jay]

No problem!

[proper turtle]

well go through that ques once agin.. tomorrow..

its about to be 1 am.. will revice the formulas and will hit bed

Good night or good day

[vital jay]

Good night to you!

[proper turtle]

Arigato Gozaimashita

[vital jay]

If you're done, use .close to free up the channel

[proper turtle]

will the message be deleted ?

[vital jay]

No, though other people will probably use the channel

That'll happen anyway though, this just frees it sooner

[proper turtle]

cool i;ll just remebre the number 13

.close

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[random sun]

Hi can anyone help me out on this? I’m confused and don’t know what I did wrong

[worn kraken]

u also can't be -5 because of the fraction in the denominator.

[random sun]

Oh so x can’t also be -5?

[worn kraken]

Yup. It results in division by zero.

[random sun]

AHHH

so I’m forgetting (-6, -5) U (-5, ♾️)

If I add that would this be entirely it’s domain

[worn kraken]

Yeah

[random sun]

Oh thank you

I never knew you would also have to take that to account for finding the domain.I just thought simplifying it more further and find the domain from there

But thank you tho

[cedar kiln]

@random sun Has your question been resolved?

[cedar kiln]

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[jade vessel]

Given a real vector space V, dimV = 3 with a non-degenerate bilinear form h, which has an isotropic vector, find possibile values of the signature of h.

[jade vessel]

no idea how to go about this

[cedar kiln]

@jade vessel Has your question been resolved?

[jade vessel]

<@&286206848099549185>

[obtuse mango]

i mean you can wlog pick a basis such that h looks like
I_p
-I_q
0

(actually non-degeneracy => no 0 term)

then think about what the existence of an isotropic tensor implies for p and q

[cedar kiln]

@jade vessel Has your question been resolved?

[jade vessel]

hmm okay

[jade vessel]

cause otherwise the determinant of this matrix is 0 right?

Is this a valid reasoning: since a vector is isotropic then we cant have this matrix to be in the form of just I_p or -I_q, since from here it would follow that the form is positive and negative definite respectively

so p >0 and q > 0

[cedar kiln]

@jade vessel Has your question been resolved?

[obtuse mango]

yeah that works

[obtuse mango]

yep

so signature is either +-1

(the one thing you have to do from here though is to show it actually works, i.e. there might not be any possible signatures)

[jade vessel]

alright

Thank you very much!

.close

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[potent sable]

For what value of lambda does a line Pos + Dir*(lambda) intersects with a triangle, with vertices A, B and C.

[cedar kiln]

@potent sable Has your question been resolved?

[cedar kiln]

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[crisp mantle]

Hello is my answer acceptable?

[dire geode]

,rotate

[uncut ridge]

seems correct, surely don't like the fact you took square roots on both sides but since the limits are [0,2] and the curve really is symmetric about the x-axis it doesn't matter

[cedar kiln]

@crisp mantle Has your question been resolved?

[crisp mantle]

okay thank you

[cedar kiln]

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[dapper vessel]

Yo bro please start writing right after the red vertical line
Or just buy a notebook that doesn't include it

[dapper vessel]

Also why @crisp mantle do you have a pfp of a dickhead

[normal cipher]

who are you to tell people how to write

Please do not randomly ping other people.

[dapper vessel]

💀 that's literally why the red line is there

[normal cipher]

If you have no math question I will close this channel.

[tropic oxide]

#discussion

[blazing zephyr]

js close it atp

[normal cipher]

.close

[cedar kiln]

Channel closed

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[normal cipher]

fair

[cedar kiln]

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[copper fern]

Question no. 8

[copper fern]

Solution suggests that cos theta is rational at only few rational multiples of π

[tropic oxide]

the words "cos(θ) is a distinct rational" throw me off

[copper fern]

I think it's something about the cos func I don't know

[tropic oxide]

do we mean that $\theta = q\pi$ with $q \in \bQ$ but $\cos(\theta)$ is another rational that's not equal to $q$?

[wraith dagger]

Ann

[copper fern]

Yes, maybe

[crimson delta]

not like that changes anything, cause you can always add 2 to q

[tropic oxide]

i guess we need only consider 0 ≤ q ≤ 1 and not worry about cos(θ) = q

[crimson delta]

I think they just mean all the distinct rational values that cos theta can take. and they are bad at writing that

[copper fern]

Should I send you guys the solution?

[crimson delta]

https://en.m.wikipedia.org/wiki/Niven's_theorem

that was my first thought

but like, who actually knows that

thats not at all obvious

its somewhat clear that you can find at least five values if you think enough

and that due to symmetry it has to be an odd number

so then you can abuse the multiple choice

[copper fern]

Nobody taught me this theorem

[crimson delta]

yes

there is also this https://arxiv.org/abs/1006.2938. turns out the argument is not as involved as I thought

[copper fern]

Ok, Ty guys 💕

[cedar kiln]

@copper fern Has your question been resolved?

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[crimson sedge]

Find intervals in which function give by y= sinx is increasing and decreasing

[crimson sedge]

Same question but 2 part of the question y= sin square x+cos square x

[quasi merlin]

!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 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

[crimson sedge]

I don't know where to begin

[crimson sedge]

.

[quasi merlin]

What does it mean for a function to be increasing?

[edgy spade]

What exactly is your question?

[dusk finch]

are you doing this part now?

[wraith dagger]

MathIsAlwaysRight

[crimson sedge]

Yes

[dusk finch]

well, whats sin^2x + cos^2x

there is an identity

[crimson sedge]

This question is from class 12 maths

Chapter 6

[dusk finch]

Yeah okay

[crimson sedge]

Application of derivative

[dusk finch]

have you heard of the pythagorean identity or sth like that

[crimson sedge]

Yes

[dusk finch]

cool, what is it?

[crimson sedge]

This equation is equal to 0

[dusk finch]

nope

its equal to 1

$\sin^{2}\left(x\right)+\cos^{2}\left(x\right)=1$

[wraith dagger]

MathIsAlwaysRight

[crimson sedge]

Oh yes

I have solved it

I directly answer the solution for that question

[dusk finch]

hmm arent you supposed to find intervals in which its increasing and decreasing?

[crimson sedge]

Yes

[dusk finch]

What does the function given by y = sin^2(x) + cos^2(x) simplify to?

[crimson sedge]

Leave this question find intervals of y=sinx

[dusk finch]

okay

[crimson sedge]

.

[dusk finch]

so how can we use the derivative to determine when a function is increasnig and when its decreasing

[crimson sedge]

Idk

Why do you think I am asking you

[dusk finch]

Well a function is decreasing when its derivative is negative

and increasing when its derivative is positive

so can you find the derivative of y = sinx

[crimson sedge]

Is this correct

[dusk finch]

which one is increasing and which one decreasing?

either way, you are missing infinitely many intervals

you only included the ones from [0, 2pi]

[crimson sedge]

First one is increasing and other one is decreasing

[dusk finch]

then it's correct, but you are missing a lot of intervals

[crimson sedge]

Is it necessary to write all

The intervals

[dusk finch]

I'd say so

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[grim ledge]

any1 know this?

[orchid whale]

Yeah

That's specific values you should know for cosine and sine

[grim ledge]

yea... but i didnt rlly learn how to read the unit circle

i js kinda memorized the chart

[orchid whale]

If you just want the answer it's ||-sin(π/6)||

Want me to explain it to you?

[grim ledge]

yea could u? but also

[orchid whale]

Wait no

It's not that

[grim ledge]

• isnt an option

[orchid whale]

I'm dumb

[grim ledge]

oh no its fine

cause i thought it was that too...

[orchid whale]

It's sine

[grim ledge]

but there isnt an option for tht

[orchid whale]

You're question is false

Like

It is obviously negative

[grim ledge]

right...

mm

i thought it was - cos of pi/6 tho

[orchid whale]

I would try sin pi / 6

No it would be - sin

Because it's "the small side of the angle"

You can do quick projections using that

[grim ledge]

isnt it the x coordinate tho

[orchid whale]

When it's the bigger side it's cos, the smaller it's sin

Yeah but the angle is not based off the x axis but the y axis

So it rotates the whole thing

[grim ledge]

mmm

okok ill try that

so um it was wrong

it was cos 2pi/3

[orchid whale]

Ohhhh

Fuck me

Cos (2pi/3)= - sin(pi/6)

[pastel vault]

yeah, because the angle from the positive x-axis is pi/2 + pi/6

[orchid whale]

I should have took a closer look at the answers

[pastel vault]

and then for the x-coordinate you use cos

[grim ledge]

ah

okayy thanks

[pastel vault]

if you're done type .close

[grim ledge]

.close

[cedar kiln]

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[summer igloo]

When we say can prove congruency between 2 isosceles triangles using: S-A-S congruency test, what angle is being referring to?

[oblique flare]

given it's a isosceles i would say the angle between the same length sides

[summer igloo]

We're told that the 2 base angles of an isosceles triangle are always congruent to each other. So, is it the top angle we are referring to?

[pastel vault]

you can use any of the 3 angles

[summer igloo]

Oh, so at the top then.

[pastel vault]

as long as the angle is between the two sides

[summer igloo]

The thing is, I'm working on a problem where no angles are given, just that the 2 vertical sides of the isosceles triangle are the same measure.

[pastel vault]

send the problem image then

[oblique flare]

the triangle might be rotated though

[summer igloo]

Let me send a screenshot....

Here it is:

They never give any angles.

[pastel vault]

well you know that angles ABD = CBD

so it remains to check the corresponding sides of SAS are congruent

AB = BC (definition of isosceles triangle)

DB = DB (reflexivity)

[summer igloo]

So they share the common line which is the altitude leg and that tells us what?

Is knowing the actual measure of the apex angle unnecessary, is that what we are learning here?

[pastel vault]

that's one pair of sides being congruent

[pastel vault]

yeah! it doesn't matter what it is

[pastel vault]

it just matters that these angles are the same

[summer igloo]

Okay, thats good enough for now. Thank You.

.close

[cedar kiln]

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[cedar kiln]

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[summer igloo]

I like to use the word "apex" when referring to the vertex at the top of a triangle but the AI search tells me that saying just vertex is more correct and precise. Is this true because it seems to be a little weak reasoning to me.

[pastel vault]

apex is the better word for the vertex at the top

[summer igloo]

Oh good, I thought so myself. I guess the AI isn't all it's cracked up to be.

This was the AI response: "In geometry, the vertex at the top of a triangle is simply called a vertex. It's one of the three points where the sides of the triangle meet. While the term "apex" can be used to refer to the highest point of a shape, in the context of a triangle, "vertex" is the most precise and commonly used term, according to some math resources. "

But then again I guess mathematicians don't always agree on everything.

.close

[cedar kiln]

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[tropic oxide]

.reopen

[cedar kiln]

✅

[tropic oxide]

@summer igloo "apex" is used sometimes when talking about an isosceles triangle to mean the one vertex where the two equal sides meet

ie the one across from the base

or in 3d geometry it's used for the "tip" of a pyramid

[summer igloo]

Yes, and that's the context in which I raised this question because it makes it easier to understand in my opinion.

[tropic oxide]

well there isn't really a rule against using the word at all

[summer igloo]

So, we prove congruency in an isosceles triangle by splitting it into smaller triangles by what's referred to by Khan as "dropping a perpendicular"....

From the apex to the base.

[pastel vault]

yeah

that's a super common technique

split into two congruent right-angled triangles

[summer igloo]

It's all coming together for me, slowly but surely. Thank You both.

.close

[cedar kiln]

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[cedar kiln]

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[torn marsh]

For Q3, I got the same answer except mine was in positive version, this one is a negative

can someone explain why this is the case

[tropic oxide]

gonna need to see your work

but i have a decently strong hunch

i am not gonna say it until i see your work though

[torn marsh]

ok nvm, i see why

nah dw, i did a mistake

.close

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[sacred dove]

that looks like an AP

Arithmetic progressions

Have you used them before?

youre right

do you think 1, 2, 3, 4, .... 477 look like an AP?

do you know how to find the sum of the first nth terms of an AP?

also, to be clear , you dont need AP for this

but its useful incase you come across things like 2 + 4 + 6 ... (even number)

or some other multiples

to simplify it for you, you might want to know the formula for calculating the sum of the first N natural numbers

sure

[wraith dagger]

ritam.in4k 🍡

[sacred dove]

moojy, here you go ^

[wraith dagger]

ritam.in4k 🍡

[sacred dove]

you got it

yup

in your case, yes

Carl Friedrich Gauss

[cedar kiln]

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[nova snow]

very famous story he was in class one day and his teacher made him add up all the numbers up to 100 like 1+2+3+..............+100 while his classmates took a long time he found a shortcut which was that formula

yes

[sacred dove]

depends if you are willing to work towards that 😄

out of topic tho

[cedar kiln]

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[drowsy path]

$how do i solve (e^x - e^-x - 2cosx)/sin^2x$

[wraith dagger]

dexa.cld

[drowsy path]

l hospital

l hopital

[proud vigil]

$\lim_{x\to 0}\frac{e^x-e^{-x}-2\cos(x)}{\sin^2(x)}$?

[wraith dagger]

;(

[drowsy path]

yes thats the question

[proud vigil]

You need to use L'H?

[drowsy path]

i need to solve it using it

[proud vigil]

Okay, differentiate

[drowsy path]

can we tho?

dont we need 0/0 or inif/infi?

[proud vigil]

Yes

Why are you asking to solve using L'H if it isn't in an indeterminate form?

[tropic oxide]

then verify that you have one of those forms first.

what does the numerator approach?

what does the denominator approach?

[drowsy path]

when we plug in the values it is -2/0

[proud vigil]

So what can you conclude

[drowsy path]

hmm

i donot know tbh

[tropic oxide]

that we're going to be in violation of the legally binding requirement to use L'H

[drowsy path]

yeee

[proud vigil]

What happens when you divide anything by 0?

[tropic oxide]

what's the limit of -2/x as x->0

hold up

[drowsy path]

infi

[proud vigil]

or yeah, that's more formalized

[tropic oxide]

!xy

[cedar kiln]

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.

[drowsy path]

ok

[tropic oxide]

i think there MIGHT be a typo in the question

[drowsy path]

it isnt istg

[tropic oxide]

so show a screenshot

[proud vigil]

maybe + infront of e^(-x)

[proud vigil]

No harm in sending

[drowsy path]

its -

bruuuuu

wait

[proud vigil]

💀

[drowsy path]

Here

[proud vigil]

Ok, did it ask to solve all of them using L'H?

[drowsy path]

yes 😭

I mean

Its an

[proud vigil]

Where

[drowsy path]

It says evaluate

But its an exercise from l’h rule

so basically the same?

[proud vigil]

How do you know?

No, not the same

[drowsy path]

i got a book

not the same?😭

wait

really?

[proud vigil]

"Evaluate" can mean to just compute the limit

[drowsy path]

hmmm

but our teacher told us to do it by l’h

💔💔

[proud vigil]

if there's no context, just go normally

You can't use L'H on every limit problem

[drowsy path]

true

[proud vigil]

You ALWAYS, and I'm capitalizing for a reason, subsitute first to see if you need to do any manipulations

[drowsy path]

alree

but just to let you know

i have all the questions by l’h

So i think there may be a trick to it?

[tropic oxide]

i think this may have been a typo on the authors' part

but it isnt your job to fix

[drowsy path]

hmm probably

the answer in book is 2

I got 1

[proud vigil]

I'll check

[drowsy path]

by violating l’h

[tropic oxide]

,w lim[x->0] (e^x + e^-x - 2cos(x))/sin^2(x)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by ann_dec

[tropic oxide]

well

yeah ok

they typo'd

[drowsy path]

lmao😭

[tropic oxide]

and the -e^-x should have been a +e^-x

[drowsy path]

yea

[tropic oxide]

[drowsy path]

There are other incorrect too 💀

[proud vigil]

Yeah, that's correct

Oh yall already WA'd it

[drowsy path]

Like limit x->0 lnx/cotx

Author wrote answer -1
But i got 0

[proud vigil]

,w lim x->0 ln(x)/cot(x)

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by exiled_hype

[proud vigil]

You can always use a software to double check

[drowsy path]

Alr

[proud vigil]

If WA isn't working, use desmos (geometric approximation)

[drowsy path]

hmmm okay

tan5x/tanx
Limit x—>pi/2

I got 1/5

Author = 2/5

,w lim x->0 tan5x/tanx

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by syu4xz.7

[drowsy path]

wut

Wait what

how is this incorrect?

[tropic oxide]

your handwriting...

[drowsy path]

it was an race between me and bro

😔🙏

mb

[tropic oxide]

bruh

why are you racing at all

math is not a speedrun or a race

[drowsy path]

for fun😭🙏

[drowsy path]

Yea hea

i am redoing it

[tropic oxide]

ok well go and redo it yeah

WITHOUT your brother in the picture

[drowsy path]

ALRRRR

done

[tropic oxide]

your n, u and x are still very much confusable for each other

[drowsy path]

there is no n ( is my handwriting that bad 😭)

[tropic oxide]

but it looks like now you're actually getting it?

[drowsy path]

😭😭😭😭

alr i get it 😔🙏

i will improve

[drowsy path]

,w lim x->pi/2 tan5x/tanx

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by syu4xz.7

[drowsy path]

the answer is 5 💔

wait what

[drowsy path]

uh huh

my baddddddd

i was using x tends to zero in the first calcualtion thats why it showed 5

My mistake

its corrrect

😭🙏

thanks yall

.solved

[cedar kiln]

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[summer igloo]

Can we say with certainty that 2 sides of a triangle that share a common vertex (apex) and are equal in length then we can conclude that at minimum this is an isosceles triangle (could be equilateral though) and therefore the 2 base angles will be congruent as well. So, in reality, we have a very simple way to prove an isosceles triangle with 2 equal side lengths (by definition of isosceles triangle) will have 2 congruent base angles. This is a very simple yet easy truth to understand, if I do have all this right.

[tropic oxide]

Can we say with certainty that 2 sides of a triangle that share a common vertex (apex) and are equal in length then we can conclude that at minimum this is an isosceles triangle (could be equilateral though) and therefore the 2 base angles will be congruent as well.
yes we can

[summer igloo]

Very good stuff. Thank You!

.close

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[rocky sky]

i have never used this channel and i dont want this to become spam or something, but the fact that poeple here help with math is so nice. Very cool ppl

just to appreciate, im a little stuck rn but i think i can manage

idk what that means but im in college

[whole steppe]

Are this trignometric signs in different quadrants?

Do you know unit circle

What do you hvae a doubt in

Study what exactly

Which part of trignometry

[quasi merlin]

So typically the channels are for single questions. Best to attempt said questions and come here for help with solving them. Imo that's the best way to practice this kind of stuff anyway

[whole steppe]

Havent you done that in 10th

[cedar kiln]

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[paper bluff]

how does (a + 1/a)(b + 1/b)(c + 1/c) turn into (a^2 + 1/a^2) + (b^2 + 1/b^2) + (c^2 + 1/c^2) + 2

[tropic oxide]

using abc = 1 im pretty sure

if you expand out the product you get one term of abc = 1, another of 1/(abc) = 1

that's your 2

and then e.g. bc = 1/a and cyclic permutations thereof so a/(bc) = a/(1/a) = a^2

[paper bluff]

oh yea

alr

ty

.close

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[sly oar]

Whats the expression of this ?

With

N

[slender ginkgo]

Combination function prolly?

[modest vapor]

btw , to find the solution , you can use the king rule

[cedar kiln]

@sly oar Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[fallen musk]

Hello

[fallen musk]

Well $x^2+y^2 \leq1$ is a circle equation right?
In question 7 i don't how I approach it to sketch it with other set

[wraith dagger]

Dynosto

[fallen musk]

I mean in question 7 what might be set X

[proper palm]

do u remember what is the geometric representation of an equation like x^2+y^2=r^2

[fallen musk]

It's circle right?

[proper palm]

exactly

in ur case u don’t have an equality but <=

what do u think it should be

[fallen musk]

dunno

[proper palm]

this is the case = and also <

so for = it’s a circle

and < represents the inside of a disc

[fallen musk]

Oh got it

[proper palm]

so finally what is X ?

[fallen musk]

If I sketch on R^2 it's whole circle with radius 1 right?

Y is kinda a line where x => 0

[proper palm]

exactly it’s a closed disc

[fallen musk]

Yes

[proper palm]

no its a plan

the variable y is free, we only require that the abscissa be taken from the real numbers >=0

[fallen musk]

Oh wait in Y y kinda is anything yeah free variable

[proper palm]

yeah

can u draw Y

[fallen musk]

Wait I can

It's one side plane in Cartesian plane

[proper palm]

yeah, which side ?

[fallen musk]

Right

[proper palm]

perfect

[fallen musk]

Thankyou

.close

[cedar kiln]

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[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
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[shut nimbus]

i don't know how b,c,d = to those numbers. 🥹🥹🥹

[dusk finch]

it has to do with multiplicity

[worldly chasm]

Do you recognize b, c, and d as roots of the polynomial?

Or negative roots rather

[shut nimbus]

I know the roots but I don't understand how can I identify which one is for b,c,d

I don't know the correct order

[cedar kiln]

@shut nimbus Has your question been resolved?

[vital jay]

Well we could start by looking at b

The options there are only +2 or -2, right?

[shut nimbus]

yes

but why there is +2, cuz the line didn't pass through x= 2

[vital jay]

You need to swap the sign

Since (x+2) is 0 when x=-2, and 4 when x=2, right?

[shut nimbus]

oh, rịght right

[vital jay]

It's a bit counter intuitive, huh?

So does that answer why c and d are like that?

[shut nimbus]

by the roots on the graph, but how can I know c= -4 but not -1

[vital jay]

I'm sorry I'm a bit confused by what you said

You're saying you don't understand why c = -4 and d = -1? What do you mean "but not -1"?

[shut nimbus]

Like, for example without the answer, how i can identify c= -4 and d= -1. I don't know the order 🥹🥹🥹

[vital jay]

Oh! The order doesn't matter

[shut nimbus]

really

[vital jay]

Yeah, you could have c = -1 and d = -4

[shut nimbus]

cuz there are cube and square

[vital jay]

It's just that the limited answers force that c = -4 and d = -1