help-23

[high isle]

Wait how did you get a decimal, can you show me your work

[scarlet pivot]

I erased it

[high isle]

Uh

How did you do it though

You did this right?

Or did you do 5a-39=3a+27

[scarlet pivot]

I got the answer

[high isle]

This is wrong, as they aren’t congruent

[scarlet pivot]

Next

[high isle]

Nice

So

It just gives you y

So you can just plug in

8(4.5)-8=28

[scarlet pivot]

Yeah

[high isle]

6(4.5)+1=28

[scarlet pivot]

Then

[high isle]

7(6)+6=48

[scarlet pivot]

Wait

[high isle]

9(6)-6=48

[scarlet pivot]

Does this prove it’s a triangle

I mean

[high isle]

Nah

[scarlet pivot]

Parallelogram

[high isle]

It doesn’t it proves it a parallelogram

[scarlet pivot]

I need to prove

That’s RSTV is a parallelogram

[high isle]

Remember that it’s not always drawn to scale

So we can’t say that it angles

Luckily, this makes a rectangle

[scarlet pivot]

Can’t I just do

8y-8=6y+1

[high isle]

Yeah but you have y already so it’s not necessary

[scarlet pivot]

Then how do I prove

It’s a parallelogram

Wth

[high isle]

Well a paralegal

[scarlet pivot]

yeah

[high isle]

Um

Actually it’s been awhile but

[scarlet pivot]

wait

I got it

[high isle]

So opposite sides parallel

[scarlet pivot]

8y-8+6y+1=360

[high isle]

Um

[scarlet pivot]

Or 180

[high isle]

It’s not an angle

[scarlet pivot]

frick this bro

<@&286206848099549185>

[high isle]

;-;

[scarlet pivot]

you can do the next one

ur a better helper at the ones you understand

[high isle]

A parallelogram is a rectlinear figure where opposite sides are parallel

[scarlet pivot]

yes

ok

Ik

[high isle]

I understand how to solve this one also

[scarlet pivot]

bruh

O thought

“It’s been a long time”

[high isle]

Nah but I remember it

[scarlet pivot]

alr

[high isle]

💀

I’ll explain it to the best of my ability

[scarlet pivot]

bro you don’t understand how long I have to study for

I still have to read for 2 hours

[high isle]

How long

[scarlet pivot]

any parent snake me

make

I’ll be up till 1 am

Most likely

[high isle]

Are you home schooled?

[scarlet pivot]

no

private school

[high isle]

You have a big test tmrw?

[scarlet pivot]

yes

AP bio, AP geo, math, Spanish

I take CIS Spanish

[high isle]

Ap bios fun

😏

So is ap phys

[scarlet pivot]

I’m in 9th grade bro

[high isle]

Nice

[scarlet pivot]

You

Senior

?

[high isle]

I’m a junior

In multivarible rn

Just trying to help out

[scarlet pivot]

What’s to at

Alr wtv

lock in.

I can’t flunk this quiz

[high isle]

?

Mhm

[scarlet pivot]

I need to keep my 100% in every class

[high isle]

You probably just started your semester

[scarlet pivot]

I’ve had a 97% and higher every single year since 6th grade

no

I started 3 months ago

we have tris

[high isle]

Nice

[scarlet pivot]

2*

Months

[high isle]

This is a rectangle, and notice how both of the opposite sides are parallel

[scarlet pivot]

What the heck is this

oh

showing it’s parallel

and congruent

[high isle]

And this fits perfectly with the definition of a parallelogram

[scarlet pivot]

got it

[high isle]

Mhm

[scarlet pivot]

bro ik

😭🙏🏻

[high isle]

Oh you got it now?

[scarlet pivot]

no

[high isle]

Oh ;-;

[scarlet pivot]

I’m tryna

get the question

how

to show

[high isle]

Well first realize that the opposite lengths are equal

[scarlet pivot]

8y-8=6y+1

[high isle]

Mum

Mhm

[scarlet pivot]

Then solve that

[high isle]

Plug in 4.5

[scarlet pivot]

K

[high isle]

You can just plug in 4.5

Notice how they are equal

[scarlet pivot]

No I don’t

Cuz I haven’t solved it

Yet

[high isle]

8(4.5)-8

[scarlet pivot]

28

[high isle]

6(4.5)+1

Notice how they are equal

Now

[scarlet pivot]

Yeh

[high isle]

7x+9, 9x-6

X=6

[scarlet pivot]

😑😑😑😑😑😑😑😑😂😀😂💣😂💣💣💣😑👿😩🙀🙀🫣🙀🫣🫣🫣😶‍🌫️😶‍🌫️

[high isle]

?

[scarlet pivot]

Idk

[scarlet pivot]

=

[high isle]

Mhm

[scarlet pivot]

Answer

[high isle]

Plug it in

7(6)+9=51

Huh

[scarlet pivot]

48

okay then

[high isle]

No its +6

Mb I read it wrong

7(6)+6=48

[scarlet pivot]

bruh

[high isle]

Lmao

[scarlet pivot]

So 60

[high isle]

No no no

[scarlet pivot]

Bro

What r you on

It’s -6

[high isle]

7x+6=9x-6

Plug in 6

[scarlet pivot]

BRO

THE ANSWRR IS 48

=48

[high isle]

Yeah

[scarlet pivot]

THEN WHYD U SAY ITS PLUS 6

alr wtv

[high isle]

Instead of +9 lol

Sorry for not clarifying

[scarlet pivot]

Apology accepted, you are officially now a good boy.

[high isle]

But like now that we know that rs and vt=48

Just think of that as L

[scarlet pivot]

okay

[high isle]

💀

[scarlet pivot]

?

Next bro

Next

Now what

I hate math

[high isle]

St and rv=28

[scarlet pivot]

I hope it kills itself

[high isle]

It gets fun once calc

[scarlet pivot]

Alr then what

I have this so far

[high isle]

😐

Blank

[high isle]

Tf bro

[scarlet pivot]

?

[high isle]

If you have a problem with the teacher 😭

[scarlet pivot]

I got it right, right?

[high isle]

Just learn it on your own

That’s what I did

[scarlet pivot]

No

[high isle]

W=28

[scarlet pivot]

She’s there for emotional support

[high isle]

L=48

Chill

[scarlet pivot]

Bro wdym L IS 42

Oh

48

[high isle]

What

[scarlet pivot]

alr

got it

Now what

[high isle]

This is basically the formula of the rectangle

[scarlet pivot]

I alr wrote that down

[high isle]

💀

[scarlet pivot]

Rectangle my ah

[high isle]

Okay so since it’s a rectangle

We can say it’s a parallelogram

As opposite sides are parallel

[scarlet pivot]

🤓☝️

okay

[high isle]

🗿

[scarlet pivot]

That’s all you had to say

[high isle]

Bros 13

[scarlet pivot]

Now I write

It’s parallel

that’s it

done

see how easy it wss

[high isle]

💀

You needed to prove it was a rectangle first

In order to make that statement

[scarlet pivot]

okay

[high isle]

Next problem?

I gotta do ap lang soon so like

lol

[scarlet pivot]

bro

ur actually confusing me

just write down the answer

@helper

[high isle]

What’s your next problem

[scarlet pivot]

no

[high isle]

Don’t you have another

[scarlet pivot]

I need this

bro how does this prove it

[high isle]

Bro didn’t listen to my lecture

💀

Okay so notice how

[scarlet pivot]

I in fact did not damn well

[high isle]

RSTV

[scarlet pivot]

OKAU

[high isle]

This is a closed shape

[scarlet pivot]

SHOKAU

[high isle]

And since we know the sides of the closed shape

[scarlet pivot]

THEN

[high isle]

?

Tf

[scarlet pivot]

JUST TYPE

OMG

[high isle]

;-;

Then it proves it’s a rectangle

[scarlet pivot]

IVE SOENT 2 DAMN HOURS ON 5 PROBELMS

I COUDVE FINISHED MY CHORES AND MY READING AND MY STUDYING FOR AP GEOHRAOHY

NOW IM COOKED

NOW IM UP TILL 3 AM AND IM GONNA HAVE MAD EYEBAGS

[high isle]

Well pay attention to my lecture lol

[scarlet pivot]

AND THEY ARE GONNA LEAVE ME

Alr

[high isle]

Are you gen alpha

[scarlet pivot]

Lock on

yes

I’m 15

Bum

[high isle]

I’m 16

[scarlet pivot]

one year apart

heh

[high isle]

Mhm

Me in multivarible calc

[scarlet pivot]

R u a a girl?

[high isle]

I’m a boy

[scarlet pivot]

lol

HELP ME

@round mango I see you

[hard crest]

.close

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[onyx narwhal]

I just sort of need a sanity check here; for context, my prof is really emphasizing not skipping steps when showing our work for assignments. Right now I am doing a bunch of row reducing for some matrix problems, do you think it would be fine if i did something to two lines at the same time or should i play it safe and really break up my work?

[lean otter]

dual enrollment?

[plucky elk]

You can skip steps if you can do it correctly in your head

[onyx narwhal]

fair enough, that's why the work i have written down is missing some steps but i was just wondering if it's worth breaking up into two, heres an example

[plucky elk]

It really doesn't matter

[onyx narwhal]

thank you 👍

thats all i needed to hear

if riemann himself says so then I might as well

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[mellow mountain]

how do i solve this

[mellow mountain]

how do i solve for sine, cosine and tangent of x/2

the triangle has hyp3 and sides 1, -2rt2

for sine ima put my work 1s

[fiery merlin]

Wait, what's the problem they give you?

Is the problem csc(x) = 3 and they want x? Or is the problem related to a 1, -2 sqrt(2), 3 triangle?

[mellow mountain]

they want me to find sin(x/2), cos(x/2), tan(x/2)

[fiery merlin]

I'm still lost on what the actual question and information they give you is.

[mellow mountain]

corrected work

[fiery merlin]

What did they give you?

[mellow mountain]

info: csc x = 3. 90<x<180
question: find sin(x/2), find cos(x/2), find tan(x/2)

so what i have is that the triangle has sides of length 1, -2sqrt2, and hypotenuse 3

[mellow mountain]

and using half angle formulas i got these

[fiery merlin]

One of those sides has a negative length.

[mellow mountain]

yes ik

-2sqrt2

[fiery merlin]

Right. Triangles have sides with positive lengths.

Anyway, with csc(x) = 3, what's sin(x)?

[mellow mountain]

1/3

[fiery merlin]

OK, what's cos(x)?

[mellow mountain]

-2sqrt2 / 3

[fiery merlin]

How did you get that?

[mellow mountain]

mistype

[fiery merlin]

OK, how did you get that?

[mellow mountain]

cos(x)= adj/hyp, since 3^2 - 1^2 gives the other side, b^2 = 8, b= 2sqrt2. since the angle is between 90 and 180 it has to be in quadrant 2

and we're thinking in terms of a unit circle (kinda) so the side is -2rt2

[fiery merlin]

You should use the Pythagorean identity.

[mellow mountain]

how

im supposed to use the half angles to get the exact answre

[fiery merlin]

Right, and the half angle formulas use cos(x).

[mellow mountain]

yea

so im plugging in cosx which is -2sqrt2 / 3

and im having trouble simplifying

[fiery merlin]

The Pythagorean identity is sin^2(x) + cos^2(x) = 1.

[mellow mountain]

yes i know

[fiery merlin]

So, cos^2(x) = 1 - sin^2(x), so cos(x) = +/- sqrt(1 - sin^2(x)). sin(x) = 1/3, so cos(x) = +/- sqrt(1 - 1/9) = +/- sqrt(8/9) = +/- 2 sqrt(2)/3, which is what you have.

Now x is in the second quadrant, and cosine is the run in the unit circle, so we want the negative value, which you have.

[mellow mountain]

ive found cosx already

[fiery merlin]

So, (\sin\qty(\frac{x}{2}) = \pm \sqrt{\frac{1 - \cos(x)}{2}}).

[mellow mountain]

i know what the half angle formula is

[flat frigate]

Chai T. Rex

[mellow mountain]

my problem is simplifying the radicand when i plug my cosx in

into an actual number

[fiery merlin]

So, we have (\pm \sqrt{\frac{1 - \frac{-2 \sqrt{2}}{3}}{2}}).

[flat frigate]

Chai T. Rex

[mellow mountain]

yes i know

into sqrt(1+[2sqrt2/3]/2)

[fiery merlin]

So, we have (\pm \sqrt{\frac{3 + 2\sqrt{2}}{6}}).

[flat frigate]

Chai T. Rex

[mellow mountain]

ok this is where you gave me the step i needed

thank you

[fiery merlin]

No problem.

Now we decide whether it's plus or minus.

[mellow mountain]

1 sec

so now we have

[fiery merlin]

OK, good.

Can you simplify it more?

[mellow mountain]

sqrta * sqrtb = sqrtab when both #s are real right

[fiery merlin]

As long as they're nonnegative.

[mellow mountain]

so itd be sqrt(18 + 12sqrt2)

[mellow mountain]

ok

[fiery merlin]

Let me check something.

OK, checked it.

OK, now the Pythagorean identity can be used to find cos(x/2) if you want to go that way.

[fiery merlin]

It would be better to use this version for sin(x/2).

[mellow mountain]

i have to rationalize it

[fiery merlin]

Oh, I mean rationalize it to get the answer for sin(x/2).

But then go back a step to make sqrt(1 - sin^2(x/2)) easier.

That'll remove the square root, then do 1 - that, then you add the square root back and simplify.

Hmm, I guess either way wouldn't be too hard.

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[stone wolf]

@vocal rampart

<@&286206848099549185>

[ionic tide]

This is a Parallelogram

[safe radish]

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

[ionic tide]

AB // DC and AD // BC

[stone wolf]

oh

[ionic tide]

ab = dc, ad = bc

[stone wolf]

yea I did that

so i got y = 6

and

x = 3

I just dont know how to find angle DAC and angle DAB

[ionic tide]

ADB = DBC = 59

using a total angles in triangle = 180

to find DAC

[stone wolf]

so we have 180 - 59?

[ionic tide]

• 49

180 - 59 - 49

[stone wolf]

62

so DAC is 62

degrees

[ionic tide]

cause AD // BC to DAC = ACB = 62

[stone wolf]

ohhh

so now

to find angle DAB I would start where?

[ionic tide]

You see BFC = FAB (CAB) + ABF (20) (Cause properties of exterior angles of triangle)

49 - 20 = 29

[stone wolf]

mhm

[ionic tide]

DAC + BAC = DAB = 62 + 29 = 91

[stone wolf]

so dab

is

91 degrees?

[ionic tide]

yes

WAIT

[stone wolf]

yea?

[ionic tide]

DAC = 62

no 72

[stone wolf]

yes

oh

wait its 72?

[ionic tide]

yea

so DAB + 101

[stone wolf]

• or equals?

[ionic tide]

=

EQUAL

[stone wolf]

okk

I have one more question can i send that or do i have to reopen

the ticket

cause its an assignment

this is the other quesiton

its the last one

[ionic tide]

Perimeter = 2(AB or DC + BC or AD)

i just saw

2y + 1 = 3 - 4w (AB = DC)

[stone wolf]

I am confused

[ionic tide]

AD = BC (3x - 2 = x - w + 1)

[stone wolf]

Okayy

we need to find w tho

right?

[ionic tide]

this just

let me think more time

[stone wolf]

okk

[ionic tide]

Cause this is Parallelogram

AB = DC, AD = BC

💀

this one..

really complicated

I think you take:
22 = 2(2y + 1 + 3x - 2)

AB + AD = 12 = 2y + 3x

take this is number 1

[ionic tide]

take this number 2

[ionic tide]

take this number 3

[ionic tide]

take this number 3

use number 2
w = 1-y/2 (4)

use number 3

W = 2x - 3 (5)

You use from number 4 and 5

y = 7 - 4x

change y for number 1 (2y + 3x) = 12

x = 2/5

change x for y + 7 - 4x

y = 27/5

so AB = 2(27/5) +1 = 11,8

@stone wolf

sorry this is really dizzy

ill go rn

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[delicate bramble]

Whats the weird wave thing between X and N

[fair matrix]

~ is the "weakly approximates" symbol.

[delicate bramble]

ok thx

.close

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[delicate bramble]

What are these symbols

and

[rugged arch]

,, \varphi \phi

[flat frigate]

mmmm7

[delicate bramble]

What do they mean

[rugged arch]

they can mean many things

u need more context

[delicate bramble]

For example here

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[rugged arch]

first one looks like the probability density function

[safe radish]

Please don't occupy multiple help channels.

[rugged arch]

the second one is the cdf

[delicate bramble]

But what does the symbol do

[rugged arch]

nothing

could've just said f(x) = ...

and F(x) = ...

[delicate bramble]

Oh

[rugged arch]

.close

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Channel closed

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[rugged arch]

btw use your own channel 😭

with .reopen

[delicate bramble]

What why did the bot close it

I didnt even have it open for so long

.close

[rugged arch]

it's cuz u closed it

😭

[rugged arch]

^

[delicate bramble]

Well now i did, but the bot did it automatically

.close

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[zealous dirge]

(2(2+1)+1) = 7
2.7 + 1 = 15
2.15 + 1 = 31
2.31 + 1 = 63
2.63 + 1 = 127
is there any other way to approach this problem ?

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[unique aurora]

How can I go about solving this?

[unique aurora]

i know that the angle DOB is 100

But i dont understand how the 32 degree angle relates to solving z

[unique aurora]

or would it be 80?

[dry vapor]

the 32 is there so you calculate BDC

[unique aurora]

OOOH

[dry vapor]

Then z = BDO - BDC

[unique aurora]

yepp i got 8 for z

[dry vapor]

nice

[unique aurora]

thx for ur help :)

.close

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[unique aurora]

wait can u also help with this one :D

ive got x is 30

but idk how to get y

[autumn kite]

whats the blue angle?

[unique aurora]

same as x

so 30

[autumn kite]

ye

[unique aurora]

i wanted to use cyclic properties, so that 180- 95 would be y, but im guessing it wouldnt work cuz idk the center

[autumn kite]

can u tell what quadrialteral is ABCD?

or else

ABCD are _______ points

[unique aurora]

uh, they arent cyclic right?

[autumn kite]

ye

[unique aurora]

oke

[autumn kite]

so thats a cyclic quad

[unique aurora]

mhm

[autumn kite]

and using the properties of cyclic quad

[autumn kite]

,,..

[unique aurora]

D plus Y = 180

[autumn kite]

not full y

y-x

[unique aurora]

OH SO Y INCLUDES THE 30

[autumn kite]

ye

so what the angle y?

[unique aurora]

i got y is 115

[autumn kite]

yes correct

[unique aurora]

yay thxx

.close

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[lean otter]

Help pls

[hardy monolith]

!da2a

[safe radish]

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/

[rustic goblet]

what do you need help with?

[lean otter]

I cant do trigonemntry

[lucid trout]

sine

[lean otter]

so sin (46/480?

sin(46/48)

[lucid trout]

yes

no

wait

the sin of the angle is equal to 46/48

[autumn kite]

figure out the angle you have to find

[lean otter]

this angle

[lucid trout]

yes, denote it $\theta$

[flat frigate]

isomorphic to god

[lucid trout]

then $\sin \theta = \frac{46}{48}$

[flat frigate]

isomorphic to god

[lean otter]

how do i do that on a calculator

[lucid trout]

use the arcsin

function

[lean otter]

73.74

[flat frigate]

isomorphic to god

[lean otter]

so

its

73.7

[lucid trout]

i'll confirm what it is in degree

[lean otter]

Okay ty

[lucid trout]

i got 73.4 here

[lean otter]

OMG

ITS RIGHT

U have no idea how long ive been stuck on that for

wait i have another

[lucid trout]

okay

[lean otter]

am i allowed to send multiple

[lucid trout]

i think so

you need to calculate the angle on top?

use cos

[lean otter]

so cos (34/27) ?

[lucid trout]

nooo

[lean otter]

27/34

[lucid trout]

you need to do something like this

and then

$\cos \theta = \frac{27}{34}$

[flat frigate]

isomorphic to god

[lean otter]

Thats what i did

[lucid trout]

no

[lean otter]

this one

[lucid trout]

you did cos(27/34)

but isn't it

we need to apply the cos function to the angle

and this is gonna be equal to the fraction of the sides

by the trigonometric relations

and now you can you the inverse function of cossine, which is arccos

to find the angle theta

[lean otter]

inverse

so the -1

nect to cos

next

[lucid trout]

yes

[lean otter]

how do i put into calculator

[lucid trout]

$\cos^{-1} \right(\frac{27}{34}\left)$

like this

do you know how to do it?

[flat frigate]

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

[lucid trout]

damn

[lean otter]

No

[lucid trout]

but how you did to find the other one

because you used the inverse function of sine

[lean otter]

arcsin

arccos

arccos(27/34)

i cant

[lucid trout]

yes

[lean otter]

0.653241929

[lucid trout]

yes, but it's in rad

you want degrees

so multiply by 180

[lean otter]

how do i change it

[lucid trout]

and divide by pi

[lean otter]

okay

37.4?

[lucid trout]

yup

[lean otter]

iIts wrong

it changed the question bc i got it wrong too much

[lucid trout]

okay

,ask arccos(23/34) * 180 / pi

[flat frigate]

Results provided by WolframAlpha

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

Requested by orz.orz.orz.orz

[lucid trout]

try 47.4

wait

what angle we need to calculate

the one at the top or bottom?

[lean otter]

theres a help video

[lucid trout]

i don't understand english very well

but if you can tell me

[lean otter]

idk if that hgelps

[lucid trout]

nah we don't need it

[lean otter]

so this angle

i think

[lucid trout]

hm, do you tried answering 47.4?

[lean otter]

its wrong

[lucid trout]

okay, so must be the other angle

,ask arcsin(23/34) * 180/Pi

[flat frigate]

Results provided by WolframAlpha

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

Requested by orz.orz.orz.orz

[lucid trout]

42.5

[lean otter]

wait wouldnt u round up the second decimal

[lucid trout]

oh need to do that?

sorry then

[lean otter]

i think so

YES

ITS 42.6

[lucid trout]

nice

[lean otter]

I have 3 more do u have time

[lucid trout]

yes, send them all

[lean otter]

thank u

[lucid trout]

but wait

[safe radish]

@lean otter Has your question been resolved?

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[stray sentinel]

how do i find the value of x approaching to negative 8 in the right side in this example?

[severe pond]

trace along the function from the right of -8 and see where it gets you

[stray sentinel]

so from the hollow circle in the left side of the cartesian plane i just trace a function going to the right?

so like

or am i seeing the wrong thing 😭

[severe pond]

you have your lefts and rights mixed up sir

[stray sentinel]

OH

i still dont get it im kind of confused with the graph im sorry T_T

[west crow]

is there somone who understand frensh

[severe pond]

for x > -8

if you approach from that side closer and closer to the point x = -8 where do you get to

[stray sentinel]

-6?

[severe pond]

yes

[stray sentinel]

okay i get it now

thank you knief

[severe pond]

you’re welcome

[stray sentinel]

.close

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[fair crane]

does this involve the multinomial theorem
specifically the first part
is it talking about i + j + k
OR
just the individual values of i, j, and k being odd or even?

ie
(2,1,0) is even with an odd value, and
is 2+1+0 = 3 its odd

[fair crane]

ummm, this is an occupied channel, please post the question in a channel under the 'AVAILABLE' sub head

#❓how-to-get-help

[nocturne remnant]

oh ok

[fair crane]

...umm....

<@&286206848099549185>

[nocturne remnant]

(chat gpt helps better in my opinion)

[safe radish]

@fair crane Has your question been resolved?

[fair crane]

<@&286206848099549185>

[fair crane]

!nogpt

[safe radish]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[nocturne remnant]

Ok

[fair crane]

.close

[safe radish]

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[fair crane]

i got no help

[safe radish]

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[sacred rose]

looking for some help with simplifying this expression, ive used equivlencies to simplify into $\frac{\frac{\frac{1}{cos(x)sin(x)}}{1}}{sinx}$

[flat frigate]

LARS5

[sacred rose]

not sure what the next step would be, ive looked on online calculators and i dont understand how they get to their next step

[covert yoke]

Nice start now multiply by sin/sin

[sacred rose]

alright let me try

[loud wren]

you can use keep change flip and “flip” that 1/sin term to make it $\frac{1}{\cos(x)\sin(x)}\cdot\sin(x)$

[flat frigate]

;(

[loud wren]

straightforward from there

[sacred rose]

intresting ok

let me see if i can finish it then i will close thanks!

thanks alot i got it !

.close

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[serene sequoia]

Can anyone help pls

[fickle monolith]

BPT

use Basic proportionality theorem

[serene sequoia]

Sup

Can you explain with drawing if you can

İ tried but failed

[fickle monolith]

if i tyell you, can you just draw those yourself

i'm bad at digital drawing

[serene sequoia]

Hmm okay

Np

[fickle monolith]

draw a horizontal line parallel to EF from D to AB

name that, for example. DG

[serene sequoia]

Okay

[fickle monolith]

gotcha?

[serene sequoia]

İ did

[fickle monolith]

ok first of all, you know BPT right?

[serene sequoia]

Umm i think yes

[fickle monolith]

ok now notice that it is given that 3BD = 2DC

[serene sequoia]

Is it if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion, yes?

[fickle monolith]

yep

[fickle monolith]

.

[serene sequoia]

Okay bd=2k

Dc=3k

[fickle monolith]

umm just find BD/DC

what will be BD/DC?

[serene sequoia]

🙄

[fickle monolith]

use this info

[serene sequoia]

2/3?🤔

[fickle monolith]

yep

now

[serene sequoia]

Then

[fickle monolith]

according to BPT

[serene sequoia]

Yes

[fickle monolith]

DG/AC = BD/DC

[serene sequoia]

Aa

[fickle monolith]

wait

no

typo

[serene sequoia]

Dg is 2x?

[fickle monolith]

BD/BC=DG/AC

[serene sequoia]

2/5=2x/10?

X=2

[fickle monolith]

umm yeah

congo

[serene sequoia]

Thanks

And

Lastly

[fickle monolith]

yeah?

[serene sequoia]

Oh

Answer is wrong

:/

[fickle monolith]

what

wait

we need EF

not DG

[serene sequoia]

Yeah actually

[fickle monolith]

EF=DG/2

[serene sequoia]

20=10x

X=2

-_-

[fickle monolith]

umm

[serene sequoia]

Interesting..

[fickle monolith]

i'm genuinely stuck

[serene sequoia]

(Kramnik) :)

[fickle monolith]

are you sure it's incorrect

[serene sequoia]

Me too

Yes

[celest sonnet]

hey what class are you in

@celest sonnethi

[serene sequoia]

Hi

[serene sequoia]

Do you have any opinion about this qurstion

Geometry Question

[celest sonnet]

nah , hear what i am asking is this in what class are u in

joseph

[serene sequoia]

11

[celest sonnet]

oh in what country

[serene sequoia]

Azerbaijan

[celest sonnet]

hmm what is the wuestion

[serene sequoia]

@fickle monolith oh, answer is correct, I checked it wrongly sorry😂

[celest sonnet]

let me see if i can be of any help

[serene sequoia]

Answer is 2

[celest sonnet]

what was the question

[fickle monolith]

good to hear that

i got trust issues with my math for a few minutes bro

[serene sequoia]

Jajajaj

Thanks for help

[fickle monolith]

you're welcome

and alse we're in same grade

if you're done then close the channel

[serene sequoia]

Yes i am

[fickle monolith]

type .close if done

[serene sequoia]

.closr

.close

[safe radish]

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[maiden pond]

I need help with drawing a few tringles for Geometry for yt vid.

[maiden pond]

Step one:

Script:
“First, I’ll show you how to inscribe a circle in an acute triangle. An acute triangle has all angles less than 90°.”
Action:
Draw an acute triangle (all angles are less than 90°).
Label the triangle and its angles.
Script:
“To inscribe a circle, we need to find the incenter, where all three angle bisectors meet.”
Action:
Draw one angle bisector from one angle to the opposite side. Do this for all three angles.
Use a second color to mark the incenter, where all three angle bisectors meet.
Draw the inscribed circle inside the triangle, touching all three sides.

Step two

Script:
“Now, let’s move on to circumscribing a circle around the triangle. For this, we need to find the circumcenter, where the perpendicular bisectors meet.”
Action:
Draw the perpendicular bisectors of two sides of the triangle. This is done by finding the middle of each side and drawing a line that’s at a right angle to that side.
Use a second color to mark where the perpendicular bisectors meet. This is the circumcenter.
Script:
“The circumcenter is the point where the perpendicular bisectors meet, and it is the center of the circle that goes around the triangle. I’ll draw that circle now.”
Action:
Draw the circumscribed circle around the triangle, making sure it touches all three corners of the triangle.

Step 3

Script:
“Now, let’s look at how the circumcenter changes for different triangles. We’ll look at an acute triangle, a right triangle, and an obtuse triangle.”
Action:
Draw an acute triangle. Explain that the circumcenter is inside the triangle.
Draw a right triangle. Explain that the circumcenter is at the middle of the hypotenuse.
Draw an obtuse triangle. Explain that the circumcenter is outside the triangle.

** Pretty simple draw three things**

i need pics of those tringles

so i can have a example

[safe radish]

@maiden pond Has your question been resolved?

[safe radish]

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[lean otter]

"make a piecewise fuction using 3 different functions and ensure the following "

[lean otter]

how do you make sure they are integers

like the endpoints

[dull sequoia]

Well

Constants are very nice functions

f(x) = 0 ensures you’ll have integer y coordinate

You just need to pick the domain to also have integer endpoints

[lean otter]

what do you mean by that I don’t really get it

[fiery merlin]

OK, so you have a piecewise function with three parts.

One of them needs to be a trigonometric function.

The graph of each part must meet up with its neighboring parts.

And the meet up points have to be at (integer, integer).

Does that all make sense?

[lean otter]

yes I understand that I was just wondering what are some like tips to make sure they meet up at coordinated with integer values

[fiery merlin]

OK, so what you want to do is to pick integer x values for the meetup points.

Like maybe -1, 0, 1 or something.

Oh, wait.

Like -1 and 1, since there are only two meet up points.

You pick the functions so that at x = -1, the y values of the neighboring functions come out to the same integer.

Does that make sense?

[lean otter]

Yes that makes sense but If I make the equation for the first meet up point to be an integer my second end point like x=1 the y value ends up as a decimal

[fiery merlin]

OK, is the middle function the trigonometric one?

[lean otter]

It can be in any order

[fiery merlin]

Right, but I mean in your scenario here ^

[lean otter]

ohh no I was using a parabola

[fiery merlin]

Oh, OK.

What's the parabola polynomial?

[lean otter]

^2

[fiery merlin]

Yes, but I mean like x^2 + 3x - 2 or something.

[lean otter]

I did it in vertex form

[fiery merlin]

I'd recommend in factored form.

If you're going to use a parabola.

a(x - root)(x - root)

But with a change.

[lean otter]

So north roots would be on the x values of the intercepts?

Both

[fiery merlin]

Well, what are the y values of your meetup points?

I mean the goal.

What do you want them to be?

[lean otter]

what do you mean

[fiery merlin]

Like I could make it happen at (-1, 1) and (1, 1) with the parabola x^2.

Or I could make it (0, 1) and (2, 1) with (x - 1)^2.

Or I could make it (0, 3) and (2, 3) with 3(x - 1)^2.

Or even (x - 1)^2 + 2.

[lean otter]

oh yes I understand f

[fiery merlin]

OK, so let's shift a bit.

What trigonometric function do you want to use?

[lean otter]

Sine or Cosine but preferably sine

[fiery merlin]

OK, so sin(x).

Where does sin(x) have (integer, integer) coordinates?

[lean otter]

0,0

[fiery merlin]

Any others?

[lean otter]

90,1 180,0) (270,-1), (0, 360)

[fiery merlin]

Have they taught you radians yet?

[lean otter]

oh my bad

I just do t have pi symbol on my phone so I thought to use degrees

[fiery merlin]

Oh, you can just write pi.

In math, they generally use radians except early on in math teaching or on things like maps and directions a ship is moving.

[lean otter]

👍 I’ll rewrite the coordinates using radian

[fiery merlin]

OK, but make sure to try to find (integer, integer).

[lean otter]

Would there be any other ones since 3.14 isn’t rational

[fiery merlin]

You're correct. There aren't any, because the x value has to be an integer, and you can't multiply pi/2 by an integer to get an integer x that we need to get an integer y.

Like (k pi/2, 0 or -1 or 1).

You'd need to find an integer k so that k pi/2 was an integer.

Because you'll notice that it's (0 pi/2, 0), (1 pi/2, 1), (2 pi/2, 0), (3 pi/2, -1), ....

An integer times pi/2 makes an x value that gives an integer y value.

But then the x value is irrational rather than an integer.

Except with 0 pi/2.

So, (0, 0) is the only (integer, integer) for sin(x).

So, what does that mean?

That means that it can't be the middle function.

Do you see why it can't be the middle function?

[lean otter]

yes I understand

because the second intersection won’t be on a integer coordinate

[fiery merlin]

Right.

[lean otter]

coordinate with integer values

[fiery merlin]

So, do you want it to be the left or right function?

[lean otter]

which do you think would be better?

[fiery merlin]

Oh, either one works nicely.

[lean otter]

The last function also has to connect with a. Point

But the left function would be fine

[fiery merlin]

OK, so we have sin(x) which connects with the next function at (0, 0).

What kind of function do you want to be the middle function?

[lean otter]

Parabola

Or actually maybe exponential

or logarithmic

[fiery merlin]

OK, which one?

[lean otter]

Logairthmic

logarithmic

[fiery merlin]

OK, now we have to be careful because log(0) is undefined.

So, what can we do to adjust for that?

[lean otter]

(X+k)

Log(x+k)

[fiery merlin]

OK, and what k would work so that x = 0 gives log(x + k) = 0?

[lean otter]

k=1

[fiery merlin]

OK, so we have log(x + 1).

When would log(x + 1) have another (integer, integer) coordinate?

[lean otter]

X=9

[fiery merlin]

OK, so log(9 + 1) = what?

[lean otter]

(9,1)

[fiery merlin]

OK, so we have (\log_{10}(x + 1)) from (0, 0) to (9, 1).

[flat frigate]

Chai T. Rex

[fiery merlin]

Is that the second meetup point you want or do you want a different (integer, integer)?

[lean otter]

I believe that’s fine

Also would the sin function be in the 2nd quadrant ?

Sine

[fiery merlin]

At the meetup point, no. It would be at angle 0, which is between the first and fourth quadrants.

[lean otter]

yes but before it?

[fiery merlin]

Oh, it goes through all four quadrants.

-(1 pi/2) is between the third and fourth, so you get all the fourth quadrant angles between 0 and -(1 pi/2).

Then, between -(2 pi/2) and -(1 pi/2) you have the third quadrant.

Then, between -(3 pi/2) and -(2 pi/2), you have the second quadrant.

And so on.

Oh, sorry.

[lean otter]

I meant for the graph

[fiery merlin]

Backwards.

Oh, it's just a sine wave.

[lean otter]

Yep

so back to the logairthmic

So how would we get the parabola to intersect the point ?

(X-8)^2?

[fiery merlin]

Oh, you want a parabola for the right function?

[lean otter]

That’s what I was thinking

Or a polynomial

[fiery merlin]

(9 - 8)^2 = 1 means that you have (9, 1) in it, so it meets up.

[lean otter]

yes

but at the end I believe you must connect it to a final point

like in this case the parabola or the last function to a point for example (12,25)

[fiery merlin]

They probably don't want that.

I'm saying that because with sine, you can't find another (integer, integer) to the left of (0, 0).

I could be wrong about what they want.

[lean otter]

No they didn’t mention it but the teacher said that at the end you will have to connect to a final point

So the parabola will have to have to intersect with a final integer coordinate

[fiery merlin]

OK, but you'd need (13, 25).

[lean otter]

I just created a random point

not a specific one

to give an example of what I mean

[fiery merlin]

Oh, OK.

[lean otter]

But I don’t know how to make the final one have both integer points

Points of intersection

[fiery merlin]

Well, it's (x - 8)^2, right?

[lean otter]

yes

[fiery merlin]

Well, the nice thing is that any integer squared is an integer.

So, you can just pick any x.

[lean otter]

I de

See

Do you think there is a specific order of functions which is the optimal

most optimal

[fiery merlin]

No, there's no way of ranking your choices, as long as they work.

So, no way of getting the best, since any correct solution is just as good as another.

[lean otter]

I see

[fiery merlin]

When I saw your problem, I thought of doing simpler functions just to get it done.

Like y = sin(x) until (0, 0), then y = x until (1, 1), then y = 1 from then on.

[lean otter]

You can’t use linear functions

[fiery merlin]

Oh, OK.

Then I'd probably use y = sin(x) until (0, 0), y = x^2 until (1, 1), then y = 1/x from then on.

[lean otter]

why 1/x

[fiery merlin]

Oh, just because it's a simple nonlinear function that meets up at (1, 1).