help-13

[misty talon]

why did only the last one get changed and not the top fraction

[latent bloom]

We can prove it this way

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \cdot \left( \frac{c}{d} \right)^{-1} = \frac{a}{b} \cdot \frac{c^{-1}}{d^{-1}} = \frac{a}{b} \cdot \frac{d}{c}$

[wraith dagger]

VulcanOne

[latent bloom]

This is where it came from

[misty talon]

alright

so back to my task how would i do it

x+y/4 * 2x/y?

[latent bloom]

Yeah

[misty talon]

the answer should be x^2+xy/2y

[latent bloom]

Yep

You can simplify further

[misty talon]

how

[latent bloom]

$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$

[wraith dagger]

VulcanOne

[misty talon]

confused

[latent bloom]

$\frac{x^2 + xy}{2y} = ???$

[wraith dagger]

VulcanOne

[latent bloom]

Using the same property

[misty talon]

right…

but i have 4 on the bottom

[latent bloom]

4?

[misty talon]

yes?

[latent bloom]

Where did the 4 come from?

[misty talon]

it was there from the start

[latent bloom]

No no

What you reached was $\frac{x^2 + xy}{2y}$

[wraith dagger]

VulcanOne

[latent bloom]

This is correct

[misty talon]

well thats just the answer i have on my laptop

thats not what i got to

[latent bloom]

Ooooh

[misty talon]

i dont know what i did wrong but i got to x+y/4 * 2x/y

[latent bloom]

Well

2x^2 + 2xy

Divided by 4y

Take a 2 as a common factor

2(x^2 + xy)

Divided by 2(2y)

You're gonna be left with

x^2 + xy

[misty talon]

can you explain using the bot its way easier to understand for me

[latent bloom]

Oki

$\frac{x+y}{4} \cdot \frac{2x}{y}$

[misty talon]

yes

exactly what i have

yes

[latent bloom]

Wait

[misty talon]

waiting

[wraith dagger]

VulcanOne

[latent bloom]

$\frac{2(x^2 + xy)}{4y}$

[wraith dagger]

VulcanOne

[latent bloom]

$\frac{x^2 + xy}{2y}$

[wraith dagger]

VulcanOne

[misty talon]

uh

[misty talon]

this is what’s confusing me

[latent bloom]

Oki

From the one before it

$\frac{2x (x + y)}{4(y)}$

[wraith dagger]

VulcanOne

[latent bloom]

Agree?

[misty talon]

think so

[latent bloom]

Alright

We can take the 2

And simplify it with the 4

Since 4 = 2•2

[misty talon]

yes

[latent bloom]

So it will be

[misty talon]

1/2

?

[latent bloom]

$\frac{x (x + y)}{2(y)}$

[wraith dagger]

VulcanOne

[latent bloom]

Yep

[misty talon]

alright

then doesnt that become x^2+y/2y

?

[latent bloom]

Yes

[misty talon]

but i need x^2+xy/2y

atleast thats what it says the answer is

[misty talon]

you still there?

[latent bloom]

Yeah

[latent bloom]

This is correct

[latent bloom]

The x^2 + y is not

Not correct

[misty talon]

so what did i do wrong 🤣

[latent bloom]

Because y is missing an x

[cedar kiln]

@misty talon Has your question been resolved?

[misty talon]

.close

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[narrow owl]

Who needs help i gotchu

[obsidian coral]

Not the purpose of a help channel to try and request to help people. You just help who you can

.close

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[mental crow]

X is randomly selected from range [-2,8] , if event A = { X <0 }. Find the probability of P[A]. The question is, how will the outcome be affected if the range is discrete and if instead of a range we have a distance.

[red pumice]

X is uniformly distributed on [-2,8]

?

[mental crow]

Yes

[red pumice]

what exactly do you mean if instead of a range we have a distance

a distance is just a number

[mental crow]

well yeah. So this is a question from a greek book. Which in clear translation is X is selected in the distance [-2,8] . So in the solutions the answer is P[A] = 2/10, where the 2 values are -2 and -1. But what I wrote is 2/11 . The solution claims that its only 10 values in the range which I believe it does not include 0.

[red pumice]

you are right its 2/11 for the discrete case

[mental crow]

but X is selected in [ -2 , 8] which this denotes range and in a range 0 exists

[red pumice]

0 should be in the rang

i think the book is wrong

you understand it well either so i wouldnt worry too much about it

[mental crow]

well the professor solved it. so.

Since you agree with the solution I will go ahead and close this. Thanks!

.close

[cedar kiln]

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[slow thicket]

What I suppose to do next? I have to find x of derivative of f(x) that equals to 0

[dire geode]

"have to find x of derivative of f(x)"

Why do you have x minus question mark

[slow thicket]

nvm that what I have to find and from what equation

just my note

[dire geode]

Are you solving for critical points? Just show the original question

[slow thicket]

Solve equations of F'(x) = 0, equation a)

[dire geode]

Use a trig identity to express f' only in terms of either sine or cosine. Then use quadratic formula

[cedar kiln]

@slow thicket Has your question been resolved?

[slow thicket]

I barely to understand what identity to use, like I used sin^2(x)+cos^2(x) = 1 but it makes equations with squares of 1 - sin^2(x) or 1 - cos^2(x), make 2sin(x)cos(x) to sin(x)cos(x) + cos(x)sin(x) and 1 make sin^2(x)+cos^2(x) and tried to factor out equation, but it's also doesn't make a sense

[dire geode]

u=sin(x) and quadratic formula on u

[slow thicket]

?

[dire geode]

Read the first sentence

[slow thicket]

Read what I did write before: "I barely to understand what identity to use"

[dire geode]

If u=sin(x) what's cos(x) in terms of u?

[dire geode]

Solve for cos(x) using your first equation

[slow thicket]

💀

[cedar kiln]

@slow thicket Has your question been resolved?

[dire geode]

,w solve sqrt(2)(cos(x)+sin(x)) -2sin(x)cos(x)-1=0

[wraith dagger]

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[dire geode]

Try writing the term with sqrt(2) as a single trig function with x +- pi/4

The second term is just sin(2x)

[slow thicket]

and what next? Like I've tried to make first of two terms to sum of two angels and other identifies seems to be not helpful in this case somehow

[dire geode]

Use cos(pi/4) for one of them in your first equation instead of sin

[cedar kiln]

@slow thicket Has your question been resolved?

[cedar kiln]

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[little trellis]

if -5a^-1,5 is the result for the 2. derivative what does that mean?

[little trellis]

i am trying to see if its a maximum or minimum

[cosmic steppe]

What

[little trellis]

so if the result was -1 its a maximum

for -5a^-1,5 its just no solution?

[cosmic steppe]

Okay my guy I'm gonna need context

You can't just list a set or a gradient or a point like that

Wdym by -5a^(-1),5

Like I need context

[little trellis]

sorry english isnt my first language. I did the derivative.

[cosmic steppe]

I need the original problem

Oh you use commas instead of decimal points ....

[little trellis]

i hope this helps

[cosmic steppe]

Yeah so $10a^{-0.5} = 0.1$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

Which

If you use exponent laws and identities

$$\frac{10}{\sqrt{a}} = 0.1$$

[wraith dagger]

Umbraleviathan

[cosmic steppe]

And then it should be easy

[little trellis]

oh i mean i am looking for the second derivative

to check if its a maximum or not

[cosmic steppe]

What did you get for the second derivative

[little trellis]

if its < or > 0

[little trellis]

thats the -5a^-1,5

[cosmic steppe]

I see

[little trellis]

i just want to know what that tells me

[cosmic steppe]

Find a first, and then find U''(a)

The second derivative tells you concavity

If f'(a) = 0, and f''(a) < 0, then f(a) is a max

If f'(a) = 0, and f''(a) > 0, then f(a) is a min

[little trellis]

for finding a i would multiply with the root a and then divide by 0,1 and then do ()^2

[cosmic steppe]

You would

[little trellis]

and then its a = (10/0,1)^2

right?

[cosmic steppe]

Yeah

[little trellis]

so 10000 i guess

[cosmic steppe]

Mmhm

[little trellis]

a = 10000

[little trellis]

but since for the 2. one its -5a^-1,5 we cant tell if its a max or min right

or is it max

[cedar kiln]

@little trellis Has your question been resolved?

[cosmic steppe]

_ _

[little trellis]

did you write something?

your message shows as blank here

i cant really tell, do we have to solve for a again ?

[cosmic steppe]

No you plug in a

You already found a

[little trellis]

oh my god

no waaay

[little trellis]

so its a max right

[cosmic steppe]

Yes

[little trellis]

Thanks !!

.close

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[pale osprey]

how do i solve this

im supposed to get ln4

[crimson sedge]

Is this log as in ln or another base?

[sacred grail]

just work it out from the answer being ln4

[dire geode]

,w integral 1/sqrt(e^x-1)

[wraith dagger]

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[dire geode]

I guess set u=sqrt(e^y-1)

[sacred grail]

yeah

[cosmic steppe]

That's one hell of a u sub

Oh wait

Yeah it'll become 2/(u^2 + 1)

Bruh

[sacred grail]

dust settles pretty nicely

[cosmic steppe]

That's a very sneaky one

Sneaky sneaky 😠

[sacred grail]

not much else you can do tbh

[cosmic steppe]

At least arctan isn't a pain in the ass ...

[sacred grail]

if you try u=e^y - 1 you need to another sub which brings you to 2/(u^2 + 1) anyway

[cedar kiln]

@pale osprey Has your question been resolved?

[pale osprey]

bruh

they really expect us to come up with that

tf

[cedar kiln]

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[sonic cove]

Does anyone know how to solve this?

[violet night]

you can find where the intersect, use that x coords as upper and lower limits

and you can also note that x+y=6 is the 'top' of the area

so that integral minus the other one gives you the area

[sonic cove]

do I still have to derive y=x^2+4x ?

[violet night]

you dont derive anything here

you have y=x^2+4x and y =6-x

integral of upper function minus integral of lower function with respective bounds gives the area enclosed by the curve and line

[onyx karma]

Is this 2 separate examples or 1 task?

[violet night]

it is one task

or else it makes no sense

[sonic cove]

its one task

[violet night]

@sonic cove try what i've wrote out

[sonic cove]

alrighty, also do you guys have any guides for solving integrals?

[violet night]

not sure myself, some other people might know , what I wrote is the correct way to solve this but you could find a book or two in #books-old

@sonic cove

[sonic cove]

I see, Thank you so much dude!!!

[cedar kiln]

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[viral swallow]

hey guys, I'm having a problem with a homework question. Our teacher hasn't been here for 2 1/2 weeks now and she said a question similar to this will be on a test next week. Our supply has just been useless no offense to her just doesn't know any of the material. In particular the bearing and angle of depression... Can someone help me with how this diagram is supposed to look?

[viral swallow]

I understand the questions when it either has angle of depression/elevation or bearing. But a question like this that has both it's really hard to draw the diagram. There isn't an answer key for us to check if we're even doing it right either and when I looked up those homework help tutorials I couldn't come across a question like this

[cedar kiln]

@viral swallow Has your question been resolved?

[viral swallow]

no

[gusty forum]

i instinctively typed draw a diagram then saw that's what you're struggling with

you'll probably need more than one diagram since this is 3 separate triangles you're dealing with unless very comfortable with 3d visualisation

the first step is drawing a birds eye view of the situation with D,N,M

[viral swallow]

I tried doing the bird's eye view diagram but ended up with only 2 triangles... I don't even know how there's supposed to be a 3rd one...

[gusty forum]

so the birds eye view gives you a triangle

and you should understand that the length between N,M is the quantity you're looking for

and to get that you need more information

and since it's a bird's eye view, it's as if D is at the same height as N and M

now use this information to draw more diagrams that might help you to determine the lengths of DN and DM in your bird's eye view triangle

[viral swallow]

I'm still ending up with 2 triangles... Is this supposed to look 3D or something? I have no idea how to do it if so

[gusty forum]

if you want to encapsulate everything as one diagram it'll be a 3d shape composed of 4 triangles, of which we care about 3 of them

but drawing it all in one place is really hard, so drawing the 2d faces that are helpful to us as separate diagrams helps to simplify

[cedar kiln]

@viral swallow Has your question been resolved?

[viral swallow]

thanks man, but still lost.. Anyone else? <@&286206848099549185>

[gusty forum]

relevant diagram

now fill in the details

D' being the point D on the left, changing notation might've been better :p

[viral swallow]

ohhh okay, this makes sense now. This is completely different than the other questions. Thanks a lot man

[viral swallow]

.close

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[past pebble]

if a,b and c form an ar sequence
a , b , c
is it true that
2, a^2+4b^2+c^2 , a^4+16b^4+c^4 make up a geo sequence?

[past pebble]

please this problem took away 3 years of my lifespan

[gusty forum]

let the arithmetic difference be k and rewrite b,c in terms of a and k

then you can probably just expand the bottom after a gigantic slog

[past pebble]

i decided to express 2b as a+c

so that
4b^2=(a+c)^2
16b^4=(a+c)^4

[gusty forum]

seems like a better idea

[past pebble]

and we have about 8 mins to solve this btw 🫠

[sacred grail]

speedrun

[past pebble]

because this is gonna be on our exam

[sacred grail]

well it seems to work

[past pebble]

PLEASE SHOW ME HOW

[sacred grail]

not sure if theres a shortcut with the algebra but

,w 2a^2(a+c)^2 + 2(a+c)^2c^2 + 2c^2a^2 - (a^4 + (a+c)^4 + c^4)

[wraith dagger]

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[sacred grail]

thats equal

so you get

[gusty forum]

with your sub of 2b=a+c it's actually really quick

[sacred grail]

and you're done

[gusty forum]

because with how specific the numbers are it's almost certainly true so you just sub 2(a²+(a+c)²+c²)² = blah

[past pebble]

yeah ok i did that but how does that prove it

[sacred grail]

well just in the same way that the middle term in AP is AM

the middle term in GP is GM

up to sign*

[past pebble]

did i need to expand it or nah

oh wait i forgor

[sacred grail]

there might be a shortcut but even then the expansion isnt that bad

[past pebble]

i forgor the ^2

[sacred grail]

thats what you get from the expansion

[past pebble]

OMG I DID IT

tysm dreamsnow yumeyuki

and iv as well

thats the kanji in your name right

[sacred grail]

[past pebble]

ty

.close

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[haughty crest]

Can someone help me solve this without brute forcing? Q: Calculate the order of element 23 in a group (Z51, + mod 51)

[haughty crest]

$\subsection{Order of element 23 }

We will calculate the order of the element $23$ in the group $(\mathbb{Z}^+_{51},+ mod\ 51)$. The identity element of the group is $0$ (because we know that $e+a=e$ : $23 + 0 = 23$).\

In $\mathbb{Z}_{51}$ the order of an element a is the smallest positive number k for which:

$\underbrace{a+a+\dots +a}_{\text{k times}} \equiv 0 \mod51$\

We want $23\times {k}\mod 51 \equiv 0 \mod 51$. We try to find a way to solve this without brute forcing every combination (because I tried to brute force it, it lead me nowhere):\$

[tropic oxide]

you want 23*k not 23^k

since your group's operation is addition, taking the "k'th power" of an element will look like multiplying it by k

so really you are solving $23k \equiv 0 \pmod{51}$

[wraith dagger]

Ann

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

[tropic oxide]

note that 23k ≡ 0 (mod 51) is equivalent to saying that 23k is divisible by 51

[haughty crest]

Yeah, so it's not. So we have to iterate k until it is equiv to 0 mod 51.

Thats the thing, I havent found a way to find k without brute forcing this.

Hint: k is probably 51

,w 23 * 51 mod 51

[tropic oxide]

no, we don't need to iterate anything...

[wraith dagger]

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[tropic oxide]

observe that 23 and 51 are coprime.

[haughty crest]

so their gcd is 1?

[tropic oxide]

it is, but that's not the conclusion i'm about to type.

[haughty crest]

🙂

[tropic oxide]

23 and 51 are coprime, which means that 51 can only divide 23k if 51 divides k itself.

[haughty crest]

okay good point and keen observation

though what would happen, if they werent coprime

[tropic oxide]

ak = 0 (mod m) would be equivalent to (a/d)k = 0 (mod m/d), where d = gcd(a,m)

and a/d and m/d would be coprime

[haughty crest]

Yeah I saw that here too: https://math.stackexchange.com/a/1944327

So in fact, what you wrote and case 2 on the link. It's the same?

I just didnt understand the case 2.

[tropic oxide]

yes, what i said just now is the same thing

with slightly different notation and phrasing

[cedar kiln]

@haughty crest Has your question been resolved?

[cedar kiln]

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[ebon pecan]

Can anybody solve it, please?

[south tundra]

4y = 9 - 2x, try plugging this into the second equation

You'll end up with a quadratic equation in x

[ebon pecan]

Thanks.

[cedar kiln]

@ebon pecan Has your question been resolved?

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[robust pewter]

Find the break points of the function, if they exist. Plot a function graph

[robust pewter]

Help

[cedar kiln]

@robust pewter Has your question been resolved?

[cedar kiln]

@robust pewter Has your question been resolved?

[cedar kiln]

@robust pewter Has your question been resolved?

[cerulean sail]

A start would be to compare what happens at $-\pi$ and at 0...

[wraith dagger]

chartbit

[cerulean sail]

E.g. what happens to $\sin(x)$ as $x$ decreases to $-\pi$? What is $y$ when $x=-\pi$?

[wraith dagger]

chartbit

[cerulean sail]

...though with that said, how do you define a break point?

[dire geode]

https://math.stackexchange.com/questions/3112809/what-is-the-breakpoint-of-a-piecewise-function

Sounds like jump discontinuity

[cerulean sail]

Just came from that exact page, hence my question 😂

My thoughts were that one of them wouldn't have been a break, but that answer has me doubting a bit(!)

[cedar kiln]

@robust pewter Has your question been resolved?

[manic acorn]

This isnt jump disc as far as i remember, this is infinite disc no?

[cedar kiln]

@robust pewter Has your question been resolved?

[dire geode]

Read the link

[dire geode]

.

[cedar kiln]

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[hushed bough]

hey guys can someone help with me with identifying linear vs non linear differntiation equations?

[hushed bough]

is there a rule or something

[cedar kiln]

@hushed bough Has your question been resolved?

[cedar kiln]

@hushed bough Has your question been resolved?

[cedar kiln]

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[crimson sedge]

i dont understand what im doing wrong here

[gusty forum]

knowing how janky some of these software are it might only accept 0.2%

[tranquil oracle]

or maybe they don't want you to include the % sign

[crimson sedge]

not thhat

[gusty forum]

yeah, that too, it might not want the percent sign

[crimson sedge]

nope

yea its that and this

idk how to read taht

[tranquil oracle]

12.0

ah, try 0.20%

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[urban ore]

I think its 1024

But I cant figure it out

[brisk dirge]

Hlo what's the full question

[urban ore]

Thats the function

[dire geode]

That's not a question. What are you supposed to find or show

[urban ore]

I think what R equals

Or G

[dire geode]

Just show the original question

[urban ore]

Thats the question

[dire geode]

That's not the full question

[urban ore]

Idk I was just told to solve it

[dire geode]

That's an equation

[dire geode]

Show the instructions

[urban ore]

Thats exactly what I got

[dire geode]

Show this

[urban ore]

I was told in real life to solve it

[dire geode]

Then that's unclear and you need to ask for further instructions

[urban ore]

Ok

[crimson sedge]

[brisk dirge]

[cedar kiln]

@urban ore Has your question been resolved?

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[patent hearth]

why do you pick 8pi and 3pi and how did they turn into pi/4 and 2pi/3

[modern compass]

you pick those because they reduce to known values on the unit circle.

they reduce because 3/12 = 3/(3 * 4) = 1/4

[patent hearth]

why can't i get the same answer with 7pi/4 and 4pi/3

[dire geode]

Try it

[patent hearth]

i did

i got -1-root3/1+root3

[coral imp]

How did ya break 11pi/12 Into that tho?

[patent hearth]

i looked at the unit circle found two values that the num adds to 11 and the denominators multiply to 12

[dire geode]

That's not how fractions add

[coral imp]

Hey wtf?

[patent hearth]

yikes

[coral imp]

[patent hearth]

unfortunate

[coral imp]

True

[patent hearth]

wait so how am i supposed to do it

[dire geode]

Like in the solution

[patent hearth]

alright thanks

[dire geode]

https://www.cuemath.com/numbers/addition-of-fractions/

Should give that a revieq

[coral imp]

,w (1-√3)/(1+√3)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by anand#0990

[coral imp]

,w -2+√3

[wraith dagger]

Results provided by WolframAlpha

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

Requested by anand#0990

[coral imp]

000

[patent hearth]

https://tenor.com/view/kante-gif-21755046

.close

[cedar kiln]

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[earnest pendant]

Anyone knows how to find the L in this

[earnest pendant]

<@&286206848099549185>

[cedar kiln]

@earnest pendant Has your question been resolved?

[cedar kiln]

@earnest pendant Has your question been resolved?

[cedar kiln]

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[bold adder]

I'm going through Ross' A First Course in Probability, and came across a question in the Conditional Probability and Independence Chapter:
A girl is taking 3 exams. The probability that she passes the first exam (E1) is .9. If she passes the first exam, then the conditional probability that she passes the second one (E2) is .8, and if she passes both the first and the second exams, then the conditional probability that she passes the third (E3) exam is .7. Given that she did not pass all three exams, what is the conditional probability that she failed the second exam?

I found the correct answer by drawing a tree diagram and calculating P(^E2) / ( P(^E1) + P(^E2) + P(^E3) ), but is there a general formula for this and could anyone help me understand it (pls @ me if you can)? TIA

[upper abyss]

General formula for which situation?

You've found the formula for "failed second, given did not pass all"

[bold adder]

For consecutive, dependent(?) events

[upper abyss]

Like, if there was more than three tests?

[bold adder]

yeh

The way it's written I assumed Id use Bayes theorem, but couldnt work it out that way

[fast hazel]

so you want to find P(E2'| (E1 u E2 u E3)') and youre given P(E1) = 0.9, P(E2 | E1) = 0.8, P(E3 | E1 n E2) = 0.7
some things that might be useful to consider are P(A|B) = P(A n B)/P(B) in general and (possibly) demorgan's laws from first glance, i think you should be able to get what you need right :D

[bold adder]

actually I think I know (lmk if im right) - Bayes theorem: P(A|B) = P(BA)/P(B), where B is she does not pass all three tests, A = she fails test 2, and BA is where she doesnt pass all three tests and fails on test 2 (= A).
P(A) = 0.9*(1-0.8), and P(B) = (1-0.9)+(1-0.8)+(1-0.7)

It's a lot easier to visualise P(B) with the tree diagram

[upper abyss]

Note that is not Bayes' theorem, but the definition of conditional probability

And a few applications indeed gets the answer. But I'm wondering if there's a smoother way

[bold adder]

There was another question from the same chapter I couldnt work out, maybe theres a common trend

[latent zinc]

stop studying math

ok thanks

.close

[bold adder]

"An ectopic pregnancy is twice as likely to develop when the pregnant woman is a smoker as it is when she is a nonsmoker. If 32 percent of women of childbearing age are smokers, what percentage of women having ectopic pregnancies are smokers?"
I got the answer, again by drawing a tree diagram, but doesnt feel very convincing

[upper abyss]

E = Ectopic preggo
S = smoker

Then:
P(S) = .32
P(E | S) = 2P(E | -S)

We can follow through the definitions:
P(ES) / P(S) = 2P(E(-S)) / P(-S)

Can use a venn diagram or other tricks to get that:
P(E(-S)) = P(E) - P(ES)

Which means that:
P(ES) / P(S) = 2[P(E) - P(ES)] / [1 - P(S)]

And P(ES) is solvable from this

We really want:
P(E | S) = P(ES) / P(S)
So this solves the problem

That's the most mechanical way to do this, but total probability would be smoother here

That is, your tree diagram technique is the way I'd go

[solid juniper]

ectopic preggo bruh 💀

[bold adder]

I see, I missed how to formulate this part

P(E | S) = 2P(E | -S)
I like being able to prove it, even if a visual representation is faster

[upper abyss]

Oh, that's in the question

An ectopic pregnancy is twice as likely to develop when the pregnant woman is a smoker as it is when she is a nonsmoker

P(E | S) = 2P(E | -S)

[bold adder]

Yeh haha I just didnt know how to write that as an equation

cheers

[upper abyss]

Np. Feel free to ask if you have anything else!

[bold adder]

No doubt Ill have more questions down the line

.close

[cedar kiln]

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[cedar kiln]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[digital shell]

Hello, how can I solve this?

[sonic thistle]

Trigonometry

[maiden lodge]

Well, any thoughts?

[digital shell]

No I have no idea how to even approach this

[maiden lodge]

Well, this is related to trigonometry. Think of formulas that you lately learned.

[digital shell]

for 30-60-90 triangles I learnt that the ratios are 1: square root of 3 : 2

[maiden lodge]

What about sin, cos, tan? Familiar?

[digital shell]

no, I haven't learned that yet

this is about 30-60-90 triangles

[sonic thistle]

Use this

To find all the sides

[digital shell]

I don't know how to convert

[sonic thistle]

Multiply it by 6

Since you know a side is 6

[maiden lodge]

Alright, so which of the 1: squareroot 3: 2, does 6 represent? (like which position, the longer or shorter side.

[digital shell]

the square root of 3

[sonic thistle]

No

Wait

[digital shell]

it's opposite to the 60 degree angle

so XY should be

[maiden lodge]

How would you do to make squareroot 3 to 6?

[digital shell]

I have no idea

[sonic thistle]

That's confusing

[maiden lodge]

$\sqrt{3} => 6$

[wraith dagger]

Potet

[maiden lodge]

Like, what do you multiply with to get 6.

[foggy merlin]

6/sqrt3

[sonic thistle]

Yes i know but i think it's confusing for him

[digital shell]

I don't know

[sonic thistle]

Herels just told you

[digital shell]

I don't understand this

[maiden lodge]

What do you multiply with 2 to get 4?

$2 => 4$

[wraith dagger]

Potet

[digital shell]

2

[maiden lodge]

What do you multiply with squareroot of 2 to get 2?

$\sqrt{2} => 2$

[wraith dagger]

Potet

[digital shell]

itself

but I don't understand how it relates

to my problem

[maiden lodge]

Well, since the ratio is 1:sqrt3:2, when one of the side increases, the other sides increases too.

[digital shell]

according to the ratio side ZY should be 2 times as long so I should be able to multiply 6 with 2 to get the length

[sonic thistle]

No

This only works for the side opposite to the 30 degree angle

[maiden lodge]

According to your explanation, does a 90 degree triangle have a hypotonus of 5 when the side are 4 and 3?

[digital shell]

yea I realized that but I don't understand why. or the logic behind it

[sonic thistle]

Yes

Thats why you need trigonometry for this question

Your teacher wasnt really inspired

[digital shell]

I should be able to solve this using the ratios for a 30-60-90 triangle

[maiden lodge]

Think of the Pythagoras's theorem.

[digital shell]

I don't have a teacher

[sonic thistle]

Why lol

[digital shell]

I learn over internet

khan academy

[sonic thistle]

What grade are you in

[digital shell]

I am not in school

[sonic thistle]

?

[digital shell]

I graduated

[sonic thistle]

Ok

And why are you doing this

[digital shell]

to learn math

[sonic thistle]

And how in the world dont you know trig

[digital shell]

bad education

[sonic thistle]

Sad

[digital shell]

yeah but i'm trying to remedy that

[sonic thistle]

There is no point in doing this without trig

Trig you will need even in university

30 60 90 triangles no

[digital shell]

Yes but right now i am learnign special right triangles not trig

so I need to know this aswell

[sonic thistle]

No you dont

Its useless

[digital shell]

I will be able to apply this method to special right triangles

[sonic thistle]

Which wont be as effective as trig

[digital shell]

well I figured I should still know this

can't hurt to gain knowledge on different methods

[maiden lodge]

Well, knowing the ratio of the sides is a bit beneficial.

[sonic thistle]

Eh

If you say so...

Anyway

I'll teach you a theorem

For the 30 60 90 triangle

[digital shell]

alright

[sonic thistle]

If you want

[digital shell]

yes would be much appreciated

[sonic thistle]

Ok

In a 30 60 90 triangle

The side opposite to the 30 degree angle is always half the lenght of the hypothenuse

You can use this

[digital shell]

yeah from the ratio

[sonic thistle]

Yeah

[digital shell]

but I don't know how to convert

that's the problem

[sonic thistle]

If you label the side opposite to the 30 angle with x

Then whats the hypothenude?

[digital shell]

2x

[sonic thistle]

Very good

Now

You have a right triangle

With sides x, 2x and 6

What can you use to find x?

(A very popular theorem)

[digital shell]

I need to convert the 6 to the longer side

[sonic thistle]

Nk

No

What theorems do you know that work in the roght triangle?

[digital shell]

pythagoreas

[sonic thistle]

Good

Use that

Tell me what you get

[digital shell]

I get 6

[sonic thistle]

6 what

[digital shell]

x = 6, when I label the opposite of 30 with x

[sonic thistle]

No

You did something wrong

$6^2+x^2=(2x)^2$

[wraith dagger]

Master Oogway

[sonic thistle]

Right?

[digital shell]

yeah

[sonic thistle]

So you get

[digital shell]

x = 6

[sonic thistle]

$x^2+36=4x^2$

[wraith dagger]

Master Oogway

[sonic thistle]

Right?

[digital shell]

oh I forgot to multiply the 2 aswell

[sonic thistle]

Ok

So?

Whats x

[digital shell]

x = 3

[sonic thistle]

No

[digital shell]

6 = 2x

3 = x

[sonic thistle]

No

[maiden lodge]

Have you learned to solve equations?

If not, you might gonna to use compare method.

[sonic thistle]

Just use the quadratic formula

[digital shell]

how?

[crimson sedge]

\hrulefill\par
Author: Blackpink Lover ♡

Given information;
$$Y = 30°$$
$$X = 90°$$
$$XY = 6u$$

To find;
$$YZ$$

Solution;
$$X+Y+Z = 180° (all angles of triangle add up to 180°)$$
$$90+30+Z = 180$$
$$Z = 180-90-30$$
$$Z = 90-30$$
$$Z = 60°$$

$$Cos(Y) = cos(30°) = \frac{\sqrt{3}}{2}$$
$${\frac{6}{YZ}} = \frac{\sqrt{3}}{2}$$
$$YZ = \frac{12}{\sqrt{3}}$$
$$YZ = 6.92....$$
$$x = 6.92u$$

God, am I terrible at LaTeX

[sonic thistle]

He doesnt know trig

[digital shell]

I haven't learnt any trigonometry

[sonic thistle]

Nora

Cmon

[crimson sedge]

Ok, then we should do it without trig

[sonic thistle]

Its a simple ecuation

[digital shell]

this is just simple special triangle problem where I need to convert the side

[sonic thistle]

Nora

[digital shell]

but the problem is that I don't know how to convert the ratios

[sonic thistle]

Solve the ecuation

And you re done

Cmon

[digital shell]

I don't know how

[sonic thistle]

Quadratic formula

Nk

[digital shell]

I don't have constant

[sonic thistle]

No

Wait

Yes

[maiden lodge]

Why? There's no need for that.

[sonic thistle]

x^2+36=4x^2

[crimson sedge]

@sonic thistle are we allowed to use 30-60-90 theorem has it's proof in trig but direct require trig ?

[sonic thistle]

Move the x^2 to the other side

36=4x^2-x^2

36=3x^2

Divide both sides by 3

12=x^2

x=sqrt12

[crimson sedge]

Ohh quadratic equation is an interesting approach indeed

[digital shell]

there is all ratios

[sonic thistle]

X= plus or minus sqrt 3

[digital shell]

so I just need to conevrt

[sonic thistle]

Done

[digital shell]

to longer side

[sonic thistle]

I said done

Are you reading what i wrote

Or did i waste my time

[digital shell]

I am reading

[sonic thistle]

Solving that

[crimson sedge]

@sonic thistle is my answer correct ?

[digital shell]

but I don't understand how that will help me

[sonic thistle]

We are literally done

[digital shell]

I need to convert the ratios

[sonic thistle]

We found x

The hypothenuse will just be 2x

[maiden lodge]

That is a direct approach of the question. Speaking of solving the question with the ratio, you need two triangles to compare.

[digital shell]

incorrect

[sonic thistle]

Incorrect?

Ur correcting me

Ok

[digital shell]

im just saying the site

according to that it's incorrect

[sonic thistle]

Yes it's correct

[maiden lodge]

An triangle 1, where the ratio is 1:sqrt3:2, and the triangle 2, where 6 is one of side's value.

[sonic thistle]

The x i found

[crimson sedge]

@sonic thistle the answer isn't ± 3 sqrt tho
It's actually
12/sqrt{3}

[maiden lodge]

Since it's lengths, so negative is not included.

[digital shell]

the answer is 4 sqrt of 3

[sonic thistle]

Yes

Exactly what i got

[digital shell]

but I can't just take the answer

[sonic thistle]

I got 2sqrt3

And i told you

[digital shell]

I need to learn how to solve this problem

[sonic thistle]

The hyputjenuse is 2x

So 4sqrt3

[digital shell]

the hard part should be to learn the formulas it should be easy to just convert the ratios

so how can I convert to longer side

[sonic thistle]

Do you understand what i did?

[digital shell]

yes

[sonic thistle]

Good

Do you understand that we solved the problem?

[digital shell]

you solved it. I couldn't do it

[sonic thistle]

You just had to solve the equation

I told you the exact steps

Right?

[digital shell]

yes but nevermind that I need to convert the ratios

[sonic thistle]

Yeah i'm out

Bye

[digital shell]

ok

thanks for help

<@&286206848099549185> anyone able to help me with this problem please

[cedar kiln]

@digital shell Has your question been resolved?

[clear berry]

You just need to use some trigonometry

Assuming we are talking about the question that is pinned

First you need to identify the perpendicular, base and hypotenuse

[clear berry]

you there?

[digital shell]

yes

but I don't know trigonometry

this is about special right triangles

30-60-90

so I am supposed to use the formula to convert the sides

[clear berry]

yes

[clear berry]

also yes

[lusty grotto]

hi

[clear berry]

First things first, identify the hypotenuse, base and height/perpendicular

[digital shell]

hey

I found the sides and formula here

[clear berry]

okay, but why do you have 3 number in the ratio?

[lusty grotto]

do u know sohcahtoa

[digital shell]

for the 30-60-90 ratios

[clear berry]

you don't need that

[digital shell]

never heard of

[clear berry]

First things first, identify the hypotenuse, base and height/perpendicular

[lusty grotto]

sine = opposite / hypotenuse?

[digital shell]

but i am supposed to use that to solve it

[lusty grotto]

u know this?

[digital shell]

no

[clear berry]

I don't think so

[digital shell]

I have not learned any trigonometry

[clear berry]

ohhh, I see. So, this is not a trigonometry question but a ratio question

got it

[digital shell]

yes

[lusty grotto]

all right what is the ratio between the lengths of YZ and YX?

[digital shell]

from sqrt 3 to 2

[clear berry]

Then just use the ratios and the pythagoras theorem

1 : sqrt(3) : 2 is the ratio of XZ, XY and YZ I am guessing

In particular XY : YZ is root(3) : 2 ?

[digital shell]

but the problem is that I don't know how to convert

I don't think I have worked with problems that had 3 ratios

[clear berry]

Btw how did you get these ratios?

[digital shell]

opposite of 30 angle is 1

60 is sqrt 3

and 90 or the hypotenuse is 2

so should be easy to just convert them

[clear berry]

huh? How do you know that?

[lusty grotto]

okay XY : YZ : ZX = sqrt(3)/2 : 1 : 1/2

[digital shell]

the ratios

[lusty grotto]

multiply thru by 2 u get sqrt(3) : 2 : 1

[digital shell]

not the sides

lengths

[clear berry]

Yeah, how did you get the ratios? Is that given?

[digital shell]

I don't understand this

[digital shell]

yeah the ratios is the same for all 30-60-90 triangles

it's a formula

[clear berry]

I see, that makes sense, okay so

Would you agree to this - XY : YZ is root(3) : 2

All I have done is left one ratio out

[digital shell]

yes

[clear berry]

Also, do you know that ratios are just fractions

[digital shell]

I need to convert from the sqrt3 to 2

i thin so

[clear berry]

So, XY : YZ is root(3) : 2 is same as XY/YZ = root(3)/2

$\frac{XY}{YZ} = \frac{\sqrt 3}{2}$

[wraith dagger]

numbpy

[clear berry]

Then can you find YZ from this?

[digital shell]

I don't understand how you got to that equation

[clear berry]

You agreed that ratios are fractions right?

There's another way to do this

assume r to be the common ratio then find r

[digital shell]

yes 1:2 = 1/2

but could you explain what steps you did

[lusty grotto]

How do you write XY : YZ as a fraction

[digital shell]

XY / YZ

[lusty grotto]

Right

How do you write root3 : 2 as a fraction

[digital shell]

sqrt3 / 2

[lusty grotto]

Right

But now do you agree that XY : YZ = root3 : 2?

[digital shell]

but when converting from smaller one shouldn't you multiply instead?

[digital shell]

but XY is 6

[lusty grotto]

Yes so u can write 6 instead of xY

So then XY : YZ is the same as 6 : YZ

[digital shell]

yeah

[lusty grotto]

So what do u not understand

[digital shell]

the conversion

how do I convert the 6 to the longer side

[lusty grotto]

What do u mean longer side

[digital shell]

hypotenuse

x

sqrt3 to 2

[lusty grotto]

U don't need to convert 6to the hypotenuse, I dont know u mean by that

[digital shell]

I know the length of XY because it's given, but now I need to get the length ox ZY by converting the 6 to the larger side by using the formula

so I can get answer

[lusty grotto]

U dont get the answer by "converting 6 to the larger side"

Whatever that means

[digital shell]

ratio conversion

[lusty grotto]

Can u show me an example of what u mean

[digital shell]

ok

for example if I knew the length of ZX, I could convert that length to get the length of x by taking double of ZX

because of the ratio

1:2

now I need to do the same with sqrt3:2

but I don't know how

maybe I explained it poorly but I just need to find the solution to this problem

[lusty grotto]

Oh

Let's say u had a ratio of 1:5 maybe instead of 1:2, then what would u do to find x?

[digital shell]

I would multiply by 5

5 times larger

[lusty grotto]

How about if u had a ratio of 1:0.5

What would u multiply by

[digital shell]

I could multiply with 0.5

[lusty grotto]

Yes that's right

Right but 1 : 0.5 = 1 / (1/2)

?

[digital shell]

1 : 0.5 = 1 / 0.5

[lusty grotto]

Yes 0.5 = 1/2?

[digital shell]

yes

[lusty grotto]

Yes so 1 / (1/2)

[digital shell]

yeah

[lusty grotto]

Can u simplify this fraction

$\frac{1}{\frac{1}{2}}$

[wraith dagger]

SilverSoldier

[digital shell]

1 * 2/1

[lusty grotto]

So 1 / (1/2) = 2 / 1?

[digital shell]

yeah

[lusty grotto]

So 1 : 0.5 = 2 : 1

[digital shell]

yea

[lusty grotto]

Okay

Okay so sqrt3 : 2 = sqrt3 / 2

Can u covert this fraction to a fraction with 1 in the numerator

[digital shell]

no

[lusty grotto]

U know equivalent fractions right?

[digital shell]

yeah I think so

[lusty grotto]

What is an equivalent frction to 1/2 ?

[digital shell]

2 / 4

[lusty grotto]

Yeah

How did u find this?

[digital shell]

I multiplied both sides by 2

[lusty grotto]

Yes

U can also divide both top and bottom by the same number and find an equivalent fraction right?

[digital shell]

yeah

[lusty grotto]

Right

Now tell me an equivalent fraction to roots3 : 2

Root3 / 2

[lusty grotto]

What can u multiply or divide both top and bottom by, to get an equivalent fraction with one in the numerator?

[digital shell]

divide by sqrt 3

[lusty grotto]

Yes, can you do that and send me the equivalent fraction u get

?

[lusty grotto]

Right

So root3 : 2 = root3 / 2 = 1 / (2/root3) ?

[digital shell]

yes

[lusty grotto]

Can u write this fraction as a ratio now?

[digital shell]

don't know how

[lusty grotto]

Well exactly how u wud anything else

a / b = a : b

Here what is a, what is b

B can itself be a fraction even

For example 1 / (1/2) = 1 : (1/2)

[lusty grotto]

Yes

Now this is the ratio between the sides u need

What did u tell me u wud do if the ratio was 1 : 0.5 earlier?

But 1 : 0.5 = 1 : (1/2)

[digital shell]

multiply by 0.5

[lusty grotto]

So if u had 1 : (1/2) what wud u multiply by

[digital shell]

0.5

[lusty grotto]

So 1/2

If u had 1 : (2/3)

What wud u do

[digital shell]

multiply by 2/3

[lusty grotto]

Yes

Now u have 1 : (2/root3)

What do u multiply by

[digital shell]

2/sqrt3

[lusty grotto]

Exactly

I guess that solves ur problem

[digital shell]

how

[lusty grotto]

This way

Now u know the length of YX

[digital shell]

I still have no idea how any of that applies to my problem

[lusty grotto]

And u want to know the length of YZ

And u know the ratio between them is 1 : (2/sqrt3)

[digital shell]

how did you get that?

[lusty grotto]

ok what do u say is the ratio between them?

[digital shell]

sqrt3/2

[lusty grotto]

right

so sqrt3 : 2

[lusty grotto]

and u showed me this

so sqrt3 : 2 = sqrt3 / 2 = 1 / (2/sqrt3) = 1 : (2/sqrt3)

so the ratio between them is 1 : (2/sqrt3)

is that okay?

[digital shell]

yes

[lusty grotto]

so?

[digital shell]

so I should multiply by 2/sqrt3?

[lusty grotto]

yes

wait

[lusty grotto]

here u multiply the length of ZX by 2 to find x, BECAUSE u know that the ratio ZX : x is 1 : 2

[digital shell]

yes

[lusty grotto]

now u know the ratio of XY : x is 1 : (2/sqrt3)

so in the same way, to find x, what must u multiply by what?

[digital shell]

2/sqrt3

[lusty grotto]

yes multiply what by this?

[digital shell]

multiply XY by 2/sqrt3

[lusty grotto]

exactly

so okay?

[digital shell]

but that gives me wrong answer

[lusty grotto]

what do u get for x?

[digital shell]

12/sqrt3

[lusty grotto]

yeah this isnt wrong

[lusty grotto]

this is 12 * sqrt3

not 12 / sqrt3

[digital shell]

oh but there is no

[lusty grotto]

try rationalizing it

get an equivalent fraction for 12/sqrt3

maybe thats one of the options

[digital shell]

the answer is 4 * sqrt 3

but I don't know how to get to that

[tranquil oracle]

$\frac{12}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$

[wraith dagger]

Element118

[digital shell]

I don't understand

[cedar kiln]

@digital shell Has your question been resolved?

[clear berry]

@lusty grotto is he still stuck there?

[crimson sedge]

Didn't we solve that ?

\hrulefill\par
Author: Blackpink Lover ♡

$$\underline{Given}$$
$$Y = 30°$$
$$X = 90°$$
$$XY = 6u$$

$$\underline{Finding}$$
$$YZ$$

$$\underline{Solution}$$
$$X+Y+Z = 180°$$
$$90+30+Z = 180$$
$$Z = 180-90-30$$
$$Z = 90-30$$
$$Z = 60°$$

$$Cos(Y) = cos(30°) = \frac{\sqrt{3}}{2}$$
$${\frac{6}{YZ}} = \frac{\sqrt{3}}{2}$$
$$YZ = \frac{12}{\sqrt{3}}$$
$$YZ = \frac{12}{\sqrt{3}}\cdot{\frac{\sqrt{3}}{\sqrt{3}}}$$
$$YZ = \frac{12\sqrt{3}}{3}$$
$$YZ = 4\sqrt{3}$$

@digital shell here

[digital shell]

no that is trigonometry

[wraith dagger]

Vanilla's Social

[digital shell]

I haven't learned that

[crimson sedge]

U already got the fraction 12/√3 by the help of other people right ?

Just look at few of my last steps

I changed 12/√3 to 4√3

[digital shell]

yeah I don't know what cos means

[digital shell]

yes i'm still stuck

[crimson sedge]

If u got the fraction 12/√3 by the help of them
U don't need cos

U can solve it without cos

[digital shell]

I did but I don't know how to go from there

[clear berry]

Are you having problem converting root(12)/3 to 4 root(3)?

[crimson sedge]

I went ahead from there
If u look at the last few steps u will see 12/√3 to 4/√3

[crimson sedge]

@clear berry I did that here already
I am just telling him

[clear berry]

ah ok, cool

[digital shell]

yes but you don't explain how

[digital shell]

yes

[clear berry]

Multiply root(3) on both numerator and denominator

[crimson sedge]

\hrulefill\par
Author: Blackpink Lover ♡

Well when u have
$\frac{12}{sqrt{3}$ to get rid of the root from both denominator and numerator u multiply both of them by $sqrt{3}$

;-;

[digital shell]

oh

I see

[clear berry]

$\frac{12}{\sqrt 3}$ to get rid of the root from both denominator and numerator u multiply both of them by $\sqrt 3$ (edited)

[digital shell]

so you multiply so they cancel out in the denominator

[wraith dagger]

numbpy

[crimson sedge]

\hrulefill\par
Author: Blackpink Lover ♡

Then u will get the fraction
$$\frac{12{\sqrt{3}}}{3}$$

[clear berry]

yes, so in denominator you will be left with 3, on numerator you will get 12 root(3), finally divide to get the answer

[wraith dagger]

Vanilla's Social

[digital shell]

ok I think I understand now

[clear berry]

I think you can proceed from here

[crimson sedge]

Now when u divide 12/3

U get 4

Hence 4√3

[digital shell]

yeah

Thanks for the help

.close

[cedar kiln]

Channel closed

Closed by @digital shell

Use .reopen if this was a mistake.

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[tiny socket]

I have a series of length n = 43, now I build a new series that every item in it is equal to k elements in the first series, why is the new series length is 44-k and not 43-k?

[mossy mango]

i mean

if u have as series

1,2,3,4,5

and another series with k=3 elements

1,2,3

the length of the 2nd sequence is 3

which is 5+1-3

not 5-3

[tiny socket]

well i guess you right, didnt looked at it like that