help-17

[mild grove]

i'll try

[sleek moss]

It's a statistical question

H1: >m0

[hushed pewter]

@brisk vigil you need to open your own channel for help
#❓how-to-get-help

[vocal sleet]

@sleek moss Has your question been resolved?

[brisk vigil]

I don't know how to turn to bot so i just handwrite it

I don't think p-value can reach 0.01, It's too small---

nicespiderman I assume there is something wrong with ur calculation~

[vocal sleet]

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[analog nova]

the ratio between the edge length of a regular tetrahedron and its slant height is? considering all of its faces are equaliteral

[analog nova]

النسبه بين طول حرف مثلث ثلاثي منتظم الاوجه و طول ارتفاعه الجانبي

if you can answer in arabic that would be better thanks

[kind light]

consider one of the slant faces, its an equilateral triangle say with side a

the slant height is just the height of the equilateral triangle

[analog nova]

there's a rule where the edge length x and the base height is y
so 3x²=2y²

i tried to go with that

but um..

[kind light]

do you mean 3x^2=4y^2?

[analog nova]

no

wait

it's

3y²=2x²

where y is edge and x is base height

I'm pretty sure

do you want the proof? @kind light

[kind light]

thats just wrong no?

[analog nova]

In a regular triangular pyramid, the faces are twice the square of its edge length = 3 times the square of its height

i think i fucked up

i know what i did

oh my ducking god

[kind light]

making sure, you meant slant height right? maybe there was a mistranslation?

[analog nova]

no height

[kind light]

the red one?

[analog nova]

what i wanted was slant height / edge height

[analog nova]

the rule is for the red one

[kind light]

yeah

[analog nova]

i fucked up

SO MUCH

[kind light]

tldr tou want to find red here and use pythag

[analog nova]

do you wanna see a glimpse of what i did

[kind light]

sure

[analog nova]

i assumed x was edge height

and l is base height

so 3x²=2l²

x=(root 6/3) l

slant height = 2/3 l² - (1/2 l)² for pythagores

the orange line

and so i got 2 after dividing the answer x by root 6 / 6 l which is the orange line

@kind light

how hard did i fuck up

[kind light]

.

[analog nova]

yes

how is it x

[kind light]

call it x

you should get like (example) x:3x so it would be like 1:3 for example

[analog nova]

@kind light

[kind light]

rmemeber this red line is also x

[analog nova]

@kind light

[kind light]

your finding ch right?

[analog nova]

yes

so ch²=bc²-(x/2)

[kind light]

stop fixating on 3y^2=2x^2

[kind light]

yes and whats bc?

[analog nova]

edge length

which is l

[kind light]

ok

[analog nova]

wait it's l yeah

[kind light]

so use this

[analog nova]

how

there's no relation

between x and bc

[kind light]

you just said it was x

[analog nova]

l

[kind light]

dawg

[analog nova]

consider it l

[kind light]

ok call it l

then forget the whole x thing

[analog nova]

okay

[kind light]

so BH would be l/2 right?

[analog nova]

no?

wait

how did i not realize

ba=bc

so 1/2 ba = 1/2 bc

so just direct substitution

how am i so dumb

ch² = bc² - bh²
ch = root ( bc² - (1/2 bc)²) = root 3/2 bc

root 3/2bc/bc=root 3 /2 = ch = bh

@kind light

[kind light]

yea

[analog nova]

i did not consider they were equaliterals

so what the fuck did i get

@kind light thanks btw

[vocal sleet]

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[mighty horizon]

On a German motorway, black cars are four times more common than
cars of other colors. Most black cars are driven by men: 60% of men drive black cars, while 20% of women drive
cars of a different color. We observe the cars on the motorway. State the probabilities in percent, rounded to whole numbers.
What is the probability of observing a man driving a
black car?
What is the probability that the car is not black?
We see a black car. What is the probability of a woman driving it?

1. P(B|M)=P(B∩M)/P(B)
   0,8*0,6/0,8=0,6

2.1/1-4/5=1/5

3.P(B|W)=P(B∩W)/P(B)
0,8*0,4/0,8=0,4

Can someone tell me if that is correct?

[mighty horizon]

<@&286206848099549185>

[tough nymph]

1 is wrong

3 you have condition backwards but ans is right

[vocal sleet]

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.

[mighty horizon]

And 2?

[tough nymph]

It’s right

[mighty horizon]

Can u give me the right method for 1 and tell what do i have change exactly on 3

@tough nymph

[tough nymph]

1 is not conditional

3 flip your conditions

Its condition on black car not woman

[mighty horizon]

So it would be P(W|B)=P(W∩B)/P(B)? @tough nymph

[tough nymph]

Yes

[mighty horizon]

You 100% sure on that?

[tough nymph]

Ye

[mighty horizon]

Can you do me favor and give me a hint what to change on 1 exactly? I'm completely lost on that @tough nymph

[vocal sleet]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

@mighty horizon Has your question been resolved?

[dark kiln]

i tried to solve it and i got men don't exist

maybe you mistranslated it idk

[vocal sleet]

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[wraith ferry]

i need help on a math question in this stupid packet i have to do over break pls help

[vocal sleet]

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/

[wraith ferry]

i've tried to answer this question but i'm not sure how to exactly approach it help pls

[drifting jackal]

Please post the question. No one here is psychic and can read your mind on what the problem is

[wraith ferry]

my bad i was trying to see how this worked

the question is number 9

i've tried different ways but get stuck each time

[drifting jackal]

What did you try?

[wraith ferry]

i tried to multiple the exponents together but also keeping the parenthesis

but i asked my mom and she said it was wrong

[drifting jackal]

What would this look like?

[drifting jackal]

Yeah that's fine to do

[wraith ferry]

that's right?

[drifting jackal]

Yes

That's the third exponent rule

[wraith ferry]

ohhhh

but meaning that i have to make it a single whole number exponent what does that mean

[drifting jackal]

The exponent should be a whole number

[wraith ferry]

ohh ok thanks so much

[vocal sleet]

@wraith ferry Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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[uneven mango]

Base edge of a right square pyramid and the height of the pyramid are 4. The radius of the sphere inscribed around the pyramid is? Ans: 3

[kind light]

inscribed around?

inside right?

[uneven mango]

No outside, the pyramid is inscribed inside the sphere

[kind light]

ohh

im not sure how to explain this, but if you visualize it, the radius would be the circumcircle of the triangle in the plane that contains the 3 vertex

you can find a the sides of the triangle and find the circumradius of it, aka the radius of the sphere

[vocal sleet]

@uneven mango Has your question been resolved?

[vocal sleet]

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[uneven mango]

.reopen

[vocal sleet]

✅

[uneven mango]

So we should look in triangle OIAk: IAk is 2sqrt2 , how do we find OI?

[kind light]

i mean ABC

[vocal sleet]

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[vast shale]

How can i multiply vectors?

[vast shale]

Let's say (4i + j + 2k)((1+4µ)i + ((39/2)+µ)j + (-10 + 2µ)k)=0

How can I find µ

[hidden gyro]

dot product?

[vast shale]

If I knew what that is I wouldn't have asked

[hidden gyro]

what is the exact qn

i mean

with formatting and everything

[vast shale]

The exact question is the question I asked

[solar needle]

did they use . as multiplication symbol

[vast shale]

Yes

But what if they didn't? Wouldn't it be the same

[hidden gyro]

no

[solar needle]

no it wouldn't

[vast shale]

Ah

[hidden gyro]

if they didnt use dot symbol

multiplication isnt defined

on vectors

[solar needle]

there are multiple ways to 'multiply' vectors so we need to specify that we're using the 'dot' multiplication

[vast shale]

So now I just multiply the corresponding vectors and add them ignoring their direction?

[hidden gyro]

not rlly

when you are doing * product

(ai+bj+ck)*(di+ej+fk) = ad+be+cf

[vast shale]

What about dot multiplication then

[royal mauve]

2+2 divide by2

[hidden gyro]

that is dot product

* = .

[vast shale]

Then why not use a dot lol

[hidden gyro]

type setting is hard

[royal mauve]

Please answer me

[vast shale]

What's the different multiplication symbol then

[hidden gyro]

the dot is supposed to be in the middle

[vast shale]

That would use a different way

[hidden gyro]

AxB

is something different

[vast shale]

When should I be using each

[hidden gyro]

uhm

[vast shale]

And what if I use no multiplication symbol like I did here would that count as dot multiplication or is that just wrong

[hidden gyro]

that is wrong

[vast shale]

Aha alr

[vast shale]

And this

[hidden gyro]

uhm

[vast shale]

Uhm

[solar needle]

uhh the problem will use the corresponding symbols for each one

but if youre asking about applications then the dot product has to do with projections and the cross product has to the with the area of a bounded parallelogram

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

Alr ty

[vocal sleet]

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[deft anvil]

Why is the probability for 4 white cups not 5c4x12c2/16c6

[hidden gyro]

it says atleast 4 cups

so

4 white cups or 5 white cups or 6 white cups

[vocal sleet]

@deft anvil Has your question been resolved?

[vocal sleet]

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[versed plank]

Hi

[versed plank]

I dont know when to use sin cos and tan

Part B

[vale frigate]

Resolve into an x component and a y component

Then u can complete a force triangle and find the angle

[versed plank]

Already tried

How do i know if i have to use sin cos or tan?

@vale frigate

[vale frigate]

Use the definitions

Do u know sohcahtoa?

[vocal sleet]

@versed plank Has your question been resolved?

[versed plank]

Nope

[hollow kite]

from here you can find area of triangle using Heron's formula or such, and then use A = 1/2absinC formula

Or 1/2acsinB or 1/2bcsinA formula, depending on where the angle is and what angle you need to find

[vale frigate]

U haven't learned how sine, cosine, tangent etc are defined in terms of right triangles?

[vocal sleet]

@versed plank Has your question been resolved?

[vocal sleet]

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[blazing depot]

how do i figure out the %

[bronze osprey]

hate that wording, inversely proportional is better to say

anyways

if y decreases by 20%, how much is left (as a multiple of y)?

[blazing depot]

80?

80%

[bronze osprey]

great

so like inversely proportional means y = x/k for some constant k

or x * y = k = constant !

so x must increase by 1/0.8

(a factor of 1/0.8, so don't forget the original multiple of 1 = 100%)

jesus the options are all wrong

[vocal sleet]

@blazing depot Has your question been resolved?

[mild grove]

maybe it's when y is 100% and then decrease to 80%

letting x gain 20%

[bronze osprey]

yeah like either they mean x increases by 25%, now that's correct

or actually y was supposed to increase by 20%

etc

[mild grove]

yeah the question is really fucked up

[vocal sleet]

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[vast shale]

guys..anyone here?

[vast shale]

.reopen

.close

[vocal sleet]

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[vast shale]

.reopen

[vocal sleet]

✅

[vast shale]

so basically..
the og question is
there are 2 CN
|z1|<1<|z2|

[dense cedar]

Cyanide ? CN ?

Cartoon Network?

[vast shale]

complex numbers

an we hafta prove |1-Z1*conj of Z2|/|Z1-Z2| <1

[dense cedar]

Ok

[sage cipher]

multiply numerator and denominator by |z2|

[somber cloud]

Can u send the picture of ur problem

[vast shale]

wait a min

[vast shale]

tried it doesnt help

[vast shale]

here is the picv

[sage cipher]

in the numerator take z2 inside, and in denominator keep it outside

and tell me what you find

[vast shale]

k

its 1/z2 - z1*(z2conj/z2) in num

and do i take z2 outside from denom too?

wait

ho gya

nvm

.close

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[vocal sleet]

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[robust juniper]

if the powers are even it approaches 0

[robust juniper]

if odd it approaches 1

why

[small surge]

Cause 0^0 is 1

But 0^1 is 0

And then the calculation is done in descending order

So if it's even every 0^0 can be expressed as 1 so you get 1

But if it's odd you end up with 0^1

[robust juniper]

how exactly do we solve x^x at x->0

[small surge]

We defined it to be 1

There's lots of videos on it

It's the same thing as 0! Is 1

It's just easier if you have that

[dim pumice]

no it's not generally defined to be 1

[small surge]

It kinda changes depending on context but I normally take it as 1

[dim pumice]

if you take it as a function x^y then it's not continuous at (0, 0)

[small surge]

It's indeterminate but you would usually take it as 1

In like combinatorics and algebra and the sort

And I consider this to be an algebra problem

[robust juniper]

can we not solve this

?

[dim pumice]

it's more of calculus/analysis, especially with how we even define x^y for reals in the first place

[small surge]

Not really

[dim pumice]

we can

first write x^x as e^(x ln(x))

we can solve for the limit of x ln(x) first

[robust juniper]

but then we have the function whole limit we are trying to solve in the function

[dim pumice]

how?

[robust juniper]

wait no

sorry

xlnx is 0

so x^x at 0 is 1?

[dim pumice]

we were considering e^(x ln(x)) though

but e^x is continuous, so

[robust juniper]

its 1?

[dim pumice]

yeah

[robust juniper]

ok

ty

[dim pumice]

then maybe there is a pattern for x^...^x

[robust juniper]

wdym

[dim pumice]

if we try to solve for the limit of x^x^x now

[robust juniper]

is e?

lny=x^x lnx

x^x and lnx at 0 is one

so the limit is e???

[dim pumice]

wait so

x^x^x = e^(x^x ln(x))
then the limit of x^x ln(x) is just -infinity, as x^x goes to 1

[robust juniper]

ah so it s 0

e^ -infinity is 0

k got it tysm

my dumass wrote ln0 as 1

.close

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[chrome jay]

Lucie has drawn three squares whose sides measure whole numbers of centimeters. Two of these squares are identical. The sum of the areas of the three squares is equal to 2025 cm².

What is the perimeter of the square that is different from the other two?
There could be 1 or more solutions to this.
How would I solve this
I think i have a base formula: 2a^2 + b^2 = 2025, but this alone won't help much.

[sullen wigeon]

we can think of this problem as he following, can't we?:

[chrome jay]

how

[sullen wigeon]

2025=45^2

and we have a formula for a right triangle

[chrome jay]

right

[chrome jay]

?

[sullen wigeon]

it's a Pythagorean triple

[chrome jay]

is there another way to solve this

something simpler perhaps

[lyric fjord]

if the side of the different square is equal to b, then what we're trying to find is 4b, right?

its perimeter

[chrome jay]

yes

though still don't understand how i would start

[lyric fjord]

have you tried anything?

[sullen wigeon]

my thought process is that we get to this equation and then we can deduce that y is odd because otherwise x cannot be a whole number and then we can start trying?

[lyric fjord]

oh right

[chrome jay]

ok that makes sense

[lyric fjord]

2a^2 = 2025 - b^2
2a^2 = 45^2 - b^2

[chrome jay]

i think i can figure it our from here

thank you

.close

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[sullen wigeon]

any restrictions for the angle?

[spark surge]

yes

1 sec

Find the number of solutions to the inequality (in degrees) that are multiples of a and that exist in the interval (0°; 360°]

[atomic jasper]

!original

[vocal sleet]

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.

[sullen wigeon]

this is how i see it

[vocal sleet]

@spark surge Has your question been resolved?

[vocal sleet]

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[trim stratus]

does ED=CD?

[sullen wigeon]

why would it be

[trim stratus]

Have been stuck here for 15 minutes

[hidden turret]

this is a good question

[atomic jasper]

!status

[vocal sleet]

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

[visual marsh]

ED is not equal to CD

[trim stratus]

I just know DBA=90 and CED=15

[visual marsh]

i got it

[trim stratus]

how

[visual marsh]

the first part and the answer to your ques

gimmi a sec

[hidden turret]

Ok I know we arent supposed to give answers but im genuinely confused if my answer is right

[visual marsh]

what did u get for angle bdc?

[hidden turret]

10 degrees

[visual marsh]

like i can give a hint but it would be little long

[hidden turret]

What did you get

[visual marsh]

i got 80 degrees

check my solution

shud i send it here?

[atomic jasper]

!nosols

[vocal sleet]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[visual marsh]

or can i dm u? just to check

[hidden turret]

probably got it wrong

[visual marsh]

u or me?

[hidden turret]

me

Is C the intersection between the triangle looking thing and the circle

[visual marsh]

@trim stratus lets consider the blue angle as x

and angle bdc as y

so angle cbd is also equal to y

fine uptil now?

[trim stratus]

trying

[visual marsh]

see now u have 2 variables

so now u need to get 2 equations atleast to solve them

[trim stratus]

x+2y=165

[visual marsh]

yes

and another one

[trim stratus]

umm

[visual marsh]

whatever u have drawn in the question is perfect

name out all the angles and check for another eqn

[trim stratus]

I don’t get

[visual marsh]

if i tell this u will get the answer ezly

but if u get it by yrself it wud be helpful

[trim stratus]

is it about the triangle BDE?

[visual marsh]

u will get the same eqn as above

ok what all triangles do u see?

[trim stratus]

ECD EBD CDB BDA EBA

oh

-x+y=90?

so y = 25

[visual marsh]

from which triangle?

-x+y=90?

[trim stratus]

CBA+CDA=180

[visual marsh]

w8 how??

[trim stratus]

🗿

can you tell the answer

[hidden turret]

Yeah i got 25 next time i did it

[visual marsh]

try in tri bda, ull get ans

[trim stratus]

Maybe I am right

25 and 115?

[hidden turret]

which angle is 115?

[visual marsh]

hmm

maybe i got wrong

lemme check

[trim stratus]

what’s yours

[visual marsh]

tf did i do

i got x as 5 and y80

[trim stratus]

doesn’t seems to be 80 XD

[hidden turret]

<DCB i got 130 degrees

@trim stratus what did you get for the ratio

[trim stratus]

I am asleep for now

[hidden turret]

my bad

[trim stratus]

ig just close this help section

[hidden turret]

.close

[trim stratus]

nah it’s because it’s 3:06am here

[visual marsh]

im gonna solve this bs shit

[trim stratus]

same with me

[visual marsh]

abcd is a cyclic quad

ye 25 and 115

[trim stratus]

thanks

[visual marsh]

its too early to say thanks

2nd part is a bigger pain in the ass

[hidden turret]

bro its 2:3 if you look at the image the solutions are basically there

[visual marsh]

bro i almost got it

i got 2*root3 * cos25

AB/BC

[hidden turret]

oh pause

[visual marsh]

this question was really good ngl

wanna know how? @hidden turret

oh no

its 3.42

[hidden turret]

what even was the last problem

[visual marsh]

AB:BC

3.42/1

what did u get?

[hidden turret]

i got 1.5

which probably isnt right

[visual marsh]

whats that tool u used?

[visual marsh]

..

[hidden turret]

its just geogebra

[vocal sleet]

@trim stratus Has your question been resolved?

[visual marsh]

man how do i draw it

its too tough and timetaking

[hidden turret]

ive used it for a while so im used to it

[visual marsh]

should i show u my working?

[hidden turret]

sure

[visual marsh]

give me 5 mins ill write it properly

[hidden turret]

this chat is probably gonna be closed though

[visual marsh]

dms?

if u r fine with it

[hidden turret]

yeah sure

[vocal sleet]

Channel closed

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[vocal sleet]

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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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[sturdy night]

chat gpt o1 pro says the answer is B

[rugged orchid]

Perhaps it didn’t understand the idea of the arrows

Typical questions like this would go left to right which would yield B as an answer

This question is slightly out of the ordinary and chatgpt is by its nature not amazing at dealing with new phrasing of questions

[sturdy night]

mhm

[silk osprey]

why are you relying on chatgpt lol

chatgpt is notoriously shit at anything stem

[sturdy night]

what should i use

[rugged orchid]

It really isn’t that bad

[silk osprey]

your brain

[sturdy night]

nah the new version is decent at math

o1 pro

[rugged orchid]

It’s good you just need to know how to use it

[sturdy night]

true

[rugged orchid]

It’s good that you’ve found a discrepancy in its answer and what your brain tells you and are now asking about it

And didn’t just blindly trust it

[sturdy night]

what i dont understand is why is the 0 there

[silk osprey]

they didn’t trust it probably because the teacher or whoever marked D as the answer

[sturdy night]

yes

[silk osprey]

it wasn’t on their own intuition

[rugged orchid]

What do you mean about the 0?

[silk osprey]

just had two conflicting answers

[sturdy night]

why r the arrows pointing to the 0

[silk osprey]

coordinate system

for position

[rugged orchid]

This shows that your understanding is similarly poor as chatgpt

[sturdy night]

yes

[rugged orchid]

But your car is starting on the right side

[silk osprey]

it’s position is positive and the arrows point to the left indicating it has a negative velocity

[sturdy night]

ok i get it

[rugged orchid]

It’s moving to the left towards

[sturdy night]

i couldnt picture it

[rugged orchid]

Neither could chatgpt

[sturdy night]

ye

ok so

normally the arrows always point to the left

so i got confused

[rugged orchid]

Point to the right you mean

[sturdy night]

ye

[rugged orchid]

Well technically speaking

I’d prefer if the 0 was where the car starts

Since this would otherwise indicate position rather than displacement

And velocity is displacement over time not position over time

But it’s probably a bit pedantic to talk about that

[tender field]

it is hard to learn real-analysis

[sturdy night]

ok i still dont get it

i dont get it cuz that zero messes me up

doesnt it mean the time is 0

so why is the arrow with the greater velocity going to it

oh shi i get it

[vocal sleet]

@sturdy night Has your question been resolved?

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[wide grotto]

What is A^{2024} ?

[wide grotto]

or what is the trick to solve that question

[vapid solar]

Try writing $A=XY^T$ where X and Y are to column. Since the rank of A is 1, you can find such X and Y

[wide grotto]

an then?

[twin meteor]

TimourX

[wide grotto]

and what does T stant for, is it the transposed matrix?

[vapid solar]

And then, when you calculate $A^2$, you have $A^2=XY^TXY^T=X tr(A)Y^T$

[twin meteor]

TimourX

[vapid solar]

yes

[vapid solar]

because Y^TX=tr(A)

[wide grotto]

what is tr(A)?

[vapid solar]

the trace of the matrix

[wide grotto]

what is a trace?

[vapid solar]

ah ok you don't know

do you want the complete solution without this or you want to continue searching ?

[wide grotto]

no, I was just working my way trough some old exams from our university, but our semester isnt over yet so thats probably why I cant solve that problem

we will probably talk about it in one of our next lessons, so its alr

thank you very much

[vapid solar]

you don't need the trace

the solution is easy without elaborated math tools

[wide grotto]

but I think this is the expected way, because in question 1 I was asked to find two vectors (6x1) \in X and (1x6) in Y, such that A = X * Y

[vapid solar]

huh no it's not easy but if you write down things and do elementary manipulations, then the problem becomes easy to solve

[vapid solar]

yes

[wide grotto]

so ill probably need that trace thing

I mean just calculating A^2 and looking for patterns would probably also do the work, but like I said, thank you very much :)

[vapid solar]

not really to be honest, the trace is just X*Y with the notations of your exercise, you don't need that notion to calculate it

[wide grotto]

oh okay

[vapid solar]

ur welcome

[wide grotto]

have a nice day

.close

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[mossy goblet]

Any idea

[vocal sleet]

@mossy goblet Has your question been resolved?

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[vagrant mesa]

We have an isosceles triangle with a base length of 12 cm and a height of 18 cm. We need to divide this triangle into three trapezoids with the same area. Can anyone please give their opinion on how to solve problem this ?

[hollow kite]

Area of the triangle = 3 * Area of trapezoid

Probably.

[lethal salmon]

break it into 9 equal smaller triangles and you see each 3 is a trapezoid

[vagrant mesa]

oh wow thank you

it was so easy XD, thank you have a nice day

.close

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[chrome jay]

Lucie has drawn three squares whose sides measure whole numbers of centimeters. Two of these squares are identical. The sum of the areas of the three squares is equal to 2025 cm².

What is the perimeter of the square that is different from the other two?

So far I plotted some equations that could help with solving this problem, though every time I try solving them, using the equations, I find that I am missing something.

The equations: 2x^2 + y^2 = 2025 -> 2x^2 = (45-y)(45+y) and 2a^2 = 2025 - b^2

[vocal sleet]

@chrome jay Has your question been resolved?

[chrome jay]

<@&286206848099549185>

anyone

.close

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[rigid lake]

How can I calculate the determinant easily by applying some identities of the determinant?

[dense cedar]

C1 = C1+C2 +C3

step 2, take 3-lambda out

[rigid lake]

I can so that? I thought you can only do one at a time, for example C1 = C1 + C2 and then C1= C1+C3 but I guess it's the same thing

[dense cedar]

Yeah same

Step 3, R3-R1 and R2-R1

[rigid lake]

(3-λ)(3-λ)(1-λ)

[dense cedar]

?

[rigid lake]

The determinant of the matrix

[dense cedar]

(1-l)(1-l)(3-l)

Redo r2-r1

[rigid lake]

It will be 0, 3-λ, 0

[dense cedar]

(-1-l)-(-2)

-1-l+2

= 1-l

[rigid lake]

Oh bruh, for some reason I forgot to put the - in front of the 1

[dense cedar]

NGL this is happening to me recently many times ! 😭

I'm on 3 hrs of sleep maybe that's why !

[rigid lake]

Dang that's very relatable I really rarely get a proper night's sleep nowadays

And I'm making ridiculous mistakes

Are you a math major?

[dense cedar]

It's my second major

1st one is electronics engineering, wbu ?

[rigid lake]

I'm chemical engineering, first major

First year

[dense cedar]

1st yr

[rigid lake]

Electronics is cool, I was between Chem and electr

[dense cedar]

Yeah ! Imma get rid of chem, it's only in 1st sem !

[rigid lake]

Chem is boring imo, and we don't even do chemistry 🤣 all we do is physics and math, I've seen the next years subjects too

That's why I got into Chem eng, because they do a lot of math and physics

And a little chem

[vocal sleet]

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[main cosmos]

a quadrangle with a given angle alpha is inscribed in a given circle of radius R so that its area is the greatest

[main cosmos]

How do I even start?

[pallid temple]

post the original question because there's no question lol

Like what are you supposed to find

[lethal salmon]

whats a quadrangle

[pallid temple]

Bassically a quadrilateral

[lethal salmon]

goofy

[main cosmos]

I mean the task from a book looks like that

But probaply maximum area

[pallid temple]

Can you post a picture

[main cosmos]

But its in differen language

[pallid temple]

just post it that's fine I'll translate

[main cosmos]

39

[half imp]

is the angle fixed in place in the circle?

or can it be pointed in whatever direction

[main cosmos]

I mean we o ly kniw it is an angle inside a quadragle

And thst the radious of the circle IR R

Is R*

[half imp]

ok so it's not fixed inside the circle yet

[main cosmos]

And we need to find the maximum area of the quadragle

[vocal sleet]

@main cosmos Has your question been resolved?

[vocal sleet]

@main cosmos Has your question been resolved?

[vocal sleet]

@main cosmos Has your question been resolved?

[lyric fjord]

isn't the quadrilateral with the largest possible area inscribed in a circle just a square?

alpha would then be 90?

[vocal sleet]

@main cosmos Has your question been resolved?

[main cosmos]

may be but proof it

but

in this case no

[vocal sleet]

@main cosmos Has your question been resolved?

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[crisp cradle]

<@&286206848099549185>

Can someone help me prove this

I have done the first part

But the part about the $\frac{1}{n}$th of an integer

[twin meteor]

Abir

[crisp cradle]

I just cant prove it

[woeful igloo]

Dude, have some patience ok? Stop closing the channel rightafter pinging people

is this on an exam or something?

why are you so impatient

[crisp cradle]

Not on exam

[crisp cradle]

Idk

It's on homework p-set

[woeful igloo]

So, if you want the coordinate to be within 1/n, you understand that the triangle would need to be scaled?

(we can determine the approriate scale later)

[crisp cradle]

Yea

[woeful igloo]

And, since that coordinate is an irrational number, you can pick two rational numbers such that p/q is less than m (the irrational coordinate) and (p+1)/q is larger

do you follow me till now?

[dense cedar]

Still it won't be perfect

[crisp cradle]

oKAY, THEN?

[woeful igloo]

you scale it up by q/(p+1).

[crisp cradle]

What do you mean by "Scale up by q"

Do you mean increase each side length by q

Or by q times

[woeful igloo]

sry mb. I had a typo

[crisp cradle]

Ok

[woeful igloo]

q/(p+1)

[crisp cradle]

Q/(p+1) times?

[woeful igloo]

you increase the length of triangle from 1 unit to q/(p+1) units

oh wait, i have messed up a bit

let @dense cedar give his proof

[crisp cradle]

@dense cedar

Pls give your proof

[woeful igloo]

Ok, I solved the mess. Let r be the irrational coordinate. Then you can choose two rational numbers to sandwich the said irrational between them.
Let the said rational numbers be in their reduced form such that,
$$\frac{np-1}{nq} < r < \frac{p}{q}$$
Now, scale it up by the factor of $q$.

[twin meteor]

Facter10Br4g

[crisp cradle]

Ehat do you mean by scale up

I am not able to understand 😭😭

[woeful igloo]

increase all the lengths to q times their original values

[crisp cradle]

And what will it give me

?

[woeful igloo]

bigger triangle

[crisp cradle]

Okay, but will it helo prove the 2nd part

Which says within 0.1 of an integer can its coordinate be

?

[woeful igloo]

Maybe I can help you better if you show what you get by increasing the size

[crisp cradle]

On increasing each side

[woeful igloo]

yes

[crisp cradle]

The coordinates become scale factor x each coordinate

For any two coordinates

@woeful igloo

[woeful igloo]

[crisp cradle]

Am i right?

[woeful igloo]

Can you calculate the numbers? Take some p, q and n and do a sample calculation

[crisp cradle]

n=side right?

[woeful igloo]

nope

[crisp cradle]

Then

[woeful igloo]

p q and n are any integers

[crisp cradle]

But what are the

Coorfinates? Side length?

[woeful igloo]

such that they satisfy the condition here

[crisp cradle]

Ok gimme 5 mins, Imma try it

[woeful igloo]

You have a triangle, with coordinates as (0,0), (2,0) and (1, sqrt3)

[crisp cradle]

Ok

[woeful igloo]

now rest of the coordinates are all integers and only sqrt3 is irrational

you should choose appropriate p, q, n such that $$\frac{np-1}{nq} < \sqrt3 < \frac{p}{q}$$

[twin meteor]

Facter10Br4g

[crisp cradle]

p=4, q=2, n=1

@woeful igloo

[woeful igloo]

ngl, thats the simplest case. Its not gonna be of much use

try with n=10

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[vestal lynx]

Hey, I'm just thinking about 1+1 and how many interpretation options there are.

So far I have

Arithmetic

1+1=2

Boolean algebra

1+1=1

AND and OR

1+1=0

XOR

binary system (base 2)

1+1=10

Link operator

"1"+"1"="11"

Does anyone still have ideas for other interpretation?

[calm pecan]

i mean if you're talking about other bases then...

[half imp]

1+1 = π-1 (engineering)

[vestal lynx]

Hmm, I mean topics

[vestal lynx]

:0 uhhh

that looks interesting

I try to google and understanding this

[calm pecan]

it's a joke

the joke being that $\pi=3$

[twin meteor]

Percy

[calm pecan]

also the actual engineering truth is that $1+1=\pi=1=e$

[twin meteor]

Percy

[hybrid flicker]

= cos(x)

more rigorously

[vestal lynx]

the engenier constante😂 in electro normaly pi is used as 3,14

engeniers are grate ❤️

[vestal lynx]

?

[hybrid flicker]

don't worry, more engineering jokes

that cos(x) = 1

[vestal lynx]

1+1=cos(x)?

only I know the imaginary triangle with 0 i and 1

[calm pecan]

noo that would be 2 cos(x)

[hybrid flicker]

2cos(x) = ecos(x) = 1cos(x)

they're not wrong

[vestal lynx]

:0 ohhh interesting something I learn new

[calm pecan]

okay fair

[vestal lynx]

ahhh ok thx

is e meaning that the number doesnt metter?

eulersche or something I heard but not sure what this mean

[hybrid flicker]

quick pause: I hope you're not taking this seriously

[vestal lynx]

xD no I just try to understand

what the idea is behind

[hybrid flicker]

then forget everything that was said before

[vestal lynx]

and I now that pi is not = 3😂

know

[hybrid flicker]

engineers just keep approximating things so we dunk on them

and say they just approximate every number to 1 eventually

[river kettle]

g = pi^2

[calm pecan]

yes

[vestal lynx]

jeah that is what I talking too in electro its enough if u say 3,14 instead of 3,1415...

[calm pecan]

the only truth you have left to seek is that $\pi \equiv \sqrt{g}$

[twin meteor]

Percy

[hybrid flicker]

I mean that's kinda how the pendulum was invented

[calm pecan]

$\LaTeX$ where?

[twin meteor]

Percy

[calm pecan]

ig it's just not loading for me huh

[hybrid flicker]

this one not loading for you?

It's fine to me

to go back to the original question

[vestal lynx]

thx guys for the ideas 😄

[hybrid flicker]

there are many different ways to interpret "1+1"

the "+" referring to addition and the "1" referring to the neutral element can be associated to more than just real numbers for example

[calm pecan]

oh someone beat me to it goddamnit

lmao

[vestal lynx]

uhhhh yeah ur right

the imaginar values

[hybrid flicker]

So we call a set with an operator "+" a group (most likely abelian if you use "+" since it's supposed to be commutative)

and the "1" implies there is also an "x" operator

and its the neutral for that operation

(neutral for "x" means 1 x a = a x 1 = a)

so we're most likely in a ring

https://en.wikipedia.org/wiki/Ring_(mathematics) see this if you're interested

but coming back to some of your examples

[vestal lynx]

I hear about rings but My matz knowledge isnt so big that I understand this now

Ahh perfekt thx

[hybrid flicker]

(R,+,x) is the ring of real numbers

1+1 = 2 in the usual sense there

(F2,+,x), the set of remainders modulo 2 is also a ring (and a field)

it's a ring with only two elements: 0 and 1

(since any odd integer will have a remainder of 1, and any even integer will have a remainder of 0)

1+1 = 0 in that ring

the boolean algebra (Boole, x,+) is also a ring

1 means True, 0 means false

"+" means or

"x" means and

1+1 = True or True = True = 1

[vestal lynx]

true modulo with rest classes... I know that

[vestal lynx]

:0

[hybrid flicker]

Just to let you know

Boole algebra is F2 but you swapped the meaning of 0 and 1 and swapped + and x

I think that's it

moreover

(Boole, XOR, and) is exactly (F2,+,x)

without swapping anything

so 1 XOR 1 = 0

[spiral turtle]

There are fields of characteristic of any natural number greater than or equal to 2, which all have very slightly different definitions of + involving modulo

I'm not sure if this is different enough for your purposes though

[hybrid flicker]

Yes, and in terms of finite fields, you can find fields of any size p^k where p is prime

in those fields, 1 + 1 + ... + 1 (p times) = 0

we say they have characteristic p

[spiral turtle]

(generally, to construct fields of size p^k with k ≠ 1 you find a polynomial that is irreducible over the field of size p with degree k, and adjoin a root of that polynomial to Z/pZ. If that is gooblygook to you, then I can provide a concrete example if you like.)

[hybrid flicker]

Eg. for a field of size 4, I can consider a root of the polynomial x^2+x+1 and "adjoin" it to F2

[spiral turtle]

So if this root is α then each of your numbers will be thought of as in base α. So 11 is 1 * α^1 + 1 * α^0. If we have 101 then we have 1 * α^2 + 0 * α^1 + 1 * α^0, and we use the fact that α is a root of x^2 + x + 1 to see that α^2 = -α - 1, so 101 = 1 * α^2 + 0 * α^1 + 1 * α^0 = 1 * (-α - 1) + 1 = -α + 0 = α = 10

(so we can always simplify any value with more digits than 2 into a value with 2 or fewer digits)

[hybrid flicker]

We're getting very into very wibbly wobbly stuff

[spiral turtle]

(also note that the choice of polynomial is not always unique; however, it's always possible to find a mapping from one field of size p^k to another field of size p^k which preserves the + and × operations, and is called an automorphism, so all fields of size p^k are essentially the same field)

But yeah, this is rather far afield

[hybrid flicker]

Let's not talk about addition of points on elliptic curves

Anyways there are so many types of addition

[spiral turtle]

Or group operations in general?

[hybrid flicker]

well commutative group operations

still a lot

[spiral turtle]

Well to be fair, one of the examples given in the pin is concatenation, which is not commutative

"1" + "2" ≠ "2" + "1"

[hybrid flicker]

fair

but that's not a group operation

[spiral turtle]

Haha true

@vestal lynx sorry for dumping a bunch of weird math shit onto your thread.

Did you have any open questions?

[vestal lynx]

all is fine now I collect enought example what 1+1 can be

[hybrid flicker]

This question was a lot more productive than opening a help channel saying "1+1"

[vestal lynx]

Hmmm I searched for examples that a truth is not every only 1 valid truth

I read stuff about philosophy and existenz and yeah I know many topics at once

but I find my way 🙂

ty all

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[vast shale]

i dont understand the norm

[modern ledge]

is there more context to the rest of the question

or a translation by chance

[split wind]

Did you mean Euclidean Norm?

[vast shale]

yeah

[vast shale]

it is in portuguese

[split wind]

Well, for a vector in R^n
e.g.
x = (x1,x2,x3,...,x_n)
we have the Euclidean Norm
= √((x_1)²+(x_2)²+(x_3)²+...+(x_n)²)

[vast shale]

ok?

[split wind]

do you have more examples so that i can explain?

[split wind]

e.g. x=(1,2,3) then ||x||=√(1²+2²+3²) = √14

reading

[split wind]

so, since we have B is on positive side of x-axis, and A is on the negative side of the z-axis
A=(0,0,some number)
B=(another number,0,0)

and vector AB, is calculated as (-1,0,-z)

so Euclidean Norm (or the length of the vector) is √((-1)²+0²+(-z)²)

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@vast shale Has your question been resolved?

[vast shale]

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[dark surge]

How do I find the equation of the straight line which passes through (4,-2) and is parallel to the line with equation y = 2x + 1

[mental egret]

Since it's parallel, the slope remains same. So the equation will just be a replica, i.e., y - 2x = (-2) - 2(4) passing the replica through given point

[dark surge]

Could you say that a bit simpler plz

[maiden stratus]

if you cannot see anything, i can send parts

[dark surge]

Could I dm u and ask for help there?

[maiden stratus]

when you have parallel lines, the slope remains the same, as said Arya. This means that they have the same steepness and progress at the same rate.

[maiden stratus]

yeah

you can

[dark surge]

Alright thanks

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[waxen star]

does anyone know how to graph the boxed section on this graph with an exponential function

[waxen star]

preferably not trial and errored because I wanna understand the working out

I thought about this equation

where d = 37.55

but I don't know how to get a b and c

[bronze osprey]

can you send the Desmos graph link?

[bronze osprey]

what I will say is that you have too many variables here, which is slowing down your process

$-ae^{-bx + c} + d = -ae^{-bx} e^c + d$

$=(-ae^c) e^{-bx} + d$

[twin meteor]

south

[bronze osprey]

what this means is that you just have $-ae^{-bx} + d$

[twin meteor]

south

[bronze osprey]

and as you have figured out already, you must have $a, b, d > 0$ to match the graph

[waxen star]

yea sure

[twin meteor]

south

[waxen star]

uhh how do I send it

[bronze osprey]

just save your graph and then copy the link

[bronze osprey]

to save you need to sign in with your Google account

[waxen star]

https://www.desmos.com/calculator/r7vv8vu7cb

yup tysm

[bronze osprey]

alright I'll take a look

[waxen star]

thank you so much

[bronze osprey]

right so what we are going to do is to use two of the points in your data

say (60, 30.4) and (80, 35.1)

[waxen star]

okay

[bronze osprey]

so $30.4 = -ae^{-b \cdot 60} + 37.55$ and $35.1 = -ae^{-b \cdot 80} + 37.55$

[twin meteor]

south

[waxen star]

right

[bronze osprey]

,calc 30.4 - 37.55

[twin meteor]

Result:

-7.15

[bronze osprey]

,calc 35.1 - 37.55

[twin meteor]

Result:

-2.45

[waxen star]

do I use like

simultaneous

[bronze osprey]

then what we are going to do is to divide both equations, cancel out the a

[waxen star]

to solve a b c

[bronze osprey]

yes!

[waxen star]

oh alright i got it then

tysmmmm

[bronze osprey]

there's no need for c actually

[waxen star]

oh yea

tysmmm

that helped

[bronze osprey]

$\frac{-7.15}{-2.45} = e^{-60b - (-80b)}$

[twin meteor]

south

[bronze osprey]

yeah np!

[waxen star]

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[sour thistle]

Task:
I'm supposed to look at the vectors v_1, v_2 and v_3 and find a Lambda, for which the three vectors are linearly independent. How would I go about finding that Lambda? I set the three vectors equal to the zero vector and transformed the matrix equation so that the bottom row is empty. That means I can give the x_3 a factor like t right? So I can just write x_3=t. But then what?

[sour thistle]

The weird german text just says I can't use the determinant to figure when the matrix is linearly independent because there are more rows than columns.

[oak magnet]

How can you make the 8 disapear ?

[oak magnet]

You can avoid the last line since its always true

[sour thistle]

Ah yeah I can add 1/3 of II to III and then Lambda+2.5 is isolated

[oak magnet]

Yes

[sour thistle]

Wait so when are you supposed to introduce some letter like t? I thought the last line means "you can give x_3 whatever value you want, it will be true" (if we call the third column x_3) . And then I always used say t=x_3 to calculate x_1 and x_2

[oak magnet]

But here you have 1 pivot per column so all variables are principals

Look an example

What you say about t is neccessary if lambda has a certain value

[sour thistle]

English is my second language so I don't really understand that, does 1 pivot per column mean something like one plane per column regarding the vectors? And what does principals mean in this case

[oak magnet]

English is mine aswell, but when you do gauss

Pivot de gauss

Principals variables are the ones who are not free

A pivot is the first non zero value of a line in the matrix

What i meant is that

You solve lambda + 2,5 = 0

[sour thistle]

So when my Lambda is -2.5 I have infinite solutions because the line then says 0*x_3=0?

[oak magnet]

And x_3 became a free variable

So it has to be different than -2.5

[sour thistle]

The fourth row confused me, does that just do nothing when there is one row more than columns and it's only zeros

[oak magnet]

First row is always true

No matter we doing

So its not useful to keep it

Imagine it as an eqn

0 = 0

In a system

And you write it each time you make an operation

Thats boring