help-10

[pearl charm]

hmm

what do u mean by an orthonormal basis

[royal basin]

ok forget about it

i'll assume you have not heard of that before

do you at least know what a basis is

[pearl charm]

yes

[royal basin]

right

[pearl charm]

like linearly independent vectors

[royal basin]

do you know what the standard basis of the Cartesian plane is

[pearl charm]

no i don't know that

[royal basin]

do the names i and j ring any bells

[pearl charm]

yes

i = (1,0)

j = (0,1)

[royal basin]

yeah, those guys are the standard basis

[pearl charm]

oh, ok

[royal basin]

what makes the standard basis special is that

• the two vectors in it are perpendicular to each other, and
• both of their lengths are 1

that is what "orthonormal" means

[pearl charm]

oh, ok

ok

i understand that

[royal basin]

u and w here share the same properties, is what i am saying.

so you can now think about the coordinates of the endpoint of v

[pearl charm]

u and w....

wait what do u mean as in property

[royal basin]

.

these are the properties im talking about

[pearl charm]

ohhh, ok

r u saying that

we can use that to get coordinates of v?

endpoint of v?

[pearl charm]

how would we get that

is there like a formula or

[royal basin]

do you know trigonometry

[pearl charm]

yes

[royal basin]

specifically the unit circle

[pearl charm]

oh, i do, but not rlly

[royal basin]

bruh

[pearl charm]

wait

[royal basin]

then you are fucked

[pearl charm]

x = cos theta

y = sin thetea

[royal basin]

ok you are a bit less fucked

[pearl charm]

so v would be

[royal basin]

now you just need to correctly identify what your theta is from the diagram

[pearl charm]

cos ( 210), sin (210)

is that right?

[royal basin]

sure

[pearl charm]

-sqrt(3)/2

-1/2

[royal basin]

if i were more annoyed i would probably blurt out some more random numbers in an effort to show you how ridiculous it is the way you're communicating rn

[pearl charm]

oh.....

cos (210) = -sqrt(3)/2

sin (210) = -1/2

is that better?

@royal basin ...

@royal basin

please

i don't know what do do after getting v

or the coordinates of v

@royal basin ?

[royal basin]

the more you ping me the more time i will stall on purpose before replying to you.

[pearl charm]

oh...

i'm sorry

i'm sorry

[royal basin]

i am really annoyed that you have pinged me three times now.

recall what coordinates mean in terms of decomposing a vector in a basis. look at your diagram.

[pearl charm]

im sorry

[royal basin]

it is honestly as if you are helpless or clueless or both.

[pearl charm]

kind of both

[royal basin]

it is very hard to help you when you can barely do anything on your own

like

[pearl charm]

we got the coordinates of v right?

[royal basin]

v = cos(210°)w + sin(210°)u

[pearl charm]

oh shoot

imma be honest

i completely forgot that w and u existed

[royal basin]

now look at the problem and convert this equation into the form they ask for, and i forbid you from pinging me for this

i know you're able to do it

[pearl charm]

cos(210) w + sin(210)u - v = 0

a = sin(210)

b = -1

c = cos(210)

ohhh yay

so that's the problem done right?

am i correct?

[royal basin]

yeah sure

[pearl charm]

ok

thank you

wait don't go yet

it says it's wrong

i submitted

sqrt(3)/3 for a/c

2sqrt(3)/3 for b/c

why is this wrong

[royal basin]

screenshot the feedback you are getting

[pearl charm]

there is not feedback but i will

send u what i gotr

[royal basin]

you entered the values into the system and it told you "FUCK YOU WRONG ANSWER"

[pearl charm]

it gave me this

[royal basin]

wait why does the red error box have a minus sign in it

where'd that come from

try submitting again but making sure there isn't a minus sign...

[pearl charm]

thats me being stupid

yea i submitted again

[royal basin]

these values you've put should be correct

[pearl charm]

hmm

well maybe we made a mistake?

[royal basin]

no, you have my word that our values for a, b and c are correct.

oh

wait hold on

did i get us bamboozled??

[pearl charm]

oooo

[royal basin]

yes i did oh my god fuck.

i switched u and w around unwittingly.

a and c should then switch

[pearl charm]

oh well lol

yep

that was it

thank you

.close

[obtuse pebble]

Channel closed

Closed by @pearl charm

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[oblique pebble]

.

[oblique pebble]

Ah damn sorry, I had to go to bed when you replied :/ was late for me

I can reply to what you said now.

Hehe, yeah. Hello again

Oh, right. Oops, sorry. Forgot the division yeah 😅

Yes, right. I got that part.

Ahaaa, so you need to use tan(theta/2 + theta/2). Interesting. Didn’t think about that

Uhh, sorry if I’m pinging you a lot now

[warm shale]

amfabolous

[oblique pebble]

(From this one)

But alright, I’m assuming you’re asleep now, but I can wait ‘till your return.

By the way, are you Norwegian by any chance

[obtuse pebble]

@oblique pebble Has your question been resolved?

[wanton spoke]

@everyone

[obtuse pebble]

@oblique pebble Has your question been resolved?

[fluid holly]

...it's not english right?

[flat gate]

Oh I’m sorry

I come late

[flat gate]

that's Norsk

not English

[oblique pebble]

I wrote a translation up in the replied comments

[oblique pebble]

No problem! :)

[fluid holly]

am i blinded?

[oblique pebble]

oh wait, I sent the wrong pic here 🤦‍♂️

Sorry

It’s 18b

and the translation is here (sorry, is a bit messy, the channel closed when I went asleep)

[flat gate]

nonono, my time is 6 hours earlier than yours

[oblique pebble]

Ohh, I see

[flat gate]

I'm UTC+8 and Norwegian is UTC+2

so do you have any problem now

[oblique pebble]

Hm right

[flat gate]

for my solution

[oblique pebble]

Well, I still don’t quite see how I get tan(theta/2) alone from this? (Which is what I got from your solution)

Oh wait

[flat gate]

they have a same form

[oblique pebble]

It’s obvious rhat tan(theta/2) is then t

Yeah right

Aha!

Nice

[flat gate]

and in my country, they were called almighty formulas

or Tangent half-angle formula

[oblique pebble]

Interesting

[oblique pebble]

That’s neat. We have never learned those

[flat gate]

you can try to deduce them by yourself

[oblique pebble]

Well I’m going to save those, they will probably come in handy later :)

[flat gate]

it's not hard, in fact

[oblique pebble]

Oh nice. I’ll try later

Well thank you very much once again

[flat gate]

oh, i'm a Chinese, in fact(

I just translate with the help of the software

[flat gate]

that's no problem🥰

[fluid holly]

ha,long time no see

[oblique pebble]

Ah alright. Cool!

[flat gate]

are you in CN, too>

?

[oblique pebble]

I see

[fluid holly]

是，但是这句话不是俗语吗(

[flat gate]

草

看着名字很像CN人 但是我不敢随便发中文（

[flat gate]

您还要说什么吗，没有我就让这位把频道先关掉了（

[fluid holly]

没了，我在研究他这个题目是说的啥玩意

[flat gate]

就是一个复数

第一问证明 这个复数落在一个圆S上

就是单位圆

[fluid holly]

e

[flat gate]

第二问证明 题目中的参数t

[fluid holly]

为什么t^2+1在单位圆上

[flat gate]

他抄错题目了

是两个相除 不是相乘

[fluid holly]

(

好吧

[flat gate]

就是辐角theta=arg(w) 的一半的正切值

就是国内的万能公式

套了个模子

[fluid holly]

好吧，打扰了

[flat gate]

😕

这有啥，没事的（

[fluid holly]

hhhhhh,@oblique pebble u can close this channel as u wish

[oblique pebble]

Alright

.close

[obtuse pebble]

Channel closed

Closed by @oblique pebble

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vital star]

Is this a correct way to solve this quartic equation?i figure out a way to solve quartic equation is some special situation.

[pseudo swift]

your solutions are fine yes

@vital star

[vital star]

ok

[pseudo swift]

and now if you change one coefficient you're screwed

that's how quartic equations be

[vital star]

...

[pseudo swift]

but yeah you got it

[vital star]

Could a human solve this?

[pseudo swift]

there's ways to reduce quartic equations to more manageable forms I guess

just like cubics

[vital star]

Ya

But

[pseudo swift]

it would still be a pain tho

[vital star]

Ya

Anyways thx

.close

[obtuse pebble]

Channel closed

Closed by @vital star

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

How many bit ternary strings are there of length 10 where there are at least four 0's or 00 at the beginning

[timid silo]

So this is inclusion-exclusion

But I'm definitely fucking up something because I'm getting 3^8 which seems too large

I guess I should start with the at least four 0's: I am getting 3^6 for that via product rule but I'm thinking that's wrong?

[royal basin]

"bit ternary strings"?

do you mean bitstrings or ternary strings

[timid silo]

Ternary strings sorry. Any of the slots can have 0,1, or 2

[royal basin]

so you're looking for strings of the formats

00yxx xxxxx
0000x xxxxx

where the y can be 1 or 2 while each x can be anything

correct?

[timid silo]

The y can be 0 as well

It's just that the first two are necessitated to be 0

[royal basin]

ok then the first format subsumes the second??

and it's just 00xxx xxxxx?

[trim portal]

3^8 would then be the correct result

[royal basin]

can you show the problem exactly as it was stated

[elfin burrow]

does “at least four 0s” mean four 0s in total (not necessarily at the beginning)

[royal basin]

cause this is strangely redundant as is

[timid silo]

This was on my midterm. I said it word to word more or less

[timid silo]

Yes indeed

Can be four 0's in any position, but there are at the minimum 4

[royal basin]

oh wait ok so

a string is valid iff it has ≥4 zeros in any position OR begins with 00

is that correct

[timid silo]

Yep

[elfin burrow]

4 zeros in any position?

[timid silo]

Yes

[royal basin]

any special instructions for how you must calculate it?

if not i have a method that doesnt directly involve incl-excl

[timid silo]

No and that's what made me confused

I was unsure on how to particularly calculate it

[timid silo]

Oh what is it?

[royal basin]

i'd count the invalid strings

ones that start with anything but two zeros and have at most three zeros total

so there are 8 possibilities for the first two symbols: 01 02 10 20 11 12 21 22

in the first four, the rest of the string has to contain ≤2 zeros

in the last four, ≤3

[timid silo]

Oh that's really intuitive

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wind orchid]

hey guys, may i ask why it will have such a strange result. (i1 is got from the website https://www.integral-calculator.com/)

thx!

ClearAll["Global`*"]
\[Tau] = 1;
k = 1;
l = 1;
\[Lambda] = 6;
\[Delta] = 6;
Subscript[i, 
   1][\[Theta]_] := (\[Lambda] ArcTan[(
     2 (k + \[Delta]) Tan[\[Theta]/2] - 2 \[Tau] - l)/Sqrt[
     4 \[Delta]^2 - 4 k^2 - (2 \[Tau] + l)^2]])/Sqrt[
   4 \[Delta]^2 - 
    4 k^2 - (2 \[Tau] + l)^2] - (\[Lambda] ArcTan[(
     2 (k + \[Delta]) Tan[\[Theta]/2] - 2 \[Tau] + l)/Sqrt[
     4 \[Delta]^2 - 4 k^2 - (2 \[Tau] - l)^2]])/Sqrt[
   4 \[Delta]^2 - 4 k^2 - (2 \[Tau] - l)^2];
Subscript[i, 2][\[Theta]_] = 
  Integrate[(\[Lambda]*l*Sin[\[Theta]])/(
   4 (\[Delta] - k Cos[\[Theta]] - \[Tau] Sin[\[Theta]])^2 - 
    l^2 Sin[\[Theta]]^2), \[Theta]];
Plot[Subscript[i, 1][x] - Subscript[i, 1][0], {x, 0, 2 \[Pi]}]
Plot[Subscript[i, 2][x] - Subscript[i, 2][0], {x, 0, 2 \[Pi]}]
Plot[NIntegrate[(\[Lambda]*l*Sin[\[Theta]])/(
  4 (\[Delta] - k Cos[\[Theta]] - \[Tau] Sin[\[Theta]])^2 - 
   l^2 Sin[\[Theta]]^2), {\[Theta], 0, x}], {x, 0, 2 \[Pi]}]

[wind orchid]

and the left right limit for x=pi is such an interest result

[obtuse pebble]

@wind orchid Has your question been resolved?

[wind orchid]

<@&286206848099549185> sorry

.close

[obtuse pebble]

Channel closed

Closed by @wind orchid

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[worldly narwhal]

my channel keeps disappearing

[obtuse pebble]

Please don't occupy multiple help channels.

[worldly narwhal]

how do i solve this

for latus rectum

why does my channel keep going away

[nocturne minnow]

Make sure that is pointing down

[lapis gull]

because you're trying to occupy multiple channels

[nocturne minnow]

No

.close

[obtuse pebble]

Channel closed

Closed by @nocturne minnow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[calm lotus]

Hello! I tried to solve this limit, but got a wrong result. The correct answer is 0.1
Where did I do a mistake?

[royal basin]

you cannot let one instance of x approach infinity but not the other

you would have gotten infinity*0 if you had done the substitution properly

[calm lotus]

Can you please tell me which step is wrong? I can't find out

[calm lotus]

Okay
Why is it wrong?

[royal basin]

you cannot let one instance of x approach infinity but not the other

when you do that you essentially turn your function into a function of two variables and assert that the limits are interchangeable, which in general they may not be

[calm lotus]

So common multiplier of x should approach infinity as well? But then I get infinity*0, isn't it undefined?

[royal basin]

no, infinity*0 is indeterminate.

this means that if you get that when evaluating a limit, it means you need to backtrack and do something different algebraically.

[calm lotus]

I saw another solution which works, but I can't understand why this one doesn't work

[fringe pier]

its like

when you leave the outer x intact

and put value in bracket

which will give you zero

its not excactly zero

but a number close to zero

so when multiplied by infinity,

its indeterminate

its like very big*very small

[calm lotus]

ok, I got it

So how should I start evaluating such limit?

[fringe pier]

rationalization

[calm lotus]

But why only rational expressions work?

[fringe pier]

infinity - infinity is like that

by rationalizing, you get something in a denominator

which can be evaluated easily

by ignoring lower powers of x

[whole dock]

You are trying for a form that is in f(x)/g(x) so you can divide by the highest power of the variable

Such that you are left with a constant number

[calm lotus]

I know there is a method where you divide both numerator and denominator by variable with highest power in denominator, and then many terms approach 0 and you get a ratio

[fringe pier]

thats when there is denom

here its gives another indeterminate form

using your method, you will always get zero

[calm lotus]

Where can I learn how to evaluate such limits? I don't know other methods

I mean limits to infinity

[fringe pier]

as i said

rationalization

[calm lotus]

multiplying by conjugate?

[fringe pier]

for your question,

just multiply the same thing with positive sign

(and divide)

[calm lotus]

but then I get sqrt in denominator

[fringe pier]

yea

then you can ignore lower powers

in division, they dont matter much

but in subtraction, they do

[calm lotus]

Why not in division?

[fringe pier]

its like

10000+100/20000+50

even more bigger

we can ignore the 100 and 50

these numbers are so large

error tends to zero

for subtraction

(10000+10)-(10000+20)

you cannot ignore it

[calm lotus]

why? Error is pretty small

[fringe pier]

just think about it

[fringe pier]

no

it isnt

just think like

its root(x^2+x)-root(x^2+1)

say you ignore x and 2

you will get answer zero

but if you evaluate it, the plus x will add some value to root, which after subtracting leaves a normal value

[calm lotus]

I think I got it

[fringe pier]

just think of it like
10000000001-10000000000

[calm lotus]

ok

[fringe pier]

but
10000000001/10000000000

is one

[calm lotus]

Ok, I think I understand now

[fringe pier]

nice 👍

[calm lotus]

I will try to evaluate with rationalization. Thank you!

[obtuse pebble]

@calm lotus Has your question been resolved?

Channel closed

Closed by @calm lotus

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[flint imp]

Is (-2x-b)/(1-x) the same as (2x+b)/(x-1)?

[sage geode]

Yes

[flint imp]

How do I change it to the latter form?

[sage geode]

Are you told to change it? It looks already simplified I misread the question, yes, just multiply by (-1)/(-1)

[timid silo]

multiply by -1/-1

Guys help

[sage geode]

This channel is taken, open your own one

[timid silo]

Oh sorry I thought this was discussion and ppl were talking

I’ll do that rn

[flint imp]

Ahhhh smart! Thank you

[flint imp]

The second form was the answer in the booklet, so I just wanted to make sure they were the same and that I would be able to see why in future questions

Ah ok I see your edit

Thank you!

[obtuse pebble]

@flint imp Has your question been resolved?

Channel closed

Closed by @flint imp

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[signal egret]

Hi, i need help with finding out the square root of large numbers

[signal egret]

like 3 digit or 4 digit

idk how to do that

[ripe vector]

can u send me a pic of the problem?

[signal egret]

sure

sorry i forgot to

[ripe vector]

thats not square root lol

does it allow the use of a calculator?

[signal egret]

yea but i would need to put it under a radical no?

and no i cant

like i would end up with 4 in the nth spot then root 243 to the power of 5?

[rich plume]

try to write 243 as a power of 3

[hollow schooner]

@signal egret if u have trouble with how to convert find all the prime factors of the number

[ripe vector]

u know how u can make it so $a^{\frac{x}{y}} = a^{x \cdot \frac{1}{y}}$?

[warm shale]

hairdome

[hollow schooner]

tryy finding prime factors of 243 u will realise which number would give u the thing u need

[ripe vector]

wait no wrong equation

[hollow schooner]

owo

[signal egret]

im so sorry ik this is a dumb question but prime factors are numbers that multiply to 243?

[hollow schooner]

uk this right

[signal egret]

how do you even know to use 3 tho

[hollow schooner]

what numberr divides 3?

i mean

243

[ripe vector]

js test each number out and see if it divides into 243

[signal egret]

okay

[ripe vector]

i think

[hollow schooner]

like i checked if its divisible by 2?

no

then 3

it iss

[ripe vector]

make sure its prime tho

[signal egret]

okay

then yea it would be 3 because you can easily divide it by 3

3 times 1 is 3 and so that cancels out, i leave 1 on top as the first number, and then 24 divided by 3 is 8

and when i multiplied 81 and 3 it adds up to 243

[hollow schooner]

yes

in terms of prime factors u get 3 five timess for 243

u expresss that as 3^5

then do the simplification

[signal egret]

ohh okay and 3^5 is 9 times 9 times 3 which is the same as 81 times 3

okayyy im somewhat getting it

[hollow schooner]

after ur done with that

here a quesstion for u

[signal egret]

okay

tysm

[hollow schooner]

if u do more u will undersstand how to find and what to do to simplify

[signal egret]

yea exactly

so for my initial question the solution is 243?

or am i wromg

[hollow schooner]

can u sshow me ur work

[signal egret]

okay

That’s what I have written down

[hollow schooner]

okay you got 243= 3^5

[signal egret]

Yes

[hollow schooner]

now put that back in the main thing

243^4/5

[signal egret]

Okay

I set it up like this?

[hollow schooner]

u have written 243 = 3^5 right?

[signal egret]

My next thought is to multiply the 2 exponents

[hollow schooner]

means 243 is 3^5

[signal egret]

I forgot to write the equal sigh. But yes

Because they’re equivalent

[hollow schooner]

Yes

when u put the value there

[signal egret]

Wait so do I do this?

Because if so I got 4

And when I put that as my exponent above 3 my final answer is 81?

[hollow schooner]

YES

[hollow schooner]

yyes

[signal egret]

YESSSSSSSSS

[hollow schooner]

a^m^n is a^mxn

Good

[signal egret]

Yea I have that in my notes

Tysm

[hollow schooner]

wait boy

[hollow schooner]

do that

[signal egret]

Okay I’ll try

[hollow schooner]

https://youtube.com/shorts/TWRUleXZ1f4?feature=share

[signal egret]

I have a similar question to the one you sent so it’ll help

[hollow schooner]

also if u dont know prime factorisation?

[gritty shuttle]

SORRY CAN SOMEONE HELP ME? WHO KNOWS HOW TO SOLVE AND JUSTIFY THIS PROBLEM

[hollow schooner]

my guy u should go to help (available channelss)

[gritty shuttle]

ohhh okiii thank u

[signal egret]

I watched the vid

That helped

So prime numbers are numbers that can’t be divided by themselves right?

Like

9 can be broken up into 3x3 and so 9 isn’t a prime number

That’s my understanding

[hollow schooner]

by any ynumbers other than themselves

like 3 is only divisible byyy 3

or 29 is onlyy divissible by 29

i prefer to do it in a box

like

u want the prime factorisation of this

is it divisible by 2?

yes

write 2 outside and divide by 2

and write the quotient down

then u get this

135 is divisible by 3 since 1+3+5 is divisible by 3

and just like that

[signal egret]

I think I might Need help with long division too smh I haven’t done it in like years

[hollow schooner]

its not long division

[signal egret]

Like in general I haven’t done math in 3 years let alone long division back in middle school

But aren’t you dividing the 135 by 3?

And getting 45?

[hollow schooner]

yes

then 45/3

15

then 15/3

5

prime factors would be

[signal egret]

5 and 3 right?

[hollow schooner]

for 15 prime factors are 5 and 3

[signal egret]

Ohh okay I kinda see it now in the way you sent it

I’m working on the one you sent

So far I know that 55^2 gives me 3125

That’s how far I’ve gotten smh

[hollow schooner]

u should post ur problems on Help(Available) channels

this is occupied

[hollow schooner]

show how u got

[signal egret]

Let me eat rq and I’ll be back sorry

[hollow schooner]

sure

i also have to do smthn

u ccan dm me later

[signal egret]

Okie

Should I close this and just dm you?

[hollow schooner]

upto you

mma be busy for an hour rn

so nah

[signal egret]

Okay

So this is what I have rn on my paper

Sorry for messy writing

[hollow schooner]

what are u doing all those calculations for

[signal egret]

i just wanted to find a number that if i square it, itl give me 3125

and so i got 55^2

[hollow schooner]

that gives 3025 not 3125

also dont blindly try to find numbers like that

as i said before

prime factorise them

prime factorise 3125

and then show me

[signal egret]

ok ill try

[subtle robin]

can i just ask what does ^ mean

[hollow schooner]

raised to the power

[subtle robin]

oh k

[hollow schooner]

5raised to 2 5^2

[subtle robin]

kk

[signal egret]

ughhhh bro im so dumbbbbb

youve explained it and i still dont get it

im trying the method you showed me

[hollow schooner]

i think u need

https://youtu.be/NFcOa-DBJj0

[signal egret]

ill watch it rn

thanks

[hollow schooner]

Good

[signal egret]

so i kinda get what to do with a 3 digit number

but the one you gave me is a 4 digit number so i imagine that the first 2 numbers should be a number in the hundreds multiplied by a 2 digit number?

my mind is hurting over this i stg lollllllll

[hollow schooner]

no u have to do it the same way

like did in the video

3 digit 10 digit doesnt matter

[limpid plume]

with prime factorization, it was a really tedious process but what i did was i went through all the numbers like 25, 49, 9, 16, 4, etc...

eventually the numbers just sorta came to me

so like 98 would be 7root2

easy peasy

and other numbers you have to memorize like the squareroot of 625 is 25

also, another way i thought of prime factorization if i couldnt budge anything i would divide it by a number (four for example), and divide it into multiple numbers so that i could multiply them together to eventually get a perfect square

[obtuse pebble]

@signal egret Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fringe rivet]

so does sinx start at 1 to be 90 degrees and cosx start at 0 to be 90 degrees

[tardy epoch]

what does "start at 1" mean

[fringe rivet]

like say there is a graph

x=1=90 degrees

x=2=180

and so on

thats for sin at least

for cos

im assuming

its

x=0=90

[tardy epoch]

x=1=90 degrees is nonsense

[fringe rivet]

x=1=180

[fringe rivet]

use this as an example

[tardy epoch]

are you just learning how to plot sin?

[fringe rivet]

and cos

[tardy epoch]

https://www.youtube.com/watch?v=Vw-RwPBWS8g

[fringe rivet]

fund the angles as well

[tardy epoch]

https://openstax.org/books/precalculus-2e/pages/6-1-graphs-of-the-sine-and-cosine-functions

[fringe rivet]

Thanks ill view the video

.close

[obtuse pebble]

Channel closed

Closed by @fringe rivet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tame plume]

Can anyone explain why I can't use log instead of ln

[knotty crow]

can you use scientific calculator?

if so, then I don't see obstacles

[pseudo swift]

,w factor 872

[warm shale]

Results provided by WolframAlpha

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

Requested by _aplatypus#0

[pseudo swift]

ok lol

[tame plume]

Yes I can but I'm just trying to understand why it won't work

[knotty crow]

how won't?

[tame plume]

I did it yesterday and it didn't work but let me try again maybe I did it wrong

[knotty crow]

(ignore that inverse notation of log where base comes as second)

[tame plume]

Honestly now that I'm trying to solve with log, Idk how to do it. Anyone mind to explain it more?

[tame plume]

Reading trying to understand this

[knotty crow]

first of all

can you put this expression on a calculator in a proper way?

[tame plume]

I think I'm just not really understanding the fundamentals of logs really i just kinda do what my teacher told me to do

Oh it worked

I think it was cause yesterday I was dividing log 872 by log 9

[knotty crow]

here is nothing to understand I'd say because result isn't "nice" (some irrational number), basically concept is we are looking for such a number that 9 raised to its power gives 872

e.g.

let's take a simpler one

[tame plume]

Yeah I understand that part I just I haven't familiarized myself with these questions

[knotty crow]

$\log_{9}81 = ...$

[warm shale]

modus7591

[tame plume]

So it looks really odd when trying to isolate for x

[knotty crow]

yes, this might be new

new type of equation

[tame plume]

But how come I can't do something like divide the logs by each other to get x?

[knotty crow]

divide by log of base 9?

or what

[tame plume]

I remember I did this yesterday and it was wrong

[knotty crow]

because

calculator often interprets log as log of base 10

[tame plume]

Oh wait it worried

Worked

I just I was just losing my mind yesterday

[knotty crow]

good

or typo

[tame plume]

Yeah probe

Are there any times where I should use Ln instead of log to solve for x or something?

Like this question my teacher gave

He said something about how the bases aren't the same so you have to use Ln but I don't really understand

[knotty crow]

here log denotes natural log

right?

[tame plume]

Yeah

Wait

Log means log base 10

[knotty crow]

in fact we can use other bases too, that doesn't matter since

[tame plume]

Yeah that's the part that confuses me

[knotty crow]

according to this

we can show that

[tame plume]

OK I'm gonna need a minute to understand this

[warm shale]

modus7591

[knotty crow]

or we can use other base

2, 10, 100 etc.

thing is in math we used to operate on natural log, it's common thing

but as you can see, other bases works as well

[tame plume]

i think i get it

10 to the power of x is going to be whatever is next to the log , it doesnt matter what the log base is

cause the result is the same

so e to the power of x should give the same result

.close

[obtuse pebble]

Channel closed

Closed by @tame plume

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stiff kindle]

Four circles of unit radius are drawn with centers $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$. A circle with radius 2 is drawn with the origin as its center. What is the area of all points that are contained in an odd number of these 5 circles? (Express your answer in the form "a pi + b" or "a pi - b", where a and b are integers.)

[warm shale]

funwiththepros

[stiff kindle]

<@&286206848099549185>

[hybrid gull]

“After 15 minutes, feel free to ping Helpers.”

[stiff kindle]

ok

[hybrid gull]

It’s obvious this message wasn’t read

[stiff kindle]

can you help me?

[warm canopy]

have you drawn a picture

[stiff kindle]

yes

I have it

[rich peak]

well, why dont you send it then

[stiff kindle]

ok

[warm canopy]

thats not an accurate picture, use coordinates

[stiff kindle]

I used graphing paper

[warm canopy]

ok?

[stiff kindle]

I guess it works

[warm canopy]

your picture is wrong, so graphing paper isn't magical it seems

[stiff kindle]

How it is wrong?

[warm canopy]

none of those 4 small circles have the correct center

[stiff kindle]

oh, right

Ill send another photo

wait I need to go

bye!

.closw

.close

[obtuse pebble]

Channel closed

Closed by @stiff kindle

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tight patio]

What does this mean

[tight patio]

Like just explain I wanna actually learn this

Cause I have 0 idea

[oak bear]

P is for permutations

Like how you can arrange a number of things

Like this

[tight patio]

Ohhh P = Perm

I did not know that so sorry

[oak bear]

np

[tight patio]

So what does the numbers below mean?

12^3?

1320 Perm

[oak bear]

Kinda funny that miguel o harra is asking for permutations

[tight patio]

?

[oak bear]

No

that is not it

[tight patio]

shhhh Im an artist not a math kid 💀

[tight patio]

oh

then what?

am i doing wrong

[oak bear]

Just do this

[oak bear]

I thought you're going to calculate the possibilities of a canon event

[tight patio]

I already hate u 💀

[tight patio]

wdym?

what is n

what is r

[oak bear]

N is the number of your items

[tight patio]

n = 12?

[oak bear]

Yeah

[tight patio]

r = 3?

[oak bear]

And r is the number of the available slots

Yeah

[tight patio]

soo its

12/ (12-3)

12/9

[oak bear]

so it means you can only have 3 slots

[tight patio]

1.25

[oak bear]

Add the factorial

You still need to have the !

[tight patio]

WHat is the factorial!!

[oak bear]

so 12!/9!

[tight patio]

what diff does that make 💀

[oak bear]

It does

Factorial is just the arrangment of things

Like for example

[tight patio]

alr

[oak bear]

In how many ways can you write this

[tight patio]

so 12!/ 9! is my final answer?

[oak bear]

NOt yet

[tight patio]

oh

[oak bear]

How many ways can you write a,b, and c

[tight patio]

9 ways

[oak bear]

No

[tight patio]

I mean 6

[oak bear]

Yeah

You can write it in 6 ways

[tight patio]

so I have t write all 6 ways!

?

[oak bear]

We have 3 letters

and we there are no limited slots unlike your question earlier

[tight patio]

I hate this chapter 😭

[oak bear]

so 3!

[tight patio]

Alr tysm

[oak bear]

or 3 x 2 x 1

[tight patio]

yeah

[oak bear]

that's what factorial is

[tight patio]

so the final answer is???

I just have to say what that means

so that means nothing but 12!/ 9!

damn Im dumb

[oak bear]

12 x 11 ... x2x1 / 9x8x...x2x1

You can just do cancellation

Cause im pretty sure that you can

[tight patio]

Alr tysm

[oak bear]

np

[tight patio]

.close

[obtuse pebble]

Channel closed

Closed by @tight patio

Use .reopen if this was a mistake.

[tight patio]

Dude u saved me tysm

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[willow fractal]

im not sure how to do the

multiplying portion

[warm shale]

kebesque

[bold bane]

That notation actually indicates that it is a composite function, f of g(x).

[willow fractal]

uhh

[warm shale]

kebesque

[willow fractal]

so i have to do g(-2)

first

and then multiply f by that?

or

[bold bane]

Yes, that is the usual symbol, but you can find plenty of examples on the internet where they just use a dot to indicate composite.

[warm shale]

kebesque

[willow fractal]

oh so

iuts

-18

[bold bane]

I do wish there was more consistency. 🤷‍♂️

I'm merely pointing out that some people use a dot and some use a circle. I do find it annoying myself that some people did not get the memo about using a circle specifically for composite functions.

[willow fractal]

ok

so i solevd this one out

but im not sure about the domain

im (pretty) sure its sqrt x-1 over x+5

but idk how to find the domain of it

??

[bold bane]

Always refer to the domain of the original functions when determining the domain of the combined function.

[willow fractal]

hm

ok

yeah i still

dont know how to solve this

[bold bane]

What is the domain of sqrt(x-1)?

[bold bane]

And what is the domain of 1/(x+5)?

[willow fractal]

(-infiity, -5) U (-5, infinity)

[willow fractal]

not sure about this one

[bold bane]

Can you have a negative value inside of the square root?

[willow fractal]

no

so its everything negative?

thats out of bound

[bold bane]

So the value inside of the square root must be 0 or greater.

[willow fractal]

so the domain would be

1, infity

[bold bane]

Yes. Now combine that with the other domain you found however use x ≠ -5. You will notice that the two domains overlap and you can omit the latter.

[willow fractal]

ok

thank you!

[obtuse pebble]

@willow fractal Has your question been resolved?

Channel closed

Closed by @willow fractal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

I know how to solve this

but if the questions says in radians

we obviously include the value of pi right?

like when converting to degrees to radians

[high lily]

don't erase numbers for no reason

[timid silo]

its not like in terms of pi?

[timid silo]

?

[high lily]

thought you meant deleting pi entirely/not writing it at all

[timid silo]

i meant like

multiplying pi with it

for example instead of 3pi /2 radians

you would do

(3x3.145) / 2 radians

[high lily]

keep pi as pi unless told otherwise

[timid silo]

okay

but in this scenario

u would multiply pi right?

[high lily]

multiply what by pi

don't think of pi coming up when dealing with radians as a must

[timid silo]

.close

[obtuse pebble]

Channel closed

Closed by @mellow aurora

Use .reopen if this was a mistake.

[high lily]

if calculations lead to something like 2radians, that's completely fine.

apply the appropriate formulas etc, whether or not the the exact result actually contains pi depends on the values in the question

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[buoyant bear]

for a one one fxn the fxn should be Strictly increasing or decreasing or it can inc/dec but discontinous at some points.

[buoyant bear]

talking about derivative ofc

[brisk grove]

sorry but i didn't get a single thing you just typed

what's is fxn? what are you asking?

[buoyant bear]

like assum we have a fxn

and we have to find that the fxn is whether

one one or many one

[nocturne minnow]

Is fxn = function?

[buoyant bear]

yes

so we take the derivative to find itz one one or manyone

for one-one

there is a condition that

the fxn should be strictly increasing or decreasing

so here my ques is

that should it be

there are case of discountinity

[brisk grove]

there is no such thing as "many one"

[buoyant bear]

like assum this is a

stricly inc fxn

[brisk grove]

and no there is no general condition

it can be discontinuous everywhere and still be one-to-one

[buoyant bear]

and just assum there is a discountinuty

so will it still be one one

or it will be many one

[buoyant bear]

haven't you have heard of many one?

[brisk grove]

actually I haven't

is that a thing

[buoyant bear]

nvm then

i will ask some one

[brisk grove]

just a non-injective function?

[buoyant bear]

yes

[brisk grove]

google says it's just a function that's not one-to-one

alright

are you talking about real functions btw

[buoyant bear]

yes

nvm ig i complicated that

it would be better in person to person better

thanks man for the help @brisk grove

.close

[obtuse pebble]

Channel closed

Closed by @buoyant bear

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[silent jolt]

d/dx tan(1/(x^2+1))

[silent jolt]

sec^2x (1/x^2+1)(-2x/(x^2+1)^2

sec^2 (-2x/(x^2+1)^3))

idk where i went wrong

[raw hinge]

$[tan(\frac{1}{x^2+1})]'$

[warm shale]

_shachar

[silent jolt]

ye

[raw hinge]

trying to solve it, just needed it to be more clear

[silent jolt]

alr

[twilit pelican]

this doesnt look wrong?

[high lily]

,W d/dx tan(1/(x^2+1))

[twilit pelican]

oh wait

i see where he went wrong

you placed it inside sec

[silent jolt]

?

wdym

[twilit pelican]

$\sec^2\left(\frac{-2x}{(x^2 + 1)^3}\right)$

[warm shale]

blanketism

[high lily]

$f(x) \cdot k \redneq f(kx)$

[warm shale]

ℝamonov

[high lily]

also you have an extra x next to the sec^2 in the first line

[twilit pelican]

$\sec^2\left(\frac{1}{x^2 + 1}\right) \cdot \left(\frac{-2x}{(x^2 + 1)^2}\right)$

[warm shale]

blanketism

[silent jolt]

yes

[twilit pelican]

you cant combine those two parentheses together

you leave them separately as 1/(x^2 + 1) is the argument of secant

while -2x/(x^2 + 1)^2 is outside of secant

[silent jolt]

whats argument of secant

[twilit pelican]

just whats inside the secant function

[silent jolt]

how do u combine the two then

[twilit pelican]

you dont

[high lily]

you dont

don't feel the urge to forcibly combine stuff

[silent jolt]

how do u end up with

nvm

so u can multiply the sec^2 by whats outside

.close

[obtuse pebble]

Channel closed

Closed by @silent jolt

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[marble nymph]

I have no clue what to do here

[marble nymph]

I am so lost

Can anyone help

[obtuse pebble]

@marble nymph Has your question been resolved?

[marble nymph]

<@&286206848099549185>

[sacred lichen]

there are many ways to parametrise curves, are they looking for a particular method?

or end result I suppose

[marble nymph]

simple one

idk

[sacred lichen]

then you can just start with finding some function for these curves

like focusing on a), you should be able to at least write an implicit function for a circle of radius 5. that would be a starting point

[obtuse pebble]

@marble nymph Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow schooner]

How can i show that area formed by the flashlight is max

when its at the

end?

its swinging

idk which method to use

[obtuse pebble]

@hollow schooner Has your question been resolved?

[obtuse pebble]

@hollow schooner Has your question been resolved?

[shrewd wasp]

doing the calculations will be a bit of a hassle so I'll try to give a verbal explanation

Let the flashlight the same shadow on each screen from away a distance of 40 cm, parallel to the screen where the photons come out.

simply every time it swings it will always cast the same shadow length on a wall 40 cm away and parallel to it

but we're looking for a fixed wall shadow area

therefore, whenever an ellipse occurs, the area of its shadow relative to the ground will always be smaller than the area of the ellipse

thus since we simply project each shadow 40cm from the lantern relative to the ground

will be maximum when the projection is equal to itself

You can also see this when you functionalize the field of the flashlight to the angle of oscillation. But photons are emitted at an angle other than the flashlight regardless of the angle of oscillation, so you can get the angle of emission perpendicular if you want.

[obtuse pebble]

@hollow schooner Has your question been resolved?

[hollow schooner]

understood

[obtuse pebble]

Channel closed

Closed by @hollow schooner

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cunning sonnet]

I moved the decimals 5 places over in the beginning, I though I had to move them back once I have divided it??? Also it’s one decimal off? How come

[obtuse pebble]

@cunning sonnet Has your question been resolved?

[cunning sonnet]

#help

[lament cairn]

When doing This I tend to use the bus stop method as this complicated

[cunning sonnet]

I need to know how to move the decimals around for chemistry classes

I just don’t know why I don’t have to move them back in this and why I’m off one decimal

[lament cairn]

Oh I sadly don’t know much

[cunning sonnet]

That’s okay thanks trying to help

For

[glossy basalt]

one decimal from?

[cunning sonnet]

Being correct I think

[glossy basalt]

i mean, what's the answer?

you mean 55.2083 right?

[cunning sonnet]

Yea but mine came out 5.52083 and I also thought , since I had moved the decimal 5 places to the right in the beginning that I would have to move them back but for some reason I don’t think I do because the answer i got is much close to the correct answer without moving them again

[glossy basalt]

always put the decimal the same as the dividend

[cunning sonnet]

Ahh you went 48 into 2650 instead of 48 into 265