help-17

[tired echo]

if 3x=cosec theta and 3/x=cot theta find the value of 3(x^2-1/x^2)

[lime gorge]

$\csc \theta = 3x \newline \cot \theta = \frac 3x \newline 3(x^2 - \frac {1}{x^2}) = ?$

[twin meteor]

northsteve

[lime gorge]

Ok that’s ugly spacing

[tired echo]

fr

[lime gorge]

What have u tried

[tired echo]

thats the thing idk how to solve this at all

the reason i hate trigno is every question is diff

[merry python]

Find an expression for x and 1/x

[tired echo]

3x=cosec theta

x=cosec theta/3

[merry python]

Yes

[tired echo]

then?

[merry python]

And 1/x?

[tired echo]

1/x=cot theta /3

[merry python]

Yes

[tired echo]

im stuck hee

here

[merry python]

Now can you factor x²-1/x²

Difference of two squares

[tired echo]

how exactly?

[merry python]

do you know a²-b² formula

Its (a+b)(a-b)

[tired echo]

yes

so apply it?

[merry python]

Yes

[tired echo]

(x + 1)(x - 1) / x²

[merry python]

Wait

My bady

You don't need it

[tired echo]

oh

[merry python]

You got x=csc(theta)/3

[tired echo]

Yes

[merry python]

Find value of x²

[tired echo]

i didnt understand

[merry python]

Just whole square both sides

[tired echo]

1/x^2=cot^2 theta/9

and

x^2=cosec^2 theta/9

[merry python]

Yes

Now just put those valuez

Into the equation

[tired echo]

like wdym put

[merry python]

You got x^2=(csc^2(theta))/9
Put that value of x^2 into 3(x^2-(1/x^2))

Same for 1/x^2

[tired echo]

so ((cossec^2 theta)-(1/cosec^2 theta/9)

this fr is confusing

[merry python]

The cosec^2(theta) also has 9 as its denominator

And you got 1/(x^2)=(cot^2(theta))/9 put that value

It would be better if you try solving it on a paper

[tired echo]

so ((cossec^2 theta/9)-(1/cosec^2 theta/9)

[merry python]

...

[vocal sleet]

@tired echo Has your question been resolved?

[vocal sleet]

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[left zodiac]

Is R^I supposed to be understood as the cartesian product where for each element in I we assign an element in R to it?

[paper depot]

sure

another way to phrase that is that R^I is the set of all functions from I to R

or, the set of all real-valued functions on I

[left zodiac]

Ok, great. Thanks

.close

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[vast shale]

I would like some hints on how to solve this problem. I'm clueless where to start
(z1 and z2 are complex numbers)

[frigid flax]

is this complex numbers?

could you give additional context?

[vast shale]

Yes

[frigid flax]

the abosolute value of a complex number is just the modulus correct?

[vast shale]

Yes

[frigid flax]

ok

[vast shale]

Since I was clueless, I tried substituting x1+iy1 and x2+iy2, but the expression became extremely messy within some steps

[frigid flax]

have you tried expanding it?

or does it become cursed

[vast shale]

Let me check

that worked lol

[frigid flax]

everything cancels nicely?

[vast shale]

Yes

[frigid flax]

ok

[vast shale]

Thank you

[frigid flax]

np

well

[vast shale]

.close

[vocal sleet]

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Closed by @raw gazelle

Use .reopen if this was a mistake.

[vast shale]

.reopen

[vocal sleet]

✅

[vast shale]

Yes?

[frigid flax]

i didn't do much

[vast shale]

I wouldn't have even thought of expanding without your hint lol
I was too indulged into thinking about this on argand plane

[frigid flax]

lol alr

happy to help ig

[vast shale]

.close

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[hazy wraith]

Put together your secret message spell using the following powers and ingredients.

Powers

a. Frost 39
b. Nullification 35
c. Telekinesis 83
d. Empathy 91
e. Time Manipulation 36
f. Invisibility 19
g. Levitation 57
h. Clairvoyance 25
i. Pyrokinesis 61
j. Hydrokinesis 68
k. Healing 62

Ingredient

l. Ivy 49
m. Dragon's Blood 29
n. Tansy 77
o. Hawthorn 13
p. Hyssop 96
q. Rue 78
r. Unicorn Hair 11
s. Willow Bark 54
t. Basil 16
u. Juniper Berries 32
v. Moonflower 15

For the spell to be effective, you must make sure the numerical value of the spell is 876
The numerical value of the spell is calculated by adding up the numerical values of the powers and ingredients you choose.
For example, if you want a spell with the numerical value of 181, you would put together the following powers and ingredients:

c. Telekinesis 83 + f. Invisibility 15 + m. Dragon's Blood 29 + s. Willow Bark 54 = 181

So, the Answer will be !cfms

[hazy wraith]

someone help me solve this

because no matter what I do I cannot solve it

and my history teacher put it

HELP

<@&286206848099549185>

[silent plaza]

h

[hazy wraith]

?

please I beg help

[silent plaza]

please wait

[hazy wraith]

alright

thank you

[obtuse radish]

does the order matter?

[hazy wraith]

nope

you can put any letter first

[obtuse radish]

and is the "!" constant or another variable

[hazy wraith]

the first one need to be 7 letter second is 6 letter

[hazy wraith]

no need

wait hold up

[hard atlas]

this is the so-called subset sum problem. there should be calculators online if you wanna cheat. it's a famously hard problem

[obtuse radish]

and unless u want to look for an algorithm...

whats stopping u from using brute force

i doubt this is even a valid "question" to ask

u r making others do ur labour

[hazy wraith]

ah

sorry then

I just sit for 2 hour

and cannot solve it

sorry to disturb I guess I thought this could help

[hazy wraith]

you perhaps know any way I could solve?

hold up

I got the answer

but somehow is not correct

acdegijkmnopqsu

39+83+91+36+57+61+68+62
29+77+13+96+78+54+32

[hard atlas]

well lots of information online. I suppose the classic way is dynamic programming

[silent plaza]

@hazy wraith

[hazy wraith]

the hint was that 3 power are not need to be used

[silent plaza]

To create a secret message spell with a numerical value of 876, you can combine the following powers and ingredients:

Powers:
a. Frost 39
c. Telekinesis 83
d. Empathy 91
g. Levitation 57
i. Pyrokinesis 61
k. Healing 62

Ingredients:
l. Ivy 49
p. Hyssop 96
q. Rue 78
s. Willow Bark 54
t. Basil 16
u. Juniper Berries 32

Total power value: 393
Total ingredient value: 325

To achieve a total value of 876, you can use the following combination:

Powers:
a. Frost 39
c. Telekinesis 83
d. Empathy 91
g. Levitation 57
i. Pyrokinesis 61
k. Healing 62
Total power value: 393

Ingredients:
l. Ivy 49
p. Hyssop 96
q. Rue 78
s. Willow Bark 54
t. Basil 16
u. Juniper Berries 32
Total ingredient value: 325

The spell can be represented by the following arrangement:

acdgi + lpuqstu = 393 + 325 = 718

To reach a total value of 876, you need to add an additional ingredient:

v. Moonflower 15

The revised spell arrangement becomes:

acdgi + lpuqstuv = 393 + 340 = 876

Therefore, the secret message spell using the given powers and ingredients, with a numerical value of 876, can be represented as:

acdgi + lpuqstuv

[hazy wraith]

and 4 ingredient are not needed

DAM

[hard atlas]

chatgpt?

[hazy wraith]

wait hold up the hint he gave us was 3 power was not needed and 4 ingredient was also not needed

@silent plaza still not right

[hard atlas]

add up all numbers and check the difference to 876

then try to make that with 3 powers and 4 ingredients

thats a much smaller search space

[hazy wraith]

no it like

8 power and 7 ingredients

[obtuse radish]

does chat gpt give unique results? i got this:

To create a secret message spell with a numerical value of 876, you can combine the following powers and ingredients:

d. Empathy 91 + c. Telekinesis 83 + q. Rue 78 + t. Basil 16 + u. Juniper Berries 32 + v. Moonflower 15 + m. Dragon's Blood 29 + s. Willow Bark 54 + p. Hyssop 96 + o. Hawthorn 13 + r. Unicorn Hair 11 + j. Hydrokinesis 68 + l. Ivy 49 + k. Healing 62 = 876

So, the secret message spell would be: "!dtquvmsporgljklk"

[hazy wraith]

to make 876 numerical

[hard atlas]

chatgpt gives bullshit

do not use it

for math

[obtuse radish]

i refuse to believe my man did that by himself

its not something i'd consider maths

its just computation

[hard atlas]

stupid distinction in this case

[hazy wraith]

Put together your secret message spell using the following powers and ingredients.

Powers

a. Frost 39
b. Nullification 35
c. Telekinesis 83
d. Empathy 91
e. Time Manipulation 36
f. Invisibility 19
g. Levitation 57
h. Clairvoyance 25
i. Pyrokinesis 61
j. Hydrokinesis 68
k. Healing 62

Ingredients

l. Ivy 49
m. Dragon's Blood 29
n. Tansy 77
o. Hawthorn 13
p. Hyssop 96
q. Rue 78
r. Unicorn Hair 11
s. Willow Bark 54
t. Basil 16
u. Juniper Berries 32
v. Moonflower 15

For the spell to be effective, you must make sure the numerical value of the spell is 876
The numerical value of the spell is calculated by adding up the numerical values of the powers and ingredients you choose.
For example, if you want a spell with the numerical value of 181, you would put together the following powers and ingredients:

c. Telekinesis 83 + f. Invisibility 15 + m. Dragon's Blood 29 + s. Willow Bark 54 = 181

So, the Answer will be cfms

(HINT: Only 3 Powers & 4 ingredients are NOT part of the spell 👀)

[hard atlas]

let me rephrase: chatpgt is forbidden on this server. dont use it or get banned

[hazy wraith]

there that the hint

[obtuse radish]

im not sure if that has humorous intent but i got no pings abt changed rules

[hard atlas]

it was changed weeks ago. check the rules

[obtuse radish]

it seems so

[hazy wraith]

my brainw as frying because of that top there

I spended 2-3 hour to get bs result

[hard atlas]

8 powers and 7 ingredients to make 876 is equivalent to 3 powers and 4 ingredients to make (total sum)-876

and the second is much easier to solve

at least for our brains cause the numbers are smaller

[hazy wraith]

ok now my brain is more fried

[obtuse radish]

do they not ping here? thats so stupid

[hard atlas]

take it up with the moderators

they have the revision message which is visible unless you muted the channel

it is also in #changelog

[mild flower]

also chatgpt is really terrible at math

[hazy wraith]

my brain

is frying for 3 hours

I cannot solve it

[vast shale]

can anyone help me with math

[hazy wraith]

create a channel for help

my brain

it frying more

I cannot crak the secret message

haiya I am gonna cry

[hard atlas]

if you have eg 6 numbers {1,2,3,6,7,10} and want to find 4 that sum to 12, then you can also notice that all 6 together sum to 29, so (your four numbers)+(last two number)=12+(last two numbers) = 29, so the last two numbers sum to 17

which is easier to solve cause its only two numbers you have to worry about

here 17=7+10 so you choose all numbers except 7 and 10

in your problem, the total sum of all numbers is 1046

1046-876 = 170

so you are looking for 3 powers and 4 ingredients that sum to 170

and that is doable

[vocal sleet]

@hazy wraith Has your question been resolved?

Channel closed

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Use .reopen if this was a mistake.

[hazy wraith]

.reopen

[vocal sleet]

✅

[hazy wraith]

!ACDEGHJKLMNPQSU

found it

.close

[vocal sleet]

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[vast shale]

help

[vast shale]

f(x) = THE SQUARE ROOT OF x-2
g(x) = 5x + 2

Find: g(f(18))

how do i solve this i dont understand how to write it out

[soft walrus]

do you know function notation?

[vast shale]

im gonna say no

[soft walrus]

alright that's fine :))

so first just begin with f(x)

$f(x)=\sqrt{x-2}$

[twin meteor]

XxMrFancyu2xX

[vast shale]

yes

[soft walrus]

we use function notation because it's easier to know what we inputted for a given input

in this case $f(6)=2$

[twin meteor]

XxMrFancyu2xX

[vast shale]

so 4

[soft walrus]

do you see why?

[vast shale]

yes

so what do i do with my 4?

[mighty dust]

put it inside the g function

[vast shale]

and thats it?

[mighty dust]

I suppose

[vast shale]

oh so easy

thank you

i can take it from here

.close

[vocal sleet]

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[soft walrus]

wait

the question is not asking for f(6)

it's asking for f(18)

.reopen

[vocal sleet]

✅

[mighty dust]

But it's right

[soft walrus]

wdym?

[mighty dust]

I mean that he got 4 from f(18), which is right since the square root of 18-2 is equal to 4

[half kite]

@vast shale

[vast shale]

yes yes

[half kite]

do u know the answer of 0 1/2

[soft walrus]

ohhhh ok ok 😅

i thought he was talking about 4 from 6-2

ok nvm we all good

[mighty dust]

yeah no problemo

[soft walrus]

haha my bad people

[vast shale]

do not fret

thank you again

[soft walrus]

have a good day sorry kinda ghosted you there 👻

[vast shale]

youre all good lol

.close

[vocal sleet]

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[vocal sleet]

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[tribal mauve]

can someone explain how they got this

[timber cypress]

Hello

Which step are you stuck on

[tribal mauve]

the last one

how did they get x^3

[timber cypress]

They squared both sides

[tribal mauve]

ah okay thank you

i was a bit confused how they got 3 from 3/2

[timber cypress]

You're not confused now, yes?

[tribal mauve]

yes

thanks

[vocal sleet]

@tribal mauve Has your question been resolved?

[timber cypress]

. close

.close

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[coral plank]

I tried to multiply all of the bottom together and then multiply 6 by 2x+5 and 4x² - 25, 2 by the denominators except its own and 60 by the denominators except its own too and I eventually got (64x³ + 160x² - 400x - 1000)/16x⁴ - 200x² + 625

but that doesbt look right because of the x⁴ and x²

[paper depot]

right not write

but also uh

you do realize 4x^2 - 25 = (2x-5)(2x+5) right

[coral plank]

omg

[paper depot]

also missing parentheses around the denom in your thing

[coral plank]

okay one second

ok so [2(2x+5) + 6(2x-5) + 60]/[(2x+5)(2x-5)]?

but also how do you get the Bx + C because it would be 4x² ?

on the denominator

[paper depot]

clean up the numerator

[coral plank]

(4x² + 12x + 40)/(4x²+25)

[vocal sleet]

@coral plank Has your question been resolved?

[coral plank]

no

help @paper depot

or anyone

[mild flower]

that should be 4x^2 - 25 in the denom

[paper depot]

how are you getting 4x^2 + 12x + 40 from 2(2x+5) + 6(2x-5) + 60

also yeah denom fucked up too

[coral plank]

I don't know wtf

I think I have stupid disease

today

[vast shale]

can you try writing down everything again

[coral plank]

I wrote that in my answer on paper I swear

[vast shale]

you have nothing to prove to us so you dont have to go that far...

[coral plank]

it's embarassing

Iwait a min

I'll try

okay wait I might be onto sometjing

is it 8/2x-5

(2x-5)

[mild flower]

[vocal sleet]

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[vocal sleet]

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[steady valve]

A
fair die is weighted so that the probability of rolling a side with
n dots on it
(1≤n≤6) is the proportion of the number of dots on that side to the total number dots on the die. Find the probability that if this die is rolled twice, the sum will be a 7.

[steady valve]

how can i solve this without listing all the cases

[flat whale]

listing out all the cases is the fastest way

[steady valve]

really

thats annoying

like i did that

but im too lazy to calculate

is there a way where i can find a summation formula

or something

bc i quickly summed 1 to 6 using n(n+1)/2

[livid grotto]

i mean you went through the effort of pulling up discord, opening a help channel and having this conversation

couldve probably done it by now

[flat whale]

what summation formula do you think exists

[steady valve]

i figured out a summation formula

[flat whale]

great

do .close since you're done

[steady valve]

ok

.close

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[torpid sequoia]

$\int _0^{\pi }cos^3\left(x\right):\cdot sen^5\left(x\right)dx$

$t=sen\left(x\right)dx$ ; $dt=cos\left(x\right)dx$

$\int _0^{\pi }dt^3\cdot t^5dt$

[twin meteor]

Chuti | Spanish

[torpid sequoia]

does this even exist?

should I do dt^3 or no

[regal bane]

Lol dt³

This is why differentials are bad

You can't do that, no. You can only change the dx to a dt

[soft walrus]

I have never seen the "sen" function is it "sec"?

[regal bane]

sin but for some languages

[soft walrus]

ahhh

[regal bane]

I'm thinking OP is Spanish?

[torpid sequoia]

Sorry

is

sin

[regal bane]

Oh lol it's in the name

[torpid sequoia]

Yeah 😄

[soft walrus]

helps a little doesn't it 🥴

[regal bane]

A little less impressive yeah

[soft walrus]

anyways @torpid sequoia consider $\cos^{2}(x)=1-\sin^{2}(x)$

[twin meteor]

XxMrFancyu2xX

[torpid sequoia]

I'm aware of that, yes.

[soft walrus]

then maybe try ur sub :))

[torpid sequoia]

shoudl I use it?

Let me try

[torpid sequoia]

u talking to me?

[soft walrus]

yep!

[torpid sequoia]

my subdiscord?

math in spanish you mean?

[soft walrus]

oh no sub = substitution

[torpid sequoia]

oh

lmfao

🤣

[soft walrus]

no worries, probably should talk in formal english instead of being lazy and typing in slang 😂

[torpid sequoia]

ok I'm doing random stuff

look at this lmao

idk how should I solve it rly

like thats wrong though

ok wait I got to $t^5 - t^7$

[twin meteor]

Chuti | Spanish

[soft walrus]

:))

now life is easy!

[torpid sequoia]

how so

[soft walrus]

you can integrate that really easy

[torpid sequoia]

life aint easy

[soft walrus]

well fine

I just a 61 on my final

but yk

Touché

[torpid sequoia]

idk I have to work, study, and study

anyways

who cares 🤣

I see the final result was 0 since this was the int from 0 to 0

but then why did I even went through all of that process

[soft walrus]

but you wont next time :))

[torpid sequoia]

you are really happy bro 😄

[torpid sequoia]

cause I'll find out that this is an int from 0 to 0 ?

[soft walrus]

if ur never happy, then well, why live life is my philosophy

[torpid sequoia]

I'm not happy nor sad, I'm just living life 😎

haha

not complaining, just doing math

[soft walrus]

the dream

[torpid sequoia]

not for me tbh 🤣

[soft walrus]

but the next time you can skip some steps

[torpid sequoia]

I would love to be studying the theory of asynchronous programming right now

not ints, but ok

haha nice emoji

[soft walrus]

for me that's ints and I'm stuck reviewing the stupid Kreb's Cycle

[torpid sequoia]

idk whats Krebs Cycle

tbh

[soft walrus]

Bio

[torpid sequoia]

I barely know what an int is...

cons of going to public school in argentina

[soft walrus]

you seem to be pretty good at them man, math is amazing don't give it the cold shoulder because of a bad school experience :))

[torpid sequoia]

oh no I'm not having a bad school experience

but I struggle with maths

also I got a 3 in the first exam and I studied a lot and when I saw my mistakes, they were just so stupid! I could have easily passed with at least a 7 ;/

anyways, thanks for helping me out

[vocal sleet]

@torpid sequoia Has your question been resolved?

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[onyx meadow]

Of the vehicles in a parking lot, 38.75 percent are trucks and 52.5 percent are cars. What fraction of the vehicles in the parking lot are neither trucks not cars

[onyx meadow]

So the way I did this was I knew if 38.75% was trucks then 61.25% will not be trucks

And since 52.5% is cars then 47.5% would not be cars

Am I doing it correctly?

So far

[marsh mural]

wouldnt it be easier to add them

you know that 90.25% are trucks or cars

soo the rest would be neither

[onyx meadow]

That's true 🤦🏻‍♀️

Thank you

[marsh mural]

goodluck

[onyx meadow]

I over thought it

How do you convert a decimal to a fraction

Like 0.0875

@marsh mural

[marsh mural]

875/10000

which is

7/80

[onyx meadow]

Okay I see

Thank you so much

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[eternal glacier]

should v (vector) have the arrow above it?

for proper notation

i've seen it written without sometimes

[hidden kelp]

the arrow signifies it's a vector, not just a random variable

[eternal glacier]

and do you prefer ai + bj?

or <a,b>

[hidden kelp]

I mean if you write:
v = (a, b)
or something alike, it's really clear that it's a vector, so I could see it written without, but otherwise just put an arrow

[eternal glacier]

"ai bj"

[hidden kelp]

what's up with that?

[eternal glacier]

https://tenor.com/view/beavis-and-butt-head-laughing-gif-19758205

[hidden kelp]

oh

xD

[eternal glacier]

both represent the component form of a vector

[summer lichen]

https://tenor.com/view/beavis-and-butthead-tv-show-cartoon-norwood-hairline-gif-15692969

[hidden kelp]

I've never seen it written as "ai+bj" though, where do i and j come from?

[eternal glacier]

hmmm yeah

[summer lichen]

it's a linear combination of the basis vectors i and j

[hidden kelp]

is it standard notation that i = <1, 0> ?

[summer lichen]

yeah sometimes it's written as i hat and j hat

$\hat{i} : \hat{j}$

[twin meteor]

keto11

[eternal glacier]

not to be confused with unit vector

1

[summer lichen]

wait avidrunner

[hidden kelp]

unit vector = <1, 0> or <0, 1>

[summer lichen]

it's your help channel

[hidden kelp]

yeah it is

[summer lichen]

what was your question?

[hidden kelp]

↑

[eternal glacier]

basis vector and unit vector mean the same thing?

[hidden kelp]

not exactly. I think a basis vector is whatever you use to do a linear combination

correct me if i'm wrong Keto

[summer lichen]

oh yeah it should, but sometimes it's just implied or it's written without cause people are lazy

[eternal glacier]

|u|=1 is the magnitude of vector u

1 is the magnitude, and therefor the unit vector

[summer lichen]

it can also be OV which is the vector from the origin to v

[eternal glacier]

too many ways to learn the same thing with different notation

[summer lichen]

basis vectors can be unit vectors but in general they just define a coordinate system

[eternal glacier]

it's like learning Python, C++, Java syntax altogether... gotta learn them all

wish math was more standardized but i digress.. it is what it is.. too late to change it..

i guess another way to look at it: a school should follow one syntax for teaching math

should, but most likely doesn't..

gotta learn them all.. it is what it is...

[worthy citrus]

there are reasons for different syntaxes existing, people werent just like oh youre writing it that way? fuck you ill write it this way

[livid grotto]

flabby sheaves

[summer lichen]

Leibniz Lagranage and Euler notations for derivatives in a nutshell

[flat whale]

pretty sure physicists said conjugate linear in the "other component" for inner products, just as an FU to mathematicians

[eternal glacier]

whats a good reason to write a vector ai+bj rather than <1,3> ?

[worthy citrus]

lol this is the one exception

[flat whale]

avid: exception? must be the norm

[livid grotto]

it was useful in my recent symplectic geometry exam

[worthy citrus]

look at this symple dude

[livid grotto]

[eternal glacier]

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[hidden flame]

Ignore pencil marks, but this seems kinda tough? Try to solve this without using soh cah toa

[mild flower]

finding the area or what?

should just need pythagoras

i think 💀

[final zephyr]

not even that if ur finding area

[urban edge]

Not enough information 💀

[final zephyr]

oh wait lol

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@hidden flame Has your question been resolved?

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@hidden flame Has your question been resolved?

[hidden flame]

^

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@hidden flame Has your question been resolved?

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@hidden flame Has your question been resolved?

[lost bane]

what is bro trying to do

[vocal sleet]

@hidden flame Has your question been resolved?

[hidden flame]

Area

[lost bane]

area of what

euclid is calling

[gaunt pendant]

Leibniz is ringing

[mild flower]

it's underconstrained

[vocal sleet]

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[loud heath]

-2 + 3 = 1

[flat whale]

khan's a good start
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inverse-functions-intro/a/intro-to-inverse-functions

you should just post your actual question

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[mild phoenix]

help me with trig identities

im not understanding what they are asking me to do

[karmic imp]

Basically simplifying so it's one trig function

[mild phoenix]

im not sure how to use identities

i have my final tomorrow i just need to understand it

[karmic imp]

For the first one, what's csc equal to?

[mild phoenix]

1/sinθ

[karmic imp]

And that's getting multiplied with cos

What's the result of that

[mild phoenix]

cosθ/sinθ

?

[karmic imp]

And that simplifies to?

[mild phoenix]

cot

oh

[karmic imp]

That's it

[mild phoenix]

what about 2

[karmic imp]

What's 1 - cos^2 equal to?

[mild phoenix]

umm

-cot^2?

[karmic imp]

No

You need to review trig identities, like this

[mild phoenix]

sin^2θ

[karmic imp]

Do you see something on there that could be equivalent to 1 - cos^2?

[karmic imp]

Yes

So now what do you have?

[mild phoenix]

(1-sin^2θ)/(sin^2θ)

[karmic imp]

No

[mild phoenix]

oh

im dumb lol

[karmic imp]

You just said 1 - cos^2 is equal to sin^2

Right?

[mild phoenix]

yes

sin^2theta + 1

is cos^2θ right

[karmic imp]

No

[karmic imp]

.

[mild phoenix]

-sin^2θ-1

[karmic imp]

No

Stop guessing

[mild phoenix]

i gotta write it down

i cant do alg in my head

[karmic imp]

I asked what 1 - cos^2 is equal to

You stated sin^2

[mild phoenix]

cos^2θ

equals

[karmic imp]

Why are you focused on the denominator?

[mild phoenix]

-sin^2θ+1

oh

sin/cos=tan

[karmic imp]

No

Yes sin/cos = tan

But that's not the answer to your problem

[mild phoenix]

oh

its sin^2

[karmic imp]

What is?

[mild phoenix]

1-sin^2θ

is cos^2theta

[karmic imp]

Stop focusing on the denominator

[mild phoenix]

k

idk what direction to go in

[karmic imp]

I am asking you what 1 - cos^2 is equal to

[mild phoenix]

sin^2θ

[karmic imp]

What is the expression you have now?

[mild phoenix]

(sin^2θ)/(cos^2θ)

[karmic imp]

And that equals what?

[mild phoenix]

tan^2θ?

[karmic imp]

Yes

[mild phoenix]

thanks man

now 3

[karmic imp]

Try it on your own

I suggest getting it in terms of sin and cos

[mild phoenix]

yeah im lost

[karmic imp]

Did you try what I suggested

[mild phoenix]

im confused

tan=sin/cos

just use that??

[karmic imp]

Yes

[mild phoenix]

i mean what do i do now

[karmic imp]

What do you have when you wrote that in terms of sin and cos?

[mild phoenix]

[(sinθ)/(cosθ) + cotθ]/(sinθ)/(cosθ)

[karmic imp]

What's cot in terms of sin and cos?

[mild phoenix]

1/[(sinθ)/(cosθ)]

[karmic imp]

And that's equal to?

[mild phoenix]

1/tan = cot

idk

[karmic imp]

Look at the image I sent

What is cot in terms of sin and cos

[mild phoenix]

cos/sin

[karmic imp]

Yes

Do you know how to combine fractions?

[mild phoenix]

no

[karmic imp]

You don't know how to add fractions?

[mild phoenix]

not without a common denominator

[karmic imp]

Can you find a common denominator?

[mild phoenix]

cosine

[karmic imp]

No

[(sinθ)/(cosθ) + cosθ/sinθ]/(sinθ)/(cosθ)

That's what you have, correct?

[mild phoenix]

yes

[karmic imp]

Can you add the fractions in the numerator, using a common denominator?

[mild phoenix]

i cant

one denominator is cosine

the other is sine

[karmic imp]

Do you know how to find a common denominator

[mild phoenix]

wait gimme a sec

ok

now i have cos^2theta + sin^2theta

divided by sin^2theta

[karmic imp]

What was the common denominator of the numerator?

[mild phoenix]

1/sin^2theta now

thats csc

csc^2θ

did i go the right direction

i just did costheta times sintheta as the denominator

i remembered how to combine fractions

i crammed recently for sat so my math brain is ruined

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[sour pendant]

Why can you use the cross product of two vectors to get the plane parallel to the original two vectors

[sour pendant]

i don't understand why you can take the function for the cross product vector, find a constand, and it becomes the plane parallel to the original 2 vectors

[worthy citrus]

planes are uniquely determined by their normal vector and a point on the plane

so you're using some points on the plane to find the normal vector

[sour pendant]

oh oh i see

so each point in the normal vector is a parallel plane to plane parallel to the original 2 vectors

?

and the constant shifts that plane

[worthy citrus]

"each point in the normal vector" i dont quite follow

but i think you mean there are many parallel planes with the same normal vector

[sour pendant]

yes

tha'ts what i mean

[worthy citrus]

then yeah spot on

[sour pendant]

okay this makes sense thakn you

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[quasi roost]

Linear Algebra, Im not sure how you could get A to be alone on 1 side and have no A on the other. I did the first step I believe is correct then stopped there (i could find the inverse if needed but not sure if that would be wasting time or not)

[thin vale]

is $(A+B)^{-1}=(B^{-1}+A^{-1})$

[twin meteor]

AustinU

[thin vale]

try testing it out with A=B=I

[quasi roost]

sorry not sure what you mean

[thin vale]

let's say we wanted to test this property of matrices in general

for any matrices A and B

we want to know if it is true

you can test it out by letting A and B both be the identity matrix

try 2x2

it will be clear if the property holds or not

[quasi roost]

yeah that property makes sense but not sure how that helps in the question

[lyric fossil]

it's not a property

[lyric fossil]

your first step is incorrect
does (AB)^-1 = A^-1 * B^-1?

[quasi roost]

oh i see what you mean now thanks

but now i’m on step 0 and still unsure how to make A alone

[lyric fossil]

well look at the equation

and try messing around with it

[quasi roost]

i can get A- alone on the left side at most i can’t get pass that even thought i could inverse À- and get A it makes the other side even more complicated

[lyric fossil]

multiply the right by A^-1 on both sides

[quasi roost]

ok and you get A-1[]A-1 on the left side

[lyric fossil]

no

let's go back

you start with A^-1[] = ...

what is the inverse of A^-1B

that is, what is $(A^{-1}B)^{-1}$

[twin meteor]

maximofs

[quasi roost]

B-1A?

[lyric fossil]

yes

im going to call those other two matrices B and C

because i don't want to write them out

inverting both sides we get

$B^{-1}A = C - 2A$

[twin meteor]

maximofs

[quasi roost]

ok yeah i see that

ok i see how you solve it now

thank you

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[urban obsidian]

not sure what i should use as u here

[urban obsidian]

assuming it is u-sub

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@urban obsidian Has your question been resolved?

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[urban obsidian]

.reopen

[vocal sleet]

✅

[urban obsidian]

<@&286206848099549185>

[soft walrus]

why not just $u=9z$?

[twin meteor]

XxMrFancyu2xX

[viral copper]

Does that really accomplish all that much though lol

[soft walrus]

i mean makes life a little easier but not much as far as computation goes lol

[viral copper]

$\frac 19 \int (u^5 + 4u^2)(u^3 + 1)^{12} \dd u$

[twin meteor]

neonperseus

[viral copper]

You can factor our u^2 and substitute u^3 = t

That will help a lot

$\frac{1}{27} \int (t + 4)(t + 1)^{12} \dd t$

[twin meteor]

neonperseus

[viral copper]

If you wanna go further you can say t + 1 = v

[vocal sleet]

@urban obsidian Has your question been resolved?

[urban obsidian]

so you mean like a double substitution

[urban obsidian]

honestly this doesn't look that much easier to compute right? Lol

[urban obsidian]

so you'd have like integral of (v+3)(v)^12

and then i have to undo subbing like 3 times right

I've not done multiple substitutions before, could i get a headsup

I'm familiar with the process but just need to know i'm not going astray

[viral copper]

Yes

[viral copper]

It's not that big of a deal

[urban obsidian]

i will try right now

and show

[mild flower]

where'd that u^2 go?

[urban obsidian]

whoops

[viral copper]

into the differential element

[mild flower]

right ofc

[viral copper]

$u^3 = t \implies u^2 \dd u = \frac 13 \dd t$

[twin meteor]

neonperseus

[mild flower]

yep just brain wasn't working

[urban obsidian]

Lol

[viral copper]

Happens to the best of us

[urban obsidian]

whoop sorry i had to do something but continuing from where we left off, we'd have:
$\frac {1}{27} \int (v+3)(v^{12}) \text{ dv }$

[twin meteor]

hii_

[viral copper]

Now just distribute v^12 and use the power rule

[urban obsidian]

integrating we have:
$\frac{1}{27} \left[\frac{v^{14}}{14} + {\frac{3v^{2}}{2}}\right]$

[twin meteor]

hii_

[viral copper]

$\frac{1}{27} \left ( \frac{v^{14}}{14} + \frac{3v^2}{2} \right ) + C$

[urban obsidian]

so what do i sub in here?

[viral copper]

Oh well

[urban obsidian]

v = t+1

[viral copper]

Now work backwards

[urban obsidian]

and then t = u^3

[viral copper]

Yes

[urban obsidian]

and u = 9z

[viral copper]

Yep

[urban obsidian]

so v = u^3 + 1 or v = (9z)^3 + 1

right?

[twin meteor]

neonperseus

[urban obsidian]

oh yeah lol

[viral copper]

Yup

[urban obsidian]

okay that's nice

for some reason i thought this was going to be super convoluted back subbing

because i was thinking about something else i guess

so multiple substitutions are a good thing i guess

[viral copper]

As long as it's all algebraic it's not that bad

[urban obsidian]

wdym?

[viral copper]

If you had a trig sub or something in between it would get pretty nasty

[urban obsidian]

But still doable right?

oh i see what u mean actually

right yes that makes sense

[viral copper]

It is doable

[urban obsidian]

cuz of all the solutions u have to take into account

[viral copper]

That's basically how you do $\int \sqrt{\tan x} \dd x$

[twin meteor]

neonperseus

[urban obsidian]

oh damn

I'm reviewing my calculus and don't quite remember trig substitutions

When i reach there soon i will try that

[viral copper]

It's not very different from regular u subs

[urban obsidian]

it's basically just x = tan(theta) or something of that form, i guess?

[viral copper]

You just use a trig ratio instead of a new variable

[viral copper]

Generally yes

[urban obsidian]

I remember there was weierstrass too right? Is that part of trig sub

[viral copper]

Yeah that's tan x/2 = t

Technically it's not a trig sub but yeah

[urban obsidian]

ah so just half angle

why is it not trig sub when you're technically using trig functions

[rugged orchid]

And you use half angle identities for it

[viral copper]

It's used to go from a trig integral to a rational one

[urban obsidian]

oh yeah makes sense

thanks!

[viral copper]

Also I've heard of a second sub with the same name that being x = (1 + t)/(1 - t) so idk what Id call it

[urban obsidian]

No clue lol

i think i've seen euler's sub

in the trig sub page or something when i was reading something

[viral copper]

Euler's sub is like

The one with square roots and shit

[urban obsidian]

isn't that for rational functions too

[viral copper]

yeah but I've never used it personally

[urban obsidian]

would you even be required to know all of this subs lol? Tbh i only knew usub, trig sub, partial integration, and weierstrass

is something else of importance?

i just use my code for numerical approximations for the most part

so idk if there's other techniques that might be ubiquitous enough for me to have to learn them

[viral copper]

I never memorized them

It's just stuff you pick up along the way

[urban obsidian]

I see

I think that should be all for now

Thanks

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[rapid viper]

Quick question; I'm a bit confused as to how exactly the answer is simplified to what's completely at the bottom

[rapid viper]

I understand the integration process, just confused how exactly you'd simplify the result into what's presented at the end :)

[river minnow]

Just rewrite (x^2 + 1)^(3/2) as (x^2 + 1) * sqrt(x^2 + 1) and make common denominators

[rapid viper]

ohhh okay thanks

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[barren quiver]

How do I do this

[late ingot]

first and second derivatives

[barren quiver]

Okay I got

4-2t and 8t-3t^2

[late ingot]

thats v_1 and v_2

[barren quiver]

And for the second derative

I got

-2 and8-6t

[late ingot]

thats a_1 and a_2, now find when a_1 = a_2, then take that x and plug it into the v's

[barren quiver]

10-6t

5/3

[late ingot]

write it out every time, stops you from making mistakes

yes 5/3

now plug and chug for v

[barren quiver]

2/3

and 5

Okay thank you

How long will you be here for

[late ingot]

idk lol, if not me someone else will help

derivatives are fairly basic here in this server.

[barren quiver]

Okay

I need help with another question

[late ingot]

[late ingot]

$V_{sphere}=\frac{4}{3}\pi r^{3}$

[twin meteor]

b0ngl0rd

[barren quiver]

Yeah

And the I did the derative

Which is

dv/dt =4/3pi3r^2dr/dt

Hello?

[late ingot]

well whats our rate of change of the radius?

[barren quiver]

dv/dt*9 = dr/dt

[late ingot]

how do you suppose that

[barren quiver]

I dont know

[late ingot]

we need to set up an equality

[barren quiver]

How do we do that

[late ingot]

last part of that problem gives it to us

dV/dt needs to be equal to 9pi*dr/dt

[barren quiver]

Okay

Now what

[late ingot]

you have dV/dt

set it equal to 9pi*dr/dt

solve for r

[barren quiver]

So dr/dt cacnel out

[late ingot]

yep

[barren quiver]

3/2

[late ingot]

looks good to me

[barren quiver]

Okay thanks

.close

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[tidal trail]

How to rasionalise the numerator?

[hushed tree]

You can you L'Hopital for this

[lusty shadow]

How to do this?

[hushed tree]

Use*

[hushed tree]

#❓how-to-get-help

[tidal trail]

2x / (sqrt6X^2 + 6x) + 3x sqrt 2

[hushed tree]

Did you multiply by the conjugate of the numerator?

[tidal trail]

Yes

Denominator too

[hushed tree]

Good

You mean you multiplied the denominator too

Not with the conjugate of the denominator

Right

[tidal trail]

Yes

[tidal trail]

Yep

[hushed tree]

Good

The 2x at the top is correct

At the bottom it seems wrong

[tidal trail]

Ye

It's funny

Oh lol

Mf times the 3x into the sqrt

[hushed tree]

?

[tidal trail]

It shld be:

2x / 3x ( sqrt 2x + 2 + sqrt2 )

[hushed tree]

Wait

So you have 2x on the top

And x(....) on the bottom

What can you do

[tidal trail]

1 / 2sqrt2

Sth's wrong

[hushed tree]

Just answer this

[tidal trail]

Factor out x

[hushed tree]

No

[tidal trail]

?

[hushed tree]

4x/xy

What can you do here

[tidal trail]

Factor simplify same thing

[hushed tree]

No

Its not

[tidal trail]

To get 1 / 2sqrt2

[hushed tree]

Wrong

[tidal trail]

2x / 3x ( sqrt 2x + 2 + sqrt2 )

[tidal trail]

4/y

[hushed tree]

Yes

Do the same

[tidal trail]

Mmm same thing

But sth's wrong

One of my working is wrong

[hushed tree]

2x/(x×(sqrt(2x+2)+sqrt2))

[tidal trail]

Nvm it's not the working

It's the fking bracket

Yep thanks

.close

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[hushed tree]

Np

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[mild herald]

doubt

[mild herald]

the red bit is the question

blue bit is the method

which ive used

it is wrong

and i know the answer is e^5

and ik the method how to get that

but i wanna know why this method doesnt work

im relatively new to limits so if anyone could explain in easy-ish terms

that would be great

[atomic pine]

short answer: you cannot plug in infinity for some cases

[cursive matrix]

the problem is, you calculated the limit of inside the brackets while also NOT calculating the limit in the exponent

[atomic pine]

"intuitive" explanation: if you plug in infinity you get$$ (1^+) ^\infty$$ which isn't necessarily 1

[twin meteor]

qwertytrewq_hashtag_7770

[atomic pine]

its important to know when not to plug in infinity, for example: when you get answers like $$1^\infty, 0\times \infty, \infty+\infty, \infty -\infty$$

[twin meteor]

qwertytrewq_hashtag_7770

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[mild herald]

ah

[mild herald]

so basically

i cant sub x=infinity only inside

and leave the power as is

?

[mild herald]

right okay, thank you

[atomic pine]

hopefully you will eventually learn a more formal definition of limit, and things may make more sense, but at the moment, just understand that plugging in infinity could be really weird some time.

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[dapper lark]

Would anyone happened to know the 6th question? Im kind of stuck on it

[dapper lark]

just the thing for a

[unreal hound]

Do you know any conclusions for the expression 1-cosx?

There's a separate formula for it

[floral seal]

no

[unreal hound]

What do you suggest

[unreal hound]

You rearrange the terms and you get what i was saying

[floral seal]

Its confusing isnt it?

[unreal hound]

Not really, no

[floral seal]

fine

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[dapper lark]

.close

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[vast shale]

but I dont quite understand how this mathematically makes sense?

oh okay

.close

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[summer urchin]

why we didnt calculate one of the lines

[dusky niche]

The line crossed out is not part of the perimeter

The perimeter is the distance along the outside of the figure

[summer urchin]

oh so always we do that?

[dusky niche]

Yeah for the perimeter. You can image the perimeter as the path you would walk if you were to walk around the figure 😄

[summer urchin]

thank you

can u help me with this

[dusky niche]

I'm a CS and Economics student, haven't slept a whole lot, give me a second to check what I'm doing 😄
Then I'll confirm / deny if another mathhead hasnt taken it before ^^

I'm sorry but I do not have the mental power for trig currently