help-0

[grand tiger]

have u even prepared for the exam

this is a very basic question which u should do if u have an exam today

im sorry but u cant do much in 7 mins

do u even know

what slope of a line is

what is it

wonderful

what a definition

looks like u havent studied

go like this come home and study

sorry i live in india

not sure

are u talking about

the medical aspects?

[austere warren]

how do i do it in terms of y then? i thought shells along y axis is in terms of x

i'm not sure where to separate the integral on the x axis

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[rough raptor]

anybody can prove the question (b) ?

[keen pasture]

a) is there for a reason

[drowsy bronze]

The person who made this test wrote that the answer is A which is 3. But I think there are only two possibilities. My reasoning : I assigned variables to each digit as such: a < b < c < d and c = d/2
there is no 4 so d can only be 6. And if d is 6, then c is 3. now it looks like this: a < b < 3 < 6
the digits are from 0-9. So the possible combinations should be either 0 < 1 < 3 < 6 or 1 < 2 < 3 < 6.

[keen pasture]

#❓how-to-get-help

Open a new channel

[rough raptor]

can u be a little specific?

i dont's know the corresponding between a) and b）

[keen pasture]

Have you tried using a)? Because this is too short that I cannot give you a hint without telling you the solution

[keen pasture]

You know that z is not real. So a) applies which tells us that z conjugate is also a solution. Also the given factor theorem might be helpful

[rough raptor]

i got it , but how can i express "linear factor" in maths? is " k(x-α)" correct?

[keen pasture]

You can say P(x) = (x-a)Q(x)

[keen pasture]

Just one thing

A lot of people including myself missed this when they got this question in linear algebra 1

Factorization theorem only works in the same field. So if you factor out (x-a)(x-a conjugate) Q(x) will be a complex polynomial

Not sure if it is demanded to show that it is still a real polynomial, but we had to do it.

[rough raptor]

so , according to this question , i should set p(x) = q(x)(x-α)(x- α conjugate) to solve this question?

[keen pasture]

Yes

And then multiply the last two together

[rough raptor]

oh, i got it, thank u very much ,cause my first language is not English, so it's a little difficult for me to understand the question, thanks for you patience

[keen pasture]

You're welcome

[rough raptor]

.close

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[small raft]

((r + 1)/2)^2 - (((p - q))/2)^2 = p * r, r is a prime, so are p and q. For every r, is there a way to know if there is always a suitable p and q?

[weak field]

Use a²-b²

[lone heart]

@small raft Has your question been resolved?

[tawdry spire]

can I have help

[wise spruce]

(r + p + 1 - q)(r + q + 1 - p) = 4rp

Figure out how that 4 is split between the two brackets

[lone heart]

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[autumn swallow]

Hi, need some help, how did they simplify (1+sinx)/(1-sinx) to 1/(1-sinx)?

[hybrid heron]

1-sin^2 x = (1+sinx)(1-sinx)

[wise spruce]

I don’t think they saw the ^2

[autumn swallow]

Oh, forgot I can do that, thanks

[hybrid heron]

yeah

[autumn swallow]

[Forgot it's a fraction]

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[quartz cedar]

I need to find sin alpha and cos alpha. I’m not sure what to do next

Hmm, what about this?

Maybe it could be like this, but the numbers turn out to be huge, any other idea?

[obtuse fox]

Hello

[quartz cedar]

Hello

[obtuse fox]

How you doing

[quartz cedar]

I'm struggling for a long time to solve it, but I can't get a single idea

[obtuse fox]

Okay

I am solving your question wait

[quartz cedar]

Thanks for the help, of course :)

[obtuse fox]

Probably won't get it but worth a shot

[quartz cedar]

<@&286206848099549185>

[obtuse fox]

I am trying

BRO

NO MORE

I got the value of sin Alpha

but I can't no more

God damn

[quartz cedar]

How much is it?

[obtuse fox]

Let me send the solution

I will tell you something

Definitely

the value of Alpha

Is not the multiple of 30

[obtuse fox]

BRO

Whatttt

[quartz cedar]

This is the answer, I’m not sure how they got it

Are we missing something here or?

[quartz cedar]

Bro💀

[obtuse fox]

NOT EVEN DONE BRO

WHAT THE HELL

[quartz cedar]

It’s 17 not 14💀

[obtuse fox]

What

[quartz cedar]

Yes💀

[obtuse fox]

WHAT

BRO

IMPROVE YOUR HANDWRITING

BROOO

BRUHH

OOF

Ok

I am calm

[quartz cedar]

Ik it sucks I write fast

[obtuse fox]

Not at all angry that I wasted like 20 minutes of my time

Not at all

I could have been solving my paper

No not at all

Okay nvm

At least you got the steps though

Am I right?

[quartz cedar]

No

[obtuse fox]

WDYM

BRUH

you have destroyed my love for Trigonometry

jk

[quartz cedar]

I only got that cos alpha + sin alpha is = -17/13 and if you look at answer that’s correct

[obtuse fox]

Wait

[quartz cedar]

If we subtract them we got correct

[obtuse fox]

You didn't even send me the original question?

[quartz cedar]

I did

[obtuse fox]

Wait

Oh shit

The original question was 2 scrolls above

I derivated all that shit from 2 lines

BRuhhhh

[quartz cedar]

Damn :/

[obtuse fox]

bruhhhh

okay

just do What I did in the pictures

But put 17 instead of 14

[hot swallow]

close

[quartz cedar]

?

[hot swallow]

i got cos alpha = 5 root 2 /13

probably should have solved it on a paper neatly

[quartz cedar]

It’s this second if my handwriting is bad

[hot swallow]

i will tell you what i did

[quartz cedar]

Sure

[hot swallow]

since you have cos beta

you can get sin beta

draw a triangle

now since you want angles in alpha, convert the alpha + beta = pi/4

to your needs

thats what i did

maybe i messed up the calculation

[quartz cedar]

This problem is definitely wrong😭

[hot swallow]

beta being pi/2 to pi dosent affect sin

unless

[quartz cedar]

I mean the problem I have

[hot swallow]

yeah no

[hot swallow]

try googling it

[quartz cedar]

I’m not sure how to google it

[hot swallow]

google lens

translate

[quartz cedar]

I’ll just skip this problem

¯_(ツ)_/¯

.close

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[fathom badge]

<@&286206848099549185>

[storm ridge]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fathom badge]

i dont know where to begin

[storm ridge]

Try finding the rate of flow of water (units- m³/hr)

Which is basically the volume of water that flows per hour
Volume can again be found out using area*length
Also the speed is 15km/h, which means that the water travels a distance of 15km in 1hr

[lone heart]

@fathom badge Has your question been resolved?

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[fathom badge]

.close

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[hot swallow]

do you understand what the question means by "alternate question"?

[heady solstice]

unfortunately i don't

[hot swallow]

the question should be a bit more clear

it says he has to answer ALL the questions

this could mean, answering all 16 questions

or answering all 8 questions

is the answer 256?

[heady solstice]

maybe "alternate question" means there is another question when you can't answer the first question

[heady solstice]

i am not aware of the answer

[hot swallow]

kind of, basically theres two questions which you CAN attempt BUT you need to attempt only one

out of two questions, you attempt one

Thats 2 chooses 1

[heady solstice]

exactly what i mean

i think it's 64 since 8*8=64

[hot swallow]

where did you get 8?

[heady solstice]

there are 8 questions

needed to be solved*

[grand tiger]

is it 256

[heady solstice]

i am not aware what the ans is

[grand tiger]

bro see simple logic

a question has an alternative

which means it has 2 options to be attempted

there are 8 questions

so 2^8

dassit

[heady solstice]

really?

[hot swallow]

youre correct

[grand tiger]

wdym by really

[hot swallow]

but

for each question

you have a choice

[grand tiger]

yeah

so 2 options

[hot swallow]

you need to choose 1 out of 2

for 8 questions

@heady solstice try this

[grand tiger]

is the answer 256

[hot swallow]

ofc

[grand tiger]

cool lol

[heady solstice]

thanks guys

[heady solstice]

sure

btw those are really long videos

[hot swallow]

yes

maths isnt short

watch one video to realise the depth

[grand tiger]

u either learn it properly or 0

thats math for u

[heady solstice]

do i need to watch all those in that playlist?

[grand tiger]

are u a jee student

cuz i just saw

its for jee

[heady solstice]

no

i am not from indian.

[hot swallow]

need

no

[heady solstice]

india*

[hot swallow]

oh

[grand tiger]

then ignore

[grand tiger]

i thought too hes an indian

name

[hot swallow]

dosent matter if you understand hindi

[grand tiger]

lol

[hot swallow]

if you dont, then mb

[heady solstice]

i do understand hindi

[hot swallow]

then watch them

dont solve every question

[grand tiger]

oh then watch

yes

[heady solstice]

ok i will

[hot swallow]

adjust according to your syllabi

and close the channel if youre done

[grand tiger]

u study for the jee?

[heady solstice]

alright. i was practicing for olympiad

[grand tiger]

ohh

then u should do even more

lol

[heady solstice]

more in the sense?

[grand tiger]

like

do all of the videos

and practice tough questions

[heady solstice]

really appreciate all your time.

.close

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[vocal tapir]

when they say that integrals are an accumulation of a rate function, what do they mean?

what's a rate function?

[vocal tapir]

afaik integral is the accumulation of the sum of the surfaces for the integrated function(?) (best I can remember)

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[hot swallow]

kinda

[hot swallow]

@vocal tapirdid you understand?

[vocal tapir]

yeah

[hot swallow]

okay okay

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[solid creek]

I need a little help with logarithms

[solid creek]

My working out so far

Question:

$5000 is invested at 6% p.a. compounded annually.
Find how long it will take for the original investment to double in value.

working out

10000=5000*1.06^n
2=1.06^n
log10 2 = n log10 1.06

What do I do from here?

[lone heart]

@solid creek Has your question been resolved?

[sand canopy]

cant just do the log1.06 and caculate using caculator?

[solid creek]

Nah because I need to find the value of n

Either way what would I do at that point?

[grand tiger]

ohh

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[lean river]

hi

[gray isle]

please don't use these help channels to just say hello.

if you want to just chat then

[lone heart]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

@lean river Has your question been resolved?

[lean river]

ok

i don't have any question but i can do this

if i have question i will ask

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[raven turtle]

Two different answers for the discrimant before and after simplifying equation

[swift grail]

Yes. Discriminant isnt like roots

It wont always be the same however you write the equation

Wait actually should it be the same?

[raven turtle]

It should be the same

But I don’t know why it’s not

[swift grail]

No actually its just scaled by the constant ig

I was right the first time i think

Like discriminant of $x^2 - x - 1 = 0$ is $1 + 4 = 5$ while $2x^2 - 2x - 2 = 0$ its $4 + 16 = 20$ its just scaled by $2^2$

[ocean seal]

casework

[swift grail]

You cant look at the discriminant of an equation , i mean you can it will give you same info but the point is as you scale the equation it will get scaled by that number squared

You scaled it here by 10/3

So your discriminant got 100/9 times bigger

[raven turtle]

But they will always give the same info?

As in how many solution s

[swift grail]

Yes if its positive , real solution. If its 0 double , less than zero complex

Basically $D = b^2 - 4ac$ if you scale the equation you scale each coeficcient by $k$ therefore new discriminant is $(bk)^2 - 4(ak)(ck) = k^2(b^2 - 4ac) = k^2D$

[ocean seal]

casework

[raven turtle]

Ok kl I get it

Thank you

.close

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[cosmic quiver]

how can i find the value of this expression if the the interval of a is not given

[cosmic quiver]

i have to do abs(a-3)

but first of all i need the interval of a because of the 4th degree of radical

[lethal belfry]

Can you translate the question please

[cosmic quiver]

it just says the solve the expression

do you know what to do? @lethal belfry

[lethal belfry]

not too sure

but isn't the first term just a-3

and so on

[cosmic quiver]

no

the expression under radical cannot be negative

[lethal belfry]

yes, but any real number raised to the power of 4 is posiitve

[heady solstice]

isn't the ans 2a-2?

[wary pilot]

(a-3) + (2a - 1 )+ (2 - a)

[heady solstice]

exactly that's what i did

[forest marsh]

assuming that they are positive real numbers no ?

[wary pilot]

2a -3 -1 + 2

so 2a-2

doesnt matter i think

nvm

[heady solstice]

they are positive since it is raised to the power 4 also 2 and negative numbers don't have square root.

[forest marsh]

power of third doesn't matter for this case so ?

[wary pilot]

for the third root it has to be pos

[heady solstice]

yeah cause the variable is same for all. i.e "a"

[wary pilot]

soooo

ig answer is 2a-2?

a >= 0.5

[forest marsh]

negative numbers does have a third root, it's define

[wary pilot]

o

oh

-8 cube root is -2

[forest marsh]

so isin't it true for all real numbers that it's equal to 2a-2

[forest marsh]

ye

[wary pilot]

i forgor

[heady solstice]

how can you say that?

[forest marsh]

he solved the case of 2a-1 >= 0

[heady solstice]

ohh!

[wary pilot]

wait maybe is for all real numbers

does it matter that its negative

oh wait its gotta be more than 2

no

[heady solstice]

how can negative numbers have square root?

[wary pilot]

less than 2

not square root

cube root

[forest marsh]

they cannot have a square root it's undefined for x<0

[wary pilot]

i think its

2a-2 for a <= 2

[heady solstice]

i am getting confused.

[wary pilot]

me too

[heady solstice]

do we need to specify what are the possible values of a ?

[forest marsh]

yes you right

[wary pilot]

i think so

because if a is 3 for example

then its like undefined

[forest marsh]

a € ]-inf ; 2 ]

[wary pilot]

what

[heady solstice]

yes i got it this time.

[wary pilot]

op not here

[lone heart]

@cosmic quiver Has your question been resolved?

[lone heart]

@cosmic quiver Has your question been resolved?

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[alpine sable]

hello, just a simple question can we manipulate functions
like this
f(x) = 1/x
y = 1/x
x=1/y
and is it valid if I do like this:
f(x) = 1/x
x=1/f(x)

[woven harbor]

yes

and that is called the inverse of f(x)

because it undoes the function

[alpine sable]

okay sir thank you 🙏🏾

what if its 2/f(x) (i know its not an inverse function i am just asking for information)

is it still valid

.close

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[waxen turtle]

For A I think

[waxen turtle]

That I cant

Idk

It looks like it fluctuates weirdly as it gets more positive but idk

But maybe like yes fr becerra It looked like it suddenly started to get really positive and really negative idk 😭

[rich quiver]

There's only 2 variables

Solve for a and c

[waxen turtle]

i already did the other questions

But it says using the table

@rich quiver

<@&286206848099549185>

[swift grail]

Question?

[waxen turtle]

Question A

[swift grail]

What did you do?

[waxen turtle]

Idk if x=4 and -4 is enough to say it's end behavior

[swift grail]

Well basically you have enough info to calculate all coefficients

So ig yes

[waxen turtle]

it says using the table

like

Without the other stuff

Fr

The table

[haughty sun]

first use the point (0,9) to find the value of C

[swift grail]

Yeah

Using the table i see i can calculate all the coefficients

And thats it

[haughty sun]

then use the point (3,0) to find A

[swift grail]

You dont have to calculate them

[waxen turtle]

no like if u didn't have the given stuff

just with the table

[haughty sun]

just replace the x and y

[waxen turtle]

by looking at it

I already found all the stuff

[swift grail]

Well yes basically you have 4 points and 3rd degree polynomial

It is defined

[waxen turtle]

but like is looking at the table enough

[swift grail]

Yes

[waxen turtle]

how

wat reason

[swift grail]

4 points , 3rd degree polynomial

Thats the reason

[waxen turtle]

no just the table

like if u weren't given that info

u just had the table

[swift grail]

What is in the table?

[waxen turtle]

stuff

[swift grail]

What

Its table of points

[waxen turtle]

do u think this is good

also idk why the paper turns white in the picture it's baby blue irl 😭

[swift grail]

1. Idk why you said including leading term , im pretty sure its already included if you say you want to calculate all terms.

2. Dont start any reasoning/proof with "i mean"

[waxen turtle]

OK

My teacher is so chill tho😭

[waxen turtle]

cuz it was most important imo

anyways

The rest of it is good right

@swift grail

[swift grail]

The rest of A is good i mean its pretty much all of A. I didnt look at other Q's

[waxen turtle]

plz skim them

[swift grail]

Looks good

[waxen turtle]

Ty

.close

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[swift grail]

I would maybe just say in B with big steps

Going positive to negative in step of 1

I mean actually it isnt that important

Even if you had who know how small steps you wouldnt know

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[lapis spoke]

.

What is the value of L that is used in the equation at the start ?

[lapis spoke]

It's not even given here

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[lyric relic]

Suppose that a unicycle with a wheel of radius 9 inches is rolled 4 feet.
a. Through what radian measure of an angle has one spoke on this wheel traveled?
b. How many revolutions has the wheel made?

[lyric relic]

im gonna start off by saying I know this is probably really easy and I'm jsut not seeing it, but any help is greatly appriciated!

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[lyric relic]

<@&286206848099549185>

[cyan torrent]

Question

[lyric relic]

This is what I am trying to figure out

I just don't know where to start

[cyan torrent]

Okay

go on

[lyric relic]

So basically what I know is that I have the point of the tire in the first postion that touches the ground, and i have to figure out the radian measure of that arc length at the ending point.

[lyric relic]

I'm not sure wehre to go from there

.close

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[alpine sable]

Hello

[alpine sable]

I need help

[solemn juniper]

!da2a

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

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[unborn notch]

hi i have a quick question

[unborn notch]

in these examples when we're substituting, we also account for the new intervals

my question is, why did we not do the same for the intervals here

[alpine sable]

maybe because there was no substitution

[unborn notch]

are u not substituting ln(sinx) with a variable

then using the chain rule

[alpine sable]

i dont see any substitution in that image

[unborn notch]

how did we get to the answer then

if we're not substituting

[alpine sable]

idk thats the image you sent

[unborn notch]

????

[alpine sable]

you solved it no?

[unborn notch]

its an excersice the professor solved

so no i didnt

hence why im asking

[alpine sable]

I would do t=sinx

theres probably a way to solve it without substitution

but i dont think it matters that much

[royal meadow]

you substitute maybe ln(sin(x)) for u and then you could change the bounds sure

but then at the end you go back to x

with the original bounds

in the previous examples, they evaluate it with the bounds for y or the bounds for u or whatever the substitution was because there's y's and u's in the final expressions

but in the final expression for the third one, it's x in there

so you use the x bounds

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[unborn notch]

ah

ty

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[ebon meadow]

this is impossible question ngl

[placid zinc]

What's your strategy?

[ebon meadow]

i have no idea 💀

[lethal belfry]

Do you know how the derivative of say arctan(x) is derived?

use a similar strategy

[ebon meadow]

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[lethal belfry]

did you get it? Or do you need any further help?

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[quick bone]

Here, it tells you that the "average of the age variable is 31". If we ignore the percent on the bottom, the answer is 37. Now, if we take into account the percent on the bottom, the answer is 52 (I got 52 by using the equation in the image where x = 0.1)

But the questions tells you the "average of the age variable". I just want confirmation whether 52 is the right answer or 37. Thanks : )

[fallen verge]

it says to find the age

if youre not sure, its a good idea to try reading the question again

[quick bone]

I did but my answer for the age is either 52 or 37, but im not sure which one is correct

[fallen verge]

you have to use percentages

so it would be 52

imagine if i said there are two people aged 20 and one person aged 50, their average age would be 30, not 35

a similar thing is happening, ages with more people need to be considered with more weight

another way to think about it is having 100 people, would you only count one person who has a certain age?

[quick bone]

ok that makes sense, thanks for the help

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[abstract axle]

maybe im being stupid but idk how to find the common denominator here

or wtv restrictions are

wait nvm i figured out how but what are restrictions

[serene junco]

Remember we cannot divide by 0, division by 0 is undefined

In other words, your denominator cannot be equal to 0

[abstract axle]

oh

is that it

simpler than i thought yay

[serene junco]

Yeah, so do you see what x values you need to restrict?

so that your denominator never equals 0

[abstract axle]

3

[serene junco]

yep, that's all 👍

[abstract axle]

ohh okay

thank you

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[lapis spade]

is the laplace transform 0

or

1/s^2 - pi/s

[tacit arch]

Show your work

[lapis spade]

lemme take a photo

heres what i did

[tacit arch]

What's u(t)

[lapis spade]

heaviside step function

t-shifting theorem?

[tacit arch]

Your simplification is wrong

u(t) = 0 for t<0

But |t-pi| is not 0 for t<0

[lapis spade]

wait so hat would the simplification be?

[tacit arch]

Maybe u(-t) somewhere

[lapis spade]

would the piecewise function be okay tho?

just getting the laplace transform of the piecewise function is wrong?

as in wrong in the simplification of it

i tink i get it now

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[muted zinc]

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[muted zinc]

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[past relic]

#help/0

#help-0

How do I do this

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[fallen citrus]

In a Right Triangle, the shortest side is 20. The difference between the length of the 2 other sides are 2. How long is the longest side.

[fallen citrus]

i came to the conclusion that, a = 20, b= x and c = (x+2).
dont know if its right or where to go from here

[merry depot]

use pythagorean theorem

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[tough bloom]

I'm curious on how to set up the integrals here. I've completed only part a thus fra

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[tough bloom]

<@&286206848099549185>

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@tough bloom Has your question been resolved?

[tough bloom]

<@&286206848099549185>

[waxen flame]

What's your question?

[tough bloom]

Hi! I'm having trouble setting up the integral in part b. Is the image visible?

[waxen flame]

Yes.

What have you done so far?

[tough bloom]

I've done the work to find the points of intersection. I haven't figured out the height

for a shell method integral

[waxen flame]

Do you understand that you will need two integrals?

[tough bloom]

I do. So I believe they will be -1 to 2/3 and 2/3 to 4

is that correct?

[waxen flame]

How are you getting those intervals?

[tough bloom]

Given the points of intersection are (3, 2/3) and our lower bound is -1, I used the 2/3 as a midpoint (IE where the separation occurs) and then 2/3 to 4

probably wrong, but that was my process

[waxen flame]

Are you trying to use the Disc method?

[tough bloom]

I'm attempting to use shells

Could you walk me through this problem? I have some others in the problem set and a reference would be nice to see the process

[waxen flame]

https://www.geogebra.org/classic/hjbwem6m

Look at that graph first.

[tough bloom]

okay.. are the bounds from 0 to 0.5?

[waxen flame]

0 to 0.5 and 0.5 to 3

[tough bloom]

right

[waxen flame]

Does that give you a better idea of how to setup an integral using the cylindrical shell method?

[tough bloom]

I think so. Would the height of the first integral be abs(4-(-1)) ?

[waxen flame]

4 - (-1) will give you a positive value. The absolute value is unnecessary if you calculate the height correctly.

[tough bloom]

okay, and is radius defined by one of the functions - an integer? I think I remember that

[waxen flame]

Refresh the graph.

[tough bloom]

Okay I see the radius now

[waxen flame]

Do you understand how to setup the integral now?

[tough bloom]

Honestly no haha. I'm so tired rn. My issue is that I'm attempting to use the numerical values of r(x) and height, but that is clearly wrong.

[waxen flame]

Realize that the radius, r(x) = x, which is the variable you are integrating.

And the height, h(x), is calculatable using two integrals, one from x=0 to 0.5 and the other from x=0.5 to 3. The reason for the two different integrals is that the height is calculated differently in those two intervals.

[tough bloom]

okay gotcha. So radius = x and height is our function at different points?

[waxen flame]

Yes.

[tough bloom]

would it be of the form x*(2/x)

[waxen flame]

The cylindrical shell method uses the formula for circumference times the height.

2πrh

[tough bloom]

right

i was taking x to be r

and 2/x to be jh

h

with the assumption of 2pi as well

[waxen flame]

The height in the first interval is 4 - (-1).

[tough bloom]

right

first interval is

integral from 0 to 0.5

2pi(5x)dx?

[waxen flame]

Yes, and the height of the second interval is 2/x - (1 - 1/x)) which are the upper and lower bounds of the height.

[tough bloom]

Okay that makes sense. The computed value is about 22. The expected value is 23.56, do you know where that small discrepancy would arise from ?

and thank you

[waxen flame]

Not sure.

You left out the radius in the second integral.

[tough bloom]

Yep, gotcha. Thanks so much and sorry for the long process lol

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[sonic veldt]

factor fully: 4x^4 − 2x^3y − 3xy^3 − 9y^4

[chilly pike]

take out the greatest cmomon factor

from each term

[sonic veldt]

ive actually got up to 2x^2(2x-y) - 3y^3(x+3y)

nott sure what to do next tho

something about

difference square thing

@chilly pike

[chilly pike]

yeah one sc

sec

[sonic veldt]

okk

[gray isle]

consider grouping them in a different way

$\blue{4x^4 - 9y^4} \red{- 2x^3y - 3xy^3}$

[ocean seal]

ℝαμΩℕωⅤ

[sonic veldt]

(2x^2+3y^2)(2x^2-3y^2)-xy(2x^2+3y^2)

not sure what to do next

[chilly pike]

take out (2x^2+3y^2)

(2x^2+3y^2)[(2x^2+3y^2)-xy]

[sonic veldt]

ohh yeah

all of that is correct

apart from the -xy

waitt

no

the answer is (2x^2+3y^2)(2x-3y)(x+y)

[gray isle]

wait

you made a sign error

$\blue{(2x^2+3y^2)}(2x^2\red{-}3y^2)-xy\blue{(2x^2+3y^2)}$

[ocean seal]

ℝαμΩℕωⅤ

[sonic veldt]

ohh

so then it would become

(2x^2-3y^2)-xy

and then become

(2x^2-3y^2)(2x^2+3y^2)-xy

[gray isle]

missing ()

[sonic veldt]

wait

[gray isle]

and no

[sonic veldt]

without the powers?

[gray isle]

your expressions are in the wrong place

pq - pr
factoring out p gives
p(q-r)

here, your p = blue stuff
q = (2x^2-3y^2)
r = xy

[sonic veldt]

uhh

im actually rlly new to this

im not suree

[gray isle]

do you have any issue with

pq - pr
factoring out p gives
p(q-r)

[sonic veldt]

i get that but im not sure how to do it with this

[gray isle]

same idea

note that in
pq - pr

p is the common factor

what is the common factor in your expression?

[sonic veldt]

(2x^2+3y^2)

[gray isle]

yes

pq is the first term,
what's the first term in your expression?

[sonic veldt]

(2x^2+3y^2)(2x^2-3y^2)

[gray isle]

and what's being multiplied to your
p = (2x^2+3y^2)

[sonic veldt]

for the second one its -xy

[gray isle]

what is it for the first term

(2x^2+3y^2)(2x^2-3y^2)

[sonic veldt]

(2x^2-3y^2)

[gray isle]

yes

now put all that together

$$\underbrace{(2x^2+3y^2)}{p}\underbrace{(2x^2-3y^2)}{q} - \underbrace{xy}{r}\underbrace{(2x^2+3y^2)}{p}$$

[ocean seal]

ℝαμΩℕωⅤ

[sonic veldt]

if i pull out p the common factor, do i keep q and r as they are?

for example

(2x^2+3y^2)((2x^2-3y^2)-(xy))

[gray isle]

yes

[sonic veldt]

ohh okay

[gray isle]

q,r just represent stuff multiplied to the common factor, whatever they may be

doesn't really matter if they're monstrosities, don't let that intimidate you,
factorisation of stuff like that comes down to
the distributive property

anyway this chunk on the right

((2x^2-3y^2)-(xy))
can be simplified/factorised further

[sonic veldt]

sorry back

[sonic veldt]

okok

is it because it has more common factors

like x and y?

ohh

i think i get it now

[gray isle]

no, its a quadratic trinimial

[sonic veldt]

ohh

ohhh

[gray isle]

consider a simplified version:
would you be able to factorise something like this
2x^2 - x - 3
and if so, how?

[sonic veldt]

find the product of -3 and sum of -1

??

two numbers i mean

waitt

since its non-monic

the product of -6 and sum of -1?

[gray isle]

yeh

[sonic veldt]

(x+2)(2x-3)?

[gray isle]

you messed up somewhere

[sonic veldt]

o

[gray isle]

for non-monics, the pair of values you found there are used to split the middle term, the proceed with factorisation by grouping
you can't really use them directly in end result if that's what yuo tried doing

[sonic veldt]

ohh right

2x^2 + 2x -3x - 3

2x(x+1)-3(x+1)

(2x-3)(x+1)

[gray isle]

yes

2x^2 - xy - 3y^2
similar idea applies here
instead of
the product of -6 and sum of -1?
it'll be
product of -6y^2
and sum for -y

for 2y, -3y
only difference is the extra y

[sonic veldt]

2x^2 +2xy - 3xy - 3y^2?

[gray isle]

yeh

[sonic veldt]

2x(x+y)-3y(x+y)

(2x-3y)(x+y)

ohh wow no way

(2x^2+3y^2)(2x-3y)(x+y)?

[gray isle]

yeh

good work

[sonic veldt]

thank uu

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[small silo]

Hi

[small silo]

This partial derivative looks really difficult to me. Is there a reasonable method I might be missing?

I'm thinking I need to take the derivative of ln, then use the quotient rule to differentiate what's within ln, which is quite a lot of work.

[rustic coral]

Note this is a constant

Then recall $$\ln \left(\frac{a}{b} \right)=\ln(a)-\ln(b)$$

[ocean seal]

Civil Service Pigeon

[small silo]

Oh yes, that helps a lot, will give it a go

That worked, thanks 🙂

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[wary pilot]

that fraction part is the same as

1-1/256

[foggy pecan]

( 3 + 6 + ... + 30 ) + ( 2 + 1 + 1/2 + ... + 1/256)

[wary pilot]

idek

[foggy pecan]

first sum is arithmetic, while the other is geometric

yvw)

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[wary pilot]

@alpine sable close the post

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[waxen glacier]

Hello

[waxen glacier]

I need help

Lesson of sequences

[wary pilot]

k

post your problem

[waxen glacier]

1 min

Understand arabic?

[wary pilot]

no

[waxen glacier]

Exercise is in Arabic 🙂💔

[wary pilot]

just post a pic

ill translate

[waxen glacier]

Ok

I want to solve it because it will decide whether I fail or pass 🫤💔

[wary pilot]

oh wow

google cant even translate it

f sorry

[waxen glacier]

Sorry if you can't understand it

Vn A geometric sequence with a field N and positive terms

V2 + v3 = 20/9
V1 × v3 - V2 = 4/9

Find v2 than q (Basis) and V0

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[vapid steppe]

how did they get the answer for 8

[waxen glacier]

No

[fervent kestrel]

,rccw

[vapid steppe]

idk how they picked between C and D

[fervent kestrel]

A. The velocity is not always uniform like that so it can be hard to show that at 3/4 maximum height it's at 1/4 its velocity

B. Potential energy is increasing since the object is slowing down and is reaching a higher height

C. Assuming K is kinetic, it should not necessarily be 3/4 at that point.

D. U is I think potential energy and at that point yes 3/4 of the energy should be potential energy

[vapid steppe]

for option B so you take the derivative of potential energy to show that it is increasing

[fervent kestrel]

I mean yeah thats one way of going about it

[vapid steppe]

u take it with respect to time right

[fervent kestrel]

Yes

[lone heart]

@vapid steppe Has your question been resolved?

[lone heart]

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[lofty heath]

,rotate

[uneven palm]

nvm unpin mine

[lofty heath]

.close

[lone heart]

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Available help channel!

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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!

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[rigid shale]

How do I even

[rigid shale]

its in C btw

Idunno how to start

[alpine sable]

what does the bar above the second z represent

[steep girder]

Complex conjugate

[swift grail]

You can always factor

[summer dirge]

it’s the complex conjugate

[summer dirge]

Try writing z as a+bi

[swift grail]

Make your problem a little easier by doing the problem in cases

[slender gull]

Find |z| then multiply by z^2

[swift grail]

$(z^2 - 4\overline{z})(z^2 + 4\overline{z}) = 0$

[ocean seal]

casework

[swift grail]

You can turn it in to 2 easier problems

[rigid shale]

a^2 - b^2 = (a-b)(a+b)

you used this right?

[swift grail]

Now its at most quadratic if you plug z = a + bi and ż = a - bi

[swift grail]

Yes

[swift grail]

Im not saying you should do it but you could do it

[steep girder]

Good idea imo

[swift grail]

Yea im looking if there is anything easier

I dont think there is

I mean wait a sec

[rigid shale]

oh yeah we can separate

[swift grail]

Write $z = r\cdot e^{i\theta}$

[ocean seal]

casework

[swift grail]

That seems easier

[rigid shale]

seems scaryyyy

[swift grail]

How about if we write it like $z = r \angle \theta$

[ocean seal]

casework

[swift grail]

Less scary?

[rigid shale]

[grim wedge]

looks less scary

[rigid shale]

cant we just go with this?

and then do the other one?

[swift grail]

No you solve this first

Where did the b^2 go

[grim wedge]

https://tenor.com/view/coyskis-chinese-chinesenewyear-newyear-phillipogi-gif-27444359

[rigid shale]

oops

[swift grail]

I mean only problem i have with that is you have to solve system of equations

While in other one i think you solve for r and angle seperately

Which is a little better

[grim wedge]

umm.. your welcome guys?

[swift grail]

I guesss

[rigid shale]

I never used it before

[sudden igloo]

Euler's form

[swift grail]

Like for example
$z^2 = 4\overline{z}$ we can write it like $r^2 \angle 2\theta = 4r \angle -\theta$ or

$r(r\angle 2\theta - 4\angle -\theta) = 0$

[ocean seal]

casework

[rigid shale]

maybe its not a part of my class?

bcs I have never seen this thing before...

[swift grail]

Yeah but this will make your life alot easier

Because as you can see from that you get few solutions one is obvious $z = 0$ and you have $r\angle 3\theta = 4\angle 0$

[ocean seal]

casework

[swift grail]

Now you just make angles equal and make absolute values equal

But ofc for angles you can have $3\theta = 2\pi k$

[ocean seal]

casework

[swift grail]

Yea you are probably confused. So any questions?

This is called polar form btw

We write the absolute value of a complex number and then its angle

[rigid shale]

haha many
how did you get from the first form to the second one (with the angles)?

[swift grail]

Ok so you know when you multiply complex numbers the angles add?

So if $z = r\angle \theta $ then $z^2 = r^2\angle 2\theta$ or if you want its basically $z = re^{i\theta}$ so when you square it the exponent doubles

[ocean seal]

casework

[swift grail]

And conjugate of z is just has the negative angle thats pretty self explanatory if youve seen them in the complex plane

[rigid shale]

ahhhh
I really appreciate the help but this may be a little to advanced for me...
I think Ill just stick to the first (inefficient) method

[swift grail]

Yeah sure

[rigid shale]

sry for wasting you time

[swift grail]

Basically you know how to do it the first method?

Imaginaty part is zero and Real part is zero. That gives 2 equations you just have to solve it.

It should have 4 solutions

Actually ....

[rigid shale]

ok this is for the first half

[swift grail]

Something seems wrong

[swift grail]

Look at your $(a + bi)^2$

[ocean seal]

casework

[swift grail]

Thats not what it should be

[rigid shale]

ahhh I see

let me fix it and resend

[swift grail]

Sttill 1 mistake while squaring

[rigid shale]

[swift grail]

And 1 mistake in the distribution

If you are unsure rather send only expanded and then solve after you get conformation

[rigid shale]

what exactly is wrong in this part?

[swift grail]

b²

Coefficient

[rigid shale]

(bi)^2?

but then you open it and i^2 = 1

[swift grail]

Is i² = 1

[rigid shale]

yes?

I hope?

[swift grail]

What is i?

[rigid shale]

ohhhhhhhhhhhh

[little patrol]

Yeah

[rigid shale]

ok I will solve it now

hopefully in a correct way

wait this has no soultions

maybe the second half would have one

ok final answer there is a single soultion which is b=0,a=2

im gonna close the room now

thanks for the help @swift grail

.close

[lone heart]

Channel closed

Closed by @rigid shale

Use .reopen if this was a mistake.

[swift grail]

Missing few sols

[rigid shale]

.reopen

[lone heart]

✅

[swift grail]

Like (0 , 0) , (4 , 0) trivial solutions

Let me see where you made a mistake

[rigid shale]

I thought that both equations need to be true for a soultion to form

like an a and b that work for both of these

[swift grail]

When you have $ab = 0$

[ocean seal]

casework

[swift grail]

At least one has to be 0

Not all

[rigid shale]

yeah I know and I checked each one of these independtly

[swift grail]

So the thing you had
$2b(a + 2) = 0$ you have $2$ cases

[ocean seal]

casework

[swift grail]

$b = 0$ or $a = - 2$

[ocean seal]

casework

[swift grail]

You should get 2 sols for both cases

[sudden igloo]

U have considered B=0 and a=-2 whereas it is b=0 or a=-2

[rigid shale]

ok