math-help

[silver pier]

3^(1+1+1)

and 9 = 3^2

so 3x9 = 3^(2+1)

[ashen wind]

i mean in the 3x3^2(3n+1)

[silver pier]

oh

thats the ques

[ashen wind]

wait

i get it

i get it

i know the answer

btw

thank you for ur help @silver pier & @ember kernel

thank you so much

u guys make my day better

i am like thinking this question for half an hour

[real onyx]

hey guys hi

greetings folks

[cyan night]

try setting a = 2^x b=3^y then u get a+b=59; 256a-b^3 = 13

[cyan night]

what

[civic fern]

Step by step solution anyone?

[gentle axle]

Anyone got any resources to help me understand this question?

[civic fern]

https://math.stackexchange.com/questions/1165782/find-the-fractional-representation-p-q

[civic fern]

yep see above

[gentle axle]

👍

[civic fern]

👍

[gentle axle]

Anyone have any resources for understanding how to simplify a DNF

[sick cave]

Just use the simplification table dude stop being lazy this is EASY 😐😐😐

[gentle axle]

Im sorry i genuinely do not know

Im asking for some sort of lecture video because my lecturer has a heavy french accent and i cant understand a word of it

[sick cave]

Braaaah

What kind of university is it

Well let me send you something

[gentle axle]

Its just your regular UK university with terrible lecturers lol

[sick cave]

Look dude I have some good notes the thing is it's in Greek. 😐

[gentle axle]

Ahh understandable dont worry about translating it all just for my sake

Im going to try pestering my french friends to help me understand the lecture lol

[sick cave]

Keep looking never give up brotherman

[gentle axle]

we're all gonna make it

[sick cave]

may Zyzz keep you safe

[cinder yacht]

wth XD

[hollow blade]

yo not sure if you got your french friends to help but i just finished an exam i have some notes that might help shed some light on the matter

And when it says to turn into a DNF this is some examples of what that will look like (variable with a line over it means the same as NOT variable)

EDIT: removed laws because I think it just means convert into DNF clauses (pic above)

[fiery lintel]

Does anyone know any free resources for the ACT math section?

[obsidian brook]

IM BACK WITH ANOTHER PROBLEM...

So basically I have this matrix I need to find x and y. I used simultaneous eq but in the end I can only find that the solution could not satisfy the whole matrix but only to certain eq in the matrix. So is the answer suppose to be a lot of solutions?

As you can see (sorry for the messy work), they have different solutions to satisfy different eq I used.

[dusty saffron]

Heyy I think you made a mistake in writing the second column of solution

[obsidian brook]

second column?

[dusty saffron]

I solved it and it checks out

x=5,y=-1

[obsidian brook]

oh

wait...which second column? the whole thing or which row?

[dusty saffron]

Let me send you the solution

[obsidian brook]

Cuz I'm really careless at expanding.... 😅

[obsidian brook]

sure

[obsidian brook]

I just realised I copied the second matrix wrong...

[dusty saffron]

Ooofers

You got it now?

[obsidian brook]

yeah

[dusty saffron]

Alrighty 👍

[obsidian brook]

I copied the question worng

[dusty saffron]

Haha

[obsidian brook]

thanks man!

WHYYY MATHS....I love you but why don't you love me back?

[dusty saffron]

Anytime bud

[dusty saffron]

It will ;) be patient

[obsidian brook]

https://tenor.com/view/bruce-lee-bow-master-smile-gif-12365468

Thanks again comrade!

[austere rover]

how do i compute the correlation matrix for M = ( 2.67 -3.33
-3,33 8.67) ?

[obsidian brook]

what does this little 10 on the top right mean? XD

[blissful hedge]

I think it multiplies 10 times it self :>

[obsidian brook]

so you mean all the entries I need to multiply it ten times as in 2^10, 0^10?

[blissful hedge]

No you multiplies the matrix 10 times

I do it by find the formula

Like do it 3 times then find general formula

[ember kernel]

In terms of matrices, A² = AA

[obsidian brook]

uh huh

[ember kernel]

So A^10 = AAAA...AA (10 times total)

[blissful hedge]

I study in vietnam and this is our solution :>

[blissful hedge]

absolutely

[obsidian brook]

yoooo what is my lecturer telling me to do? XD

so I need to like rewrite the whole thing 10 times?

XD

[ember kernel]

Yep

[blissful hedge]

Noooooo

[ember kernel]

Yep yep

You do

[obsidian brook]

I don't know whether this is correct or just plain sarcasm

[ember kernel]

But you'll soon enough find a pattern that makes the calculations much faster

Trust me, start by computing A³

[blissful hedge]

Thats how i solve it :>

This is an example :>

[obsidian brook]

yea

it does makes sense

[blissful hedge]

Have you done

[obsidian brook]

nope

I'm still confused af

I'm just gonna do it like how you do it

[civic fern]

I love ur to do lists man lol they r too cute and productive...i read them

[blissful hedge]

Oh thanks I just started to do it yesterday and absolutely fail :>

[ember kernel]

Do you know what matrix multiplication is ?

[obsidian brook]

Yea I know that...

[ember kernel]

Well

[obsidian brook]

so I have to do that 10 times in a row

[ember kernel]

Yes

[obsidian brook]

oh my

[ember kernel]

Nonono

Just do it

[dusty saffron]

Ayyo

[ember kernel]

I told you, you'll see a pattern

[dusty saffron]

Can't you make it identity matrix?

[ember kernel]

And won't have to do it 10 times

[obsidian brook]

Alright...Imma just rush in

[obsidian brook]

wah?

[ember kernel]

Start off by computing A, then A², then A³ = A²A, then compare

[civic fern]

lmao ok 💀

[dusty saffron]

I'll try to check a bit cuz I swear it was lot easier that way

[civic fern]

why do you give me the smartest kid in the school vibe 😭 I mean in +ve wayy...

[dusty saffron]

Do u know about row transformation?

[obsidian brook]

Nope

no idea

[dusty saffron]

Damn it

It would've been a 2 minute question that way

You know about identity matrix?

[blissful hedge]

I think talk would be easier to understand

[dusty saffron]

What

[blissful hedge]

Can we talk in the study room TvT

[dusty saffron]

Me?

[ember kernel]

I'm an engineer undergrad so I went through all this stuff and those struggles too

But thanks, I take that as a compliment !

[dusty saffron]

You know about row transformations ?

[civic fern]

woww haha<3

[ember kernel]

Of course I do, I know they're valid for solving systems, but I'm not so sure you can apply them for matrix multiplication

[dusty saffron]

You can then it's easier to solve the exponent I mean you won't have to use it in multiplication

Cuz you can transform it in identity matrix and then it's so easy

[dusty saffron]

I think that works?

[obsidian brook]

I just realised that the matrix is symmetrical

[dusty saffron]

That's what I'm telling u

Trying to tell I mean

[obsidian brook]

ok

so how am I going to solve it?

XD

[dusty saffron]

Hold up

[obsidian brook]

I lazed around during my first semester and I hit rock bottom...now tryna make things better XD

[blissful hedge]

Me toooooo

[dusty saffron]

I am sending you solution

Just a minute

[obsidian brook]

sadge

[ember kernel]

Before you do

@obsidian brook have you solved it yet ?

[dusty saffron]

Oh yeah that's important

[obsidian brook]

not yet...still in the middle of solving

[ember kernel]

What are you computing right now ?

[obsidian brook]

A^2

[dusty saffron]

I have solved it

[ember kernel]

Ok, afterwards just multiply A² by A to get A³, by then you'll be able to spot the pattern I've talked about

[dusty saffron]

Umm...

[obsidian brook]

send em here

I'll try to do both solutions

cuz i have 3 more days before the due date so it's fine

[ember kernel]

It's important you understand it by yourself

[obsidian brook]

exactly...i'm doing a trial and error kind of thing

[dusty saffron]

Sorry my bad

Just wrote exponent wrong

[ember kernel]

Yeah

[obsidian brook]

why? XD

[dusty saffron]

Replace 200 for 32×32

And that's it

[dusty saffron]

Is that right then?

[ember kernel]

No, I was just confirming there was a mistake with the 2^10

[obsidian brook]

ohhh

[dusty saffron]

Just make it 2^10 instead of 200

[blissful hedge]

Did row transformation make change to the value of the matrix ??

[dusty saffron]

Nope

[obsidian brook]

wait you can change rows in a matrix? whaa???!

[dusty saffron]

Any 2 rows or colums can be interchanged

Not row with column tho

There are some other too

[dusty saffron]

Not really change but interchange

[obsidian brook]

and it doesn't affect the answer?

wow

[dusty saffron]

Haha

You got it now?

[dusty saffron]

There are some other transformations if you would like me to send

[obsidian brook]

nah I'm good

Imma just do both your method and @ember kernel

[dusty saffron]

Alrighty you got this question?

Ohh okayy

[obsidian brook]

I guess so.... XD

I'll update on what my lecturer will answer tho

[dusty saffron]

That method might be too complicated tho

[dusty saffron]

Sure

[gritty cloud]

Guys any help to find A,B values

[sharp ferry]

i assume it is given that f(x) is continuous at x=0?

[gritty cloud]

y

[sharp ferry]

because only then can you solve this question

usually its asked in this fashion

[gritty cloud]

yeah yeah my camerashot is bad

[sharp ferry]

nah so basically if f(x) is continuous at 0

then

the limit x-->0+ 2sinx/x should be equal to a

[gritty cloud]

ok i got it then what ?

what can i do with 2sinx/x

[sharp ferry]

do you know the standard limit formula of x-->0 sinx/x?

it can be derived but its almost always taught as a formula to remember for later

[sharp ferry]

basically break it down to 2* lim x-->0- sinx/x

and lim x-->0- sinx/x =1

here is a geometric proof for it @gritty cloud

but i dont think you would need to prove this while solving this question you can directly use the result

[gritty cloud]

Thank you very much 🌹🌹

[drifting siren]

(My sisters workbook) how can I solve E?

[rocky shale]

does anyone know what method / technique to use for first part of the question?? - any help appreciated thx

[left knoll]

Can someone help me with this integration?

[polar heron]

maybe try substituting z=y-x

[supple island]

this is 2 integrals one in dy and the other in dx

[dreamy oasis]

Can anyone help me? Question's translate: what is the value of the integral?

[quartz epoch]

guise any one know how i can solve this?

i need hilpe

help*

[supple island]

ok so first of all we can express this as x²/(x²-2x+2), we can't do partial fraction decomposition here so we'll do a little trick, we want 2x-2 to appear on the numerator, because that's the denominator derivative, so and that integral is easy cuz it's just ln, so we want our expression to be something like (2x-2)/(x²-2x+2)+aand we want this to be equal to x²/(x²-2x+2), if we sum a we'll find out that a=1

from there it's trivial

[dreamy oasis]

True

[supple island]

i can also write this down if you prefer @dreamy oasis

[dreamy oasis]

Could you please write, it's hard for me to understand @supple island

[supple island]

@dreamy oasis

[dreamy oasis]

@supple island thank you so much

[supple island]

np

[near gate]

the result should have been 1 a=?

[blissful hedge]

you mean a^2 - 2a = 1 find a??

[near gate]

yyes

[blissful hedge]

its 1+sqrt(2) and 1-sqrt(2)

Sqrt is square root

[thin portal]

Hey guys does anyone know matlab?

[sick aurora]

Hey guys, I'm a beginner in math, can someone solve this question and send the solution for me to understand

[dusty saffron]

Heyy do u know the answer of the question?

I have solved it just gotta make sure I got it right

[dusty saffron]

Matlab?

[sick aurora]

heyy

the

question wants to know if the equalities are true

[dusty saffron]

What's the equality

[sick aurora]

is letter D

[dusty saffron]

I got it

[sick aurora]

can you send a picture of the resolution?

[dusty saffron]

Yess

[sick aurora]

oh thank you

[dusty saffron]

Hopefully you understand my solution haha

[sick aurora]

hahaha

xD

[sick aurora]

thanks

[dusty saffron]

Did you understand?...

[dusty saffron]

Feel free to ask anything if you didn't get it

[sick aurora]

ok bro

im analyszing

[dusty saffron]

Hmm alrighty tell me if you got it or not when you are done

[sick aurora]

ok bro

[tacit frost]

hey! im doing linear algebra for clumnspaces and nullspaces

does anyone know how?

[polar heron]

I have some experience with matlab, what specific question do you have?

[thin portal]

Basically its a system of couples second order odes that I wanna solve

[polar heron]

ok, so what help you need in that?

[thin portal]

I want to use runge kutta 4th order and adams bashforth 4 th order to solve the system and find x1 and x2. I already have my script for rk and ab but as for the main script im not sure how I should be doing it since this has 4 initial conditions

[knotty pecan]

for no. 2, should I simplify it first before finding the derivative?

[delicate cave]

try both, it isn't that hard, you'll learn something either ways, and figure the better method yourself 😅

[knotty pecan]

is this correct?

[ember kernel]

3rd line, denominator should be (x-1)(x+1)

Quick reminder : (a²-b²) = (a+b)(a-b)

4th line, somehow, is fine

(after you've changed the + of the 3rd line to a *)

[knotty pecan]

okay got it thanks!

[cyan night]

= sin^2a/cosa(sina-cosa) + cos^2a/sina(cosa-sina)
= sin^2a/cosa(sina-cosa) - cos^2a/sina(sina-cosa) (i did this to get the common sina-cosa in the denominator)
= sin^3a/sinacosa(sina-cosa) - cos^3a/sinacosa(sina-cosa)
= (sin^3a-cos^3a)/sinacosa(sina-cosa)
= (sina-cosa)(sina^2 + sinacosa + cos^2a)/sinacosa(sina-cosa) (applying a^3 - b^3 = (a-b)(a^2+ab+b^2)
cancelling sina - cosa on both numerator and denominator and applying sin^2a+cos^2a = 1
<=> (sinacosa + 1)/sinacosa
= 1 + 1/sinacosa
= seca* coseca + 1

hencegg

@flint sonnet

g

i can write it down on paper for you if its hard to read

[flint sonnet]

I got it now thanks a lot

[cyan night]

np

[tough geyser]

help T-T

[grand gust]

do you know the figure?

[grand gust]

this is the figure.. try it by using area of the triangle abc

[grand gust]

you can also do this by repeated use of Pythagoras theorem........ do whatever suits you best (this method might be slightly lengthy).

[tough geyser]

is the common chord being bisected by BC?

[grand gust]

yes

[tough geyser]

Thanks, that was what i was missing out

btw easier method would be to assume theta and 90-theta in triangle ABC

[cinder yacht]

u can solve this without any understanding of the problem

2 ways for that

way 1 : r1 and r2 are supposed to play symmetric roles. the only answer where r1 and r2 are treated similarly is answer (A)

way 2 : the answer is supposed to be a distance (in meters let's say). the unit for answers B, C, and D is in meter^2 if u think abt it (cuz it's meter * meter^2 / sqrt(meter^2)). The unit for answer A is in meter. so only the answer A can be true

these are possible tips when u have multiple choices

like in an exam u can answer this in 10 seconds if u use tips like this, without really using geometry

[minor vapor]

Hi can anyone help me solve part a ?

and show me the full working out please/

thank you

[tough geyser]

whoa big brain

damn ill try this if im unable to get the answer, thanks a lot

[ember kernel]

• It is given to you that r = 10 (because v(0) = 10)
• Reminder : a parabola has it minimum/maximum value at t = -b/2a (with b = q and p = a in this example). That means 3 = -q/2p, also written q = -6p (since the parabola has a minimum, you know that p has to be positive, which means q is negative)
• So you've got the expression v(t) = pt² + qt + r = pt² - 6pt + 10. Use the fact that v(2) = 4p - 12p + 10 = 5 to get the value of p. Therefore, you'll be able to use the value of q (reminder : q = -6p). Boom, you've got the full equation for v

Then, subquestion (a) just becomes easy as it's only computing the derivative of a polnomial, and then plugging t = 4

I wrote that quite quickly without thinking twice so if I made any mistake please point them out, thanks ^^

[minor vapor]

@ember kernel yep it is correct thank you very much

i still dont get what t = -b / 2a means

what exactly is that formula

i did see it once but didnt think it was that important to use it

[supple island]

it tells you the t of the minimum/maximum value of a parabula at²+bt+c, if you studied derivatives you should understand why is that

[minor vapor]

if u do dy/dx it would give u the gradient of that specifc point so in this case t = 3 right?

oh wait i get it now

thank you for your help anyway

@ember kernel

@supple island

[misty nova]

r?

[copper mango]

I got 35 is that correct?

[minor vapor]

for the question i put up ??

[copper mango]

yeah part a)

[minor vapor]

if so then thats not correct

[copper mango]

shit

[minor vapor]

i got the right answer using the method

well the formula

the part after was ez

[copper mango]

I just did Gauß algorithm

[minor vapor]

whats that ?

is that mart of applied maths mechanics

part*

[copper mango]

a way to solve linear equation systems

[minor vapor]

it isnt linear

tho

[copper mango]

no its not

[minor vapor]

the velocity time graph isnt

[copper mango]

but we know P is at its lowest at 3 right? so that would mean the derivative is = 0 at that point or 2pt +q = 0 with t=3 that is 6p+q=0 for our first equation further we know, that at t=0 v=10 so r must be 10 the last part is v=5 when t=2 so 4p+2q+10=5 or 4p+2q=-5. Now we have 2 Linear equations and can solve the system with papa Gauß

i could have done a mistake tho

[minor vapor]

q = -6p

thats where u made the mistake

u then solve for p

and there go

u get q

[copper mango]

thats the same as 6p+q=0

what did you get for p and q?

i got p=5/8 and q=15/4

[minor vapor]

• 15/4

its negative

[copper mango]

fuck now i see xD

[minor vapor]

i acc like your method. its cool

[copper mango]

i did a mistake when transferring over the 15/2

yeah in germany we use it all the time for linear equation systems for example in vectorgeometry when trying to find out intersection of lines and spans i believ

Gauß is a funny looking guy

[minor vapor]

really lmao

show me

[minor vapor]

how old are u ?

[copper mango]

19 im in my last year of highschool

[minor vapor]

he looks liek a painter really

[minor vapor]

oh im 17

[copper mango]

where are you from?

[minor vapor]

england

i am in gymnasium

[copper mango]

yeah same

[minor vapor]

in school

i learned german for 4 years

so i picked up a few terms lol

[copper mango]

nice Junge haha

[minor vapor]

haha

we should really talk on a different chat

[misty nova]

?????

[supple island]

you know AK,KB and KD? you also know that the angle AKD=90°?

[misty nova]

yes

[supple island]

ok we can do this

[misty nova]

kc=16 kb=8

[misty nova]

I've been trying to do it for 2 hours

[supple island]

ok so since AKD=90° it means that all the angles in that intersection are=90°

[misty nova]

yes

[supple island]

now we can find AC with properties of a right triangle

[misty nova]

pythagoras?

[supple island]

then we find the angle KAC, which is also the same of CAB, then we find CB with pythagoras again, for the properties of a circle we know that the angle COB=2CAB

[supple island]

yes

[misty nova]

√272

4√ 17

[supple island]

i'm not looking into numbers

just giving you a way to solve it

[misty nova]

okay

[supple island]

since we have the angle COB and CB and we also know that OB=OC=r we can find r

[misty nova]

yes

oh i understand everything thank you

[supple island]

np

[void pewter]

I could use some help with standard deviation

[left knoll]

in what sense

[void pewter]

Ima just send a ss

[left knoll]

k

[void pewter]

no idea where to start

[left knoll]

ok

do u know standard normal distribution

pdf and cdf

all of that?

i think the topic is called continuous random variable or something

@void pewter

[void pewter]

I know how to get onto that with my graphing calculator yeah

[left knoll]

ok

[void pewter]

idk what to enter in

[left knoll]

idk how to use the calculator

but i can tell u how to do it

first u have to find z score

which is (x-µ)/sigma

as in little sigma

@void pewter

understand?

[void pewter]

what is the x and what is the everything lol

[left knoll]

x is individual data value

µ (pronounced myu) is the expected value

and the little sigma is ur sd

u need to know all of this to do the question

and they need to give u a table for z values

[void pewter]

from the question I sent what do yoi plug into where

[left knoll]

so in this case

i think ur x is 2

so it would be 2 -3.3

[void pewter]

(2.2 - 0.8)/sigma?

[left knoll]

divide by 0.8

so (2-3.3)/0.8

@void pewter

then you need to use the table

cause u cant do these questions with the z table

u there @void pewter

[void pewter]

yed yes trying to understand

[left knoll]

ok ok

there is a formula

that finds something called the z score

u then look at a table called the z table to find the corresponding probability

[void pewter]

omg

I got it

no

I lied

[left knoll]

ok what did u do

nvm then lol

ok ok what calculator do u have

[void pewter]

used the calculator thing I was taught

TI-84 plus

[left knoll]

u shouldnt just use the calculator, u should understand what is happeing

[void pewter]

teacher said just to use it, once i finish this test I am doooone with this

[left knoll]

https://www.youtube.com/watch?v=eU3XLr8BlwI

watch this

it will find the z score

can i just tell u the answer acc?

@void pewter

[void pewter]

I guess sure

[left knoll]

its the last one

i think by my calculations

[void pewter]

oh hell I got 0.061

yeah you were right

[left knoll]

ok can i ask how?

[left knoll]

how do u know im right?

[void pewter]

I did it by normalcdf then entering 2 as low and 3.3 as high and 0.8 as standard deviation

[left knoll]

and u got the same answer

?

if so then yes it is correct

[void pewter]

the u thing is supposed to be what?

its 0 for me

[left knoll]

thats the mean

[void pewter]

how do I find that in this problem?

[left knoll]

its given

it says

3.3 is the mean

[void pewter]

oOoo

[left knoll]

u dont really have to do anything for this question

[copper mango]

What did you get?

0.052063?

[left knoll]

Dad???!!!!!!!!!

[copper mango]

xD

[left knoll]

yea thats the last one is it not

or am i blind

[void pewter]

I got 0.061 which was wrong

[left knoll]

FATHER

[void pewter]

you were right

[left knoll]

MY EQUAL

WE FINALLY MEET

I CANNOT BELIEVE IT

[void pewter]

I just wanna like figure out how lol

[copper mango]

yeah normcdf(0,2,3.3,0.8)

[void pewter]

oh my lord

[left knoll]

u....U TOOK MY NAME!!!!!!!!!

[void pewter]

oh my magic

I think the other elon made this make way more sense ngl

[left knoll]

I HAD TO BECOME YOUR MUSK INTEAD OF U

[left knoll]

sorry my bad lmao

i dont use the calculator

[void pewter]

it's fine lol

[left knoll]

cause i can do it on paper

my bad

[copper mango]

i believe normcdf numerically integrates from 0 to 2 let me check

[left knoll]

@copper mango father have you checked?

[copper mango]

im trying

[void pewter]

I did a few similar problems and what ya gave me works

[left knoll]

oki

[copper mango]

yes it does

I believe when we learned about normal distribution, that it can only be numerically integrated

if you calculate Integral from 0 to 2 of the normal distribution with mean of 3.3 and standard deviation of 0.8 you will get 0.052063

[obsidian brook]

@dusty saffron we just learned about this in uni... 😅

[dusty saffron]

Ohh wow haha

Well now you know

[obsidian brook]

yea

we're really late at learning about this

welp, it is what it is

[copper mango]

for a I got 22%

rounded up

exact would be 21.8065 percent i think

b should be 152

[delicate cave]

yup, both are correct!

[sharp ferry]

if they have asked by what percentage the intensity will be reduced then shouldnt it be

78%

(1-(0.97)^50)*100 no?

97% light passes through so 3% intensity reduced so for a part 22% light passes through ((0.97)^50)*100 therefore 78% reduced right

[left knoll]

father may i ask how

[wet gorge]

Yes my son ofc u can ask your daddy

[copper mango]

I just modeled the thing with an exponential funtion 0.97^x

[left knoll]

how would u do it using series

[copper mango]

what do you mean?

[left knoll]

well this is from a series and sequnces chapter

if i dont reply its ebcause i fell asleep

[copper mango]

im working on it gimme a sec

isnt an exponential function kind of a series?

you keep multiplying and multiplying

[left knoll]

||elon-musk chit chat||

[supple island]

i guess you can see this as a sequence an=(97/100)^n

no series involved here

[ember kernel]

I think he wrote series but meant sequence

[fringe timber]

Help please

[ember kernel]

Multiply both sides by sinx + cosx

done

[modest compass]

this is a proof no?

[urban pond]

pls help

[oblique current]

The first one be
Y=mx+b = 2=3*-7+b and then continue and the other one is the same

Ig it is so

The point is (-7,2) so x = -7 and y = 2

[urban pond]

pls help

[left knoll]

Guys can someone help me out with these two questions?

[supple island]

you have that cost=fee+n*additional cost, we rename the fee a and the additional cost x, you have C=a+nx, you know that 380=a+10x and 440=a+15x

2 equations and 2 variables

you should be able to do that

[ember kernel]

He sent nothing but an equation, showing how to proof that both sides are equal is the most I can do with so little information

[hearty sentinel]

Yo guys I have a discord server for only math and physics lovers.You can get help there or be a helper..if you want to join here's the link Vup576S7

[echo temple]

anyone know how do i solve this second order differential equation?

[left knoll]

Can you guys help me out here

I don’t understand part d

Where does the 21 in the working come from

Any help will be greatly appreciated

[supple island]

it's asking you what's the probability of the doctor not showing up when a patient will turn up

[waxen storm]

Could someome pls give me the step by step solution to this one?

[ember kernel]

Can't solve it now, but here's a quick plot so you can verify your answer later

[ember kernel]

System of 2 equations/2 unknowns :
7 = -1 m + b
-2 = 8m + b
Solve for m and b

Other method :
Compute the slope m = Dy/Dx = (-2 - 7)/(8 - (-1))
(D is just the classic, Greek Delta)
Then, plug in a pair of values (eg. (-1,7))
to get 7 = -1 m + b. Since you know m, you can solve for b

Tell us if you need further explanations

[waxen storm]

i actually know the answer but i would like to know the steps to it

the asnwer is 10/3

[left knoll]

So would that probability be 20/25?

Bruh idk what I’m doing wrong

Ahhhh wait I got it

[supple island]

lim x->o sin3x=3x for sin5x=5x for (1-cos2x)=2x² so you have limx->0 10x³/3x³=10/3

[left knoll]

Lemme understand it now thank you guys

[left knoll]

So where x=21 N=25 and p=0.8 where would you get x=21 from

Is that not a previous part of the question

[supple island]

in d) i don't know why 21 would be of any use

[cinder yacht]

btw this isn't technically correct but yea good way to think abt it

in maths we'd use the equivalent (~ sign), like : sin(3x) ~ 3x when x->0

and there are strict rules with it (like not being allowed to sum equivalents)

[obsidian sage]

you can either use L'Hopital's rule a shit ton of times until both numerator and denominator are not 0

[supple island]

yeah couldnt find it on the keyboard

[obsidian sage]

or you can use the maclaurin series to expand all the trigonometric terms

[waxen storm]

Right right

[waxen storm]

The thing is that my teacher told me to refrain from using the l hospital rule cus not many questions come in jee

So I had to scramble to try to find a different way

[obsidian sage]

you can try using the maclaurin series

it will work

if that's allowed in your exam

[waxen storm]

Yeah I have no idea what thT is

[obsidian sage]

oh

[waxen storm]

But thanks it gave ne enough insight to be able to solve it

[obsidian sage]

here

[cinder yacht]

lol in france we call it taylor series

[dusty saffron]

We call it taylor-maclaurin lol

[supple island]

taylor series is the general one, mclaurin is just for x->0

[minor vapor]

hi there i got a question and i dont know if this is correct. the question didnt have the answer attached.

I got 59.6

please tell me if you got different

[fringe timber]

It says get the exact value of sin(a+b) if ....

And i have to use these

And trigonometric one

[hollow blade]

i haven't done trig in a while but if I understand correctly those are both pythagorean triplet triangles: A sides=(3, 4, 5) as well as B sides=(5, 12, 13), so you would be able to plug those in using what you already know (sinA = opposite/hypotenuse = 3/5) then use the given formulas (2nd pic) to answer sin(a+b) and draw the triangle in the right degrees given on the unit circle to get the right orientation (negative y/x, etc). I hope this helps!

[supple island]

where are the triangles? also B is>180°

drawing "in the right degrees" doesn't make sense

you'lle never have an angle that gives a negative sin in a triangle

that doesn't make sense

[hollow blade]

i more meant you could decipher what quadrant it would be in

lemme draw a picture lol maybe i am wrong

[supple island]

no need

but i dare you to find a triangle that has an angle>180°

using triangles here doesn't make sense

you're given none

you are given the sin of 2 angles

that's it

[hollow blade]

so do you just plug in corresponding values into formulas above?

[supple island]

you need the cos

which you don't know

so you gotta find a way around it

[hollow blade]

but you can find using pythag triples?

or how is that not relevant?

[supple island]

you can't

B can't reasonably stay in a triangle

[hollow blade]

oh because B refers to an angle?

I was thinking this but maybe I am wrong, nvm homework doer hahaha

[supple island]

i'm not super sure you can do this for A, but if you could it would be quite smart

[hollow blade]

well i used the numbers from A so you'd have to change the numbers

[supple island]

yeah you should be able to

[hollow blade]

but that is B

edit: not B but wrote a big B for some reason

[supple island]

sinA=3/5

that's not B

[hollow blade]

in negative i meant as you can see based on the quadrant the opposite (3) or adjacent (4) etc angles would be negative thus resulting in a negative fraction.. but not sure how valid that is

[hollow blade]

i know but i wrote a big B on the paper lol

oops

[supple island]

cosA=-4/5 here thou

[hollow blade]

yea exactly

[supple island]

ok i see now what you were trying to say

i guess you could say cosB=-12/13

hm

ok sorry

what a weird approach

very nice

i shouldn't get worked up over triangles at 2 am lol

[obsidian brook]

@dusty saffron @ember kernel @blissful hedge

Got the solution from the question...it literally just means to multiply itself 10 times...dang

[dusty saffron]

Yepp told ya

[obsidian brook]

dang

hate that i tend to overthink a lot

XD

[dusty saffron]

Haha it's alright

[obsidian brook]

the third line literally told us to R2<-->R3

dude....

[dusty saffron]

Yehh

[obsidian brook]

welp

the more we know

[dusty saffron]

Now u know

[blissful hedge]

opps haha

i dont even think that way haha

[obsidian brook]

=w=

[rain walrus]

any idea how to solve

[dusty saffron]

☝️

[supple island]

a)2* 10^5* (120/100)^n=1* 10^6->(6/5)^n=5, find n
b) same thing but now you have (6/5)^n=10

do the logarithm and the solution is the next biggest natural number

[vestal yew]

hi guys, badly need your help

[dusty saffron]

What's the form of answer in that example?

[vestal yew]

using lagrange multiplier is the topic

@dusty saffron

[dusty saffron]

Ahhh sorry I don't think I can help u about it

[vestal yew]

it's fine

[supple island]

ok so given that the 3 cuts are a,b,c and a+b+c=L you want to maximize/minimize a²/4pi+b²/16+c²sqrt(3)/2 (which respectively are the area of the circle, the square and the triangle), since a+b+c=L you can express one of the variables as a combination of the others (ex. c=L-a-b) and L is known, so now you just need to study the critical points of a function of 2 variables (ex. f(a.b))

[vestal yew]

L is not given/known, that's where I am stuck.

[left knoll]

it says its L units long. That is a given right?

[supple island]

L is given

it's a parameter, but saying "it L units long" means that you know L

[north heart]

Honestly so confused as to how to approach questions like these which use multiple properties , any suggestions?

[supple island]

have you ever solved an integral using complex numbers?

[north heart]

nope

[supple island]

hm then this is quite annoying

[north heart]

how would u solve this using complex tho

[supple island]

you'd have to use properties you haven't studied yet

and i'm not even sure id it's the right way to do it

[north heart]

ik properties of definite int , not complex numbers tho

[supple island]

don't worry

[north heart]

so no hope on solving this qn?

[supple island]

i'm trying

yeah no uhhh

[warped tiger]

Hi, can someone help me with this? Does this mean the x values are -0.2, 3.2 and 6.6?

[sage osprey]

i believe so ^

[left knoll]

Can anyone help me out for the 10th sum

I am not able to factorise it with middle term split

[fleet spire]

crazy function

[midnight pond]

If you're not able to find someone to help, probably worth plugging it into Wolfram Alpha (https://www.wolframalpha.com/input?i=3sqrt(2)x^2+%2B+13x+%2B+6sqrt(2))

At least then you can get a rough idea of how to approach it

[left knoll]

You can just use the quadratic formula. It's arguably the easiest way to find the zeroes. Here’s an example. Try the same with similar quadratic equations. They are recognisable because they're written in the form ax²+bx+c=0.

[astral berry]

in the first line of working, how did they get 3e^x to 3e^2x?

[supple island]

they multiplied everything by e^x

[left knoll]

yupp I did, it showed that the roots of this quadratic equations cant be found using rational no.s

[supple island]

if you notice the term e^-x isn't there and it has beceomed e^x

cuz e^-x*e^x=1

[astral berry]

alright cheers bosss

[supple island]

np

[left knoll]

okey lemme try!!! thanks a lot!!!

[sage osprey]

yes

[sage osprey]

yeah, but the second would than be 0.0092 M right?

[queen thistle]

Hello, could someone please help me understand a continuity question? ^^

The question is « where is ln(x) continuous? »

I wrote is is continues on the domain of 0 to infinity (all real positive values)

[ember kernel]

All strictly positive real values

ln(0) doesn't exist

[queen thistle]

Thank you! I wasn’t sure if I needed to add it.

I have another question, if you dont mind me asking.

[midnight pond]

Just ask it -- no need to ask if you can ask

[queen thistle]

Oh okay. The question is « where is e^x continuous? »

I wrote as x approaches both positive and negative infinity…

[midnight pond]

An easy way to do a logical check on whether your answer is right is to plug it into a graphing website like https://www.geogebra.org/calculator, and see there are any sharp corners or discontinuities.

In the case of e^x, you're right

It's continuous everywhere (For y=e^x, y is defined for all real values of x).

[queen thistle]

Thank you!

Also, is it correct that tan(x) is continuous when x = 0

I used the substitution rule and it equalled zero

I am not sure how i could explain this

[supple island]

yup

[queen thistle]

I am questioning whether i should also mention the other lines graphed or if i should mainly focus on x=0

[midnight pond]

One way to think of where tangent is continuous is to note that there is a relation ( tan(x) = sin(x) / cos(x) ), so tan(x) is always defined as long as cos(x) is non-zero.

Like PhysStudent said, tan(x) is defined at x=0 aye

It isn't defined anywhere where cos(x)=0 though, which happens periodically

(but that isn't what you asked - i'm just pointing it out)

[thick pine]

You can use limits of sequences to prove it: Let (x_n)_n -> 0 for n -> infinity. Then f(x_n) = tan(x_n) = sin(x_n) / cos(x_n) -> 0 / 1 = 0 = f(0) for n -> infinity
https://en.wikipedia.org/wiki/Continuous_function#Definition_in_terms_of_limits_of_sequences

[queen thistle]

Thank you for the explanation ^^ (sorry @thick pine ) i have trouble understanding yours but thank you 🙏

[thick pine]

Maybe the wikipedia article I linked helps you

[queen thistle]

Yes i will take a look at it :3

[supple island]

try to think of it as if "does the function have problems?" for example 1/x is not continuous for x=0

or sqrt(x) is not continuous for x<0

[midnight pond]

To be clear, Lorenz' answer is more rigorous and a better overall answer than mine. You want to approach continuity from a "limits" perspective, but it depends on what level of education you're at

If you're at university, you want to do the limit approach to prove it

[thick pine]

Ah yeah that's true

[midnight pond]

But if at highschool, just finding an exception to the continuity should be good enough

[queen thistle]

I am taking a core calculus class, I am in 12th grade.

[midnight pond]

I see, fair enough. 👍

[queen thistle]

Thank you all for your help!

I may come back again though

[queen thistle]

Hey again. May someone give me feedback for the answer I wrote please.

Here is the work I did.

[supple island]

wdym the denominator can't be factored

[midnight pond]

The denominator can be factorised

[supple island]

(x+3)(x-3)

[midnight pond]

Also, your numerator can be factorised further

[supple island]

yep, that as well

remember a²-b²=(a+b)(a-b)

[midnight pond]

Nicely done on the numerator factorisation though- x^3 polynomials are a pain to factorise imo

Once you fully factorise everything, there's a cancellation and the answer is simplified in your question

Also, the numerator being 0 doesn't make it a discontinuity just fyi

The denominator determines discontinuities. Numerator 0's are solutions

For reference, if you plug the question into Geogebra (online grapher) to visualise the function, you get this

Solid black dots are points of interest (roots, global minimum, y intercept) while as the hollow dot is a discontinuity

[left knoll]

wtf is this????

[ember kernel]

From step 1 to step 2, the independant terms are multiplied but not the terms with x
(Should've been 6x² + ... + 12x² + ... instead of 2x³ + ... + 3x + ...

Distribution hasn't been applied properly

[left knoll]

thank you!!!!!!

[elder robin]

It's not continuous, but how do I convert it into a piecewise function?

do I just use (x-3)/(x-5) for x < 3 and x > 3?

using the same function for both cases doesn't feel right

[midnight pond]

It might be because I've just woken up, but I don't see how changing to piece-wise can make that function continuous. The x=3 discontinuity is simple to resolve because you can just make set h(x) = (x+3)/(x+5) for x=3.

The problem I have is x = -5, at which point your function suffers a discontinuity which isn't so easy to patch up.

For reference, here's your function on Geogebra

In short, hopefully someone better at math than I am can reply to this and tell you how to make that 'two infinities' situation continuous

Then again, upon re-reading your question, it looks like it's only asking how you'd fix the x=3 problem. So maybe that's all you need to do

[left knoll]

Do it manually show me the h(.) function and you should just try to make a lim_{t->Discontinuitypoint}h(t) if the limit is finit then you cand go on, and actually say that h(discontinuitypoint) = lim... , but with this one i can assure you that if she is similare to f(x) = 1/x it's continuous just need to precise the starting space of the function

[frozen sonnet]

Soes anyone know how to find perimeter of this figure? I need the answer with the workout pls

[dusty saffron]

Yess.....So what u gotta do is calculate half of the circumference of all 3 circles whose radii are given and then add them up if you still haven't got it I can show u the solution

Ohh nvm you asked for it haha I'll send u solution

[frozen sonnet]

Thanks a lot. Got it well

[dusty saffron]

Anytime!

[copper mango]

Im not sure if I agree with your answer, when you calculate pi28 that would be the perimeter of the whole circle but we only have half of it so it should be 14pi +7pi+7pi or just 28pi all together

[small sable]

circumference of a whole circle is 2pie radius tho

[copper mango]

yes 2pr

[small sable]

and did jst pie r

[copper mango]

yes r is 14 not 28 for the first circle

[small sable]

eaaa 28 is diameter right

[copper mango]

yes thats why the answer he gave is incorrect

[small sable]

he should do d/2 to find radius of first circle

[small sable]

yeaa yeaa

[dusty saffron]

Yess my bad on that one

[left knoll]

Can anyone help me solve this problem?

Help me please

[supple island]

it's t* sqrt(1+t²+t³) right?

[left knoll]

Yeah

[supple island]

ok

[supple island]

was this a question you've been given?

[left knoll]

Its my homework.

Its just a part of the question.

[supple island]

can you give the whole question then?

cuz i don't think you can integrate this

[left knoll]

Ok

Wait me a min

[supple island]

sure

[left knoll]

Here it is

@supple island

[supple island]

k

[supple island]

ok so first of all the last terme here is t^4

not t³

then it gets a bit weird

substituting wth u=t² you get integral of sqrt(1+u+u²)

[supple island]

because z'(t)²=(t²)²

[left knoll]

Lets me check again.

[left knoll]

Ah i see my wrong

What about next step? Did u solve it?

[supple island]

thing is, with enough substitutions you can get this int the form of sqrt(v²+1) but i think from there you can perform some weird substitution

i guess substitute v=tan(j)

as weird as it sounds

hmmmm

so now you have integral of 1/cos³(j)

[left knoll]

Hmmmmm

[left knoll]

Sorry but i cant find the answer

[supple island]

yeah this integral is getting pretty weird

[midnight pond]

Haha I've had a few tries at your integral but that is pretty brutal

Remove the t^3 and it's easy, but that t^3 messes everything up

[supple island]

it's actually t^4 @midnight pond

[midnight pond]

That makes the substitution a lot nicer at least, hmm

[supple island]

we could view it as the integral of sqrt(x²+1)

there's just a bunch of constants before that

[left knoll]

How u can make the original equal sqrt(x2+1)

[midnight pond]

I mean if you want clues on how to solve, you can always type into an online walk-through solver https://www.integral-calculator.com/

With the t^4, I would do u=t^2 and that's what the walk through recommends

The path it takes is clever. I got up to the completing the square bit but wouldn't have thought to do the bit it does after that

[supple island]

something like this

[left knoll]

Bro its too weird.

[supple island]

the one that calculator does is weird

but it does work and the result isn't that weird

[left knoll]

I think i have answer in that website

[left knoll]

Thank you so much for helping me .

[supple island]

Np

[brave ledge]

considered n the largest positive integer n that satisfy n(n+2022) is a perfect square number, What is the sum of digits from n

[cyan night]

you mean sum of the digits?

[brave ledge]

yes

the sum of the digits

[cyan night]

12

did you get the same answer

[brave ledge]

how...

can i see your solution

[cyan night]

im pretty sure its not the best way

n^2 + 2022n = a^2

wait sry

n^2 + 2*1011 *n + 1011^2 = a^2 + 1011^2

n^2 + 2022n + 1022121 = a^2 + 1022121

(n+1011)^2 = a^2 + 1022121

(n+1011)^2 - a^2 = 1022121

(n+1011-a)(n+1011+a) = 1022121

actually no

@brave ledge

n^2 + 2022n = a^2

do you know that

a square number can only be 0 or 1 mod 4

[brave ledge]

ah i forgot

(perfect) square number...

is it same or difference

[cyan night]

wait sry im having a brain fart

[cyan night]

this method

(n+1011-a)(n+1011+a) = 1022121 = 1 x 1022121 = 1022121 x 1 = 3 x 340707 = 340707 x 3 = 9 x 113569 = 113569 x 9 = 337 x 3033 = 3033 x 337 = 1011 x 1011

then solve for n and a

for each case

[brave ledge]

ahh i see

[copper mango]

have you tried just doing it for x = 1 and x = 2?

i think its just -1

but i dont know much about limits

you think that could be right?

doesnt matter what you put in for a positve number it will always be -1 so for x=3 it would be 3-ln(e^3+1) or 3-4=-1

[supple island]

lim x->infinity e^x+1~lim x->infinity e^x

@copper mango what the hell are you talking about

[copper mango]

xD

idk

[supple island]

@daring plover knowing that, you just know have to do ln(e^x) which should be pretty easy

[copper mango]

I got -1

[supple island]

it's 0

if you don't know how to do limits please refrain from answering question on limits

[copper mango]

how is it 0?

[supple island]

using this you get lim x->infinity x-ln(e^x)=lim x->infinity x-x=0

[copper mango]

oh you mean when its ln(e^x + 1) and not ln(e^(x+1))

really depends on what was meant

[supple island]

i mean there isn't written e^(x+1)

[copper mango]

yeah but it could be interpreted as that

[supple island]

sure whatever

for x-> infinity e^x is much bigger than 1

so summing 1 doesn't make much of a difference

so for x->infinity you could just say e^x+ 1~e^x

assuming you didn't write e^(x+1)

[copper mango]

that is correct

[supple island]

i guess you could, the result is still the same

[supple island]

you will still have to use this thou

[coral pier]

guys this is my second semester in calculus and I am stuck what shall i do

[cyan night]

where are you stuck

[coral pier]

in rate of change and the limits and the Differentiation

[cyan night]

can you be more specific

like what problems do you havea with differentiating

or computing limits

[coral pier]

okay wait a second

[coral pier]

Limit of a function at Infinity
Limits of Trigonometric Functions
Finding the limit of a function Algebraically

[brave ledge]

consider x and y are real solution that satisfy 4xy(x-1)(y-2)+8x(x-1)+2y(y-2)+3=0, what is the biggest value from 20x+22y ? anyone know the solution? im bit dumb of algebra/NT...

[idle remnant]

Could someone help me solve part (b) of this question please, I am really struggling.

[restive wedge]

anyone know how part 3 is done?

heres the marking scheme

[supple island]

ok so the maximum for the left part is 1, cuz you have 1-1/(2n+1) which is always smaller than 1 and for n->infinity 1/(2n+1)=0.
now to ln(1+1/2n)^2n, the maximum for ln(f(x)) depends on the maximum of f(x), the maximum of that is for n->infinity, but we know that n->infinity(1+1/2n)^2n=e, the fact that you have 2 doesn't change anything, you can just say that a natural number m=2n and the limit becomes lim m->infinity (1+1/m)^m=e. And ln(e)=1

you can try for smaller n and you'll find out that it still works

[supple island]

Try this

[midnight pond]

Did you get help with this?

[restive wedge]

Nice pfp bro

[midnight pond]

Thanks ❤️

[restive wedge]

sorry this is off topic but where can i get that

[idle remnant]

I kinda understand, do u mind writing it out just really simply, that would be super helpful.

[restive wedge]

wont AC be equal to aOB - OA + bOA

[supple island]

exactly what i wrote

oh yeah there's a cancelled b

yeah

[restive wedge]

i did what you suggested but it creates simultaneous equal which just cancel out

*equations

[supple island]

you probably just need OC=bOA-aOB since it's already 2 equations

[restive wedge]

This is what's coming

Oh wow I did it

Thanks 👍

[supple island]

np

[atomic dagger]

hi! I am trying to find the right answer here. I already know it's not number 1, but I'm not sure what to do with number 2 and 3? How can I find if it's correct or not ?

[supple island]

for n°2 there's no way imf c kerf

for n°3 i think you just have to try it out

[finite nymph]

Hello! can anyone help me calculating this limit?

[finite nymph]

(without L'Hôpital's rule please)

[supple island]

sure, i'll start with a hint: what's the limit for x->0 of ln(1+x)?

[restive wedge]

Are you like a volunteer helper or you just like to help ppl?

[supple island]

what's the difference?

[restive wedge]

Like idk are you part of the staff of this server or just a member?

[restive wedge]

My question was stupid 🤣

[supple island]

just a member

we can work it out, what's the answer to my question?

[finite nymph]

0

[supple island]

ok yes, but it's also lim x->0 x

right?

[finite nymph]

yes

[supple island]

ok cool

and ln(1)=0

so limx->1 ln(1+ln(x)) is?

[finite nymph]

its 0

[supple island]

yes, can you express it without substituting?

[supple island]

like this

[finite nymph]

so its same as ln(x)?

[supple island]

for x->1

yes

[finite nymph]

got it, thank youu so much for your help

[supple island]

so you got lim x->1 ln(x)/(x-1)

[finite nymph]

which is 1

thank you

[supple island]

ok it is 1 but why

[finite nymph]

well in the lesson we considered it as a usual limit XD !

[supple island]

oof

a little trick i'd use is saying y=x-1

and do the limit for y->0

so you get ln(1+y)/y

which is 1

[supple island]

cuz using this you get y/y

[finite nymph]

cleaar, thanks a loot ^^

[supple island]

np

[crisp heron]

hi could someone please help me to figure out how to find this 2 areas?

[supple island]

ok so: first of all we do the area of the whole thing, which is 4 times the integral between 0 and -3 of y=sqrt((36-4x²)/9), we can't use the whole thing cuz that's not a function, also the function is even so we can do this instead of doing it between -3 and 3.
then we need to calculate the 2 intersection points of the ellipse with h, we'll call the upper one A and the bottom one B, we'll also call C the intersection of h with the x axis.
what we're trying to do is calculate only the yellow area and find the purple one by simply subtracting it from the total area.
first we'll find the upper yellow area (over the x axis), to do that we just have to do the integral of h between C and A, then subtract it from a quarter of the total area. we have the upper yellow area.
we noe move to the below yellow area, first we do the integral of h between B and C, then we sum it to the integral of y=-sqrt((36-4x²)/9) (which is the bottom half of the ellipse) between -3 and B, both numbers should be negative but we'll treat them as positive since we're looking at the area.
now we have both the yellow areas, we just sum them to find all the yellow area, to find the purple area just do total area-yellow area

voilà

[crisp heron]

I-

i don't even know what an integral is

[supple island]

Oh

Lol

[cloud sky]

this question is making me three ticks away from a breakdown. any help pls

[delicate cave]

first attempt, third line, it should be 36x
you forgot the x

[cloud sky]

oh wow

ig i need sleep lol

thank you

[finite quarry]

how do you get the equation for this