math-help

[atomic dagger]

hi! I had a question on solving equations like sin(x) = ⍺ on a given interval.
I know I already have set solutions:
x_1 = arcsin(⍺) + 2kπ
x_2 = π - arcsin(⍺) + 2kπ.
How can I find the value of k ?

[rustic shuttle]

K is a generic integer that you use to get all the angles that would give the same sin, like sin(⍺) is the same value of sin (⍺+2π), that is the same value of sin(⍺+4π). they all give the same value so they all are solutions to the question

[atomic dagger]

but when it comes to a given interval, like [0,2pi], what would k be like?

in my opinion, k would necessarily be =0 since I was taught k was the number of times we go around the circle to fit in that interval. And since [0,2pi] encompasses the whole circle, we don't need to do any "turns"

[rustic shuttle]

in this case yeah, k would be zero

[atomic dagger]

except when i tried to solve sin(x)= -2/3, one solution's k=0 and the other solution k=1. And I don't understand why

[rustic shuttle]

yeah you would have to rewrite the second answerd (x_2 = π - arcsin(⍺) + 2kπ.) to adapt to it, like x_2 = 3π - arcsin(⍺) + 2kπ, that way K is the same for x_1 and x_2

[rotund crypt]

hey anybody knows how could I justify that lim x-->0 sin(x)/x = 1

[rustic shuttle]

L'Hospital

[left knoll]

find equation of tangent

i feel like im being an idiot this is such an easy q

my working for the question

[rustic shuttle]

what's the problem?

i think you already got the solution

[left knoll]

thats not what the answer says

[rustic shuttle]

what is the answer?

[vestal marten]

I had a question
When we solve (0.820 x 10^-7) then it'll be equal to 8.20x 10^-6 right?

[rustic shuttle]

8.20 x 10^-8

[vestal marten]

Why 8 , coz we are multiplying 10 not dividing

[rustic shuttle]

well i think this one is wrong cuz the line doesn't go to the point at x=√3

[rustic shuttle]

you are multiplying by 0.1, not 10

10^-1 is 0.1
10^-7 is 0.0000001

[vestal marten]

Oh we'll multiply by 0.1

Aaa yeah
Thanks

Lol mb

[rustic shuttle]

np

[left knoll]

ok ty

[stark root]

Does anybody know what the difference is between Lagrange remainder and the big O notation O((x-a)^(n+1))?

[left knoll]

how does the first step lead into the second step

[supple island]

sqrt(3/4)=sqrt(3)/2 and 1/sqrt(3)/2=2/sqrt(3)

[delicate elbow]

:flushed: only 13+ :flushed: are allowed to look at my about me :smirk_cat:

[teal karma]

F(x)= arctan (9x^4), anyone knows what the power series is for arctan?

[left knoll]

is this right

part b

im not sure about differentiation here

why is 460 being multiplied by -2

[finite nymph]

Hello, I need help concerning a number theory problem.
how can I find the remainder of the division of 2^(pq) modulo 2^(p) - 1?

[cinder yacht]

2^(pq) = [2^p]^q = [(2^p - 1) + 1]^q
then use binomial theorem and u find that it's equal to : (2^p-1) * stuff + 1
so remainder is 1

im not 100% confident abt this, i didnt do much number theory since highschool, but i think thats it

[finite nymph]

Yeah that's it thank youu so muuuch 🙂 !!

[ember kernel]

The derivative of a^(bt) is (b * a^(bt) * ln(a)). Check your tables of derivatives again

[left knoll]

i get that

but what u said doesnt include the coefficient of A

[thorny kettle]

Anyone up 4 math?

[left knoll]

ty

[pearl anvil]

Hey guys, I've got a problem with a combinatorics exercise. Can anyone help me or give any tips how should I solve it? Any help would be appreciated.

How many different 12 digit codes can we create for the safe, if we would like to use every even number at least once? ( the code can start with 0, and numbers can be used multiple times)```

[rustic shuttle]

The way i would do it is something like:
number of all possibilities (6^12)
subtract number of possibilities that doesnt have at least one of every even number (5^12)*3

[edgy sun]

how come in the solution there is l'hopital done?

[harsh barn]

I can´t find the solution

[rustic shuttle]

the angle in Q is the same for both triangles (RPQ and TSQ), you can get TS by comparing both triangles, since they have the same angles (same sine from angle in Q)

[left knoll]

Qual tipo de formula é essa?

[rustic shuttle]

👀

[rustic shuttle]

its the power series for arctan

[left knoll]

Well ok

[left knoll]

I never saw anything about it

I'm in High School

[rustic shuttle]

There is a whole part of calculus dedicated to studying it, basically its a way to write many things as infinite sums

we don't have it in highschool in Brazil lol

thank god

[left knoll]

But i'll beggin in hard match

Well you're a lucky guy

To be honest, i learn more at home than at school

[rustic shuttle]

If you are interested, there is a teacher from USP that made a lot of videos about calculus, and i learned everything with him, not my own teacher

[left knoll]

Are you learning about Relativity teoric?

[left knoll]

Were you approved at usp?

[rustic shuttle]

yes, but i didn't see anything about relativity theory

[left knoll]

Ok

I know it's not a math subject, but you got a 100% scholarship

[rustic shuttle]

USP is a public school

it's free

[left knoll]

I'm talking about the university

[rustic shuttle]

Yes, it is free

as long as you manage to get in through Fuvest, you don't pay anything

[left knoll]

Where am i making my mistake

[rustic shuttle]

i didnt understand the first step. sin^2(x) = 1/2 - cos(2x)/2?

[echo temple]

anyone know how i can manually calculate normal cdf using pdf?

[full quiver]

hey, sorry to bother but can someone help me with this limit? it’s simple

[floral jungle]

Does someone need help with your math problems? I am using Gauthmath, it has LIVE tutors who will give answers and step-by-step explanations 24/7 for FREE. Here's my invitation code: UY6Z4N.
https://s.mathme.xyz/lp/invite?code=UY6Z4N

[left knoll]

no advertising pls

[left knoll]

yea?

do u want me to prove it for u?

its an identity

we cant integrate by parts btw or partial fractions

thats why i used identity

[floral jungle]

Dude this is not an andvertising lol 😂

[ember kernel]

This is advertisement. You included your invitation code 🤨

[rustic shuttle]

oh no, i just never saw it, just wanted to confirm

[rustic shuttle]

maybe here

[floral jungle]

No lol … 🗿

Invitation code isnt ad dont make false statements:/

[left knoll]

He’s not making a false statement when it’s literally an advertisement

Please remove in accordance to the rules

[left knoll]

Ty

[ember kernel]

The fact you were incapable of looking the definition of advertisement up before speaking to avoid making a fool of yourself just reflects your incompetence when it comes to googling things, since you're desperately a d v e r t i s i n g your invitation code to get some extra credits for a tutoring app instead of making any effort to access the common knowledge of thousands of teachers/lecturers/researchers that you're a few clicks away from

The reason I'm so salty about it is that this has to be the 7th or 8th time YOU send that pre-written ad, and everytime you've been very defensive and annoying about it when we got mad at you for not respecting the server rules

[clever burrow]

Is the answer (pi^2)/4?

[clever burrow]

Yeahhh. Lol i didnt see this part. Absolutely correct

[cinder yacht]

too late I guess?

[full quiver]

right on time if u want

[cinder yacht]

generally when i have +infinity - infinity
i factor in by the "stronger" infinity, here e^(sqrt(x+1))
so f(x) = e^(sqrt(x+1)) * [ 1 - e^[ sqrt(x) - sqrt(x+1) ]
= e^(sqrt(x+1)) * [1 - e^t] with t = sqrt(x) - sqrt(x+1) = -1/[sqrt(x)+sqrt(x+1)]
= e^(sqrt(x+1)) * (-t) * (e^t - 1)/t

now t->0 when x->+infinity, so (e^t-1)/t -> 1 when x->+infinity
on the other hand :
e^(sqrt(x+1)) * (-t) = e^(sqrt(x+1)) * ( sqrt(x+1) - sqrt(x))
= e^(sqrt(x+1)) / [sqrt(x+1) + sqrt(x)]
= e^(sqrt(x+1)) / [ sqrt(x+1) * (1 + sqrt(x/(x+1)) ]
now e^(sqrt(x+1)) / sqrt(x+1) -> +infinity when x->+infinity
and 1+sqrt(x/(x+1)) ->2 when x->+infinity

so all in all, the limit is : 1 * (+infinity) * / 2 = +infinity

there might be an easier way

[full quiver]

got it, thank u so much <333

[cinder yacht]

you're welcome :)

[arctic cape]

hello can anybody help me with this question?

a bit confused here..

[cinder yacht]

do u know the derivative of arccos? (meaning cos^(-1), meaning the inverse bijection of cosine)

it's not 1/[cos(2x)] it's arccos(2x)

[arctic cape]

uh it is not the same? it means that i have to differentiate the d/dx (cos^-1 2x) and the answer would be -2/(1-4x^2)^-1/2

😭 uhm it is okay then, i guess i would have to ask my teacher

[supple island]

use chain rule knowing that d/dx cos^-1(x)=-1/sqrt(1-x²)

that's about it

[clever burrow]

Extremely sorry

I made a calculation error 🤡

In hurry

I am redoing and sending it

Wait 🤡 👍

[clever burrow]

I apologise for being an |stoopid| 🤡

[arctic cape]

oh..alright thx

[void hull]

guys whats 9+8 im having tons of trouble with this

[left knoll]

Dude idk this is a tough one. Have you tried expressing it as a Fourier?? Or maybe we just integrate it. Idk I’m pretty bad at math tbh

[ember kernel]

The pole of an instable filtering system whose transfer function is 5/(s²-12s-85) for example

It also works as the number of times I've seen this joke on this channel

[left knoll]

find volume of solid

i feel im making a mistake as im getting 0

im getting something else now pls someone help

[wanton lion]

it could be one and zero cause 1-1=0

so its prly 1

[left knoll]

?

about x axis

0= x³-x right

because y=0

are we supposed to search for x value

oh

[left knoll]

@blazing salmon ty

[left knoll]

hi

can u guys help me with this

how is that the length

x-2

i dont understand that

[drowsy matrix]

Hello everyone and have a nice day! I can't figure out how to solve this problem. I have to find the value of y for which the given system has at least one solution, but I can't even draw a graph. Help pls🙏🏻🙏🏻🙏🏻

[delicate cave]

we measure distance from the pivot

[left knoll]

cicada 3301

i solved that

[sullen kettle]

I have problems recognising the signs, is it:
x(y-z)>=0
y(x+1)<=0
y-z>=2x
?

[fiery lintel]

could anyone help me with quadratics, graphing, and factoring?

[fast frost]

when you minus 2 from x you’re left with the distance from the midpoint to Sam, which is what you need to take moments, and then solve the whole equation to find the length of x. I think the question doesn’t specify from what point to Sam do you measure, which makes it abit confusing.

[steel zealot]

sure

[left knoll]

lol ty

[fiery lintel]

bet

[random flame]

Hiyo can someone help with Q8? Pls ping if you do and thanks in advance!! Also yea that’s my working, but my ans is wrong

[jolly plume]

https://cdn.discordapp.com/attachments/744639856139042917/975585687426457630/unknown.png

can i get some help on this one?

[icy ice]

17X = 10^-4
X = 10^-4/17

Use the reverse formula of y=b^x is log (y) = x

Inverse*

[teal karma]

Which one is the correct solution?

[left knoll]

where am i going wrong

[cinder yacht]

two mistakes there

the primitive of 1/x^2 is - 1/x, not 1/x

and

1/(1/2) is 2, not 1/2

[long dragon]

hello guys, i have a question on chegg need answer asap, can anyone have chegg account help me pls ?

https://www.chegg.com/homework-help/questions-and-answers/three-electricians-wiring-new-home-electrician-1-need-11-days-job-electrician-2-need-5-day-q85625186#:~:text=Question%3A-,Three Electricians Are Wiring My New Home. Electrician 1 By Himself Will Need 11 Days To Do The Job. Electrician 2 By Himself Will,-Need 5 Days

Three electricians are wiring my new home. Electrician 1 by himself will need 11 days to do the job. Electrician 2 by himself will need 5 days to do the job. Electrician 3 by herself will need 9 days to do the job. If all three electricians work on the job, how long will the job take to complete? Problem 11 - chapter 18

Question 1 Develop an Input - Processing - Output model for the given problem.

Question 2 Use the Goal Seek technique in Excel to solve the problem. An accurate specification of the three parameters in the Goal Seek Window is required.

this is the problem, thank you guý

guys

[left knoll]

ty

[left knoll]

Can anyone help me this problem?

[median totem]

anyone able to help with some calc?

fourier series

[balmy light]

is anyone familiar with discrete math graph theory, need help

[ember kernel]

@balmy light @median totem Just send your question right away and someone will answer + it increases your chances I answer if you add a little polite text that explains where your problem is/what part you don't understand

[left knoll]

my brother quentin

i got the answers to a and b i was stuck on c

i saw the working out but still dont understand it

can u help me in understanding this question

quentin is such a sick guy

mans carrying me with these explanations

u underappreciated brother

may u stay blessed

[supple island]

at what point do you think the rock is parallel to OB?

[limber aspen]

hello im stuck on this question, it wants me to prove that the infinite series of that converges. thanks for the help in advance

[knotty sky]

what does right directrix mean in this question???

[left knoll]

can u guys explain what happens here

[tropic lava]

Number of ways to keep N labeled balls into K labeled Boxes?

[silver socket]

Hey guys, I have a stats question. In OLS regression, say we have a confidence interval for the coefficient of a regressor [LB,UP], and we have change in the regressor of size D. Would the confidence interval for the resulting change on the dependent variable just be [DLB,DUP]? Question is given for context, I know that in the context standard deviation is an estimate so my simple approach isn't perfect but its consistent with how this course has handled using standard deviations and means and such in OLS predictions. Thanks!!

[cinder ibex]

Hey, can anyone tell me how i can simplify this condition? I got to the P(A) and P(B) but im not like understanding what they want cause im getting confused simplifying it

[amber grail]

It’s Newton’s second law

[amber grail]

mu = 0,5 so mu x R is (4/5)*(1/2) mg = 2/5 mg

[half shadow]

i think i can help u, i just need to know if this is the subject sets or logic (im guessing sets). Also i need to know what does ' | ' mean cuz i've never used it before

[cinder ibex]

Ahh about the first question i dnt really know what u mean because im not used to the terms in english about the second question is conditional probability

its this

[half shadow]

okay as far as i understand this is how u solve these kind of problems, i can try to write the equasion for the formula but i did it by visualizing it a little

[cinder ibex]

Im sorry i just realised i should have translated something p(A)*p(b)= p(A intersection B)

The answer is actually 70/79

But tysm for answering i will compare ur resolution with mine

[half shadow]

so visualizing it was not ideal

[half shadow]

anytime, i'll try to solve the formula and i'll post if i can sorry i never used conditional probability

[cinder ibex]

I did get P(A) = 0.09/P(A')

[cinder ibex]

Thank you and no worries if u cant i just couldnt figure it out how to properly simplify the probability and thats why even with the results of p(A) and P(B) i dnt know how to answer

But we never did such "hard" to simplify in class so i dnt think this will appear

[dry hawk]

Anyone here use a soroban? Would be great to do a study sesh as I learn the tool.

[teal karma]

Help please I really need this and I’m confused

[vestal marten]

Can anyone help me with this
I'm stuck here

[mental glen]

@vestal marten why did you put an "e" as the base of your limit?

[vestal marten]

It's a method for when the limit is in 1^♾ form

[mental glen]

I think the answer is a = 3

[vestal marten]

Yes it is , but I am not able to solve after this I'm confused

[supple island]

how did you end up with x+2/x² multiplied

[sharp ferry]

exponential

[mental glen]

I solved it without the "e" method as shown cause I found that it's not an 0/0 but 2/0 and , I just did the H rule. Then I put ln of the limit's result to get the value of a

[supple island]

yeah they wrote it multiplied

[sharp ferry]

wait @vestal marten you didnt put ln?

you forgot to take the natural log

[vestal marten]

It's a formula g(x)(f(x)-1)

[sharp ferry]

isnt it e^ln ( .....)

[supple island]

with 2/0 you can't do de l'hopital

[vestal marten]

My brain isn't braining at this point lmao

[supple island]

yep

[vestal marten]

First it was 1^infinity form then iT was 0/0

[mental glen]

@supple island *my brain has left the chat *

[vestal marten]

Idk please help

[mental glen]

try with e^ln( of the limit )

[vestal marten]

Okay I did it

[sharp ferry]

i think a=3?

i solved it

[vestal marten]

Yes a=3

[sharp ferry]

need to fair the solution tho imma fair it and send coz rn its not readable 🥲

here @vestal marten

if that one wasnt clear i hope this is 🥲 i have a terrible camera

[vestal marten]

thanks for you time

[little mesa]

i tried to do this also but wasn't able to. Please send the working if you got it :D

[cinder ibex]

Hey, thanks for trying! I did not get to the answer but truth is test is in a few hours so i wont be trying again its my last test and i dnt think the teacher would ever put such complex exercise to simplify, sorry

[little mesa]

It’s okay atleast we tried haha

All the best 💚💛💚

[cinder ibex]

Yeah we did ahah. Thank you! You too 💚💛

[ashen laurel]

Can anyone help me with question 5, specifically part c?

[left knoll]

can somebody here help me find the asymptotes of this function? i know that theres a vertical one and a slant asymptote but i think i made a mistake somewhere

[left knoll]

nevermind, i had it right this whole time lmao..

[drifting siren]

How can I solve 39b? I was able to get A with direct substitution but B I can’t figure out where to start.

Oh is it an indeterminate solution?

I guess not, this is too hard 😅

[ember kernel]

There's a very popular limit that will help you solve this exercise :
sin(t)/t tends to 1 as t tends to 0

[ember kernel]

It is indeed an indeterminate case [0/0], so you need to use L'Hospital to solve it

[vestal marten]

Wish we could just do (1)^2

As sinx/x is 1

[inland rain]

Guys i need help

I have P/0=5

[left knoll]

p/0?

=5

[inland rain]

Area i cirsurfance idk how to spell

[near moth]

u breaked math

[left knoll]

Literally

[near moth]

rip

[inland rain]

Can u help me

[left knoll]

@inland rain can you give us a picture at least

Or try to explain more

How pi/0=5

[near moth]

no picture for the textbook problem

not ur writing

[left knoll]

1.You can't divide by 0

and what is p

[inland rain]

Area

[left knoll]

You divide the are by 0 ?

[inland rain]

O its cirsurfance

[near moth]

circumference*

[inland rain]

Its not zero

[left knoll]

O

Okay

You want to calculate the area

[inland rain]

Yes

And circumference

[near moth]

area is πr^2
circumference is 2πr

there is nothing in geometry dealing with dividing by zero lmao

[left knoll]

I thought it's 0 for some reasons

[near moth]

whats it

[inland rain]

Its not zero its 0

O

[near moth]

ohh

got u

its just not clear didn't saw ur msg

but why u r doing so ?

πr^2/2πr= 5
r/2=5
r=10

is that what u trying to do

[inland rain]

YOU NEED TO CALCUETE AREA AND CIRCUMFERENCE OF ALL SAME SAME SIDES TRIANGLE

Area is 5

[near moth]

circumference is for a circle

[inland rain]

Area and curczmfrence is p/o=5

P is area

[near moth]

I think its better to show ur textbook problem

@inland rain I mean just a screenshoot picture it with ur camera anything

[fair aspen]

hey does anyone know how to calculate easy trig without any device please?

[ember kernel]

Depends on what you mean by "easy trig". Formulas ? Values ? Identities ?

[winged spindle]

hey everyone , ineed a simple help on math , how did we found this ? im kinda bad at math

[lucid pivot]

You already have the steps

[winged spindle]

well yes but from this

to this

omg xDDDDDDDDDDDDDDDDDDDDDDDDDD NEVERM MND

NEVER MIND *

[ember kernel]

"this"

[green jacinth]

You want to simplfy it, so you try to obtain (x+1)`2 in the upper part.
You know (x+1)^2=x^2+2x+1. You already have x^2+2x but you need (+1). So you add it, but to keep the operation the same you also substract 1.

Then, you obtain in the upper part (x+1)^2 - 1. The rest is easy 😄

[fair aspen]

for example sin(60)

[grave elbow]

@ember kernel can you explain this to me please?

[ember kernel]

You gotta learn them by heart

Fortunately, they're quite easy to remember

The sine of 0, 30, 45, 60 and 90° are just sqrt(x)/2, where x is the position of the angle in the list I just gave (starting from 0)

That gives :
sin(0) = sqrt(0)/2 = 0
sin(30) = sqrt(1)/2 = 1/2
sin(45) = sqrt(2)/2
sin(60) = sqrt(3)/2
sin(90) = sqrt(4)/2 = 1

Notice how the inside of the sqrt's are just 0, 1, 2, 3 and 4 in order. That's the strongest way to remember I can think of

For cosines, you count starting from 4 and down to 0

And for tangeants, just practice them for 20min and you'll never forget them again

[grave elbow]

can anyone explain this to me please 🥲 my maths exam is this morning

[ashen laurel]

can you cancel the d on the LHS?

[sly island]

it has multiple answers

[delicate cave]

is the answer (a) (b) and (d) ?

[sly island]

yes

how tho

[tranquil heron]

Does this help ?

[delicate cave]

correct

also a and b must be unique as well (that is each equation has only one solution).. this can be proved by looking at graphs

[sly island]

thank you ^^

[grizzled owl]

Help me to prove that those are true or false please

Para todo= for all, existe= exists , tal que= such that

[left knoll]

No

How can you

They are not being multiplied

[primal pagoda]

Can someone help me with this item? Check Digit ISBN

Also this ISSN

Please

😢

[delicate cave]

is this related to math ?

[fair aspen]

thank you!

[elder lily]

Help please 🙋

I can't get it to a simpler form

To get a general solution

[delicate cave]

is the answer 0 ?

[sly island]

how is the places a rook can move 14?

[ember kernel]

Well a rook can either move vertically (7 squares to choose from) or horizontally (again, 7 squares to choose from), so they add up to 14

[sly island]

but what if the rook is at a corner

[ember kernel]

I suggest you look at a chessboard and count the squares yourself in that situation

Or easier :

1. ooooxooo
2. ooxooooo
3. xooooooo
   In all cases, no matter where I place the x, there are 1 x and 7 o's

[ember kernel]

When I think about it, I've been active on #math-help for a year now. So yeah, teaching that 4+3 is the same as 0+7 was, in my opinion, the best way for me to realize it's time to move on

Here are some tips for anyone who's reading this and is an active asker :

1. Ask google before this channel. That way you'll save your time and ours as well.

2. I personally hated being mentioned just for a question (e.g. "@ember kernel pls help me with this problem : ...") so make sure that, if you do that, the person you're mentioning doesn't mind it

3. Be polite when asking something and grateful when getting a response. Some answers took me an hour to make, and sometimes the askers didn't bother to read them.

4. Be specific. I took special care to ignore the messages that just contained "help" and the screenshot of a problem without further explanation on what the person didn't understand

I hope you'll all do well in school and life in general. Bye

[weary arrow]

O7

[sly island]

alright i got it thanks

[left knoll]

L’hospital

[cinder yacht]

22. y = [1-x^3] ^(1/3) works for every x, so it's true
23. y = 1.5/x works for every x>0, so it's true
24. false, cause if it's true, then x>0, and by setting y=x/2 we have x>y so it's false to say "x<=y"

[robust pike]

i tried but there's this one cos theta which i just couldnt get rid of

[elder lily]

Yes how did u get it

Oh noo Quentin left the server

[robust pike]

im prety sure the answer is not only zero

its gotta have around 2 possible answers

[bold sonnet]

it is 0

on the segment from 0 to pi you can see that this function has no roots

that's just the restriction... it doesnt have roots for all real numbers

[robust pike]

o

i should have considered that

[bold sonnet]

on paper i managed to get it to this simpler form 1/3*sin(x)cos(x)(4+cos(x))-sin(x)-1=0 which simply has no solution

nvm i messed up 😄

I'll try again

[bold sonnet]

if you graph this it has roots xd

[elder lily]

Umm

Can anyone show me how to get answer please

[bold sonnet]

I got it

I'll write down the proof 👍🏻

basically i got it to this simpler form -4(cos(x))^2+4cos(x)+2-3pi/2 = 0

and for this form that x doesn't exist

it should remind you of a quadratic formula

[bold sonnet]

okay nvm i found a hole in my proof, this won't work, i keep finding a root and that's just not possible...

made a mistake with my simpler form

this is the simpler form which has no solution (no root) from 0 to pi

[bold sonnet]

if anyone can morph this to a quadratic formula then you have your proof, i give up 😄

maybe if we used limits as x approaches 0 and pi we'd get a contradiction but that's not a solid proof..

[bold sonnet]

separate limits of course

[bold sonnet]

very cool problem btw ty for sharing

sorry i wasn't able to help 😦

[elder lily]

Haha it's been pain in my ass since yesterday

[bold sonnet]

i could only write down how i got it to that simple form

[elder lily]

Oh no it's totally fine

[bold sonnet]

and ask your teacher or someone who knows better

[elder lily]

I don't have one hehe

[elder lily]

I'd love to see that

[bold sonnet]

what i used is the sin(3x) = 3sin(x)-4*sin^3(x) identity and other basic trigonometry identities

cos(3pi/2) is undefined for us because we're restricted at a (0,pi) domain

otherwise we'd have a root which is just not possible

[elder lily]

Ohkay thanks I'll try to do something with it

[torpid root]

could someone help me with this? I couldn't find the proper method tp solve the equation

[cinder yacht]

set z = y'
the equations become :
z' + (1/x) * z = 1 + 1/x for every x!=0
z(1)=5/2
and y(1)=5/4 (that will help u find y after u find z)

i think an example of z that works is : z_0(x) = x/2 + 1
and the general form of solution of the homogenous equation associated with that differential equation is z_h(x) = a/x where a€R

[plain pendant]

hi guys,what do i do when delta is negative?

[peak pollen]

How do you answer this ?

[fast saffron]

Find the coordinates of M in terms of j and k using the mid-point formula. Using that value of M's coordinates, say (m1, m2), use H's coordinates, say (h1, h2) and equate it to the gradient of HM; (h2-m2)/(h1-m1) = 2. You'll get a linear equation between j and k.

Then use distance formula to find the value of JK and equate it to sqrt(80). You'll get a quadratic equation with j and k. Substitute either j or k from the linear equation found above to find their values.

[peak pollen]

I will never need this in life ever again but thank you a lot

[quiet coyote]

Help

1.each week a person works from 8am to 12.30pm on six days and from 2pm to 5.30pm on four days. The rate of pay is $595 per hour. What is the persons total weekly wage
.

[weary arrow]

595(6 x 4.5 + 4 x 3.5)

[naive sage]

is it possible to solve this using differentiation?

if so, how?

[bold sonnet]

well how i see this is the derivative would be a linear function

it's roots are 0 and 9 so maybe you could figure out which quadratic function it is

once you do differentiate it and plug in 2

[bold sonnet]

this is how it would look like f(x) = -x^2+9*x, but again im not sure if that's the solution

[naive sage]

i understand how to do the differentiation part plugging it in but how did you get the equation?

oh okay i understand sorry i didnt read your thing properly

[cinder yacht]

since they say estimate

oh nvm u asked abt differentiation

yea what Stevan said

[bold sonnet]

you just take this form (x +/- a)*(x +/- b) where a and b would be the roots, in this case 0 and 9 then the form would be x(x-9) if we want the parabola to cry then we just multiply it with -1 😊

[cinder yacht]

no, u cna only know that it's y = c * (x-0) * (x-9)
to find c u gotta look at some third point
let's look at the point where x=4 and y=4
that means : 4 = c * 4 * (-5)
so c = - 1/5

[bold sonnet]

yeah looks much like it

thanks @cinder yacht

[young berry]

Help pls

Someone pls help

[bold sonnet]

assume the opposite for reflection, symmetry and transitive property

find the hole

[torpid root]

thank you, I got a 9/10 on my homework

[young berry]

it is coming out to be symmetric and reflexive

[bold sonnet]

@naive sage please look at what Coly said

[bold sonnet]

then it cannot be transitive 🙂

[young berry]

I have to prove that, which I'm unable to do

[bold sonnet]

have you tried using the triangle inequality ?

|x-y|<=|x|+|y|

[cinder yacht]

ur welcome

[cinder yacht]

x=0
y=1/2
z=1
we have xRy, yRz but not xRz

[young berry]

@cinder yacht Thanks a lot:))

can someone tell me what n ∈ I means>

n ∈ I (capital i)

[sly island]

element n belongs to set I

[torpid vale]

For example, 'I' is an array of numbers: I = {1, 2, 3, 4, 5} and 'n' = 3. So, n ∈ I, because 3 is in the array. If 'n' = 8, then n ∉ I. You can imagine ∈ as a 'belongs to, is an element of"

[oblique siren]

Hi, does anyone know how to calculate the integral of this function please??

[violet mason]

this function?

[violet mason]

Probably not the fastest way but its the right answer

[oblique siren]

Thank you!!!

[little mesa]

That was beautiful to follow, good job

[violet mason]

U can also trig sub with cos and it will be slightly easier

[formal stream]

hi guys, i'm in 11th grade. I'm having trouble in answering integrals (involving substitution) in calc and i was wondering if any of you have any resources/cheatsheets you can share. this might be a really dumb question but i really need help T-T

[supple island]

integral calculator does pretty much every integral with step by step solution

[formal stream]

I'll try it out. Thank you!!

[violet mason]

yeah, if you really need help I can explain how integrals work. We can make a call, but my english is pretty bad not gonna lie. And also, I am only in cal2.

I believe I understand substitution pretty well. I already did my exams.

[weak dock]

hello first time here uhhh can someone help with this integral im hella stuck thx homies

[violet mason]

Ill try my best

[violet mason]

I have a question. is the n considered a constant?

so the answer will be have n inside right?

[weak dock]

ye

thx alot for trying homie

[violet mason]

Anytime 👍

I love maths anyway

[violet mason]

I seriously do not believe it is possible to write this integral as a function.

Do you have the answer? Also, maybe it can be represented by a series, but it is going to be very long, and may not be the answer you wanted

[weak dock]

fr?

im interested if you can write out as a series

[violet mason]

are you in calculus 3? hahahaha

[violet mason]

This is an hypothesis XD I have no idea if it works

hahahah

[weak dock]

idk what calc 3 means but im in highschool if that narrows it down

also no i dont have the answer the teacher gave us this as like a scratch your heads sorta thing but never gave us the answer

ill ask him next i meet him for sure lmao

[violet mason]

Oh nice! I will try again. It is very interesting though!

[weak dock]

thx mate

if i do ever get an answer ill be sure to tell you about it

[violet mason]

Maybe I am just being dumb and it is very easy, who knows XD

[violet mason]

Yes please!

[violet mason]

This is the series

The series can be written in a much easier way, but I didnt do it because my brain hurts 😂

Btw its messy and i didnt do the bounderies becoz I was brain storming sorry about that

[weak dock]

ay thx alot homie

maybe this was what he wanted? i have no clue again when i see him ill ask him

[violet mason]

ill am curious what he wants

[left knoll]

Aoba

[violet mason]

aoba?

[inland oracle]

Hi, I couldn't find where to post this, it's advanced math "real analysis". Can you help me by telling me how I can prove this

sorry for my bad english

[violet mason]

Sorry I have no clue hahaha.

[subtle sluice]

hi can anyone help me with this problem

[hushed jacinth]

what

is the sequence

[bitter salmon]

n^4 with n = {1, 2, ...}

so 1^4 ; 2^4 ; 3^4 ; 4^4 ; ... which is clearly 1 ; 16 ; 81 ; 256

[violet mason]

I am outside today but yeah i can help tonight with this. This is momentum or kinetic energy from physic course right?

[supple island]

the momentum is conserved here, you start with mv0 and you'll end up with 2mv1 (mv0=2mv1), where v1 is in the same direction of v0, now since one of the particles is deflected with a certain angle, it now has a velocity on the y axis, the other particle will have to compensate that velocity, since you didn't start with anyhting on the y axis. On the x axis the sum of the horizontal velocities has to add up to v1

[subtle sluice]

yes it is. thank you

[supple island]

didn't you understand my explanation?

[subtle sluice]

for some reason i didnt see your reply

ill look into it in a few

thank you

[atomic dagger]

hey! I have the complex number z= cos(2x) + isin(2x)
is it possible for me to find the modulus of z from this expression alone ?

[supple island]

yeah, absolutely, do you know how to express the trigonometric form for a generic complex number?

[atomic dagger]

no

[supple island]

welp maybe you should start with that and how to pass from one form to the other

[atomic dagger]

oh wait i get what you mean

i do just not the other way around

[green jacinth]

I supose that you have to prove that if (i) is true then (ii) is true to and if (ii) is true then (i) is true

[cinder yacht]

either u write that z =1 * exp(i * 2x) and the modulus of that is 1
or u use the general formula, for z=a+ib, we have |z|= sqrt(a^2 + b^2) if a and b are real numbers

[atomic dagger]

where is the first formula from?

[cinder yacht]

if t is a real number, exp(it) is defined as cos(t) + i *sin(t)

if u didn't study that nevermind

[violet mason]

Do you still need my explanation? ahahahaha

sorry I was out the whole day

[subtle sluice]

yes please

[violet mason]

Alright. Give me a few seconds to think how to explain it

[subtle sluice]

why is it 2mv1?

[violet mason]

Sorry

Took me long to do it coz I was doing other stuffs

[violet mason]

sorry its getting late in canada and my brain stopped working. i really dont know

[formal stream]

is this right?

[supple island]

Conservazione of momentum, you start with 2 objects with the same mass, one Is moving with v0 velocity, the other is still, the total horizontal momentum at the start is mv0, the verticale Is 0 since nothing Is moving in that direction, at the end you have 2 particles moving on the same direction horizontally, now you have total horizontal momentum mv1+mv2. Idk why i said 2mv1, for a moment i thought they were moving together as a single body i guess

[subtle sluice]

i got the same answer. thank youu

[subtle sluice]

alright. thanks again

[subtle sluice]

hi does anyone know how this works

im intuitively leaning towards the solid sphere

[supple island]

try to use energy conservation

[subtle sluice]

this formula?

[subtle sluice]

?

[supple island]

yeah

[subtle sluice]

im confused on how its going to work with the formula. can you please explain it to me

[supple island]

well, do you know the formula for the kinetic energy of a rotating body?

also do you know how to calculate angular momentum?

[subtle sluice]

alright ill look at those stuff

[supple island]

i mean you should probably study the the theory before jumping into exercises, it doesn't make much sense to do them if you don't even know what you're supposed to. Do you even know what I is here?

[subtle sluice]

nah

[supple island]

well...

[subtle sluice]

im trying to eyeball it

but does my instinct make any sense

[supple island]

why would it, you don't even know the relations

[subtle sluice]

mass distribution is closer to the center and I looks lower than others

[left knoll]

Sorry just need some help with these homework problems

Apologies @subtle sluice and @supple island for interrupting your discussion

[supple island]

remember that you can divide this into 2 formulas, one for the x axis and one for the y (things multiplied by vector i are on x and the ones multpled by j are on y)

[supple island]

a) 63° is probably in respect to EAST, b) is a second degree equation in C
i) just use the definition of scalar product ii) doesn't seem too difficult

[left knoll]

What about part b @supple island ?

Tysm for the others

[lucid hollow]

Hey there, i can't firgure it out what happened there

[violet mason]

Both sides of the equation is multiplied by the denominator of the left side

And then again multiplu by 2 both sides

[violet mason]

Do you mean this part?

[violet mason]

Seems right to me

[violet mason]

For question b, i have an idea but ngl i really dont know

Since you have dP/dt u can do the integral of (1/P + 1/(C+P)) to make it 1/P= something

And dont forget to add the constant, name it like A to avoid confusion

And then use the two datas to prove that C= 1130000

But rn im outside so I dont have a pen and a paper to validate if it make sense

If u dont mind, i can show you tnight

[dark onyx]

Trick to understand antiderivative..

Anyone?

[supple island]

can you be more specific?

[dark onyx]

I meant antiderivative chapter of highschool

[supple island]

if you mean integrals, there isn't a single way to understand how to do them

there are multiples, it depends on what kind of integral

[violet mason]

Yeah there are techniques to help you, but the most important is that you are a thinker. Think and observe. I can help if u need. We can schedule a time to call and Ill be happy to show you how I do integrals

[sage cobalt]

could someone help me with this?

[supple island]

ok so first of all, in the first step, you can't just multiply by an unknown quantity (x-3), because depending on the sign, the inequality may change.
look then very closely what happens in the 3rd step

[sage cobalt]

on the 3rd step he changed the sign when it was just adding and subtracting right?

[supple island]

yep

[sage cobalt]

alright i understand now :). Cheers

[supple island]

np

[earnest surge]

Does anyone know why in percentage questions such as this, there is always +1

Here, 15/100= .15 but they added 1 and made it 1.15

[violet mason]

PLUS

[earnest surge]

Ohh. So in what case would I leave it as .15?

[midnight grail]

Hey could someone help me with part (b) ?

[violet mason]

for example, if it asks how much more does a table from the store cost more than from a wholesaler, you have to stay with 15%

[violet mason]

im working rn sorry, Ill answer tonight if u still need it

[lucid hollow]

ty

[violet mason]

dw

[lucid hollow]

Why does e"2x-1 = 1-e"2x

@violet mason

i mean if we have 3-2, its not same as 2-3

[lucid hollow]

👆

[violet mason]

well look

it factored out the -3

[lucid hollow]

Im still confused @violet mason :/

3 goes outside and becomes -3

and then e"2x-1?

[midnight grail]

Heyy thanks so much I just figured it out (this always happens when I think of asking for help)

Thanks anyways :))

[violet mason]

HAHAHHA dw gl with ur studies

[violet mason]

You just said it

3-2 is the same as -(2-3)

[earnest surge]

Ohh thank youuu

[lucid hollow]

makes sense

[violet mason]

anytime guys

[subtle sluice]

hi can anyone help me with this problem

[hushed jacinth]

😭

helpp

[violet mason]

hahahaha lemme try

a) 3,6,9?

b)
i) 3*(1+2+3....untill 20)

you can also write 3*20*(20+1)/2

same thing for ii) 3*100*(100+1)/2 subtract with the answer of i)

[violet mason]

Sorry I dont even understand the question. Does held 12.0cm from equilibrium means that it is located at a height of 12cm?

ah I got it

lemme try

[violet mason]

I just realize are you in Waves? coz I havent learned it hahahhaa. im in computer science. But this quesiton is interesting, I remember a friend of mine showed me a similar question.

I might go learn it online when I get time

[violet mason]

ok and? what is the question
XD

draw it?

[restive wedge]

how to do part 2

[delicate cave]

Let the equation be of the form
f(x) = (x - p) (x - p)(x - r)
notice how I've repeated two roots in this form keeping one as "p" and other as "r"
now expand this expression, I won't do the expansion, but can point that the constant term will be - p^2 * r
you know this to be equal to 36, and p & r are integers
now just do the factoring and you're done

[torpid root]

could someone help me with this line integral? For the life of me I can't understand how it works

It looks basic, but I just don't understand the workflow of solving these

[violet mason]

Interesting... but what made you choose f(x) = (x - p) (x - p)(x - r). Does something prevent you change the signs of this function?

[delicate cave]

p and r are integers, you could replace p with -p and r with -r, the answer would remain the same (it would self adjust later)

[violet mason]

Yeah so the goal is to basically make a function of third degree.

[violet mason]

Its line integral something? I havent learned it yet hahahaha but it seems to be just an application of formula

[vague dagger]

gguys how to answer this

i dont understand anything

[fast saffron]

Hey, let's take the first part as other parts will be similar:

We can rewrite the equation as:
x = (17 -5y) / 2

Now, since both x and y are positive integers, the RHS in the above equation must also be an integer (as it is equal to x). Simply start plugging in positive integral values of y and check if x is a positive integer too.

When y = 1; we get x = 6. So, this is a possible solution.
When y = 2; we get x = 3.5; So, this cannot be a solution as its not an integer.
When y = 3; we get x = 1; So, this is a possible solution.
When y = 4 or greater, we get x as negative. So, these could not be solutions.

Based on above, the only solutions are (x, y) = (6, 1), (1, 3). Hope this helps 🙂

[soft plover]

Anyone know how to do 10c and 10d

[torpid root]

I believe there is more to it. I only understand that the integral is definite between x=0 and x=2, but that's it

[subtle sluice]

hi can anyone help me solve for this physics problem

[meager sleet]

how would one fine X here

[vital compass]

Is 2.8 the length of perpendicular??

[meager sleet]

yes

[haughty owl]

sin18=2.8/x

[formal stream]

Is this right?

[cinder yacht]

ye

[coral aspen]

151 ans plzzz

[coral aspen]

160 ans 😩 😩 😩

[bold sonnet]

how odd with u-swap i get a quadratic function with no roots 🤔

however it truly has an answer... idk

[supple island]

remember that arctan(1)=pi/4

so you get x²-3x+3=1

this does have roots

[past flint]

what are options C and D

[unreal ore]

16y^2 - x^2 + 2x + 64y + 63 = 0

dire need of help pls

[supple island]

i mean the inverse of a diagonal matrix is pretty straightforward

[supple island]

add and subtract 1, you'll have (16y²+64y+64)-(x²-2x+1)=0

you can recognize for both (a+b)²=a²+b²+2ab

[lofty arch]

Might be easier to take out the factor of 16 from the y terms before factorising it

Make it 16(y^2 + 4y + 4)

[left knoll]

what is the coefficient of x^2 term in the expansion of (2x+5)^6

[bold sonnet]

but we don't have arctan we have arccos ?

how'd you get that transformation ? @supple island

OH wait i see

I made a mistake with the swap

but my question still stands for arctg

[bold sonnet]

the answer is D) pi, i'll write down the solution if you want

[supple island]

Oh i read 150 instead of 151

[bold sonnet]

for 151 the quadratic is (x-1)^2=0

[coral aspen]

I got the ans it is not pi

It is pi /2

[coral aspen]

0 right ?

[bold sonnet]

Okay, let me write down my solution

[coral aspen]

Yaa

Sure thanks

[coral aspen]

Ok that looks right thanks mann

[bold sonnet]

sweet ❤️

wait you're right lmao

it is pi/2 hahahaha

i made a mistake again

[coral aspen]

Ses if this is right

[bold sonnet]

okay im confusing myself hold up...

need to check my facts

[coral aspen]

See cos inverse pi/2 is 0

9 to power 0 is 1

1-2+1=0

[bold sonnet]

basic fucking trigonometry lmao

[coral aspen]

It is correct right?

Fucking they dont even give key shit mf s

[bold sonnet]

i got it watch this, gimme a sec

[coral aspen]

Kk

[bold sonnet]

the answer is actually 0 lmao

root of cosine inverse is 1

for cosine to be 1, it's in the point of 0

[coral aspen]

Chill mate happens

[bold sonnet]

i should stick to calculus 2...

[bold sonnet]

forgot my roots it seems

[coral aspen]

I am so weak in calculus god save me

[coral aspen]

💯

[bold sonnet]

you need help with 160 ?

[coral aspen]

I want the answer

If my calculations are correct i want to check

0? Right answer

[supple island]

(1,1/2,1/3)

you wanted the inverse matrix right?

[coral aspen]

Yaa

160

Th

[supple island]

yeah it's the diagonal 1, 1/2, 1/3

[coral aspen]

K thanks

[bold sonnet]

here @left knoll

[left knoll]

ty

wait but there are more than just one sol @bold sonnet

[cinder yacht]

sin(2x)cos(pi/3) + cos(2x)sin(pi/3) = sqrt(3)/2
<=>sin(2x+pi/3) = sin(pi/3)
<=>2x+pi/3 = pi/3 + 2kpi or 2x+pi/3 = 2pi/3 + 2kpi, where k is an integer
<=> x = 0 + kpi or x = pi/6 + kpi, where k is an integer
<=> x is in {0, pi, 2pi, pi/6, 7pi/6} (since 0<=x<=2pi)

[left knoll]

ye ok this makes sense ty

[bold sonnet]

right i completely forgot

my solution isnt even right it's out of the domain

[left knoll]

its fine man, happens to the best of us ty for helping tho

[bold sonnet]

xd yeah

didn't take the domain into account silly me

[left knoll]

can i ask u another tho?

or anyone here

part ii)

like idk how to write it

[bold sonnet]

don't think i can help with geometry bro xd

[left knoll]

its vectors so idk

is that not a strong suit for u?

ik why its tru i just dk how tf to write proofs

so

[bold sonnet]

but i see there;s perhaps the use of Menelaus theorem

[left knoll]

no no i think ur over complicating it

its just vectors

[bold sonnet]

or Ceva's

[left knoll]

geometric proofs are not allowed for these types of questions

[bold sonnet]

need to revise it bro

[left knoll]

they have to be proved with vectors

[bold sonnet]

i see

[left knoll]

dude i need to revise permutations

and binomial expansion, two of my worst

[bold sonnet]

if that's your worst then you're solid

my strength is calculus if you got questions there then i can (probably) help

[left knoll]

dude how, like i dont get wtf even is pigeon whole principle xd

[left knoll]

same but i suck at trig

u?

well not suck but not my best

7/10 with trig

so ig not great

[bold sonnet]

ik trig pretty well, but as you can see i make dumbass mistakes

[left knoll]

lmaoo same

but i may comeback to u for trig

[bold sonnet]

sure thing

[left knoll]

tysm

[bold sonnet]

this includes everything from sequences, functions, integrals and series

in a real field

[left knoll]

so like finance shit as well?

with gp?

[bold sonnet]

nope im not studying actuary math

[left knoll]

ahh i see

[bold sonnet]

meaning like real numbers xd

as an algebraic structure

[left knoll]

yea yea ikik ur not insulting other fields lmao

but ty i will keep that in mind

[dusk haven]

Can anyone help me with functions?

[supple island]

just post your question, someone will answer

[cinder yacht]

what's gp

[atomic spindle]

does anyone know how you can solve this without calculator?

[cinder yacht]

math major?

[cinder yacht]

factor in e^(-x^2) in both equations
since e^(..) is not equal to 0, that means that the other factor is equal to 0

then u'll have y=0 and 5-10x-14y^2=0

meaning y=0 and x=1/2

[atomic spindle]

thank you mr gigachad

you like very beautifull btw

[cinder yacht]

O_o thank you

[fierce yacht]

Hello, I'm a 7th grade student and I need help. I do not understand how to calculate examples such as "if the pool has dimensions of 8m and 10m how big a hole will need to be dug to fit the pool into the ground", or "how much would the plaster at the house in the shape of a triangle with dimensions of 26dm and 3.9m if 1m of plaster costs 30 dollars ’. Can some1 help me ???

(I'm not just talking about these two examples here, but that I can't calculate examples of this type).

[bold sonnet]

applied maths, numerical analysis

[cinder yacht]

I see, what kind of job is there after that?

[bold sonnet]

idk honestly

i screw around and find out

[woven orchid]

Can someone whos really good at math and using a program called Geogebra help me tommorrow with math? I have preperation with 45 min before questioniong about how i solved the math questions.

[rustic shuttle]

still need it?

[bold sonnet]

If y^4 = (4-t^2)/t

what does t = ?

[trim wren]

@bold sonnet

mathway.com

[bold sonnet]

Tyt

[bold sonnet]

but i still dont understand how'd it get this expression 😔

oh I see

basic quadratic formula lmao..

[bold sonnet]

what about you bro ?

[cinder yacht]

thats a good way to see it

[cinder yacht]

applied maths, still no specialization yet, i screw around too

stats/stochastic stuff/optimization/machine learning

tho in terms of work it'll probably be quant

[left knoll]

geometric progression

[left knoll]

yes pls

[cinder yacht]

oh wow*

what stevan studies is much more complicated than geometric progression, but geometric progression is a good example of sequences/series ye

[left knoll]

A lot of people don’t know how to do this q and I’m running out of options

[tribal field]

can someone tell me where and how could i learn math for sat? thx ❤️

[bold sonnet]

i misunderstood the question then hahah 😅

[bold sonnet]

sweet ! good stuff

[torpid root]

can someone help with this? I believe the definite integral is from 0 to 2 but that's all I could manage

line integral

[restive wedge]

can anyone tell me how part 4 can be done?

ik its hard to read but thats the only way i could fit in in one image

[left knoll]

yo

im struggling with this

how do u deduce that no one only reads murder mysteries

i got probs of G

thats fine

the other 2 events im a bit confused anyone willing to help me out any help would be appreciated greatly

i just clocked

nvm guys

[rustic shuttle]

did you manage to do the other ones?

[restive wedge]

yeah they were easy

[rustic shuttle]

you can get the coordinates of B and D from the coordinates of the other point (A,C and center)

both diagonals intersect so you can get the function of the other diagonal

and you already have the lenght of the diagonal

[restive wedge]

how do you get function? you mean like equation of line BD?

[rustic shuttle]

yeah, equation

my bad

[restive wedge]

ok so i got the equation, what do i do to get B and D coordinates?

oh wait you mean solve simultaneously by using length and equation?

[rustic shuttle]

yeah

the lenght of both diagonals are the same so you have a line (equation of the second diagonal) and you have a lenght (and in the middle is the coordinates of the center)

[restive wedge]

ok lemme try that

[simple knoll]

can any1 kindly explain whats going on ?

[torpid root]

I did the line integral like this, but I don't know if this is the correct solution for these integrals. can someone check it?

[normal jacinth]

Does anyone know how to create the inverse function of this? I feel like it should be super simple but I am honestly struggling rn

[delicate cave]

y = 1 + 1/x^2
just replace x with y, to get
x = 1 + 1/y^2
now now solve for y, in terms of x
y = +- 1 / root(x-1)

this method in general is correct, but note that you cannot actually find an inverse function of the given function, because the function is not bijective.

[normal jacinth]

So would this be correct?

[left knoll]

im being dumb but how do i factor this without graphing

[normal jacinth]

Does anyone know how I could go about solving this? any good formula?

[left knoll]

What am I looking at?! 🤣

[soft plover]

i think i solved it but just to double check, is the answer 4/25

[normal jacinth]

The answer should be 0.128

[soft plover]

you got markscheme?

hmm 1min

[normal jacinth]

Yea I have to solution but what matters to me is the formula/correct way to go about it so I can reproduce it if its asked in a similar way in exams

[soft plover]

i used the geometric sequence

s infinity= a/1-r

ohhh

i got it

yea

i'll rewrite and send you the solution

[normal jacinth]

Appreciate it very much

[soft plover]

Idk if I explained it clear enough but if you got any questions then I can explain

With these questions you always write down the first few terms then you can work out the difference and 1st term and so on

[normal jacinth]

So you determine a = 1 and then go from there if im right?

[soft plover]

To find out a I worked backwards

Because I know n=2 and n=3

I worked out the difference so then I know what I need to times a by to get n=2

I'm so bad at explaining things xD

[normal jacinth]

Sorry I might be asking in a dumb way

[soft plover]

nono

you asked how i worked out a(1st term) right

[normal jacinth]

This is what I mean

[soft plover]

oh

[normal jacinth]

You determined the first value and used that to continue

[soft plover]

i sub into the equation with n=2

[normal jacinth]

Yes thats what I mean

And then you divide by 4/5

[soft plover]

Yea to work out the first term

[normal jacinth]

Because you determined that the values increases by 4 and 5 respectively for each iteration of N ?

[soft plover]

Yea the difference between each is times 4/5

[normal jacinth]

Can you explain the very last line to me

Why do you subtract Sinf from a?

[soft plover]

The equation started with n=2

So the equation is saying n=2 to n=infinity

We worked out n=1 to n=infinity

So to go from n=1 to n=2 we need to subtract 4/125

Let's say if it was going from n=3 to n= infinity then we need to take away n=1 and n=2

[normal jacinth]

Oh I see, so if it would start at n=1 then I wouldnt need to do that subtraction at all?

[soft plover]

Yes

[normal jacinth]

Thanks very much, I did actually manage to figure that one out

[soft plover]

Oh okay okay

If you got any questions and no one is replying in time then you can pm me

[normal jacinth]

If n was 3 though, would I need to modify the faction at all? I believe so right

[soft plover]

If n=3 then you subtract n= 1 and n=2 only

The fraction stay the same

You just sub into the fraction to get n=3, n=4,n=5,...

[normal jacinth]

so it would be 4/25 - 4/125 - 4/125 ?

[soft plover]

4/25 - 16/625 - 4/125

Because n=2 is 16/625

[normal jacinth]

Ah I see, thats what I thought

Thank you

[soft plover]

Np

[jovial niche]

can someone help me with the math?..

т-т

[left knoll]

you need to translate them though

[vast kettle]

Could someone help me with this sum?
So technically I can't split the limits as 0 to pi/2 and pi/2 to pi because tanx is undefined at tanpi/2. So | tanx | is positive throughout the interval 0 to pi. But my doubt here is that tanx is negative from pi/2 to pi but I cant split the limits because of whatever I said.
Thank you!

[soft plover]

you know what the answer is suppose to be?

[left knoll]

did you solve it by yourself already?

break it in to 2 parts like you did and use improper integral you can see that the integral diverges, which means the limit doesn't exist, which, again, means the integral doesn't exist

[delicate cave]

summation { 4^n / (25 * 5^n) }

take 25 outside of summation

25 * { summation 4^n / 5^n }

25 * (GP with first term 16/25 and common ratio 4/5)

[bold sonnet]

this is chaos

You have a singularity in pi/2

the tangent function by itself diverges from -pi/2 to pi/2

so by no chance in hell with it converge absolutely

the only thing you can do is prove that this is an infinite sum both diverging into the "same" infinity so to speak

just so you don't think I

am spouting nonsense here wolframalpha

and with a simple translation in the domain

nothing changes.

[bold sonnet]

and i didn't see this so yeah what he said 👍🏻

[vast kettle]

My math teacher just sent the question and asked us to solve so I assumed it had a definite answer. Thank you @bold sonnet , @left knoll for the clarification.

[urban willow]

guys

is this valid ?

i added and substracted 1

[junior vortex]

you can add and subtract but i dont think you can divide like that ,

[cinder yacht]

+infinity I believe

it's not because tan(x) is undefined at pi/2 that the integral doesn't convetge
its because a primitive of tan(x) is -ln(cos(x)) and when x->pi/2- that diverges to +infinity

[left knoll]

for this question i got the correct answer but the wrong values. the solutions have taken the time equation as t=vsintheta/g not t=2vsintheta/g which makes no sense to me as the question does not state that the path of the ball is a half parabola. am i missing something here?

also how do i do this

[ember garnet]

if you equate the horizontal component of the given equation to the distance from the far wall you get the time that the ball hits the wall. Then you just need to show that at that time the vertical component is greater than zero (above the floor) and that the vertical component has a global maximum that is less than 3 m (which the ball reaches at a time before it hits the wall). The path of the ball is in fact a parabola.

[left knoll]

yes yes i got thats for my working, however my values do not match the solution

[ember garnet]

what values did you get?

[left knoll]

uploading them now

the circled answer is mine

read from left to write

apologies i was running out of paper @ember garnet

[glossy rover]

the reason you cant cancel out is because theres 2 terms in the numerator and 1 term on the denominator, have you considered hopitals rule?

[ember garnet]

what are you trying to calculate? The time of flight?

[left knoll]

no whether it hits the ceiling and the wall

i calculated tof cause u would need that to see if it hit

@ember garnet

the solutions

[supple island]

since you're calculating velocity, you don't carry along the 1/2 of 1/gt²

so you don't write 2vy

[left knoll]

wait why

[supple island]

d/dt of 1/2gt² is?

[left knoll]

oh

yea ok

i cant diff my bad

[ember garnet]

yeah if you take the derivative of the vertical component you get -gt + Vsin_theta

[left knoll]

can someone also help me with this one pls

[normal jacinth]

How can I find the limit of this function ? I know that it doesnt work unaltered because I can't divide infinity/infinity (I guess technically I can but its not part of this exercise)

[supple island]

try to factor out x on the numerator and x² on the denominator

[normal jacinth]

L'Hospital would work too correct?

Asking because this is my solution

[supple island]

sure

but for example you could say (x+2)/(x²-2)=x(1+2/x)/x²(1-2/x²)=(1+2/x)/x(1-2/x²)

now do the limit

you'll end up with 0

[normal jacinth]

While I'm writing that down, is my approach correct though? I do get 0 as you can see but that might just be down to dumb luck

[supple island]

i mean, the conditions for using de l'hopital are met, so no, it isn't dumb luck

the approach is correct, i was just suggesting a different one

[normal jacinth]

Appreciate it, I'm trying to wrap my head around this as much as possible, I really want to understand lim

[ember garnet]

derivative of the inverse function is equal to the inverse of the derivative of the original function
so [g^-1(x)]' = 1/[g(g^-1(x))]'

[left knoll]

ok ok ty

[soft lintel]

Quelqu'un parmi vous étudie algèbre 2 peut m'expliquer le truc qu'à fait le prof dans ce passage

Voici l'énoncé de l'exercice je m'interroge sur la dernière question

[supple island]

This is an english only chat

[soft lintel]

where else can I ask about maths in french @supple island

[supple island]

not here specifically, but if you can translate maybe someone here could help

[untold spindle]

if the limit is x >>> (+,- infinite), and the power in the numerator is less than the power of the denominator then the answer is always 0. gl

[cinder yacht]

il a diagonalisé la matrice
(0 1
2 1)

pour calculer sa n-ème puissance

c tout un cours la diagonalisation

[soft lintel]

P^-1(-1002)P <- Si j'ai bien compris dans cette ligne il a appliqué la diagonalisation ? @cinder yacht

Je viens de chercher sur Youtube. Merci c'est bien ce que vous aviez dit

[analog wagon]

A rectangular wall has to be painted from x=0 to 100 Height (h) of the wall as the function x is given as x=ahe^(-abx) and h is given in terms of x. Painting per unit of wall costs $20. Find the area covered with a budget of $ 100000
options
10ahe^(-ab)
20ahe^(-ab)
25ahe^(-ab)
45ahe^(-ab)
none of these
how to solve this

[cinder yacht]

yep

[earnest surge]

I need help with this plss

[granite ledge]

what part? logarithm?

[earnest surge]

I have no idea

[granite ledge]

you might want to divide both sides by 2 then you can take a log and using log properties and putting any value for X and get your answer

[earnest surge]

Hmm ok

Thank you

[ashen laurel]

looking at a solution for some integration using partial fractions, surely B=–4 not +4