math-help

[left knoll]

I think its a) 1

[silk rivet]

thank you, sorry for late reply, been doing some math problems

[left knoll]

np bro

[junior egret]

Anyone know what c) (i) is?

[pulsar terrace]

ermmm, may i have the solution of this question?
I couldn't find the way to solve it...

[vocal zodiac]

a random variable is a description of the outcome of a statistical distribution. Thus, my hint to you is how would you describe the outcome in detailed in your question? (Keep in mind the varying sample sizes denoted by i!)

[vocal zodiac]

I am a little uncertain but simply finding the two second order derivatives with respect to their variables, and then equating that into the fraction with the corresponding numerator and denominator should give you the answer

[left knoll]

Yeah but

[vocal zodiac]

you're right

can I ask you what class this is for ? @left knoll

[left knoll]

In my country it’s class 11

[left knoll]

Quite a tricky question :’)

So my take to this is

Can we add texit please:(

[vocal zodiac]

?

what is that

[left knoll]

It’s a latex bot, similar to the mathbot here but more complex

[vocal zodiac]

no such luck huh

i calculated 2 (dy/dx) * 1/(4x + 1)

but that doens't strictly put it into x

[left knoll]

since
=tex y^2+y-x=0
We get
=tex y=\frac{-1\plusminus\sqrt{1+4x}}{2}

Finger crossed it works

[vocal zodiac]

why are u using tex lol

just ttype it

there is no tex on this server

[left knoll]

That’s sad

[vocal zodiac]

im not following your second equation

type it without tex notation

[left knoll]

Then

[vocal zodiac]

im assuming the lambda looking thing is a 1?

[left knoll]

Ah yeah it’s a 1

[vocal zodiac]

interesting

it seems like a variation of the answer i got

[left knoll]

Here we write the 1 with the” nose “

[vocal zodiac]

gotcha

that's cool

[left knoll]

Wwajt

Then we put it in this

That’s dz/dx, first order

Then we get this monstrosity

And take derivative wrt x

[vocal zodiac]

i agree with the frst part

[left knoll]

It’s a piece wise function if

[vocal zodiac]

second part not so much

[left knoll]

Ig

[vocal zodiac]

it oculd be right tho

[left knoll]

Yeah I just substituted dy = dx/(2y+1) into dz

[vocal zodiac]

mhm

yea then if that algebraically is correct

then i agree w it

[left knoll]

And squeeze this out and assume it’s a piece wise

[vocal zodiac]

works for me htne

that's an interesting question ahha

[left knoll]

Yeah

And then Photomath the whole thing gets this

[vocal zodiac]

wait

[left knoll]

The sign will be +-

[vocal zodiac]

im too lazy but

that might be what i got

yeaaa

that's what i got

[left knoll]

U have ans?

[vocal zodiac]

wait yea that's the exact answer i got

from my work, i got (2 (dy/dx)) / (4x+1)

dydx equates to the square root function

[winter grail]

z = y^2 = x- y and take derivative of it 2 times with respect to x

or just simply take derivative of original equation which = 0 since there is no x in z = y^2

[clever light]

@weary flower jest dobry z matmy jak cos

[pulsar terrace]

oh okay

[vocal zodiac]

do not listne to this

look at my messages after

[pulsar terrace]

okay

[solemn steppe]

can anyone help me ples?

[alpine nymph]

Hey boys. I need HELP
Find the electrical potencial produced by a hollow semycilinder in a point (P) located in Y axis.

The cylinder has length (L) and radius (a) and is centered in Y axis. and I have so many questions, because I think that I cannot use cylindrical coordinates, because the semicylinder is centered in Y axis.

pdta: My english is so bad, so sorry.

[full drift]

If you don't understand how this happened you might wanna revisit chain rule and product rule

[full drift]

Replace the values of X and A. This is a formula you should remember

[left knoll]

Thanks!

[soft stag]

What do i need to do in my head or my calculator to get from the solution to 0,000471. Like how do i know how many zeros?

Like from 4,705x10^4 to a proper number

[left knoll]

define "proper"

to convert from scientific notation to decimal simply count

[soft stag]

I need to get from this to 0,000471

[left knoll]

so eg its 10^-4

then move the decimal sign 4 digits to the left

[soft stag]

Alright so i just always move the decimal sign ^-n to the left

[left knoll]

yup exactly

[soft stag]

thanks man!

[slim lake]

if a+1-bi and 2b-1+ai
is the roots of the equation
x²-dx+2c+1=0 find the value of a,b,c,d € R

[loud cairn]

By selling 27 oranges for ₹10, a man suffered a loss of 50%. How many oranges he should sell for ₹10, so that he will get a profit of 50%?

[winter grail]

calculate (x-(a+1-bi))(x-(2b-1+ai)) and compare the coefficients

[solemn steppe]

im having trouble with finding an answer to the last part.

"Is the slope of the tangent line to the curve at x=a the same as the slope of the tangent line to
the curve at x=-a for any other values of a? Explain."

I think they are only equal at a=1,-1 but i feel like there could be more

[olive trail]

I think there would be more

Because when you take the derivative of the original equation all of the exponents are even

Im not sure if that’s correct but that’s what I think

[solemn steppe]

hmmm i tried plugging in a into the differentiated equation

and gathered all my terms on one side leaving 0 on the other

so a^4-3a^2+2=0

and then factored into (a^2-2)(a^2-1)

=0

so solving for a^2=2 I got plus minus rad 2 and plus minus rad 1 which is 1

so does that mean

+rad2, -rad2 would be the only other one?

[olive trail]

I think you may have made a mistake when differentiating

It should be 5a^4-15a^2+4

[solemn steppe]

wait i typed that wrong

YES thats what i did

and then gathered the -6 from the other side

so 5a^4-15a^2+10=0

and then i got

a^4-3a^2+2=0

from factoring out the 5

[olive trail]

Is the question asking for you to find all other possible values of a where the slope is the same? Or is it just asking if there is more?

[solemn steppe]

well

im pretty sure its asking both

If ther eis more, I would have to probably point out which ones in my explanation

wait

no i dont think i actually have to

the question doesnt ask to "list which ones"

sooo

[olive trail]

Then ya I would point out that all of the exponents are even so plugging in a or -a will give you the same slope I think

Might want to double check with someone but ya

[solemn steppe]

Okay thank youu

[olive trail]

Np

[glossy meadow]

Anyone know why i keep getting this wrong?

Any help is appreciated

[void talon]

does anyone know how to find the circumference of the circle x = a cos θ, y = a sin θ

[left knoll]

π.2a

[hearty estuary]

Can anybody help ?

[cyan night]

translation?

is it a proof?

[hearty estuary]

yes

[left knoll]

according to a very smart friend of mine

all of the fractions except n!/n! reduce to 0 when n approaches inf

leaving n!/n! which simplifies to 1

[hearty estuary]

well, unfortunately, the form 0xinfinity, is an undeterminate form which means that even tho the result is the same, the proof is wrong

[left knoll]

aw

whats 0xinfinity?

you mean the n!/n!

[hearty estuary]

no, that's a straight up 1

0 x infinity is the 1/n! + 2!/n! + .... (n-1)!/n! as n goes to infinity

because there are n-1 terms which is infinity and all those terms approach 0

[left knoll]

he said that

wait for me while i write in latex

then it simplifies to 1/n which is 0

[hearty estuary]

i know but that's not the problem

in limits, the zero isn't a real zero

it's a small number that approaches zero

which means that if you add or multiply infinitely many small zeros, you can't say that the answer is 0

because it could be anything

[left knoll]

ah

hmm but how about

firstly is this correct

[hearty estuary]

yes

[left knoll]

like is the 0 in this, like, the most 0 out there

[hearty estuary]

no it's still not a 0

it's a 0.00000000000000000000000000......

with something at the end

[left knoll]

huh

[hearty estuary]

but will never be zero

can you imagine the x beeing a huge number ?

[left knoll]

i thought it was accepted rigorously that it is 0

[hearty estuary]

like 9999999999999999999

[left knoll]

yeah i get that

[hearty estuary]

will 1/9999999999999999999999999999999 ever equal 0 ?

[left knoll]

well the fraction itselt isn't 0, but the limit it approaches is

[hearty estuary]

yes

i'll give u an exemple where ur friend's proof doesn't work

[left knoll]

okey

[hearty estuary]

according to your friend, the limit as n goes to infinity is just 1/n^2 + 2/n^2 + .... + 1/n right

which is 0+0+0+0+0+0++............+0 which is 0

[left knoll]

the sigma's variable is k?

[hearty estuary]

yes

[left knoll]

ah yeah

[left knoll]

yeah that'd be his ans

[hearty estuary]

well here is the real answer x)

it's a riemann sum

it's 1/2 btw

[left knoll]

that was a bit too fast can you express it a bit longer

[hearty estuary]

kay wait

you can calculate infinite sums if you can write it as 1/n Sum f(k/n)

and if f is a continuous function in [0:1]

the sum is equal to the integral of f(x) from 0 to 1

[left knoll]

wait why is the integral margins from 0 to 1 but not other values

idk what the right terminology is but

[hearty estuary]

Because here is the formula

and in our case, b=1 and a=0

and the integral is from a to b

[left knoll]

woah whats this

i mean

what is the technique;s name or smth

[hearty estuary]

Riemann sum

[left knoll]

oh yeah remember now

[hearty estuary]

btw here is all the indeterminate forms

whenever you introduce the limit and you get one those, you have to do extra things to solve it

[left knoll]

dang

do you have the proof of that question

the factorial one

[hearty estuary]

yeah i think i found it in the meantime

smbdy else helped me

[left knoll]

nice can you share so i can give that to my friend

[left knoll]

been so long since the last time i see integral in this notation

[left knoll]

as physics student we round things a lot

[hearty estuary]

this isn't the whole solution, it's only the main idea, you still have to show than Sn converges so you can replace it's limit and S(n-1) limit by the same one

but it's easy, all you have to do is show that it's a growing sequences and that it's smaller than a number, like 2 or 3

[left knoll]

S_(n-1) is literally S_n only from 1 to n-1 instead to n

right

[hearty estuary]

no

you have to change every n to n-1

which means that the denominator also should be (n-1)! instead of n!

[left knoll]

sheesh

[hearty estuary]

that's why i brought the n out of the sigma

[left knoll]

ah get now

[hearty estuary]

and when the sequence converges

The limit of sn = sn-1 = sn-2 ...

[left knoll]

and how did L come to existance

[hearty estuary]

it's the limit

when you introduce the limit as n goes to infinity to the expression , Sn and Sn-1 turn to L

[left knoll]

ah ah

[hearty estuary]

it's a super helpful trick cause u can solve problems like this in seconds

if you prove that Un converges, you can just set L=2/3 L+ 1/3

[hearty estuary]

college ?

[left knoll]

so its just proving the convergenceness of S_n-1 now?

yuh college but doing non homo dif eq now

💀

[hearty estuary]

i just graduated highschool and like in order to enter good unis, the physics problems are so aids to me

[left knoll]

anyway when this happen S_n-1 is convergent --> S_1 is also?

[hearty estuary]

No

[left knoll]

gawd

[hearty estuary]

the notion of convergence is only introduced with limits

so you have to prove that the whole sequence is convergent

[left knoll]

ok imma need some time to look all these things again

good chat

its getting late here so imma call it

thanks for the info

[hearty estuary]

thanks, have a good day

pleasure meeting u

[left knoll]

yeah u too

[solemn steppe]

anyone willing to help?

[tawny python]

#math-help
You can use product chain rule and
if u=x^n
u'=n x^(n-1)

[uncut yoke]

@solemn steppe i

[candid rivet]

can someone help me to find the maximum of f(x)=ln(1+x)ln(1+ 1/x)

[steel berry]

what have you thought of?

[candid rivet]

i tried taking the derivative

[steel berry]

yea thats good

what happened

[candid rivet]

i can't find the sign of the derivative

also x is a positive and non zero real

[steel berry]

whats its derivative?

[steel berry]

ok so lets hope you did d/dx correctly which i believe you did

so now u set it to 0

xln(1/x+1) - ln (x+1)=0 right

so xln(1/x+1) = ln (x+1)

here you can leverage a logarithmic property to get rid of the ln

think of it, log(a^b)=bloga

ok i honestly havent tried it yet so im not certain if (1/x+1)^x = x+1 is solvable

[candid rivet]

so (1/x+1)^x=x+1

[steel berry]

tes

yes

[candid rivet]

yeah idk

[steel berry]

have u tried graphing the function yet

[candid rivet]

no but i'm pretty sure that f' is negative then positive and equals 0 at x=1

uh no f' is positive and then negative

[steel berry]

1 is a clear solution

[candid rivet]

indeed

[steel berry]

ok so

(1/x+1)^x =x+1

common denominator

((x+1)/x)^x = x+1

(x+1)^x/x^x= x+1

(x+1)((x+1)^(x-1)/x - 1)=0 right

x+1 cant be 0 due to some logarithm restrictions

(x+1)^(x-1)/x = 1

x=1 is the only valid sol for this

@candid rivet what u think

[candid rivet]

isn't it x^x rather than just x

at the bottom ?

[steel berry]

yes yes

sorry

but yea

x=1 is the sol

it doesnt change much lol

[candid rivet]

so we have (x+1)^(x-1)=x^x

[steel berry]

what

yea

ph yea

you divide both sides by x^x

[candid rivet]

yeah but how de we know there aren't other solutions ?

[steel berry]

because based on the algebra we did

the only possible zeroes for f’(x) are -1 and 1

x=1,-1

i believe

try graphing

[candid rivet]

okk thank you very much

[steel berry]

is x=1 the only sol in the graph?

also we havent checked second derivayive test

[candid rivet]

yes it is

[candid rivet]

doesn't look much better to analyse

[steel berry]

well we are just plugging x=1 in and determining the sign

is it negative or positive at x=1

[candid rivet]

negative

[steel berry]

thats goos

goos

good

so itx max at x=1

[worthy willow]

what formula do i use to solve this?
Determine the position of the particle R at any time, t.

[left knoll]

Is that everything the question says?

[rigid solstice]

Guys Can someone help me with this? Ty in advanced

[vocal zodiac]

sounds like an integration question

[winter grail]

use binomial formula for right side then look for value of x

and x-3x >= 0

[worthy willow]

A particle is moving in the xy plane starting from the origin with an initial velocity in x of 15 meters per second and an initial velocity in y of – 10 meters per second. The object moves at constant velocity in x and constant acceleration in y. The acceleration in y is -1 m/s? (a) Determine the total velocity vector 7, at any time, t. (Ans.: V; = 15i - (10 +t)j) (b) Determine the position of the particle † at any time, t. (Ans.: 8 = (15+)i – (10t +{{2);) What is the position of the particle after 5 seconds? (Ans.:r = 97.63 m, 0 = 39.819)

[worthy willow]

A particle is moving in the xy plane starting from the origin with an initial velocity in x of 15 meters per second and an initial velocity in y of – 10 meters per second. The object moves at constant velocity in x and constant acceleration in y. The acceleration in y is -1 m/s? (a) Determine the total velocity vector 7, at any time, t. (Ans.: V; = 15i - (10 +t)j) (b) Determine the position of the particle † at any time, t. (Ans.: 8 = (15+)i – (10t +{{2);) What is the position of the particle after 5 seconds? (Ans.:r = 97.63 m, 0 = 39.819)

[vocal zodiac]

you have the answer?

im a little confused as to the random numbers u have in the question . Why did you equate 8 =

[left knoll]

I think you know how to do a)

Position on the x axis: x=v_x.t

Position on the y axis (v_0y is the initial velo on y axis)

Combined position in the plane:

[stray totem]

here r my solutions - but i'm not so sure about the first and second question of yours so you should definitely verify that

I got a quick question here why is sin(arccos(-x)) an even function, and how do we determine that?

[bold atlas]

the 1st and 2nd are correct acc to the solutions given, but here in the 3rd step can u explain why -2y is there, sry for bothering much but im new to differentiation(started 2 days ago) so...pls bear with me 😭

[stray totem]

ah so the -2y is the derivative inside the bracket which u need to do for chain rule

no worries!!!

[left knoll]

and then the graph of sin(arccos(-x)) is this

[stray totem]

Yep I know all of that but how would you do it algebraically

[obsidian cipher]

Hey guys 🙋🏽‍♀️ if anyone need a little bit push for studying and focusing with colleagues e.tc add me! We already have make a group "learn and grow with friends" where u can feel free to connect whatever you want, trust the process and fond the courage again! 💫

[left knoll]

hmm can i make the claim that arccos(x)=arccos(-x)? or must we prove that

[stray totem]

yeah you would need to prove that - wouldn't that be however simply pie - arccos(x)

[hushed talon]

Adrian, Boris, Chase and Daniel are teachers who each teach a different course: one of them teaches Literature, another History, another Language and another Biology.
The following is known:

• Chase is friends with the Language teacher.

• The history teacher doesn't know Boris nor the biology teacher.

• Daniel and the biology teacher are friends of the language teacher

• Adrian's only friend is Daniel

Who teaches the language course and who teaches History in that order?

[vocal zodiac]

boris & daniel

[vocal zodiac]

is my guess lolol

[hushed talon]

It's Boris and Adrian ;_;

I have the answer but not the way of solving it but I think Im close :')

[supple island]

ok so the hints give us the following infos:
-chase isn't the language teacher
-Boris is neither the biology or the history teacher
-daniel is neither the biology or the language teacher

@hushed talon

that's for the first 3 hints

with the 3rd and the 4th we know that adrian isn't the language teacher, so we know that the language teacher is either Boris or Chase and the other must be the biology teacher

[hushed talon]

Alright, because of adrian can only have Daniel as his friend he can't be the biology teacher because the language teacher is Boris so that leaves only to Chase to be the biology teacher. Now knowing that the history teacher doesn't know Boris nor the Bio teacher it can't be Daniel because Daniel is friend with Boris so it can only be Adrian the History teacher and leaving Daniel to Literature teacher

thank you!

[supple island]

np

[mystic oriole]

Any advice to learn integral calculus?

And hi

[winter grail]

this should help you with the intuition
https://www.youtube.com/watch?v=rfG8ce4nNh0&t=128s

and just practice

[vital steppe]

Solve please, the red mark

[left knoll]

guys how do you do this problem?

is the answer 1?

[remote ridge]

help please

[left knoll]

did you try splitting it like this then integrate only blue line (and take absolute value of that)

[livid quartz]

I would appreciate it if someone could show me the solution to the first sub point.. 🥲
Determine the real numbers x and y from the equations:

[delicate cave]

find area of the sector of the circle having angle pi/4
subtract the area of isosceles triangle OPQ from it

[left knoll]

ik how to do it

wanted to confirm answer

[delicate cave]

equate real and imaginary parts

[delicate cave]

B according to me

[left knoll]

mm i got D?

[ember garnet]

I think it's B too.

[left knoll]

explain?

[ember garnet]

Area of circular sector is pi*8²*(pi/4)/(2pi) = 32pi/4
Area of triangle is (1/2)*8*8*sin(pi/4) = 32/√2

[ember garnet]

For (a), you get:
3x-y + (2x+2y)i = 1 + 6i
So you need to solve the system of equations
3x - y = 1
2x+2y = 6
which has the solution x=1, y=2

[livid quartz]

Thank youu, @delicate cave & @ember garnet!

[vocal zodiac]

add two integrals subtracting blue function from red for (2 -> 4) and then subtracting red function from blue for (4 -> 5)

[vapid ocean]

Ban this man

[unborn mulch]

hello

can someone help me with thus

[left knoll]

guys

is the vertex of a parabola differentiable

[supple island]

why not?

[ember garnet]

I think 3,4,5, and 7 are true. 1 is an approximation so not exactly equal.