help-41

[golden karma]

I actually want to use it to prove that something is convergent

[split kraken]

oh hmm

if everything already converges, then this should play nicely

or rather, if the both of the RHS series converge, then there's no need to worry already

the LHS will just converge

[golden karma]

“If sum from 1 to infty (a_n^2) is convergent so
Sum from 1 to infty of |a_n|/n is also convergent”

I wanted to use this here

[split kraken]

maybe just preface this inner product by only allowing it to work when the infinite sum of a_nb_n converges or something

[golden karma]

Ye

[split kraken]

I don't think we need C-S for this

well...

we can use it yes

okay, sure. let's use it

do you have any ideas?

(please ping me when you come back, I will forget about this channel if you don't)

@golden karma

[golden karma]

Yes i did
Sum (|an|/n)^2 <= sum(a^2_n) * sum(1/n^2)

So it converges

[golden karma]

@split kraken

[split kraken]

yes, that works

I'm pretty sure C-S is totally fine in this case because both of the RHS series converge

on the space of convergent sequences, what I wrote earlier is totally fine as an inner product

@golden karma if you're done here, be sure to close the channel

[golden karma]

Ye

Ok thank you so much

.close

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[unreal nacelle]

Can someone please help me with question no 8

[unreal nacelle]

<@&286206848099549185>

[tropic wadi]

!15m

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[plush ice]

can you provide book 📖 you are using ?

[unreal nacelle]

This is a collection of questions provided by the coaching I am studying in so I don't know which book is this from

[unreal nacelle]

Why do you want the book

[plush ice]

i just liked the problems in that book so got interested

[unreal nacelle]

Ohh

@plush ice Could you help me solve this problem

[plush ice]

can you provide drawing ?

[unreal nacelle]

This is how the diagram is supposed to look like

[spare belfry]

Interesting question

[unreal nacelle]

@spare belfry hello

[spare belfry]

Esp

Wsp

[unreal nacelle]

@plush ice Here is the drawing

@spare belfry could you help us solve this question

[spare belfry]

I’ll give it a try

But don’t put high expectation on me

[plush ice]

so i have coutple of questions: why points D,E,F are mentioned and what is delta ?

[spare belfry]

Forgot to mention, The area of the triangle is k/2

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[willow jolt]

How would I know whether to use the product or quotient property?

[willow jolt]

this is my work so far:

2log5(x)-log5(2)+log5(x)
log(x^2)-log5(2)+log5(x)

[split kraken]

you have to use both

[split kraken]

good so far

have you tried using the product/quotient properties yet?

[willow jolt]

yes

so i would evaluate from left to right?

meaning I use quotient property first?

[split kraken]

it shouldn't matter

[willow jolt]

true

[split kraken]

try it, and see what you get

[willow jolt]

log5((x^2)/2)+log5(x)

then product property

[split kraken]

good.

after applying product property, what do you get?

[willow jolt]

log5((x^3)/2)

[split kraken]

done

[willow jolt]

no wait

[split kraken]

[willow jolt]

don't i need to simplify to log10

[split kraken]

why should you need to?

log 10 is just as arbitrary as log 5

[willow jolt]

ok

i just thought bc log 10 was the default one

that people would want it to be in that form

[split kraken]

in the sciences, log10 is default

in math, log e is default

in CS, it's log2

[willow jolt]

so ln

[split kraken]

yeah

[willow jolt]

this is alg 2

so log5 should be good right?

[split kraken]

I don't see why it shouldn't be fine lol

[willow jolt]

ok

[split kraken]

[willow jolt]

ty for all your help

hope you have a good rest of your day

.close

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[split kraken]

you too!

[solar gust]

That is definitely your outro mate

[split kraken]

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[unreal vortex]

hello, i am trying to implement some algorithm or whatever you call it in programming, but i cant figure out the maths behind it
i have a variable size cube, made of smaller unit squares, the size of the cube represents the number of squares on the faces of the cube, i want to find the center of each smaller square on each face of the cube, but i cant figure out how to get those points

[unreal vortex]

like this would be one side of the cube(3x3x3 for this example)

i want to get these points

2x2x2

[vestal hatch]

How large is the cube and where are the corners?

Also what's a "constant volume cube"

[unreal vortex]

Fixed

[unreal vortex]

you have all the data about the cube and its all variable

[proper egret]

are you working with squares or cubes?

[unreal vortex]

i am saying the cube faces are made up of smaller regular squares

like this is 3x3x3 (the cube is stylized but its still the structure similar to above with smaller squares) each square on each face of the cube has a red dark dot representing its center

sorry about the sun

[vestal hatch]

Well if the volume is fixed clearly the side length is not variable

So what is the side length

[unreal vortex]

i mentioned above i edited the original question

[vestal hatch]

Oh that's what you meant by fixed

[unreal vortex]

i translated something in my code to something else when i asked the quesiton so that ones on me

[unreal vortex]

the little squares are of fixed size

[vestal hatch]

is the cube aligned with the x/y/z axis or can it be at a weird angle

[unreal vortex]

aligned

[vestal hatch]

ok

then take for example the bottom face

let (x,y) be the corner with the smallest x,y coordinates

To get a center, add s/6, 3s/6, or 5s/6 to x and also add one of those to y

[unreal vortex]

you have access to the center directly if that helps

[vestal hatch]

hmm

yeah that might make things slightly more convenient

[unreal vortex]

yes making your own problem and giving yourself everything you need > problems from text books

[vestal hatch]

so I'd cycle through every face one by one

For example, to get to the top face, add s/2 to the z-coordinate of the center

s is side length yeah

[unreal vortex]

ok

[vestal hatch]

Let's say it's an n x n cube

[unreal vortex]

sure

[vestal hatch]

For n=5 for example

[unreal vortex]

nxn would be number of squares that make it up?

[vestal hatch]

Yes

[unreal vortex]

aight

[vestal hatch]

add -2n/5, -n/5, 0, n/5, 2n/5 to the x-coordinate

and do the same to the y-coordinate

like a nested loop to generate all the centers

oh and multiply by s

so add -2ns/5, ..., 2ns/5

in general we're starting from [-(2n-1)/2 * s]/n and incrementing by s/n n times

[unreal vortex]

thats dandy and all

but what if n is even

do you just remove the 0?

[vestal hatch]

This description still works, if you look carefully it never hits 0 for even n

it'll give -3s/8 -s/8 s/8 3s/8 for n=4

for example

Just skipping the 0 wouldn't work otherwise

[unreal vortex]

huh i thought these were just fixed numbers now i dont understand

[vestal hatch]

Actually I guess we're technically only incrementing n-1 times but that's unimportant

[vestal hatch]

Try with n=4 yourself then

These are all the possible numbers we add to the x/y coordinates

[unreal vortex]

i dont understand how these numbers work

is this supposed to be a pattern

or do you literally just hard code these numbers/formulas

[vestal hatch]

It's this pattern

The specific example I gave you was for n=5

[unreal vortex]

woops missed that

[unreal vortex]

[-(2n-1)/(2*s)]/n ?

[vestal hatch]

No the s is outside the parens

[unreal vortex]

ah ok

[vestal hatch]

multiplied

[unreal vortex]

brb gonna test this

[unreal vortex]

erm i may have an annoying remark

what if its a cuboid

[vestal hatch]

then you need to replace s with the side length along the axis you're adding to

[unreal vortex]

ah and i assume n as well?

[vestal hatch]

if n is different depending on the axis then yes

you'd kinda treat each axis independently with its own s and it's own n

[unreal vortex]

alright thank you so much for the help, i was doing a similar approach but my formula was waaaaay off than yours, thanks

[vestal hatch]

You're welcome

[unreal vortex]

.close

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[spare galleon]

I

[spare galleon]

As the first servant of lord Mickey

Command you to answer my question

[split sail]

?

[spare galleon]

What is 2(1/2)

Do not question me

[split kraken]

2.5, I presume

[spare galleon]

“Presume”

I can smell the wrong use of word

Shouldn’t it be “assume”

[split kraken]

well, I am a bit tired tonight

[spare galleon]

What had you done?

[split kraken]

either way, it's probably 2.5cm/hr

[spare galleon]

It is so slow

[split kraken]

that makes sense, yeah?

candles don't burn that fast, as far as I know

[spare galleon]

You’re so smart

Knowledgeable

Intelligence

.close

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[mighty hare]

i got cos(theta) can someone double check

[wild vale]

why would that be the case?

[little dagger]

that's correct

[wild vale]

that is wrong

[little dagger]

how?

[little dagger]

1/cos theta*

[mighty hare]

its 1/cos(theta)

[wild vale]

there you go

[little dagger]

I just woke up

I read his answer as 1/cos theta

[wild vale]

sec(θ) and cos(θ) cancelled out, left with sin(θ)/cos(θ) multiply by 1/sin(θ) which is 1/cos(θ)

[little dagger]

yea

[little dagger]

^^

[mighty hare]

.close

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[minor night]

i have no idea how to do this

we are allowed to use our classpads which have a solve function and a normalpdf and cdf function too but idk what to input to make it work

[wild vale]

maybe you want to transform this to standard normal first

[distant herald]

if you're allowed to use invnorm, you can also kind of abuse the symmetry of the distribution to find k

[minor night]

how?

[minor night]

how?

i missed a few lessons lol

i can use invnorm btw

[wild vale]

then that is easy. you still need to transform it to standard normal first tho

think about it this way. the mean is where the distribution is centered. So if you want to move this graph to have center at the 0, you probably want to translate it by...

[minor night]

20

[distant herald]

iirc invnorm lets you put the mean and std, and you say the area to the left of what you're looking for, so you know that 0.4342 is on each side of the mean because of symmetry. that means that the area to the left of 20+k is 0.5 + 0.4342 = 0.9342

[minor night]

wait

idk

[minor night]

its mean, tail setting (left, right, centre), SD and probability value

[distant herald]

oh the tail settings make it even easier

older calculators always just did the left

[minor night]

i put in what you said and it was right

do you mind explaining it a little more for me?

[distant herald]

what part didn't make sense?

you could've technically done it a little faster using the centre setting for the tail but i didn't know you had that option

[minor night]

my brains just hurting atm i got a headache

how would the centre setting make it easier?

[distant herald]

all good, left means the area under the distribution to the left of the value you're considering

so the area under the distribution from (-infinity, a) where a is some number

you know that since the distribution is symmetric and the area represents probability, the total area underneath is 1, so the area to the left of the mean (the center) is 0.5

[minor night]

yep

[distant herald]

and similarly since your values 20-k and 20+k are symmetric about the mean, you know that the area to the right of the mean is half of that area

so 0.8684 / 2 is the area from 20 to 20+k

and you know that the area from (-inf, 20) is 0.5

which means the area to the left of 20+k is 0.5 + 0.8684/2 which is where the 0.9342 came from

[minor night]

yep

[distant herald]

so you'll get a number for 20+k from that calculation and it's just solving for k

[minor night]

yeah

idk why i was confused lol

[distant herald]

this extra math i did using the symmetry is only necessary here cause you're using a left tailed test

[minor night]

i need to go take a panadol

[distant herald]

so you need to account for all the area to the left

but since centre tailed is an option

[minor night]

how would you do it with center bc i messed around on the calc trying to figure it out before i came here

[distant herald]

that accounts for the area for some interval symmetrically distributed around the center

i think

idk my calculator never had that option

what does your calculator ask you to input when you select centre?

[minor night]

same stuff

[distant herald]

mean, std, prob?

[minor night]

if i do invNormCDF (centre, p=0.8684), sd=5, mean=20) it gives me 12.46

[distant herald]

what did you get for k using the left tailed method?

[minor night]

if i do the method that u said, i get 27.54 and then i just take 20 to get k

[distant herald]

hm in that case i'm not too sure about how the center method works

you might want to look that up specifically about how your calculator does that

[minor night]

alright its ok

[distant herald]

afaik that setting should make this calculation quicker since the interval is symmetric about the mean

k above and k below

[minor night]

idk what its even solving for when i put that in though

thanks anyway

[minor night]

you have my dads name btw but my dad sucks at maths

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[amber wasp]

Please don't occupy multiple help channels.

[spare galleon]

I cannot understand the highlighted line

[tropic wadi]

bro please close your previous channel

[spare galleon]

sorry

[mint nacelle]

it's a cone basically

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@spare galleon Has your question been resolved?

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[simple drum]

Can someone explain to me why this linear transformation is from R^3 to R^4?

[sudden jewel]

multiplying a 4x3 matrix with a 3x1 vector results in a 4x1 vector

[simple drum]

Oh okay

How do i find the base of ImT?

.close

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[simple drum]

How to solve this?

[indigo cloud]

wdym by <=

also this clearly isnt enough unless you failed to mention that T is supposed to be linear

[simple drum]

T is a linear transformation

[simple drum]

In the first line ?

[indigo cloud]

yes

[simple drum]

T goes from R^3 to R^2x2

[indigo cloud]

ok second line

[simple drum]

T(1,9,9)=(9 0 12 82)

(2x2 matrix)

[indigo cloud]

ok so the <= is a typo

[simple drum]

Yes

[indigo cloud]

find out the linear combination a(1,9,9)+b(0,1,9)+c(0,0,1)=(3,23,-8)

then use that T is linear

[simple drum]

What do u mean ?

[indigo cloud]

do the other thing first

[indigo cloud]

ok

[simple drum]

Calculation mistake c=1

[indigo cloud]

I am gonna call the vectors (1,9,9) etc as u,v,w

so now you know (3,23,-8)=3u-4v+w, yes?

[simple drum]

Yes

[indigo cloud]

so T(3,23,-8)=T(3u-4v+w)

now, what does it mean that T is linear

[simple drum]

That if i substitute u, v, w i get the answer?

Idk

[indigo cloud]

what is the definition of a linear map

[simple drum]

Its mapping between two vector spaces that perserves the operations of vector addition and scalar multiplication

[indigo cloud]

in symbols?

[simple drum]

T(u+v)=t(u)+t(v)
T(a*u)=at(u)

[indigo cloud]

good now look at the right side of this

could you apply these two properties?

[simple drum]

Yes

Is this correct?

[indigo cloud]

yes

[simple drum]

Ty for the help

.close

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[sick echo]

I have a quick question

[sick echo]

Basically I want to learn how to integrate integrals like the Gaussian integral but I don’t want to know how to do but but I want to learn the techniques that are required to integrate it then try and derive it on my own

So what techniques or things would I need to learn?

I think i need to know how to use Jacobean matrix?

Anything else I need to know how to use?

[sick echo]

For example I learn how to integrate a similar integral then using the knowledge and techniques I have just learnt I then attempt to integrate the Gaussian integral

[amber wasp]

@sick echo Has your question been resolved?

[honest dagger]

Polar integrals

[amber wasp]

@sick echo Has your question been resolved?

[sick echo]

Is this all?

[amber wasp]

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[woven junco]

Find the function from this graph. It is a natural logarithm graph that has been shifted horizontally and vertically. Rather I only have 1 point to work with

[woven junco]

I'm kind of stumped at this one, maybe I forgot something?

So where I've been trying to get at is using (-2, -1) as a point, and using the general form f(x) = a ln(x + c) + d I've found d and c, but can't figure out where to get to for a

So: f(x) = a * ln(x + 3) -1

Rather, a = 2, as one can get from the answer

I'm just confused at how they get to it

[drifting rover]

look at where it crosses x and y, shift ur graph up one and compare values

[woven junco]

Could you please give me another pointer?

[drifting rover]

ok lets consider ln(x)

[drifting rover]

you just compare each value with what you have and try solve from there

so like you see where a ln(x+3) - 1 = y
for diff values of y and x

thats what id do, but also in general knowing what a vertical stretch of ln looks like

as it gets spread out more if that makes sense

[woven junco]

OK, I'll try that

[woven junco]

Would I not need to know for certain a second point?

I mean, in the textbook I'm using

We can kind the key point and the x-intercept

But for the key point I need a

[drifting rover]

i would approximate

[woven junco]

sure

I would go for (-0.28, 1)

yay I solved it, thank you

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[obtuse jolt]

Can I have help with 3

[keen pawn]

Hint: $cos(2x)=1-2sin^2(x)$

[grizzled pagoda]

ƒ(Why am. I here)=I don't Know

[obtuse jolt]

Thank you

Can you help me with 16

And can you answer it I wanna double check

My answers

Please

[tropic wadi]

show your work

[obtuse jolt]

Ok

[jovial field]

Lol

Correct it feels

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[amber juniper]

im having some trouble with this question, the fxy derivative is correct but my fyz is wrong apparently

[plush ice]

what is derivative of yz with respect to y

what's your mistake

[amber juniper]

im not sure but my lecturer just says the partial derivative for Fyz is wrong

the first part is partial der. with respect to y

which is correct

but the partial derivative with respect to z is wrong

[plush ice]

it's not correct

[amber juniper]

partial derivative to y step is wrong?

[plush ice]

yes

this is not correct

[amber juniper]

could you explain further, because for my working im getting this unless it has to be done another way?

[plush ice]

oh sry i thought you were differentiating with respect to y first

ok then first part is correct

[amber juniper]

what about for the second part tho

[plush ice]

that is wrong

[amber juniper]

could you explain how to do it correctly or my error?

[plush ice]

so we use rule :
(f*g)'=f'g+g'f

first

f=y
and
g=cos(x+yz)
in our case

[amber juniper]

ah i see because we have y in the function and we have to differentiate to y

[plush ice]

icorrected the formula

[amber juniper]

alright thank you

[plush ice]

you are welcome

[amber juniper]

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[rapid stag]

Please help me

Someone pinged me and told me the answer is two

But i dont know how to do it

[keen pawn]

this is an indeterminate form, notice that first

[rapid stag]

Yea.. its 0 right?

[keen pawn]

not necessarily

$0 \cdot \infty$

[grizzled pagoda]

f(why am i here )= idk

[rapid stag]

Ouh

so what do i do now..

[keen pawn]

,w lim _{x \to \infty} x^2(sec(2/x)-1)

[grizzled pagoda]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[rapid stag]

Wow..

[keen pawn]

I'll preface this by saying I'm not sure, but I still want to try to help you, is that fine?

[rapid stag]

i should have checked using wolfram instead of photomath

[rapid stag]

Yeah, sure

[keen pawn]

$\L= lim_{x \to \infty} x^2(sec( \frac{2}{x})-1)$

oops

[little dagger]

does he still need help?

[grizzled pagoda]

f(why am i here )= idk

[keen pawn]

now take the log of both sides

[rapid stag]

How..

[little dagger]

wait i got better way and easier

we can write sec(2/x) in terms of cos

and then take lcm

and apply expansions of taylor series

[keen pawn]

wait

[little dagger]

till x^2/2!

[keen pawn]

I don't think that's required either

$cos(2x)=1-2sin^2(x)$

this may help

[grizzled pagoda]

f(why am i here )= idk

[rapid stag]

Ohh

[little dagger]

ohhh yeah

true

[keen pawn]

How are you so smart lol, I would have never noticed that

[little dagger]

as i got exam of that tmrw

XD

[rapid stag]

😲

[keen pawn]

ah, good luck.

[little dagger]

thanks

[rapid stag]

I got that on Tuesday

[keen pawn]

A competitive exam?

[little dagger]

na

coaching exam

(tuition)

[keen pawn]

ah, cool, jee ke liya?

[little dagger]

haa

:/

[keen pawn]

awesome, good luck.

[little dagger]

phy ne maar di hai

[keen pawn]

Sorry

[rapid stag]

Wait i dont quite understand

[little dagger]

substitute x as 1/t

that should change limits to 0

and then apply

[keen pawn]

OK, @little dagger can help you from here, i'mma dip

[rapid stag]

Like that?

[little dagger]

yk substitution method?

[rapid stag]

Uh yeah? I did change x to 1/t

[little dagger]

you forgot to change limits

[rapid stag]

Wait i forgot the limit goes to zero

[little dagger]

yea

take lcm

[rapid stag]

How

[little dagger]

it would be

[rapid stag]

[little dagger]

1/cos(2t)

it's an angle

like this lcm

[rapid stag]

Wow

[little dagger]

then apply this

[rapid stag]

Ohhhh

[rapid stag]

Why do i get -2

[little dagger]

send ur work

[little dagger]

you cannot reduce like that

[rapid stag]

Oh the 1-2sin²t?

[rapid stag]

Its not supposed to be like that?

Oh wait

[little dagger]

you cannot cancel out like this

[rapid stag]

I lost the (1/t)²

[little dagger]

from num and deno

[rapid stag]

Hm, i mean if limit goes to zero i can cancel out the sine

[rapid stag]

(thats what my teacher said)

[little dagger]

but with (1/t^2) i dont think

do you know sinx/x = 1?

[rapid stag]

Yeah..

[little dagger]

for lim ending to 0

so which gives us

[rapid stag]

Yeah... So thats why i cancel it out

[little dagger]

sin x = x for lim ending to 0

wait wait

[rapid stag]

im sorry i know im dumb

[little dagger]

nono

[rapid stag]

Oh

[little dagger]

i think

[rapid stag]

Because cos 0 is 1

Ohhh

[little dagger]

becuase 1/t^2 you cannot cancel out

[little dagger]

yup

[rapid stag]

Omg thankyou so much

[little dagger]

np

[rapid stag]

Can you break this down for me tho?

[little dagger]

what is

1-1/3

[rapid stag]

2/3

[little dagger]

how you did it

use the same logic here

[rapid stag]

How do i do it

[little dagger]

wait

see

cos (2t) is an

angle (2t)

you cannot seperate them

[rapid stag]

Oh so its supposed to follow wherever cos goes

[little dagger]

yup

they are bff

[rapid stag]

Ohh omg

[little dagger]

same goes

with sin x, cosx, secx, tanx

cotx

cosecx

all the trig ratios

[rapid stag]

Tysmmm

[little dagger]

np

:))

[rapid stag]

Thankyou!

[little dagger]

done

np

[rapid stag]

.close

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[grand rivet]

did i do it right?

[grand rivet]

mode 14

mean approx 13.62

median = 14

The mode is the most appropriate form of average for this distribution because it represents the most common size sold

B

Mode: £160,000 and £165,000 (bimodal)

mean = £158,000

median = £165,000

The median is the most appropriate form of average for this distribution because it is not affected by the extreme value

C

Mode = 30

mean = 19.47

median = 18.5

The median is the most appropriate form of average for this distribution because it is not affected by the extreme values

U can react with ticks and crosses with which is right and wrong if thats easier

sorry for the big question i just wanna make sure i understand it properly

[grand rivet]

<@&286206848099549185>

+close

!close

.close

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[mystic lotus]

Okay no one talk here unless you're actually helping with the question

[distant herald]

if <b> is convergent, then you know that the difference between the values of b_n and b_(n+1) must be getting arbitrarily small for large n

[distant herald]

what does that tell you about how the value of b_n - b_(n+1) behaves for large n?

yeah it gets arbitrarily close to 0

hmm i'm actually not sure if there's some obscure counterexample for a diverging, intuitively the sequence converges to 0, i'm not too sure what that says about the series

[tropic wadi]

@olive holly as I've tried the summation of a_n forms a telescoping series

okay😭

[distant herald]

💀 his approach might actually be helpful, the telescoping part is probably what i missed

[tropic wadi]

I literally spent my 15 mins for nothing

[distant herald]

a_1 + a_2 + a_3 + ... = b_1 - b_2 + b_2 - b_3 + b_3 - b_4 + ...

and you know that b_n converges to 0

since the series converges

so as terms telescope and cancel, the contribution from larger and large b_n vanish

which means a_1 + ... = b_1

so yeah telescoping is def the right approach

[mystic lotus]

Sorry to interrupt

The OP was an alt of a banned user, we've just found out

.close

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[distant herald]

how did you even find that out 😭

[tropic wadi]

💀 and bro wanted me to ban

[tropic wadi]

mods being mods

[distant herald]

he just messaged me and said he was arjunn

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[lilac birch]

.repoen

.reopen

[bronze shuttle]

why is this true? it should be -1

[little dagger]

take lcm

since its in negative power

[bronze shuttle]

what

[little dagger]

first make it to +ve

n^-2x = 1/n^2x

so your numerator will be

(n^2x-1)/n^2x

[bronze shuttle]

yeah i see it now

ty

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[keen pawn]

Notice that $n^{-2x}$ tends to 0

[grizzled pagoda]

🏳🌈f(why am i here )= idk

[bronze shuttle]

yeah they should've wrote it like he said

[vestal hatch]

What if x=0?

[bronze shuttle]

=0

[little dagger]

can solve like this too

[vestal hatch]

which doesn't approach 1

[little dagger]

how

it does

simplify denomintor like that

and you get 1

[vestal hatch]

How does 0 not approach 1?

[little dagger]

oh, i was talkin about diff thing

and you are diff thing

so yea miscomunication

[vestal hatch]

The limit is sign(x)

[little dagger]

.

[vestal hatch]

Yes I'm just confused because the problem is wrong

[amber wasp]

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[vale garnet]

is this right?

[vale garnet]

im not sure

but i think i did everything right

[amber wasp]

@vale garnet Has your question been resolved?

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[burnt haven]

can somebody teach me how to handle a constant

[solemn escarp]

?

[burnt haven]

like i dont undersatnd how they went from the first step to the second

ik the arctan integration

but the sqrt 3

basically

1 / 1 + s^2 would be arctan s

but what if its 1 / 3 + s^2

how do u handle that

[keen pawn]

see, what is the derivative of 1/(1+x^2)?

[burnt haven]

2x / (1+x^2)^2

[burnt haven]

this ^?

[keen pawn]

uh

wait

[tropic wadi]

$\frac{1}{3+s^{2}}=\frac{1}{3}{\cdot}\frac{1}{1+(\frac{s}{\sqrt{3}})^{2}}$

wtf

[keen pawn]

I meant arctan(x)

[burnt haven]

d/dx of arctan(x)

?

[grizzled pagoda]

77²

[burnt haven]

oh

oh yeah

[tropic wadi]

then u-sub for s/sqrt3

[burnt haven]

omg

yeah

im stupid

thanks

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[visual mountain]

How to solve this without knowing the height

[cerulean fossil]

you can use trigonometry to find the height

one sec

https://imgur.com/aKE3d86

x is the height you're looking for, since FG = 9 and AF = GB, you can find the base of one of the right triangles (AF or GB)

[visual mountain]

Is it 6

[cerulean fossil]

AF = GB = 6

[visual mountain]

Yea,

[cerulean fossil]

now you can use the pythagorean theorem or trig in of the right triangles (ADF or CGB) to find x

[visual mountain]

Ok thanks

It’s 8 right?

So a?

[cerulean fossil]

yes

u got it

[visual mountain]

Ok ty

[cerulean fossil]

cheers

[visual mountain]

.close

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[grand rivet]

is the answer to the mean x = 6.5 and the value of a is 2

[tired girder]

What have you done ?

S(4x-1) = 4(S(x)) - 25 = 625 or , 4s(x) = 650 or s(x)/25 = 26/4

S(x)/25 = bar(x)

[tired girder]

X= 6.5 is correct

[grand rivet]

i just put it in

and wored oiut htis

[grand rivet]

thx

[tired girder]

This seems correct too bro

🙂

[grand rivet]

cheers thx

[tired girder]

Glad to help !

[grand rivet]

can i ask u for one more question i wanna make sure i understand that too

[tired girder]

Yeah why not I will try my best

[grand rivet]

ok gimme a min

ok it end up being two questions

[tired girder]

Okk

[grand rivet]

so this one is the height of the rectangle 0.75 cm and x = 15 and for b is the mean approx 26.55 grams

so i used the frequence density formula to get x

and then used that x value back int othe frequency density formula to get the height

[tired girder]

Hm

[tired girder]

That's the methodology

[grand rivet]

i didnt know it was called that i just thought it worked lol

[tired girder]

One moment

[tired girder]

Do you want me to check calculations ?

[grand rivet]

yea cuz then i know if i understand it properly or not

[tired girder]

2x = 3 cm you see

[grand rivet]

this is wat i did

[tired girder]

1-10 frequency height is 3 cm

[tired girder]

Why 2x/10 ?

Are you using another metric ?

[grand rivet]

cuz i thought the frequency was 2x and frequency density is 3cm and class width = 10

[tired girder]

See when the frequency is 2x the height is 3 cm

No we don't need class width to determine the height

[grand rivet]

yea but we need it to find x no?

and we need x to find the height

[tired girder]

We can simply visualise it

In a histogram all rectangles have the same base width

When the frequency is 2x , the height is 3 , * frequency is plotted vertically

So when frequency will be x , it will be 3/2 = 1.5

Your method is completely correct and must be done when we have variable class widths

For this case it's pretty simple

[grand rivet]

ohhhh

faiiirrr

so x= 1.5 and the height = 1.5

[tired girder]

Yeàh

[grand rivet]

ok and now wat bout b

[tired girder]

Lemme see

[grand rivet]

this is wat i got

[tired girder]

For mean we need to consider the class median

For 0-10 length class it will be 5 , for 10-20 it will be 15 like that

Now what we will do is (2x×5+4x×15+...)/(2x+4x+...)

The formula is

Summation(x_i × f_i)/summation(f_i)

[tired girder]

And we can't find x with the given information , we can only determine height

Are you getting me ?

[grand rivet]

i get everything but i am slight confused when it comes to the formula

[tired girder]

Have they given any data like total stones ?

[grand rivet]

all the data they give us is in the screenshot

[tired girder]

Then it doesn't seems possible to find x

Hey

Wait

Wait

[grand rivet]

wait i send the wrong answer i got

V

[tired girder]

I am solving it wrongly

I haven't

Noticed

51-70

The class length is 20

Why didn't you say me brooo 😭😭😭

[grand rivet]

ups sry

i confused myself for a sec lol

mb

[tired girder]

I said for variable length your formula is valid 😭

No mb mb

Ok so we start again

[grand rivet]

= 7567.5

[tired girder]

Yeah this is correct !

[grand rivet]

so that does work then good

this question was very confusing for me when i was doing it lol

[grand rivet]

how bout this one sorry if i am asking alot

[tired girder]

3 = 2x/10

So 2x is basically 30 , which holds good

But we can't consider frequency to be that value

Because if we calculate in another metric

Consider in meter , we will get a different value for x

So , as the question asks , you write 15 , but I hope you understand why it's actually invalid

[grand rivet]

sry i went toilet

[tired girder]

S(x) = -7
S(y) = 35
So this is correct

[tired girder]

This one ^

[grand rivet]

can u react to the one ur talking bout

[tired girder]

Yeah divide next

So s(x) +s(y)/30

I'm extremely sorry for the second question, i didn't notice huh !!

[grand rivet]

so it ends up as this

[tired girder]

Yeah !

[grand rivet]

np ur the biggest help lol i been trying to get help with these questions since yesterday and no one helped lol

[tired girder]

Nah I'm really sry man , it wasted much time !

[grand rivet]

nah ur the goat lol im thankful for helpimg me with ur time

if there is any other questions can i just @ or reply to ur message if u have time?

[tired girder]

Thanks bro !

[tired girder]

Yeah ofcourse

[grand rivet]

aight appreciate it

[tired girder]

Ok cya

[amber wasp]

@grand rivet Has your question been resolved?

[grand rivet]

u there btw i have 2 questions i wanna check with u

[tired girder]

Yeah bro

[grand rivet]

ok w gimme a min

icl this is a simple one b ut i forgot how to a stem leaf diagram

and for this one i just wanna make sure the mean is approx 3.07

the main question i need help with is

[grand rivet]

sor for taking a little while sneding it

[tired girder]

Ok np

[tired girder]

You need to make the stem leaf diagram first

As all are two digit numbers

A vertical plot of 1-6 would work

And make next two columns to incorporate the datas of the units place

For the seperate ones

[grand rivet]

ok that makes sense

[tired girder]

,calc 6+18+15+16+12+7+8+10

[grizzled pagoda]

Result:

92

[tired girder]

,calc 92/30

[grizzled pagoda]

Result:

3.0666666666667

[tired girder]

Correct

[grand rivet]

ok now for the last and the one im most confused about

[tired girder]

You know what's cumulative frequency?

[grand rivet]

not exactly

[tired girder]

You need help with b c or d ?

Or the graph ?

[grand rivet]

the graph

b and c and d i think i can do

[tired girder]

See what cumulative frequency means is we add the previous frequency to it

[grand rivet]

but i do need to check those with u later if possible

[tired girder]

For example ≤100 =200

≤150 = 800

So 100 ≤ x ≤150 = 800-200 = 600

X is number of schools

So in this way we could easily make a frequency distribution from the cumulative frequency distribution by forming classes. But that's not necessary always

Now we will do the graph

It's quite simple as they say pupils frequency to schools graph

This is not the typical histogram

We will consider points here and rough draw it

Pupils on x axis , schools on y axis

On x axis make that distribution as said 2cm = 100 pupils

Now we will consider the centre of class nd plot it at 800 matching the horizontal axis

Are you getting me ?

[tired girder]

Hey there ?

[grand rivet]

yea im here

im kidna getting it

[tired girder]

Wait lemme send one example 1 min

See this

On x axis we will similarly plot number of students

And on Y axis plot the school number maintaining the scale

Then you can form something sort of this

[grand rivet]

hmm ok

so

[tired girder]

A graph is recommended , as your class lengths are variable

[grand rivet]

kinda like this?

[tired girder]

Yeahh

[tired girder]

Are the plots correct?

Idk but this is what you need to do actually

[grand rivet]

i think so

i think i get the general idea

aswell

ok ill be back wih b c and d

cya in abit

[tired girder]

Yeah bye , I gtg bro , I will be on at night you can DM me if you face àny problem

[grand rivet]

aight cya gn

sry for the late response

[amber wasp]

@grand rivet Has your question been resolved?

[tired girder]

Gn bro !

[grand rivet]

+close

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[stoic locust]

.hello

.close hello

[urban jetty]

how did we expand it

[cedar plaza]

can you show the whole expression

[cedar plaza]

they use the last double angle formula

with some rearranging

[urban jetty]

can you elaborate on how we can apply it to 1/4 cos^2 (2x)

[cedar plaza]

add 1, divide by 2, multiply by 1/4

[urban jetty]

ahhh

[amber wasp]

@urban jetty Has your question been resolved?

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[rotund timber]

How can I find solutions where there is no finite 𝑛 or where 𝑥3 and 𝑥4 are unbounded?

<@&286206848099549185>

[fierce burrow]

huh?

i have been called

oh

sorry, im having trouble reading it :/

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@rotund timber Has your question been resolved?

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[rotund timber]

.reopen

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✅

[rotund timber]

<@&286206848099549185>

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@rotund timber Has your question been resolved?

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@rotund timber Has your question been resolved?

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@rotund timber Has your question been resolved?

[twilit blaze]

מה הכוונה? זה נראה לי נכון

[rotund timber]

הצלחתי

זה היה למצוא פתרון כללי

לא הבנתי כל כך כי הם ביקשו ממני למצוא פתרון, וחשבתי שהם רוצים מספר סופי

[twilit blaze]

הבנץי

אז אני סוגר

.close

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[zinc harbor]

is this proof correct? i'm trying to prove a straight line from point a to point b is one of the shortest paths (as in has minimal length, but possibly not unique)

[severe scroll]

first

[blazing stream]

second

[zinc harbor]

sorry for bad latex

[zinc harbor]

probably should have sent photo
thanks!!!!

[severe scroll]

wait what are you trying to say

oh oops

oh yeah for uniqueness do what i said and deleted

[zinc harbor]

was reading then looked away what happened

[severe scroll]

i thought it was wrong

but it’s not

the hint is to use special orthogonal coords and then if your path has any normal component then you can make an inequality

[zinc harbor]

wait so like

[simple hare]

I think you are integrating the derivative which maybe doesn't make sense because you are treating it like a scalar when you should be thinking of the gradient

And you're using FTC on it

For your last step

That's my interpretation of what you wrote, is that correct?

[zinc harbor]

what do you mean with this

wait imma reply to what smay said

[zinc harbor]

like make orthogonal basis with (possibly scaled) b-a and then use that to check if the curve deviates from being straight line?

[severe scroll]

wait i mean coordinates, not just a basis, take a to (0,0) and b to (1,0) with an affine transformation of R^2, is what i mean. the context for this trick is the motto (something like) “homogeneity of R^n lets the geometry be the same everywhere”

you can find the transformation

and then calculate the speed of a curve in those coordinates

[zinc harbor]

oh okay

it seems easier to calculate after transformation

how do you know it's order preserving though

like

[severe scroll]

what do you mean by order preserving

[zinc harbor]

if curve X length =< curve Y, then after transformation that still applies

[simple hare]

I meant that you are trying to do the integral inside the norm but inside the norm you are dealing with the gradient of the function and so I don't think you can do the stuff you are trying to do

[severe scroll]

the length of each curve in this case will be a positive scalar multiple of the original length, prove that yourself

[split kraken]

I saw "HSF" on the help channel, and I was so confused LOL

[simple hare]

Like you're defining an integral which integrates a vector function

[zinc harbor]

i'm pretty sure norm inequalities work for vectors too

[simple hare]

Yes