help-23

[flat frigate]

kalman_filtERIC

[upbeat ginkgo]

n = 0 to 4 of 2n + 1

[white umbra]

okay yeah perfect

now what about

(\frac{u^1}{1} + \frac{u^3}{3} + \frac{u^5}{5} + \frac{u^7}{7} + \dots)

[flat frigate]

kalman_filtERIC

[white umbra]

how would you write that using the sum notation

[upbeat ginkgo]

n= 0 to infinity of u^2n+1/2n+1

[white umbra]

good, perfect

now what about

(\frac{u^1}{1} - \frac{u^3}{3} + \frac{u^5}{5} - \frac{u^7}{7} + \dots)

[flat frigate]

kalman_filtERIC

[white umbra]

so every other one has a minus sign

[upbeat ginkgo]

n = 0 to infinity of (-1)^n u^2n+1/2n+1?

OHHH

[white umbra]

yes! perfect

yessss

[upbeat ginkgo]

THAT'S WHY THEY PUT -1!

caue it's ALTERNATING

[white umbra]

yessssss

so then we got

[\tan^{-1}(u) = \sum_{n=0}^\infty (-1)^n\frac{u^{2n+1}}{2n+1}]

[flat frigate]

kalman_filtERIC

[white umbra]

are you alright with that?

[upbeat ginkgo]

yes!

[white umbra]

woooo

okay now lemme ask you

what about (\tan^{-1}(x^2))

[flat frigate]

kalman_filtERIC

[white umbra]

bc that's what the problem was about

how can we write that in the sum notation

[upbeat ginkgo]

we can just replace it with u right?

[white umbra]

yup

so it'll be

[\tan^{-1}(x^2) = \sum_{n=0}^\infty (-1)^n\frac{(x^2)^{2n+1}}{2n+1}]

[flat frigate]

kalman_filtERIC

[white umbra]

Or, you can simplify with exponent rules

[\tan^{-1}(x^2) = \sum_{n=0}^\infty (-1)^n\frac{x^{4n+2}}{2n+1}]

[flat frigate]

kalman_filtERIC

[upbeat ginkgo]

mhm

[white umbra]

alright

so now the tricky part

well

idk if it's actually that tricky

we're gonna need to integrate this thing

[\int_0^{0.1}\tan^{-1}(x^2),\dd x = \int_0^{0.1}\sum_{n=0}^\infty (-1)^n\frac{x^{4n+2}}{2n+1},\dd x]

[upbeat ginkgo]

so use u sub?

[white umbra]

nah we won't even need u-sub

[upbeat ginkgo]

oh

[white umbra]

oops forgot the dx at the end

[flat frigate]

kalman_filtERIC

[upbeat ginkgo]

wait

gimme a sec

wouldn't it be this?

actually, let me post all my work

[white umbra]

yeah good! that's how you would do it without the sum-notation

how do you know how many terms are enough, though?

[upbeat ginkgo]

btw, I take no credit for it

[white umbra]

to get six decimal places of accuracy

[upbeat ginkgo]

I was following along something

[upbeat ginkgo]

uhh

idk

[white umbra]

haha no worries, that's good practice

[upbeat ginkgo]

that's the issue

should I use desmos?

[white umbra]

that's one way you could do it

you could just add up enough terms until there's no doubt about six decimal places

another way is with "lagrange error bounds", but idk if you've learned about those yet?

basically it tells us the maximum amount of error this approximation has

[upbeat ginkgo]

doesn't sound familiar

whichever method you'd prefer though, i'm cool with

[white umbra]

ah okay

then yeah, adding it up with a calculator is okay

[upbeat ginkgo]

ok

let me plug it in rq

[white umbra]

I'll post a picture of the lagrange error bound formula here for completeness, just in case it rings any bells

[white umbra]

btw the way you would do it with this sum notation is that you would integrate every term in the sum, so the integral of x^(4n+2) becomes x^(4n+3)/(4n+3), and then you plug in x=0.1 and x=0 like you did

[upbeat ginkgo]

this looks like Taylor Series

is it not?

[white umbra]

yes, exactly

it's a method for calculating the maximum error that you get from a taylor series

if you only add up the first few numbers of the series

[upbeat ginkgo]

hmm ok ok

[white umbra]

if you haven't learned it in class though, just ignore it

[upbeat ginkgo]

I'll definitely keep it in mind

[white umbra]

the result of this is
[\begin{split}\int_0^{0.1}\tan^{-1}(x^2),\dd x &= \sum_{n=0}^\infty \left.(-1)^n\frac{x^{4n+3}}{(2n+1)(4n+3)}\right|^{0.1}0\&= \sum{n=0}^\infty (-1)^n\frac{(0.1)^{4n+3}}{(2n+1)(4n+3)}\end{split}]

[flat frigate]

kalman_filtERIC

[white umbra]

so that's another way to write the same thing that you ended up with on the last line here

except using the sum notation

and it gives a general formula for each term in the sum, so you can calculate as many terms as you want without having to redo the whole problem

[upbeat ginkgo]

I see

this method is WAY more efficient

[white umbra]

yeah the tricky part was just trying to write the beginning equation in sum-notation

but if you practice a couple things, then you'll get the hang of it pretty fast

and then integrating it is super easy because every term in the sum is just x^(something), so you just use the power rule to get x^(something + 1)/(something + 1)

this is one of the reasons why taylor series are so useful!

they give super easy approximations to everything

[upbeat ginkgo]

quick question though, where did the 4n+3 come from?

on the top and bottom?

[upbeat ginkgo]

oh nvm

this explains it LOL

mb mb

that makes a LOT of sense

it's all clicking

thank you so much!

I really really appreciate you taking time out of your day to patiently teach me this

https://tenor.com/view/crying-meme-black-guy-cries-sad-man-thank-god-for-my-reefer-hood-news-gif-1799983865423589252

[white umbra]

you're welcome! :)

[upbeat ginkgo]

.close

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[shrewd matrix]

I need help for this differential equation y=x(y')^2+(y'')^3

[shrewd matrix]

I tried and the only solution was x or zero. That's good ?

That's my work. Sorry for french languages

@meager igloo

<@&286206848099549185>

@vernal patio

@white umbra

[safe radish]

@shrewd matrix Has your question been resolved?

[safe radish]

@shrewd matrix Has your question been resolved?

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@shrewd matrix Has your question been resolved?

[cunning pasture]

,w time france

[flat frigate]

Results provided by WolframAlpha

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Requested by anshulyolo121

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[mighty mango]

Can someone conclude with me the derivative of inverse tan function

[mighty mango]

Bc idk where to start

Tan-1(x)=y so tan(y)=x

[rose plume]

implicit differentiation

[mighty mango]

Should i differentiate eith respect to y or x

[mighty mango]

Yeah- ik but whats next

[rose plume]

u need dy/dx

so differentiate both sides wr to x

[vale oriole]

im

[mighty mango]

Just a question bc idk the english terminology, whats short for 1/cos

[vale oriole]

implicit works but this can also be proven using the derivative of inverse functions

[vale oriole]

sec

[mighty mango]

Kk

[mighty mango]

So (sec(y))^2 *dy/dx=1

Dy/dx=1/(sec(y))^2

Isnt that (tan(y))^2

[vale oriole]

there is an identity involving tan^2 and sec^2

[mighty mango]

So… plugging y=tan-1(x)

[vale oriole]

not true, 1/sec^2 = 1/(1/cos^2(x))

[mighty mango]

Cosine?

[vale oriole]

yes

[mighty mango]

Sec is 1/tan right

[vale oriole]

no

sec is 1/cos

[vale oriole]

u even said here

[mighty mango]

Why did u tell me its sec then?!

[mighty mango]

OH

Wait i meant 1/tan

[vale oriole]

that is cot

but i wouldnt focus on that

cuz there is an identity that uses tan^2 and sec^2

[mighty mango]

We were working on tan(y)=x from the start

[vale oriole]

correct

[mighty mango]

Yes adding them =1

[vale oriole]

almost

[mighty mango]

Substracting them-?

[vale oriole]

tan^2 + 1 = sec^2

[mighty mango]

Dy/dx * cot(y)^2=1

[mighty mango]

Oooh right

[mighty mango]

So dy/dx is 1/cot which is- tan

Tan(y)^2

[vale oriole]

no

[mighty mango]

Huh

[vale oriole]

i told u before dy/dx is 1/sec^2 which is cos^2

[mighty mango]

But how?!

Its 1/cor

[vale oriole]

becuase sec^2 is 1/cos^2

[mighty mango]

WAIT

Goddamn it

Im stupid

I dervied tan(y) incorrectly

Ok yes dy/dx=cos(y)

[vale oriole]

cos^2

[mighty mango]

Yes

[vale oriole]

but thats besides the point

because i didnt want u to do this

i want u to use the identity tan^2+1=sec^2

[mighty mango]

So- want me to switch 1/sec^2 into 1/tan^2 +1

[vale oriole]

right

[vale oriole]

.

[mighty mango]

So sqrt(sec^2 -1)

=x

[vale oriole]

...

[mighty mango]

Idk what u want me to do

[vale oriole]

tan(y)=x

what is tan^2(y)?

[mighty mango]

Aha

X^2

[vale oriole]

right

[mighty mango]

So x^2=sec^2 -1

[vale oriole]

no, we have already solved dy/dx

remember that our derivative needs to be in terms of x

1/tan^2(y)+1 is our derivative

and we just worked out that tan^2(y) =x^2

therefore the derivative is 1/x^2+1

[mighty mango]

Aha

Is that it

[vale oriole]

yes]

[mighty mango]

Damn

Okay ty

.close

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[split fulcrum]

not sure where to start

[desert pasture]

11 marks ? 💀

[vale oriole]

theres multiple parts

[desert pasture]

ah

[wanton agate]

Because O(4,5) is the midpoint of AB(as the centre of the circle) a) is obvious

[vale oriole]

note that since A and B are on the circumference of the circle, therefore the center of the circle is the midpoint of AB

therefore we know the midpoints of their x coordinates must equal the x coord of the center and likewise for the y coordinates

better than giving him obscure hints

[safe radish]

@split fulcrum Has your question been resolved?

[vale oriole]

not gonna argue with you, I personally tutor someone who takes this course, some people learn by demonstration, and question 29 is one of the very last questions on the paper which is going to be difficult for someone who takes the course so I think its best to provide a fair bit of help for someone trying to answer this.

aight fine by me, for someone who is clearly older than me, ur acting pretty immature

[split fulcrum]

I’m back

Sorry was making food 💀

[vale oriole]

right, sorry for this mess

idk whats his problem

[split fulcrum]

Lemme read up lol hold on

[split fulcrum]

Sorry could you break this up a bit circles confuse me lol

Yeah

[vale oriole]

right, so a midpoint is exactly half way between any 2 points, so that means that the x coordinate of the midpoint is halfway between the x coordinates of A and B since A and B are points on the circumference of the circle, their midpoint must be the center of the circle

[split fulcrum]

Right so I see that the midpoint of AB must be the centre of the circle but how do we find a and b using this?

[vale oriole]

<@&268886789983436800>

[wanton agate]

Consider that because the midpoint of AB is the centre of the circle, the horizontal distance(difference of x coordinates) from A to the centre and from B to the centre is equal

[safe radish]

@split fulcrum Has your question been resolved?

[split fulcrum]

.close

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[tender solar]

help pls

[covert yoke]

!da2a

[safe radish]

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

[covert yoke]

Also leading with help means that your actual question doesn't get pinned in the channel 😉

[tender solar]

consider a covergent sequence $(a_n)_{n \in \mathbb{R}}$ converging to some a

KKomrade

[covert yoke]

o7

[flat frigate]

reg

[gusty trench]

do you mean that a_n is in R and n is in N? otherwise you're indexing your sequence with R?

[covert yoke]

As written it doesn't make much sense

It seems to be indexed by R, but there is no smallest R, so no beginning of the sequence

Which makes it more like a function really

Maybe they intended something like

$(a_n \in \mathbb{R})_n$

[flat frigate]

OmnipotentEntity

[covert yoke]

But messed up the typesetting and didn't find it before publication?

[tender solar]

now if we take some $\epsilon_1 > \epsilon_2 > 0$ then there are $R_1, R_2 \in \mathbb{R}$ respectively such that the distance between the an and a is less than the respective $\epsilon$ for n > the respective R

[flat frigate]

reg

[tender solar]

aa i just want to index w some uncountable set

maybe [0,1]

[covert yoke]

You can index with an uncountable set

But you lose sequences

[tender solar]

function* ?

[covert yoke]

Exactly

A function can be thought of kinda sorta like a "sequence indexed by the reals"

[tender solar]

my question is does this imply $R_2 \ge R_1$

[covert yoke]

\ge

[flat frigate]

reg

[tender solar]

if so how

[covert yoke]

Assume that R_1 < R_2 and you get a contradiction pretty quickly

[tender solar]

dym greater than

[covert yoke]

Oh actually you don't

Because you didn't specify tight bounds

Ok so

Here's an example

[tender solar]

what is this

[covert yoke]

Let's say we have the function/sequence tanh(x)

This has a limit as x->inf of pi/2

We can choose two epsilon, for concreteness we can choose 0.1 and 0.01

ε1 = 0.1, ε2 = 0.01

Now the question is, can I choose R1 such that R1 > R2?

Yes.

I can choose R2 to satisfy the inequality

And then choose R1 larger

Because any R bigger than arctanh(pi/2 - 0.1) satisfies the first

[tender solar]

R2 should be bigger if ε2 is smaller no?

[covert yoke]

So R2 can be any value provided it is large enough

Let R2* be the inf of this set

So R2 is in the set (R2*, inf)

Similarly, R1 is in the set (R1*, inf)

Notice that while R1* and R2* follow the rules you want

We don't have to be conservative in our choice of Rn

We can choose any R1 or R2 in this set, so we can choose any ordering to our R1 and R2

[tender solar]

yess i mean the inf

why should they follow

it makes sense but trying how to prove it

[covert yoke]

inf standing for Infimum

[tender solar]

for countable set i put n = R1+1 and done

[tender solar]

yes

[covert yoke]

Sorry just noticed I used inf for infinity as well

[tender solar]

no i mean infimum

[covert yoke]

So I felt I should disambiguate

[tender solar]

[covert yoke]

Ok, then you should specify this, and then you can assume the opposite for the purpose of contradiction.

Then the proof is pretty straightforward.

If R1* is larger than R2* then this implies that |a - f(R1)| < ε1 is true for all values of R1 larger than R1*, but for any R smaller than R1* there exists some Q larger than R such that |a - f(Q)| >= ε1.

[tender solar]

aaaa

but that can't be because

infimum

so true

[covert yoke]

If we choose R to be between R1* and R2* then Q is also between them

Which means that Q is after R2* and provides a value larger than R2* such that |a - f(Q)| > ε1 > ε2

But by definition R2* is the smallest value of R2 such that |a - f(R)| > ε2 holds for all R > R2*

So we have a contradiction

[tender solar]

by Q you mean between an R (smaller than R1 *) and R1 *?

[covert yoke]

Right so if R1* is the Infimum of all Rs to where this holds, then for every R ≤ R1* there is some R1* ≥ Q ≥ R such that Q differs by more than the epsilon.

[tender solar]

wait even if R2* isn't an infimum it's fine right, we just want R1 * to be the infimum so that Q less than it would mean the distance can be greater

[covert yoke]

R2* doesn't need to be the Infimum, no.

We just need R1* to be the Infimum, and R1* > R2 for some R2 > R2*

Then we have the contradiction.

Because we can find a Q > R2 where the inequality, which should hold for all R > R2, doesn't hold

[tender solar]

yuss kinda took inf for granted here before

got it ty

also tinkaton

[covert yoke]

Yesssss

[safe radish]

@tender solar Has your question been resolved?

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[light gull]

Hii

[light gull]

I need some help here

Heyyy

Hayo

Hiyo

Hummm

Is spamming okay ?

[glass carbon]

Have you tried multiplying by conjugate?

Or l'Hospital if you know

[light gull]

I know hospital but my teacher always tell me to avoid it

Dou think conjugate gonna worj

[glass carbon]

It's a good habit.

[light gull]

I mean i tried but i got too confused

I guess there is a trick

Because my teacher always give us like chose and have a tricky way to solve

@glass carbon

[glass carbon]

well, let's see what you did

[flat frigate]

Modus

[safe radish]

@light gull Has your question been resolved?

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[strange glade]

Question C

[strange glade]

Where did I go wrong

the answer

[lime dust]

Second step is wrong

[strange glade]

what is wrong with the second step?

[lime dust]

x^2 +5x/2 is not equal to (x+5/4)^2

You have to subtract 25/16 to that to be equal

[strange glade]

Ok thanks

.close

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[buoyant solstice]

We need to show with induction, that this term is correct for the nth derivative of sqrt x

[buoyant solstice]

I have no clue in the Induction step (when k -> k+1) how to solve the part with the products of (2j-1)

[faint seal]

what is f(x)?

[buoyant solstice]

sqrt(x)

[faint seal]

I see

[faint seal]

another term just gets added to the product

$f^{(k)}(x)=\frac{(-1)^{k+1}}{2^k}\prod_{j=1}^{k-1}(2j-1)\cdot x^{-\frac{2k-1}{2}}$

[flat frigate]

kheerii

[faint seal]

assume this as our induction hypothesis

assue this is true for some k, then we wish to prove it for k+1

[buoyant solstice]

yes

[faint seal]

differentiate both sides of this

[buoyant solstice]

f^{(k+1)}(x) = \frac{d}{dx} \left( \frac{(-1)^{k+1}}{2^{k}}\prod^{k-1}_{j=1}(2j - 1) \frac{1}{\sqrt{x^{2k-1}}} \right)
\end{align*}

$f^{(k+1)}(x) = \frac{d}{dx} \left( \frac{(-1)^{k+1}}{2^{k}}\prod^{k-1}_{j=1}(2j - 1) \frac{1}{\sqrt{x^{2k-1}}} \right)$

[flat frigate]

Ant1m0n

[faint seal]

yeah

[buoyant solstice]

so we get to this point

[faint seal]

$f^{(k+1)}(x)=\frac{(-1)^{k+1}}{2^k}\cdot\left(-\frac1{2}\right)\prod_{j=1}^{k-1}(2j-1)\cdot(2k-1)\cdot x^{-\frac{2k-3}{2}}$

[flat frigate]

kheerii

[faint seal]

do you see how I got that?

[buoyant solstice]

give me a second

[faint seal]

I just rearranged a few things

[buoyant solstice]

ah ok you didnt derive you just switched some parts

[faint seal]

I did differentiate

and THEN i switched some parts

[buoyant solstice]

ok ah i see and then we get to the same part as if we just added k+1 "manually"

so the solution is to derive the first function of which we assumed that it is correct

[faint seal]

what?

[buoyant solstice]

if im not mistaken this equals

[buoyant solstice]

this

[faint seal]

yeah it does

I just did the differentiation

and this matches your induction hypothesis (why?)

[buoyant solstice]

because i just showed that for k+1 (the next derivative) i can either manually add one onto k or just derive the first function

i hope you understand what im trying to say

[faint seal]

yeah, your english is not the best but I did understand what you said

[buoyant solstice]

its hard to explain in english for me im sorry

but thank you very much

but i have one last question, why didnt anything "happen" to the products of (2j-1) ?

!quit

.close

[safe radish]

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[wet shadow]

Hi I was doing a question labeled "Give the vector 225 m/s [35.0°W of S], calculate its x compnentet." and got the awnser 146m/s and wanted to make sure I was doing it right

[safe radish]

@wet shadow Has your question been resolved?

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[noble flicker]

This is basically giving you T and asking four fourier transform of T'

i am not sure how to find T'

delta4(t+1) can be written as delta(t+1-4) = delta(t-3)

but that t^2 confuses me

[stoic dune]

You shouldn't find T'. You don't need it. Instead, take advantage of a Fourier transform property

[safe radish]

@noble flicker Has your question been resolved?

[noble flicker]

Which one i already looked at all of them

The second to last?

I am still not sure how to find F(t^2d(t-3) @stoic dune

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[lilac vapor]

I'm using DeMoivre's theorum to find an indicated power, and the answer must be in rectangular form. I understand how to solve the majority of the problem. I'm just not understanding how they got 0, and 1 here.

[lilac vapor]

cos(-33/2) in degree mode gives me 0.95881

in radians -0.702

so it's clear to me that they're not inputting these into a calculator. I'm just missing how they're getting 0 and 1

[final halo]

-33PI/2

[lilac vapor]

=-51.836

still totally different

asfjiosf now I'm missing the cos

[final halo]

in rads

[lilac vapor]

still the calculator is not helpful it is giving 1.7e-12

[final halo]

thats the calculator giving up calculating how small it is because its actually 0

so probably use a better calc

[lilac vapor]

ti-84 plus ce not good enough for a trig class?

[final halo]

well it seems not unless you can tell when the answer should be zero but your calc cant handle it

,w cos(-33pi/2)

[flat frigate]

Results provided by WolframAlpha

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

Requested by icaird

[lilac vapor]

I think next time I see 1.7e-12 stuff I'll think 0 now. it's worked for everything else this class

[final halo]

but you could have also calculated this by hand by adding multiple of two pi onto -33pi/2 until you get to a value you know the cos of

[lilac vapor]

but that is helpful so thank you

also I did not realize it had to be in rads

[final halo]

if you see pi in an angle argument it 99% of the t ime implies theyre using rad

[lilac vapor]

make sense

.close

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[topaz jolt]

I need help with number seven, nine, 10, 11, and 12

[red delta]

7. let the initial amount of candy be x

She took 10

Remaining:x-10

Remaining/4 =2

(X-10)/4=2

Find x

[topaz jolt]

Oh hi

Yo, so one thing about me is that I’m a visual learner and I won’t understand it if you just explain it

[uncut juniper]

i have x candy here

[topaz jolt]

Bro is an amputee

Let me just read what you said

I’ll try to understand

[frozen veldt]

We could also solve the problem in a slightly more creative way by doing the steps in reverse

[topaz jolt]

I’m just trying to get it done

Yo David, how would you write all of that in a single problem?

So I guess all of the problems have to look similar to number eight

That’s how my teacher wants me to do it

Two step equations

[red delta]

Attempt from where I stopped

[topaz jolt]

It’s just hard to do it like that because I need to be shown things, I can’t just be told how

I’m a visual learner

Even though you written it down, I still can’t understand it

[red delta]

😣

[topaz jolt]

Like I could have all of the steps and I don’t know how to implement them onto paper is what I’m trying to say

Nothing I can control, It’s just how my brain is.

[frozen veldt]

What really happened:

1. There's some amount of candy that we don't know
2. We take out 10 pieces
3. Divide the amount of candy in 4 (and give that amount to each child)
4. We find that each child got 2 pieces of candy

Doing the steps in reverse

1. One child has two pieces of candy
2. Multiply this by 4 to get the total amount of candy that got handed out, i.e. 8
3. Add 10 pieces of candy to get 18
4. There's 18 pieces of candy on the table

[topaz jolt]

I think you’re supposed to do that in two steps

Wait I’ll just read it

Wait, is that two steps?

[frozen veldt]

I wish I could turn the whole thing into an animatic

[topaz jolt]

The first 4

[topaz jolt]

Is there anyway you could try to do it on paper and take a picture?

So I’ll have an idea

I know it sounds like I’m just getting the answer, but I’m sure the other ones are similar to that and I can implement that into the other problems

I hope there is similar. I don’t really know much about the problems. I’ve been sitting here for hours.

I’m just hard to work with

That I do apologize for

[frozen veldt]

I would first try to understand it by physically seeing the situation unfold and only then would I translate it to math language. But since I can't come over to your house and act it out I'll try to jump straight to scary math language

There's some amount of candy that we don't know, let's call it x

Then we take out 10 pieces, so we have x - 10 pieces of candy left

Then we divide that amount of candy among 4 children, so we have (x - 10) / 4 pieces of candy for each child

We know that the amount of candy that each child got was 2, so therefore (x - 10) / 4 = 2

The equation is formed step-by-step by following very carefully what Aliyah did

[topaz jolt]

Sorry, I’m still not understanding

[frozen veldt]

Let's say there's 18 pieces of candy on the table

there could be more, there could be less, we don't know

but let's just say there's 18 and see what would happen

[topaz jolt]

So before you say anything else do I just write 18 right now?

On the paper?

[frozen veldt]

you can write it on an unimportant scratch paper

because writing stuff down is good

[topaz jolt]

I’m just gonna write it down on the paper because I have to show my work

That’s the problem. I know the answer. I just don’t know how to get there

[frozen veldt]

but writing stuff down without knowing what's about to happen means you might have to erase stuff later

[topaz jolt]

I can erase

All right, so I have 18 written down

[frozen veldt]

okay

Now if you take out 10 pieces, how do you describe that mathematically?

[topaz jolt]

18-10?

[frozen veldt]

yes very good

[topaz jolt]

So I have 18-10 on my paper so far

[frozen veldt]

so now, instead of writing down the result, treat 18-10 as a number on its own

[topaz jolt]

Ok

[frozen veldt]

pretend you don't know how to subtract 18-10

if we added five candy to the pile, we could still write 18-10+5

to write down how much candy we have

even if we don't know how to carry out the computation

[topaz jolt]

Are you supposed to do an equals something after this because this looks familiar?

[frozen veldt]

well, instead of adding 5 candy to the pile, if we recall the instructions, we actually divide the amount of candy in 4

[frozen veldt]

let's not have an equals sign yet

we're just forming some kind of expression

[topaz jolt]

Ok

So I have 18-10+5

Like you said

[frozen veldt]

So what happened was

1. There's some amount of candy that we don't know
2. We take out 10 pieces
   3) Divide the amount of candy in 4 (and give that amount to each child)
3. We find that each child got 2 pieces of candy

The adding five candy was just an example, that never actually happened in the story

[topaz jolt]

Wait, divide?

OK now I’m confused because I don’t know how to divide from 18-10+5

Am I supposed to erase that?

[frozen veldt]

well let's think about that

in mathematics, if you have lots of numbers and symbols and stuff, but you see it as one big thing, you can put parenthesis around it and do something to it

So if you have 18-10+5 candy on the table and you want to divide that by 4, then you could write (18-10+5)/4

And the idea is that (18-10+5) is seen as one big collection of candy that you divide by 4

[topaz jolt]

Like this?

[frozen veldt]

yess exactly

very good

Could you describe verbally what that expression means in terms of candy?

[topaz jolt]

I can’t

[frozen veldt]

that's okay

we interpret 18 as being 18 candy on the table

can you try to guess what 18-10 might mean?

like how you could interpret that

[topaz jolt]

You just do 18-8?

Which is 8

[frozen veldt]

18-8 is 10, isn't it?

Or what do you mean?

ohh ok

I see what you mean

[topaz jolt]

Your right

I made a mistake. I was just thinking incorrectly.

Thinking fast

Yo, wait a minute

[frozen veldt]

well you said 18-10 is 8 and that's good because that's true

[topaz jolt]

That was AutoCorrect

My keyboard acted up

I meant to say fast, but I was trying to type then it wasn’t working then that came up

[frozen veldt]

that's okay

[topaz jolt]

I did not mean to call you fat ass

[topaz jolt]

Ok

Thank you

[topaz jolt]

Yes, I was thinking 18-10

[frozen veldt]

yess

[topaz jolt]

Because I had a memory of that and I thought that’s what I saw

[frozen veldt]

You know how to compute 18-10 but do you know the interpretation of what that subtraction really means?

[topaz jolt]

I do not

[frozen veldt]

it's very important to be able to connect math to things and actions in the real world

because humans are not naturally good at math but we are naturally good at sensing the real world

and also lots of math problems in school involve a verbal real world description that you have to write in the language of math

[topaz jolt]

Wait, I think I did this before

These problems I just don’t know how to remember it, but I have the worksheet on how I did it in the classroom

[frozen veldt]

you can interpret 18-10 as an action where you start with 18 candy and you take away 10 candy and the result, the number 18-10, is how many you're left with

[topaz jolt]

8

[frozen veldt]

yes, the result is of course 8

but the result in this case is less important than the visual in your head

[topaz jolt]

Eight is the answer for number seven?

[frozen veldt]

can you verify that?

do you know how you could verify that?

[topaz jolt]

18-10=8

I don’t know what you mean by verify

[frozen veldt]

well it's certainly true that 18-10=8

but is it true that Aliyah started with 8 candy

that's the problem we're trying to solve

[topaz jolt]

I’m sorry I’m just not understanding anything

I still only got 18-10+5/4

[frozen veldt]

I think you're doing a great job

you're just very eager to solve the problem

while I'm trying to teach you mathematical thinking

[topaz jolt]

I’ve just been sitting here for hours and this is just consuming my day, I’m not trying to ramble on. I’m just saying. Sorry that sounds like I’m just complaining.

I just didn’t do so good this year and this is summer school

Had a tutor, but didn’t end out so well

She was just busy a lot of days

Sorry for just rambling on

[frozen veldt]

Well I understand your frustration but paradoxically if you try less to solve the problem and try more to just have fun with the math then you might end up learning useful skills that will actually help you solve more problems faster in the long run

[topaz jolt]

And the tutor wasn’t that great because I still didn’t understand a lot of stuff

I was kind of having fun with the math then I just got stuck for hours and hours

It’s just so hard trying to learn it through text

I hate how my brain is like that

[frozen veldt]

Do you have access to paper where you could scribble down some notes that you don't have to erase later?

[topaz jolt]

Yeah

[frozen veldt]

I think that would be helpful

[topaz jolt]

It’s just I wish I could go back in the classroom because I have all of this on a different piece of paper because we did all of these problems

Many days ago

I don’t know why we’re doing it again

[frozen veldt]

Do you think you would understand the solution if you saw it?

[topaz jolt]

What do you mean?

[frozen veldt]

like, they're not giving you these problems because they want you to produce the right symbols that a teacher wants to see, they're giving you these problems because

1. these are problems that can be solved

2. these are descriptions of actions that someone in the real world might do that you can describe using numbers and symbols

3. they want you to both improve as a problem solver and especially they want you to learn to describe things that someone in the real world might do using the language of numbers and symbols

So if you think the adults are stupid and this is all useless and you just want to enjoy your summer then my honest response is that the skill of writing stuff down in the language of numbers and symbols turns out to be incredibly useful in life and there is a reason for why they're teaching you these things, so I would re-evaluate your position

And if you've never really thought about why you're doing these things, then maybe now you have

And my question to you is what do you think would help you understand how numbers and symbols describe the real world

Because if you think seeing the full solutions actually helps you then it would take me about 30 seconds to give you the solutions to all these problems

[topaz jolt]

I don’t think adults are stupid

Your not

[frozen veldt]

I can give you the full solutions if you'd like

it might be against the server rules or guidelines but I can do it, I don't care

whatever you think is helpful

[topaz jolt]

Do whatever you want

If it’s against the rules, just do it in DM

[frozen veldt]

all I'm saying is that math is not about symbols, it's about connecting symbols to physical actions that your brain understands

[topaz jolt]

Wait, are you saying giving me the answers? I mean, I would find the answers and figured out tomorrow anyways.

Wait, not just the answers I mean how to get them

Is that what you’re trying to say?

[frozen veldt]

I mean ultimately I just want to help you

[topaz jolt]

I’m sure he’ll explain it tomorrow and then it’ll finally click

[topaz jolt]

I appreciate that

[frozen veldt]

for what it's worth, I think so too

[topaz jolt]

I appreciate you being dedicated to helping someone like me

[frozen veldt]

you're very lucky to have a tutor

[topaz jolt]

You?

Well, I had a tutor, but not anymore

[frozen veldt]

well you're in summerschool or something

[topaz jolt]

Just too many problems, my dad having too many problems with the tutor

It’s a long story

My dad didn’t like the place

But that tutor just always made me feel stressed, I’m not talking you down on her. I’m just saying from my experience.

Just had an attitude

[frozen veldt]

I think you have lots of potential but you could use some more self-confidence. And you should start loving dead-ends and doing useless things and using lots of scratchpaper and getting stuck, because that's what math is all about

[topaz jolt]

For one I’m just trying to write down the problem and I know she can clearly see what I’m writing but she says no erase it has to be “neat”

She knows what I’m trying to write down. It just makes it harder for me.

[frozen veldt]

She's wrong

Math should not be neat

[topaz jolt]

Exactly

[frozen veldt]

for the vast majority of the time it should be messy and indecipherable to everyone but you, until it clicks in your brain, and then you give out the "clean" argument

[topaz jolt]

She’s talking about you have to write an = with the spacing in the exact way she wants me to

Math is not neat, my teacher told me the people that are good at math have bad handwriting

I have bad handwriting. I just don’t know everything about math.

I’m good at math and I’m dedicated to it when I actually know what I’m doing

I was doing completely fine before these

And a way she taught me was I need to solve it on my own and have her solve it and compare answers but in reality I never know what I’m doing and I always get it wrong and then she just tells me the answer

That never helps

She always ends up, just telling me answers

That’s not what a tutor is supposed to do

Anyways, I gotta stop babbling

[frozen veldt]

It's very interesting to hear about your experience

and I'm sorry that the tutoring didn't work out too well

[topaz jolt]

It’s alright

I’ve been doing fine with everything until now

I haven’t been needing her help

But now I’m just stuck and I’ve been stuck for three hours

I just wish you were here in real life so you could just show me one step at a time and have me write it down because that’s how I learn

It’s like a foreign language when it’s just through text

[frozen veldt]

still waiting for the scientists to invent teleportation

[topaz jolt]

I can’t visualize what I need to do through my head

[topaz jolt]

Same

I can tell you would make a great teacher, but the only reason why we’re not getting anywhere is because of my learning style

You’re great at teaching. I’m just not great at understanding through text

That’s why it’s taking a while

[frozen veldt]

You're a great student because I can see that you want to learn

[topaz jolt]

I do, I still just want to get this done because that’s what a teenagers mindset is but I still want to know how to do it

[frozen veldt]

Would you want to try a simpler problem that I'll try to make a little more visual?

[topaz jolt]

I want to know how to do it because I can’t just put the answer and call a day. He knows that I could just search it up so the grade is work, not the solution

[topaz jolt]

I’ll see if that’ll help

[frozen veldt]

Okay. I have a mystery box here with some of amount of dots

???
???
???

Now I'll add in 3 dots. Here's what my box looks like right now:

. . .
. . . .
. . . .

[topaz jolt]

No, that’s part of it

[frozen veldt]

<@&268886789983436800>

[white umbra]

Banned them

[frozen veldt]

thanks

[topaz jolt]

Three-year-olds can’t even do that like, what is this guy talking about?

[stuck yew]

💀

[frozen veldt]

just a troll

[white umbra]

They're just trolling, ignore them; they're gone now

[topaz jolt]

Ik but still

Anyways

[frozen veldt]

Now my question is. How many dots did I have in my mystery box originally?

(EDIT: yeah we can move into DMs if you'd prefer.)

(EDIT 2: we moved to DMs)

[safe radish]

@topaz jolt Has your question been resolved?

[safe radish]

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[modest plaza]

guys how do i go abouts solving this

[safe radish]

Please don't occupy multiple help channels.

@modest plaza Has your question been resolved?

[safe radish]

@modest plaza Has your question been resolved?

[modest plaza]

.close

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@thin dirge Has your question been resolved?

[safe radish]

@thin dirge Has your question been resolved?

[safe radish]

@thin dirge Has your question been resolved?

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[round hill]

yo someone pls solve it

@raven vessel

pls

[quick crater]

!15m

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cloud citrus]

Try drawing lines to make similar triangles

[round hill]

can i get the answer

[quick crater]

!noans

[safe radish]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[round hill]

Fuck you

[left gyro]

lmao

[round hill]

dog yall never helped me

[safe radish]

@round hill Has your question been resolved?

[safe radish]

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[somber cape]

I'm having trouble understanding why the gradient points in the direction of the greatest increase in height for a point, given that the gradient is Fx + Fy

[somber cape]

So if I have a point

let me try drawing it first and making sense of it

Given this contour map and the purple point

ive drawn the direction of the partial derivative in the x and y direction

and then the gradient would be in the direction of them added right

so the gradient tells us the direction of greatest increase in height

idk if im confusing something but wouldn't Fy have the greatest increase in height for that point?

my understanding must be wrong somewhere and im not sure where

[safe radish]

@somber cape Has your question been resolved?

[safe radish]

@somber cape Has your question been resolved?

[safe radish]

@somber cape Has your question been resolved?

[safe radish]

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[lean otter]

Anyone ?

I can not find any counter examples

[atomic pebble]

how about

sqrt(x) and x^2 ?

[lean otter]

The f•g is uniformly continuous

[atomic pebble]

oh sorry wait um

so sqrt(x) is uniformly continuous

[lean otter]

Don't know

[atomic pebble]

it is

but lets find something else instead of x^2

[lean otter]

The composition is f•g(x) = x

[long oracle]

because im pretty sure the statement is false

try and prove it

[lean otter]

Okay so I need to prove the statement

[long oracle]

if youre unsure

[long oracle]

wait, which statement? It's false though

However what is true, is that the composition is always uniformly continuous; that's not the statment in your question

[lean otter]

The negation

[long oracle]

Yeah

in such case, yeah try to prove the negation of the statment

[lean otter]

There is a powercut. I will come back later

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

!resolved

[grim plover]

.close

[safe radish]

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[sand tree]

why 4(3-5x^3)^3 exists if there's no dy/du ?

[covert yoke]

I don't see u or du on this board?

Also d/dx(2+3x^(-1)) isn't -3

[sand tree]

idk how to name it, the and said there's 4(3-5x^3)^3

[covert yoke]

Ah

Ok, so one way you can define the product rule is by setting one of the two functions f and g and name them as variables u and v

So dy/dx = u dy/dv + v dy/du if x = uv

[sand tree]

why it's 0 + (-1)..... and not 0 * (-1)......

[covert yoke]

That's part of d/dx(2 + 3x^(-1))

This is equal to d/dx(2) + d/dx(3x^(-1))

And d/dx(2) is 0

[sand tree]

like 3(2-4) = 3(2) + 3(-4)

[covert yoke]

Sorta yeah, but it only works with so-called "linear operators".

The derivative is a linear operator.

@sand tree ^

Anyway, I need to go afk. Best of luck!

[sand tree]

.close

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[jagged crystal]

In a bag of 10 black balls and 5 white balls, you pick up 3 and keep 1 back in the bag. What's the probability of both being different colours?

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<@&286206848099549185>

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[wooden remnant]

I tried it, couldn't solve further than first substituting a+x² as u and then later U as a²cos²x

[lean otter]

Ok

Can you try something else?

Can you put x=atanu?

[wooden remnant]

Okay thank you

I got it

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[barren bronze]

hey understand this is physics but i figured its math too. if you guys think its inappropriate ill remove it

[barren bronze]

need help with all the questions

[lean otter]

Did you split the force vector into it's components?

[barren bronze]

i dont really know what that means sry, can u explain?

[lean otter]

2 min

We just discussed it above?

[barren bronze]

ok so Fv is gravity right and Fh is the pushing?

[lean otter]

Say F is the resultant of vectors Fv and Fh

[lean otter]

No

[barren bronze]

ya using Pythagoras right?

[lean otter]

Yep!

So what do think Fv would be?

[barren bronze]

Sinus of F?

Or F Sin 45

[lean otter]

I think you mean F sin(theta)
Never heard of the word sinus

[lean otter]

Correct

[barren bronze]

ya exactly

[lean otter]

And Fh ?

[barren bronze]

Fh is F cos of theta

[lean otter]

Yes

Now you have the components of F

Draw them

[barren bronze]

but we dont know F ?

[lean otter]

Let's just keep it as F

We will find it soon

Do you know what a Free body diagram is?

[barren bronze]

ice read it but dont really understand

[lean otter]

It's a figure representing all the forces acting on a body

[barren bronze]

Something like this?

[lean otter]

Here you have the applied forces F,and the weight of the body

[lean otter]

Yes

But rather than F , represent it's components

[barren bronze]

how we know that?

Is it Fsin ^2 + F Cos ^2?

[lean otter]

We just discussed it above?

[barren bronze]

ya my bad Fv and Fh

[lean otter]

Yes

[barren bronze]

So the line parralel to g is Fh?

[lean otter]

Are you sure,think again.

Fh is directed along x axis while g is directed along -y

Nvm

[lean otter]

Which line are you talking about?

[barren bronze]

Like this

or did i meess up?

[lean otter]

Yeah

Its wrong

[lean otter]

You do get this right?

[barren bronze]

yes sort of

[lean otter]

Okay

Try drawing the force due to gravity here

[barren bronze]

so i draw like picture?

[lean otter]

That would do too

[barren bronze]

,rotate

[barren bronze]

(Ft for total )

[lean otter]

Where is the force due to gravity here?

[barren bronze]

Isnt that Fv?

[lean otter]

No

Fv would be the vertical component of F

[barren bronze]

,rotate

[lean otter]

Say you have a box
You are pushing it from above with force Fv then
Would Fv be equal to the force due to gravity?

[lean otter]

Correct

Now

The question says "pushed across with constant speed "
What does this statement tell you about it's acceleration and force

[barren bronze]

we can use equations of motion right? Bwcause acceleration is uniform

[lean otter]

Horizontal force*

[lean otter]

Read the statement again

It is not the acceleration which is uniform

[barren bronze]

Velocity

[lean otter]

Yes

So acceleration would be?

[barren bronze]

Not uniform or velocity / timee

[lean otter]

No

We have acceleration as difference in velocity/difference in time

[barren bronze]

Oh yes delta v/ delta t

[lean otter]

Since velocity is constant difference would be 0 thud giving you the acceleration of the body as 0

Agreed?

[barren bronze]

Yes

[lean otter]

Okay,before we proceed any further
I forgot something

[lean otter]

You should represent the direction of normal force too

[barren bronze]

can we do that? i mean isnt normal force on same place as Fv?

[lean otter]

Wdym "same place"?

[barren bronze]

its the same quantity as mg but opposite and goes straight up

[lean otter]

No

[lean otter]

This would be the case when no other vertical force is acting on the body

But that's not what is happening here

[barren bronze]

does it go sideways to the top right?

[lean otter]

We have a vertical force Fv

[lean otter]

Normal force is always perpendicular to the point of contact Between the 2 objects

In this case the ground and the box

[lean otter]

So what is the direction of N?

,rotate

[barren bronze]

it goes up atleast😅

nvm its prolly wtong

[lean otter]

Well,?

[barren bronze]

if it is perpendicular wouldnt that go the the side?

[lean otter]

The point/ line of contact BTW the box and the ground

[barren bronze]

Under Fv?

[lean otter]

It's this

[barren bronze]

oh

[lean otter]

So what the perpendicular dicular direction of this line?

[barren bronze]

to the x axis

[lean otter]

Brb

[barren bronze]

or to the right

[barren bronze]

ok

[lean otter]

This itself is the x axis

How can a line perpendicular to it be x axis itself?

[lean otter]

No

[barren bronze]

true

[lean otter]

Well it's y axis

[lean otter]

Now redraw this

And forget about F since you have mentioned it's components

[lean otter]

...

[lean otter]

.

[barren bronze]

Damm im very bad at this

[lean otter]

It's alright

My way to expressing on how to solve it is quite bad

[barren bronze]

no i think its the way ur supposed to, but tell me next step

[lean otter]

Did you change this?

If yes send the pic

[barren bronze]

no how do i do that?

I put N up right as Y?

[lean otter]

Yes

[lean otter]

Why did you change the directions of Fv and Fh ?

[lean otter]

They are correct over here

[barren bronze]

oh i didnt realise i changed them

[lean otter]

You are presuming that only one force can exist along a particular direction

[lean otter]

If I am right about this

Then your presumption is wrong

[barren bronze]

i guess i am wrong

or i think

[lean otter]

Well have you changed your FBD ?

[barren bronze]

was the figure right? But the Fv and Fh wrong spots?

[lean otter]

Wrong directions, yes

[barren bronze]

in that case i changed it by switching Fv and fh

[lean otter]

Pic

[barren bronze]

so what nect

[lean otter]

This is the correct FBD

[lean otter]

This is wrong

[valid jetty]

question

@lean otter

[barren bronze]

yeah thats true

[lean otter]

@valid jetty will continue from here

[valid jetty]

frictionless surface?

[lean otter]

I gtg,sorry

[lean otter]

No

[barren bronze]

np thanks for the help man

[valid jetty]

but coeffecient of friction?

[lean otter]

Didn't say it in the question but check (iv)

[valid jetty]

ahh ic i got it

[barren bronze]

this is question

[lean otter]

^

[valid jetty]

i think u cut out friction part

[valid jetty]

ye saw the pinned msg

in d

[barren bronze]

no thats all

[lean otter]

Alright I will l3ave,
Sorry again

[valid jetty]

@lean otter oii

one thing

[lean otter]

Yes

[valid jetty]

dynamic friction coeff means where it is rest?

cuz they asked us to find the coeff

[lean otter]

No

Dynamic mean kinetic

[valid jetty]

i forgot the terms

[lean otter]

Kinetic friction

We never learnt the term dynamic XD

[valid jetty]

ohh

[lean otter]

It can be deduced though

[valid jetty]

okay whats dynamic now?

i just never bothered

took all as friction

[lean otter]

Kinetic...

[valid jetty]

this thing and i can take care of rest

[lean otter]

Static kinetic frictions

Remember ?

[valid jetty]

ok so basically mu

got it

[lean otter]

Alright then bye

[valid jetty]

but they asked to find it

[valid jetty]

so we assume body is at rest?

[lean otter]

Bruh

[valid jetty]

ok nvm

[lean otter]

The question says constant vrlocity

[valid jetty]

constant velocity

[barren bronze]

i think its moving

[valid jetty]

yeye

got it