help-39

[sudden zinc]

I tried a substitution, but no luck.

[sharp vigil]

note that you can integrate in either order

[sudden zinc]

yes

will it help to start with y?

I thought it wouldnt

[hard kite]

then x will be treated as a constant

[sudden zinc]

nice, helped

help

.close

[pearl pond]

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[pearl pond]

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[steady steppe]

can someone help me with calculation of eigenvector? I'm supposed to do it by hand and 227.519 is only approximation of my eigenvalue because exact form looks horrendous.

[steady steppe]

what next steps do you recommend me?

[warm current]

Yikes those are some ugly numbers. Who hates you this much?

[steady steppe]

professor of computer graphics, arguably the worst person at uni

[limber oasis]

by hand? Computer graphics?

[steady steppe]

yeah, he is mathematician but specializes in this CG

actually this is bonus task

i want those bonus points, because im note sure by other tasks

guys, do you have any ideas how to process further?

[limber oasis]

the matrix at the end is invertible, so assuming everything inbetween is correct, the desired value is not an eigenvalue

[steady steppe]

it invertible because the 227.519 is approximation of eigenvalue

i think

[crisp tendon]

u sure ur eigenvalue is 227.519?

[crisp tendon]

"just find the polynomial form of the matrix bruh"

the det(X.In - M) in question:

[limber oasis]

yeah this is peak cubic formula gone wrong material

[limber oasis]

you sure you need this?

[steady steppe]

dont get it

[steady steppe]

yeah

[limber oasis]

very specifically this matrix by hand?

[steady steppe]

unforrtunately

[limber oasis]

well, f*ck you then

best of luck with your endeavors, it appears I'm not able to help further

[steady steppe]

thanks, its awful, every student has different matrix based on birthday

[limber oasis]

oh

did you consider being born on another day?

[crisp tendon]

no way

[limber oasis]

or, do you happen to be more than 23 in class?

[crisp tendon]

this professor is just messing around

[limber oasis]

yeah unless he was very careful this might lead to untractable computations very easily

[crisp tendon]

anyway he said one eigenvector or the whole subspace?

[steady steppe]

over 50

[crisp tendon]

do the kernel of the matrix for the latter

[limber oasis]

find someone with your bday

it's likely

[steady steppe]

i think one eigenvector is enough

[steady steppe]

yeah, but it is also very likely that other people would not know how to calculate it

[limber oasis]

1. find someone who has
2. change your bday to theirs

[steady steppe]

thats also way

[pearl pond]

@steady steppe Has your question been resolved?

[pearl pond]

@steady steppe Has your question been resolved?

[pearl pond]

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[pearl pond]

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[stone imp]

I don’t get it

Ik that

First

I need to multiply the ()() thingies together

[spare lark]

Yes

[stone imp]

But the multiplication is confusing idk how to do it

Okay so

First

X times 2y

That’s 2xy right

[spare lark]

Yes

[stone imp]

Then I need to multiply x with 1/3

How do I do that

[hard kite]

multiplying by 1/3 is the same as dividing by 3

but you could just leave 1/3 as the coefficient

like just (1/3)x

[stone imp]

Huh

[hard kite]

there are many ways of writing it

[stone imp]

How do I write that in the ()

[spare lark]

$\frac{1}{3}x$

[jolly parrot]

YakuBros

[stone imp]

So it’s gonna look like that

[spare lark]

With a plus infront

[stone imp]

And the -(y/3) times 2y is -(y/3)2y

[hard kite]

it can simplified further

[stone imp]

How

[hard kite]

you have two y's multiplying

you get y²

[stone imp]

HOW

IM SO LOST

[hard kite]

um

let's say you had $x \cdot x$, how would you simplify this

[jolly parrot]

kaue

[stone imp]

Ik but

How does

-y/3 times 2y become that

[hard kite]

it's a product, so you can move terms around and it doesn't change it

$\frac{-y}{3} \cdot 2y$ is the same as $\frac{-y \cdot 2y}{3}$ which is the same as $\frac{-2 \cdot y \cdot y}{3}$ and you have two y's there so it becomes y² like this $\frac{-2y^2}{3}$

[jolly parrot]

kaue

[stone imp]

OHHHHH

I thought

You meant

The 3 disappeared

[hard kite]

noo

[stone imp]

Okay so

Is this right

So far

[hard kite]

yes

[stone imp]

Okay now I multiply -y/3 and +1/3

[hard kite]

yeah

[stone imp]

So -(y/3)

[hard kite]

noo

[stone imp]

Whyyyy

[hard kite]

you have to multiply the 3's

you would get 9

on the denominator

[stone imp]

Huuuh

Ohh

So

Y/9

[hard kite]

but with the negative sign

[stone imp]

Okay

Now

How do I

Shorten this

[hard kite]

distribute the 3

[stone imp]

How

[stone imp]

Ohhh

Okay wait

When I multiply

The three

Info the / thingies

Do I do it with the top and bottom

Or only tip

Top

[hard kite]

only the top and keep the bottom

[stone imp]

Okay wait

Okay did I do it right

[hard kite]

almost

[stone imp]

It’s the last part right

It’s 2y

[hard kite]

the 3 and the 9 don't cancel each other completly

[stone imp]

Wdym

[hard kite]

$\frac{3}{9}$ can be reduced to $\frac{1}{3}$

[jolly parrot]

kaue

[hard kite]

so you still have a 3 below the y

[stone imp]

Ohhhh

But

It’s in a /

Can it be that

[hard kite]

wym

it would be $-\frac{y}{3}$

[jolly parrot]

kaue

[stone imp]

Okay what’s the next step

I can’t put anything together

[hard kite]

there's not much to do now

[stone imp]

So it’s done

[hard kite]

the question was asking to distribute and simplify right?

[stone imp]

Exactly

[hard kite]

yeah it's done

[stone imp]

I have a strong feeling Thai will be wrong everytime it’s long it’s wrong

I’m gonna try

Wait

Yeah if was wrong

Do you want me to show u the whole calculation

If we did it wrong somewhere

[hard kite]

yeah

[hard kite]

well looks right to me

u sure you typed it correctly?

[stone imp]

Is it wrong

[hard kite]

yes it's wrong

[stone imp]

Omg

I accidentally put an x

Help

Yaya now it’s rgbt

Right

[stone imp]

My fault 😭

[hard kite]

yay

[stone imp]

I’m gonna try to do the next one myself but it looks harder

[hard kite]

good luck!

[stone imp]

Thank uuuu

.close

[pearl pond]

Channel closed

Closed by @stone imp

Use .reopen if this was a mistake.

[stone imp]

Yeah im stuck again

.reopen

[pearl pond]

✅

[stone imp]

This doesn’t feel right

[hard kite]

let me see

where did you get the x³ ?

i don't see it on the original question

[stone imp]

Ou

Now I’m lost

Where tf did I get that form

[hard kite]

[stone imp]

X/2 times x/2

OH

IF WAS

THE numbers from the question above

Went l to it

And I for confused

Got

Is this right

[hard kite]

let me see

yeah but you need to divide everything by 2

[stone imp]

Do I need to put -y^2 over a 2

[hard kite]

every term, it's like you're distributing the division of 2 to each of them

[stone imp]

What about x^2/4

How do I make the down part 2

I can’t divide x^2 by 2

[hard kite]

$\frac{\bigl(\frac{3}{4}\bigr)}{2}$

[jolly parrot]

kaue

[stone imp]

Oh man

[hard kite]

how would you simplify this fraction

that's not the answer btw

[stone imp]

I don’t kno…

[hard kite]

the 2 joins the denominator, so you have $\frac{3}{4 \cdot 2}$

[jolly parrot]

kaue

[stone imp]

But then it becomes 8

That’s not 2

[hard kite]

$\frac{\bigl(\frac{3}{4}\bigr)}{2} = \frac{3}{4 \cdot 2} = \frac{3}{8}$

[jolly parrot]

kaue

[hard kite]

the 2 joins the 4

making 8

[stone imp]

How did the x^2 become 3

[hard kite]

no, this is just an example

[stone imp]

Ohh

[hard kite]

then you apply the same logic to the other problem

[stone imp]

So it becomes x^2/8

[hard kite]

yes

but negative

[stone imp]

Is this right

Btw it’s a two over the x and the 2y

It got a bit messy

[hard kite]

noo

[stone imp]

Whyyyy

[hard kite]

you have to to it with every term, and then the 2 is gone

let me write this

[stone imp]

Okayyy

[hard kite]

$\frac{\frac{xy}{2} - \frac{x^2}{4} - y^2 + \frac{xy}{2}}{2}$ becomes $\frac{\bigl(\frac{xy}{2}}\bigr)}{2} - \frac{\bigl(\frac{x^2}{4}\bigr)}{2} - \frac{\bigl(y^2\bigr)}{2} \frac{\bigl(\frac{}{}\bigr)}{2}

[jolly parrot]

kaue

$\frac{\frac{xy}{2} - \frac{x^2}{4} - y^2 + \frac{xy}{2}}{2}$ becomes $\frac{\bigl(\frac{xy}{2}}\bigr)}{2} - \frac{\bigl(\frac{x^2}{4}\bigr)}{2} - \frac{\bigl(y^2\bigr)}{2} \frac{\bigl(\frac{}{}\bigr)}{2}
```Compilation error:```! Argument of \bBigg@ has an extra }.
<inserted text> 
                \par 
l.1421 ... becomes $\frac{\bigl(\frac{xy}{2}}\bigr
                                                  )}{2} - \frac{\bigl(\frac{...
I've run across a `}' that doesn't seem to match anything.
For example, `\def\a#1{...}' and `\a}' would produce
this error. If you simply proceed now, the `\par' that
I've just inserted will cause me to report a runaway
argument that might be the root of the problem. But if
your `}' was spurious, just type `2' and it will go away.```

[hard kite]

phone dead hold on

[stone imp]

Oh my

[hard kite]

phone alive let me fix that

[stone imp]

Okayyyy

[hard kite]

$\frac{\frac{xy}{2} - \frac{x^2}{4} - y^2 + \frac{xy}{2}}{2}$ becomes $\frac{\bigl(\frac{xy}{2}}\bigr)}{2} - \frac{\bigl(\frac{x^2}{4}\bigr)}{2} - \frac{\bigl(y^2\bigr)}{2} \frac{\bigl(\frac{xy}{2}\bigr)}{2}$

uff

[stone imp]

Huuuh

[versed mica]

you didn’t close some of these frac

[hard kite]

$\frac{\frac{xy}{2} - \frac{x^2}{4} - y^2 + \frac{xy}{2}}{2}$ becomes $\frac{\bigl(\frac{xy}{2}\bigr)}{2} - \frac{\bigl(\frac{x^2}{4}\bigr)}{2} - \frac{\bigl(y^2\bigr)}{2} + \frac{\bigl(\frac{xy}{2}\bigr)}{2}$

[jolly parrot]

kaue

[hard kite]

there you go

then you simplify each term

[stone imp]

Huh

Why didn’t it become 2y^2

[hard kite]

where

[stone imp]

Third part

[hard kite]

youre dividing by 2 not multiplying remeber

[stone imp]

But it didn’t have anything under it

And then we made it two

Doesn’t it mean

It becomes two

[hard kite]

i think you're confusing it with multiplying by 2

[stone imp]

And didn’t the four become 8

[hard kite]

it will

after you simplify the terms

they still need to be simplified

[stone imp]

How

[hard kite]

just like that one example i said with the 3

the 2 joins the denominator

[stone imp]

I’m so confused

[hard kite]

let's go one term at a time

[stone imp]

Okay

[hard kite]

so the first one is $\frac{\bigl(\frac{xy}{2}\bigr)}{2}$

[jolly parrot]

kaue

[hard kite]

hold on

do you understand why we have $\frac{\bigl(\frac{xy}{2}\bigr)}{2}$?

[jolly parrot]

kaue

[hard kite]

like how we got it

[stone imp]

Yes cause it’s all divided by 2

Yes

[hard kite]

yeah ok, so let's try to simplify this

you see the denominator is 2, and then there's another 2

[stone imp]

Yes

[hard kite]

$\frac{\bigl(\frac{xy}{2}\bigr)}{2}$ becomes $\frac{xy}{2 \cdot 2}$

[jolly parrot]

kaue

[hard kite]

because the 2 joins the other on the denominator

[stone imp]

But why

Isn’t it supposed to be divided

Why is it multiplied

[hard kite]

let me try to explain

do you know how we can multiply top and bottom by the same number and it doesnt change the fraction?

like if we have 1/2 we multiply top and bottom by 3 we get 3/6

and it's still the same as 1/2

[stone imp]

Yeah

I know that but

It’s all divided by 2

And not multiplied

[hard kite]

take $\frac{\bigl(\frac{xy}{2}\bigr)}{2}$ and multiply top and bottom by the number 2

[jolly parrot]

kaue

[hard kite]

you would get

$\frac{\bigl(\frac{xy}{2} \cdot 2\bigr)}{2 \cdot 2}$

[jolly parrot]

kaue

[hard kite]

right

[stone imp]

Aaaaa I still don’t get why were multiplying in the 2

[hard kite]

wait

and then do you see how we could simplify the top part?

[stone imp]

Where

[stone imp]

Yeah and now im lost

[hard kite]

so after simplifying that it just becomes $\frac{\bigl(xy\bigr)}{2 \cdot 2}$, which is what we had when joined the 2 on the denominator

[jolly parrot]

kaue

[hard kite]

um

[stone imp]

But why is the 2 going inside

[hard kite]

maybe other way

do you know about dividing fractions?

[stone imp]

Wdym

Give an example

[hard kite]

like $\frac{2}{3}$ divided by $\frac{4}{5}$

[jolly parrot]

kaue

[stone imp]

Nope

Never done that before

Wait

Wait

Isn’t it the

Keep switch flip method

[hard kite]

yeaa

[stone imp]

But how did it go into that

Like

My question

OH

OHHHHHH

I GET IT

[hard kite]

yay

[stone imp]

so

Wait

This is so long

The 2 stays the same

Isn’t it supposed to flip

Like

2/1–> 1/2

[hard kite]

yess

[stone imp]

So wait

One sec

I’m gonna write this

Woops

Theres supposed to be a four

There

[hard kite]

don't forget the parenthessi

[stone imp]

Wait I fix

[stone imp]

Where do I put them

[hard kite]

1/2 is multiplying the whole expression

[stone imp]

OHHHH

SO RHUS

[hard kite]

like 1/2 × a + b + c should be written a s 1/2 × (a + b + c)

[hard kite]

yess

[stone imp]

And now I need to multiply

In the

1/2

[hard kite]

yeah distribute it

[pulsar lark]

,rotate

[stone imp]

Is this right

[pulsar lark]

,rotate

[pulsar lark]

Y

Yes

[hard kite]

now combine similar terms

[stone imp]

The xy

[hard kite]

yes

[stone imp]

Can I do more

[hard kite]

those are the only similar terms

[stone imp]

So this should be the answer

[hard kite]

after you combine xy yeah

after you combine xy yeah

[hard kite]

you can simplify 2/4

[stone imp]

Ohhh

Xy/2

[hard kite]

yes

[stone imp]

It was wrong…

Did I write it wrong again

[versed mica]

what language is that

[stone imp]

Swedish

[hard kite]

,w expand (x/2 - y)(y - x/2)/2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by wkaue

[hard kite]

got it

[stone imp]

I don’t understand

[hard kite]

it was just -y² there

no /2

[stone imp]

Yeah and then we put a 2 under it

I wasn’t supposed to do that was I..

[hard kite]

no the two comes after hou multiply by 1/2

[pulsar lark]

,rotate

[hard kite]

you havent multiplied by 1/2 in that step yet

[stone imp]

So what did I do wrong

How to fix

[hard kite]

remember

[stone imp]

So I just keep the -y^2

[hard kite]

try multiplying this by 1/2

you wrote -y²/2 instead of -y² before multiplying by 1/2

[stone imp]

Uhhh

I don’t understand

[hard kite]

basically you multiplied by 1/2 twice

[hard kite]

let's start from here again

[stone imp]

Dammit

[hard kite]

you multiplied the brackets

[stone imp]

Okay

[hard kite]

and now you divide by 2 (which is multiply by 1/2)

[stone imp]

Okayyyy wait

Ignore the top

Look Only under the line

Is it right

[hard kite]

yeah, now again combine the xy similar terms

[stone imp]

It’s right

I tried it

That was impulsive

If it was wrong the question would’ve been marked red

[hard kite]

and simplify the 2/4

[stone imp]

Yes

I did

If was

Xy/2

[hard kite]

yay

[stone imp]

Thank uuuuu🤗

One last question left on lvl 5 let’s see if I can at least do this one without help

.close

[pearl pond]

Channel closed

Closed by @stone imp

Use .reopen if this was a mistake.

[stone imp]

.reopek

.reopen

[pearl pond]

✅

[stone imp]

Question

If I do

X * x^2

Does it become x^3

[late kayak]

yes

[stone imp]

Thank uuuu

.close

[pearl pond]

Channel closed

Closed by @stone imp

Use .reopen if this was a mistake.

[stone imp]

.reopen

[pearl pond]

✅

[stone imp]

I’m back

Where did I go wrong

[feral sedge]

,rotate

[feral sedge]

looks right

[late kayak]

agreed

[stone imp]

So I can’t simplify it more

[feral sedge]

right

[stone imp]

Oh yeah now it was right

I need to stop typing in wrong letters

Thanks 🙏

.close

[pearl pond]

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[pearl pond]

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• Show your work, and if possible, explain where you are stuck.
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[stone imp]

So I totally forgot what factorise was

This embarrassing

[autumn narwhal]

For example:

2x + 4 = 2(x + 2)

It's just using the distributive law

a(b + c) = ab + ac

Same thing for the other side:

(b + c)a = ba + ca

a, b, c can be anything

[stone imp]

Huh so

Wait

Give example how do I solve the first one

[ionic cobalt]

You can take out a number that is a multiple of both the coeficcients

So for example,

Since 3 is a factor of both 6 and 9

it would become 3(2x+3)

[stone imp]

Wait I’ll try

Ohhhhh

I get it now

[ionic cobalt]

Got it?😊

[stone imp]

Yes thanks 🙏

.close

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[lusty hill]

I wanted help on how to start this question

[lusty hill]

My trail of ideas for this:
first the cup itself is always parallel to the tangent line at a point it's on, so that means that it is parallel to g'(x), and so would that imply that the slope itself of the water spilling = g'(x)

the larger |g'(x)| the larger the magnitude of the rate of change of the volume of the cup gets and so there is a positive correlation between the two. So then the crux of this question is to find the relation btwn g'(x) and the ROC of volume of the water.

the volume of water = h(w^2) and that can be written as 2w^3. But it's at this point i get stuck. I was thinking maybe since the width of the cup is parallel to g'(x) we can sub it into that but I don't know if that makes sense
i'm trying to think of it as a related rates problem and idk if that is the right approach and there are other concepts connected to it

[pearl pond]

@lusty hill Has your question been resolved?

[pearl pond]

@lusty hill Has your question been resolved?

[pearl pond]

@lusty hill Has your question been resolved?

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[midnight haven]

Hey guys I require assistance with the b part of this question

[midnight haven]

[
\cos \angle OPQ = \frac{\vec{PO} \cdot \vec{PQ}}{|\vec{PO}| |\vec{PQ}|}
]

[jolly parrot]

Edmund Cloudsley (Hello CHAT)

[midnight haven]

Is this corrrect?

and then [
\cos \angle OPQ = \frac{\langle -7, -3 \rangle \cdot \langle 3, 2 \rangle}{\sqrt{(-7)^2 + (-3)^2} \cdot \sqrt{3^2 + 2^2}}
]

[jolly parrot]

Edmund Cloudsley (Hello CHAT)

[midnight haven]

and then

$$\cos \angle OPQ = \frac{(-7)(3) + (-3)(2)}{\sqrt{754}}$$

[jolly parrot]

Edmund Cloudsley (Hello CHAT)

[midnight haven]

,w evaluate -7 * 3 + -3 * 2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[midnight haven]

however this doesn't become -15

it evaluates to -27

Would really appreciate if someone can tell me where I am going wrong

btw feel free to ping me

<@&286206848099549185>

[sharp vigil]

double check your components for PQ

[midnight haven]

Oh I see my error now

vector PQ should be <10 - 7, 1 - 3> = <3, -2>

cheers mate thanks

.close

[pearl pond]

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[pearl pond]

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[rose star]

Is this graphed incorrectly?

[rose star]

Should it not be reflected

[valid peak]

yes

[rose star]

aight cool

i love an incorrect answer sheet

[valid peak]

😭

[rose star]

.close

[pearl pond]

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[pearl pond]

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[sweet condor]

Hi !

[sweet condor]

I wanted to know how to find the square time 6 of -27 ?

I did this for now but i'm super confused ,-,

should I convert -27 to 27e^(ipi) ?

since r is a positive number ?

?

@rough forge So it's it ?

[rough forge]

i am having a hard time reading, what's your question

[sweet condor]

My question is finding the solution of w⁶ = -27

[rough forge]

achso

[sweet condor]

(complexe number inclued)

[jolly parrot]

𝔸dωn𝓲²s

[sweet condor]

as my first solution yes

I add 2kpi/6 for having all solution

[rough forge]

yea that's it

[sweet condor]

Perfect I got the method done

[sweet condor]

Thanks you

!close

.close

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[junior vapor]

hello how do you do part c

[tender gate]

AHHHH

scared me

ok

lets do it

you can simplify the expression by factoring 2 from cos(2pi/5) and cos(pi/5)

[junior vapor]

hm? like turn the expression into 2(cos2pi/5-cospi/5+1/2)=0?

[tender gate]

yeah you can do that

[junior vapor]

okk where do i go from there

it looks somewhat similar to part b but idk what to do with that information :/

[pearl pond]

@junior vapor Has your question been resolved?

[junior vapor]

<@&286206848099549185>

[pearl pond]

@junior vapor Has your question been resolved?

[junior vapor]

<@&286206848099549185>

[ashen needle]

Lowk I can't help with that

I'm scared

@help

[junior vapor]

;-;

[ashen needle]

Brev

See that 2cos (2pi/5)

U can use that thing idk it's name in english so it becomes 2(2cos^2 (pi/5) - 1)

[junior vapor]

how does that turn it into exact values though?

[ashen needle]

Can you use a calculator ?

But idk to be honest

That's the only thing that got in my mind

[junior vapor]

nope the calculator don't give me exact values

[junior vapor]

rip it's ok

[ashen needle]

I'll ask my teacher

[junior vapor]

alright thanks

[dusty jungle]

once you have deduced that 2cos2pi/5 - 2cospi/5 + 1 = 0

u can use the double angle formula for cos pi/5

and turn the equation into a quadratic in terms of cos pi/5

so if u find the roots

u can find the exact value of cos pi/5 and cos 2pi/5

[pearl pond]

@junior vapor Has your question been resolved?

[prime pier]

i havent touched 4U in 3 years but if i remember correctly you have to expand part b but selecctively expand the terms that result in z^3
then u match the z^3 term on the LHS with the z^3 term on the RHS

[pearl pond]

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[unreal thistle]

how many possible cases is there for black to move the king from a4 to h4? is it possible to solve this one using combinatorics or binomial theorem?

[tropic saddle]

what moves are you allowed to do

if you are allowed to go backwards then clearly there are infinitely many options

[unreal thistle]

There will be only 7 moves. All forward

<@&268886789983436800>

[dapper kraken]

something like this should work

[unreal thistle]

We can have 3 possibilities per move for the first 3 moves.

Then if we are at the d7, then 2 possibilities for that position, if we go to e7 then again 2 cases, similarly 2 cases for f6 and g5.

[dapper kraken]

tldr for any tile on the chessboard, there are (the number) on the tile ways to get thers, for example to get to d3 there are 6 ways to go there

[unreal thistle]

it looks like the pascal triangle not gonna lie

[dapper kraken]

its simmilar but each one goes to 3 instead of 2

[unreal thistle]

what do you mean by this?

[dapper kraken]

pascals triangle would be something like this

our case would be something like this

[unreal thistle]

oh i get it, so we have 3 choices to go after every move, while in pascal we can have 2

how can I proceed after this?

[pearl pond]

@unreal thistle Has your question been resolved?

[blissful salmon]

Yes, this is the correct idea. The idea that they use here is called dynamic programming, where you write the number of ways to reach a square in terms of previous squares. You can do this because you are only allowed 7 moves, so they all must be forward, hence you can write the number of ways for each square within the red boundary as illustrated

[unreal thistle]

and do the summation of them in the end to get the answer? is there an alternative approach other than counting each case?

[blissful salmon]

also you proceed after this by just filling in the rest of the squares using the previous squares and then finding the number of ways of reaching the other side

[blissful salmon]

The number you write for H4 should be your answer

[unreal thistle]

oh okay. is there any other idea which we can use to solve this problem?

[blissful salmon]

Not that I’m aware of

[rotund hamlet]

can anyone help me this (x^2+4x+3)^2+(x+3)^2 find x to this expression has a perfect squares number

[blissful salmon]

I recommend you first open your own help channel for this problem, but what I’ll say first is that you can factorise the x^2+4x+3

[rotund hamlet]

idk

i try all the ways

[blissful salmon]

First open another channel

Because someone else was here already

From there I can help you

[rotund hamlet]

alr ok

so what channel im wondering

cuz im new

[blissful salmon]

Try any open one like #help-25

[rotund hamlet]

ok

[blissful salmon]

Sorry for the inconvenience. If you have any doubts, let me know in dms or express them here, otherwise what we have said should be enough to solve the problem

[unreal thistle]

it's fine. I was just thinking if it's feasible enough or not. appreciate the help!

.close

[pearl pond]

Channel closed

Closed by @unreal thistle

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[unreal thistle]

if it's okay can I dm about how the idea used here is related to dynamic programming? isn't it about breaking the problems into subproblems?

[blissful salmon]

Sure you can dm me, and idk what you mean by that. It’s just like finding the number of ways to reach a square in terms of other so called adjacent squares

[unreal thistle]

so it's more related to the pascal triangle right. but 3 choices instead of 2, and 2 instead of 1 on the edges

[blissful salmon]

Yeah it is, all the way up to the middle of the board. Then you kinda work backwards if you get what I mean

[blissful salmon]

Yes, you are correct in this instance

[unreal thistle]

i get it. I got confused because I thought dynamic programming is about breaking the problems into subproblems

nvm thanks for the help!

.close

[blissful salmon]

ah, no worries

[blissful salmon]

You already closed the channel before, so it’s all good

[pearl pond]

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[sharp smelt]

how am I supposed to do this

[rough forge]

without guessing?

or you just have to show it has 3 solutions

or disprove

[sharp smelt]

prove or disprove

[rough forge]

ok so

you can see it has one for x=2

so

consider two subintervals

and try to apply ivt

for that you consider

f(x) = x²-2^x = 0

[sharp smelt]

Wait

i think I have to actually find the solns

x=2 works

[rough forge]

i highly doubt that

[autumn fossil]

Are you a constructivist or sth?

[hard zephyr]

hi sorry to disturb, im new to this server and i wanna ask for help, can i just do that in any of these "help-##" channels?

[sharp smelt]

I'm a formalist'

[sharp smelt]

yes, as long as They haven't bee claimed

[autumn fossil]

you need to know that there are 3 real sols, nobody wants you to find them

[sharp smelt]

so just help xy

@hard zephyr

[sharp smelt]

I see

okay, then IVT works

[rough forge]

What is that

[autumn fossil]

similar to intuionistic logic, idk how exactly it works. They basically dont like any indirect proofs

[pearl pond]

@sharp smelt Has your question been resolved?

[pearl pond]

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[fervent galleon]

Does this use of double arrows <=> mean iff, in this context, or something else?

[fervent galleon]

When I read it as "iff", kinda doesn't seem right to me.

[rough forge]

yea you are right

"x^2" or "+-sqrt(x)" are no statements

[supple knoll]

Probably

Inverse

[fervent galleon]

I think that I intuitevly understand what the author mean, but I just wondered if that use of double arrow is standard use.

[autumn fossil]

I dont like that use

it looks like it just stands for a hyphen here

it literally just matches the function to its inverse

[fervent galleon]

yeah, I think maybe its just a like a graphics for arrows pointing both ways, without the "iff" implication.

Thanks for the help

.close

[pearl pond]

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[sharp galleon]

help w this pls

[atomic oracle]

!status

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@sharp galleon Has your question been resolved?

[sharp galleon]

1

@atomic oracle

[atomic oracle]

Find T for which

The x coordinate and y coordinate of P and Q

Are same

@sharp galleon

[sharp galleon]

wait

let me draw it out eq

man

how

does

the x coord

and y coord

help w this

[pearl pond]

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[spring crystal]

What do I do now

[spring crystal]

<@&286206848099549185>

[hallow ice]

I think something went wrong. where does the n on the denominator come from?

[spring crystal]

wdym

i did the ratio test and got this

[hallow ice]

the denominator you got is 2nln(n+1)

I think it should be 2ln(n+1) instead

[spring crystal]

oh i wrote it wrong by accident i meant 2^n ln(n+1)

actually it should jsut be 2

[hallow ice]

yes

[spring crystal]

so what do i do afterwards

[hallow ice]

okay, so if we agree that it should be

$\frac{(x-2)\ln(n)}{2\ln(n+1)}$

what does the ratio test tell you?

[jolly parrot]

LayneTheAndroid

[spring crystal]

n goes inf?

do i plug in infintie for n now

[hallow ice]

yes, you should check what the limit of the above is as n goes to infinity

[spring crystal]

yeah im confuse on that

so it becomes (x-2) times inf/ inf?

[hallow ice]

not quite. have you seen this situation before where you see inf/inf when taking a limit?

[spring crystal]

no

thats why idk

[hallow ice]

okay, so you'll need to use other methods to figure out what the limit actually

let's just focus on working out the limit $\lim_{n\rightarrow{\infty}}\frac{ln(n)}{ln(n+1)}$ for now

[jolly parrot]

LayneTheAndroid

[hallow ice]

could you use log rules to make this expression simpler?

[spring crystal]

ln(n)-ln(n+1)

inf-inf

?

[hallow ice]

that's not right

here's a hint: you can write $ln(n)=ln((n+1)\frac{n}{n+1})$

[jolly parrot]

LayneTheAndroid

[spring crystal]

how

[hallow ice]

because $n=(n+1)\frac{n}{n+1}$

[jolly parrot]

LayneTheAndroid

[hallow ice]

i just multiplied and divided by the same number

[spring crystal]

so what am i suppose to do with that

[hallow ice]

use log rules to simplify $\frac{ln(n)}{ln(n+1)}=\frac{ln((n+1)\frac{n}{n+1})}{ln(n+1)}$

[jolly parrot]

LayneTheAndroid

[hallow ice]

i.e i've done the first step, you need to do the rest

[spring crystal]

idk ive never even seen this

[hallow ice]

you know log rules, though. If you've never seen limits of the form inf/inf then I'm not sure how else to do it other than by manipulating the expression to be easier to work with

well, have you maybe seen limits of the form $\frac{0}{0}$?

[jolly parrot]

LayneTheAndroid

[spring crystal]

yeah i know to solve that with l hopital

[hallow ice]

ah okay so inf/inf is the same

the reason is that you can rewrite a inf/inf limit to be a 0/0 limit.

either way you can use L'Hopital

[spring crystal]

so i l hopital the whole thing

including the x-2?/2

[hallow ice]

yes, that's fine; that's a constant anyway

[spring crystal]

Doesn’t x-2 become 1 and 2 become 0

[hallow ice]

what variable are you differentiating with respect to when using L'Hopital?

[spring crystal]

Ok so it becomes n+1/ n?

Also does the n=2 in the sigma matter. Cus the ones I did before were n=0

[hallow ice]

if you're just talking about $\lim_{n\rightarrow{\infty}}\frac{ln(n)}{ln(n+1)}$ then yes, doing L'Hoptials would mean this is the same as $\lim_{n\rightarrow{\infty}}\frac{n+1}{n}$

[jolly parrot]

LayneTheAndroid

[spring crystal]

Wasn’t that what I was supposed to do

That’s what I did

[hallow ice]

when it comes to the radius of convergence it doesn't matter

[hallow ice]

well you started talking about the "whole thing including (x-2)/2" so I wasn't sure which you were talking about in the end

[spring crystal]

I have (x-2)/2 times n+1 /n rn

Is that right

[hallow ice]

yes

that's correct

[spring crystal]

So n+1 becomes infinite?

(X-2)/2 times inf

[hallow ice]

well $\frac{n+1}{n}$ doesn't tend to $\infty$.

[jolly parrot]

LayneTheAndroid

[hallow ice]

remember the $n$ becomes $\infty$ too

[jolly parrot]

LayneTheAndroid

[spring crystal]

It becomes 1

?

(X-2)/2 now

[hallow ice]

yes. you can get that either by simplifying the fraction or doing L'Hopital again

yes

[spring crystal]

Ok so the IOC is (0,4) I got 0<x<4) and ROC is Is x-2<1 which makes it 3?

Ioc =(0,4) and ROC=3

@hallow ice

[hallow ice]

I agree with the interval of convergence (although did you check if it is the closed or open interval). Radius I'm not sure is correct

where did you get $x-2<1$ from?

[jolly parrot]

LayneTheAndroid

[spring crystal]

Well i remember YouTube video said whatever is being raised to n power make it <1 and that’s radius

And (x-2)^n x-2 is raised to n

[hallow ice]

two things:

1. there's something else being raised to the power of 2
2. if you were just going off that, what was the point in doing the ratio test? in fact the ratio test gave you the quantity you need to bound above by 1

[hallow ice]

here (although you'd need to take the absolute value of this)

[spring crystal]

Idk that’s just what I saw

So how do I find the radius

[hallow ice]

let's just go off the working we've actually done

what does the ratio test tell you?

[spring crystal]

If less than 1 it converge

[hallow ice]

yes. if what is less than 1?

[spring crystal]

The whole thing

After ratio teat

[hallow ice]

which is what in this case?

[spring crystal]

X-2/ 2

[hallow ice]

yes (but remember the ratio test asks for absolute values)

[spring crystal]

Ok but it is positive so it doesn’t need it

[hallow ice]

is it positive? what if x=0?

[spring crystal]

Ok so |x-2/2|

[hallow ice]

yes (also better to use parantheses). That needs to <1.

$\frac{|x-2|}{2}<1$

can you use that equation to find the radius of convergence?

[jolly parrot]

LayneTheAndroid

[spring crystal]

X<4

[hallow ice]

how did you get that?

recall the definition of the radius of convergence:

for a series

$\sum_{n} a_n(x-a)^n$

The radius of convergence $r$ is the number such that the series converges for

$|x-a|<r$

and diverges for

$|x-a|>r$

[jolly parrot]

LayneTheAndroid

[spring crystal]

I got x alone by times 2 both sides and then adding 2

Am I not suppose to get x by itself

[hallow ice]

nope, the definition of radius of convergence is what I gave above, so it's in terms of |x-a|

[hallow ice]

(also you can't do that, you ignored the absolute value, but that's besides the point right now)

[spring crystal]

https://youtu.be/TGD-TP1c7i4?si=C7I458MeeVFoJ-Le at 1:20:53 he says that ROC is whatever is under the n power

So does that not work for all problems or what

[hallow ice]

it looks like he's pointing to the 1 when he says "whatever that number is, that's the radius of convergence",

so he's saying

you're looking for the thing being raised to the power of n in the series (in his case x, in yours x-2)

and the radius of convergence is the thing that bounds |thing being raised to the n| above after doing the ratio test

[spring crystal]

So x-2<1?

[hallow ice]

... no, the inequality we found from the ratio test was

$\frac{|x-2|}{2}<1$

[jolly parrot]

LayneTheAndroid

[spring crystal]

Oh so it is just 2

For the roc

[hallow ice]

you want to find the $r$ such that $|x-2|<r$ ensures the series converges

yes

[jolly parrot]

LayneTheAndroid

[spring crystal]

Ok so ROC IS 2 and IOC IS (0,4) not checked yet

[hallow ice]

yes, although double check if 0 and 4 are included in the interval or not

[spring crystal]

What does it have to do = to for brackets again

And parenthesis

[hallow ice]

$[a,b]$ means all numbers including all $a$ and $b$

$(a,b)$ means all numbers greater than $a$ and less than $b$

$[a,b)$ all numbers greater than $a$, and $a$ itself, and all numbers less than $b$

to check $0$ and $4$ are included, trying inserting $x=0$ or $x=4$ and checking if the resulting series converges or not

if it converges, then that means that number is part of the IOC

[jolly parrot]

LayneTheAndroid

[spring crystal]

So if I plug those numbers in the answer has to be less than 1?

[hallow ice]

no, the ratio test doesn't work for the end points of the IOC, you need to check the series yourself using other methods

[pearl pond]

@spring crystal Has your question been resolved?

[pearl pond]

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[pearl pond]

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[shadow geyser]

i have an exam tomorrow, and ive missed almost all my classes recently bc of lung infections and dengue, almost died, but im having trouble completely understanding binomial expansions. We only have three formulas, which are the nCr formula, the factorial expansion formula, same expansion with nCr formula, and the (1+x)^n formula. can someone give me a breakdown and teach me to do them with examples? thanks

[shadow geyser]

i can send the formulas if you want

[little sundial]

this right

[shadow geyser]

the first two contain the formulas and the last page has the sums im confused about

[little sundial]

oh

[shadow geyser]

i need one or two examples if possible

and he also gave us a different fprmula for nCr, one sec

sec* lmao

[shadow geyser]

i do get how the factorial formula turns into an nCr expansion but the problem is mostly in how we do the problems and how to work it out, and also how to find the range of values of x for which an expansion is valid

p sure theres a formula for that right

x mod is less than the root of the term/coefficient of x inside the bracket right?

[little sundial]

i dont have time to explain all this rn bc itll take a hottt minute but i wish u the best of luck and there are always lectures online too

[shadow geyser]

can someone else help me?

<@&286206848099549185>

[pearl pond]

@shadow geyser Has your question been resolved?

[pearl pond]

@shadow geyser Has your question been resolved?

[pearl pond]

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[sweet briar]

I need some help with this question. How can i tell from a derivative of a graph, where the original graph is inc/dec?

[exotic scaffold]

well

the derivative of the function at a point gives the slope of that function at that point

[sweet briar]

so between -1 and 0, the value of the derivative is positive, which means if the slope is positive, the function is increasing?

[exotic scaffold]

yes

there are also 2 more intervals on which the derivative is positive so include that in your final answer

[sweet briar]

so (-inf, -3) U (-1, 0) U (3, inf)?

[exotic scaffold]

yes

[sweet briar]

wait the wording of this question is really weird. is the graph f or f'?

[exotic scaffold]

the graph is f`

[sweet briar]

so im trying this but that doesn't seem to work

my initial thought is that im using ( ) where [ or ] is needed

[exotic scaffold]

its decreasing on (0,3) not (0,2)

[sweet briar]

ah shit i keep confusing it with mins/max

[sweet briar]

okay thanks! i was wildly overcomplicating this

.close

[pearl pond]

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[pearl pond]

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[woven frigate]

how do i determine if an interval on a graph is positive or negative?

[cinder flower]

[pearl pond]

@woven frigate Has your question been resolved?

[slate crystal]

wdym

like

is the slope of the interval increasing??

[pearl pond]

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[frail oxide]

Can someone tell me how I know if this graph is planar or not. I have been trying to shift the edges and vertexs but I cant figure it out.

[pearl pond]

@frail oxide Has your question been resolved?

[frail oxide]

<@&286206848099549185>

[wary gale]

topic ?

[feral sedge]

Keep trying

[frail oxide]

Discrete Math

specfically graph theroy

[feral sedge]

hint: there are two vertices here with two neighbors, those neighbors are also connected directly

You can basically ignore those and add them back at the end

[frail oxide]

So I can just treat it like this?

[unborn abyss]

here's a cool website where you can make a graph and move it around https://graphonline.top/en/

[frail oxide]

But is their a way to move the edges?

[unborn abyss]

wdym move the edges

you can move the vertices around

[frail oxide]

but I thought to find if something is planar the vertexs have to context without the edges crossing

[unborn abyss]

correct

[frail oxide]

so how does just moving the vertexs help

[unborn abyss]

uhm

[frail oxide]

Never mind

[unborn abyss]

this graph is planar

[frail oxide]

I just flipped A over and found it. ty

.close

[pearl pond]

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[pearl pond]

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[timid sable]

guys

[timid sable]

are you ready for my questions

[slate crystal]

just ask them

[pearl pond]

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/

[timid sable]

alright

xD

[surreal relic]

Insane that you still haven't posted your question

I will be closing the channel in 5 mins

As you have occupied this channel for half an hour without posting a question

[timid sable]

I'm sorry

yeah, the question here is to derivate this.

Do you wanna see my method?

[dusk horizon]

yes, you should always show your work

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[plush bramble]

the word is differentiate

[timid sable]

logarithm method, as you can see.

Well, the thing is that I got that monstrosity there at the end.

and, well, I don't think that's the answer. =(

what do you guys think about this.

[slate crystal]

jesus this handwriting

[slate crystal]

highkey i leave it as it is

if u try to simplify it, ur gonna put urself thru even more torture

[timid sable]

Do you mean that's correct

[slate crystal]

lemme work on it rq

[timid sable]

Okay, thank you very much.

[slate crystal]

okay yeah its correct

[timid sable]

Why tho

[slate crystal]

wdym why

[timid sable]

why is it correct

[slate crystal]

u were left with f'(t)/f(t) right?? after finding the derivative of everything on the right side of the equation

[timid sable]

Yeah.

[slate crystal]

so what did u do with the f(t) to isolate f'(t) by itself?

[timid sable]

Multiply everything by f(t)

[slate crystal]

yeah

and in this case

f(t) is just original equation

[surreal relic]

@timid sable you still have a doubt?

[timid sable]

Yeah, with the next exercise

[surreal relic]

Send it

[timid sable]

but I'm busy rn, so I will close it for now

.close

[pearl pond]

Channel closed

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[slate crystal]

the fack

[pearl pond]

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[opal urchin]

I am not sure what is wrong here

[vital estuary]

the step where you subtract 1.5x from both sides

just a tip for next time: you should expect the answer to be wrong if you get a fractional amount of people and you should check your work before submitting

[opal urchin]

hehe, got it.

alright thanks.

[vital estuary]

you simply need to combine like terms for the x part

[opal urchin]

2.5

[vital estuary]

-2.5x on the left

[opal urchin]

ty for the help

.close

[pearl pond]

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[pearl pond]

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[tawny talon]

y

[pearl pond]

Please don't occupy multiple help channels.

[tawny talon]

how do they 'get 1/2?

[pearl pond]

@tawny talon Has your question been resolved?

[pearl pond]

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