help-17

[gritty niche]

What

[solar cape]

(x-3)(x-1)=0

So your solutions are?

[gritty niche]

3 and 1

[hollow acorn]

basically what does x equal

yep

those are the roots

[solar cape]

Yeyyeyey

[hollow acorn]

the solutions

for x

[solar cape]

Les go baby

[hollow acorn]

👏

[quiet echo]

good

[hollow acorn]

we did it

[gritty niche]

But there’s 2 other solutions I have to put in

😭

[hollow acorn]

oh for y

[solar cape]

Ah for y

[hollow acorn]

well go back to the first equation

[solar cape]

Should be self explanatory

[hollow acorn]

y = x^2

[solar cape]

Let him cook

Wait let him cook fr

[gritty niche]

Sub in right?

[solar cape]

Yea

[hollow acorn]

mb mb

[gritty niche]

So y is 9 or 1

[solar cape]

Yeps

[gritty niche]

Thx bros

[solar cape]

Remember to pair up the corresponding y with the corresponding x if they ask you to

[gritty niche]

It’s all good I’m done now

[hollow acorn]

yipee

you can close the channel with .close

[gritty niche]

.close

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[calm reef]

is it possible to algebraicly derive the x and y value of 5^x*2^y=200

[calm reef]

algebraically*

[heady vine]

like you are solving for x ?

[calm reef]

yes

solving for x and y

[quiet echo]

this is an equation in and of itself, so an infinite amount of points in the reals satisfy this, Q.E.D.

[calm reef]

but is it possible to algebraically derive one of the solutions

?

WITHOUT "brute forcing" with the lack of a better word

[lost barn]

Sure, this is what diophantine equations generally try to do

[calm reef]

can you solve for these Diophantine equations algebraically? or do you need a computer for this

[quiet echo]

for $x,y\in\bZ$? you should clarify this if that is the case

[twin meteor]

;(

[lost barn]

Ye u can

I'll help u out

We should try and factor 200

Do you know what a prime factorization is?

[calm reef]

factoring the number into two prime factors?

[quiet echo]

not necessarily

what you want to do is group the factors of 5 within 200 and the factors of 2 within 200

[lost barn]

It's just finding all the primes that multiply into 200

[quiet echo]

otherwise, you won’t get integer solutions

[lost barn]

So for example, the prime factorization of 24 is 222*3

Oops

2 x 2 x 2 x 3

Which is 2^3 x 3

[quiet echo]

is this even possible?

[lost barn]

Of course it is

Taking prime factorization aint hard

[quiet echo]

||200=2x5x5x2x2||

so there is one solution set

[lost barn]

Actually nvm ur missing a 2

[quiet echo]

no?

200=2x100

[lost barn]

It's 25 * 16

[quiet echo]

no

[lost barn]

Yes it is

[quiet echo]

bro multiply it out 💀

[lost barn]

I did

[quiet echo]

,calc 25*16

[twin meteor]

Result:

400

[lost barn]

Oh wait is it 200 and not 400

[quiet echo]

👍💀💀💀💀💀💀💀

[lost barn]

Oopsies I misremembered lmaooo

[quiet echo]

type shit

@calm reef anyways if u factorize 200 u get 1 solution set

[calm reef]

i couldnt get any solution

i tried that

maybe im not built for math

[quiet echo]

200=2^3*5^2

what does that match up with?

[lost barn]

Dw ur new to this

It can be hard

[calm reef]

how did you get 3 and 2 algebraically. did you just do prime factorization?

[lost barn]

Well you just take numbers that you know divide 200

So start with 2

And you get 2 x 100

Then find a number that divides 100

And so on until you run out of divisors

[calm reef]

so there isnt a specific recipe i can follow

?

[lost barn]

Well there is

[calm reef]

beside this one

[lost barn]

You find factors of the number

Oh

If there is it's above your paygrade rn

[calm reef]

like i woulnt understand it?

[lost barn]

Yeah

[calm reef]

o you know what it is called

?

[lost barn]

I'm taking a class on it at college this semester

[calm reef]

do

[lost barn]

Idk any methods

But I'm saying if there is then it's complicated

[calm reef]

thank you regardless 🙂

didnt know about the prime factorization

[lost barn]

No problem

Prime factorization is one of my favorite things in math

I've proven a lot of things using the fact that all numbers have a unique prime factorization

[calm reef]

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[gray fox]

i tried to plug x in for t and that was wrong then i tried to integrate using 12 and that was also wrong

i think that i may have to have x as the upper bound but im not sure

[proud terrace]

According to Leibniz, $\frac{d}{dx} \left( \int_{g(x)}^{h(x)} f(t) , dt \right) = f(h(x)) \cdot h'(x) - f(g(x)) \cdot g'(x)$

[twin meteor]

ss

[quiet echo]

oh my lord

no need

[silk osprey]

nah it’s nice though

[quiet echo]

$\dv{x}\qty(\int_x^a f(t)dt)=-f(x)$

[silk osprey]

i mean you could negate it

[proud terrace]

but yeah the derivative is just -tan(x^3) lol

[silk osprey]

that’s if the upper limit was x

consider this

[quiet echo]

wait

[proud terrace]

…

[quiet echo]

i see the qn wrong

[silk osprey]

$\int_a^b f(t) , dt = -\int_b^a f(t) , dt$

[twin meteor]

;(

knief

[gray fox]

i remember this rule! should i do this?

[quiet echo]

!nosol

this

[proud terrace]

mb

[quiet echo]

iadhw0

stupid fucking bot

what the hell is the command for it

[proud terrace]

lol

[silk osprey]

yes this would help

[quiet echo]

probably if u want to stay sane

[gray fox]

okay so after i change the bounds and add the negative what is the next step?

[quiet echo]

else $\dv{x}\qty(\int_x^a f(t)dt)=\dv{x}\qty(F(a)-F(x))=-f(x)$

[twin meteor]

;(

[silk osprey]

well you’ve demonstrate already that $\frac{d}{dx} \int_a^x f(t) , dt = f(x)$

[twin meteor]

knief

[silk osprey]

now using this you can write it in the same form

$F(x) = -\int_{12}^x \tan(t^3) , dt$

[twin meteor]

knief

[quiet echo]

[gray fox]

okay so now the answer is -tan(x^3)

[silk osprey]

yep

[gray fox]

okay perfect! i had it right the first time i just forgot to add the negative when i switched the bounds! thank you!

[silk osprey]

you’re welcome

[gray fox]

okay heres another question. we didnt have a lecture on how to integrate with it equaling to y

so i dont know how to get dy/dx

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[frosty void]

im doing practice tests for logical reasoning. i am really struggling to find patterns. in any of them, how does one get better at these

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@frosty void you know you can ping helpers after 15min right?

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[native aspen]

hello

[native aspen]

im simply attempting to verify my question answers

a. x=15.27

b. X=7.2

[little bluff]

,rccw

[native aspen]

im going to bed

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[willow tendon]

And i have a doubt for a line ax+by+c why is the slope -a/b

[visual marsh]

bro equate it to 0

keep y ni one side

y = mx +c

[willow tendon]

Oh yes it comes in the format of y= mx +c

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[frail violet]

Can someone break down this scary double summation into something more digestable cuz wtf are they trying to say how is this the dot product what does the matrix A represent someone explain pls pls

[hard atlas]

write out all summations explicitly for n=3

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[frail violet]

What 💀

I don't get it

[hard atlas]

instead of say $\sum_{i=1}^3 a_i$ write $a_1+a_2+a_3$

[twin meteor]

Denascite

[hard atlas]

do that for all the sums

yes this is a bit of writing

but it will help you get more familiar with it

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[bold scarab]

im not sure how to do 6a

[frail violet]

lmao without using technology, good wording

[stone gazelle]

Start with x = log_b(a)

Apply b^(..) to both sides

[bold scarab]

a=b^x

[stone gazelle]

Now what other log do you need to mix in?

[bold scarab]

lna=xlnb

so then x= lna/lnb?

[stone gazelle]

No, we arent working with base e here

You ultimately want to write it in terms of a new base, c

So you can apply log_c now to both sides

[bold scarab]

so i use log_c instead of ln and that would be x=log_c(a)/log_c(b)

but then how would i apply that to the other stuff in 6a??

[stone gazelle]

Well that’s all the question was asking

Sub back the substitution for x and you have proven it

[bold scarab]

oh

thanks so much

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[tardy jetty]

Hi, I was just wondering, the half life and double time formula learned y = y0 (1/2)^(t/n) looks very familiar to a differential equation. Is it possible to figure out what the differential is?

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[tropic slate]

I have a rectangle that is 440 wide and 320 high. I create a 30 degree isometric projection with the rectangle on both the XY and XZ planes. I now want to calculate the width and height of the visual bounding boxes around the XY and XZ planes of the projection. I already have three of the four formulas, however I can't figure out the formula for the XZ plane height.

\[
\text{xy-plane-width} = (\text{width} \cdot \sin\left(\frac{\pi}{4}\right)) + (\text{height} \cdot \cos\left(\frac{\pi}{4}\right))
\]
\[
\text{xy-plane-height} = \text{xy-plane-width} \cdot \tan(\text{angle})
\]
\[
\text{xz-plane-width} = \text{width} \cdot \sin\left(\frac{\pi}{4}\right)
\]
\[
\text{xz-plane-height} = \, ?
\]

The dimensions and angle here are just examples, I need the formulas as the actual width, height and angle will change. Here's an illustration of the problem if that helps explain further:

[twin meteor]

Jack Sleight

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[crude yoke]

Can you guys help me find the circle that touches this parabola and the two lines?

[gritty sage]

What's the equation of a circle?

[crude yoke]

that's what I'm trying to find .-.

[gritty sage]

No, I mean (x - h)^2 etc.

[crude yoke]

ah, it's in the image

[gritty sage]

The equation of a circle is (x - h)^2 + (y - k)^2 = r^2.

[crude yoke]

Uhm… idk… what I meant earlier was finding the equation of the circle, so yeah, I don’t have it .-.

[gritty sage]

No, that's not what I'm asking.

I'm not asking for the equation of this circle.

I'm asking for the equation of all circles.

[crude yoke]

ah! yeah, I want the circle to be in this form

[gritty sage]

OK, so x = 2/3 is one line.

So, we can have (2/3 - h)^2 + (y - k)^2 = r^2.

We have (x - h)^2 + (0 - k)^2 = r^2 which comes out to (x - h)^2 + k^2 = r^2.

And then we have it touching the parabola.

[crude yoke]

Yeah… I can figure out h and k based on r using the first two conditions, but how do I solve for r with the third one? It’s so hard :(

[gritty sage]

OK, so what do you get for h and k?

(based on r)

Oh, can you show your work?

[crude yoke]

h = 2/3 + r and k = r

[gritty sage]

Looks good.

[crude yoke]

how about finding r :(

[gritty sage]

OK, so we have y = (x - 2)^2.

[crude yoke]

*-2

[gritty sage]

Oh, sorry.

(x - h)^2 + (y - k)^2 = r^2
(x - (2/3 + r))^2 + ((x - 2)^2 - r)^2 = r^2

I filled in h, k, and y.

[crude yoke]

Then… solve for x? That’s gonna be 4th order. Yeah, this isn’t looking good .-.

[gritty sage]

Hmm.

Well, let's see. The radius to the contact point on the parabola will be perpendicular to the tangent line there.

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[crude yoke]

<@&286206848099549185>?

[flat whale]

Use chai 's hint

[flat whale]

.

[crude yoke]

which contact point should I pick for the tangent calculations?

[flat whale]

That's an unknown

You keep it unknown while you solve and then at the end the equations you get will give you the contact point

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[smoky cave]

I have no idea where to start

[restive tundra]

Try and work out the maximum volume of the prism for any given height h

Then maximize the volume as a function of h

[smoky cave]

but how to calculate the volume of prisim?

how to get the side of the hexagon

is it let x

[restive tundra]

If you know how tall the prism is, then you know what the diameter of the hexagon has to be

[smoky cave]

so let the height be h

[restive tundra]

e.g. if the prism were 15 cm tall, then the hexagon has to fit into a circle with diameter 5cm

Then from there you should be able to work out the volume of the prism

Yes let the height be h

[smoky cave]

ok let me try it out

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[slow pelican]

How to solve question 2

[slow pelican]

I got here but it’s wrong

[bold hound]

In third to last row it should be -24 b

[slow pelican]

Ohhh tysm

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[gilded elm]

hello could someone help me solve this problem?

A company produces ball-shaped Christmas tree decorations. The decorations are packed in | closed boxes in the shape of a rectangular parallelepiped. | exactly 6 balls can be placed in the box so that they touch each other and all the walls of the box (Fig. 2). The dimensions of the box are 18x6x12. Calculate the volume of one ball.

[restive tundra]

Try working out the diameter of each ball first

[gilded elm]

The problem is I don’t know how to

I have this math test in 2 hours

[restive tundra]

Does this help?

[grim verge]

its a parallelpiped

[restive tundra]

A rectangular one

Afaict it's just a cuboid, otherwise the question is impossible

[grim verge]

oh

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[brave raptor]

how f(i) not equal to f(i + 1)

[brave raptor]

in the 7th line of the solution

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[sterile cradle]

part c)

not sure how to get it in that form

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[pallid forge]

what did you find the area to be?

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[random peak]

I need to check if V is a vector space over F
Is it correct to claim that is not a vector space over F since we can take a scalar constant = -1 (which belongs to F) such that -1 * v ( where v belongs to V) does not belong to V

[random peak]

if so then what is even the point of giving me customised addition defintions

[cobalt crypt]

which v do you think that is?

[random peak]

any positive number

[cobalt crypt]

okay lets take v = 69

what is -1 * 69?

[random peak]

-69

[random peak]

ah damn

[cobalt crypt]

i think you should stop and read the question

[random peak]

yep my bad

.close

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[sterile cradle]

.reopen

let me get a new one

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[soft lodge]

yo

[soft lodge]

0.00836 to 2 sig figs is what

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[pallid forge]

do you have a guess?

[whole zealot]

Can you guess what it is first?

[soft lodge]

yea

uhh

0.0084?

[whole zealot]

Yup.

[soft lodge]

.close

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[potent gulch]

How can i solve this one? I hope somebody knows to do this witout polar variables

Just show how can i do corectly the domain of integration

<@&286206848099549185>

[whole zealot]

I can't help with that, sorry...

[vocal sleet]

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[potent gulch]

.close

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[wet bramble]

hello

[silver tusk]

@wet bramble do u have a question

[atomic jasper]

do you have a question?

[wet bramble]

i want to ask if anyone here from alevels ?

[atomic jasper]

a question from maths a levels?

[wet bramble]

not yet

i'll ask if i need help

[silver tusk]

bruh

[modern ledge]

...

[atomic jasper]

only use this channel if you have a question

[silver tusk]

someone ping mods

[atomic jasper]

for general chatting you can go to #discussion

[wet bramble]

okk, sorry

[atomic jasper]

!done

[vocal sleet]

If you are done with this channel, please mark your problem as solved by typing .close

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[atomic jasper]

.close

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[sacred anvil]

Given a right-angled triangle ( ABC ) at ( A ), with ( BC = a ), ( AC = b ), and ( AB = c ).

1. Prove that ( H ) is the weighted reference point:
   • The weighted reference system is given by ( {(B, b^2); (C, c^2)} ).

[twin meteor]

adem-008

[vocal sleet]

@sacred anvil Has your question been resolved?

[mental egret]

!status

[vocal sleet]

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

[mental egret]

Also, since I've seen this Q for the 10th time, I'll just ask

[sacred anvil]

I don't know where to begin

[mental egret]

Can you clear up what is meant by "H is weighted reference point". Is there some context you were taught prior to this?

Also, what is H? Orthocenter? Some random point?

[sacred anvil]

I mean two-point weight or sentence weight

[mental egret]

Can you send a pic of the context? Any similar problems you've seen or done before?

[sacred anvil]

If we have a right triangle ABC at A, where BC = a, AC = b, and AB = c. 1. Prove that H is the probability of the sentence {(B, b^2); (C, c^2)}

any help here guys

https://tenor.com/view/someone-help-me-matty-matheson-cookin'-somethin'-matty's-essential-food-guide-for-back-to-school-i-need-help-gif-6783682195022337618

[sacred anvil]

.close

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[willow scaffold]

need help on this dif equation

[willow scaffold]

1 sec

idk how to solve for y

[atomic jasper]

have oyu heard of an integrating factor?

ah wait, y is a function of x right?

[willow scaffold]

idk what dym but i need to solve for y

[crimson coyote]

is there somone who understand frensh

[atomic jasper]

you cant just go from line 5 to 6

y is a function of x

so $\int y^2(x)dx\neq xy^2(x)$

[twin meteor]

Bonk

[willow scaffold]

what should i do then

[atomic jasper]

!original

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[atomic jasper]

can you send the full original question?

[willow scaffold]

its just like this\

it says solve the differential equation

[atomic jasper]

there must be some trick that im not seeing

sorry

i dont think i can help

[willow scaffold]

huh? what trick it literaly says solve the following differential equation XD

[atomic jasper]

yes but i mean like some clever substitution or factorisation or whatever that makes the solution pop out

[willow scaffold]

its ok

[vocal sleet]

@willow scaffold Has your question been resolved?

[gentle shadow]

what do we have to find

i can't understand spanish

[willow scaffold]

we have to solve this differential equation

[gentle shadow]

so just basic differentiation of lhs?

[willow scaffold]

in other words find y

[gentle shadow]

bruh we dont have x , how can we find y

[willow scaffold]

no x?

[gentle shadow]

y' = [-(2x+y)^2 - 3xy]/5xy-3x^2

[gentle shadow]

i meant no value for it

do we have to find it in terms of x and y?

[willow scaffold]

idk wdym

i started with y'=dy/dx

so u can integrate

[gentle shadow]

do we have to find value as only in numbers or can there be x and y

[gentle shadow]

this just algebra

[willow scaffold]

u have to find y = numbers + x

[gentle shadow]

ahhhhh

[gentle shadow]

just take integral of this

[willow scaffold]

u cant have y on both sides

[gentle shadow]

oh i forgot again that we needed integral not deravitive

[vocal sleet]

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[gentle shadow]

bro u dont need to do all dat

[outer warren]

id recommend leaving stuff in factored form for most of it
in line 2, instead of expanding everything, use conjugates

[gentle shadow]

just use power rule

[outer warren]

they're being asked to use 1st principles

[bold scarab]

the question says to use first principles..

[gentle shadow]

oh sorry man

[gentle shadow]

which question u doing?

[bold scarab]

5c

[gentle shadow]

wait lemme get paper pencil and cook

[visual marsh]

do uk binomial approximation?

[bold scarab]

i dont know binomial approximation

[candid magnet]

use L'H

[heavy wasp]

what grade u guys in

I have heart attack looking at these qs

[bold scarab]

im in 11

[heavy wasp]

interesting

[gentle shadow]

yo do u know square root difference formula

i think i finally made a break through

[visual marsh]

whic one?

[gentle shadow]

bro like sqrt(x-h) - sqrt(x) = 1/[sqrt(x-h)+sqrt(x)

basically changes signs

[visual marsh]

u mean rationalizing?

[gentle shadow]

yo

[gentle shadow]

ig by definition

[bold scarab]

yea

[gentle shadow]

so after ur 2nd last step

[gentle shadow]

split the fraction

[visual marsh]

just multiply and divide by
sqrt(x-h) + sqrt(x)

[gentle shadow]

then cancle 1 out of 2 fraction's h

then

u should get x^2[sqrt(x+h) - sqrt(x)] /h

[gentle shadow]

then just use this

and cancel out the other h

u should get x^2/sqrt(x+h)+sqrt(x)

[gentle shadow]

plus whatever u get out of this

and then substitute h with 0

and abra ka dabra

u got the answer

[visual marsh]

yea

[gentle shadow]

in the end u should get f'(x)=[5(x^3/2)]/2

[bold scarab]

ok ill try that, i just tried redoing the question a diff way and idk what i did but i got the numerator correct but no denominator

[gentle shadow]

isn't that good cuz u canceld out h

[visual marsh]

i suggest u to leanr binomial approximation
the anser comes in 4 to 5 lines

[gentle shadow]

bro its probably not allowed

[bold scarab]

im missing the 2 as a denominator lol

ok wait im gonna actually redo it using your steps

[gentle shadow]

i hope u can understand it because i am not used to no notations

[bold scarab]

.close

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[quiet scaffold]

can somone help me with geometry:)

[heady vine]

you know what is the definition of a tangent ?

[quiet scaffold]

no im not very intelligent:)

Im learning

[heady vine]

ok a tangent is a segment that touches the circle at exactly one point

[quiet scaffold]

hmm

[heady vine]

so with this definition what do you think the answer should be ?

[quiet scaffold]

AB

[heady vine]

yep that's correct

[quiet scaffold]

Im learning

i got more tho

[heady vine]

ok

[heady vine]

ok a secant is a segment that passes through the circle
so with this in mind what do you think the answer should be

[quiet scaffold]

Uhhhm

lemmw think

[heady vine]

take your time

[quiet scaffold]

I think its either ab or gh

[heady vine]

ab only touches the circle from the outside so it's a tangent
but gh passes through the circle

[quiet scaffold]

interesting

[heady vine]

you are doing great

[quiet scaffold]

so the correct answer is GH

[heady vine]

yep

[quiet scaffold]

yay i have a few more am i taking up your time?

[heady vine]

nah, it's ok really

[quiet scaffold]

one sec i have to switch to a new device

[heady vine]

ok no problem

[quiet scaffold]

I have to go sorry to take your time

[heady vine]

nah it's ok

[quiet scaffold]

Thabks btw

[vocal sleet]

@quiet scaffold Has your question been resolved?

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[rain canopy]

hi guys i have a question regarding this operation

[rain canopy]

this result gives me 1.5

(the first fraction, i mean square of 3 * square of 3 / 2)

why i get 1.5?

[mental egret]

,calc sqrt(3)*sqrt(3)/2

[twin meteor]

Result:

1.5

[rain canopy]

yeah but in the uni docs the result is 3 / 2

[mental egret]

,calc 3/2

[twin meteor]

Result:

1.5

[rain canopy]

yes

3 / 2 its 1.5

but why in the uni docs i get 3 / 2

that's my question

[mental egret]

Why √3 cos(π/6) is 3/2? Is that what you're asking?

[flat whale]

is your question why does $\frac{3}{2} = 1.5$ ?

[twin meteor]

riemann

[rain canopy]

no

my question is why this

gives this

[heady vine]

sqrt(3)*sqrt(3)/2= 3/2

[flat whale]

$\sqrt{a}\cdot \sqrt{a} = a$

[twin meteor]

riemann

[rain canopy]

the first thing i tried is using my calculator and obviously it gave me 1.5

[flat whale]

for all a > 0

[rain canopy]

but i wonder why 3 / 2 instead of 1.5

[mental egret]

,calc sqrt(3)*sqrt(3)

[twin meteor]

Result:

3

[heavy yoke]

that's just fraction vs decimal, same number

[rain canopy]

yes, i just discovered that this operation gives the plain number

[flat whale]

isn't this your question then

[rain canopy]

but now the thing is why 2

[rain canopy]

i explained badly

[rain canopy]

i don't mean why 3 / 2 = 1.5

[mental egret]

They wrote it as such because it was unnecessary to reduce 3/2 to 1.5

[rain canopy]

i mean if the result is 1.5, why the fraction in the uni docs is 3 / 2

[flat whale]

they're equal so it doesn't matter

[rain canopy]

u kidding aight?

its like

why?

[mental egret]

Do you write cos(π/4) = 1/√2 or 0.707106...??

[rain canopy]

if the result is 1.5 why write 3/2?

[flat whale]

.

[heavy yoke]

in math it's often more convenient to leave something as a fraction than to write it as a decimal, because often the decimal does not terminate

e.g. 2/3 is much more convenient than 0.666666666666666666

[rain canopy]

yeah but if i'm learning its supposed that you write the stuff correctly not because you want you write wathever.. lol, i get it thanks

so basically writing 1.5 instead of 3/2 is the same?

[flat whale]

neither is incorrect

[flat whale]

that's exactly what this means

[mental egret]

Yes, but writing √3*√3/2 = 3/2 would save your a** in the long run

[rain canopy]

i don't think (for me) it will save my ass

i prefer the "long" way because at least i can understand what's going on

[flat whale]

you should also understand fractions

if your teachers gives fractions, you should do it the long way yourself.

[rain canopy]

i understand fractions, the problem is when people writes nonsenses 😭

[mental egret]

You'll be dealing with √(10 - 2√5)/4 and (√5 + 1)/4... I hope you don't go reducing to decimals then

[flat whale]

if the long way means writing out the decimal expansion

[flat whale]

nothing about the solution is nonsense

[rain canopy]

now i checked that 1.5 + 0.86 and 3/2 + square3 / 2 are the same result

[flat whale]

you don't if you only understand decimals

[rain canopy]

hmm yeah, i mean if you write 1.5 its 1.5, not 3/2, i get its the same but for someone like me that is learning its really complicated to guess that they're both the same

anyways thank you my question has been answered

[mental egret]

Looks more ridiculous to me

[flat whale]

it takes 1 second to plug in 3/2 into a calculator to get a decimal expansion

[mental egret]

Unless you're gonna go √3/2 = 0.707106 in which case... Welp

[rain canopy]

i prefer this instead of "because i want i will do 3/2 + xxx" or we talk about guessing stuff, then i could write "eiufhn+wiue" and just let my boy guess that this means 1+1.... somewhere it should be telling what it means each term, otherwise its really hard to learn

.close

[vocal sleet]

Channel closed

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[rain canopy]

thank you guys

[mental egret]

The main focus of topic is Trigonometry, not mental math but okie 👌

[vocal sleet]

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[exotic hill]

Have I done this calculation correctly? The question is to compare both numbers and to see which one is bigger or if they are the same size.

[outer warren]

I don't understand your
<=> notation

[exotic hill]

I don't think it is a correct notation, but it was a way for me to write that i compare these two values and avoid using a equal marking

My answer is that quantity I is bigger than quantity II

[outer warren]

you could do something like
$$\overset{?}{\ge}$$

[twin meteor]

ℝαμOmeganato5

[outer warren]

personally I'd manipulate one side

[exotic hill]

Alr I will change it

[outer warren]

2sqrt(2) + 3sqrt(3) > 2sqrt(2) + 3sqrt(2) = 5sqrt(2)
therefore
...

[exotic hill]

Alr thank you!!!

.closed

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.close

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[rotund sable]

https://gyazo.com/c4e7398dde120e83ae96f87203113644
https://gyazo.com/63fe6bcd36049da5196d345a4fe25d0d

[rotund sable]

if f(x) is original, how do I descrive the change in its base to g(x)?

idk where to start

[atomic jasper]

look for the differences

[rotund sable]

do i simplify (-4x)(1/8) to -1/2 (x)

[atomic jasper]

why?

i mean, you could

doesnt rly matter

sure

[rotund sable]

so it changes from x to -1/2 x

how would i apply that tio the base?

(6/16) / 1/2 ? because its a negative exponent

or

https://gyazo.com/81a0afa97ef547d5f1ec3353854153ac

if this is right

then id do 1/ (6/16)^(1/2)

and get 1.632

my answer choices are narrowed down to either
https://gyazo.com/75ff5876467896d7f56df6f8b5ecaf6a
https://gyazo.com/6ac34b2a393d830993974955c795ec0e

and since 4 sq6 / 6 equals 1.63 would option 1 be right?

https://gyazo.com/2fe07429bee07af1e89dc819f170fe37

idk if im onto something or just on something

<@&286206848099549185>

[vocal sleet]

@rotund sable Has your question been resolved?

[vocal sleet]

@rotund sable Has your question been resolved?

[vocal sleet]

@rotund sable Has your question been resolved?

[rotund sable]

.close

[vocal sleet]

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[vocal sleet]

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[teal vine]

how is my solution wrong

[half imp]

e^(1/0) is not infinity

the limit with e is wrong

[teal vine]

yeah but isnt it the limit

as it approaches that

so when t -> ZERO shouldn't the value of e^(1/t) be e^(inf)

[half imp]

It doesn't approach infinity

[teal vine]

bcz when u approach zero for t the value becomes larger and larger

[teal vine]

yeab mb typo

[half imp]

No it shouldn't be

[teal vine]

i mean t -> zero

[half imp]

The limit of 1/t as t approaches 0 is not Infinity

[teal vine]

how come

[lost barn]

bc you havent specified which side it approaches from

[teal vine]

ohhh

yeah thats a valid point

[lost barn]

in fact, your entire calculation is incorrect bc u forgot to consider that

dont worry tho its easy to forget that while ur just trying to do the integral

[teal vine]

yea so if it was approach 0 from the right instead 1/t would have been inf

however if u approach 0 from left it would be -inf instead

[half imp]

yeah

[teal vine]

but if u take the limit by itself it would only exist if L & R limits are the same

[half imp]

right

[teal vine]

howd i fumble that 😭

okay thank u

[half imp]

For an improper integral you can probably define it as approaching from the "inside" direction

[teal vine]

the heck is an inside direction

[half imp]

so in this case from the left, since 0 is the right bound

Though you should just go with whatever your book says

[teal vine]

wait whatre u saying im so lost

[teal vine]

ur defining the integral based on the side it doesnt exist?

[half imp]

Based on the side it does

Like integral from -3 to t is defined for t in (-3, 0) at least

we can't define it for t>0

At least unless we already know that it's defined at t=0

If I were to ask about the integral from -3 to 3 for example, you might take the antiderivative and plug in 3 and -3 and subtract them

And that would be wrong, because you haven't checked that it's even defined from -3 to 0

Since there's a vertical asymptote there you have to worry about the integral being infinite

[teal vine]

yep for sure

[half imp]

So the only way to define the improper integral is to take the limit in this case from below, because the integral isn't even yet defined for t>0 until we can define it for t=0

[teal vine]

ya isnt that what we're doing

or r u talking bout the case when we have -3 to 3

cuz then we'll have to consider for the 0 by splitting it

[vocal sleet]

@teal vine Has your question been resolved?

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[fleet hemlock]

so im using this formula for rotation of point but it dosnt seems to work im not sure why

[fleet hemlock]

my point just kinda desided to move

this is the math if u need

c1p_x
is the x and so on

im so lost

this should work

is that some random float value misscalculation or smth

witch is like unfixable

[vocal sleet]

@fleet hemlock Has your question been resolved?

[fleet hemlock]

what am i suposed to do with them

why dont they just give me the formula

why is it like writen super complex what this mean

someone sayd the fist one is = to
X , Y cos0 - Zsin0 , Z sin0 + cos0

how do u get to this result

it dosnt seems to work either

why isnt theire just one formula for rotating object that work that they give u

why do i have to calculate the formula myself from the formula they give

just give me the working formula from the get go

in normal math not with those weird calculation no one can do

it amke sence the first result is x cz we have 1 0 0 si 1 x result

by why does y*cos() y*sin() = Y cos0 - Zsin0

why is theire a z out of nowhere

thi dosnt make sence

x*0 y*cos z*-sin

i get it

but it still dosnt work

x*1 y*0 z*0 = x
x*0 y*cos() z*-sin = smth

how do u merge them together

[jagged cargo]

it IS the formula

[fleet hemlock]

im so lost

[fleet hemlock]

and it dosnt work

[jagged cargo]

rotating stuff is way more complex than you think

[fleet hemlock]

my point are going evrywhere they shouldnt

[jagged cargo]

like bacteriofrog said, learn some linear algebra

[fleet hemlock]

why dont u just help me

[jagged cargo]

or, idk, manually rotate them and keyframe them

[fleet hemlock]

that sthe point of the server

[fleet hemlock]

no thats bad

it woulldnt work

[jagged cargo]

the point of the server also involves you willingly put in effort

[fleet hemlock]

i am smh

[jagged cargo]

clearly you aren't

learn some linear algebra

[fleet hemlock]

how do u not see me trying to figure out how those bracket thing work

[jagged cargo]

i can recommend you some books if you like

[fleet hemlock]

and help me

ffs

i just need help

i have all the base theory of 3d render

it work

i had a cube

it just dosnt wana rotate

[fleet hemlock]

i used this formula

but it lmissplace my point

as i said

so i need another one

i got this

i have evrything

the whole rendering and printing point prosses

the rotating just dosnt wana work

[fleet hemlock]

^

it mysplace the point my a tyna amout

why is it so hard to help ppl

[fleet hemlock]

your fucking stupid

thats not how u help someone learn

[jagged cargo]

??????????

<@&268886789983436800>

[fleet hemlock]

ive help a bunch of ppl coding

just help me like someone normal

teach me then wtf

[fleet hemlock]

why arnt u telling me

i want this thiung to work

[fleet hemlock]

as u can see here i got it relly close to working

i relly just need a heads up of whats wrong

[jagged cargo]

you need to modify all the points, not just the 4 corners

[fleet hemlock]

it just like tweaking a lil

theire is just 4 corner

[mild flower]

it might have to do with the fact that you called them "fucking stupid"

[fleet hemlock]

its a plane

[mild flower]

i don't think that's a good way to make friends

[fleet hemlock]

im not trying to make friend i want to learn

and get my thing to work i was super close

[fleet hemlock]

its like a sheet of paper if u want

so theire is only 4 corner

i canot move more they dont exist

[mild flower]

well, i'll thank you not to speak to the helpers like that. yes, linear algebra will be important for computer graphics.

[fleet hemlock]

theirs isnt more then 4 to move

ok but that dosnt mean they canot help me and come with stupid exuses to not help me

ive help a bunch of ppl on other server for coding and i never just told them go read book

its fucking rude

i explain them how it work why it work

[fleet hemlock]

i dont just want ppl to throw the done solution in my mouth like im a baby bird

i want to learn and ive fucking tryd a shit load of thing

all that for them to tell me

no u didnt

like my effort are fucking nothiung

i just spend the 3 last hour doing nothing yeah make sence

i was just siting here for a responce and not activly trying to find solution and understand

[limber falcon]

your formula is correct and so is the implementation in software, so I think it might be this

[fleet hemlock]

i just want a fucking helping hand

[fleet hemlock]

no its unfixable

[limber falcon]

since you're basing everything off the current coordinates px, pz

[fleet hemlock]

how could i make it rotate from the center of the object

[fleet hemlock]

is theire a way to fix that or nope

do i just die now

i was trying to find another formula for it that might work

[limber falcon]

one way I can think is to fix some coordinates q_x, q_y, q_z and then only change the angle variable when the keys are pressed, while setting p_x = q_x*cos(angle)-q_z*sin(angle) and similarly for p_z, on each frame

that way you'd be rotating the same point at all times, just by a different angle

[fleet hemlock]

i see

yeah that would work

thats clever

[limber falcon]

this would also make it easier to set the position of these points relative to the center of the object

[fleet hemlock]

reseting to the base point before evry calculation

[fleet hemlock]

is theire a way to move that

so i can rotate of the center of the object

insted of 0 0 0

i tough about translating the point to 0 0 0 and then translating them back

but it probably a bad thing to do

[limber falcon]

yes, suppose (r_x, r_y, r_z) is the center of the object. Then

(r_x, r_y, r_z) + (q_x*cos(angle)-q_z*sin(angle), ..., ...)

would be the point obtaining after rotating (q_x, q_y, q_z) around the y axis and then adding that to (r_x, r_y, r_z)

[limber falcon]

I think this is equivalent yes

[fleet hemlock]

so im gona need a 3d point in the midle

this merge all relly badly within my game

[limber falcon]

by the way the formula you got is just these matrices evaluated in some vector (p_x, p_y, p_z)

[fleet hemlock]

ill need to redo some stuff

[fleet hemlock]

yes thats what i meant by why do they give me a formula that still need to be calculated

why not just give me the result right away

witch i belevea is those

[limber falcon]

it's a bit easier to write the formulae in terms of matrices, but yes they're the same thing in the end

[fleet hemlock]

alr

[fleet hemlock]

i dont relly understand this

so i have

c1.p_x*cos(angle0)-c1.p_z*sin(angle0)

and i make it

what

what operation is ,

(c1.r_x, c1.r_y, c1.r_z)+c1.p_x*cos(angle0)-c1.p_z*sin(angle0)

[limber falcon]

oop , is just there to separate the entries of the vector

[fleet hemlock]

so how do i imput them

hmm

ig if im doing a x axis rotation

i just need the x center

so

c1.r_x+c1.p_x*cos(angle0)-c1.p_z*sin(angle0)

[limber falcon]

I also didn't write the other terms of the result of the x axis rotation

[limber falcon]

this is the first coordinate yes

[fleet hemlock]

this

good

so im gona need a middle point

ig i could make a 3d line funxction and all that to calculate where it is

or hardcose it

ill do that

ok

so much work

this is also not gona work for a system witch need to work on multiple sprite

[silk osprey]

@fleet hemlock

[fleet hemlock]

itt reapeard

idk how

[silk osprey]

magic

[fleet hemlock]

oh

i colapsed the chanel list

[mental egret]

an airhead!!

[fleet hemlock]

it dosnt seems to have worked

i dont understand why it keep not working

i folowed evrything

the point are in 187 and 319
so 253 should be the middle

[silk osprey]

*you’re

[mental egret]

It seems to me that the points each are rotating about their own "fixed points" defined seperately for each of them

[fleet hemlock]

no they rotate from 0 0 0

look pretty much like this

its hard to see simce no line

this whole program dosnt work anyway the camera face is at 0 0 0 so the paralax is all wrong

[mental egret]

https://youtu.be/zI7VnovtFSA?si=n2J90QiVlS-wyQ-_

Check this ._>

[vocal sleet]

@fleet hemlock Has your question been resolved?

[fleet hemlock]

what ab this

[vocal sleet]

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[near finch]

Is 1 b correct

[near finch]

I know it’s not the more effecianr way

Efficant

I hate spelling but u get my point

Same here is 1 b correct

[vocal sleet]

@near finch Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[cedar charm]

is this not 6?

[cedar charm]

my graph

[half imp]

you switched the conditions

you graphed x for x<2 and 2 for x>=2

[cedar charm]

ohh i see, thank you!!

[half imp]

np!

[cedar charm]

.close

[vocal sleet]

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[cedar charm]

.reopen

[vocal sleet]

✅

[cedar charm]

need help with part f

ill send in my work in a sec

not sure where to go after this

[solar cape]

For part f just remember the sum rule for integration

[cedar charm]

yea so is this how u do the rule

i’m confused on what to do with the constant +2

[solar cape]

From part e.) we know that $\int_{-4}^6 f(x) dx=2\pi+5$

[twin meteor]

denzio321

[cedar charm]

👍

i understand that part

[solar cape]

So it's just 2pi+5+(2(6)-2(-4)) no?

[cedar charm]

where is 2(6)-2(-4) coming from

[solar cape]

The integral of 2

[solar cape]

I thought u were saying you understood the whole sum rule

Mb

So $\int_{-4}^6 [f(x)+2] dx=\int_{-4}^6 f(x) dx + \int_{-4}^6 2 dx$

[cedar charm]

it’s just + 2 right?

[solar cape]

Wait yea mb

Typo

[cedar charm]

not 2x

[twin meteor]

denzio321

[solar cape]

Yes typo

[cedar charm]

ok i understand first half

[solar cape]

So from here can you get the answer

[cedar charm]

what is 2dx

that’s the part i don’t understand

[solar cape]

Its just taking the integral of the constant 2

Which would be 2x

[cedar charm]

i don’t think i understand it still… i’ll just ask my friend tomorrow

thanks for all the help tho

[solar cape]

No what don't you understand

Just tell me

It's probably something minor

[cedar charm]

how do u solve for that

i don’t understand taking the intergal of constants

[solar cape]

Ok what's the derivative of 2x

[cedar charm]

2

[solar cape]

So what's the anti derivative of 2

[cedar charm]

2x?

[solar cape]

Yes

[cedar charm]

so integral is just the reverse of derivative?

[solar cape]

Well in a sense

Usually we'd add a constant c

[cedar charm]

so here where did u get 6 and -4 from

[solar cape]

The bounds of the indefinite integral

-4 to 6

[cedar charm]

oh

[solar cape]

Did yall learn this in class

[cedar charm]

i learned the properties

this is what we learned

[solar cape]

Yea exactly like what you do at the bottom

Imagine 2 as 2x^0

[cedar charm]

ohhh so this part

5(3-1)

[solar cape]

Yea

Same thing as 5(3)-5(1)

[cedar charm]

i really understand it now thank you so much

you’ve been very helpful 🙏🙏

[solar cape]

Yw

[cedar charm]

.close

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[whole forge]

Hello guys

[whole forge]

Was my answer correct?

[jagged cargo]

i only checked the first question, and already i see 3 wrong answers

[atomic jasper]

a=2
b=3
c=DNE
d=2
is for question 1 right?

[whole forge]

Yes

[atomic jasper]

a, b and c are wrong

[whole forge]

Hmmm

[whole forge]

Why?

[atomic jasper]

how did you get those answers?

[whole forge]

Stock knowledge and just looking at them.