help-19

[fickle laurel]

Doing this is probablyy not the way to go since too verbose

But I’m running out of ideas

Our number is a multiple of a perfect square

But that doesn’t help us that much

Would anyone have ideas?

<@&286206848099549185>

[dreamy yacht]

Maybe a step that narrows everything down a bit is to notice that your product on the left is bigger than the sum of the digits to the 5th power. Therefore, the digits have to be less than or equal to 6

[fickle laurel]

That's a good point (because 7^5 > 10000)

Although I'm not sure how I could use that information other than accelerating my python script to find everything

[dreamy yacht]

We can go further to less than or equal to 5

[odd edge]

@fickle laurel Has your question been resolved?

[fickle laurel]

Why?

5000 would be greater than 5^5=3125

So left hand side bigger than right hand side

So I don’t think we can bound similarly to what we previously did?

[dreamy yacht]

6^5 = 7776

So if we had a 6 our first digit needed to be at least a 7

[fickle laurel]

Ah

Fair enough

Good point

Does make the search easier but still ain’t convinced that’s what my teacher suggested with analytical solution

[odd edge]

@fickle laurel Has your question been resolved?

[odd edge]

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[lilac viper]

i can help

[lilac viper]

2 + 2 is 10

your welcome

@rapid dove Mohammed alli what do you need helpå with

[wooden python]

<@&268886789983436800> troll

[mystic saffron]

No

[odd edge]

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[raw jewel]

I'm having trouble with the highlighted part I vaguely remember learning how to do this type of problem but I don't remember the reason why it works 😅

[odd edge]

@raw jewel Has your question been resolved?

[raw jewel]

<@&286206848099549185>

[woeful yoke]

?

[raw jewel]

I could use some help with this problem

[odd edge]

@raw jewel Has your question been resolved?

[rapid dove]

?

bro I never asked for help

💀

like icl last time I touched this 1-2 years ago

🙏

ussful though

[odd edge]

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[shut moon]

<@&286206848099549185>

[elfin zodiac]

#❓how-to-get-help

[shut moon]

i need help with (9 + 1) x 4 + sin(5) % 23 - 3 x 56 - 8 (x) + 452 x 2 (6 - 3) % 3.563 - 1 x (67+4) - 0 x 2 % 5 - (1) (1) (1) 0

[elfin zodiac]

$(9 + 1) \times 4 + \sin(5) \mod 23 - 3 \times 56 - 8x + 452 \times 2 \times (6 - 3) \mod 3.563 - 1 \times (67+4) - 0 \times 2 \mod 5 - (1)(1)(1)0$

[clever fjord]

Samuel

[elfin zodiac]

This?

[shut moon]

yes

[elfin zodiac]

What part you don’t know to do!

[shut moon]

times 4 + \sin(5)

[elfin zodiac]

That is because you don’t do that

Every time you see a + or a -, what’s behind is a whole thing

So the first + u see

Everything behind it is only one thing

In this case (9+1) 4

You solve to get a whole number and then you have

[shut moon]

ah i see

[elfin zodiac]

I gotta go now, sorry

[shut moon]

k

[odd edge]

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[frigid canopy]

$\int x^2 \sqrt{x-1}dx$

[clever fjord]

Why am. I here

[frigid canopy]

I subbed $x-1=u^2$

is there any other sub I can use

[clever fjord]

Why am. I here

[spiral basalt]

it should work

[frigid canopy]

yeah, but is there any more elegant sub I can use

[spiral basalt]

WA does the same thing

[frigid canopy]

ok, thanks!

.close

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Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[karmic hollow]

.close

.close

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[elfin zodiac]

This is nonsense, stop trolling

[rocky warren]

I'm not trolling

[elfin zodiac]

What are you studying?

[rocky warren]

economics

phd level

[elfin zodiac]

🙄

[rocky warren]

same

[elfin zodiac]

You didn’t even ask a question, stop wasting others time

[rocky warren]

thanks for the help

[elfin zodiac]

As I thought, u don’t even know what to ask xd

[rocky warren]

please don't waste my time...i posted my question...i need help with that derivative...

<@&286206848099549185>

Can you help me with this derivative of the image?

[latent scaffold]

What have you tried?

Surely with your economics PhD studies, you would have tried something out wouldn't you?

[rocky warren]

I don't understand the ostil tone...

[latent scaffold]

It's not hostile, I'm genuinely asking what you've tried

[rocky warren]

yes, i tried something

let me show you

[elfin zodiac]

Get ready xd

[urban dagger]

[rocky warren]

i was trying to apply the chain rule...

[latent scaffold]

Great then you're all set

[rocky warren]

thanks

[latent scaffold]

No problem! Anything else?

[rocky warren]

you can't help me...

[latent scaffold]

What do you mean? You've computed both factors of the chain rule.

[elfin zodiac]

Help u with what

It’s finished

[latent scaffold]

So it should be elementary for such an astute student as yourself to compute the derivative by applying the chain rule you started yourself!

Unless taking a product is outside the expertise of an economy graduate student, in which case you might want to look into this video 👍 https://youtu.be/GIdXklSQPAI

[rocky warren]

?!

i just asked a question...calm down

[brisk saffron]

Bruh…

[latent scaffold]

Or this one! It's my jam https://youtu.be/CcDGRLosAf0?feature=shared

[rocky warren]

.close

[odd edge]

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[latent scaffold]

Cheers lad

[tall veldt]

Stop being condescending

[odd edge]

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[latent scaffold]

Condescending? This person was quite clearly a troll making everyone here lose their time.

[latent scaffold]

With all due respect

.close

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[next parcel]

Hi community, I'm trying to use the finite element method to get laplacing for my 2d image, could you help me please?

[next parcel]

I see on wikipedia there are two methods:

the 5 point of
0 1 0
1 -4 0
0 1 0

Then the 9 point
0.25 0.5 0.25
0.5 -3 0.5
0.25 0.5 0.25

But then there is another version https://www.karlsims.com/rd.html that says it's got to be
0.05 0.2 0.05
0.2 -1 0.2
0.05, 0.2, 0.05

Which one should I use? I saw on wikipeadia that the 9 point is better for accuracy, but what's the difference between the two 9 point filters here?

Thanks very much🙏

I'm reading this wikipedia link https://en.wikipedia.org/wiki/Discrete_Laplace_operator

[odd edge]

@next parcel Has your question been resolved?

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[storm wharf]

How do I graph x^3+8x^2-11x-12?

[storm wharf]

I think I'm supposed to factor it but I forgot?

[green elm]

forgot what?

[storm wharf]

Forgot how to factor cubic functions?

[green elm]

maybe try the rational root theorem?

[odd edge]

@storm wharf Has your question been resolved?

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[hot fable]

i need help with this one

[hot fable]

i have prelucrated the sum, and it got me to sum of other junk, so I think it is not telescoping at all

[odd edge]

@hot fable Has your question been resolved?

[hot fable]

<@&286206848099549185>

[toxic monolith]

$\text{Remind that:}\text{ }\text{ }e^{x}=\sum_{n=0}^{\infty}\frac{x^{n}}{n!}\text{ }\text{ }\text{ for }\text{ }x\in \mathbb{R}$

[clever fjord]

Joanna Angel

[toxic monolith]

and now think about how to use this fact

[hot fable]

i had worked it out, but I used
e = 1/0!+1/1!+1/2!+...

the limit of series is 5e

thx

.close

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[shrewd beacon]

The area of a small rectangular window is 306 cm2

. If the length exceeds the width by

1 cm, what are the dimensions of the window?

[shrewd beacon]

I have tried substituting and I ended up getting stuck at w^2 + w = 306

What am I missing in my understanding of substitution problems like these?

[smoky mason]

hang on, is it 306 cm or 308 cm?

[shrewd beacon]

308 I think let me check

It's 306

Oh

Is it 17x18

[smoky mason]

yeah looks like it lol

[shrewd beacon]

Ok ty so much

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[cinder basalt]

I watched the video but it doesn’t correlate. I’m not sure

<@&286206848099549185>

[wise jasper]

When doing a question like this, it is important to identify three big things.

Speed, distance, and time.

Which of the three do you know?

@cinder basalt

[cinder basalt]

I know all

I know the speed equations

And how to apply it

[wise jasper]

In this question

[cinder basalt]

However the part I’m struggling with is the bearing

I’m not sure how to draw it

[wise jasper]

I think that is unimportant

not very sure though

[cinder basalt]

And you have to use trigonometry

[cinder basalt]

Its is, the example video showed it

[wise jasper]

Ok, so you are supposed to use trig

[cinder basalt]

This was the example question

That’s similar to it

[wise jasper]

Ok

[cinder basalt]

Yes

[wise jasper]

Gimme one sec

[cinder basalt]

Okay

[wise jasper]

I'll draw a figure

[cinder basalt]

By the way, here the example question says west but the actual question im doing says south

[wise jasper]

The west and south don't really matter

The only important part is the angle

[cinder basalt]

It’s because the bearing can only be measured starting from north going clockwise

I’m not entirely sure actually if it’s important

[wise jasper]

Could be better, but should suffice

Ok

[cinder basalt]

Oh I never thought about it like this

[wise jasper]

Do you know the trig ratios?

[cinder basalt]

Sohcahtoa

?

[wise jasper]

Ye

What side do we know?

[cinder basalt]

yes is it cosine to use

[wise jasper]

Ok

gj

[cinder basalt]

The hypotenuse

[cinder basalt]

Actually is it tan?

[wise jasper]

Oh wait the drawings wrong

gimme a sec

[cinder basalt]

Okay

[wise jasper]

That side is 27km

[cinder basalt]

Ohh

[wise jasper]

So we have opposite

[cinder basalt]

so we need to find the hypotenuse

[wise jasper]

We want hypotenuse

[cinder basalt]

sine

[wise jasper]

Sin of what angle

(measure)

[cinder basalt]

148-90?

[wise jasper]

Which is?

[cinder basalt]

58

27/sin(58)

[wise jasper]

so $\sin(58^\circ) = \frac{opp}{hyp}$

[clever fjord]

Dork9399

[wise jasper]

oh wait mb u alr got it lol

so what is 27/sin58

[cinder basalt]

I got 27.194

[wise jasper]

,w 27/sin(58 deg)

[clever fjord]

Results provided by WolframAlpha

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Requested by dork9399

[cinder basalt]

oh

[wise jasper]

Thats radians

[cinder basalt]

oh is that wrong

[wise jasper]

There are two angle measuring systems

[cinder basalt]

would it be different on my calculator

[wise jasper]

Radians and degrees

[cinder basalt]

ohhh

[wise jasper]

you can change your calculator back and forth

Anyway

The distance is about 31.837

[cinder basalt]

Yes

So now we divide by time?

[wise jasper]

*speed

we want to find time

[cinder basalt]

Ohh

so

wait lemme write this

divide by 6.7

I got 4.06

[wise jasper]

and we can recalculate sin(58) so that we wont make a mistake because we rounded

,w 27/(6.7 * sin(58 deg))

[clever fjord]

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[cinder basalt]

im confused because

When I did 27/sin58

I got a different ans

Even on my calculator rn

[wise jasper]

just do sin(58)

tell me what you get

[wise jasper]

Your calculator is set to radians as well

[cinder basalt]

oh

[wise jasper]

Try pressing mode and see if you can change "rad" to "deg"

[cinder basalt]

Okay

ohh I did it now

How do I know if it’s supposed to be in radians or degrees

[cinder basalt]

It says to 1.dp so is the answer 4.8?

[wise jasper]

Yes

[cinder basalt]

Thank you so much

I understand now

[wise jasper]

If you see the little circle symbol $x^\circ$ then it's deg

[clever fjord]

Dork9399

[wise jasper]

If you don't then its radians

[cinder basalt]

ohh it’s because in school they never taught us to change it

[wise jasper]

ah i see

[cinder basalt]

Thank you so much again

💕

[odd edge]

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[tawny edge]

Can you explain ratios and rates

[quasi sparrow]

https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates

[tawny edge]

Thank you

[odd edge]

@tawny edge Has your question been resolved?

[odd edge]

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[drifting edge]

Anyone have an easy way to remember eulerian vs hamiltonian path? (all edge vs all vertice)

[icy kindle]

Euler, E, Edge

[drifting edge]

Kill me

[leaden widget]

hamiltonian, like alexander hamilton, alexander hamilton fought a duel, duels are fought with pointy things, vertices are pointy

[violet parrot]

hello

[drifting edge]

DAMN NICE ONE

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@drifting edge Has your question been resolved?

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[paper moth]

can anyone help me with this, is it possible to do by using the x^2 + y^2 = r^2 formula?

[paper moth]

you have tell whether the statement is true or false

[summer river]

yes you can

[paper moth]

how?

[summer river]

what's the distance between (5,0) and (0,0)

[paper moth]

5

units

[summer river]

okay

so

what's the radius

[paper moth]

5

units

[summer river]

plug it in

x^2 + y^2 = 25

now is (6,8) inside the circle?

[paper moth]

how do we find that?

do i put x as 6 and y as 8?

[summer river]

you can graph it

[summer river]

or do this

to see what circle it would be at

[paper moth]

so with this method it would 84=25

i have to uuse the non-graph method

[summer river]

just see what circle (6.8) would lay in

like

[paper moth]

green one

[summer river]

mhm

and the radius is greater than the red one

[paper moth]

but i have to solve without graphing

[summer river]

so like

[summer river]

mhm

you can find the radius

using calculator

√(8^2 + 6^2)

[paper moth]

why square root

[summer river]

that's radius

[paper moth]

radius of the green circle?

wait

so before i got 84=25

[summer river]

mhm

[paper moth]

what do i do after this

[summer river]

draw a triangle

[paper moth]

triangle?!

[summer river]

a right triangle to find the radius

it's a triangle with base 6 and height 8

so c^2 = 6^2 + 8^2

c = √(6^2 + 8^2)

[paper moth]

so square root of 84

[summer river]

no sqrt of 100

[paper moth]

oh whoops

yes so 10

[summer river]

mhm

10 > 5

so does it lie outside of the circle or nah

[paper moth]

what does that mean

[paper moth]

this

wdym

[summer river]

10 is greater than 5

[paper moth]

ye ik that but what i am i supposed to use that info for?

like if greater does it mean it lies outside or smthing?

[summer river]

yes

if you have a point on a circle of radius 10

it's going to be outside a point on a circle of radius 5

[paper moth]

so basically we just found the distances between the points and compared them

to find out whether it lies on the circle or not right?

[summer river]

mhm

[paper moth]

can you help with this one as well

@summer river

<@&286206848099549185>

[mystic saffron]

Hey can anyone help

[paper moth]

bruh

take another channel

this one is occupied

[summer river]

ofc

[paper moth]

thanks

and also befor that

prove whether true or false

[summer river]

what's the distance between (-2,4) and (3,5)

[paper moth]

sqr root of 26

and also can we solve using the formula

x^2+y^2=r^2

so basically -2 squuared plus 4 squared should be 6^2

so it is 32 is not equal to 36 so it is false?

@summer river

[summer river]

mhm

,w distance between (-2,4) and (3,5)

[clever fjord]

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[paper moth]

So was my method correct?

@summer river

[summer river]

I think so

[paper moth]

are you sure

????

i feel like its wrong

can anyone here tell me if my method is correct?

[odd edge]

@paper moth Has your question been resolved?

[odd edge]

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[night heron]

I'm struggling to figure out how to get the bounds of this integral here

[night heron]

I know how to properly plug in G for given x and y but finding the bounds is a little more challenging than the ones I had done previously

[odd edge]

@night heron Has your question been resolved?

[night heron]

I plugged in y bounds as a->b and x bounds as 1->5 and it worked ig

Oh well

.close

[odd edge]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[modern tartan]

a^(b/c) is equivalent to the cth root of a^b.

[real breach]

So 2 √2 ^3? For the first one ?

[odd edge]

@real breach Has your question been resolved?

[signal halo]

radical form could also be sqrt(8)

cuz you do (2^3)^(1/2)

8^(1/2)

[real breach]

I’m confused

[signal halo]

do you know exponent rules

like that x^(1/2) = sqrt(x)

[odd edge]

@real breach Has your question been resolved?

[odd edge]

@real breach Has your question been resolved?

[quasi sparrow]

Use a calculator to check your work

,calc (sqrt(2))^3

[clever fjord]

Result:

2.8284271247462

[quasi sparrow]

,calc 2^(3/2)

[clever fjord]

Result:

2.8284271247462

[odd edge]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

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[gusty lynx]

for question b)

would it be correct to say that the number of successful outcomes are 1, and the number of possible outcomes are 52c5. so the correct answer would be 1/52c5?

[wicked kestrel]

it would not

actually nvm, yes it would sorry

[gusty lynx]

alright, thanks! 🙂

.close

[odd edge]

Channel closed

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[odd edge]

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[soft ravine]

Depending on the parameter a, solve the system of equations:

[soft ravine]

it is quite confisuing for me because the maximal minor doesn't depend on a

[toxic monolith]

$\text{jezeli }\text{ }2a-1\neq0\text{ }\text{ wtedy z tw, Kroneckera-Cappellego }\\\text{uklad ma nieskonczenie wiele rozwiazan zaleznych od 1 parametru z}\\\text{bo rzad macierzy jest 2}$

[clever fjord]

Joanna Angel

[toxic monolith]

a jezlei a = 1/2, wtedy latwo zzauwzyc, ze ulad jest sprzeczny, o ile nie pomylilam sie w pamiecię 🙂 haha, sprawdz

[soft ravine]

a skad jest to 2a-1

bo z tego co widze moge policzyc minor 2x2 bez a

a zatem rzedy sa rowne

ilosc rzedow jest mniejsza od ilosci niewiadomych czyli mam nieskonczenie wiele rozwiazan jednej postaci

i moze ona byc zalezna od zmiennej x i zawierac parametr a

[toxic monolith]

2a - 1, t wartosc pierwszego minora

ja wybeiram najlatwiej

tam gzie a

gdzie*

pirwsza i druga kolmna

twora minor o wartosci 2a - 1

rzad jest maksyamalnie 2

wiec wybeiram dowolny ktory daje 2

[soft ravine]

wlasnie nie wiem jak podejsc do rozwiazania bo pytanie nie jest o ilos rozwiazan tylko o rozwiazanie

[toxic monolith]

ale musisz tak dyskutowac

rozxwiazanie uladu jezeli masz parametr

czyli:

1. 2a - 1 nie jest zero, wtedy rzad jest 2

czyl uklad ma nieskonzcenie wiele rozwiazan zaleznych do 1 parametru ktory

wybeirasz jako z

iw edy

wyliczassz x i y za pomoca z

x = ...cos z

y = ... cos z

coś

🙂

antomias jezeli

a = 1/2

to recznie

wkjaldasz

mnozysz przez 2

i masz

x + 2y + 2z = 4

i wtddy rozwiazujwesz uklad

nie bedzie sprzeczny

czyli nieskonzenie tez

zresztą policz dla a = 1/2

zeby imec pewnosc

[soft ravine]

a czy moglbym w ten sposob \

[toxic monolith]

tez mozesz

z tym ze

kronecker wymaga rownosci rzedów, ale tu jest ok

czyli tobie wychodzi , chyba,z e zawsze masz jeden parametr neizaleznid od a, dla dowolnego a rzeczywistego

to samo co bsy mial z mej sugestii tez

[soft ravine]

czyli realnie w tym przykladzie nie musze sie nawet specjalnie przejmowac tym a

[toxic monolith]

tak bo udalo sie znzlezc minor, ktory daje tobie rzad 2

ale nei zawwsze tak

bywa

aj to robie automatycznie

[soft ravine]

takj tak poprostu wlasnie mylace bylo dla mnie polecenie, bo sugeruje ze cos od tego a moze zalezec, i chcialem sie upewnic czy dobrze robie

dzieki

[toxic monolith]

prosze)

[soft ravine]

.close

[odd edge]

Channel closed

Closed by @soft ravine

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

Query regarding vector spaces..

The vector obtained by plugging values into say property 7, does it need to satisfy the original condition?

Taking this question as example; if we take values of u,v which satisfy x+y+z=0

does c(u+v) also need to satisfy x+y+z=0?

[wooden python]

do you mean to ask whether you need to verify this?

because no, you don't -- assuming axioms 1 and 6 are satisfied.

[fallow saffron]

I know that we need to verify c(u+v)=cu+cv

solving both sides would give us a vector, LHS = RHS means that the property is satisfied, but I'm just curious whether the obtained vector needs to fulfil the original condition which applies to u,v i.e x+y+z=0

If yes, does it extend to other properties as well? Does the zero vector need to satisfy x+y+z=0 as well for the set to form a vector space?

[wooden python]

think you are trying to mix the closure axioms (1 and 6) in with everything

[fallow saffron]

Implying that the results from 2,3,7,8,9,10 don't need to lie in V?

LHS=RHS is sufficient

[severe veldt]

help pls

[fallow saffron]

Occupy a new channel por favor 🙏

[sharp oak]

c(u + v)
And
cu + cv

Need to be the same vector.

Note that you have this for free, because this holds for all members of R³, not just the ones where x + y + z = 0

[fallow saffron]

I know

but the vector which is c(u+v) or cu + cv doesn't need to lie in V, right

[sharp oak]

Well, u and v are in your space, so u + v must be as well, by def 1.

Likewise if u + v are in there, c(u + v) is, by def 6.

So yes, if u and v are vectors such that x + y + z = 0, then it must be the case that c(u + v) is also such a vector.

[fallow saffron]

The same applies to property 8.9?

[sharp oak]

Note that property 7 played no part in my derivation

So I'm not certain what you want to show about 8 and 9

[fallow saffron]

my query was just that

for the LHS=RHS conditions / properties

whatever resulting vector is obtained from it

does it need to lie in V i.e fulfil the condition which is x+y+z=0 in this case, for V to be a vector space?

[sharp oak]

If u is a member of the vector space, then (c + d)u is as well

By def 6

(cd)u is as well

[fallow saffron]

like if c(du) was not satisfying x+y+z=0, would V still be a vector space?

oh

[sharp oak]

It would not be a vector space!

As yes, we would need (cd)u to be a member, if u is.

[fallow saffron]

ah alright, so we don't need to bother checking that since u,v lie in V

but that's only for the given condition which is a rather convenient one (x+y+z=0)

makes sense I suppose. Thank you for your time and assistance.

.close

[odd edge]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[mystic saffron]

how do i get g(g(x))

[mystic saffron]

i got somewhat like this but idk how to simplify it

[trim matrix]

replace each x with g(x), then replace each g(x) with the function expression

[mystic saffron]

the final answer is -1/x

[trim matrix]

yes, this

[mystic saffron]

im stuck there

[trim matrix]

just simplify

[mystic saffron]

i tried but i prob did sm mistkaes i cant get the answer

[trim matrix]

what does $\frac{x-1}{x+1} - 1$ simplify to?

[clever fjord]

waris

[mystic saffron]

i genuinely have no idea how to simplify that. my bad

[trim matrix]

can you simplify $\frac12 + 1$?

[clever fjord]

waris

[mystic saffron]

i'd use calculator which is 3/2

[trim matrix]

you can't do it by hand? : |

[mystic saffron]

uhm

so thats my problem isnt it

[trim matrix]

indeed, it is

[mystic saffron]

wait

hmm

isnt it like

cross mutiply

multiply

and then add

i dont rlly rememebr it

[trim matrix]

alright, let's learn how to add fractions

let's say you have two fractions $\frac{a}b$ and $\frac{c}b$

[clever fjord]

waris

[mystic saffron]

yes

[trim matrix]

they both have the same denominator, right?

[mystic saffron]

yes, b

[trim matrix]

let's add them.
$$ \frac{a}b + \frac{c}b $$
This simply evaluates to $$ \frac{a + c}b $$

[clever fjord]

waris

[mystic saffron]

i see

[trim matrix]

the rule is this: if two fractions have the same denominator, we can add the numerators and divide by the denominator

[mystic saffron]

got it

[trim matrix]

time for an exercise. simplify $\frac{1}3 + \frac23 + \frac33$

[clever fjord]

waris

[mystic saffron]

thats just gonna give ((1+2+3)/3) sorry idk how to use the texit bot

[trim matrix]

you don't have to use the bot, just give me a simplified answer

[mystic saffron]

6/3=2

[trim matrix]

very good

[mystic saffron]

what if theres variable

[trim matrix]

we're gonna come to that

[mystic saffron]

okay

[trim matrix]

now, let's try and add $\frac{1}2 + \frac{1}4$

[clever fjord]

waris

[mystic saffron]

wait

[trim matrix]

we don't have same denominators now, do we?

[mystic saffron]

nope

but

[trim matrix]

yes?

[mystic saffron]

this is how my elementary teacher taught me 😭

i dont mind if u wanna teach another way

[trim matrix]

what he taught you is an algorithm

what i'm gonna teach you is what goes under the hood

[mystic saffron]

oh woaw

okay

sure

[trim matrix]

alright now..

multiplying a number by 1 doesn't change anything abt it, yes?

[mystic saffron]

yes

correct

[trim matrix]

let's write that sum differently. $1\cdot\frac{1}2 + \frac{1}4$

[clever fjord]

waris

[trim matrix]

i multiplied the first term by 1

do you think that changes the sum?

[mystic saffron]

no

dont think so

[trim matrix]

indeed it doesn't. because multiplying by 1 does nothing to a number

now... what does $\frac{2}{2}$ simplify to?

[clever fjord]

waris

[mystic saffron]

just 1

[trim matrix]

what does $\frac33$ simplify to?

[clever fjord]

waris

[mystic saffron]

also 1

[trim matrix]

what does any $\frac{a}{a}$ simplify to, if $a$ is any number?

[clever fjord]

waris

[mystic saffron]

its also 1

[trim matrix]

very good

that means $1 = \frac22 = \frac33 = \cdots = \frac{a}{a}$, right?

[clever fjord]

waris

[mystic saffron]

woah

yes

[trim matrix]

let's get back to our sum

$1\cdot \frac{1}2 + \frac14$

[clever fjord]

waris

[trim matrix]

we want a 4 under the first term, right?

so we can add the two fractions?

[mystic saffron]

do we multiply by 2

for both numerator and denominator

[trim matrix]

indeed

[trim matrix]

very good !

[mystic saffron]

i see

[trim matrix]

so it becomes $\frac22\cdot \frac12 + \frac14$

[clever fjord]

waris

[trim matrix]

which becomes $\frac{2}{4} + \frac14$

[clever fjord]

waris

[mystic saffron]

ahh

right

[trim matrix]

now we can add the usual way

[mystic saffron]

and we have the same denominator

[trim matrix]

indeed

[mystic saffron]

which is 4/3

i mean

3/4

[trim matrix]

correct !

[mystic saffron]

wow that was easier

[trim matrix]

now let's work with letters

okay no.. let's do another example

[mystic saffron]

uh ohh

okay

[trim matrix]

let's add $\frac12 + \frac13$

[clever fjord]

waris

[mystic saffron]

wait wait what

[trim matrix]

what whole number can we multiply 2 by to make it 3?

[mystic saffron]

dont think so

wait

1.5

[trim matrix]

indeed, there's none

[trim matrix]

that's not a whole number

[mystic saffron]

oh

i see

[trim matrix]

can we multiply 3 with any whole number to make it 2?

[mystic saffron]

nope

[trim matrix]

let's see.. what number do 3 and 2 both divide?

please go to #❓how-to-get-help

[mystic saffron]

themselves?

[trim matrix]

no i mean.. let's say there's a number a. then 3 divides a as well as 2 divides a

can you think of such a number?

[mystic saffron]

i cant

[trim matrix]

what about 6?

[mystic saffron]

oh

6/3?

and 2

[trim matrix]

indeed

6 divides both

in general, the product of two numbers is always divisible by those numbers

[trim matrix]

remember this

now let's back to our sum

[mystic saffron]

so how do i add this

[trim matrix]

$\frac12 + \frac13$

[clever fjord]

waris

[trim matrix]

we want to make the denominator the product of the two denominators

what do we multiply 2 by to make it 6?

[mystic saffron]

3

[trim matrix]

very good. so it becomes $\frac36 + \frac13$

[clever fjord]

waris

[mystic saffron]

2 times 3 and 3 times 3??

oh

nvm

numerator and denominator

[trim matrix]

indeed

and what do we multiply 3 by to make it 6?

[mystic saffron]

oh

OHH

OHH

I SEE WHERE THIS IS GOING

3 TIMES 2

[trim matrix]

indeed

[mystic saffron]

2/6

[trim matrix]

indeeed

$\frac36 + \frac26$

[clever fjord]

waris

[mystic saffron]

((3+2)/6)

[trim matrix]

now we can add it the usual way

[mystic saffron]

5/6

[trim matrix]

indeed

now.. time to introduce letters

[mystic saffron]

ohno

lets see

[trim matrix]

let's add $\frac{a}b + 3$

[clever fjord]

waris

[trim matrix]

what are our denominators?

[mystic saffron]

uhhhhhhhhhhhhh

b

[trim matrix]

b and?

[mystic saffron]

1

b and 1

denominator

[trim matrix]

indeed

what number is divisible by both b and 1?

[trim matrix]

do you remember this?

[mystic saffron]

uhm

issit 1

[mystic saffron]

i have a hard time trying to understand what does that even mean

[trim matrix]

did you use this fact?

[mystic saffron]

no 🙏

[trim matrix]

do you know what it means for p to be divisble by q?

[mystic saffron]

q/p ??

[trim matrix]

it means p/q is a whole number

[mystic saffron]

oh

p can be divide by q

and the answer will give a whole number

is what it means

[trim matrix]

here's what it means: let x and y be two numbers. if we want a number k which is divisble by both x and y (that is, both k/x and k/y are whole numbers), the we can find such a number by simply taking the product of x and y.

what is the produc tof x and y?

[mystic saffron]

does that mean both x and y is divisible by k

[trim matrix]

no, it means k is divisble by both x and y

[mystic saffron]

so its like k/x and k/y

[trim matrix]

indeed

now, tell me, what's the product of x and y?

[mystic saffron]

what does product even mean in mathematics

[trim matrix]

: |

[mystic saffron]

mb english aint my first language

issit like value

or

or

what

[mystic saffron]

IM SORRY 😭 🙏

[trim matrix]

the number you get by multiplying two numbers is called the product of those two numbers

now do you know what a product is?

[mystic saffron]

wait

gimme a minute

im trying to understand

[mystic saffron]

"by multiplying two numbers" these 'two numbers' is the same number

[trim matrix]

any two numbers

[mystic saffron]

right

[trim matrix]

no, they don't have to be the same

although they can be

but it's not necessary

[mystic saffron]

hm

[trim matrix]

tell me, what's the produc tof 2 and 3?

?

[mystic saffron]

wait

I DONT UDNERSTAND

[mystic saffron]

whats the product of 2 and 3

issit 6

i have no idea im just guessing

[trim matrix]

what do you get when you multiply 2 and 3?

[trim matrix]

yes

[mystic saffron]

so product basically means multiply

[trim matrix]

i just told you what a product is, why are you having to guess

[trim matrix]

yes

[mystic saffron]

im having a hard time

okay

so

lets get back

to where were we before

[trim matrix]

not yet

more exercise !

[mystic saffron]

oh

really

OKAY

[trim matrix]

what's the product of 4 and 8?

[mystic saffron]

OKAY

32

[trim matrix]

what's the product of 3 and 9?

[mystic saffron]

27

[trim matrix]

you better not be putting these in your calculator : |

[mystic saffron]

uhm

^_^

[trim matrix]

: |

what grade are you in?

[mystic saffron]

we dont talk about that

9

[trim matrix]

: |

[mystic saffron]

yeeaaaa

im gonna go to 10th next month

so yeaaaaaaaaaaaaaaaaaaaaaaaaaa

[trim matrix]

sigh

[mystic saffron]

HEP

[trim matrix]

okay.. what's the product of a and b?

[mystic saffron]

ab

[trim matrix]

VERY GOOD !

[mystic saffron]

i get that

[trim matrix]

see, no need for a calculator !

[mystic saffron]

D:

[trim matrix]

alright now..

The product of two numbers is divisble by both of those numbers.

[mystic saffron]

i see

[trim matrix]

Tell me, what's the product of x and y?

[mystic saffron]

xy

which means

[trim matrix]

And what is a number that is divisble by both x and y?

[mystic saffron]

xy can divide by x and y

[trim matrix]

very good !

[mystic saffron]

I SEE

WOAOAWOAOWOOA

[elfin salmon]

assalamualicum

[trim matrix]

okay, we're making progress

let's see.. $\frac{a}b + 3$

[clever fjord]

waris

[trim matrix]

what are the denominators?

[mystic saffron]

b and 1

[trim matrix]

and what number is divisble by both b and 1?

[mystic saffron]

wait.

[trim matrix]

sigh

[mystic saffron]

i think i need to jump off a cliff to get my brain working

[mystic saffron]

my brain stopped there

[trim matrix]

let's do this again

[mystic saffron]

isnt any number is divisible

by those

[trim matrix]

The product of two numbers is divisble by both of those numbers.

What is the product of b and 1?

[mystic saffron]

its

b

[trim matrix]

very good

then what number is divisble by both b and 1?

[mystic saffron]

whic means

both b and 1 is divisible by b

[trim matrix]

noooo

[mystic saffron]

:sOB

[trim matrix]

it means b is divisible by both b and 1

[mystic saffron]

wait

let me

oh

ok

okay

the product of two number is divisible by both of those two numbers and in this case the product is b and the two numbers is b and 1

FINALLY

😭

[mystic saffron]

IS THIS CORRECT

[trim matrix]

correct

this is gonna take longer than expected and i've gotta go now

[mystic saffron]

[mystic saffron]

NOASODAODASDSABDQWEQ

😭

[trim matrix]

but i'll tell you this: you really, REALLY need help with your algebra. you can learn it from here: https://www.khanacademy.org/math/algebra-home

[mystic saffron]

okay

i will

do i close

[trim matrix]

i suppose you could wait for someone else

[mystic saffron]

ill close and try to do it, ill ask for someone else later

thank you so much

[trim matrix]

good luck kid

[mystic saffron]

you've been helpful

.close

[odd edge]

Channel closed

Closed by @prime lark

Use .reopen if this was a mistake.

[odd edge]

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Send your question here to claim the channel.

Remember:
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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!

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

[safe sky]

Give triangle ABC. On the outside of ABC are 2 right isosceles triangle ABD and ACE. O and T is the intersection of BE with AC and CD. AH is perpendicular with BC and intersect with DE at M. Proves that M is the midpoint of DE.

[odd edge]

@safe sky Has your question been resolved?

[timber atlas]

this one might be better to understand

[safe sky]

thank you

[odd edge]

Channel closed

Closed by @safe sky

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[abstract shell]

Question - I'm creating an AI logic in a traffic simulation to have cars detect their closure rate speed. Basically I need a value of Car1's distance to Car2 and how quickly the value is dropping for each calculation. What is the best formula to achieve this?

[abstract shell]

I've figured out the cars distance. But only need to figure out how to calculate the speed in which the distance is dropping.

[leaden karma]

what other information do you have about the cars?

[abstract shell]

Their speed in mph is available.

For both cars.

So their distance from each other and speed is available.

Currently I don't have the logic of direction the vehicles are, to see if they are facing each other or away from each other, but I can set this up. Would this help?

[frigid canopy]

if you know their directions you could find their relative velocities

[abstract shell]

I'm using the Unreal Engine. I am able to get their velocity right now. Just not knowing if car1 is facing car2 or driving away.

[frigid canopy]

and based on their relative velocities you could find the distance between them

[frigid canopy]

ah, ok

In that case I'm not too sure, sorry

[abstract shell]

No worries, thanks for the suggestion.

[odd edge]

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[abstract shell]

.close

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[warm root]

can there be more than one general solution?

I almost got same ans but with negative sign

[odd edge]

@warm root Has your question been resolved?

[inner wedge]

As c is a constant the sign doesn't matter

[warm root]

So there can be more than one solution?

[odd edge]

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[dusty fern]

This is the step by step walk through for part of a problem in my textbook, but I can't figure out how the last two steps happened

[wet raven]

Multiply the numerator and denominator by 10 to get the third line

[dusty fern]

That I could get

What I can't get is line 4

And from there to b-2

[wet raven]

Thats just a factorization

[dusty fern]

I understand factoring out 10

Wait

My bad, I wrote the problem wrong

Still stuck on the last part though

I don't think x+10b-10 factors

Unless I split it up....

Then I'm still stuck with x/10 + b - 1

Oh but x=-10 so that becomes a 1 as well

Just ignore me.

[odd edge]

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[solemn apex]

i need to solve this but im having trouble figuring it out

[solemn apex]

i was given this chart

[summer cradle]

what is the question?

[south plume]

are you supposed to proce that or solve for x?

[solemn apex]

i have to prove it

[solemn apex]

1/cosx=secx but im unsure how to turn cscx/cotx into that or something else

im just confused

[summer cradle]

it is often a good idea to write everything with sin and cos

[south plume]

try to express everything in terms of sin and cos

[summer cradle]

also this reference sheet is crazy

[south plume]

yes

[solemn apex]

loll

[south plume]

now multiply top and bottom by sin

[solemn apex]

ooohh thank youuu

i get it now

.close

[odd edge]

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[mystic saffron]

How

I tried my best

Ping me if you answer

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

<@&286206848099549185>

I have to wait like

15 more mins

?

<@&286206848099549185>

[zinc wigeon]

what have you done so far?

sorry for not answering i was coding

can you show anything that you have done so far

[mystic saffron]

I did not do much

Except finding out

That the origin , focus and centre must lie on a straight line

Which didn't help me in any way

[zinc wigeon]

tbh i cant really help with this, sorry man

i wish i would

<@&286206848099549185> someone help him

[mystic saffron]

Yeah mate no problem

[mystic saffron]

Fr

[gilded vector]

where does your name come from

[mystic saffron]

Inheritance Cycle