help-36

[torpid zenith]

so it's not 2 has input a and goes to 2, rather 1 has input a and goes to 2?

[dull ravine]

1 has input a and goes to 1

[torpid zenith]

oooh okay

[dull ravine]

See what happens with ea in the e-nfa

That’s why

[torpid zenith]

hmm I did a table and followed the constructions in a video but I failed 😂😂😅 I think these e-NFAs I need to think a bit more instead of following a pattern

but makes sense, when a is looped at the end it's not the same as when it could loop with e-NFA at the beginning

bruh moment

that was a quick ban

[dull ravine]

I think a pattern is sufficient tbh. Maybe you can see where you went wrong if you try to reconstruct it

[torpid zenith]

okay I will try around and maybe I will get it someday

.close

[final saddle]

Channel closed

Closed by @torpid zenith

Use .reopen if this was a mistake.

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[molten shale]

Hello!

I’m stuck on this simple problem

Apparently the answer is 10+2, 21 squared

All I’m seeming to find is the 21 and I square that and it’s 441

After that I’m kind of lost

Just confused on how it’s not just 21

[formal trail]

we can write this as [ (\sqrt 7 + \sqrt 3)^2 = (\sqrt 7 + \sqrt 3)(\sqrt 7 + \sqrt 3) ] we need to expand this out using distributivity (FOIL, etc)

[soft zealot]

cloud

[molten shale]

Oh

What?!!?!?

How am I watching so many tutorials and none of them say this

[formal trail]

what do (1) and (2) represent?

[dull ravine]

$\sqrt{7}^2 = 7$. Square root and square cancel out.

[soft zealot]

FirstNameLastName

[dull ravine]

Same with $\sqrt{3}^2=3$ or any $\sqrt{x}^2=x$ for that matter

[molten shale]

YES YES ok

[soft zealot]

FirstNameLastName

[molten shale]

so whatnow tho LOL!

[dull ravine]

Well what do you have

What is the term equal to

[molten shale]

i just have 3 and 7 but 2 of them each

3x7

21

[dull ravine]

Write it as an equation

[molten shale]

how do i get the 1o{

10+2 in the front of the equation?

[dull ravine]

$(\sqrt{7}+\sqrt{3})^2=…$

[soft zealot]

FirstNameLastName

[dull ravine]

Write it like that

[molten shale]

ok

[dull ravine]

Cause idk what you mean by this

[molten shale]

the answer is 10+2(21)squared

how did the 10+2 happen wtf

[molten shale]

i ended up getting this idk LOL

[dull ravine]

Nobody knows what you mean by this

[molten shale]

i dont even know myself

[dull ravine]

Write it like that

[molten shale]

HAHA

[molten shale]

ok i rewrote like this lol

igot 21 squared so far

not a bad startish

[dull ravine]

$(a+b)^2=a^2+2ab+b^2$

[soft zealot]

FirstNameLastName

[dull ravine]

You recognize this?

[molten shale]

no

but i cna try

yeah idk

[molten shale]

i searched up how the answer happened and it was this

but i was never taught this idk how to use

HI!

should i ask chat gpt

yes

i was able to answer the first 2 questions

for some reason the answer is 10+2 21!?!?!?!?!

this is the next page lol

[molten shale]

14 squared and 9 squared

wait

or is it

49 i mean

and 9

yes

ima actually lost after the 2nd step

huh!?1/!?/

ok imma do this

Hi

Oh sorry yeah I did that

It’s under the f

Thank u!

7 21 and 3 27

[dull ravine]

Where does that 27 come from

Also, add these terms. So 7+sqrt(21)+…

[molten shale]

My fault I think I missed typed on calculator

It’s supposed to be 21s

[dull ravine]

Them just floating in the air don’t mean anything

[molten shale]

On

So I add the numbers and get 10?

[dull ravine]

Add them and see what you get

[molten shale]

I think I’m doing this wrong again

Dammit

@rocky tusk

[dull ravine]

What did you ping knief for

[rocky tusk]

hello

[molten shale]

hes the ruler!

HI

[rocky tusk]

💀💀💀

[molten shale]

KNIEF!!!!!!!!!!!!!

HEY!!!!!

omg

hes actually here haha

[rocky tusk]

bruh you had two greens

[molten shale]

help me pleaseeeeeeeeeeeee

[rocky tusk]

nevermind

3 greens

💀💀

[molten shale]

LOL

i missed u so much

[rocky tusk]

clouds probably number 1 helpful too

[molten shale]

everyone here is very helpful

shoutout to everyone here

knief but we know ur the ruler

[rocky tusk]

ok

and they couldn’t help you?

what’s the question

[molten shale]

I got about that far but I think I’m missing some steps

I might have to go back

[rocky tusk]

$(a+b)^2 = a^2 + 2ab + b^2$

[soft zealot]

knief

[rocky tusk]

in your case we have a = sqrt(7) and b = sqrt(3)

[molten shale]

i dont know how to input those values

[rocky tusk]

if you don’t have this memorized then you can just foil

[molten shale]

YES

how do i foil

[rocky tusk]

well you seemed to have multiplied the terms instead of adding them

remember the distributive property, we can start with the simple case

$a(b+c) = ab + ac$

[soft zealot]

knief

[rocky tusk]

yes?

[molten shale]

uhm yes

[rocky tusk]

now suppose instead of "a" we had a binomial such as a + b

$(a+b)(c+d) = (a+b)(c) + (a+b)(d)$

[soft zealot]

knief

[rocky tusk]

then we can use the distributive property again

on each of those two terms

[rocky tusk]

do you follow up to this point so far

[rocky tusk]

the a + b is functioning as the a in this example

[molten shale]

imtrying foil again

[rocky tusk]

you can do that as well

multiply each term in the first binomial by each term in the second then add each

so if we had

$(a+b)(c+d) = ac + ad + bc + bd$

[soft zealot]

knief

[molten shale]

LMAO i think im getting a differnt answer everytime

[rocky tusk]

happens

[molten shale]

i can only get up to this part

[rocky tusk]

but you’re not adding the terms for some reason?

[rocky tusk]

^

[rocky tusk]

why are you multiplying them

[molten shale]

oh

i just did the square root of everything and simplyfied it

[rocky tusk]

use this

you have

$(\sqrt{7} + \sqrt{3})(\sqrt{7} + \sqrt{3})$

[soft zealot]

knief

[molten shale]

wait

am i not supposed to be doing 7 times 7

then 7 times 3?

then 3 times 7 and 3 times 3

[rocky tusk]

sqrt(7) * sqrt(7)

[rocky tusk]

sqrt(7) * sqrt(3)

[rocky tusk]

sqrt(3) * sqrt(7) and sqrt(3) * sqrt(3)

but you add each of those together

after multiplying those pairs

[molten shale]

ok so i got the pairs

i add the numurals

its 10

[rocky tusk]

see those 4 you had on the left, add them together

don’t multiply them

[molten shale]

oh

i got 100

and 30

[rocky tusk]

what

[molten shale]

i added 49 and 21 for the first row of foil

[rocky tusk]

$(\sqrt{7} + \sqrt{3})(\sqrt{7} + \sqrt{3}) = \sqrt{7} \cdot \sqrt{7} + \sqrt{7} \cdot \sqrt{3} + \sqrt{3} \cdot \sqrt{7} + \sqrt{3} \cdot \sqrt{3}$

[soft zealot]

knief

[rocky tusk]

this results in

$\sqrt{49} + \sqrt{21} + \sqrt{21} + \sqrt{9}$

[soft zealot]

knief

[rocky tusk]

$\sqrt{a} + \sqrt{b} \neq \sqrt{a+b}$

[soft zealot]

knief

[rocky tusk]

if thats what you’re doing

[molten shale]

this is not what i was doing lol

[rocky tusk]

why this?

[molten shale]

im kind of confusedhere thoo ahhhhhhhhhh

i get like a square root of 100 when adding all

then square root of that is 10

[rocky tusk]

you cant add the insides of the square roots

[molten shale]

which the 10 is in the answer

[rocky tusk]

you got here yes?

[molten shale]

YES! KNIEF THE RULER

square root of 100

[rocky tusk]

ok well, let’s simplify two of those square roots

what’s the square root of 49?

[molten shale]

WAIT WHAT

I tought i waas added them LOL

[rocky tusk]

what number, when squared is 49

[molten shale]

7

[rocky tusk]

indeed

now what’s the square root of 9

[molten shale]

3

[rocky tusk]

so

[rocky tusk]

we can rewrite this as

$7 + 2\sqrt{21} + 3$

[soft zealot]

knief

[rocky tusk]

but we know 7 + 3 is 10

so

$10 + 2\sqrt{21}$

[soft zealot]

knief

[molten shale]

thank u so much

ok wait

hold up

[rocky tusk]

✋🏻

[molten shale]

how about the other 21

[rocky tusk]

i combined them, hence the 2

[molten shale]

why did i even add them all

[rocky tusk]

^

remember

x + x = 2x

[molten shale]

wouldnt it be 21 squared

[rocky tusk]

no

[molten shale]

without the 2 in front

[rocky tusk]

(x)(x) = x^2

we had sqrt(21) + sqrt(21)

[molten shale]

oh

[rocky tusk]

not sqrt(21) * sqrt(21)

[molten shale]

i think it all went into my brain

cant thank u enough knief

[rocky tusk]

anytime

[molten shale]

imma try the next question but the next page looks horrifying

[rocky tusk]

it looks like fun

you’ll enjoy yourself

letters don’t have to be scary

[molten shale]

yes i do enjoy learning alot

im nearing the end of the unit so its getting much harder

[rocky tusk]

but you know more

[molten shale]

AYYYYYYY

ok

so i got the question almost right

[rocky tusk]

which one

[rocky tusk]

d or f?

[molten shale]

how is this the answer

F

[rocky tusk]

why did you write 2sqrt(3)

it’s sqrt(3) * sqrt(3)

not sqrt(3) + sqrt(3)

[molten shale]

oh

so does the squared 3 x square 3

equal 3 squared 3?

i thought would just be 2 of them

i swear every question with negative signs get me

do u have any tips for when u encounter a negative sign knief

[rocky tusk]

$\sqrt{3} \cdot \sqrt{3} = 3$

[soft zealot]

knief

[rocky tusk]

in general, $\sqrt{x} \cdot \sqrt{x} = x$

[soft zealot]

knief

[rocky tusk]

there aren’t many other than just be aware of it and know how it functions

[rocky tusk]

because this is really just $(\sqrt{x})^2$

[soft zealot]

knief

[rocky tusk]

sqrt and square cancel

or you can think of it like

$\sqrt{x} \cdot \sqrt{x} = \sqrt{x \cdot x} = \sqrt{x^2} = x$

[soft zealot]

knief

[rocky tusk]

@molten shale

[molten shale]

knief i actually cant do a single question anymore

i just got used to doing some algebra

it took me i think a week and half to actually have it down

[rocky tusk]

:/

[molten shale]

do u think thats alot

[gray delta]

In this case, shouldn't it be in absolute value?

|x|

[rocky tusk]

learning math takes time

[rocky tusk]

well sqrt(x^2) = |x| on its own yes

[gray delta]

Here, he could also think of it as raised to the 1/2, and then, because it's a product, the exponents are added: 1/2 + 1/2 = 1

[rocky tusk]

but starting from sqrt(x) * sqrt(x), that’s always x even if x < 0

but of course imaginary numbers are a bit in the future

and she won’t be dealing with that

[molten shale]

want to see my last page?

[gray delta]

That's when the headaches start, and smoke comes out of my ears 😵‍💫

[rocky tusk]

nah it’s not that bad, just a bit weird at first

[molten shale]

Would u say the last page is difficult

[rocky tusk]

well, it depends

for who

[rocky tusk]

you should be the judge of that

[molten shale]

whats 3 squared x 3 squared?

[rocky tusk]

81

[molten shale]

using foil tho

[rocky tusk]

there is nothing to foil

it’s just one term times one term

we use foil for binomials

$(a+b)(c+d) = ac + ad + bc + bd$

[soft zealot]

knief

[molten shale]

why are they giving me only binomial questions

uggh

[rocky tusk]

because that’s what they do in algebra

suffocate you with binomials and factoring

@molten shale i have to go eat

@gray delta maybe you can help with the rest

[gray delta]

yeap

[molten shale]

3 squared x 3 squared @gray delta do u think u have it in u?

its using foil tho

[gray delta]

I just need to print the photos a little bigger so the exercises look better

[molten shale]

thank u

[gray delta]

you mean this?

[molten shale]

that is correct

it aint that simple tho

[molten shale]

Does 3 squared

3 squared x 3 squared

i honestly dont know

[molten shale]

yes exaclty!

i get that far

but 3 squared x 3 squared

[gray delta]

Remember that you always multiply the first from the first parenthesis by the first from the second parenthesis, plus the first from the first parenthesis by the second from the second parenthesis...

[molten shale]

would that be 2 squared

[molten shale]

yeah i kind of forgot the plus part

thanks so much

it starting to make more sense

adding and subtracting rational expressions was hard

but i had it down

now its multiplying them

but they giving me binomials for some reason

[gray delta]

Remember that if the base is the same (in this case, the number 3), the exponents are added. In your problem, you have it as a root (that is, raised to the 1/2)

[molten shale]

exactly

it throws me off but i think i have it

[gray delta]

If you think of it this way, then products with exponents different from 0 will become easier for you.

[molten shale]

3 squared x 3 squared is just 2 3 squared right?

[molten shale]

ive tried using this technique before

[gray delta]

Yes, I think I understood you; it's just that I'm translating it, lol

[molten shale]

sometimes it dosent work idk why

[gray delta]

this is GREAT

[molten shale]

3 squared x 3 squared PLUS

OMG

[gray delta]

i think this is right

[molten shale]

is it easier to add all the numbers first

then move on to the 3 squared?

[gray delta]

3+25

[molten shale]

yeah thats the right answer

ur smart asf

[gray delta]

-5-5=-10

[molten shale]

can u go step by step on how u added them together lmao

im not sure if i should just put all the numbers together

and thendo the 3s

[gray delta]

ok wait a second 🤓

[molten shale]

i appriciate u so much @gray delta

i want to be able to lock in!

do u have any tips also on what to do when u see negative signs in ur questions lol

[gray delta]

The only thing you do is rearrange the numbers to get them in the correct order, and then you add them (depending on whether you have an addition or subtraction in front); that’s all.

[molten shale]

y

your a life saver

thank u so much

i honestly didnt know the 2 3 square roots cancel out

and it just becomes 3

thank u soooo much

[gray delta]

I apologize if it takes me a long time; it's just that I don't know how to use the text, and also, I translate some things

[gray delta]

In reality, they are raised to half of 1, that is, to 1/2. Then, since it’s a product of the same thing (in this case, 3), their exponents are added: 1/2 + 1/2

[molten shale]

omg

1/2 + 1/2

when u put it like that

it actually makes so much more sense idk why i didnt think of tht LMAO

[gray delta]

1/3+1/3 = 2/3

1/4+1/4=2/4=1/2

[molten shale]

ty so much i itry to remember that

[gray delta]

Add more exercises if you want

[molten shale]

question d

dont give me the answer yet tho lol

[gray delta]

idk if this is correct

6=2.3

[molten shale]

the answer is -6 -6 square 2

[molten shale]

i didnt even get that shit

OMG

[gray delta]

maybe the more complicated on that excercise is remember this

2.3=6

[molten shale]

wdym

[gray delta]

Just to remind you that 6 can be expressed as the product of 2 x 3

Always keeping the square root, obviously, then you can distribute it

[molten shale]

i understand it a bit

lol

[molten shale]

why did u add these all together tho

the -6 plus -2

u didnt add it way earlier in the steps

[gray delta]

The first -6 is the result of the product of 2. (-3)

2x(-3)

sry

[molten shale]

ok i see where i went wrong

[gray delta]

(-2)x3

[gray delta]

show it 🤓

[molten shale]

u did -2/3 x /3 but u didnt multiply the 2

i multiplied and added the 2 to everything

i also didnt make the 6 back into a 3 and 2

lol

i get up the last row and honestly it gets so confusing

why doesnt it add to -8

u did everything perfect by the way

haha

[gray delta]

give me a second i will try to write all again 😄

[molten shale]

the answer is correct

[molten shale]

omg

ur the best

ok so u cant moosh everything together across the plus sign right?

u have to do the right side first or left side

this is very interesting

so hard

[gray delta]

It has to match that it’s not multiplied by something else; in this case, one of the -6s is multiplied by something else (the square root of -2), if that’s what you’re referring to

sry

2

[molten shale]

oh ok

that makes sense

thank u so much!

there is no way i could mess up the next question

[gray delta]

If the + I always put in front confuses you, you can multiply it by the - that you have later. I do it to keep the clarification of the -

i mean this

[molten shale]

im imagining there is a bracket between both sides bascially

and u have to complete the one side before mooshing them

[gray delta]

If you have the ability to not get confused by the signs, you can multiply the + by the - from the beginning and continue

[gray delta]

👍

[molten shale]

oh no problem thank u so much

[gray delta]

show more

[molten shale]

im trying this right now

im like halfway

im getting 8

3 squared

omg i hope this is right

-13!?!?!??

oh no

[gray delta]

the e. ?

[molten shale]

yes

[gray delta]

you did it the same

[molten shale]

yeah and i just made the 4 cancels out

so i jus made it 0

i ended up with 12 /3 on one side

and -4 /3 on the right side

so i added them together and had -8

[gray delta]

(-4).4=4.(-4)=-16

3-16=-13

🤣

[molten shale]

why 4 no cancel WHATT

the 4 become part with the squared 3

wow

i thought it was just a normal 4

[gray delta]

the only things that are cancelled are thos in between

[molten shale]

make so much sense

[gray delta]

4(root3)-4(root3)=0

[molten shale]

root 3 x 4

[gray delta]

exactly

[molten shale]

equals root 4 3?

damn

ur a geniussssssssssssssssssssssssssssssss

they really got me with that question

[gray delta]

you mean this? you can change the position of the numbers, but is still the same thing 🙂

Just remember not to get confused and end up putting a square root on the 4, lol

[molten shale]

this one looks fun

[molten shale]

imma try this 1more time 1 sec lol

omg

i cant do it

im so lost

[gray delta]

If you look at the second term, you have a 2 multiplied by a square root, multiplied by a 3, multiplied by another square root. Since they are all being multiplied, you can multiply the 2 by the 3, since they are raised to the same power (raised to 1)

[molten shale]

is that legal

ok let me try this again 1 sec

[gray delta]

Yes, because after all, they are all numbers that are multiplying with each other; you don’t have anything adding or subtracting among all those values, just products

[molten shale]

wait how about hte 2/5 x /5

the

[gray delta]

2/5 x /5= 2.5 =10

[molten shale]

wait 2.5?

no way

[gray delta]

I skipped that part because we had already seen it before, and I assumed you had already figured it out

/5 x /5 = 5

[molten shale]

how does 2/5 x /5 work again i forgot

[gray delta]

forget about the 2

[molten shale]

AHHHH the goddamn 2

one sec imma do it for real this time @gray delta

[gray delta]

🫣

[molten shale]

i swear i was on the right track my first try

idk what happened

im sorry

one sec

im doing it rn

[gray delta]

the other way of thinking

Remember, in a product, their exponents are added

[molten shale]

10 plus 2x5?

i was canceling out square roots and making them multiplication

idk where i went with this goddamit

[gray delta]

The square roots of 5 that you crossed out were correct.

[molten shale]

I started crossing out stuff from the other side after that lol

[gray delta]

2./5.3./3 = 2.3./3./5

[molten shale]

Omg

Ok

Wait

I think I get it

lol

[gray delta]

💯 🔥 👏

[molten shale]

It’s just so confusing to me that the number of the square root can now be moved around

I thought it was apart of it but I guess since there isn’t a like base we just do that

[gray delta]

The order will not change their product, as long as you keep the square roots with the corresponding numbers; it will be the same

i will change /3./5 for a Q

[molten shale]

Thank u!

Ur actually the besttt

So if I have 2 negative square roots

Can I cancel them and make a negative number

[gray delta]

follow this one

[molten shale]

Also I thought negative square roots aren’t a thing wtf

Wait what

Is this a formula

[gray delta]

it is an example, It's not a formula; it's an example so you understand what you need to regroup

[gray delta]

the last one is wrong

[molten shale]

Ok

Thank u

[gray delta]

-/3.3./3

[molten shale]

Wouldn’t it be -3 x 3

=0?

[gray delta]

YEEEEESS!!

🤠

😎

[molten shale]

YAYYYY

[gray delta]

-9

[molten shale]

LMAO

[gray delta]

THEN you can add that -9 with the first 10 🤓

10-9=1

[molten shale]

So many 3s

[gray delta]

dont forget the last one have a -

an its .

[molten shale]

Omg

[molten shale]

I have 4 3s on the right side

Damn

[gray delta]

I just changed their places and put the square roots of the 3 at the end so they can combine into a 3.

and the (-1).3 = -3

[gray delta]

This may seem obvious, but it's worth clarifying

[molten shale]

Why -1

Wait

U can put minus 1 in front of the negative 3 squared

There is no way

[gray delta]

I put the ... to indicate that it is the last term of the product of the two binomials

[molten shale]

I’m so lost 😞

Ok so the 3 cancels

I’m still left with 5 plus -3plus 3 tho

Can I finish off both sides now?

[gray delta]

look this

watch the D

[molten shale]

Yes I’m following so far

Thank u btw lol

[gray delta]

You must not forget that you are doing a product, meaning you multiply the second from the first parenthesis with the second from the last. Notice that in your notebook, you wrote that you are adding them

2./5.3./3= 2.3./3./5

[gray delta]

2.3=6 then 2.3./3./5 = 6./3./5

[gray delta]

dont forget -/3./5 is C

[gray delta]

here

[molten shale]

Wait am I forgetting a whole section?

[gray delta]

then you have to add -/3.3./3 (the last one)

look this -/3./5 -/3.3./3

You multiplied them all together, and those would be the last two terms

[molten shale]

Really

Ok

Imma try that way lol

Let me rewrite the question

Thanks so much !!

[gray delta]

🫡

[molten shale]

Can I do it like this do u think?

[gray delta]

yessss

[molten shale]

omg

[gray delta]

the first one /5./5 is 5

and the last one -/3./3 is -3

with the 3 is -9

[molten shale]

Oh it’s -3

[gray delta]

yep or (-1).3

its the same thing, hehe

[molten shale]

How about the other 2 brackets

Do I just smoosh em?

[gray delta]

yeah

because you have /5./3 in both

/5./3.. /3./5 the same thing

[molten shale]

Would the -/3 and /3 be 0?

[gray delta]

You're missing the two in the middle

[gray delta]

Here, you can't cancel because you're not multiplying the two terms; notice that you have a + in the middle, you're just adding them.

[molten shale]

Awww

[gray delta]

The first and last terms you did correctly; you just have the two in the middle left. Try rearranging them so you get /3./5 in both

the second one 2./5.3./3 you can write it 2.3./3./5

[molten shale]

Thank u!

[gray delta]

Remember, the order doesn’t change their product. If you take a calculator and multiply the same numbers in any order (without repeating them, of course), the result is the same

[gray delta]

yeah

[molten shale]

Can I cancel out the roots now?

Or they are just left like that

[gray delta]

you can add

2.3 =6

[molten shale]

Oh right

[gray delta]

6./5./3 - /5./3 = ...

i did this 🤓

It's just so you can see that you get more or less the same thing

[molten shale]

So do I do 10 plus negative 6

And add everything ?

[molten shale]

Oh

Wait

I do 3x5

wtf???

[gray delta]

YES YOU CAN DO IT!! BUT... dont forget the root

[molten shale]

YOURE A LEGEND!!!!

[molten shale]

But I have a 5 and 3 on each side

[gray delta]

YEAH ... remember /5./3=/3./5 You can arrange them so that both terms are in the same order

6./5./3 - /5./3

or 6./3./5 - /3./5

[gray delta]

In that same step, you could apply this, or leave it for the end

[molten shale]

Hmmm

So I wouldn’t have 2 15s?

[gray delta]

it doesnt matter what number is /3./5

put a name on that number for example K

then you have 6K - 1K

6-1 =5

[molten shale]

OH

ok ok

[gray delta]

if K is /3./5

then the result is 5./3./5

[molten shale]

yes

[gray delta]

AND THEN you have /3./5 = / (3.5)

3.5= 15

then you have /15

[molten shale]

ok so those 2 brackets equal 15

but i still have 10 + 15 + (-6)

[gray delta]

think on this way

[gray delta]

-6? are you sure 🤔

[molten shale]

-1/2 x 1/2

gets rid of the bracket then -3x3?

[gray delta]

right

[molten shale]

omg

-9

LOL

no way

[gray delta]

-/3.3./3 = (-1)./3.3./3 = (-1).3./3./3 = (-1).3.3=-9

[molten shale]

10 + 6 + (-9)

[gray delta]

dont forget the /5./3

[gray delta]

Remember that the -9 is an integer term that you have without square roots; you should combine it with the 10 from the beginning

[gray delta]

The only two terms that are multiplied by the square root of 5 and the square root of 3 are the two in the middle. Then you have the whole 10 from the beginning and the -9 that you have left at the end of the whole operation

[molten shale]

So I do 10-9 first?

[gray delta]

yeap

and you can add the two in the middle to each other because they are multiplied by the same thing (the two square roots)

[molten shale]

The /-3 and /3 don’t cancel out?

[gray delta]

not because you have 6 of them

and 1 of them

[molten shale]

i have 6 of them

[gray delta]

6-1=...

[molten shale]

but the 5 isnt minus is it

[gray delta]

dont forget the -/3./5

[molten shale]

5

ok

wow

WOW

[gray delta]

6./3./5 - 1./3./5 = ...

yeah

5./3./5

[molten shale]

what a adventure

[gray delta]

then /3./5 = ....

[molten shale]

thank u soooooo much

im keeping this sheet of paper in case

Hi Vlankiyo

im going to take a shower do u think u could watch over the next 2 questions i have when im back later?

[gray delta]

this is the end of my exercise

[gray delta]

okey

[molten shale]

THANK U!!!!!!!!!

I APPRICIAITE U SO MUCH

u dont understand

[gray delta]

no problem i need to drink some

[molten shale]

i really do

thank u

[final saddle]

@molten shale Has your question been resolved?

[molten shale]

is ur pfp guts from bezerk?

[gray delta]

yeeah

one of the best mangas 🤓

[molten shale]

the ending of the movie ruined it for me

hes cool tho

i think imma pick 2 final questions

[gray delta]

lets goo

[molten shale]

so atleast i know how to do each them so i could do a whole page on my own later

ok

this

and this

how do u even know where to start

[gray delta]

I'm thinking about what it means to expand 🤔

[molten shale]

the answer is 2x^5, 1/3 3

i tried putting the x's in a fraction and adding them

[molten shale]

i got the 2 and 3

cant seem to simplfy the xs

[gray delta]

yeah the b is easy

[molten shale]

how do i get x5 here?

[gray delta]

Supposedly, the three terms are being multiplied here, right

[molten shale]

yes

they end up being x 15

then simplyfied again

the 24 gets simplified so i just factored it

idk how to factor the xs tho

hm should i try it the same way

[gray delta]

I understand that since they have the same variable and it is a product of three, their exponents should be added

3.2=6

4.6=24

3.8 = 24?

[gray delta]

im thinking 🐒

[gray delta]

this is wrong why i put 13

im and asshole

[molten shale]

noooooooooooooooo

i just factored the 24

lol

i have learned so much today from u

THANK U!!!!!

im actually so tired now

Vlankiyo is one of the smartest and best

let it be known ❤️

i love u have a goodnight

[molten shale]

YES

[gray delta]

8=2.2.2

so the 3root of 8 is 2

[molten shale]

u made the second question look soo easy btw

thanks so much lol

[gray delta]

see you next time

have a good night

👍 🤠

[molten shale]

goodnight! Thanks sooooo much!

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[silent tartan]

how to prove this identitiy

[final saddle]

@silent tartan Has your question been resolved?

[vital crag]

Find the derivative one component at a time

Start with two dimensions first

B = 2 by 2 matrix

[silent tartan]

I have tried nothing good came out

This is what i get

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@silent tartan Has your question been resolved?

[silent tartan]

.close

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[dire sky]

Hello

[dire sky]

I have electrical network applications on linear algebra

I should get equations from this circuit

but I am so lost

I know I should I use kirchoff's law. Current in= Current out for a junction and we should move with the current flow

but here is just so complicated

can anyone help me ?

here it says direction of path 1 but we have I_1 and I_2 so direction of what

[final saddle]

@dire sky Has your question been resolved?

[spare hinge]

make some equations for all the junctions

so current in = current out

and then also focus on the loop law

[final saddle]

@dire sky Has your question been resolved?

[dire sky]

How can I know if a IR should be negative or not

[spare hinge]

wdym

you're just adding eveyrthing coming in and eveyrthing going out

oh the loop law

think of each resistor as a drop, the classical water analogy

the voltage drops around the circuit and then once it reches the battery, it is at zero for any loop,

[soft zealot]

adam

[spare hinge]

rearranging would lead to:

[soft zealot]

adam

$$ V_1 - V_2 - ... + \epsilon = 0 $$

[spare hinge]

hence the law that the sum of all the electric potential differences around a loop is zero.

[spare hinge]

excuse me V_1 should be negative as well

[final saddle]

@dire sky Has your question been resolved?

[dire sky]

Okay thanks

[final saddle]

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[crude nimbus]

hello

[inland kettle]

using epsilon delta?

[crude nimbus]

yea I think so

[fast creek]

supposedly yes

[crude nimbus]

I understand the left side but not the stuff on the right side

whats the reverse 3 thingy

[inland kettle]

epsilon

[crude nimbus]

what about the other symbol

[soft zealot]

ren

[inland kettle]

$\delta$

[soft zealot]

ren

[crude nimbus]

howd they know to take it positive

[barren hound]

definition of limit

[crude nimbus]

.close

[final saddle]

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[upper silo]

yo

so I have gotten stuck at $(i-1)x+(5+5i)y=25i-2$

[soft zealot]

sealpup321

[upper silo]

the answer is $z=2+5i$

[soft zealot]

sealpup321

[upper silo]

but I dont see what I can do from here

well I have something "nicer" $-2x +10iy = 23i-27$

[soft zealot]

sealpup321

[final saddle]

@upper silo Has your question been resolved?

[upper silo]

<@&286206848099549185>

[final saddle]

@upper silo Has your question been resolved?

[upper silo]

<@&286206848099549185>

[final saddle]

@upper silo Has your question been resolved?

[devout tulip]

Collect the terms with i and the ones without i in the first member

The second member is -2 + 25 i

So, if $z=x+iy$, then $2(x+iy)-3(x-iy)=-2+25i$

[soft zealot]

cristorenzo99

[devout tulip]

Simplify the first member of the equation: $2x +2iy -3x +3iy=-2+25i \implies -x + 5iy = -2 +25i$. Now, put the real part of $-x+5iy$ equal to the real part of $-2+25i$ and do the same with the imaginary part.
You should get:
$
\begin{cases}
-x = -2\
5y = 25
\end{cases}
$

which gives you $x = 2$ and $y = 5$. Because $ z = x + i y$, then $z = 2 + 5i$.

[soft zealot]

cristorenzo99

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@upper silo Has your question been resolved?

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[mild sentinel]

f(2)=4a-2b+3

left side = 4

right side = 4a-2b+3

how do i go from there

[barren hound]

well, you have 4 = 4a - 2b + 3

that's two unknowns

you need another equation

why don't you look at the seam at x = 3?

[mild sentinel]

what do i do

[barren hound]

the same thing as you did

except for f(3) instead of f(2)

[mild sentinel]

ok

ok so f(3)=6-a+b

left side = 9a-3b+3

[mild sentinel]

right side = 6-a+b

[barren hound]

okay so left side = right side

now you have two equations and two variables

you should know what to do from here ;)

[mild sentinel]

hmm i dont think so?

[atomic moon]

Gauss pivot

[barren hound]

looks like we're not close to that yet

[barren hound]

um why not

isn't that what you did for f(2)?

[mild sentinel]

yeah but they are not equal

[barren hound]

they're not?

[mild sentinel]

well how is 9a-3b+3 = 6-a+b

[barren hound]

well it could be, if a and b are appropriate values

[mild sentinel]

oh ok

so what now

[barren hound]

remember what we're trying to do:

[mild sentinel]

yeah

[barren hound]

so....

you have two equations

and two variables

this should be ringing bells in your head

[mild sentinel]

not really 😭

[barren hound]

from algebra

[atomic moon]

{

Hint

[mild sentinel]

yeah no

[barren hound]

it's a system of equations, does that mean anything to you?

[mild sentinel]

do i have to find the discriminant

[barren hound]

you have to watch this https://www.youtube.com/watch?app=desktop&v=oKqtgz2eo-Y

[mild sentinel]

i know how to solve a system of equations

[barren hound]

okay... do that

[mild sentinel]

but with what numbers

functions*

[barren hound]

4 = 4a - 2b + 3 <------- this is from f(2)
9a-3b+3 = 6-a+b <-------- this is from f(3)

these are the two equations you found

[mild sentinel]

ohhhhh

sure

[atomic moon]

Deal with a and b as if they were x and y

[mild sentinel]

a=1/2 b=1/2

[atomic moon]

This works

I bet a and b are real numbers so its fine

[mild sentinel]

so thats it right

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[spice field]

Hello I have a probabilty and statistics question

[spice field]

How many 3 digit numbers can be made from the digits 1, 2, · · · , 9, if each digit can at most be repeated
twice?

[stray mesa]

Wait does repeated twice mean it appears 2 times or 3 times

[inland kettle]

twice

i assume

[cursive bough]

!status

[final saddle]

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

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[inland kettle]

;-;

[stray mesa]

;-;

[inland kettle]

delete that lmao

[stray mesa]

How much more simple can I make it

[inland kettle]

explain the steps

[stray mesa]

Mmm ok

[inland kettle]

clue them in

delete the sol though

[stray mesa]

Oh wait I just realised my initial solution is wrong haha

[desert mantle]

sometimes its easier to count the numbers you are not allowed to make

[stray mesa]

Ooo good idea

[stray mesa]

Ye just do that

[inland kettle]

(that's called finding the complement; it's much, much easier)

[final saddle]

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[cosmic agate]

test

[cosmic agate]

guys need integral calculus help

[final saddle]

@cosmic agate Has your question been resolved?

[final saddle]

@cosmic agate Has your question been resolved?

[final saddle]

@cosmic agate Has your question been resolved?

[uneven solstice]

which question? @cosmic agate

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[deft fjord]

sm1 help

[hybrid heath]

What have you tried so far?

[deft fjord]

idk

i was never taught this

[hybrid heath]

For sure

[deft fjord]

can u help please

[onyx peak]

hmm it gives you a video tutorial, doesn't it?

[hybrid heath]

okay, the table is basically saying that, for whatever number $x$ is, $f(x)$ will be the number just below it. For example, if $x$ is $0$, then $f(x)$ will be $5$. And if $x=1$, then $f(x)=7$, and so on.

[soft zealot]

SWR

[deft fjord]

yes but i dont understand

[hybrid heath]

Do you understand this bit?

[deft fjord]

no

not rlly

i understand a bit

[hybrid heath]

Basically I'm trying to explain how to read the table. The top row are values of x, and the bottom row are values of f(x).

And when values are in the same column (e.g. the red rectangle), you should you read it as "When x=0, f(x)=5"

[deft fjord]

so 5 = ax0 +b

is the first one?

so how do i calculate the answer

@hybrid heath

[hybrid heath]

Yes. $5=a\cdot 0+b$

[soft zealot]

SWR

[deft fjord]

how do i calculate a and b

[hybrid heath]

Start here and you can solve for b

[deft fjord]

b=5

how do i workout a

[hybrid heath]

You'll need to look at a second point. A second (x, f(x))