help-0

[quiet folio]

Same but sat looks way easier

[willow edge]

respectfully what the fuck is this problem. can anyone help me get this started? number 100 part a only (part b is a computational assignment tomorrow). i’m supposed to derive the velocity formulas

i’m about to start my next class so please ping!!

[oak chasm]

https://cdn.discordapp.com/attachments/359052604149465088/885202138140131398/image0.jpg

@alpine sable OK, so the first line is y = 4x + 4.

So, we need to pick an x.

Pick an x that's on one of the lines of the graph.

[alpine sable]

Oh ok

Um

[oak chasm]

See the lines on the x axis?

[alpine sable]

Yea

[oak chasm]

There's one at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, and 10.

Those are the grey lines that cross the x axis.

Does that make sense?

[alpine sable]

Oh yea

[oak chasm]

OK, so pick one of them.

Which one do you want to use?

[alpine sable]

So I can pick from -8 to 8?

[oak chasm]

Yes, but it should be where one of the grey lines crosses the x axis.

[alpine sable]

then -4

[oak chasm]

OK, so:

y = 4x + 4
y = 4(-4) + 4

See how I filled in x with what you picked?

[alpine sable]

Yea

[oak chasm]

y = 4(-4) + 4
y = -16 + 4
y = -12

See how I did the math?

[alpine sable]

Yea

[oak chasm]

OK, now that goes below -10 on the y axis.

So it's off the graph.

We need it a little higher.

Now there's a 4 in front of the x.

Since it's positive, the line goes up as you go to the right.

If it was negative, the line would go down as you go to the right.

Does that make sense?

[alpine sable]

Yea I guess

[oak chasm]

OK, so we need it a little higher than -12 to fit on the graph.

So, we need to go to the right because it goes up as you go to the right.

So, let's try x = -2 instead of x = -4.

That's the next grey line over.

y = 4x + 4
y = 4(-2) + 4

See how I filled x in with the -2 I picked?

[alpine sable]

Yeah

[oak chasm]

Some thing as last time, just with a different x.

y = 4(-2) + 4
y = -8 + 4
y = -4

So, we have x = -2 and y = -4.

Does it make sense how I got those?

[alpine sable]

Yea

[oak chasm]

OK, so that's the point (-2, -4).

Mark that point on the graph.

[alpine sable]

Oh ok

So on question 11

Ok got it

[oak chasm]

OK, now we pick one more point on that first line, y = 4x + 4.

We tried x = -2.

What should we try next?

[alpine sable]

Um

[crude glen]

can i get some help wtih limits

[oak chasm]

@crude glen Sorry, this channel is busy.

[alpine sable]

Idk

Wait

Lemme think

[oak chasm]

Well, it can be any of the places where the grey lines cross the x axis.

[alpine sable]

I guess 8?

[oak chasm]

y = 4x + 4

Now fill in x with 8 in parentheses.

What do you get?

[alpine sable]

y= 4x(8) + 4?

[oak chasm]

Almost. You're replacing x with (8), so the x is gone and the (8) shows up where the x used to be.

So, y = 4(8) + 4

[alpine sable]

Ohh

Ok

[oak chasm]

So, what's 4(8) + 4?

[alpine sable]

Um

Omg I feel so dumb right now..

Uh

Shoot lemme think

Ummmm

I can’t even think rn

😓

[oak chasm]

OK, what do you do first?

There's a multiplication and an addition, right?

So, which comes first?

[alpine sable]

Multiplication

[oak chasm]

OK, what's 4 times 8?

[alpine sable]

32

[oak chasm]

OK, what's 32 + 4?

[alpine sable]

36

[oak chasm]

So, y = 36.

Now y = 36 is too high to be on the graph.

So we need to pick a lower x.

So, we got x = -2 and that worked, but x = 8 is too high.

So, a trick is to pick the next one up from x = -2.

What's the next line that crosses the x axis after x = -2?

[alpine sable]

Um

It’s uhh

-3??

[oak chasm]

Nope.

[alpine sable]

Oh

[oak chasm]

List off the places where a line crosses the x axis, starting from the left side of the graph.

Do you see where it crosses at -8?

[alpine sable]

No where?

[oak chasm]

Do you see the x axis?

[alpine sable]

Yea

[oak chasm]

Do you see the vertical lines that cross it?

[alpine sable]

Yea

[oak chasm]

What's the one farthest to the left?

[alpine sable]

Wait

So on the y axis?

[oak chasm]

No, on the x axis.

[alpine sable]

-8

[oak chasm]

OK, what's the next one after that?

[alpine sable]

-9? Or does that not make sense and do you mean after the number or like before it so like -7?

[oak chasm]

I mean look at the line at x = -8.

The line that goes up and down (the vertical line) there.

Do you see it?

[alpine sable]

Yeah

[oak chasm]

OK, what's the next vertical line to the right?

[alpine sable]

I’m so like confused

[oak chasm]

Do you see the 9 vertical lines?

[alpine sable]

On the x axis?

[oak chasm]

Yes.

[alpine sable]

Like the small lines?

[oak chasm]

Yes, the gray lines.

[alpine sable]

Oh yeah

[oak chasm]

OK, which one is just to the right of x = -8?

[alpine sable]

-6?

[oak chasm]

Where does it cross the x axis?

Right!

What's the one to the right of that?

[alpine sable]

-4

[oak chasm]

Good, and it goes up by 2 each time, right?

[alpine sable]

Yea

[oak chasm]

So, we got x = -2 before.

What's the vertical line to the right of that?

[alpine sable]

0?

[oak chasm]

Right.

So, we'll try that one.

[alpine sable]

Oh ok

[oak chasm]

x = 0

y = 4x + 4

Fill in x with (0).

What do you get?

[alpine sable]

y = 4(0) + 4?

[oak chasm]

Right, and what's 4(0) + 4?

[alpine sable]

Wait

Ok

So

4 x 0 is 0

0 + 4 is 4

Right

[oak chasm]

Right.

So, y = 4.

[alpine sable]

Yay!

[oak chasm]

Good job.

Now, we have the point x = 0 and y = 4 or (0, 4).

So, mark that point on the graph.

Did you mark it?

[alpine sable]

Wait

Ok

Done

[oak chasm]

We have two points marked on the graph: (-2, -4) and (0, 4).

Now get a ruler.

Or a piece of paper.

Make the edge of the ruler touch both of those points.

[alpine sable]

Oh no I have to go sleep now😓

[oak chasm]

Well, let's do this one line.

It will only take a minute.

[alpine sable]

Oh ok

[oak chasm]

So, make the edge of the ruler touch the two points you marked.

Then the ruler will cross two sides of the graph.

Like the outer edges of the graph.

Draw a line from where it touches one side all the way to the other side where it touches.

You'll have a line that goes from one side of the graph to another side of the graph.

Does that make sense?

[alpine sable]

Yea

[oak chasm]

,w plot y = 4x + 4 from x = -10 to 10 from y = -10 to 10

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

It will look something like this ^

[alpine sable]

@oak chasm My mom is going to take my phone now

[oak chasm]

OK, you can ask for more help later.

[alpine sable]

But my math teacher told me to finish 4,6,8,11 before I go to school, because I need to finish it before he sees it cause he will go around the class and see everyone’s homework and then grade them, so how can I finish all of them by tommorow??

@oak chasm

Do you mind explaining all the the other questions in private dms then I’ll solve them tomorrow? @oak chasm

Ok have to go now

Bye

[willow edge]

<@&286206848099549185> reposting with ping this time since it’s been an hour and such number 100, part a only (i’m doing the computational for part b tomorrow). i have no idea how to go about deriving this?? i started with some separation of variables, but when i integrated, i got an arcsinh, which is nowhere near what i’m looking for. any pointers would be awesome. no i don’t know the book it’s from, but this is for modern physics

please ping in response!! i'm working on other stuff at the same time

[simple hamlet]

i did not get it i was not trolling

[sly mantle]

i didn't say that. i said

don't answer leading questions meant for others

[upper kindle]

what is 6÷0

[wary stream]

Undefined

[surreal oak]

Determine the general term of the sequence

help

bruh

2n + 1

this

[surreal oak]

on this

[oak chasm]

@surreal oak So, do the sequence x².

[upper kindle]

:(

[oak chasm]

0, 1, 2, 3, 4
0, 1, 4, 9, 16

What are the differences?

1, 3, 5, 7

Just like yours.

[surreal oak]

+1?

[oak chasm]

Right, x² + 1.

[surreal oak]

thx

[oak chasm]

No problem.

[wary stream]

That is the answer

[upper kindle]

ik but like eh

yes very big brain

[harsh belfry]

Could use a hand here

I think I may have missed a step

If we square the expression:

we end up with

In order to get the derivative we must put this through the power rule n*x^n-1

so x^1.2 becomes

[oak chasm]

No, sqrt(x + 4) is not sqrt(x) + sqrt(4).

Use the derivative limit.

[harsh belfry]

I'm not following

[ocean seal]

Chai T. Rex

[harsh belfry]

Am I unable to do it via this method?

its what I was taught in class.

[oak chasm]

No, as I said, sqrt(x + 4) is not sqrt(x) + sqrt(4).

It also says to use the limit process.

[harsh belfry]

Alright, I'll try it that way then

I may be looking at this wrong

wouldnt

[oak chasm]

No.

You can't do anything to the inside of a function without a reason for it.

[gray vapor]

never touch an argument

[oak chasm]

There is no law that allows you to do what you did.

[harsh belfry]

I see

[oak chasm]

Instead, multiply top and bottom by the conjugate of the top.

[harsh belfry]

Sorry if I messed it up but it should end up looking like this right?

[oak chasm]

Not quite.

The top will be a difference of squares.

(a + b)(a - b) = a² - b²

[ocean seal]

Chai T. Rex

[oak chasm]

Then the top is (a - b)(a + b), which is a² - b².

[ocean seal]

Chai T. Rex

[oak chasm]

See how I got that?

[harsh belfry]

currently working it out myself on paper properly

had to grab my jorunal

give me a second so I can finish it and check my work with yours

[oak chasm]

OK.

[harsh belfry]

Sorry!

I just need practice with conjugates

since we're past conjugates I'm not well practiced (very briefly instructed)

[oak chasm]

Well, you don't specifically need a conjugate. You can change the sign in the middle of a binomial.

Then you have (a + b)(a - b) or (a - b)(a + b).

That gives you a² - b².

So it gets rid of square roots.

x + sqrt(3)

(x + sqrt(3))(x - sqrt(3))
x² - 3

No square roots.

[oak chasm]

x - sqrt(3)

(x - sqrt(3))(x + sqrt(3))
x² - 3

@regal rover Sorry, this channel is busy.

[regal rover]

ok thanks

[harsh belfry]

I think the square roots are really messing me up when understanding

I'm trying to FOIL it right now

[oak chasm]

Don't FOIL it directly.

[harsh belfry]

not sure how to foil with square roots

[oak chasm]

FOIL (a + b)(a - b)

What do you get?

[harsh belfry]

aahhhh

ok ok ok

smart

uploading image

Alright

That isnt what you have

[oak chasm]

Right.

[harsh belfry]

wait wait

[oak chasm]

Well, it's almost there.

[harsh belfry]

I think i see what I did wrong

second

[oak chasm]

No, you did it right.

You just need to square the things on top.

[harsh belfry]

oh?

Oh alright, I don't need to correct anything then?

(just to clarify)

[oak chasm]

No, it's good, just need to work from that.

[harsh belfry]

Alright

so from what I see

[oak chasm]

No.

You can only cancel factors.

Things that are multiplied together into the top and bottom.

[harsh belfry]

ah I see its added and subtracted

[oak chasm]

That thing you cancelled isn't multiplied into the whole top and the whole bottom.

What you need to do is square the things on top.

What's (sqrt(x + h + 4))²?

[harsh belfry]

^ I've been told that by my teacher multiple times and I keep forgetting that. My bad.

OH

OH OH I'm stupid

got it

[oak chasm]

Right, and that's what I had.

[harsh belfry]

It was starting right at me and I didnt see it

Alright

But what do i do about the square root on the bottom?

[oak chasm]

First, simplify the top.

[harsh belfry]

cancel out the h?

[oak chasm]

Yes.

[oak chasm]

Now sqrt(x + h + 4) is continuous.

So, what does that mean about the limit?

[harsh belfry]

uh

I obviously don't know the number of the limit so i know you're asking something else

Not sure what to say though

[ocean seal]

Chai T. Rex

[harsh belfry]

this is my derivative

[oak chasm]

You just fill in what you're going towards.

Does that make sense?

[harsh belfry]

this is f'

[oak chasm]

This is a different f.

This is for all continuous f.

[harsh belfry]

hm?

ah

the function of k is equal to the function of a when the function is continous

[oak chasm]

When the function is continuous, and you're doing the limit as the input goes to something, the limit is f(something).

[ocean seal]

Chai T. Rex

[harsh belfry]

Ok

Got it.

[oak chasm]

So, sqrt(x + h + 4) is continuous.

So, you can fill in 0 for h.

Since you have h → 0 for the limit.

[harsh belfry]

Alright.

[oak chasm]

Right, now simplify the bottom.

[harsh belfry]

1/2?

[halcyon narwhal]

is anyone in chat that can help me with basic math

literally basic lol

[oak chasm]

What's the full expression?

[oak chasm]

@halcyon narwhal Not in this exact channel, but you can find another #questions channel that's not in use and ask a question you want help with.

,w derivative of sqrt(x + 4)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

And that's the derivative.

[harsh belfry]

holy shit

😓

I will be visiting this convo later to review this

thanks man, you were great

[oak chasm]

OK.

You're welcome.

[dim vine]

Just as a curious question, could that answer be changed to 1/(2sqrtx+4)

[halcyon narwhal]

are you able to potentially hop on a call literally for a sec?

[oak chasm]

@dim vine If you put parentheses around the x+ 4.

[dim vine]

i mean

[oak chasm]

@halcyon narwhal Sorry, I don't have a microphone.

[dim vine]

2 * sqrtx + 4

[halcyon narwhal]

I just need to stream something

you can type

[dim vine]

Can i ask

my q

[oak chasm]

@dim vine 1/(2 sqrt(x + 4)) is fine.

[harsh belfry]

?

[dim vine]

ye dw

[harsh belfry]

did you mean this

[dim vine]

I meant if u multiplied inside the sqrt by 4

[oak chasm]

OK, that's fine.

[dim vine]

But idk if that makes sense

[oak chasm]

@dim vine 1/sqrt(4x + 16) is fine.

[dim vine]

ah ok cool

[harsh belfry]

ohh I see what you meant

[halcyon narwhal]

matemathics? off topic voice?

[dim vine]

well it would be 4*

[harsh belfry]

yeah actually wouldnt 4x+16 be more simplified?

[oak chasm]

Well, it needs to be 4(x + 4) in the square root.

No, the 2 in front is more simplified.

[harsh belfry]

ah i see

[halcyon narwhal]

anyone else feel free to join lol

[oak chasm]

They want you to take out as many factors from the square root as you can.

[dim vine]

How would I do e on this q?

I think all the required info is in parts a and c

[dim vine]

<@&286206848099549185> sorry to be annoying. This question has me completely lost and the questions afterwards all involve similar stuff so I was hoping someone could teach me how to do it

[wary stream]

Looks very physics heavy, try asking in the physics server, linked in #old-network

[dim vine]

Oh whoops

I don't even do physics :9

[glass lichen]

It's... still a physics problem

[dim vine]

yep, have just joined the server. ty

[jade patrol]

hi can somebody help me with some frriends?

pls dm then

me and ym friend are in a call so we can add u

[glass lichen]

are you gonna ask the problem or...?

[alpine sable]

inequality whose solution set is {-∞;+∞} can anyone help?

[jade patrol]

yes?

[glass lichen]

is that meant to be an interval?

(-inf,inf) not {-inf, inf}

[alpine sable]

ooh yes

i mad

(-inf,inf)

[glass lichen]

e^x>0

or, any base for the exponential

[robust crow]

is this channel busy?

[jade patrol]

the problem is that we are programierung python "ki" we we discuss if you have 52 cards decks u know ur 2 and the one from the dealer then u have to divide bei 49 right? that is our question

enebody understand

[alpine sable]

thank you @glass lichen

i dont know how i didnt get it first time

XD

[glass lichen]

or if you know a function never gets below a certain point, that's also sufficient

[wary stream]

What kind of butchered English is this?

[glass lichen]

ex x^2>-10000

(or literally any negative number)

[alpine sable]

ooh okay

[robust crow]

What's the name of this kind of equation?

[tall kayak]

mod function

[robust crow]

thank you

[wary stream]

No, I don't think so

[alpine sable]

absolute value equations might be.

[tall kayak]

yes may be thats the exactname

[wary stream]

That, absolute value equations

[robust crow]

sure

[upbeat shadow]

Does anyone know the best method to review/learn calc 1 and 2 in a day

[wary stream]

In a day?

That's too much material

[tall kayak]

tf

[upbeat shadow]

Ik but does anyone know the best way

[wary stream]

Calc 1 is dense already, and then calc 2 on top of that

[upbeat shadow]

What resource teaches the fastest

[wary stream]

This is not recommended at all

[upbeat shadow]

Yea I have a multivariable preassessment and it’s the only thing I can do

Tomm

[wary stream]

That is not anyone's fault but yours for not reviewing calc 1 and 2 sooner. As I stated, those two topics are dense already, so to review everything, it takes days, not hours

Maybe even weeks

[upbeat shadow]

Ok, just wanted to know how much experience do you have?

[wary stream]

In what specifically?

[upbeat shadow]

Math

[wary stream]

I'm an engineer, so a good amount

[upbeat shadow]

Nice

Yes I guess I’m screwed

[wanton spade]

the height in feet of a firework t seconds after it is launched is modeled by A(t) = -16t^2 + 105t + 10. Find its average speed from 1 to 3 seconds

[oak chasm]

Go to Khan Academy and take the course challenge at the bottom of the calculus 1 and calculus 2 courses.

[upbeat shadow]

Will do, thx

[oak chasm]

https://www.khanacademy.org/math

No problem.

[abstract junco]

i need help

[upbeat shadow]

Subtract both sides by 5, then multiply each side by 4/3

[abstract junco]

k

[spring summit]

yall know this

[safe roost]

Yes

i could give you the answer but i'd rather help you through the reasoning

f(x) = k is a constant. So what does that mean?

(ok i'll give you a hint: that means that k is a straight line)

so what they're really asking is: when a straight line goes through this function... where does it need to be to "cross" the line of the graph of the function 3 times?

[bold mantle]

Help

I don't even know where to start with this problem

[fathom sequoia]

how do i factorise a quadratic when a > 1 can someone help

[ocean seal]

SubGui

[astral dagger]

@bold mantle

[astral dagger]

divide by 3 first

or a, in general

then complete the square for what is inside the parenthesis, just don't forget to do the opposite multiplied by 3 out

[bold mantle]

Help?

Pls

[astral dagger]

note (10000=10^4), then by the first property, (10000^{\frac{3}{4}}\cdot (x^4)^{\frac{3}{4}}\cdot (y^8)^{\frac{3}{4}})

[ocean seal]

SubGui

note \(10000=10^4\), then by the first property, \(10000^{\frac{3}{4}}\cdot (x^4)^{\frac{3}{4}}\cdot (y^8)^{\frac{3}{4}}\)

[fathom sequoia]

First calculate 10,000^(3/4)

[astral dagger]

by the second property, you multiply the powers

[bold mantle]

Wdym by the second property

[astral dagger]

this one

I pinged you after that

[fathom sequoia]

which is 1000

then multiply x^(4 times 3/4)

then y^(8 times 3/4)

he's using fancy words like property it makes it confusing just ignore what he's saying

[bold mantle]

Ok

[fathom sequoia]

heres an image for clarification

[bold mantle]

How is 10,000 (3/4) = 1000?

[fathom sequoia]

wait a sec wrong image

[bold mantle]

Ok

[fathom sequoia]

because

[bold mantle]

I saw something like that in class today

How hard would u say this math is?

[fathom sequoia]

grade 9 or 10

[bold mantle]

Then why are they making an 8th grade do it?

[fathom sequoia]

not sure, but I don't think the question itself is impossible for an 8th grader to do

[bold mantle]

I don't even know where to start with jt tho

It may be possible for an 8th grade, but it sure is very difficult

[fathom sequoia]

how about I cast my screen and I will work through it with you

[bold mantle]

So like vc?

Sure

[fathom sequoia]

yeah but I can't talk as my mic is not working, but I'll cast my screen

[bold mantle]

Ok

[rose prism]

6n-9=8(n-2)-4n+5

i keep getting 1

is it supposed to be -1?

[limpid kernel]

i think its -1

[alpine sable]

Sub it back in: 6-9=8-4+5

[rose prism]

varibles?

[alpine sable]

Yes

[rose prism]

and is 15 = 2r considered no solution?

[zenith bough]

How do I find line that contains point M(2,3,1) and is perpendicular to p: (x+7)=(y+2)/2=(z+2)/3

i have 0 ideas, this really goes over my head

I have spent over 5 hours on this

<@&286206848099549185>

any idea is helpful

[rose prism]

i got 5 with this

may of did something wrong idk

i got 1 again

but i did something wrong with the negative

i figured it out

my dumbass did 6n - 4n = -2

[oak chasm]

@wind river Please don't post a question to multiple channels. See the rules and tips for getting help in #❓how-to-get-help.

[sage cloak]

Hey, can someone please explain how this identity is true please? I proved it easily but i can't understand the logic behind it.

[astral dagger]

it has to do with pascal triangle

[oak chasm]

@sage cloak Use the second image to do binomial n, n - r.

[sage cloak]

I've done it and got the identity

[oak chasm]

You're looking for a more intuitive explanation?

[sage cloak]

Yep

[oak chasm]

OK, so if you choose 3 elements out of 10, that's 10C3.

[sage cloak]

Yea

[oak chasm]

The unchosen elements are 7 out of 10, right?

[sage cloak]

yes

n = 10 , r =3

[dark granite]

The number of ways of choosing r people to invite to your party from a group of n people is the same as the number of ways of choosing n-r people (to NOT be at your party) from that same group of n people

[oak chasm]

So, if there are 10C3 ways to choose the 3 elements, there are 10C3 ways to have the 7 elements left over.

So, 10C3 = 10C7.

You can choose the 7 elements directly or you can choose them by choosing the other 3 elements that aren't in the group of 7.

If I pick 3 out of 10, I'm also picking the 7 out of 10 as the leftovers.

[sage cloak]

So 10C3 of picking 3 elements and 10C3 of not picking 7 elements?

[oak chasm]

Well, you get two groups.

If you pick 3 out of 10, you get the group of 3 that you chose. You also get the group of 7 you didn't choose.

So, if there are 10C3 ways to get a group of 3, there are 10C3 ways to get a group of 7 leftovers.

Does that make sense?

[sage cloak]

hmm give me a sec

I keep thinking that n-r represents the others combinaisons that we didn't pick

[oak chasm]

Or, if that doesn't help, think of a contest where you have 3 winners out of 10 people.

You can either choose the 3 winners or you can choose the 7 losers.

Either way you go, the ones you didn't choose are in the other group.

[sage cloak]

Yea, but how would it be equal?

[oak chasm]

Well, each selection of 3 out of 10 gives you 3 selected and 7 unselected.

[sage cloak]

yea and 10CP3 gives you the number of combinaison you can do

[oak chasm]

You can do it like this:
SUUUSUUSUU

That's 3 selected, 7 unselected.

Does that make sense so far?

[sage cloak]

Yep

[oak chasm]

OK, now flip them:
USSSUSSUSS

See how that's 7 selected, 3 unselected.

[sage cloak]

yup

[oak chasm]

So for each way you select 3 it corresponds to exactly one way of selecting 7.

[hushed pasture]

$\begin{pmatrix}
n\
n-r
\end{pmatrix} = \frac{n!}{(n-r)!(n-(n-r))!} = \frac{n!}{(n-r)!r!}$

[oak chasm]

You flip the selections.

Does that make sense?

[sage cloak]

yes, it's only reversed

[oak chasm]

OK, if they correspond one-to-one, there are the same amount of both.

[sage cloak]

omggggg

since they both contain the same number of obj

objects

Ok, i get it

[ocean seal]

Salah

[sage cloak]

You can make the same number of combinaison bc you have the same elements

[hushed pasture]

@sage cloak this is the proof

[oak chasm]

They use that in sets, too, to tell if sets have the same number of elements.

[sage cloak]

3 selected and 7 unselected will give the same thing as 7 selected and 3 unselected. At the end of the day, you have 3 of one and 7 of another.

[oak chasm]

If you can put the elements of one set into a one-to-one correspondence with the elements of another set, they have the same number of elements.

Right.

[sage cloak]

Thanks so much @oak chasm ❤️

[oak chasm]

You're welcome.

[sage cloak]

Yep i saw the proof and managed to get it but i was unable to understand it intuition wise

[oak chasm]

Another thing is this:

Let's say you want to break a group of 10 into groups of 3 and 7.

10!/(3!7!)

Let's say you want to break a group of 10 into groups of 2, 5, and 3:
10!/(2!5!3!)

[sage cloak]

does x!+y! = (x+y)!?

[oak chasm]

Try it with an x and y.

3! + 5! = (3 + 5)!

[sage cloak]

oh lmao

nvm

Thanks for the help again i appreciate it

[oak chasm]

No problem.

[ember token]

i need help

just to confirm something

[dark granite]

confirm what?

[ember token]

The formula for a volume for a circle is:

[oak chasm]

Just ask. You can also see rules and tips for getting help in #❓how-to-get-help.

[dark granite]

this doesn't make sense

volume for a 2 dimensional object???

[oak chasm]

What formula do you have?

[ember token]

V=4/3pi*r to the 3

i meant sphere

[oak chasm]

That's for a sphere.

But that's correct.

,w volume of sphere with radius r

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[ember token]

if the radius is 14

[dark granite]

then plug in r=14

[ember token]

would the volume be:

11494.0403219

?

[oak chasm]

,calc 4/3 pi 14^3

[ocean seal]

Result:

11494.040321934

[oak chasm]

Yes.

[ember token]

thanks i just wanted to confirm

[oak chasm]

You can use https://wolframalpha.com to confirm.

Just ask it volume of sphere with radius 14

,w volume of sphere with radius 14

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[ember token]

thanks

[oak chasm]

No problem.

[ember token]

i asked because the number seemed exaggerated to me

[oak chasm]

Yeah, cubing makes the numbers big.

14 is about 10

10³ is 1000

[unborn dome]

can someone help me out with this?

think first one is 0

[oak chasm]

@unborn dome Right.

So, what you do is you find the highest degree of the two polynomials.

[unborn dome]

and if its greater

[oak chasm]

Let's say that's degree d.

[unborn dome]

im assuming

its infinity

[oak chasm]

Then you divide top and bottom by x^d.

So, all the terms get divided by x^d.

So, the terms that are smaller than x^d in exponent will be like 1/x^(d - n), which goes to 0.

<@&268886789983436800>

[low jewel]

wth?

[unborn dome]

😦

[low jewel]

lol he deletin, continue w maths ig

[unborn dome]

woa

too far

[night geyser]

banned already

[unborn dome]

@river brook not cool

[low jewel]

@night geyser have a good day fam

[oak chasm]

@unborn dome So, the leading term of the higher degree polynomial is the coefficient of the original leading term.

[unborn dome]

right

[oak chasm]

And the other terms are all zero.

[unborn dome]

WAIT pause

@oak chasm if what you're saying is right, then this would technically be 0?

btw this is just like review , the teacher hasn't gone over this topic yet so im really grateful for your help

thats why im like super lost lol...... teacher/professor hasnt even gone over it 😦

[ocean seal]

Chai T. Rex

[unborn dome]

huh

[ocean seal]

Chai T. Rex

[oak chasm]

All the terms with x in the denominator go to zero.

[unborn dome]

ah.....

[ocean seal]

Chai T. Rex

[unborn dome]

might i ask, why do you divide every term by x^2? is it because its the leading coefficient or

[oak chasm]

You take the degrees of the two polynomials.

1 on top. 2 on bottom.

The maximum is 2.

You divide top and bottom by x² (the exponent is the highest degree).

[unborn dome]

ah

so you base it on the maxinum

Ill keep that in mind

thank you very much @oak chasm for helping a lost soul like me

[oak chasm]

You're welcome.

[unborn dome]

I'm going to finish up this granola bar lol, i really should skip my bad habit of studying before food

[oak chasm]

@unborn dome I was looking at the solution for another problem. It looks like you want the degree of the denominator.

[unborn dome]

? which other problem

the answer was 0 wasnt it i even got it right poggies

[ocean seal]

Chai T. Rex

[oak chasm]

If you divided by the highest degree, you'd get 1/0 inside the limit, and then you wouldn't know whether to give ∞ or -∞.

So, it's divide top and bottom by x to the denominator's degree.

Does that make sense?

[fathom sequoia]

how can i simplify this more

[bold mantle]

Very quick question

What is the thing for 35, like for 100 its 10^2.

[crisp grail]

someone just asked a question, try another channel

[crisp grail]

its a bit less than 6 tho

5.91 and its the square root

[bold mantle]

I need it with an exponent pls

Whay about cubed root

[thorn vortex]

$(\sqrt{35})^2$

[crisp grail]

first simplify the inner brackets, then do the outer one

[ocean seal]

Pealover

[thorn vortex]

there your exponent

[bold mantle]

Ok

[fathom sequoia]

they are saying I can factorise it more, can you give me an example

[crisp grail]

ah oh you wanna factorise

[ocean seal]

VincentBH

[fathom sequoia]

yeah what about it

[crisp grail]

you can factor that out

[fathom sequoia]

ah k

[crisp grail]

you see how?

[fathom sequoia]

can you show an example

[crisp grail]

I can solve it and then you see if you see how that works

[fathom sequoia]

ok

[ocean seal]

VincentBH

[fathom sequoia]

Ah Ok, I see it now, thanks

[crisp grail]

aight gl

[alpine sable]

My work^. What am I doing wrong 😞

[thorn vortex]

@alpine sable your answer seems true

definitely true

[alpine sable]

hm yeah

that’s weird. well thanks for the confirmation

[sage cloak]

Hey, could someone please explain what this identity mean please?

I was given the example of a group of n-1 boys and 1 girl. (n-1, r) would be the number of ways of choosing r kids across all boys

but what would (n-1, r-1) be?

It says that it would be the numbers of ways of choosing r-1 boys + 1 girl what i have some difficulty grasping it

because n-1 represents the whole boy group

[placid zinc]

Sometimes this is also called nCr

nCr represents the number of ways to separate r objects from an n-object pile

@sage cloak

[sage cloak]

Yep

[placid zinc]

(n-1 r-1)
Is the number of ways to separate r-1 objects from a pile of n-1 objects

[mighty sinew]

try drawing pascal's triangle you'll see it immediately

[sage cloak]

I haven't seen it yet, give me a sec

[placid zinc]

I mean this identity is why Pascal's triangle works

[mighty sinew]

actually it might not help if ur trying to understand what it means

yeah lmao

[placid zinc]

But yeah you can see this in Pascal's

[sage cloak]

But according to my example what would the n-1,r-1 mean?

[placid zinc]

(n-1 r-1)
Is the number of ways to separate r-1 objects from a pile of n-1 objects

[sage cloak]

Yes i know that

[placid zinc]

Not too sure what your example is

[rose prism]

anyone know how to find one solution?

[sage cloak]

Take a group of (n-1) boys and 1 girl

[placid zinc]

Channel busy@rose prism

[rose prism]

ah

alr

[sage cloak]

(n-1,r) would be number of ways to separate r objects from all the boyd

boys

(n-1,r-1) would be ?

[alpine sable]

can anyuone help me

[placid zinc]

@alpine sable
Channel busy

@sage cloak
So what's the objects that we're separating from the boys? Why is there a girl?

[sage cloak]

kids mb

idk why theres a girl

[placid zinc]

Consider this:
There's 10 people, and we need to take 3 of them for a job.
There's 10C3 ways to do this.

[sage cloak]

yea

[placid zinc]

I think you may be asking a different question than you posted, haha. Are you struggling to answer one of your problems?

[sage cloak]

Nope, just trying to understand the identity

Haven't really tried the problems yet

[placid zinc]

See it in the algebra
nCr = n!/r!(n-r)!

[sage cloak]

yup

[placid zinc]

After doing that, then playing with it a bit, you eventually get the identity

[sage cloak]

ok i will try,thanks

[fickle canopy]

Hello can anyone please help me with this problem? I think the first step is 2x-1log9 = xlog36 based from my teacher's explanation. Idk what to do next :((

[placid zinc]

Don't get too caught up with the logs, this is a linear equation in x

(2x - 1)a = xb

Solve for x

@sage cloak
Actually, I should have given you an example, not a proof.
(6 3) + (6 4) = (7 4)
This is exactly what happens with Pascal's triangle.

Add two numbers in the triangle, get the number below them

[lapis forge]

I’m stuck on these two questions, can someone help?

[fathom sequoia]

can someone help me factorise

i cant find an answer

[fickle canopy]

@placid zinc how do I solve for x?

[sage cloak]

Haven,t really touched the pascal triangle yet ahahha so would take me a lot of time to check

[fathom sequoia]

Wait nvm I solved it

[placid zinc]

This is generated by a rule:
Add any two numbers, you'll get the number below it

[fathom sequoia]

have I factorised this incorrectly:

[placid zinc]

This happens to generate nCr because of Pascal's identity

[fathom sequoia]

like why tf is the stupid app saying I did it wrong

-_-

or maybe I am stupid

[placid zinc]

Yes, that is not yet factored

Because of the + that exists outside of brackets

[fickle canopy]

Isn't nCr like a combination formula or was it permutation

[fathom sequoia]

how do I get rid of it they didn't teach me

[placid zinc]

Notice you've got
xa + 2a
(If you disguise 5x - 1 as a)

Can you common factor that?

[fickle canopy]

How do I do that?

[fathom sequoia]

nvm guys ofund the answer

[outer hearth]

okay cool

i put 9*9! and for some reason didn't get the same answer as when i did 9x9x8x7x6 etc all the way to 1. Why is that

[mighty sinew]

u probably made a typo somewhere lol

[outer hearth]

oh i did

lol

[placid zinc]

To solve a linear equation:

• Put all terms with an x on one side, all terms without an x on the other
• Common factor that x
• Divide as you need

[fickle canopy]

That's not how my teacher did it though

I have to explain my answer in class tomorrow

She used the laws of exponential equations

[mighty sinew]

wha-

also, this set is countable, right?

[placid zinc]

No she didn't lol.

@mighty sinew
Yes.

[mighty sinew]

wonder how i can prove it

[dim pasture]

can someone help me w this

[placid zinc]

@mighty sinew
#proofs-and-logic message

[fickle canopy]

Um I was absent but that was our lesson and here are some examples of what she did

[mighty sinew]

oh shit thanks @placid zinc

[placid zinc]

Neat! But these aren't the same question

The ones in the picture can be solved with an easier method, because the bases are related.

Your problem is quite different, because 9 and 36 are very different

[outer hearth]

How do I stop overthinking math?

[mighty sinew]

u dont

lmao

[loud cedar]

eat grass

https://tenor.com/view/touching-grass-touch-gif-21219969

[lyric ocean]

can anyone solve it with the full calculation.

[glass field]

yep

[placid zinc]

I can

[lyric ocean]

can u show me it bcuz i dont rlly understand

[placid zinc]

So this is a parabola that opens upwards. So, if it has no zeroes, then it is above the x-axis

Is there an easy way to tell if a parabola has no zeroes?

[fathom sequoia]

guys I'm in grade 11 and each year we get a copy of last year's assessment, and the questions in last year's assessment were very hard, like this one: (How do they expect me to solve this.)

It is not fair the material is super easy but the assessments are very hard

[placid zinc]

Take the difference between them
You care about the roots of that difference

So the roots of:
(a - d)x² + (b - e)x

Which are 0, and (e - b) / (a - d)

No second root if e = b

Not a parabola at all if a = d

[fathom sequoia]

ok thanks

wow looks hard

good luck with it

[quick shoal]

I'll try to help you, gimme a sec

I'm thinking, the inside angles of a polygon with n sides add up to 180(n-2). And if we redraw it like this:

[placid zinc]

Something something circle theorem

[thick latch]

can someone help me?

can i make the sin to sin^2a = 1/3

orr??

[quick shoal]

the angles inside a dodecahedron is 144 right?

(10-2)*180 / 10 = 144

[thick latch]

anyone?

[fathom sequoia]

How do I simplify (perhaps I am stupid): $\sqrt[2]{531441^{\frac{1}{3}}}\sqrt[2]{x^{\frac{14}{3}}}$

[ocean seal]

TJ89899889

[kindred warren]

it is saying $5341441^{\frac{1}{3}}^{\frac{1}{2}} x^{\frac{14}{3}}^{\frac{1}{2}}$

[ocean seal]

Tra-Guy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[kindred warren]

shit

i dont know how write it

[fathom sequoia]

my app has auto latex

I just copy and paste whatever I wrote and it converts it to latex

[kindred warren]

oh

ill just write it and send to you

[fathom sequoia]

ok

[high bloom]

I'm being asked to prove that there is always a value greater than any random constant in a polynomial

this would be straightforward if I could take the limit and show that it tends towards positive infinity, but I'm being asked to do this without using calc/limits

[kindred warren]

@fathom sequoia

[quick shoal]

I could only get this far sorry. I'm not sure how to get the angle x. There's some theorem I'm missing.

Oh..right dodecahedron is 12 sides, not 10. My numbers are wrong then

[fathom sequoia]

so you mean the exponent is 1/3 to the power of 1/2 or you mean the new exponent would be 1/3 times 1/2

[kindred warren]

yeah

1/6

[fathom sequoia]

ok I got $1441^{\frac{1}{6}}x^{\frac{14}{6}}$

[ocean seal]

TJ89899889

[kindred warren]

do you mean 5341441

[north bridge]

can soenone help me

with these problems

[teal vessel]

sure i can try

[fathom sequoia]

yeah

[kindred warren]

yeah then you're correct

[fathom sequoia]

Fro some reason it's still saying it's not factorised to the fullest

[kindred warren]

oh

ok so $5341441^{\frac{1}{6}}x^{\frac{7}{3}}$

[alpine sable]

can someone help me pls

pls

[ocean seal]

Tra-Guy

[wary stream]

It says test, so we can't help you with tests

[alpine sable]

;-;

ok

sorry

[fathom sequoia]

we can give you a hint I guess

you don't always need to play by the rules 100%

[alpine sable]

haha

[devout sigil]

Use a circle property

[wary stream]

It's academic dishonesty to be helping people on tests

[fathom sequoia]

you can give a hint

a nudge

don't be that guy

[wary stream]

I don't think that's possible

[fathom sequoia]

even at school during a hard test I've asked a teacher for assistance

[wary stream]

If you want to get banned for helping someone in a test, so be it

[fathom sequoia]

no I don't know how to answer the question

also perhaps many questions here are from tests and you don't know

[wary stream]

That's getting assistance from the teacher. Get assistance from a discord channel is different

[fathom sequoia]

ok

[misty mortar]

What rule do I use for this?

[glass lichen]

hint |1/4|<1

[misty mortar]

But the n doesn't match though.

I think that would work for 2^n/8^n

[glass lichen]

yeah.. so pull it off

$2^{n-1}=2^{-1}2^n$

[ocean seal]

Mosh

[misty mortar]

ooooooooooooooh

thanks

[north bridge]

ok thx

did u get it

[teal vessel]

mhmm

[north bridge]

o could u tell me

[teal vessel]

do u just need answeres or method too??

[north bridge]

umm for now jsut ans

i want to know if my ans r correct

[teal vessel]

okay 1 sec i have to type this out

[north bridge]

but ill tlel u if i need method

k

[misty mortar]

What did I do wrong here

[north bridge]

u type it out lol

[teal vessel]

@north bridge
part 1 ... 2-3 and 6-7 or
2<t<3 and 6<t<7
part 2... 1.35<t<4.78

part 3... 8-(-6)/7 so v=2m/s
part 4...22.18 meters

part 5... not really sure about this one but i think its the dourt graph

[teal vessel]

sorry for the delay

[north bridge]

np wait so qs

[teal vessel]

yeah?

[north bridge]

this is a positiont ime graph

yk that right

[meager leaf]

brah how to solve this

[teal vessel]

yes

?

what is the issue?

[north bridge]

so like i thought 2a would be

1<x<1.88

[meager leaf]

asking me?

[north bridge]

and 6(<x<7

[teal vessel]

nah

[north bridge]

cus it said to the rightof the origin

[teal vessel]

well it is asking the time for which it is to the right

if the question was while it is moving to the right ur answer was correct

while y>0 then it is to the right

[north bridge]

wdym?

[teal vessel]

well can u join streams?

[north bridge]

ye

where is that

[teal vessel]

isk this ersver tbh

[north bridge]

the 8kbs one

[split trail]

can someone help me with 8

i got the positive answer as -7

and the negative answer as -15/2

but in the answer key it says that the negative is -5

<@&286206848099549185>

[misty mortar]

?????

[wanton beacon]

May I get some help on question 45?

All parts

[kindred warren]

when it says 'interpret the function in terms of the context' it's basically telling you to apply an implied domain

since the context is 'test scores' then you can't have negative test scores can you?

[kindred warren]

the particle is moving to the left when it's velocity is negative

[wanton beacon]

Right but

What about part b and c

[kindred warren]

for part b, just replace f(t) with 308

then solve for t

[wanton beacon]

And a?

[kindred warren]

do you mean c

[wanton beacon]

The graphing

[pale spade]

the cost of goods and services in a urban area increased 1.5% last month. At this rate, what will be the annual increase rate?

answer is 19.6%

how come

[wanton beacon]

@kindred warren confused on the graphing

[kindred warren]

do you know how to graph a linear function?

[covert nimbus]

Help pls

[wanton beacon]

Not rlly

I don’t think

[kindred warren]

so you just have to find two points, then draw a straight line through them, but in this case, the graph cant be on the negative side since test scores cant be negative

[wanton beacon]

So where will the 0.8 go and where will the 72 go

[kindred warren]

0.8 is the gradient, at 72 is the y intercept

so (0, 72) is one point

now you can find another point by subbing in any other value

anyway, i need to go rn

[wanton beacon]

Alright, got it, thank you very much

[fathom sequoia]

Hey

does anyone kno wwhere to start in this question

me and my dad have been trying to solve it to prepare me for the exam but we've been having trouble

[teal vessel]

idk how to solve it

but i sure can try

is that fine
?

[fathom sequoia]

well I don't know where to tart

start*

with it if you know what I mean

[teal vessel]

i think that its gonna be done with the formula b^2 -4ac >0

[wary stream]

Not possible with this equation because that's a cubic function

[teal vessel]

long divison

[fathom sequoia]

I didn't learn this at school

[teal vessel]

well i-

[fathom sequoia]

we get easy questions

[teal vessel]

have u learned the laws like

alpha + beta + gamma = -b/a

[fathom sequoia]

no i dont know what that

is

?

[teal vessel]

then

[fathom sequoia]

what is alpha beta gamma

[teal vessel]

how i can solve this question so u can understand

[wary stream]

Are you referring Vieta's formula?

[teal vessel]

i do not know

[fathom sequoia]

idk I followed the material required thoroughly

why are they giving me work that is above my level.

[teal vessel]

yes

[fathom sequoia]

no wonder the students were crying last year

[teal vessel]

[teal vessel]

[fathom sequoia]

(btw this is the exam from last year, but my teacher recommends I work through it.)

[teal vessel]

wha?

what grade are u in?

[fathom sequoia]

11th

[teal vessel]

ohhh... have u guys studies vieta's laws?

[fathom sequoia]

it was the exam for 11th grade students last year

[fathom sequoia]

no wtf

I never heard that word

You know some things in life annoy me more than others, but giving students questions that are impossible to solve with the material you've taught is just...

[teal vessel]

these ones

[wary stream]

You realize that we're all overthinking this