help-0

[ocean seal]

Chai T. Rex

[oak chasm]

Now the limits are each simpler than what you had before.

Then the exponent on the first one is a positive integer, so you can use the power law on that one.

You can use the constant multiple law on the second.

And the third is a constant function, so it's that constant.

[edgy sand]

oh wow

yea that seems way easier

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[oak chasm]

Which is 1.

[edgy sand]

definitely saves more time

[runic canopy]

Is this chat free?

[edgy sand]

i have 2 more questions then you can goo ahead sry @runic canopy

[runic canopy]

Np

[oak chasm]

So the limit laws work, but the continuous-around-what-the-input-is-going-towards rule is faster.

[edgy sand]

yea i was gonna say lol

but i think its still good to know them

[oak chasm]

You need to know the limit laws, though.

Sometimes the function isn't continuous around where the input is going towards.

Then you can't use the shortcut.

Limit laws and L'Hospital help there.

[edgy sand]

got it bet,

think you can help me with a few more?

i seem to get them like this

[oak chasm]

Maybe one more.

[edgy sand]

okay

[oak chasm]

I have to go soon.

[alpine sable]

$\textit{Simplify.}\frac{2-k}{(\frac{k}{5})+1}$

[golden nymph]

I can continue if you can’t

[ocean seal]

! Future

[oak chasm]

@alpine sable Sorry, this channel is busy.

[alpine sable]

ok

[golden nymph]

Multiply 5 up and down

[oak chasm]

@edgy sand OK, so the derivative tells the slope at a point on the function's graph.

So, what's the slope of g at x = 3?

[edgy sand]

-6?

[oak chasm]

That's the value of the function.

Which gives you the y coordinate.

Is the y coordinate usually the slope of the function?

[edgy sand]

no

[oak chasm]

Right.

The derivative of the function gives the slope.

[edgy sand]

ohh

4

[oak chasm]

Right, so the slope is 4.

And it happens at the point (3, -6), right?

[edgy sand]

okay and then along with the y coordinate we can find theg raph

yep

[oak chasm]

So now use point-slope form.

Since you have a point on the line and the slope.

Nope.

That's slope-intercept.

[edgy sand]

oh

y-y1=m(x-x1)

?

[oak chasm]

Right.

[edgy sand]

okay mb

y+6 = 4(x-3)

[oak chasm]

Good.

So that's your answer.

[edgy sand]

thats my tangent line right

[oak chasm]

Yes.

The tangent line is at the point on the original graph.

And it has the slope of the function at that point.

[edgy sand]

makes sense thank you

[oak chasm]

No problem.

[edgy sand]

doo you have to go now?

[oak chasm]

I can maybe do 5 more minutes.

[edgy sand]

okay

the definition is just the formula

to find derivate of function

which im p sure you know lol

[oak chasm]

What formula is that?

The limit?

[edgy sand]

yea h -->0

[ocean seal]

Chai T. Rex

[oak chasm]

What's f(8)?

[edgy sand]

8

[oak chasm]

OK.

What's f(8 + h)?

[edgy sand]

what is h in this case?

[oak chasm]

A variable.

[edgy sand]

not sure what f(8 + h) would be if h is unknown

[oak chasm]

Like we're getting h closer and closer to 0 without touching 0.

So h is a bunch of different values, so we leave it as h.

Now here's how you get f(8 + h).

[hoary shell]

f(8 + h) is your function f(x) but u sub (8+h) into x

[oak chasm]

f(x) = sqrt(7x + 8)

Now you have x on the left.

f(x)

f(8 + h)

Now x has been replaced with 8 + h on the left of the =.

So, replace x with 8 + h on the right.

[edgy sand]

8

[oak chasm]

No.

Replace x with 8 + h on the right.

[edgy sand]

f(x) = 8???

ohh

[oak chasm]

f(x) = sqrt(7x + 8)
f(8 + h) = sqrt(7(8 + h) + 8)

See how I replaced x with 8 + h on both sides?

[edgy sand]

yep

[oak chasm]

So that's how you take f(x) and get f(something).

You replace the x with something on the left, so you do it on the right, too.

So, simplify sqrt(7(8 + h) + 8).

[edgy sand]

sqrt(64 +7h)

[oak chasm]

Right, but with parentheses since sqrt is done before +.

sqrt 64 + 7h = sqrt(64) + 7h.

But you want sqrt(64 + 7h).

[ocean seal]

Chai T. Rex

[old whale]

Solve the questions below in 4 ways:

1. Substitution method
2. Elimination method
3. Mixed method (elimination and substitution)
4. Graphic Method

[oak chasm]

@old whale Sorry, this channel is busy.

[rocky cape]

they using the thing

[quartz osprey]

how do you do this ?

[oak chasm]

@quartz osprey Sorry, this channel is busy.

[quartz osprey]

aite ill come back later

[old whale]

Can you guys help me? I really don't understand math, especially during a pandemic

[oak chasm]

@old whale Please read the rules and tips for getting help in #❓how-to-get-help.

You can find an unused #questions channel and ask your question there.

[old whale]

Alright

[oak chasm]

If you get no help 15 minutes after asking, you can call @Helpers.

@edgy sand So, how do you work with that limit?

[edgy sand]

with sqrt(64 + 7h) right?

[oak chasm]

@thorny pier Sorry, this channel is busy.

[thorny pier]

oh my b

[ocean seal]

Chai T. Rex

[oak chasm]

What do you do next?

[edgy sand]

next, idk but id try to cancel the h

[oak chasm]

You can only cancel factors of the entire top and bottom.

[edgy sand]

so

[oak chasm]

h is a factor of the entire bottom.

But you can't factor it out of the top.

[edgy sand]

could we multiply by the inverse of the numerator to get rid of the sqrt?

[oak chasm]

Well, no, but we can use difference of squares.

a - b is what we have on top.

(a + b)(a - b) = a² - b² is a difference of squares. a² is a square, b² is a square, a² - b² is a difference of squares.

So, multiply the top with the top with a changed sign in the middle.

Then multiply the bottom by that.

So that you multiply the top and bottom by the same thing.

That keeps the value the same.

[ocean seal]

Chai T. Rex

[edgy sand]

thats what i said lol

[edgy sand]

.

[oak chasm]

Oh, that's not called an inverse.

[edgy sand]

well i meant switch the sign lol

my bad

[oak chasm]

Inverse means reciprocal or negative value.

[edgy sand]

yea my bad on that one but thats what i was thinking tooo

[oak chasm]

Oh, OK.

So, you get difference of squares on top.

[ocean seal]

Chai T. Rex

[edgy sand]

okay right

64 cancels out on top

[oak chasm]

Right.

Now you can factor out an h on top and bottom.

[edgy sand]

nice so 6h/sqrt(64+7h) + 8

[oak chasm]

Nope.

A few minor mistakes.

Try again.

[edgy sand]

oh my bad

7/sqrt(64+7h) + 8

[oak chasm]

Good. One thing, though. If you write fractions in chat, you have to surround the top and bottom by parentheses unless it's just a number or just a variable.

7/(sqrt(64 + 7h) + 8)

[edgy sand]

yea im assuming you know what i mean

now we can plug in 0 right?

[oak chasm]

Well, it's good to do it that way because the other way is wrong.

Division comes before addition (PEMDAS).

So, 7/sqrt(64 + 7h) + 8 = (7/sqrt(64 + 7h)) + 8.

The fraction doesn't include the 8.

But you want it to, so you need the parentheses.

So, now we can fill in h.

sqrt(64 + 7h) is continuous when h is zero.

[edgy sand]

so denom. comes oout to 16

[oak chasm]

Right.

So, 7/16.

Let's check.

[edgy sand]

7/16

[oak chasm]

,w derivative sqrt(7x + 8)

[edgy sand]

so just plug it into our original function to check

[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]

,w 7/(2 sqrt(7(8) + 8))

[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]

So, that works.

[edgy sand]

ooh intot eh derivative function

wait you plugged into the derivative function right?

[oak chasm]

Yeah, but we never got the derivative function.

[edgy sand]

not the given one

[oak chasm]

Right.

I asked Wolfram Alpha for the derivative.

[edgy sand]

right

[oak chasm]

Then I filled in 8 for x.

[edgy sand]

makes sense

wow thanks so much this made sense

[oak chasm]

You're welcome.

[edgy sand]

you gotta go now right

[oak chasm]

Yeah, time to relax and sleep 🙂

[edgy sand]

aight peace out

[oak chasm]

Have a good day/night.

[edgy sand]

@hoary shell if youre still on, i need help with a last one

[hoary shell]

sure

[edgy sand]

thanks

so the formula is given

im mainly unsure on which numbers froom the coordinate to plug in

[hoary shell]

ah ok

ur doing part b right?

[edgy sand]

nah ignore the -16

[hoary shell]

ok

[edgy sand]

its a failed attempt

[hoary shell]

so the x would still be x then the f(x) is your y

so i think it would be -12 - f(a) on top and -3 - a on bottom

[restive tendon]

how would i solve this?

it says algebraically, a bit confused on that part

[edgy sand]

(x^2 + 7x - 12 -f(a))/(x-3)

like this?

[surreal meadow]

#help-9

[hoary shell]

no not quite actually

you would just put x^2 + 7x, then plug in -3, which becomes -12

[edgy sand]

oh

[hoary shell]

and the f(a) part stays

[edgy sand]

so then its (f(a)+12)/(-3-a)

[hoary shell]

wait wait

i explained wrong

ok so it is f(x)-f(a)/(x-a) as x-> a

[dawn scarab]

\

[hoary shell]

what you had first is right

my bad

[edgy sand]

which one

[edgy sand]

thjis?

[hoary shell]

this one

yeah

[edgy sand]

ok

now replace x with -3?

[thorn hound]

does anyone know about descartes rule of signs

[hoary shell]

i think replace the a with -3

then it instead of x -> a it would be x -> -3

so then you would do limit x-> -3 of (x^2 + 7x - f(-3))/(x + 3)

[edgy sand]

okay so then

replace x with -3?

[tardy plank]

how do you find the domain of this?

[hoary shell]

yes SlyDaw but if you try to replace x with -3 right away you will get 0 in the denominator since it is x + 3

[edgy sand]

ah

[hoary shell]

the top is x^2 + 7x - 12 so u need to factor it

and then most likely there will be a x+3 that cancels with the bottom

then plug in -3 for x that should give you the slope

[edgy sand]

you cant factor it

a sign is wrong somewhere

is it +12?

[hoary shell]

oh yeah

it is

[edgy sand]

okay so i get x+4

which is then just 1

[hoary shell]

great

[restive hill]

Hi Goodmorning! Can anyone help me?

[edgy sand]

so taht would be my i

now i use y-y1=m(x-x1)?

[hoary shell]

yes for part b

[edgy sand]

oh what about ii

[hoary shell]

ii we do like the other problems where you sub (x+h) for x

here we will do (a + h) for a

[edgy sand]

ah oka

makes sense

and then the graph is the bottom left one im assuming

[hoary shell]

yes

[edgy sand]

based oon the others

okay cool

thanks soo cmuch

[hoary shell]

npnp 🙂

[tardy plank]

does anyone know the answer to my question

[hoary shell]

unfortunately I cant answer your question can I ask where it is from though?

[tardy plank]

It's from a textbook for practice

[fair osprey]

What is it?

[tardy plank]

how do you find the domain of this?

[glass lichen]

domain is where you're well defined

the numerator is well defined for all inputs, since it's a polynomial, so the problem is the denominator

what cant a denominator be?

[tardy plank]

y = x and y = x^3

got it

thanks

[pulsar locust]

Recall that a matrix M ∈ R
n×n is “orthogonal” if MMT = I^n, where In is the n×n identity
matrix. (a) Explain why the rows of any given orthogonal matrix are mutually perpendicular. (b)
Explain why each row of any given orthogonal matrix has unit length.

(a) Explain why the rows of any given orthogonal matrix are mutually perpendicular.\
The rows of any given orthogonal matrix are mutually perpendicular because \
if $$ M = (m{i,j})i,j $$, then for all i,j, the i,j-th component of MMT is the dot product between the i and j for the rows $$ \sum{k=1}^{n} { m{i,k} m{j,k} } $$ \
if i = j then we have :
$$ \sum{k=1}^{n} { m{i,k}^2 } = 1 $$
The row vectors are orthogonal, with unit vector, thus mutually perpendicular.

(b) Explain why each row of any given orthogonal matrix has unit length.

[ocean seal]

burga

[pulsar locust]

Explain why each row of any given orthogonal matrix has unit length

Each row of any given orthogonal matrix has unit length because in order for it to be an orthogonal matrix it must have unit length to satisfy identity equation

[alpine sable]

hey guys can someone tell me how u get 4x/4 = 16/4 after adding 7 to both sides https://cdn.discordapp.com/attachments/837421885172088863/890059325547110460/image0.jpg

[eternal cedar]

how would i solve this

[eternal cedar]

dividing both sides by 4 would the step after

[astral dagger]

apply derivative rules and finally use the given values

first is product rule, the two others are quotient rule

[eternal cedar]

so f(5)g'(5)+f'5)g(5) and plug in stuff?

[alpine sable]

so do i add 26 to both sides on this one or somethings

[eternal cedar]

if you are solving for v subtract 8 from the right side

[alpine sable]

so would the work look something like this?
26=8+v
-8 -8

[eternal cedar]

yea

[radiant barn]

Hello

[eternal cedar]

18=v

[alpine sable]

so what would it look like after

[eternal cedar]

wdym

[alpine sable]

i subract 26-8

i get 18

and i substract 8-v

what do i put in

v/8?

[eternal cedar]

26 = 8 +v , subtracting 8 from both sides leaves (26-8) = (8+v-8) which simplifies to 18 = v

probably made that more complex than needed

[maiden raptor]

Help pls

[alpine sable]

what do i write after this

thats what i meant from earlier

[eternal cedar]

18=v

final answer

[alpine sable]

so i just put a equal sign

and then v under the -8

[eternal cedar]

if they want you to show that work then yes

maybe put it under the other 8 for clarity

[alpine sable]

is this it

[eternal cedar]

yes

[alpine sable]

thx

also why subsract 8 from both sides

but other times you can add from both times

[hoary shell]

depends if it was v - 8 then u would add 8 to both sides

[eternal cedar]

if you do the same thing to both sides of an equation it can be whatever

addition or subtraction

[eternal cedar]

welp i failed this

[alpine sable]

Okie

i hope you get your problem solved

thx

[somber osprey]

Ello

[formal flint]

Did I do this correctly? ( getting the value of k in vertex form of quadratic function )

[coral pagoda]

another thing that will probably make this easier is to notice that your vertex (x=1) is your root

[hoary shell]

oh yeah bc the discriminant is 0

[coral pagoda]

$-3x^2+6x-3=0 \iff x^2-2x+1=0 \iff (x-1)^2=0$.

[ocean seal]

dackid

[coral pagoda]

which results in x=-1

although yes, that is not what I was looking at.

Similarly, -b/2a is -6/2(-3)=1

so your vertex and root are at the same point. So yes, k must be 0

[formal flint]

ok thank you

[coral pagoda]

you still need help on that area question?

[pearl wraith]

i found my mistake

[coral pagoda]

hmm, alright. p.s, you should have a square root of 2 in there somewhere.

[gilded aurora]

i got the answer as 25th day of the month, is this correct ?

[pearl wraith]

actually yeah i need help again

[coral pagoda]

Well, you were close.

[coral pagoda]

Here you want to look at the least common multiple of 2,4,6, and 8

Okay cool. This isn't that bad. Do we agree that Area= length x width?

[pearl wraith]

yes

(10+2x)(4+2x)

[coral pagoda]

oh my bad lad, it is the 25th. You are absolutely right :p

[coral pagoda]

Not quite actually. x is how much it changes, so it would JUST be x, not 2x

so we have 2A=(l+x)(w+x)

Now we need to solve for x

[pearl wraith]

no but its a square in a square

and we know the sides

[coral pagoda]

which are 10 and 4, and we want to add them both by the same amount, which is what we call x

[gilded aurora]

Thanks brother 🙂

[coral pagoda]

You bet!

We do not know what x is, but it is our job to find it.

On the other hand, there is a simpler way to go about this

[autumn rivet]

when x approaches infinity and cosx does not exist. Do we just ignore it?

[coral pagoda]

$A=lw \Rightarrow 2A=2lw$.

[ocean seal]

dackid

[coral pagoda]

Do we agree with this?

[coral pagoda]

not at all. I am helping someone right now though.

[coral pagoda]

do we agree @pearl wraith ?

[pearl wraith]

HM

hm

[coral pagoda]

it's just some simple algebra. All I did was multiply both sides of the equation A=lw by 2, giving 2A=2lw

[pearl wraith]

that wouldnt work though because 20 x 8 does not equal 80\

since 80 is the doubled area

[coral pagoda]

At what point did we say the length and width are doubled?

That is not the claim I made. Please slow down

[pearl wraith]

man you put a 2 beside the l

[coral pagoda]

Do we agree with what I have written so far

[pearl wraith]

No

[coral pagoda]

That twice the area is twice the length times width

[pearl wraith]

Yes but the rectangle must be expanded equally on both sides

[coral pagoda]

I am aware

We have made no claims about the sides, we have only scaled the product (length times width)

Have you taken algebra yet?

[pearl wraith]

bro yes

[coral pagoda]

Okay, so if we multiply two sides of an equation by 2, the equation is still very much true.

So if A=lw, then 2A=2lw

that is just algebra.

If we can agree with this part, then we can actually start saying things about the dimensions of the length and width themselves

[pearl wraith]

okay

i agree

[coral pagoda]

Okay cool. Well, $2=\sqrt{2}\cdot \sqrt{2}$.

[ocean seal]

dackid

[coral pagoda]

So we can rewrite our expression: $2A=(\sqrt{2} l)(\sqrt{2} w)$

[ocean seal]

dackid

[coral pagoda]

And viola, both the length and width our root 2 times larger than they were previously.

[pearl wraith]

are you high

[coral pagoda]

no

[alpine sable]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[coral pagoda]

Any further questions?

[alpine sable]

1+1 ?

2+2 = 5????

[pearl wraith]

0=1-1?

[coral pagoda]

If you still believe I am wrong, then you need to refine your intuition on the problem. This is a perfectly normal part of the math experience, so there's nothing wrong with it.

Getting a bit off topic, can we take this too #discussion please?

Thx

all good mate

By the way, we can generalize this idea. If we have an n-dimensional object and we want to scale it's 'volume' by some factor of c ($c>0$), If the sides are of equal length, then all of the sides have been scaled by $\sqrt[n]{c}$.

[left tendon]

help me to answer my modules

[ocean seal]

dackid

[alpine sable]

yo does anyone know of a good graph theory book? I want to get my feet wet

[coral pagoda]

I have Intro to graph theory by Richard Trudeau.
Looks like a good starting place

[pearl wraith]

trudeau is a trash PM

[alpine sable]

that went from 0 to 100 rq lol

[coral pagoda]

Yea, taking a further glance at it, it seems like a good one

[alpine sable]

any suggestions Atlas? I am about to google the one you suggested

I thinkn I have seen this book before laying around some where

maybe in the physics department...

[placid zinc]

"Trudeau is a trash PM" An intro to graph theory

[alpine sable]

https://www.google.com/search?q=Trudeau is a trash PM"

lol

[coral pagoda]

Ah, I was wondering what PM meant

[alpine sable]

i think google broke

[placid zinc]

We have now voted him in a third time

Better than conservatives, I guess.

[coral pagoda]

#discussion

[alpine sable]

but yea. thx for the book

[coral pagoda]

You betcha

[alpine sable]

does all math follow Set thoery?

seems like it is everywhere

[coral pagoda]

What do you mean exactly?

[sacred aurora]

No it doesnt

Math has some loopholes and weird stuff that cant be yet explained

[alpine sable]

Seems like nature is modeled by Set theory

[sacred aurora]

Not really

[coral pagoda]

In general, sets are a very useful way to describe things

[alpine sable]

^^

[hoary shell]

I see a lot of sets, maps, spaces, but I only really understand very very basic set theory taught for algebra

[alpine sable]

im reading some graph theory and set notation lol

[coral pagoda]

Doesn't surprise me one bit

[alpine sable]

you model a circuit.. set notation

[hoary shell]

like an electric circuit??

[coral pagoda]

You form a group, set notation

[alpine sable]

like any system in general

[coral pagoda]

Keep in mind a 'set' is general af. It is just a collection of objects.

[sacred aurora]

Set are ez for us to visual but they jus a perspective

[coral pagoda]

Hmmm, debatable.

[sacred aurora]

?

[alpine sable]

but yea, you model an electrical circuit using set notation

[coral pagoda]

But yes, if there is some collection of objects you want to keep track of, you make a set out of it.

[hoary shell]

wow

[alpine sable]

right...

like a linear equation

[coral pagoda]

Now, the more interesting sets are ones that have certain properties attached to them.

Hell, the collection of all polynomials is a set.

[hoary shell]

could the collection of platonic solids be a set?

[sacred aurora]

Bruh

[coral pagoda]

Sure! If you have a collection of anything, you can make a set that contains all of those elements

[sacred aurora]

Im leaving this chat losing braincells

[alpine sable]

so quick question on notation

(x,y) is not the same as [x,y] or {x,y}?

[coral pagoda]

[x,y] may mean something else (based on your book).
But (x,y) is usually an ordered pair and {x,y} is the set containing x and y

[hardy gulch]

nope

[alpine sable]

https://www.mathsisfun.com/sets/symbols.html

[hardy gulch]

[(x,y) \coloneq {{x}, {x,y}}]

[alpine sable]

lol

[ocean seal]

ricey

[coral pagoda]

That might be a book decision on ricey's part. That's not a general definition and should not be seen as such

[hardy gulch]

this definition also means that (x,y) = (y,x) iff x = y

[hardy gulch]

i think most discrete math texts use this definition; kurtowski's definition

[coral pagoda]

(x,y) can also be an interval, or an ordered pair.

In other words: you don't know until the book tells you xp

Also, context is important

[hardy gulch]

oh

my bad then

[alpine sable]

so does that mean that linear algebra uses set notation

[coral pagoda]

Well, in order to have a set, you must have a universal set that contains such a set.

Does such a set exist in $\R ^n$?

[ocean seal]

dackid

[alpine sable]

and how do we check?

[coral pagoda]

Well, ready to feel silly?

[alpine sable]

lol

[coral pagoda]

Any set in $\R^n$ is contained in $\R^n$. So $\R^n$ is our universal set xp

[ocean seal]

dackid

[alpine sable]

what if the set contains a time function?

and the function is not continous?

[coral pagoda]

Well, the function is not an object in R^n

What are objects in R^n?

[alpine sable]

im not sure.. i was thinking of space

anyhow.. thanks for the book lol

[coral pagoda]

Well...an object in R^n is just a point. Namely, points of the form (x_1, x_2,...,x_n)

[alpine sable]

yea but would not that point be located somewhere in space?

[coral pagoda]

Sure is. And that 'space' is R^n

[tired venture]

Can anyone help me? 😫

@coral pagoda

[coral pagoda]

Pick 2 of the 10. I will help with those.

Fair?

[tired venture]

Ok

Number

2,10

@coral pagoda

[coral pagoda]

I'm still here. No need for pings

[tired venture]

Ok sor

[coral pagoda]

Alright, let's take a look at 2

[tired venture]

Ok

[coral pagoda]

I assume you have some familiarity with balancing equations in algebra.

Is that a safe assumption?

[tired venture]

Yes

[timber scaffold]

there is a space to ask a question

[coral pagoda]

Okay good. When dealing with a quadratic, it is always a good plan to get everything on one side and set it equal to 0.

As an example, if I have x^2=x-5, I will subtract x and add 5 on both sides to get x^2-x+5=0

Now do this for #2 and tell me what you get when you are finished.

[timber scaffold]

the product of cuberoot of 7 and squareroot of 5

[coral pagoda]

Please ask somewhere else. I am helping someone else out right now

[timber scaffold]

okay sorry for disturbing

[coral pagoda]

Nw

[coral pagoda]

While I wait, there really isn't much you can do with this. That is as simplified as it gets. So if you want the actual answer, then I would like to direct you to your handy dandy calculator.

[timber scaffold]

can you give me actual answer]

[surreal meadow]

dackid, can it not be expressed in terms of $\sqrt[6]{}$?

[ocean seal]

maximo

[tired venture]

What is the answer? @coral pagoda

[coral pagoda]

Sorry, that is not what I am going to do.

If you just want the answer, you will have to ask elsewhere

[coral pagoda]

Sure, but is it really simplified?

[surreal meadow]

🤷🏻‍♂️ it seems like that's what they're looking for

[ocean seal]

dackid

[coral pagoda]

Does not look very simplified to me :p

[surreal meadow]

$\sqrt[6]{735}$

pffffft

[ocean seal]

maximo

[surreal meadow]

its beautiful 😻

[coral pagoda]

Unpleasant

[surreal meadow]

to each their own

[coral pagoda]

Own their to each

[coral pagoda]

The goal of the homework is to get you better at solving these types of problems.
If I give you the answer, which I won't, you will only know how to solve that problem. But if there is a problem just like it, you'll be screwed.

Get out of this 'I just want the answer mindset.' It's only gonna screw you.

[loud cedar]

indeed

[surreal meadow]

🤝

[alpine sable]

yea thats a fact... change the mindset.. it comes and bites you later on in Uni if you get in STEM field

when you submit a lab report right at 11:59 pm when it is due lol

talk about living on the edge XD

do not follow my example children

[small gale]

OOOOHHH

thank youuuuu my friend!!!!

[harsh nimbus]

madristas!

also very annoying question 6b

[small gale]

ye 😄

[unborn parcel]

Hey, could someone help me on my piece wise function on question channel 6?

[alpine sable]

How do I find the second row of patients who don’t have endocratis?

[coral pagoda]

I'm taking pure math, and you no longer have algorithms (i.e. the quadratic formula) to solve problems. I would be screwed if I had that mindset.

[alpine sable]

Yea, I am actually going through that. I messed up in my math courses and it is coming to haunt me in QM

I learned and dumped a lot of information lol

[coral pagoda]

QM??...you fool!

[alpine sable]

how so?

I mean.. double majoring looked good on paper when I signed it lol

[coral pagoda]

Oh for sure, but QM is a whole 'nother beast.

So hopefully your math game is strong

[alpine sable]

oh yea.. the math is insane

[coral pagoda]

Pretty sure we are talking about quantum mechanics right?

[alpine sable]

its rusty atm but im sharpening up

yea quantum

Y’all wanna help me real quick this is basic stats

im in stats atm lol i need help myself.

[surreal meadow]

do you need help with this?

[harsh nimbus]

i think i know how to do it but i am not sure lol so just wondering

do i find derivative->put into mx+b=y?

[surreal meadow]

normal is perpendicular to the tangent

[harsh nimbus]

yeah

[coral pagoda]

That fact that we are writing people as decimals bothers me greatly :p

[harsh nimbus]

oh yeah -1/m

[alpine sable]

You have to for the system :p

I found it out tho

[coral pagoda]

Ayyy nice! My condolences to the half a person that has endocartitis

[alpine sable]

what if math is teaching us how to build a Skynet...

[coral pagoda]

Math is teaching us a lot of things, so it probably can (pretty sure a joke flew over my head)

[open moat]

help

[pallid cave]

can someone explain how the +2 came in x,y

it was a -1 but howd it become +2

[austere star]

Can anyone help me? I have school in 10 minutes and I haven’t done my homework

[surreal meadow]

sure lemme just stop time

[wary stream]

10 minutes is not enough time to finish a homework assignment

[austere star]

It’s like 5 questions

[wary stream]

Unless it's a 1 question hw

[placid zinc]

That's like 2 minutes per question!

[pallid cave]

could anyone explain

[austere star]

can anyone help me please

[coral pagoda]

If it's a 1 question hw assignment, it'll probably take more than 10 minutes to solve :p

[wary stream]

Like I said, if you don't understand the concept well enough, 10 minutes is not enough time to do 5 questions

[austere star]

I mean 10 minutes until I get in the car

I’ll do it on the way there

[coral pagoda]

It is also not our job to just give you the answers.

[austere star]

not the answers

[wary stream]

And like 5 pieces of paper

[austere star]

I said I need help with homework

[pallid cave]

do i just go to another channel then...?

[austere star]

is anyone willing to help me or not

[coral pagoda]

Probably a good call rum rum

Questions-0 is almost always active

[austere star]

?

Please

[coral pagoda]

Now you're getting impatient. What do you need help with?

[wary stream]

Not sure if you saw this image before, that's pinned

[coral pagoda]

Lol, I feel that :p

[subtle nebula]

am i missing something here or the answer is really 180

ok nvm sorry

i misunderstood

[austere star]

it’s literally a number line.

[coral pagoda]

No, it definitely isn't

[subtle nebula]

yup i thought its asking for the sum of all interior angles lol

[coral pagoda]

That's not a very interesting question :p

[austere star]

can you?

[coral pagoda]

It is hard to help if you do not actually tell us what you need help with

[wary stream]

Post the problem and someone will come and help

[sick torrent]

Can someone help me in question-2

Plz

[next hatch]

ive tried to substitute different values of k and do the ratio test

am currently working through k=3

but im not sure how to properly determine it

[coral pagoda]

Lol, that's a terrible plan. However, ratio test is a good idea

[next hatch]

channel's being used bro

[austere star]

😐

[coral pagoda]

Apply the ratio test for the variable k. In order for it to converge, that ratio needs to be less than 1.

[next hatch]

ohhh

OHHH

[wary stream]

That person was here before you

[next hatch]

they didn't post the question

snoozed losed

[coral pagoda]

So find the values of k that make it less than 1

[wanton beacon]

2. <

[next hatch]

rightttttt gotcha

[coral pagoda]

Multiple people can be helped

[austere star]

bro what

[wary stream]

Don't give answers

[next hatch]

so essentially just do ratio test and find k

[wanton beacon]

Oh ok

Sery

[alpine sable]

double check 2

[austere star]

Can you help

I have 45m

[open moat]

Sam purchases 10 tickets in total. Buisness class costs $1200/ticket, ecnomoy class costs $700/ticket. Since Sam purchases a lot the travel agent gives him a discount Sam pays 10% off for buisness class and 60% off for economy class. If hr pays 31% less that the price, wuat 9s the total number of tickets he buys for economy class?

help

[next hatch]

god damn im never posting a question in #help-0 again lmao this is a mess

[wary stream]

True but it's prefer to help one person at a time because helper multiple at once can get super confising

[coral pagoda]

By this I mean solve the inequality
$\frac{a_{n+1}}{a_n}<1$, where $a_n$ is the nth term in your sequence.

[ocean seal]

dackid

[alpine sable]

if you would have tried to have done the HW, you would have been done with it by now my young friend

[next hatch]

yes

[austere star]

will you help me

[sick torrent]

Can someone please help me in #help-2

[wary stream]

No

[alpine sable]

How do I calculate #2?

[austere star]

ok

[next hatch]

too easy ill try this and lyk

[austere star]

can someone help

[wanton beacon]

Yes @austere star

[next hatch]

bro stop spamming

[wanton beacon]

So for number 1

0.1 is greater since there are less 0s

[austere star]

never did?

[wanton beacon]

For number 2

[coral pagoda]

That's what I like to hear!

[wanton beacon]

0.07 is larger

[austere star]

It’s a decimal number line

[open moat]

help

help

help

[wanton beacon]

Oh I see

[wary stream]

I think they wanted help with 11 - 15

[open moat]

help

[wanton beacon]

Ohhh

Ok

[open moat]

help Sam purchases 10 tickets in total. Buisness class costs $1200/ticket, ecnomoy class costs $700/ticket. Since Sam purchases a lot the travel agent gives him a discount Sam pays 10% off for buisness class and 60% off for economy class. If hr pays 31% less that the price, wuat 9s the total number of tickets he buys for economy class?

[wary stream]

No

[open moat]

y

[next hatch]

#❓how-to-get-help

[open moat]

Sam purchases 10 tickets in total. Buisness class costs $1200/ticket, ecnomoy class costs $700/ticket. Since Sam purchases a lot the travel agent gives him a discount Sam pays 10% off for buisness class and 60% off for economy class. If hr pays 31% less that the price, wuat 9s the total number of tickets he buys for economy class?

ok

[wanton beacon]

So for 11 you could do 6 1/2 for example

Just draw out your vertical number line

[next hatch]

find a channel that's not being used bro

[open moat]

k

[wary stream]

Because you keep spamming, trying to get people's attention

[alpine sable]

i want attention

[austere star]

I think 11 is 1/6 2/6 3/6 4/6 5/6 6/6 7/6?

[wanton beacon]

Well no

Because they aren’t mixed numbers

So

U have to include the 6

Then yes

[austere star]

Oh

so

[alpine sable]

think of the whole numbers

[wanton beacon]

So 6 1/6, 6 2/6, etc…

[austere star]

6 1/6?

ohhhhhh

[austere star]

so all of them are mixed numbers right

[wanton beacon]

Right

[austere star]

so until 7 the mixed number is 6

[wanton beacon]

Exactly

[austere star]

alright let me write it down rq

[wanton beacon]

Alright

[sick torrent]

Is this correct?

And I’m not sure how to do the bottom part with variables

[spiral aspen]

Bro my math is so boring. I’m a sophomore. I just wanna get to that stuff

Calc 😍

[alpine sable]

you can start reading it

[austere star]

done

[wanton beacon]

Have you written 6 1/6, 6 2/6, 6 3/6, 6 4/6, 6 5/6 ?

[austere star]

yes

[wanton beacon]

Great

[spiral aspen]

I’ve tried watching YouTube videos but it doesn’t get me very far. What do you recommend?

Khan academy maybe?

[alpine sable]

James Stewart Calculus 8th edition

[spiral aspen]

I need a sort of progression so I’m not jumping to random places

[austere star]

positive fractions less than 1, with an interval of 1/12 between each pair of fractions

[spiral aspen]

Alright thanks

James Stewart Calculus 8th edition

[alpine sable]

only watch the videos if the concept is not so clear or you can ask here 🙂

[spiral aspen]

👍

[wanton beacon]

So, 1/8, 2,8, 3/8, 4/8, 5/8, 6/8, and 7/8

[spiral aspen]

Thanks bro I appreciate it

[austere star]

isn’t it 1/12

[wanton beacon]

Sorry, yes

And so forth

[austere star]

1/12 etc?

[wanton beacon]

1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 11/12

Yep

[austere star]

alright

[spiral aspen]

I heard some of the FRQ’s for BC were nutty. Something about a yo-yo or something?

Oh

What’s the major jump between AB and BC?

Yea

Correct verbiage

[sick torrent]

Is this right?

[spiral aspen]

Gotcha

I’m doing piecewise functions right now I’m bored out of my mind

I’m in Algebra 2/Pre-Calc

[sick torrent]

I have no clue

Why

[austere star]

Next one

[wanton beacon]

Ok so you just increase 0.4

[austere star]

Decimals between 11.4 and 15.0, with an interval of 0.4 between each pair of decimals

[sick torrent]

Ohhhhh

[wanton beacon]

11.8, 12. 2, all the way up until 14.6

[austere star]

don’t really understand still

[sick torrent]

Right that makes sense so then x->-1 would be DNE

[austere star]

I don’t understand

[sick torrent]

Also the last part with the variable is confusing I don’t understand how to do that question

Yes

[wanton beacon]

Ok so 11.8, 12.2, 12.6, 13.2, 13.6, 14.2, 14.6

• 0.4 basically

[austere star]

oh

[sick torrent]

How do you find that?

[austere star]

am I supposed to start with 11

[wanton beacon]

With 11.8

[austere star]

okay

[wanton beacon]

Because you are doing 11.4 and increasing by 0.4 interval

[sick torrent]

Oh

[austere star]

until how much

until 15 right

[wanton beacon]

14.6

Right but you wouldn’t include 15

[austere star]

ah okay

[wanton beacon]

Because you need to write up until 15

15 not included

And 0.4 less than 15 would be 14.6

[sick torrent]

That’s what help formulas said

Don’t mind my Vaseline in the corner 💀

[wanton beacon]

14. Is very similar to 13.

Except this time you are increasing by an interval of 0.3

[austere star]

Decimals greater than 7.2 but less than 9.6 Use an interval of 0.3 between each pair of decimals

[wanton beacon]

Right so

I almost have to go @austere star

[austere star]

last question?

Or no

[wanton beacon]

Sure

So

[austere star]

alright

[sick torrent]

My friend told me the right answers

Yes that makes sense

Yea

Thank you so much for your help

[austere star]

Can you help

14-15

can you?

I need to go in like 20

7.2 and add 0.3 until 9.6?

so 7.5, 7.8 etc?

[alpine sable]

Vector calculus and guess what...

more Set notation lol

[austere star]

oh

nope

0 is a

origin

oh

what about number 15

What do I do in it

I’ll just leave it

[coral pagoda]

Good lord. I get it now

[austere star]

Thanks for the help @violet ore

[alpine sable]

Anyone know what this limit means?? The definition is "$F(x)$ is right-continuous, or, for every number $x_0$, $\lim_{x\downarrow{x_0}}F(x)=F(x_0)$"

[ocean seal]

jswatj

[alpine sable]

Yeah... idek

its a down arrow

No

and the author wrote a sideways arrow for the typical $\lim{x\rightarrow{-\infty}}$

[ocean seal]

jswatj

[mortal void]

HEY

bye

[old whale]

please help me for number 2, the problem of finding sets

[alpine sable]

Ohh i see

thank you

[mortal void]

unlucky me i thought its still going so didnt asked

[alpine sable]

does it imply from the right side?

[near pier]

Hey guys can someone help me?

[pallid cave]

its almost been an hour since i sent my question in #help-5 could someone please help 😐

[vital oak]

What's gradient in physics

Graph

[near pier]

This is my qs if someone could be kind to help me out

[kindred warren]

since they are like terms, you just add the numbers infront of the pronumerals

[near pier]

Oh okay thx

[vital oak]

.

[pallid cave]

@vital oakits gonna take an hour go have a coffee and a snack while u wait

[near pier]

Could u solve it and send pls

[kindred warren]

Currently taking a shit

[near pier]

Oh okay later ig lol

[kindred warren]

Lol

[alpine sable]

How do I solve 6,7, and 8 with this table

How do I solve 6,7, and 8 with this table?

<@&286206848099549185>

Hehehehe please help me🥺🥰

[gleaming zodiac]

69

just go with it

answer = 69

[near pier]

Can someone solve this and send pls

[woven echo]

have u considered making the text smaller and harder to read

[near pier]

<@&286206848099549185>

ig

[gleaming zodiac]

i think he already did that lol

[woven echo]

lol

[alpine sable]

Question 0 channel is mine find your own 😜 🥰

[gleaming zodiac]

xD

[flat vale]

ig my ass read the rules

[minor willow]

is this can be true that a 3d differentiable curve can have infinitely many tangents at a particular point??

[alpine sable]

Yes Kenyans

[graceful trench]

it is okay to ask algebra question here

[alpine sable]

Yes Go to like channel 5 or something tho pls🥰

[graceful trench]

thanks Robby

[alpine sable]

hey guys, I had a trouble understanding the location of Horizontal asymptotes.....I mean, I know the cases but I can't find why they are true......any help for that?

[edgy sand]

you doont know what a horizontal asymptote is? @alpine sable

[alpine sable]

no I do know what they are

but I am having trouble locating horizontal asymptotes

[edgy sand]

can you explain what a horizontal asymptote is to me then?

[alpine sable]

uhh sure

[alpine sable]

Just google it

So, basically, in a rational function suppose f(x) = x+1/x^2+1....so if x approaches infinity......y will approach a value b.....same we can do for negative infinity.......so we will observe that the value b would be the horizontal asymptote.....

[edgy sand]

im teaching him @alpine sable

i obv know what it is

[alpine sable]

really bad definition but I have not contemplated on it

[edgy sand]

okay

so you know the defintion of it

but youo cant show it to me on a graph right?

[alpine sable]

I can if you give me a graph

basically what ure saying is that it tends to the x axis?

but never reaches it

[edgy sand]

im confused, you said you dont know how to locate it

but now youre saying you can show me on a graph

[alpine sable]

but if you give me a function I cant tell you the asymptote without drawing a graph

[flat vale]

bruh @edgy sand just tell him how to get hori asymtope

[alpine sable]

oh I think he's saying he can see the asymptote but if he gets a question like "what is the horizontal assymptote" he doesn't k ow what to do

[flat vale]

just do lim x-> inf

and if the output is not inf than it's a hori asym

[alpine sable]

yes

[edgy sand]

theres 2 ways i know of, oone is graphin the other is algebraically

aka calculus

[alpine sable]

I dont know algebraically

[flat vale]

idk y ur dragging this convo lol

[edgy sand]

scroll up and read or help no one is dragging anything

[alpine sable]

I am studying this in college algebra........we've not been introduced to limits........

Nice spamming this chat over a simple question

[flat vale]

bruh ikr

[edgy sand]

what are yoou on wtf?

[alpine sable]

@edgy sand hes saying he can see the asymptote but if a question asks him for it, he doesn't know what value or number to write

[edgy sand]

yes i know taht now

[alpine sable]

Just do it in dms @edgy sand

[edgy sand]

no

this is the channel for help

[alpine sable]

uhh....

[edgy sand]

im noot gonna give him the answers straight up

ill help him get to it though

idc if it requires me typing a lot

[flat vale]

just think of it as if x reaches inf and y approaches to a certain value, then it's a asymptote

[alpine sable]

could u also say tho that x tends to 0

since it gets closer to 0 but never reaches it

[flat vale]

asymtote is simply a behaviour of a function

[flat vale]

??

[alpine sable]

h->0

on the x axis

[flat vale]

ehhh no?

[alpine sable]

oh wait nah

I'm thinking of something else

nvm

[edgy sand]

just make sure you also look at -inf

[jovial edge]

Hi

How do I find this? Is it just based on guessing?

Since I get that 178.5 is the 97th value

[alpine sable]

hey guys, sorry I was afk

[jovial edge]

So the 100th and 101th value must be larger than 178.5

and thus I can eliminate 177.5 and 178.5

[opal wing]

So I have a simple question that I missed somewhere in my math career

But how did they get to this number? I know they just added it but I mean, how did they know to choose this number?

[jagged imp]

Its the coefficent of the x term divided by 2 and squared

so (3/2)^2

[vital oak]

1hr is up answer this question anyone

[vital oak]

https://tenor.com/view/ted-teddy-bear-say-that-again-say-that-one-more-time-seth-macfarlane-gif-15957709

[jagged imp]

uh in general gradient is the slope of a graph

[opal wing]

Completing the square if I remember correcrtly?

[jagged imp]

it could also mean the slope of a plane

[jagged imp]

yeah

[opal wing]

That is right, okay thank you

[rocky cape]

Hey does anyone know how to do this ?

I tried differentiating, but you can't differentiate different parts of one equation.

[vital oak]

thanks

[alpine sable]

Is x^(2/3) = cuberoot(x) * 2

?

Since ^1/3 equals cuberoot

Oh

Would x^(3/4) = fourth root of x^3?

And so on…?

[crystal mirage]

hi again

how this works

[alpine nacelle]

if a, b and c are consecutive it means that a = b-1

c = b+1

so 3b = 0 and b = 0

you need a = -1, b = 0, c = 1

[craggy elbow]

if anyone would kindly explain me how to do only the (iii) one. if i find out how to do it i may be able to do the next one too right?

[alpine sable]

I feel like this problem is very similiar, I’ve gotten it down to x^(3/2) = 5

How would I solve for x?

Is that another identity?

[alpine nacelle]

ceil(x) = floor(x)+1 if x is not an integer

[craggy elbow]

⌈x⌉ = ⌊x⌋ + 1?

[alpine nacelle]

yes

[craggy elbow]

what does that mean tho

[alpine nacelle]

you can replace ceil

[craggy elbow]

we were just exaplined what floor and ceil is

[alpine nacelle]

floor(x) = the greatest integer n such that n < x

ceil is the smaller > x

[craggy elbow]

yea

⌈x⌉ is like if ⌈2.1⌉ then answer is 3 right?

[alpine nacelle]

yes

[alpine sable]

I am slow today sorry lol, but thanks.

[craggy elbow]

i just dont get it 😞

[alpine nacelle]

floor(2.8) = 2

[craggy elbow]

yea thats obv

[alpine nacelle]

so you need more help for the actual problem ?

[craggy elbow]

i dont know what do i have to do in the question

[craggy elbow]

i get these things i have the notes

there can be so many solutions

like if you take x = 1

or 2

or any integer

the answer will be correct

[alpine nacelle]

indeed

[craggy elbow]

infinite solutions?

[alpine nacelle]

indeed, but you need to find them all

so you need to figure out if there are non integers solutions

[craggy elbow]

damn is that possible

[alpine nacelle]

maybe, who knows before looking for it :p

(there are non integers sol)

[craggy elbow]

so i have to find out non integers so i have to try all the non integers from - infinity to +infinity

[alpine nacelle]

sqrt(2) is a sol

for example

can you guess why ?

[craggy elbow]

sqr just gets cancelled

sorry the sqrt

gets cancelled

[alpine nacelle]

there is a pattern that is even more interesting

I let you think about it

[craggy elbow]

all sqrt just you know fit the solution

[alpine nacelle]

nope, x = sqrt(5) won't be a solution

[craggy elbow]

how?

(5)^1/2 x 5^(1/2) = (5^(1/2))^2

[alpine nacelle]

floor(sqrt(5)) = 2 but the ceil is 3

and their product is 6

not 5

[craggy elbow]

ahhhhh i get it now