help-0

[indigo jetty]

Hmm, actually there's another way to do it

[vagrant flax]

ahh hmm

[indigo jetty]

notice you are given A and B, 2 points on the circle

[vagrant flax]

yep

[indigo jetty]

You are told the centre of the circle is on the x-axis

[vagrant flax]

i can find the equation of the line

[indigo jetty]

so one thing for sure is

[vagrant flax]

yes therefore x is something while y=0 right?

[indigo jetty]

the coordinates of the centre is (a, 0)

yup

[vagrant flax]

yess

[indigo jetty]

so what can you tell about the lines that connect A to the centre and B to the centre?

should be doable from there

[vagrant flax]

Ohh i can find the gradient of A and centre and gradient of B and centre

[indigo jetty]

no need

[alpine nacelle]

C is at the same distance from A than from B. It is true for the midpoint of AB too

What is the line that goes through both ?

[vagrant flax]

Line l?

I guess

[alpine nacelle]

l doesn't go through the center of the circle

Perpendicular bisector of AB does

[vagrant flax]

Yep its besically intersecting circle C

[vagrant flax]

Ahhhh okayy

[alpine nacelle]

Your perpendicular bisector intersects the x-axis at the center of the circle

[vagrant flax]

Ohhh

let me try work it out

[tacit flax]

hi can anyone help me solve this one https://cdn.discordapp.com/attachments/509460208737845248/897272369893220372/unknown.png

[indigo jetty]

@vagrant flax the other method which i was talking about is to realise that the two line segments connecting A to the centre and B to the centre are the radii, so they have the same length

[alpine nacelle]

Yup, works too, but they asked him to find midpoint of AB, so I guess he learned in class that the perpendicular bisector is the line with points at equal distance

So he could find this way by thinking a bit

[vagrant flax]

Ohhhhh i get you, you use them to find X, distance formula is needed for that!

[vagrant flax]

Melo thankyou so much, i got x=9

[indigo jetty]

yup, both methods work

[vagrant flax]

Ken G thankyou soo much too!!

[indigo jetty]

i just listed the one that came to my mind first lol

[vagrant flax]

😂

Yall are legends

got maths test in 2 days time !

[quartz osprey]

i have no idea how this is wrong

[alpine nacelle]

-(n-3) = -n+3

You got tricked by the sign

the exponent of x should be -n-3, so n+3 if you put it in the denominator

[vagrant flax]

the error is in n-3

[vagrant flax]

Yep!

[quartz osprey]

n-3?

ohhh

let me read up

sec

[vagrant flax]

yep its n-3

[quartz osprey]

uhh i might need to redo it

i dont really understand the problem through reading lmao

[vagrant flax]

i can show you working out if you want

XD

[quartz osprey]

sure if youre willing to lol

[vagrant flax]

Okay just a second

[quartz osprey]

lemme flip it thank you

[analog vortex]

Hello, I need a bit of help in here

$$lim_{x\to\infty}\frac{(7-x)(3+3x)}{(3-2x)(11+7x)} = lim_{x\to\infty}\frac{21+18x-3x^2}{22-x-11x^2}$$

this is the furthest I’ve went - I don’t think it’s possible for me to factorize back in a different form or use the polynomial (?) technique and find 3/11. I know I can use l’hospitals easily, however I wasn’t taught that in my course yet so I am looking at alternative ways to find the answer. Can anyone drop some hints as to what I can possibly do next?

[lime tangle]

hmmmm

table of values?

@analog vortex

[glass lichen]

divide through by x^2

[lime tangle]

or that

[ocean seal]

rolla

[glass lichen]

$\lim_{x\to\infty}\frac{21x^{-2}+18x^{-1}-3}{22x^{-2}-x^{-1}-11}$

[ocean seal]

Mosh

[glass lichen]

leaving 3/11

[analog vortex]

that's what I tried to do... but for some reason it wasn't accepted as an answer

[glass lichen]

oh cause you messed up expanding

$(3-2x)(11+7x)=33+21x-22x-14x^2$

[ocean seal]

Mosh

[analog vortex]

oh hahaha alright thank you

[glass lichen]

so yeah, double check your expanding, then it's just read off the leading co-efficients

in general $\lim_{x\to\infty}\frac{f(x)}{g(x)}$ where f and g are both degree n, the limit is the ratio of leading co-efficients

[ocean seal]

Mosh

[glass lichen]

proof is similar to the trick of dividing by x^2, just instead use x^(degree of f and g)

[small hatch]

for what values of x is f(x) < 0?

[alpine sable]

8??/

can i get help with b

not a

a is 30 and i know

[flint badger]

What does the "f(x) < 0" part mean

Can you try to figure that out first?

[small hatch]

what value of y is less than 0

[flint badger]

Close, the question is basically saying: "what values of x make the result (y) < 0

So at what point in the graph is y < 0?

[small hatch]

-7, -4, -2, 10

would 0 count?

[flint badger]

Ok @small hatch I assume its asking for an interval

So x = -7 would give a y result < 0, yes

but

There's also infinitely many others

So you actually have to give me a range

[small hatch]

the teacher put this

for one of the previous ones

idk if it plays a part

[flint badger]

Oh really?

Umm

[small hatch]

yeah. i dont know what it means though

there is no explanation to it

[flint badger]

Oh wait there's dots on the graph right?

Like points plotted along the curve?

[small hatch]

yea

the ones i listed have dots

[flint badger]

Ok I guess thats how they want you to do it

So then yes that's right

Just make sure to put x = -7, -4, -2, 10

[small hatch]

okay one sec

[flint badger]

Think about the question you asked

Is 0 < 0

?

[small hatch]

no

its equal to

[flint badger]

Exactly

so you wouldn't include that

[small hatch]

if it was 0 <= 0 it would be included

[flint badger]

Yea

[small hatch]

alright

[flint badger]

Hmm

weird how your teacher made it like that

[small hatch]

so then when it asks for greather than

[flint badger]

Normally teachers would make you give a range

[small hatch]

i make the points above the 0?

[flint badger]

So like

Yea

[small hatch]

this is another problem she did

[flint badger]

Oh yeah thats just plotting the graph of a parabola

Do you have any questions for that?

[small hatch]

no thats simple really

[flint badger]

I don't know why she makes you give individual points though

[small hatch]

i have a question for a diff one just give me a bit to get to it

[flint badger]

because there's technically infinitely many points

when f(x) < 0

It's the RANGE that matters

Like from (-8, 0), f(x) < 0

[small hatch]

yeah she teaches weirdly, not sure why

[flint badger]

The "(" and ")" notation means it's not included

[small hatch]

okay how about this:

If f(-5)=f(b) and -5 ≠ b, what is the value of b

@flint badger if you're still available

[flint badger]

I'm very confused

Man maybe I'm just slow today

[small hatch]

yeahhhh same.... 😂

[flint badger]

I'm not getting this

Is there anymore information provided?

I really don't get what they're asking here LMAO

[small hatch]

lmfao nope. i'll send you the whole page

[flint badger]

OHH

[loud sentinel]

Hey guys where the negative go

[flint badger]

I completely forgot you were using the graph before

also I believe you put f(0) and not f(b)

[small hatch]

oh yeah oops 💀

[flint badger]

Ok basically what it's saying is that

Well first evaluate what f(-5) actually is

[thorn sundial]

do you guys know this?

[small hatch]

okay

[flint badger]

Because you can evaluate that right

f(-5) is basically just saying: "If I plug in a value of -5 for x in this function, what y value do I get?"

[small hatch]

correct

[flint badger]

So what is f(-5)

[small hatch]

0?

[flint badger]

Not quite

[small hatch]

it doesnt have a point on the graph

[flint badger]

If you put -5 for x into the graph

What corresponding y value would you get

Imagine it's (-5, y)

Try to figure out what y is

[small hatch]

it looks like -4?

[flint badger]

Yeah exactly

The point would be (-5, -4)

[small hatch]

how though?

[flint badger]

So now you know what f(-5) is right

[small hatch]

the point isnt marked

[flint badger]

It doesn't have to be

Don't let the other question throw you off

[small hatch]

okay

[flint badger]

In the other question the points did matter

Because she was asking which points were below 0

And she was asking for the x value of those points lol

So you know f(-5) = -4

[small hatch]

okay understood

yes

[flint badger]

so if f(-5) = -4, and f(-5) = f(b)

What is f(b)?

[woven river]

egg dog when you get a chance could you help me?

[flint badger]

Yeah sure

[woven river]

okay i just need help evaluating a few questions

[small hatch]

f(b) = -4

[woven river]

when you’re finished

[flint badger]

Yeah so what other point in the graph do you get -4

And I shouldnt say point

[small hatch]

-4?

[flint badger]

But for what other x value (in this case it's b) do you get -4

Exactly

[small hatch]

so the value of b is -4

[flint badger]

Both f(-4) and f(-5) give you -4

Correct

Does it make sense?

[small hatch]

sort of

[flint badger]

What are you confused about

[small hatch]

let me check

[flint badger]

b and x are just the values you plug into the function

[small hatch]

again

[flint badger]

f(x) or f(b) is the corresponding y value

I can help you @woven river

[woven river]

great okay

[flint badger]

,rotate

[woven river]

.rotate

[woven river]

whooos

[flint badger]

It's ok

Alright so what do you think g(3) means in this sense?

[woven river]

um is ir okay if we do a few

[flint badger]

Yeah

[woven river]

i think i have 2 other questions okay

[flint badger]

Yeah we'll get to those, so just think about what g(3) means

[woven river]

(3) would go where x is correct?

[flint badger]

Yes so

every function has a name ok,

this one is called g

and it takes in an input, x

[woven river]

ok

[flint badger]

so the function would be written as g(x)

= whatever

[woven river]

yup

[flint badger]

So it says if I put in an input of 3, what will I get

In other words, if I set x = 3, what do I get

So yes, you're replacing x with 3

[woven river]

alright yeah i understand so far

[flint badger]

So just plug in 3 for x, and then evaluate it

[woven river]

would i keep the parentheses

?

[flint badger]

wdym

$g\left(3\right)=2\sqrt{4\left(2\right)-3}+3$

Should look something like this

Oops not 2, I meant 3

bruh

wait

[woven river]

lol

[flint badger]

$g\left(3\right)=2\sqrt{4\left(3\right)-3}+3$

[ocean seal]

eggdog

[flint badger]

You're still evaluating g(3) right

[woven river]

yeah that’s what i was staying to say

[flint badger]

You're not done

[woven river]

okay

[flint badger]

And whenever you plug in a value for a variable

You should put parantheses

[dusk tiger]

Egg how are you still going at this 😂

[woven river]

he’s been doing this for a while

?

[flint badger]

I take breaks lol

Of course I do, I have my own work

[woven river]

egg are you still in hs?

[chilly spruce]

Which equation represents the line that passes through the point (1,5) and has a slope of −2?

[flint badger]

Yeah

[dusk tiger]

Yeah he helped me at 10 this morning and it’s now 8

[flint badger]

@chilly spruce Hold on this channel is occupied

Try asking it somewhere else, but dont spam every channel

[chilly spruce]

ok sorry

[flint badger]

Its ok

@woven river Let me know when you're done evaluating it

[woven river]

basically plugging in 3 right?

[flint badger]

Yeah

[woven river]

yup done

[flint badger]

Now work it out

You have everything you need to work it out

[woven river]

okay should i come back with my answer?

[flint badger]

Yeah

[woven river]

alright

[small hatch]

hey eggdog

there is another similar question i just want to make sure im right

[flint badger]

Sure

[small hatch]

b = 3.5 ?

[woven river]

i’m sorry egg what would 4(3) be?

[flint badger]

its the same as 4(3)

4 * 3

[woven river]

oh okay

[dusk tiger]

Wouldn’t it just be 0 since it’s halfway

[tardy plank]

how do I find where this is continuous?

[flint badger]

So you know g(-6) is 2 right

[woven river]

would it be 6?

oh i’m sorry

[buoyant edge]

@tardy plank sin is continuous everywhere,

[small hatch]

isnt it 3

[flint badger]

No that would be

g(-8)

Wouldn't it

At -6, y = 2

So where else is y = 2

or in this case, g(b)

[flint badger]

how did you get 6?

Could you take a picture of your work

[tardy plank]

@buoyant edge how would you use algebra to prove that in this case though so I can figure out other similar problems

[woven river]

well i do have a question

what is the bar on top of the numbers called again

[flint badger]

$\sqrt{ }$

[ocean seal]

eggdog

[flint badger]

you mean this?

[woven river]

yeah

[flint badger]

That is a square root

[woven river]

okay i forgot

[flint badger]

@woven river I would suggest first knowing what these operations are before tackling these problems

[woven river]

let me redo this

[small hatch]

how would y = 2 at -6? wouldnt it be at -5?

[flint badger]

Do you know what a square root means?

[buoyant edge]

@tardy plank look up proof that sin is continuous; you need epsilon-delta definition for that

[woven river]

yeah i do

[flint badger]

oh im sorry

I misread the graph

smh im sorry

you're absolutely right

[small hatch]

youre fine

haha

[flint badger]

At what other x is y = 2

ok good

[small hatch]

none

wait do you mean 3 again

[flint badger]

no I would say at g(4) its pretty close to 2

OH MY GOD

im actually stupid

ok you know what

[small hatch]

what happened 😂

[flint badger]

3.5 would be a good guess yeah

I don't know man I thought it was still 2

[small hatch]

haha

[flint badger]

g(3.5) would be close to 3 yes

[sick torrent]

I will pay someone 50 cents to do my homework for me

Take it or leave it

[small hatch]

okay, thank you!

[flint badger]

1.5 would also work @small hatch

[maiden saffron]

HELP

Emerge by

[flint badger]

oh as well as -9, they'res a bunch of points before it

that still give you an output of 3

[small hatch]

oh

i see

it asks for one tho

so any works

[flint badger]

An exact one would be best

Meaning an integer

[woven river]

egg dog would it be 4 square root 3

like the operation

[small hatch]

-9 has a point, does it matter?

[flint badger]

I guess you should use that then

As you did for the f(x) < 0

[flint badger]

How'd you get it

[small hatch]

okay

[flint badger]

$g\left(3\right)=2\sqrt{4\left(3\right)-3}+3$

[ocean seal]

eggdog

[flint badger]

If you evaluate this properly, you should get g(3) = 9

[small hatch]

thank you so much eggdog! great pfp btw

[flint badger]

Which means that if we were to graph this, an x value of 3 would give us 9 as the output

[flint badger]

np

[small hatch]

what grade r u in btw? you said youre still in hs

[flint badger]

Im a sophomore

[small hatch]

oh damn.. what math classes u taking!?

[flint badger]

Calculus II atm

[small hatch]

wtf youre actually crazy smart

[flint badger]

Nah nah lmao

[small hatch]

yesss whaat... i take pre calc next year (junior year)

[flint badger]

@woven river Sorry I have to leave right now

[woven river]

this is how

[flint badger]

You forgot about the -3 + 3 part

[small hatch]

cya!

[flint badger]

4(3) = 4 * 3 but there's still the -3 inside of the square root and the +3 on the outside

[flint badger]

Bye

[woven river]

oh shoot

[flint badger]

See if someone else can help you, I have to eat dinner

[woven river]

and cya

okay

[flint badger]

Bye :/

[buoyant kayak]

how did you go from 4(3)-3 to 4*3 under the root?

[woven river]

isn’t 4(3) times

like 4 time 3 = 12

-3 9

+3 12

right

@buoyant kayak

[buoyant kayak]

the +3 is on the outside of the root, right?

[woven river]

yes

i’m sorry what does that mean

[buoyant kayak]

well you can't just bring a number from outside the root inside the root

[woven river]

wait would i bring that down

so 12 + 3

[buoyant kayak]

?

where are you getting 12

[woven river]

i don’t know anymore then

then it would be 9

i’m sorry right

[buoyant kayak]

yes, 9 is under the square root

and what is the square root of 9

[woven river]

3

[buoyant kayak]

so now you have 2(3)+3, right?

[woven river]

yes

[buoyant kayak]

and what is that?

[woven river]

9

[buoyant kayak]

right

[woven river]

is that all

my answer is 9?

[buoyant kayak]

i'm not sure what your question is

[woven river]

okay let me post

[buoyant kayak]

alrighty

[woven river]

,rotate

[buoyant kayak]

ah, then yes

your answer is 9

[woven river]

oh okay could we do my other question?

i just have 2 more

[buoyant kayak]

sure

[woven river]

let me get them

[radiant bronze]

At which points tangent line to f(x) = 1/(x2 – 25) is horizontal and at which points is it vertical?

[buoyant kayak]

so plug in 1 for x

evaluate the root

[woven river]

yup got that

[buoyant kayak]

then order of operations

what did you get?

[woven river]

let me do the math lol sorry

would it be 1

[buoyant kayak]

the root?

[woven river]

yes

[buoyant kayak]

yes

and what is the square root of 1?

[woven river]

1

lol

[buoyant kayak]

right

so now you have 2(1)+3

and what is that?

[woven river]

4

im sorry 5

[buoyant kayak]

right

[woven river]

makes so much sense

lost one um

[buoyant kayak]

so what's 3(-1)?

[woven river]

2

[buoyant kayak]

?

$3\times -1$

[ocean seal]

a disappointing son

[woven river]

oh jeez

-3

[buoyant kayak]

right

and now $4\times (-1)^2$

[ocean seal]

a disappointing son

[woven river]

sorry internet uh 16?

[buoyant kayak]

remember your order of operations

parenthesis, exponents, multiplication and division, addition and subtraction

which one comes up first?

[woven river]

ok i’m

multiplication

[buoyant kayak]

i meant in the order that i posted

[woven river]

parenthesis

[buoyant kayak]

right

and do you see anything that has to be done in the parenthesis?

[woven river]

yeah

[buoyant kayak]

does the -1 need to be changed?

[woven river]

yes

[buoyant kayak]

anything happening to that in the parenthesis?

are you sure?

it's just the -1 in parenthesis there

nothing else is with it

[woven river]

then no

[buoyant kayak]

right

now move on to the next one

which is...?

[woven river]

exponents

[buoyant kayak]

see any exponents?

[woven river]

yes

[buoyant kayak]

so can you evaluate that?

(-1)^2?

[woven river]

yes

[buoyant kayak]

what is it?

[woven river]

jeez

-1?

[buoyant kayak]

we can rewrite $(-1)^2$ as $(-1)(-1)$

[ocean seal]

a disappointing son

[woven river]

yup

[buoyant kayak]

what happens when we multiply a negative by a negative?

[woven river]

positive

[buoyant kayak]

so what is (-1)^2?

[woven river]

1

[buoyant kayak]

right

now multiply it by 4

[flint badger]

This is crazy @buoyant kayak now that I just realized what your pfp was I cant unsee it

[woven river]

4

[buoyant kayak]

correct, so now you have -3+4-5

[flint badger]

I dont know how but i didnt notice it at first, anyways sorry to interrupt

[buoyant kayak]

now you can just add and subtract from left to right

egg i'm not sure what you mean lol

[woven river]

yeah

[buoyant kayak]

my pfp is my friend from high school

[flint badger]

I didnt notice it was a face rotated 90 degrees counter clockwise

[woven river]

-4

[buoyant kayak]

oh

lol

[buoyant kayak]

right 👍

[mossy stirrup]

how do i do this with steps?

[placid zinc]

That means for every billion parts you take, 8 of them are lead

[woven river]

@buoyant kayak i have one more

if that’s fine

[buoyant kayak]

sure

[woven river]

one moment

it’s find the intersection between the filling functions algebraically

a tad blurry

sorry

[buoyant kayak]

,rotate

[woven river]

i do not the POI

Im just unsure how to find it algebraically

[buoyant kayak]

alright, so you want to know when these functions equal each other

[woven river]

ok

im sorry

was it my turn to talk or

[buoyant kayak]

yeah you're good

[woven river]

um was it when these functions equal one another

i’m lost on that

[mental hearth]

after he's done

so for ur problem replay

if you want to find the x where they intersect set them equal to eahc other

[buoyant kayak]

so if you want when these functions equal to each other, what do you reckon you should do?

[woven river]

find x

?

[mental hearth]

you would do -5x +2. = 2x -5 but you should undrstand why

then solve for x

[buoyant kayak]

best to not tell the answers

rather let them figure it out

[vestal aspen]

Hey

[mental hearth]

k

[woven river]

still lost

[vestal aspen]

Can someone help me

[mental hearth]

op im next for help when im done u can put question

[vestal aspen]

Ok

[mental hearth]

you'd call this systems of equation right

[woven river]

yeah

[mental hearth]

generally there are 3 solutions to it

infinite solutions
one solution
or no solution

can you guess when there would be infinite solutions

[woven river]

yeah

[mental hearth]

when

[woven river]

i take that back

my apologies

[mental hearth]

think about it

if you have two lines that intersect at every single point

there is only one way for that to happen

they'd have to be the same exact line

[woven river]

yeah i think i understand

but for this problem it’s only one solution

[mental hearth]

yea it is one solution

do you know when it'd be no solution

[woven river]

i don’t i’m sorry

[mental hearth]

nah ur good just trying to help

it would be when they have the same slope

do u understand why

like if you had 2x+7 and 2x - 3 and graphed it they would never intersect

[woven river]

oh

[mental hearth]

because from 7 and - 3 they would go up or down the same amount and never touch

[woven river]

i understand that

[mental hearth]

ok now we can go to the problem

so you'd set them equal to each other is the first step

reasoning behind it is

they are equal to each other at the place they intersect

[woven river]

yup

so would i have to find f

first

then plug that into g

sorry if all over the place

[mental hearth]

you'd find x

[woven river]

yes

[mental hearth]

f and g are two functions

[woven river]

i meant x im sorry

[mental hearth]

x is the same in both f and g when they intersect

so solve for x then plug it into either one for y and you have the location of where they intersect

[woven river]

could u run this down step by step

im so tried sorry

[mental hearth]

ur good

[woven river]

i’ve gotten through ap psych and remember i had alg 2

[mental hearth]

dang u cna do ap psych but not thisl ol

ur good

[woven river]

yeah i guess lmao

[mental hearth]

call ap psych ap quizlet

[woven river]

seriously tho

lmao

[vestal aspen]

can someone help

[mental hearth]

chill

ok so the first step is set them equal to each other

-5x +2. = 2x -5

[woven river]

alright i have it

[mental hearth]

what'd u get for x

[woven river]

one moment

[wanton beacon]

Very quick question, how can I explain that I know two ratios are equivalent?

[mental hearth]

if you simply both they are the same numerical value

ex 3/4 6/8 both simplify to 0.75

idk if thats satisfactory

[woven river]

okay um 1?

[mental hearth]

yea

and plug that into f or g

and you have the location of the intersection

ur done

[woven river]

1,-3?

[mental hearth]

ye

[woven river]

wow

that ez

well not really

thanks so much mam

man

[mental hearth]

np

[ivory gulch]

looks like you guys are finishing up, i dont want to interrupt so just lmk when you're done

[woven river]

we’re done

what math do u take?

[ivory gulch]

lol

nvm

its all good

[mental hearth]

calc ii

[woven river]

you’re senior?

[mental hearth]

nah college freshman

[woven river]

oh

[vestal aspen]

bro someone help me

[mental hearth]

i took bc but school doesnt take credit

so im retaking 2 but i forgot everything

[woven river]

yeah i have a kid in my class ima sophomore and he takes ap clad

calc

it’s nuts

like how the hell

[mental hearth]

at my school ppl took it freshman year 💀

but its a magnet so it makes sense

i took it junior

[woven river]

yeah i go school for law

i behind i guess

[vestal aspen]

👍

[mental hearth]

nah ur good

[woven river]

all my friends take pre clac

[mental hearth]

u can try to skip/catch up over the summer

[woven river]

but then i’m taking 3 aps so it’s killing me

[mental hearth]

op how hard is ur question

[woven river]

i def will

[gray reef]

Huh

[mental hearth]

bruh

you could do that in like a min

dont u just use f=ma

[vestal aspen]

Ik I just forgot

[mental hearth]

thats more of a physics thing

than math

[vestal aspen]

I forgot the formula

[mental hearth]

use f= ma

[vestal aspen]

Yeah it is physics

Thanks

[mental hearth]

F= MA is the most important physics formula bro

nah u gotta be taking physics 0

jk

physics is gonna get real later on

[vestal aspen]

This is my first year doing physics

[mental hearth]

what'd u get

[vestal aspen]

I’ll do it rn

21.78

[mental hearth]

ye u got it

if the mass is in kg its correct

[vestal aspen]

Alright

It is

[mental hearth]

ur good then

[dry echo]

Can someone help me?

[mental hearth]

how hard

[dry echo]

This is my work

Where am I going wrong? is my equation even correct?

[mental hearth]

we went from basic arithmetic and algebra to calc 😭

[dry echo]

RIP

[mental hearth]

i came here for calc help too cuz i havent done it in a min

[raw shard]

related rates problems are so hard lol

[mental hearth]

annoYing

[raw shard]

i can try to help

probably won’t be of much help though lol

anyways give me a minute

[dry echo]

Better than nothing man

ok thank u!

[atomic lodge]

Can anyone help me with question 20

I think it’s false

But I am not sure

[dry echo]

Try to graph it

[raw shard]

i don’t see anything wrong so idk

maybe go though it again and pay a lot of attention?

[mental hearth]

dang i forgot what its called

tangent line is horizontal when the function changes from up to down or down to up but its. abit more tehcnical

its been a min

prolly false though

i think you could have horizontal tangent lines with no x intercepts

[dry echo]

I think this is it?

so it is correct then

[raw shard]

@mental hearth sounds right

[dry echo]

is this about my problem?

[raw shard]

yes

[dry echo]

oh I've done it 3 times, I get the same answer and the website says it's wrong :(

[raw shard]

go through it again and pay a lot of attention maybe

i’m not very good at these either

[dry echo]

oof

thank you for your time though

[raw shard]

no problem

hopefully you get an answer eventually

[mental hearth]

its vertex form ibut idk how i should do

[raw shard]

@dry echo wait i have a stupid idea but i’ll try anyways

[dry echo]

I have one try left

[mental hearth]

<@&286206848099549185> i helped two ppl and im down bad 🥺

[dry echo]

so I should make sure it is the correct one lol

We only get 3 tries

[mental hearth]

need help w this

[raw shard]

oh ok

[dry echo]

man, how am I gonna pass calc 1

[raw shard]

i was gonna say you did the derivative of the radius instead if the derivative of the diameter, but idk if that matters

probably not

yeah you should wait for someone else instead of doing my ideas lol

[dry echo]

isn't that what I'm supposed to do? since the formula uses radius

[raw shard]

idk it was just an idea

[dry echo]

oh I think you might be right

maybe I need to multiply my answer by 2

[raw shard]

no way lol

big brain moment if i’m right

[dry echo]

actually scared to plug it in tho

[silk pivot]

https://gyazo.com/2c641499e1d3d9ed4d21e81190fe85c3

[raw shard]

i don’t blame you

[dry echo]

ok so now the question is

do I plug the negative

or the positive since the question already asks for decreasing?

[mental hearth]

nah im gonna take an L on this hw there are 11 more 😭

[raw shard]

i’m trying to differentiate it, just a minute

[wind pagoda]

aye bruh it be like that sometimes 😭

[tropic dagger]

can someone walk me through how to convert y = ax2 + bx + c to vertex form symbolically (just with variables, no actual values?)

[dry echo]

I submitted

[mental hearth]

my hw is similar are we in the same class 👀

nah its not

[dry echo]

And almost got it right, shouldn't have plugged in the negative

jesus christ

@raw shard Take a look at that lol

I mean it is decreasing so I thought it should be negative

[wooden sorrel]

hallo i have a hemisphere of radius R and i have to integrate over all the vectors in it. i declared that if i look at it like stacked disks all the horizontal components cancel so to get the vertical component i just do integral from 0 to R of pi r^2 * r dr

is that legit

i dont really know if the integral i wrote makes sense but the spirit of the question is to basically get the average vector in the hemisphere

[buoyant edge]

It's legit.

[wooden sorrel]

kool

[buoyant edge]

You're just applying spherical symmetry to 1/2 a sphere 🙂

[wooden sorrel]

guess so

[raw shard]

@dry echo bruh

idk how it’s not negative

oh wait

[wooden sorrel]

should have been tipped off when the question said the surface area was decreasing at a positive rate prolly

[dry echo]

The question asks the rate at which it decreases so it's assuming we don't need the negative in our answer

[raw shard]

it says the rate at which it decreases

[dry echo]

Yeah

[raw shard]

well i almost got it right lol

[dry echo]

Either way, I'm glad I found the correct way to solve this

WIth your help @raw shard

thank you!

[raw shard]

looks like i don’t completely suck at these problems lol

no problem

[dry echo]

yeah not as much as I do lol

Although it was introduced to us today

[raw shard]

yeah that was hard for me too

way too many chain rules right there

implicit differentiation and normal chain rule in one

[dry echo]

yeah lol

[buoyant edge]

What made you think the first limit is 21?

[craggy niche]

Hi @buoyant edge

21 is a mis input, the only correct answer of these is F(3) = 3

I was messing around with the system to see if it would give me minus points on wrong answers

For the most part, I'm confused on the different lim-->x notations and how to read the graph.

[buoyant edge]

Well let's start from the top

[lilac kiln]

Hey, from A ∈ R^(n×n) and xT(Ax) > 0 for x ∈ R^(n×n) except x = 0, and A symmetric, how do you prove that A is invertible (and thus the rank is n)?

[buoyant edge]

Channel is occupied.

[craggy niche]

lim x --> -1^-

That means x is being approached from a upwards angle, is it not?

• means approaching from below afaik

[buoyant edge]

"downward angle"? it just means that we're approaching -1 from the left

So our test values are getting bigger

[craggy niche]

yeah my bad, I mean to say that we're traveling upwards as the values increase due to the slope of the line

[craggy niche]

I understand this, but my issue is what to look for here. There are two lines on this graph

[buoyant edge]

Yes, that's a jump discontinuity

[craggy niche]

I see

[buoyant edge]

So the limit will not exist there.

[craggy niche]

Does that mean the answer to the question is DNE?

[buoyant edge]

Not to the first one

[craggy niche]

ok, so it is.

Oh

[buoyant edge]

Because the jump isn't at -1

it's at 1

[craggy niche]

I'm so dumb, you're right

[buoyant edge]

Not dumb.

You rushed a little bit, that's all.

Let's get back to the question

[craggy niche]

At -1 you will be approaching 1 from a value greater than 1, from what I understand.

[buoyant edge]

Yes.

[craggy niche]

How would I note that as an answer though? x>1 ?

[buoyant edge]

It's just given by the graph. These are things you can tell by inspection.

Clearly, F(x) is approaching 1 as x gets closer to -1

[craggy niche]

Alright, the first 3 answers in that case are 1, with #4 being "2"

F(-1) = 2

[buoyant edge]

Yes.

Since it approaches 1 as x approaches -1 from the left and from the right, the limit exists.

and is 1.

[craggy niche]

Understood

[buoyant edge]

However, as you can see, at x = -1, F(x) = 2

That is called a hole.

[craggy niche]

Duly noted

In the hole a limit = DNE

correct?

[buoyant edge]

You're asking if there is a hole at the limit, then the limit does not exist?

[craggy niche]

This is my progression so far btw ^

[craggy niche]

yes

[buoyant edge]

No, that is not true.

Regardless of what the function's value is at that point, the values around it are approaching that value.

And that's what a limit tells us

What the function approaches

So, for x = -1, clearly the function value gets closer and closer to 1

but F(-1) != 1

That doesn't matter here, though, because the line tells us we are getting closer and closer to 1, which is what we want.

Make sense?

[craggy niche]

Yessir

[buoyant edge]

Great.

Alright, now for $\lim_{x \to 1^+}$

[ocean seal]

Chris24

[craggy niche]

Am i to click the right answer as a reaction?

[buoyant edge]

No no no those are latex things lol

I was just trying to be clear

[craggy niche]

Ah my bad, yeah

[buoyant edge]

Look at the graph: as we approach 1 from the right, where is the function going?

[craggy niche]

towards y=4

[buoyant edge]

Nice.

[craggy niche]

Cheers mate, i've finished the question

I'm just going to take some notes of what you've written

[buoyant edge]

Nice job!

[craggy niche]

May I post more afterwards or is there a limit?

[buoyant edge]

As much as you want! Just try to be courteous to others (i.e. don't interrupt channels when others are working together).

[craggy niche]

Understood, should I give this channel some time for others to post or go ahead with the next one?

I have some problems regarding continuity / other limit functions

[buoyant edge]

It's not that strict: if it looks free, it probably is. If it's not, someone will let you know.

[craggy niche]

Alright, i'll post them here

[buoyant edge]

Sounds good.

[craggy niche]

The thing to note here is that I have never done a question as such. I've learnt about limits just today, but my professor dropped this in our homework and I am somewhat confused. I can definitely discern each of the functions themselves as a separate x value of f(x), but what is with the braces "{" and how do these work?

Should each function equal itself, as in 8-x-x^2=2x-3

Where I then plug in the limit?

[buoyant edge]

Those braces define a piecewise function

[craggy niche]

I understand that x-> 4- is -12, 4+ is 5, but what is the third (x->4)

[buoyant edge]

So for certain values of x, the function is defined one way, but for other values of x, the function is defined another way

DNE

Since the limit is not the same from both left and right

The function doesn't "settle down", so to speak

[craggy niche]

I see, so in this case it's about the function producing two differing graphs which cannot meet at one point where x=4

[buoyant edge]

Yeah, that's the idea

[craggy niche]

That was much easier than I thought, for it being something I was unfamiliar with...

[buoyant edge]

Since the limit is not the same from both sides, it does not exist

[craggy niche]

I have another question in this problem set. I've used what you taught me to deduce #1, #3, #4, and #5. #2 should be DNE because there are two function lines at f(1), right?

Note that -1 and -3 seem to be incorrect as well(?)

Nope, it's -3...

Could you perhaps explain why in this case?

[raw shard]

there’s no limit there

it’s just f(1)

[craggy niche]

The software notes that f(1) = -3 is a correct answer

[raw shard]

it is

[craggy niche]

But why was it -3 over -1?

[raw shard]

you see how there’s a whole on one of the graphs at 1?

and not a hole anywhere on the other graph

it isn’t defined there on the blue graph

it is on the green one

[craggy niche]

I see

[raw shard]

remember this says nothing about a limit, just what f(1) is

[craggy niche]

The hole means that it doesn't count as a limit and the solid circle should be the one noted as the answer?

[raw shard]

yes

[craggy niche]

Understood, i appreciate it

[raw shard]

no problem

[craggy niche]

This seems more confusing due to the -INF values. What does it mean by continuity on (-INF, INF)?

[raw shard]

@craggy niche pretty sure it means it’s continuous everywhere

[craggy niche]

How would one note that as an answer though?

[raw shard]

what exactly do you mean

[craggy niche]

I don't understand what you mean by that, and how i would note that as an answer on my quiz :/

[raw shard]

it means it is defined everywhere

no holes

[craggy niche]

It's continuous everywhere, yet what do i write as the answer? It's asking for a single value for some reason

"DNE" and "INF" are not valid answers it seems

[raw shard]

basically what value of c makes 16-c = 4c+5

[mellow wren]

Excuse me

[raw shard]

what

[mellow wren]

I need a bit of help with inequalities

[raw shard]

this channel is occupied, go to another one please

i can help in a minute

although i can’t guarantee i will know how to do it

[mellow wren]

Alr I tried getting help in 8

But nobody will help

[craggy niche]

I see, so this should be 2.2

That was correct. You found that by equating the two functions to themselves, right?

[raw shard]

yeah

at x = 4

[craggy niche]

ok, i've written it down as a note. Thank you

[raw shard]

no problem

[tardy basin]

Hey simple question

If there are 436 Water Tiles

And Feebas only spawns on 6 of them with a 1/73 encounter rate

Would that be written like this? (1/73)*(6/436)

[raw shard]

my guess is yes

looks right

[tardy basin]

Or like 1 - ((72/73)*(430/436))?

[tardy basin]

What would this calculate?

Confusing myself 😂

[raw shard]

i just put it in math terms as i read it and got what you first sent

[tardy basin]

Ok gotcha, but when do you do the 1 - (...) ?

[raw shard]

sorry i don’t know, what you sent just looked right to me so i said yes

[tardy basin]

Oh no worries

[alpine sable]

yooo

its dobbs

why do i recognize you?

[tardy basin]

youtube prob :p

[alpine sable]

most likely

i think remember seeing you a long time ago back when i was into pokemon

[alpine sable]

this seems like it would make sense

i mean im no genius at math

i see things if they work then they work

and this just kinda seems to work

[pastel pelican]

sorry isn't your discussion over? if its not i can delete my post

[alpine sable]

can't see why you can't keep it up

[tardy basin]

Oh go ahead Payrim!

Maybe repost it so its the newest message

[pastel pelican]

ah okay ❤️

hello
i have problem understanding left inverse injective and right inverse surjective
i've been reading the proof for couple of times, i know the definition of surjection and intection

if we call f:A->B and g:B->A
what is the Identity function here calling it I?
is I the same as Id_A?

is f^-1=g? why i didn't see that notion here

how does the right inverse work? if set B be surjective but not injective, then it can share some same range in order to surject (we can't use D-{something}), so then if A wants to imaged to B then one element of the domain goes to 2 or more elements in the range, which is impossible
are we using some of the elements?

why can't f be surjective if right inverse does not exist?
if a=!b but f(a)=f(b) it still is surjective but right inverse doesn't exist

if right inverse in a surjective function of A->B->A exists (B->A be g) then it must be bijective

[karmic quail]

“write cos x in terms of tan x” it gives the pythagorean identity, then the next step is to “take reciprocals”.. how come?

[pastel pelican]

go another channel mate

[pastel pelican]

wait f^-1=!g ? cause we are taking some of the elements from B
if f:A->B be surjective then g:B->A cannot be also surjective or its not a function at all
so function g is limited/reduced of f^-1? (that all of the set B images to A but doesn't surject A)
and selected elements from b get imaged to themselves like identity function, but not all elements in b get imaged to themselves

[rich basin]

could anybody please help me, been waiting for 1 hour in question 1

[serene stream]

can someone just tell me what n means in this case?

i am very much a beginner

I am learning sets right now

[wary badge]

Could someone please help me on providing this identify

[raw shard]

@alpine sable only one of those fractions can be simplified

you don’t see it?

[chrome notch]

How do you explain this?

[hardy gulch]

i think your question is missing some information

[chrome notch]

You only have to explain how to solve an infinite geometric sequence

You don't have to solve it

[noble sinew]

“If the r in the formula…”

If what with the r?

[gray isle]

there are probably parts
i)
ii)
conveniently cut off

[chrome notch]

Yeah that's my problem like how do we find r

If its infinite

[fallow pagoda]

any even number so 22/100 can be

[noble sinew]

Post the full question, if that is the full question skip it because it isn’t actually asking anything

[chrome notch]

Wait

[noble sinew]

Yeah like I said whoever wrote it forgot to write it probably

Maybe they mean for what r does the sum equal a_1/(1-r)

But hard to tell

[chrome notch]

Well can i atleast know how to find the answer for a infinite sequence?

[noble sinew]

It gives you the result right there

It is equal to a_1/(1-r) when |r|<1

[alpine sable]

Hi

[chrome notch]

Okay okay

[alpine sable]

How do you do question 1?

[fast oak]

Hello

[crystal raft]

hi

[fast oak]

How to solve 1

[pastel pelican]

<@&286206848099549185>

[marble saffron]

hey how do you solve the limit of (x+1)/(x-1) when x goes to 1

[solemn juniper]

Start by just plugging it in. What do you get when you insert x=1?

[marble saffron]

well it divides by 0

2\0

@solemn juniper

[solemn juniper]

Ok, good

Now examine the left- and right-hand limits separately

[marble saffron]

okay what about them?

[solemn juniper]

What happens as you approach 1 from the left?

[marble saffron]

it goes to negative infinity

[solemn juniper]

Indeed

[marble saffron]

and otherwise to positive infinity

[solemn juniper]

So then what can you say about the limit?

[marble saffron]

it doesn't exist

[solemn juniper]

Easy as that

[marble saffron]

thank you,but is there a way of writing it this down

[waxen spruce]

Quick question- how can you solve this type of question (calc ab)
At what points on the curve f(x)=________ is the slope equal to ____

[solemn juniper]

Writing what down?

[marble saffron]

well how would I know it approaches negative infinity and positive infinity without trying different values for x

is there another way ?

@solemn juniper

[solemn juniper]

Have you seen the notation $1^-$ and $1^+$ before?