help-23

[iron flare]

Yep

The other one is a little trickier as it isnt just a coordinate in brackets by it but you can see it too

6,0 is where that other line that comes down ends up

so not the same line

It's (0,0)

See where that line starts coming up from

(0,0)

So now we have two coordinates which is all we need to find slope

Let's make (4,4) coordinate 1 and (0,0) coordinate 2

What is y1-y2 and x1-x2

(4,4) = (X1,Y1)

(0,0) = (X2,Y2)

It doesn't matter which way you do it TBF but this way will be easier

What is y1-y2

Yep

And similarly so is x1-x2

Slope is (y1-y2)/(x1-x2)

So what is it here

Yep

So to summarise

H'(3) = f'(3) + g'(3) = 0 + 1 = 1

[safe radish]

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[lavish relic]

How do i solve this

Ping me

[strong token]

x^2 - 5x + 6 > 0

[lavish relic]

Base?

[strong token]

(x-3)(x-2) so :

domain is when :
x > 3 or x < 2

[magic junco]

Don’t forget x-5

[lavish relic]

So we can ignore the base?

[strong token]

ye also the x-m5

x-5

no u cant

[lavish relic]

We solve like x-5≥ 0

?

[strong token]

ye it cant be 0

so >

[magic junco]

There are two requirements
a. The base should be greater than zero
b. The base can’t be 1

[lavish relic]

Ok so x-5 falls in positive domain and we take the intersection of the whole?

[magic junco]

Find the intersect part between this and x-5>0
Don’t forget to mention x-5≠1

[strong token]

its:
x < 2 or x > 3 but since we need the base to be x-5 > 0 then the domain is x > 5 and x!=6

[lavish relic]

Ok got it

[magic junco]

!done

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.close

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[brazen parrot]

how did they turn 1/root3 to 5pi/6

[desert pasture]

that's tan(5pi/6)

[brazen parrot]

i tried to multiply by 180/pi

[desert pasture]

,w tan (5pi/6)

[flat frigate]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[solar hazel]

#help-8 message lol that looks exactly like this

[brazen parrot]

oh

[solar hazel]

the formatting i mean

not the question

[brazen parrot]

lol

our schools buy

from the same company

i think

yeah hes in the same server as me

WACE

[brazen parrot]

what is 1/root3 in degrees?

[desert pasture]

you mean 5π/6?

[brazen parrot]

,w 1/sqrt(3) in degrees

[flat frigate]

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Requested by nutgun.

[brazen parrot]

what value of tan

equal to 1/sqrt(3)?

in degreez

,w tan-1(1/sqrt(3) in degrees

[flat frigate]

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[brazen parrot]

GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[desert pasture]

what exactly are you trying to do

@brazen parrot

[desert pasture]

you still here

[safe radish]

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[snow sigil]

I'm using

[smoky nacelle]

I'm using stuff too

what're you using

where can i get some /j /j /j

[snow sigil]

I'm using wolframalpha and made a function:

f[x,y,z] := ((Partial[arccos\(40)Divide[x,sqrt\(40)Power[x,2]+Power[y,2]\(41)]\(41),x]) cos(arctan(- cot(z))) + (Partial[arccos\(40)Divide[x,sqrt\(40)Power[x,2]+Power[y,2]\(41)]\(41),y]sin(arctan(-cot(z)))))

How do I instruct it to take the function, insert something for x and y and take the derivative for z?

Like this:

d/dz f(cos(z)*c,sin(z)*c,z)

[smoky nacelle]

Oh god what

[knotty pier]

a picture of that function would be better...

[snow sigil]

alr sec

[smoky nacelle]

Idt you get image perms?

[knotty pier]

we do

[smoky nacelle]

do you?

Okay you do alright

[knotty pier]

lol this is maths server

[lime dust]

<@&268886789983436800>

[knotty pier]

how could u possibly type everything out

[snow sigil]

https://latex.codecogs.com/png.latex?\large&space;\dpi{300}\bg{transparent}\color{white}\begin{pmatrix} \frac{\partial}{\partial x} \cdot \arccos(\frac{x}{\sqrt{x^2 %2B y^2}}) %26 \frac{\partial}{\partial y} \cdot \arccos(\frac{x}{\sqrt{x^2 %2B y^2}}) \end{pmatrix} \cdot \begin{pmatrix} \cos(\arctan(- \cot(\alpha)))%20%5C%5C%20%5Csin(%5Carctan(-%20%5Ccot(%5Calpha)))%20%5Cend%7Bpmatrix%7D

[smoky nacelle]

Yeah fair

[knotty pier]

?

[snow sigil]

that's the function. My question is purely about how to write in wolframalpha the instruction below

[smoky nacelle]

Can't you be like find d/dz for f(x, y)

[snow sigil]

like, i can define it, it works in wolfram, but idk how to then write to do this:

d/dz f(cos(z)*c,sin(z)*c,z)

[smoky nacelle]

if you clearly specificied the function as f(x,y)?

[snow sigil]

i mean function is f(x,y,z) or f(x,y,alpha) in the picture i sent

I mean, I can write

d/dz f(cos(z)*c,sin(z)*c,z)

in wolfram, the problem is that I don't know how to make it execute after defining the function, I tried separating it with ; but it doesn't seem to do what I want it to.

[smoky nacelle]

Wolfram is a pain at times ngl

[snow sigil]

i mean it just doesn't consider f of before. If I just add f(cos(z)*c,sin(z)*c,z) without the derivative thing, it just gives this:

it doesn't consider the definition of f when evaluating the second instruction separated by ;

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[snow sigil]

Is there any free software that can do something like the function in the picture = 0, solved for z? I want to have all solutions for z in terms of c

[snow sigil]

I thought wolframalpha might be able to, but I don't know how to tell it "solve for z" since it has 2 variables

[summer crow]

pretty sure if you type x instead of z, it will treat c as the constant and solve it in terms of c. But wolframaplha is defo not gonna be able to solve that without premium. I don't have premium so idk if it can solve it with premium

[snow sigil]

alr thank you

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[runic spoke]

Hi

[runic spoke]

I was wondering how to do question 2b

F(x) is (x-4)^2 (x/-1)

[icy lance]

you just need to find the turning point of f, then apply the transformations

that get you to (-1,-8) in a hor translation and a vert stretch

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[kind hamlet]

to find the determinant of A

cant i just multiply the diagonals of U?

so 15?

[median vigil]

we know that det(A) = det(PLU) = det(P) det(L) det(U), and since det(P) = det(L) = 1, that would be the correct determinant

[kind hamlet]

then why the professor put -15 as the determinant

where did the minus come from

[median vigil]

oh i see, the determinant of P is -1

[kind hamlet]

huh

oh

right

thanks!

.close

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[brazen parrot]

how would i do this

[desert pasture]

well, it contains 14 carbon atoms

so let the total molar mass be x

[brazen parrot]

oke

[desert pasture]

can you do it from here?

[brazen parrot]

wait i think

let me check

[severe pond]

do you know the atomic mass of carbon

[brazen parrot]

yehs its on my periodtic talb

I DONT NEED THISS NOT LOOKING

[desert pasture]

use that then

[severe pond]

so if you have 14 carbons

what’s the mass of all 14 of them

[brazen parrot]

168.14

[desert pasture]

,calc 16*12.01

[flat frigate]

Result:

192.16

[brazen parrot]

whyd u do 16

[desert pasture]

my bad

,calc 14*12.01

[flat frigate]

Result:

168.14

[desert pasture]

ok

looks right

now what?

[brazen parrot]

by using percentage composition equationb

[desert pasture]

,w 94.34% *x =168.14

,clac 849700/4717

,clac 849700/4717

[eternal carbon]

clac

[desert pasture]

,calc 849700/4717

[flat frigate]

Result:

180.13567945728

[desert pasture]

I think this should be the answer

[desert pasture]

if you're calculations are right, this should be right

[brazen parrot]

what is diff between

ionic and molecular

[desert pasture]

you have to balance electrons too

for instance $Ag^+ + e^{-} =Ag$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

ah, I remember struggling with this at school, the memories

shouldn't have said that

sorry

[desert pasture]

shoulnd't have said this

[desert pasture]

makes sense ?

[brazen parrot]

ya

[brazen parrot]

naur its ok

hows it trans but-2-ene?

[desert pasture]

the methyl groups are on opposite sides of the double bonds

if the groups are all dissimilar you use the Cahn-Ingold-Prelog rules

[brazen parrot]

whast that

[desert pasture]

a way of assigning priority to diff groups

ok, gtg

sorry

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[twin cave]

We're learning derivatives in pre-calc and I'm having trouble applying it to our homework. It's due tomorrow, so I'd really appreciate help on the first problem in order to get the hang of the process to solving

[twin cave]

This is it and I've gotten up to a certain step but am stuck from there

[tardy plinth]

so basically

you know that when you're finding the derivative it's the slope of a line AT a certain point?

and since slope is a rate of change you need to use a value a teeny tiny bit off of the original

yes?

so yk the formula like (f(t+h) -f(t))/h

would give u the derivative

do you want me to?

i can also show u a MUCH simpler way of doing it

do yk the power rule?

[twin cave]

could you be more specific?

[tardy plinth]

okay yea

[frigid locust]

i think they want them to use definition of derivative

[tardy plinth]

so just plug it into the function

like lim x-> infinity (equation)

[twin cave]

we're doing lim h -> 0 if that changes anything

[tardy plinth]

no it does not

[twin cave]

alright

[tardy plinth]

what's the step you get stuck at

[twin cave]

I did plug it in as you said earlier but I think my problem might be simplifying or something like that

[tardy plinth]

do you have like your work i could see?

[twin cave]

I gotchu one second I'll send pictures of the steps

Ignore the add slider part I used desmos for the equation formatting rq since it's convenient

[tardy plinth]

okay so you need to factor out an h so that the h in the denominator disappears

[twin cave]

how so?

[tardy plinth]

also wait one second i'm going to solve this out

[twin cave]

also that -4x in the last step should be a -4h

[tardy plinth]

yes

[tardy plinth]

because if the limit is h->0, and you plug 0 in for h the equation would have no solution

[twin cave]

yes

I meant how do you factor it out apologies

[hot summit]

in the first step, the -4x term should be +4x instead since you’re subtracting a negative

[tardy plinth]

does this make sense

the whole point of this is to substitute h for 0, that's why you simplify it out so far bc in the instantaneous velo function h cannot be 0 (it's in denominator)

so now the derivative is the function for the slope of the tangent line (instantaneous rate of change) so you can plug in those values above like -2, 1, etc.

[twin cave]

got it thank you so much

[tardy plinth]

ofc !!

[twin cave]

have a nice night

[tardy plinth]

u too

[twin cave]

.close

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[carmine saffron]

I need to prove the sum is equal to the expression on the left

which is fine, i just got stuck on the last part

I don’t know how to add those fractions so that the right part of the equation is equal to the left part

the highlighted part is where i’m having trouble, everything else I get

[hot summit]

just multiply the first term by 2/2

since you know that 2^(k+1) = 2*2^k

$\frac{2 \cdot (2^k-1)}{2 \cdot 2^k} + \frac{1}{2^{k+1}} = …$

[flat frigate]

mud ツ

[hot summit]

simplify that

[safe radish]

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[carmine saffron]

omg thanks

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[fallen pier]

Q2

[fallen pier]

How do I solve algebraicly

[oak tangle]

you're using the wrong formula, it's nP3=n!/(n-3)!

[fallen pier]

Ohhh

Ty

.close

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[frosty sail]

my x cord is right, my y cord isnt

how do i find my y

input the x into the equation, but idk how to solve rught???

[thin bridge]

,rotate

[thin bridge]

can you show a clear attempt at your simplification

[hollow crest]

What you did was correct

Just simply further

Put X=-b/2a to get y

[frosty sail]

,rotati

,rotato

,rotate

[frosty sail]

yeah i did i cannot bedmas LOLLL

heres answer

[hollow crest]

Bedmass?

[frosty sail]

or pemdas

whichever one

its dame thing righttt

[hollow crest]

$\frac{a\times (-b)^2}{(2a)^2}+b\frac{-b}{2a}+c$

[flat frigate]

Monarch of Eternal Night

[hollow crest]

If you simplify

You'll get

$\frac{-b^2}{4a}+c$

[flat frigate]

Monarch of Eternal Night

[hollow crest]

@frosty sail

[frosty sail]

i need step by step

[frosty sail]

wait but at the top, its -b^2 + 4ac

in my answer key

[hollow crest]

Yes

So multiply by 4a in numerator and denominator

[hollow crest]

I already sent it

It's just subtraction

[frosty sail]

OH I GET IT NOE

[frosty sail]

wait im so confused

[frosty sail]

is this right

then cancel a and b^2

how is -2 leftover😭

[hollow crest]

Now subtract

1/4-2/4

[hollow crest]

.

-1/4

[frosty sail]

what

[hollow crest]

Bruh

Subtraction

[frosty sail]

i got -1/4a +c

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[versed wave]

Let $\bar{ab}$ be a number with 2 digits. When dividing this number by its digit sum we yield 6, the sum of its digit product and 25 is a number that is the reverse of the given number. Calculate $a-2b$

[versed wave]

through blind guessing i found the number to be 54

my question is, can this be solved without guessing?

[restive herald]

Someone please answer
The domain of the inverse trigonometric function arcsin(x) is:

[versed wave]

,,
\begin{cases}
\frac{\bar{ab}}{a+b}=6\
ab+25=\bar{ba}
\end{cases}

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[restive herald]

ok

[west hinge]

ab underscore is 10a+b no?

There problem solved

[versed wave]

ah, makes sense

so its just a system of equation

[silent token]

And ba is 10b+a

Yep

[versed wave]

right, thanks

.close

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[rapid ore]

Help for a function

[burnt notch]

!da2a

[safe radish]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[rapid ore]

Alberto

Sono italiano mi serve aiuto per una funzione

[empty gyro]

!original

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[empty gyro]

please translate if possible

[burnt notch]

In italiano non cambia comunque 😅
https://nonchiederedichiedere.com

[rapid ore]

find the coefficients a b c d so that the graph of the function has asymptotes the lines x=0 y=x - 3 and has a minimum point on the x axis

Study the function that is obtained with the values ​​of p and q found in the previous point
(a = 1, b =-3, c= 4, d= 0) and plot its graph.

Find the equation of the tangent line to the graph of the function at its point of
abscissa - 1.

Calculate the area of ​​the triangle that this tangent line forms with the asymptotes of the function

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[versed wave]

A cook plans to make 7 dishes throughout 3 days Monday, Tuesday and Wednesday; Tuesday will always have 3 dishes. 2 of the dishes are hors d'oeuvre, 2 are main dishes consisting of Honey glazed ribs and Braised carbs, the remaining 3 are desserts consisting of Grilled banana pie, Pomelo pudding and Strawberry mochi. The cooking plan must follow these conditions:

• The cook does not make Grilled banana pie on Wednesday
• The cook does not make 2 hors d'oeuvre in 1 day
• At least one dessert is made along with a main dish in a day
• There exists a day where the cook makes at least 2 desserts

Hypothetically, if Pomelo pudding is the only dessert made on Wednesday, which of the following statement must be true?

1. The cook made dishes consisting of all categories on Tuesday
2. The cook made Braised carbs on Tuesday
3. There is an hors d'oeuvre made on Tuesday
4. Strawberry mochi is made on Tuesday

[versed wave]

i dont know where to start tbh

i made a diagram where tue must have 3 dishes, mon must have 1/2/3 dishes and wed must have 3/2/1 dishes

pomelo pudding is put on wed, but from there i dont know how to use the information given to extrapolate the rest

[spice furnace]

You can just construct various cases

Maybe there is some programming based approached.

[safe radish]

@versed wave Has your question been resolved?

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[timber atlas]

Can someone explain what’s happening around the u-sub?

[timber atlas]

from the let u=x+2, i don’t understand after that

[split ether]

du = -sinxdx must be some sort of a typo here

[timber atlas]

oh i see

ah that makes sense then

huge typo there

thanks

.close

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[lilac sun]

can anyone tell me how do you solve this

[knotty pier]

ever heard of pythagorean theorem?

[pure arch]

erm, actually, it's called the pythagorean theorem, not the pythagoras theorem because pythagoras himself didn't invent it, it was one of his students which were called pythagoreans 🤓🤓

[knotty pier]

oh lol

[narrow ridge]

[knotty pier]

@lilac sun

[safe radish]

@lilac sun Has your question been resolved?

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[fresh lynx]

im stuck with just the general proof, mainly the beginning

[fresh lynx]

(circle theorems)

[tepid nymph]

let's connect the point B and centre O --> a line BO,
do you see what u can do with this newly added line?

[fresh lynx]

i mean my only guess would be similar triangles, or the angle at the centre from subtended arc but idk fully

actually wait yeah it would be an icolsceles triangle, so base angles be the same

[tepid nymph]

uh-huh, yup u got it

now what can u do next with this new info?

[fresh lynx]

not too sure honestly

[tepid nymph]

it's oke, we can work this thru tgt

[fresh lynx]

thank u :D

[tepid nymph]

this is what we got so far right?

[fresh lynx]

yeah

[tepid nymph]

BOD is a triangle and we know 2 angles so we can find the other angle which is the angle BOD

[fresh lynx]

so, 2x + (new value) = 180, or would that value be y?

[tepid nymph]

not yet

2x + the angle BOD = 180

so we can get the angle BOD

which will be 180-2x right?

[fresh lynx]

yeah

[tepid nymph]

now we got the BOD, this is still on the circle, what can we say about the relation between BOD and BCD

and this has something to do with what u previously said

[fresh lynx]

the angle at the centre is twice the angle connevted to the circle subtended on the same arc

[tepid nymph]

yuppp exactly

so we can find the BCD

[fresh lynx]

which would be 90 - x?

[tepid nymph]

yess

[fresh lynx]

ahhh i get it now

[tepid nymph]

let's look at here

now we just need to use the relation between y and the angle BCD

[fresh lynx]

would it be cyclic quadrilaterals?

[tepid nymph]

yup

[fresh lynx]

alright

so 90 - x + y = 180 ?

[tepid nymph]

yes

[fresh lynx]

ahhh i get it now

[tepid nymph]

so we will get what the question is asking

yay

[fresh lynx]

thank you so much 🫂

[tepid nymph]

np np ✨

[fresh lynx]

appreciate it man, you have a good one

❤️

[tepid nymph]

u too

[fresh lynx]

.close

[safe radish]

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[tawdry needle]

What is the question here

[knotty pier]

yea whats the problem?

[tawdry needle]

Oh didn't even see it

Its written

Smol

[knotty pier]

lol

[subtle gust]

Curved surface are of cone is pi * radius * l, curved surface area of cone is 2 * pi * radius * height

[snow jungle]

i got 56.2

cuz i found the surface area of each shape

[tawdry needle]

@snow jungle
Have you tried splitting the shapes into smaller easier shapes ?

[snow jungle]

i mean

lateral area

i got lateral area of each shape

so its the surface area of the whole shape

[tawdry needle]

You mean
Cylinder right?

[subtle gust]

Can you show your calculations

[subtle gust]

That's correct

[subtle gust]

Shouldn't it be 56.5 then instead of 56.2

[snow jungle]

oh

thats not an option tho

its supposed to be one of these

[snow jungle]

r u sure its correct then?

[subtle gust]

It should be

My calculator gives the same

[snow jungle]

alr maybe the choices r rounded then

i got 3536 for this

[untold anchor]

seems right fr

[snow jungle]

did u solve it or

like r u guessing

[untold anchor]

i solved it

[snow jungle]

oh nice

[untold anchor]

fr

[snow jungle]

thx

stay here pretty please

[untold anchor]

👍

[snow jungle]

i still need help

[untold anchor]

ok

[snow jungle]

alr

[snow jungle]

i got about 25 cm

[untold anchor]

yeah i got that too

fr

[snow jungle]

W

did u get 45 for this or nah?

@untold anchor

uh

<@&286206848099549185>

[untold anchor]

yeah

mb

fr

[snow jungle]

oh u got that?

[untold anchor]

yeah

[subtle gust]

The volume to length ratio

[snow jungle]

alr im on this one now

lmk what u get

i have mine

[untold anchor]

i got 169

fr

whatd u get

[snow jungle]

uh what

i got 395.8

[untold anchor]

whatd you do

[snow jungle]

i found the volume of the cylinder and subtracted the 3 spheres

[untold anchor]

yeah that’s what i did

[snow jungle]

what did u get for areao f the cylinder

and what did u get for the area of the 3 spheres?

[untold anchor]

508 for cylinder and 339 for spheres

[subtle gust]

Same, 169.646...

[untold anchor]

yeah

[snow jungle]

uhm hold on

ooh shoot ur right

i found my error

i accidentally found the area of the spheres by squaring it in the formula

not cubing

alr thx

[untold anchor]

it happens fr

[snow jungle]

alr 169.646 right?

[untold anchor]

yes

[snow jungle]

alr thx

also

this would be a triangular prism right?

[untold anchor]

yeah

🔥🔥🔥

[snow jungle]

W

1038.2?

[untold anchor]

yeah

[snow jungle]

W

[untold anchor]

🗣️🗣️🗣️🔥🔥🔥

[snow jungle]

now its time for the finale!

[untold anchor]

frrr

[snow jungle]

uh im not done yet

but tell me what u get

[untold anchor]

37.7 for the cone and 33.5 for the ice cream so it fits fr

[snow jungle]

W

i got that too

[snow jungle]

how the hell did bro solve so quickly lol

[untold anchor]

frr

[untold anchor]

desmos 🗣️🗣️🗣️🔥🔥🔥

[snow jungle]

W

is this a W explanation or nah?

[untold anchor]

🗣️🗣️🗣️🔥🔥🔥

[snow jungle]

wait

taco

can u help me with this

cuz i got something different

than the options

[untold anchor]

lemme look at it rq

[snow jungle]

the last calculation is what i got

but those r the options

[untold anchor]

yeah i got what you got too

[snow jungle]

dam

[untold anchor]

fr

[snow jungle]

alr maybe they rounded pi or something

[untold anchor]

probably

fr

[snow jungle]

yo

u get 21 for this?

and 3 for this?

[untold anchor]

yeah i got 21

what’s lateral area

[snow jungle]

lateral area is like all the area besides the bases

i mean

surface area without the bases

[untold anchor]

oh fr

[snow jungle]

so its just liek the surface area laterally i guess

[untold anchor]

yeah i got 3

fr

🗣️🗣️🗣️🔥🔥🔥

[snow jungle]

alr cool beans

thx

thats it for now

[untold anchor]

frr

remember to .close

[snow jungle]

yo what math r u in?

[untold anchor]

[snow jungle]

oh ye i will

[untold anchor]

iii

fr

[snow jungle]

uh

idk waht that even is

but W help

i might need some soon

[untold anchor]

fr

np

[snow jungle]

.close

[safe radish]

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[surreal scaffold]

Hi. Is there an explanation to why this is related to a centripetal force acting on the string? It is about the speed of a wave on a string, and the derivation of the formula.

[safe radish]

@surreal scaffold Has your question been resolved?

[safe radish]

@surreal scaffold Has your question been resolved?

[safe radish]

@surreal scaffold Has your question been resolved?

[magic junco]

Question in #help-21｜아리스킨충1 message

.close

[safe radish]

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[bronze badge]

i need the find sum of all solution to the equation

[lean otter]

bro u on the same game

[bronze badge]

that math game?

[lean otter]

ye i was in it

[bronze badge]

ye

have u solve that problem

[lean otter]

ye

i just set log2(7x-10) * logx(2) = 2

[bronze badge]

can u explain for me

o

ok and

[lean otter]

n u know that log_a(b) * log_b(c) = log_a (c)

so i set log_x(7x-10) = 2

now its a quadratic

[bronze badge]

oh ok

i get it

[safe radish]

@bronze badge Has your question been resolved?

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[fossil jewel]

help

[fossil jewel]

x squared for graphing

x becomes 1 over 1

what bout the squared?

the question is y = x ² - 2

supposed to graph it

what do i do

[lone arch]

Well, you know how the graph of x^2 looks like

It's a standard parabola

[fossil jewel]

it's x ²

what's a parabola?

x becomes 1/1

but what do i do with the ²

[lone arch]

What do you mean?

[fossil jewel]

x is an understood one

[lone arch]

x is the variable, yes

[fossil jewel]

so what do i do with the ²

[lone arch]

It does not become 1/1 though

[fossil jewel]

i was told it graphs as 1 over 1

[fossil jewel]

i am confused

y = x ² - 2, i graphed the -2

then i made X into 1 over one, like i was told

what is the ² supposed to do

do i do 1 over 1 ²

[lone arch]

What do you mean with "I made x into 1 over 1". Why do you do that?

[fossil jewel]

Becuase I was told that x is an understood 1, and i put it over 1 becuase you always put something over one to make it an impropper fraction so it can be graphed

[lone arch]

What does "understood 1" mean?

[fossil jewel]

How do you not know what an understood one is

[obsidian ginkgo]

Can you write what you mean by understood 1 and send a picture?

[fossil jewel]

i'm so confused

[obsidian ginkgo]

I think theres a language barrier

[fossil jewel]

hold up

y = x ² - 2

shouldn't the x be a one if there's no info about it?

[lone arch]

No

[fossil jewel]

i found a youtube video

cna i sendit

[lone arch]

Yes

[obsidian ginkgo]

We are trying to graph the function: y = x^2 - 2

[fossil jewel]

https://www.youtube.com/watch?v=aX0Xfc3epXk

i was just tought that x is always going to be a 1 if there's nothing known about it'

[fossil jewel]

yeah

[lone arch]

That's true, yes. But it's not actually x that is 1

[fossil jewel]

but 1 = x

[lone arch]

It's the coefficient of x^2

[fossil jewel]

ohhhh wait

crap

1 to the power of 2

and then 1 is put over 1

because your graphing it

and you can't just put the x OR y, you have to put both

unless y or x = 0

is that correct

[lone arch]

and then 1 is put over 1
because your graphing it

Just because you are graphing it, you don't need to do that

[fossil jewel]

bruh

wait

so x is 1

then 1 -2

-1

[lone arch]

Yes

[fossil jewel]

so it's 1 over -1?

[lone arch]

No, for x = 1, you have y = -1

[fossil jewel]

Yes

1 over -1

in a fraction

[lone arch]

If you want to, you can write that as a point: P(1, -1)

[fossil jewel]

yes

[lone arch]

But not as a fraction

You might be mixing something up

[fossil jewel]

then where did i get fraction from

ok so the answer to the problem y = x² -2

graphing the points would get

(0, -2)

and

(1, -1)

[lone arch]

Maybe you've seen something like

And mistook that as writing them as fractions

But it's just a table

[fossil jewel]

forget about fractions i got it mixed up

[lone arch]

Yeah

[lone arch]

Yeah

[fossil jewel]

Ok thank youi

should i close it now

[lone arch]

You should also use some negative x, like x = -1

See what you get for y

And x = -2

[fossil jewel]

ok

wait

i got y = -3

i did -1² -2

[lone arch]

Be careful

[fossil jewel]

because y = that equation

[lone arch]

$y = (-1)^2 - 2$

[flat frigate]

Kepe

[lone arch]

The - is also in the brackets

[fossil jewel]

that's what i did

y = -3

ohh

[lone arch]

There's a difference between $-1^2$ and $(-1)^2$

[flat frigate]

Kepe

[fossil jewel]

i'm using a TI-30x

and i multiplied -3 ²

not (-3)²

[lone arch]

Yeah, you need the brackets

[fossil jewel]

it's just -1

[lone arch]

Or otherwise it will just square 3 and then add a minus infront

[fossil jewel]

ok

[lone arch]

Yeah, 1 - 2 = -1

[fossil jewel]

what do i do if there's a square root symbol over everything

y = x+3 and x+3 is under a square root symbol

[lone arch]

$y = \sqrt{x + 3}$

[flat frigate]

Kepe

[lone arch]

Well, the same principle.

You plug in e.g. x = 1

[flat frigate]

Kepe

[fossil jewel]

How do you make those fancy equations

with the code

[lone arch]

It's called LaTeX, don't worry about that for now

[fossil jewel]

ok

TeXit

[lone arch]

If you want to study mathematics you should learn it at some point though

[fossil jewel]

ok

so

y = 2

but what about x

[lone arch]

Well, what did we plug in

x = 1

[fossil jewel]

ohhh

ok

is x horizontal?

[lone arch]

Yes

[fossil jewel]

ok good

so i got (1, 2)

[lone arch]

Yeah

[fossil jewel]

what about all the other points

[lone arch]

Well, you can just pick some x you want to plug in

[fossil jewel]

i'm supposed to graph the squiggly line, right?

[lone arch]

Yeah

[fossil jewel]

ok

what's a good X

or is it just anything

[lone arch]

But before that, you need some other x values so you know how it will look like, or you can't graph it

[lone arch]

Yeah

[fossil jewel]

ok so i can just make x = anything?

and it will work?

[lone arch]

Yeah, you could take x = 100 and see what you get

[fossil jewel]

or does x +3 have to be a square root

[lone arch]

No, it's just that if you use something like $x = 0$, you will get $y = \sqrt{0 + 3} = \sqrt 3$ and that doesn't have a "nice" value

You can type it into your calculator though

It will give you something around 1.7

[fossil jewel]

$x = 0$ --> $y = \sqrt{0 + 3} = \sqrt 3$

the > means it yeilds the equation tot he right?

[flat frigate]

AstroKnight187

[fossil jewel]

there we go

[lone arch]

Ah

Yep

[fossil jewel]

-> is like an arrow

ok

so how would i graph it

the squiggle line

[lone arch]

Well, which points do you have now

[fossil jewel]

(1,2)

[lone arch]

Yes

[fossil jewel]

that's it

[lone arch]

Well, with just one point, we can't graph it

[fossil jewel]

do i just make x anything

and then i get the y

[lone arch]

Yeah

[fossil jewel]

ok

brb

let me figure out something

wait

do i have to do the sqr root of x +3?

whatever x would be?

[lone arch]

You pick whatever x, for example x = 5. Then you plug that into sqrt(x + 3). For example for x = 5, that would be sqrt(5 + 3) = sqrt(8)

Then if you don't know what sqrt(8) is (it doesn't have a nice value), you type that into your calculator

[fossil jewel]

i used x = 3

and i got y = sqr rt of 5

[lone arch]

You mean square root of 6

[fossil jewel]

wiat

what the hell did i just do then

oHh

yes

sqr rt of 6

[lone arch]

Yeah

[fossil jewel]

i meant 2 but wrote 3

[lone arch]

Now 6 isn't a perfect square, so its square root won't have a "nice" value

[fossil jewel]

so how am i supposed to do it

[lone arch]

It will be around 2.24 if I recall correctly. Type it into your calculator

[fossil jewel]

type what

oh

[lone arch]

sqrt(6)

[fossil jewel]

2.449489743...

[lone arch]

Yep

[fossil jewel]

ok

[lone arch]

You can round it to 2.45

[fossil jewel]

so how do i graph 2.45

wait

could i theoretically use numbers for x that would equal a perfect sqr

[lone arch]

Yeah, of course

[fossil jewel]

ok

[lone arch]

Those would give you "nice" points

[fossil jewel]

might as well spare the extra time an do that

so if x = 6, i could do 6+3 = 9

and 9 would sqr rt be 3

[lone arch]

Yeah

[fossil jewel]

so y =3

x =6

ok

now how do i complete it to make the weird line

[lone arch]

If you have enough points, you can just connect them

[fossil jewel]

i only have 2 points

[lone arch]

Maybe get 4 or 5

[fossil jewel]

that doesn't make the squiggle line

ok

could i mirror the ones i have on the negative side?

[lone arch]

Nope, $y = \sqrt{x + 3}$ is not symmetric to the $y$-axis.

[flat frigate]

Kepe

[fossil jewel]

like x = 6 would mean x = -6

and y = 3 would mean -3

[lone arch]

Well, try plugging in $x = -6$, Then you'd have $\sqrt{-6 + 3} = \sqrt{-3}$. Type that into your calculator

[fossil jewel]

ok

sqr root of -3 is a domain error

[lone arch]

Yeah

The square root of negative numbers isn't defined

[fossil jewel]

so how do i get more points?

[lone arch]

Well, just plug in e.g. x = 0, x = 1, x = 2, x = 3

[fossil jewel]

ok

[lone arch]

Even if the values aren't nice, you have a calculator

[fossil jewel]

can i use perfect sqr numbers

[lone arch]

Yes

[fossil jewel]

but i want to get it so that the points are on the line

ok

[lone arch]

Also plug in x = -3

[fossil jewel]

ok

i did x = -3 and got 0

[lone arch]

Yeah

[lone arch]

Can we go further to the left?

What about x = -4?

[fossil jewel]

alright let me work this probelm

imma see if i can do it

do you want me to close this channel and open another later?

[lone arch]

You can just keep it open

[fossil jewel]

k

i always get a negative number which always equals y = domain error

[lone arch]

Exactly, so anything more to the left than x = -3 gives us a domain error

Meaning the furthest we can go to the left is x = -3

[fossil jewel]

ok

[lone arch]

Since we'll get something negative under the root

[fossil jewel]

i did x = -2 and got y = 1

[lone arch]

Yeah

[fossil jewel]

ok

i'm getting a straight line

[lone arch]

x = -2 is on the right of x = -3, so that's fine

It's just for x = -4, -5, -6, -7, ... that it won't work

[lone arch]

Really? Can you screenshot that

[fossil jewel]

i can't screen shot my work book

[lone arch]

Ah

[fossil jewel]

my desktop can't do that i don't think

[lone arch]

Which points did you draw in?

[fossil jewel]

here's the points i got

(-2, 1) , (1, 2) and (6, 3)

[lone arch]

And (-3, 0)

[fossil jewel]

How'd you get that

Ohhhh

i forgot that one

ok so i did get the slope i should have gotten

[lone arch]

Doesn't seem like a straight line to me

[fossil jewel]

i didn't say it was a straight line

[lone arch]

.

[fossil jewel]

that was me being a idiot and not seeing a curve

[flat frigate]

Kepe

[fossil jewel]

it was a bit subtle for me to see until i graphed -3, 0 😂

ok

[lone arch]

Should be 0.707 or something like that if I remember correctly

[fossil jewel]

How the heck did you know that off the top of your head

0.707106

[lone arch]

Yeah

[lone arch]

[fossil jewel]

[lone arch]

So that shows us how quickly it grows at x = -3

[fossil jewel]

yeah

[fossil jewel]

yeah

wiat

i have another questin

2x -3y = 12; how do i get the y by itself?

[lone arch]

You can add something to both sides of an equation

Also subtract ofc

[fossil jewel]

Ok

[lone arch]

And multiply and divide (if it's not by 0)

[fossil jewel]

-3y / -3

and 12 / -3

Does that work

[lone arch]

Yeah

You need to divide everything by -3 if you want to do that

[fossil jewel]

Ok

Ohhh

now it's coming back to me

[lone arch]

Don't forget the 2x too

[fossil jewel]

You see, i haven't done this math in a bit

so i should know this stuff, but i'm a bit rusty

Does 2x dividied by -3 become fraction?

[lone arch]

Yeah

[flat frigate]

Kepe

Kepe

[fossil jewel]

-2/3x +1 = -4

[lone arch]

What happened to the y

[fossil jewel]

uhh

is the -3 / -3 supposed to be just y

[lone arch]

Yeah, the -3 cancel but there is still a y

The y doesn't cancel

[fossil jewel]

ok

[lone arch]

If you divided by y, it would cancel too of course, but you just divided by -3

[fossil jewel]

2/-3x + y = -4

[lone arch]

Yeah

$\frac{2}{-3}x + y = -4$

[flat frigate]

Kepe

[fossil jewel]

Now how do i make it slope intercept form

[lone arch]

Might as well write that first fraction as $- \frac 2 3 x$

[flat frigate]

Kepe

[lone arch]

Ok, so you have $- \frac 2 3 x + y = -4$ and you want to isolate $y$

[flat frigate]

Kepe

[fossil jewel]

yeh

slppe intevept form

[lone arch]

You can add something to both sides

Or subtract

[fossil jewel]

*slope intercept

[lone arch]

What's a good choice to add (or subtract)?

[fossil jewel]

Like +4?

[lone arch]

Yeah, you could do that

[fossil jewel]

Ok

[lone arch]

But we want y alone on one side

That doesn't seem to help much

[fossil jewel]

oh yeah

[lone arch]

We want the -2/3 x to go away from the left side

[fossil jewel]

3/2

[lone arch]

So what could we add (or subtract) to achieve that?

[fossil jewel]

cancel it out

with 3/2

x

and then make -4 x 3/2

= 6

[lone arch]

So multiply both sides by 3/2?

[fossil jewel]

-6