help-0

[granite crest]

send ss cant understand

[static star]

wait sorry

no ln

[granite crest]

log

[static star]

yeah

just the xsinx

[granite crest]

yes

[static star]

is that what u got

[granite crest]

it slighlty differs

[static star]

which part

[granite crest]

yes its right

if is xsinx

i sloved it further

and i got the answer in terms of y

[static star]

did u get this

[granite crest]

yes but

the first fraction

the denominator will be xsinx

did you get it ?

[static star]

no

did u get the integration by parts as

xe^x - e^x

[granite crest]

yes

[static star]

okay

i see what i did wrong

[static star]

other than this thats what u got?

[granite crest]

yeah exactly

[static star]

e^x(x-1)/xsinx + C/xsinx, x ≠ nπ, n ≠ 0

you dont have to do all the stuff here

with positive and negative x

.

[static star]

just double checkin

but thanks

[granite crest]

yes right

[static star]

why some places they have the positive and the negative cases

[granite crest]

no no if its mod then just open it

[static star]

mod is abs value?

[granite crest]

yes then you put the limit on it

the possible limit

[static star]

gotcha

so then u dont have to consider it anymore

[granite crest]

yeah

if you put limit then youll only get the possible value

[static star]

limit on the integral

so was i suppsoed to do that

[granite crest]

no not here

[static star]

okay

[granite crest]

they specify it in the question

[static star]

i see

[granite crest]

yes

[static star]

okay thank you

[granite crest]

np

[static star]

.close

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[real glen]

i understand all of this up until it goes = e^0 = 1

is it because we took the log of both sides?

[indigo talon]

Yes, since you took ln of both sides and found the limit of lny to reverse it you take e of that

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@real glen Has your question been resolved?

[real glen]

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[tough scroll]

is 1+55+55^2+55^3+...+55^90 prime or composite ???

[vale wigeon]

what do you think

[tough scroll]

So far i have already checked that 2,3,5,7,11,13,17 dont divide it

[vale wigeon]

how long is the summation?

like how many terms does it have?

[tough scroll]

91

$\sum_{r=0}^{90} 55^{r}$

[ocean seal]

Light Yagami

[tough scroll]

also equal to $\frac{55^{91}-1}{54}$

[ocean seal]

Light Yagami

[vale wigeon]

right

does 91 have any factors

[tough scroll]

13×7

[vale wigeon]

indeed

does that perhaps allow you to split the sum up somehow

[tough scroll]

?

in 7 groups of 13 ?

[vale wigeon]

try that

see if you can cook with it

[tough scroll]

,,\sum_{r=0}^{6}55^{13r}(\frac{55^{13}-1}{54})

[ocean seal]

Light Yagami

[tough scroll]

this is 7 groups of 13 👆🏻

[vale wigeon]

well then

look what you have done

[tough scroll]

oh yes understood

(55^13-1)/54 divides it

and also (55^7-1)/54 divides it

[slim kite]

I didn't understand what this step is. Can anyone explain?

[tough scroll]

thanks

[vale wigeon]

OP grouped the terms into 7 groups of 13

[tough scroll]

we make 7 groups of 13, (1+55+...+55^12)+55^13(1+55+...+55^12)+...

[vale wigeon]

^

[tough scroll]

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[alpine sable]

i know the asymptote is y=-3, but when i plug in values for x they are all resulting in points below the asymptote?

[alpine sable]

example: x=-2 makes y=-9

thats below the asymptote?

[mortal trellis]

and?

[alpine sable]

is that ok?

[mortal trellis]

why should it not be?

[alpine sable]

because if i try to put those points there is no graph line

[mortal trellis]

not sure what you mean

if thats a software issue then I cant help with that

the graph is below the asymptote. that is correct

[alpine sable]

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[languid lily]

hey there is the problem occured while integerating directly there comes the term z^2*dy how to integerate this we have no ingormation regarding the

[bleak heath]

can you provide the question?

[lone heart]

@languid lily Has your question been resolved?

[languid lily]

wait ill send pic

[languid lily]

no

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[strange fractal]

im not understanding something here

[strange fractal]

why is my answer double theirs

cuz i thought i was only finding hypotenuse

which is 1 tension

and they will be the same

[slim kite]

Nope. Since there r 2 cables, it would be 2t

[strange fractal]

i dont understand why

[slim kite]

Wait, I'll have to see ur solution properly once

[strange fractal]

i

i just found this hypotenuse

[slim kite]

See, both the cables work together to balance out the force

The weight force is 245N

And each cable handles half of that

122.5N

Hence $\cos{52.5^{\circ}}=\frac{122.5}{T_{cable}}$

[strange fractal]

so what force did i really find here?

[ocean seal]

Suika

[slim kite]

Combined force

Of 2 cables

[strange fractal]

how would u draw dat?

[slim kite]

I didn't get what u mean by this

[strange fractal]

liek how would i draw all the forces on

[slim kite]

Like, as in visualise it?

[strange fractal]

yea

i tried to do this but its wrong

[velvet veldt]

draw a free body diagram?

[strange fractal]

ya

[slim kite]

Would this be easier to visualise?

[strange fractal]

wait since forces are balanced here and its in equilibrium

force down must = force up

so Tdown + Tdown = Tup

[slim kite]

Yes

[strange fractal]

oh

[slim kite]

W = 2T_y

[strange fractal]

so i calculate these 2 forces?

[slim kite]

Yes

[strange fractal]

do i just draw 2 lines like this

to makea triangle

NVM

I GET IT

.CLOSE

[slim kite]

In lower case

[strange fractal]

.cloae

.close

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[upper stratus]

detirmine the volume. im trying to find the bounds here. what is the thought process behind this i thought the bounds would be (0 -> 2pi, 0->sqrt(3), 0->sqrt(4-x^2-y^2) )

[upper stratus]

but its acctually (0 -> 2pi, 0->sqrt(3), -sqrt(4-x^2-y^2)->sqrt(4-x^2-y^2) )

so 0->2pi is the area around the sphere we are searching for, 0->sqrt(3) is the distance but what is the last one? the outer shell?

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[upper stratus]

.close

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[young light]

When I enter in tcdf(-1E99, -4.5607, 8) in my calculator, i keep getting 9.24105 even though the answer is .00184

[forest marsh]

and the e-4 is considered in the answer ?

Here its putting the ans in scientific notation

[young light]

Oh thanks

[forest marsh]

,w tcdf(-1*10^99, -4.5607, 8)

[ocean seal]

Results provided by WolframAlpha

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

Requested by yakubros

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[somber quest]

are histograms/distribution graphs illustrating F(x) or f(x)?

[wind cloak]

uh whats a distribution graph

if you sample data and put it into a histogram it will begin approaching the pdf

[somber quest]

if the graph is called pdf then whats the graph of F(x)?

[wind cloak]

its just a graph

[somber quest]

the smooth thing you call pdf

[wind cloak]

the cdf graph isn't that useful in general

you're just gonna plug and find values from it

[wind cloak]

also idk what this means exactly

[somber quest]

should F(x) be even called a distribution function?

[wind cloak]

the graph isnt called pdf, the funcion is

[wind cloak]

its called the cumulative distribution function

[somber quest]

ohh

if we int pdf in an interval thats between 0 and +inf, what would the result look like on the cdf?

[wind cloak]

idk

its not a useful thing in general

oh wait

youre integratig the pdf

you'll get some offset version of the cdf

[somber quest]

is it a portion of the cdf or is it a transformed cdf?

[wind cloak]

its the CDF + some constant

from the properties of integrals

You're asking $\displaystyle \int_a^b f(t) \dd{t}$ right?

[ocean seal]

neon

[somber quest]

actually before that, definite int gives a number, then how can it be represented on a cdf which shows a collection of numbers? unless its just 1 x value of the cdf giving 1 single y

[somber quest]

yes

[ocean seal]

neon

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@somber quest Has your question been resolved?

[somber quest]

Holy shit fundamental laws

Thx

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[brittle lake]

Can someone explain to me how 8 comes into play

[brittle lake]

oh wait

wrong one

its in the mid

i dont understand how that symmetry thingy works

which introduces the 8

nvm i get it

.close

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[left wedge]

how should factorize this? I cant find a yt tutorial on it

[vale wigeon]

put x = k^2 and then the equation will look like a "normal" quadratic

[left wedge]

👍 that wasnt my problem but I fugred it out

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[shrewd frost]

I am not getting anywhere with this

[shell agate]

so I thnk

So we get anything by taking BD as x and DC as y

[shrewd frost]

LEMME try that

This must be right? So the answer is (4) nota?

[shell agate]

Also x^2y^2=b^2+c^2

What if we do x^2=(b^2+c^2)/y^2

nah that doesn't help

It's almost never none of these

[shrewd frost]

I mean

[shell agate]

I have a feeling it's 1

[shrewd frost]

What else can you get here

[shell agate]

We have all equations now it's how to solve it

[shrewd frost]

Did u get anything?

.close

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[alpine sable]

im confused on a and b

[alpine sable]

i don’t hmeven know how to start

[earnest slate]

idek how to read

[bleak heath]

wtf is that

[slim kite]

$a)\sum_{n=1}^\infty\frac{(-2)^n\sqrt{n}}{5^{n+1}}$

[alpine sable]

where did u get 2n

[slim kite]

Nvm

It's a bit hard to read tbh

[alpine sable]

please help im struggling with it

[sleek grove]

I'm so sorry wrong server

[bleak heath]

which 2n?

[alpine sable]

im curious what server ur sending it on

[slim kite]

$b)\sum_{n=1}^\infty\frac{\sin(\frac{1}{n})}{n}$

[alpine sable]

dawg that’s e

[lusty minnow]

wanted to ask if i did these integrals right

[slim kite]

!occupied

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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).

[bleak heath]

do you not have a better pic than this?

[slim kite]

Hint: try comparing to $\sum\frac{1}{n^2}$

[ocean seal]

Suika

Suika

Suika

[alpine sable]

a and b please

[slim kite]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[alpine sable]

i already said it

[slim kite]

Dunno where to begin?

[alpine sable]

yes

[slim kite]

Oh yeah

U said it

[alpine sable]

@bleak heath can u help me

[slim kite]

Are there any particular methods that they expect you to use?

[alpine sable]

direct comparison, limit comparison, and ratio

[slim kite]

So, for the first one, you write it in this way:

$\sum\frac{\sqrt{n}}{5(-\frac{5}{2})^n}$

[alpine sable]

uh what

[ocean seal]

Suika

[slim kite]

As n approaches infinity,

The denominator grows much faster than the numerator

Hence, the last term approaches 0

Hence the summation exists

Is that a valid proof that you can use?

[alpine sable]

.close

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[slim kite]

I'm sorry, am I being annoying?

I can stop if u want me to

[tidal vigil]

Nah you chill they just an opp for ignoring.

[slim kite]

Ok

[lusty sail]

bro just reopened the same question in a different help channel 😭

[slim kite]

Ik

That's why I thought I may be annoying

[lusty sail]

nah think he just wanted someone to dumb it down for him

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[ionic hearth]

I don't actually understand what a b and d are considered here

[ionic hearth]

a seems like a local maximum but thats wrong, d doesn't appear to be a local maximum or minimum and b seems like a local minimum

[coral steeple]

Honestly I don't know what local means, but it seems that b is local minimum

[alpine sable]

local means nearby

[coral steeple]

Between increasing and decreasing [a;c], c is the bigger value

[north rover]

I.e., the functions behavior around x=a.

[coral steeple]

I think between an increasing and decreasing

[north rover]

For a, there isn’t a second side to it.

[ionic hearth]

wouldn't that make a a minimum then?

[north rover]

It has to have both a left and right side.

[ionic hearth]

s doesn't have a right side tho

[coral steeple]

Look at graph

[north rover]

Technically speaking, the limit from the left doesn’t exist, so we can’t necessarily classify a as a maximum.

[ionic hearth]

what about b then?

is it cause b is a cusp?

[north rover]

Yes.

[ionic hearth]

and d isn't minumum and max either then

[north rover]

Yep.

[ionic hearth]

thats literally wrong though

[north rover]

There might be multiple points that correspond to each cateogry. Keep that in mind.

[ionic hearth]

it autofilled into a local minimum existing so one of them has to be a minimum, I already tried entering all of them as non mins or maxs

[north rover]

Why would a be a local minimum...?

[coral steeple]

d at the middle of the whole thing, it must be neither

[ionic hearth]

its not it just auto filled to an answer I can't leave it blank

a local minimum must exist because I cant leave that section blank

[north rover]

We determined this already.

[ionic hearth]

the thing is

[north rover]

Then just put in b instead.

[ionic hearth]

correct me if im wrong but because b isn't differentiable its not a minimum or maximum correct?

[coral steeple]

Which is b, right?

[ionic hearth]

but b is a cusp tho

derivative of minimum or max is 0 no?

[coral steeple]

Inverted cusp?

[north rover]

No, differentiability doesn’t have to imply there isn’t a minimum or maximum.

If you see it have a dip, it is a local minimum.

[ionic hearth]

💀

[coral steeple]

GG

[ionic hearth]

I already tried that earlier

[north rover]

Where did a go?

[ionic hearth]

with this answer

[ionic hearth]

old answer

[coral steeple]

Maybe b and r?

[ionic hearth]

bro ngl I don't understand this 💀

[coral steeple]

Try to find out what is local

[north rover]

I think this is just an error on the computer’s end, personally.

[ionic hearth]

r is the absolute minimum its the smallest point on the graph

[coral steeple]

I see, maybe u need to put it as well such as local min

[forest timber]

b should be a local minimum since there's a smaller overall minimum here (r) and (a, d) should be neither max nor min

[ionic hearth]

the problem is having b as the local minimum

is apparently wrong

and either theres more than 1 local minimum

[north rover]

This has been disproven.

[ionic hearth]

or b just isn't a local minimum

idk whats going on

😔

[forest timber]

oop my apologies then

I'll catch up rq

[north rover]

^ Talk to your professor about it.

[coral steeple]

Try d

It is smaller than a

[ionic hearth]

as a local minimum?

[coral steeple]

Yes

[ionic hearth]

and then for neither I put a and b?

[forest timber]

oh my I just realised that b will not be differentiable

[coral steeple]

Try it, we don't know

[coral steeple]

i has opposite half-tangents

[ionic hearth]

yeah but i've already been told that doesn't matter the minimum can still exist at that point no?

[forest timber]

minimum can't exist since a condition for a local minima is f'(x) = 0

that specific point being a kink in the graph cannot be differentiated

I don't remember the exact reason why, could be what lucifer mentioned

[coral steeple]

Try to put, "no local minimum points"

[ionic hearth]

both wrong

idk

[north rover]

^

[coral steeple]

"

[ionic hearth]

okay well I got locked out of the question

i'll ask my prof about it in class today

i don't understand

[coral steeple]

Even @north rover didn't understand

Let him know the answer when you have it.

Sometimes he makes kindful terrible mistakes, but he's a good person.

[ionic hearth]

on a side note whats all the ways to impact what a graph looks like again?

[coral steeple]

U wanna draw it?

Just imput x = 0, x = 1, x = 2, x = -1 in f(x), and draw

[ionic hearth]

.close

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[acoustic flume]

hello, i alrdy asked this before but i still need help. I need to model/find the f(x) of the shape of the guitar above the x axis. PPL alrdy told me to do largange polynomial. It does not fit the curve accurately as seen in the photo. ive tried other polynomials and diff degrees, none of them fit. SO my next approach is to do piecewise, so i cut up the guitar in the third photo can someone pls tell me what functions would be suitable for each. or give me a new approach or helping hand.

[acoustic flume]

ive been working on this for ages and im starting to lose my shi

[fickle venture]

are there any constraints on f

you can fit it exactly with a polynomial of degree n - 1 if you have n points

[acoustic flume]

idts?

[fickle venture]

ok. you have 16 points so you can use a degree 15 polynomial

[acoustic flume]

These are my points (the second table is just more detailed and a bit more accurate)

[fickle venture]

but the function may be very wonky and do weird things between the points

[acoustic flume]

hold on second pic is wrong

this

so how do i approach this😣

cuz like im thinking of piecewise but im gen tired of this

like to have 4-5 piecewise fuctions

[fickle venture]

how did you find that degree 4 polynomial in the image

if you are doing some optimization thing you can add a regularization term to try to prevent the polynomial from doing crazy things

[acoustic flume]

i js used a wbsite like this to insert said points

[fickle venture]

oh

[acoustic flume]

ive tried doing it manually as well and it aint working

ive tried geoalgebra and its awful

ignore my shakey hands but one thing i established w my teavher is that it has to look like this

[fickle venture]

you can try to find a tool for ridge regression

[acoustic flume]

cant rllt find one for free

but thx ig

<@&286206848099549185> or if someone could pls be kind enough to js find me a funcrion that actually fits cuz im exhausted as f

[mortal trellis]

https://tools.timodenk.com/cubic-spline-interpolation

[lone heart]

@acoustic flume Has your question been resolved?

[gloomy lotus]

I think with a lagrange interpolation

[acoustic flume]

if u see my message above, i did say i did lagrange

and that it is not fitting correctly

or precisely

[mortal trellis]

whatever you did is not lagrange. lagrange fits precisely through your points

it will look awful and is not what you want, but it will fit your points perfectly

[acoustic flume]

well ive tried

[wintry wadi]

this seems promising
https://github.com/maltaisn/svg-equations
can you make an svg file of that curve that you want?

it'll be parametric though, not just y=f(x)

[gloomy lotus]

Hoe many degrees you used?

[acoustic flume]

im afraid i dont know how to do that..

[gloomy lotus]

I think also this

[acoustic flume]

i mean i can do some searching

[acoustic flume]

ive tried until 5.. and above 6 is started doing like this

ig im doing smth wrong then

[gloomy lotus]

But how did You do this lagrange interpolation?

[acoustic flume]

cuz this is how i understood lagrange. just finding the precise x values and cooresponding with y

and these were the x values..

and i inputted these values into the smth like this

i mean this omne didnt accept more points so i used another wbesite and yeah

[gloomy lotus]

Look this video https://youtu.be/bzp_q7NDdd4?si=hHVtNwbJTHXCkrTv

[wintry wadi]

use this
https://svgedit.netlify.app/editor/index.html
most art programs can also do it probably

[gloomy lotus]

Forme thats not lagrange interpolation

[acoustic flume]

is there any way i can insert the photo?

[acoustic flume]

ah..

but i thought whta i had were the nodes..

[wintry wadi]

yeah, there's a picture button on the sidebar
you still need to draw it though

[gloomy lotus]

@acoustic flume put your points in Wolframalpha

interpolation {(20,3), (40,11), (60,23)}

Like this

[acoustic flume]

how do i procceed..

[acoustic flume]

give me a sec

uhm idk how to insert the values..

not letting me change anything

[gloomy lotus]

Add in the search bar

Like (3,8),(6,9), and so on

[acoustic flume]

oh

mb ill do it

[gloomy lotus]

Inside the curly brackets

[acoustic flume]

yupyup give a momentpls

[fickle venture]

just fyi lagrange interpolation may not give what you want. it will give you a polynomial that goes through all the points exactly. but what happens outside the points is up to the polynomial

you presumably want something that's nearly linear between adjacent points and there's no reason the minimal interpolating polynomial will do that

but ofc it's worth trying it first to see if it works

[wintry wadi]

your photo is from the internet right?
put the image link there

[acoustic flume]

ah.. ill shorter the x values

[acoustic flume]

yes ofc

[acoustic flume]

nah my own pic

[wintry wadi]

ah, you'd need to download inkscape or krita, or some other art program then
try the langrance thing first and ping me if that doesn't work

[acoustic flume]

imma start tweaking dawg

[acoustic flume]

dyk whats the problem..

[gloomy lotus]

Or look this code

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline

Puntos de ejemplo (debes agregar tus puntos reales)

x = [0, 1, 2, 3, 4, 5]
y = [0, 1, 0, -1, 0, 1]

Crear la spline cúbica

cs = CubicSpline(x, y)

Crear una curva suave

x_new = np.linspace(min(x), max(x), 100)
y_new = cs(x_new)

Graficar la curva

plt.plot(x, y, 'o', label='Puntos de control')
plt.plot(x_new, y_new, label='Spline cúbica')
plt.legend()
plt.show()

[gloomy lotus]

Mb lots of points idk

[acoustic flume]

let me pull out my laptop

sorry but based off the pics i sent do u think theres any effective way i can lesson the points

[gloomy lotus]

Well with this code that i send to you it's a hardcore solution to your problem xD

[acoustic flume]

let me see

dumb ass ques

does it matter which table i use

table 2 is hardcore estimate and table 1 ig the x values are kinda conrete idk

mvm imma js do tab 1

the code stops the process after some w no output

imma try the other rable myabe..

this makes no sense man

it says error in line 50??

wtf

[acoustic flume]

but why does it say from scipy.intermpolate import cubicspline, isnt that extracting smth from a file

but even if it does work how do i get the f(x) from that

[acoustic flume]

langrance doesnt seem to be working…

[wintry wadi]

have you also tried this thing?

[acoustic flume]

it kinda works, and the thing is i showed this my teacher during school and he said that theres too many piecewise functions

bc the reason im trynna find this f(x) is to use it for volume of revolution andfurther calculus

and yeah its just not working properly as u can see

like he said if i wanna do piecewise functions he’d recommend 5 max.

[wintry wadi]

oh, I don't think my method would work then

[acoustic flume]

ah

[wintry wadi]

can you share that desmos sketch?

I'll try to manually do it and share the method

[mortal trellis]

you have to decide between good fit and easy function

[acoustic flume]

hm i also lessened the points but its acting strange

[acoustic flume]

like this? https://www.desmos.com/calculator/ypt3wbhwpq

ah wait i removed some point

[wintry wadi]

yeah

[acoustic flume]

https://www.desmos.com/calculator/7co6pcb9so

[acoustic flume]

mb the code is working now look

how do i get f(x) tho..

[acoustic flume]

and thank u i gen appreciate any help at this stage

[wintry wadi]

for the first few points, until the top there, looks like aln(x+b)+cln(x+d)+f works

you should think of a function that have a shape that looks like a part of it, then use desmos's regression

[acoustic flume]

i js realized one of the points was wrong, dont think itll change much btu yeah https://www.desmos.com/calculator/kkeydzjpbk

[wintry wadi]

oh i'm missing a step, make a table only from the points in that part, then use regression

[acoustic flume]

ok

i will try that

ig its the only option atp

thank u

[lone heart]

@acoustic flume Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[whole otter]

What is the limit as n->infinity of n^(1/n)

[whole otter]

I can’t really figure it out

Feels like an Euler number but it’s not

[lone heart]

Show your work, and if possible, explain where you are stuck.

[forest marsh]

AM GM inequality maybe

[nocturne veldt]

imma latex this up cuz im bored.

$\lim_{n\rightarrow\infty}n^{\frac 1n}$

[ocean seal]

00100000

[vestal sand]

the result of this limit is : 1

[whole otter]

Why is it tho

,rotate

[forest marsh]

.

[whole otter]

What’s an AM GM inequality

I just might be stupid

[vestal sand]

because the lim x->infinity ln(x)/x = 0

[whole otter]

woah

[vestal sand]

cuz x>>>ln(x)

or you can use l hospital rule

[whole otter]

How does it relate

[whole otter]

l hospital gets me stuck

[vestal sand]

e^(ln(x)/x) = x^(1/x)

[vestal sand]

.

[whole otter]

Oh that thing exists too

Still got me stuck

,rotate

[vestal sand]

then let : ln(x) = y

and use taylor series

for ln(x)/x ( dont forget to change ln(x) to y)

[forest marsh]

You can do (1+1+ ... + 1 + sqrt(n) + sqrt(n))/n >= n^(1/n)

= 1

[whole otter]

Infinite sums of 1?

Wait how would that help tho

I’m not picking up what yall are putting down

Can we go back to the AM-GM thing

It kind of intrigues me

[lone heart]

@whole otter Has your question been resolved?

Channel closed

Closed by @whole otter

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[normal frigate]

Hello

[normal frigate]

ill take a png

to it

Can I get help with these?

[crimson dawn]

I'll help with 9 I guess

[unreal pelican]

😭

[crimson dawn]

Let's look at y=x^2-24 and y=x-12

[crimson dawn]

Who's this

[unreal pelican]

You got this

[crimson dawn]

I mean qn 9

Not 9 questions

[unreal pelican]

Yeah u got this

[crimson dawn]

Yea

Frfr

Hyped

[crimson dawn]

Solving this system of questions means finding all the pairs of x and y that fulfill the equation

Since both x^2-24 and x-12 are equal to y then x^2-24=x-12

We can then solve for values of x

Of which you will probably get 2

Because quadratic

[normal frigate]

gyatt

mb

[crimson dawn]

Ok nvm

I can't do this today

[normal frigate]

fr?

okay ill wait for another

all good

[crimson dawn]

Yea mb

Can't handle all the gyatt

[normal frigate]

have a blessed one though

[normal frigate]

mb

🙏

[quick wind]

sure bud

which one u stuck on

so u got 2 simultaneous equations on question 9

but they both equal to y

so it makes sense that x-12 should equal to x^2-24

then rearrange into a solvable quadratic x^2-x-12=0

either use the quadratic formula or factorise into (x-4)(x+3)

so x= 4 or -3. then, substitute x in and u get the y results

do that for 10 as well

[normal frigate]

1

Number 1

I have a quiz on this

Or big test

Since I was sick for it I never got to even learn it

[quick wind]

ok

[normal frigate]

(Like hospital sick)

[quick wind]

so number 1 is a parabola

or a quadratic whichever term u prefer

its either like a U or a upside down U correct?

[normal frigate]

Yea

[quick wind]

do u know when U is upright or upside down

[normal frigate]

I know when the parenthesis are negative it's upwards facing no?

Or is it the other way around?

[quick wind]

if its something like x^2, its a U

if its -(x^2), its a reverse u

as u can see, there is a -2 in front of the (x+6)^2

[normal frigate]

So if it's positive U then if it's negative it's a n

[quick wind]

yes

ok now we now know that its an n

how do we draw it

lets start simple by substituting x=0

because we love x=0

[normal frigate]

Yes

[quick wind]

-2(0+6)^2 -4

that gives us -76

since (0,-76) lies on the y axis, we can say that is the y intercept of f(x)

[normal frigate]

wait im going to draw it real quick

[quick wind]

before u draw it

u need to find the roots as well

[normal frigate]

oh okay

[quick wind]

let y=0

so -2(x+6)^2 -4=0

does that make sense

i assume it does

if we divide both sides by -2 to get rid of that ugly negative

the -4 is affected but the 0 is not

so we get (x+6)^2 +2=0

[normal frigate]

wait

sort of

im getting a little lost

[quick wind]

which part do u not understand

[normal frigate]

its mostly how Im supposed to write it

[quick wind]

the roots aka the x intercept, is where the graph touches the y axis

the horizontal line where y=0

[quick wind]

write it in the general form of a quadratic

[normal frigate]

no clue

what that means

my teacher uses the worst terms

[quick wind]

ok lemme draw smth for u hold on

[normal frigate]

okay thank you

[quick wind]

ur usual quadratic

u can see the graph pass the horizontal line, known as the y axis twice

[normal frigate]

oh like on a graph

[quick wind]

its possible there are no roots

smth like this

[normal frigate]

dawg why did it copy like that

💀

[quick wind]

an example of a quadratic having no roots

[normal frigate]

I see

can we do the equation on paper

or atleast partially

[quick wind]

ok

we have the equation f(x)=-2(x+6)^2 -4

correct?

[normal frigate]

Yes

[quick wind]

if we want to find any roots

it needs to be on the horizontal line the y axis

[normal frigate]

arent we solving for the 2 x intercepts

[quick wind]

where y = 0 everywhere

roots = x intercepts

its just a different term im using mb

[normal frigate]

oh sorry

[quick wind]

ty for uploading again i dont have to scroll

[normal frigate]

Youre welcome

[quick wind]

so does it make sense that we treat f(x) as 0

[normal frigate]

sorta

cuz we gotta set everything

[quick wind]

because in order for f(x) to have a root it needs to intersect the y axis, hence called the x intercept

[normal frigate]

to 0

at the end no?

[quick wind]

so now we have this equation

-2(x+6)^2 -4 =0

do u follow

[normal frigate]

yes

[quick wind]

heres a lil trick we can do to make solving this easier

divide both sides by negative 2

So -2(x+6)^2 becomes (x+6)^2

and 0 becomes 0 because well yknow

but keep in mind, the (-4) also gets divided by -2

so -4/-2 =2

we now get (x+6)^2 +2=0

[normal frigate]

as so

for dividing by -2

[quick wind]

yes

but the -4 is affected as well

so divide it by -2 too

[normal frigate]

yessir

[quick wind]

show me the new equation u have

[normal frigate]

yea?

no?

[quick wind]

correct!

[normal frigate]

YESSIR

[quick wind]

yay

now

minus both sides by 2

so we get (x+6)^2=-2

do u notice something odd here?

[normal frigate]

yes

we havent factored the 2 squared

no?

there should become x+6 x+6

[quick wind]

would u agree that anything squared becomes either 0 or a positive number

[normal frigate]

yes

[quick wind]

cuz negative * negative = positive

so we shouldnt get -2 at all

no value of x should give us a negative number

right?

[normal frigate]

o

yes

[quick wind]

so there are no roots to the equation

[normal frigate]

so now what?

[quick wind]

so given that the graph is an n shape as we discussed, had a y intercept of -76

just draw the thing freehand

hold on mb

sorry

sorry

[normal frigate]

oh okay]

[quick wind]

we still need to find the turning point

every quadratic has one

have u learnt complete the square yet?

[normal frigate]

not surew

were on triginometry

so probably

this was from awhile ago

just got released from the hospital around a week ago

Trig is easy though (for now)

[quick wind]

good thing the equation completed the square for us

we know that y=-2(x+6)^2 -4

and since its n shaped

it gets to a point where its y value cannot increase any more

then it goes down again

making sense?

[normal frigate]

not really

[quick wind]

for example this graph

can u see that the y value gets to a certain point

then goes back down again

[normal frigate]

Im not sure if I even need to graph for this equation

yea

[quick wind]

it says sketch the graph so

[normal frigate]

alr sec

youre right

sorry

[quick wind]

so there is a maximum value of y at some point

agreed?

[normal frigate]

no clue

[quick wind]

refer to question 7

[normal frigate]

I thought graphs could be infinite

[quick wind]

the graph looks like its going up

but it gets less steep

then it goes back down again like a roller coaster ride

so that point is called the maximum

[normal frigate]

huh

[quick wind]

because u cant get a y value higher than that

aka thats the highest the roller coaster can go before they run out of budget

[normal frigate]

Lwk if we can just do the formula and help me learn how to make the graph

[quick wind]

whats lwk

[normal frigate]

thats fine cuz my teacher no way at all taught all that

Low key

its slang

[quick wind]

ah ok

what formula u doing

[normal frigate]

ill send some of the notes

but I dont know if youll understand them

cuz i dont really

and the teacher I had didnt either

for my hospital

[quick wind]

the teacher didnt?

oh

[normal frigate]

yea

my math teacher rambles

[quick wind]

i’ll have a lookasee

[normal frigate]

sec

I needa transfer it to png

[quick wind]

considering u were in hospital

the teacher probably taught all that unfortunately

[normal frigate]

oh nah...

im cooked

dawg these are all the notes

wait

are these even the right ones

[quick wind]

thats simultaneous equations

by factorising

[normal frigate]

those are fror the graphs

mb

[quick wind]

nah i can see u have a good layout

[normal frigate]

this is what were doing im pretty sure

[quick wind]

ah using -b/2a

smart cookie

[normal frigate]

o

can we do it that way

?

[quick wind]

sure

lets expand -2(x+6)^2 -4

into a form of ax^2 +bx +c=0

firstly expand the brackets

u should get -2(x^2 +12x +36) -4

[normal frigate]

okay

this?

[quick wind]

yes

then u expand the -2 out

-2x^2 -24x -76=0

[normal frigate]

we distributed the two i see

[quick wind]

pretend u didnt see that

i make mistakes sometimes

[normal frigate]

all good dude

[quick wind]

but now we have a quadratic in the form we want

[normal frigate]

are you trying to be a math teacher?

cuz you would make a good one

[quick wind]

lets do -b/2a

[quick wind]

its an option

[quick wind]

only on discord

[normal frigate]

If youre in the US don't

possibly somewhere else not sure how they get payed

in other places

[quick wind]

but we digress

-b/2a

subbing them in we get -(-24)/2(-2)

aka 24/-4

[normal frigate]

where

ohh

[quick wind]

that divides to -6.

[normal frigate]

were trying to get rid of the x?

like single it out

from the number

[quick wind]

no we're just using -b/2a to find the maximum

[normal frigate]

im confused thhen

how should this look on paper?

[quick wind]

like how u wrote it down in ur notes

[quick wind]

theyre clear enough for the examiner

[normal frigate]

like thos

this or

get rid of the -2x<2

[quick wind]

oh no im sorry

u have to do -b/2a separately

like we have the equation in the form we want

now dont touch it

just take the coefficients a, and b from the equation

to calculate -b/2a

and we have the x coordinate for our maxmimum/vertex which is -6.

u ok so far?

[quick wind]

ik this is a lot of info to handle

[normal frigate]

wait is this better?

[quick wind]

im sorry i should rephrase again

[normal frigate]

thats how the notes are no?

[quick wind]

expand the equation into ax^2 +bx +c =0

wait hold on

lemme see

[normal frigate]

o no dont worry abt the =0 yet

just trying to find H first

and K

H comes first tho

we can set it equal to 0 later in the equation no?

[quick wind]

omg h is actually that easy :/

im so dumb

u know the (x+6) part yeah?

[normal frigate]

yea?

[quick wind]

make it equal 0, thats the highest the y value can go

so u get x=-6.

[normal frigate]

wait what

[quick wind]

we can derive it from somewhere but icbb to do it at this time of hour sorry

lets move on for now

[normal frigate]

??

this??

[quick wind]

because

if x is any other value

the -2 would affect the square

making it a negative

and the -4 at the end makes it even smaller

[normal frigate]

wait can u write down where we are now?

[quick wind]

making the inside bracket 0

[normal frigate]

because how can one make H= -6/-4

they go into common factors

but cant be distrubuted

like

they dont go into eachother

[quick wind]

no no no h is -6

the x we're finding equals h

now we're gonna find k by subbing in x=-6

then the bracket becomes 0

-2 times 0 is 0, 0-4 is -4

so k = -4

[normal frigate]

I think we're too worried on explaining it that I'm just getting lost

The Y has no maximum value doesn't matter no?

[quick wind]

if u dont get it u cant do questions like these on ur own thats the thing

[normal frigate]

Or do I gotta incorporate it

Oh

[quick wind]

the maximum value of y is -4, because the maximum value of y is k

and the x coordinate where the maximum value of y is at, is called h

lemme draw the sketch to Q1

[normal frigate]

Oh okay

[quick wind]

something like this

the tip of the roller coaster ride is at (-6,-4) and when it touches the finish line (the x axis) we’re at -76 already

thats the best analogy i can do for graphs

roller coaster rides

😭

i apologize if u still dont get it

[normal frigate]

-76 is a crazy number

😂

I sorta get it

Sorta don't

But -76 is where the y int hits b

[quick wind]

yes

[normal frigate]

Then the top of it

Is (-6,-4)

Okay that's easy

[quick wind]

yes

[normal frigate]

For now

I get that part

[quick wind]

now we need to state the domain and range

domain means the range of x values which are valid

u get me?

which is infinity

because x could be a million a billion trillion or -0.0000001 and u would still get a y value

does that make sense

[normal frigate]

Yes

[quick wind]

now the range is the range of y values which are valid

[normal frigate]

(-inf,+inf)

[quick wind]

yes

we have shown the shape of the graph

the highest y can go is -4, as it is the tippy top of the mountain

but y can go down to infinity as well

so we write the inequality y<-4

or (-inf, -4]

[normal frigate]

Okay since -4 is the highest

That makes sense

[quick wind]

ok i think ur ready to answer domain and range now

those terms are not easy to understand

good job

[normal frigate]

theyre sorta not easy

just grasping the concept

is a little hard

how do I like draw the range?

@quick wind

[quick wind]

u dont

u just state it using an inequality

[normal frigate]

wait the range is (-inf,+inf)?

[quick wind]

that is the domain

the range is (-inf, -4] because the top is -4

inclusive