help-23

[quasi bison]

you open a channel if you yourself need help

[serene star]

Using help-channels to help>>>> using help channels to get help

What a menace to society

[quasi bison]

.close

[serene star]

.close

[safe radish]

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[quasi bison]

let it sit for a few mins and itll release. theres enough channels for everybody.

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[signal sonnet]

can someone help verifying this trig identity

[hazy elbow]

what is the relation between sec(x) and cos(x)?

[signal sonnet]

sec = 1/cosx. ?

[desert inlet]

so what is sec(x)*cos(x)?

[hazy elbow]

Just expand the LHS

[signal sonnet]

bruh mb i just noticed

thanks guys

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[west notch]

I'm currently working on graphing trigonometric functions, and I'm a bit confused on how you actually get the y values since using a calculator gives me a completely wrong answer and I'm not seeing anything in the lecture on how to solve. Could someone explain to me the process of solving y=2sin(π/2) and why it = 2?

[faint raptor]

is your calculator set to degrees or radians

lemme backtrack, do yk what radians are?

[west notch]

yeah i do, and yeah it was set to degrees that was the issue. Was never taught that was even a thing lol thank you

[kindred tulip]

poor calculator givin you 3.14.../2 as a graph lol

[west notch]

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[signal sonnet]

uh this isnt a question but does this look right to u

[signal sonnet]

lol

[obtuse plover]

Yea

[thick sparrow]

Yes, coz you did not wrap the sum with bracket.

[obtuse plover]

$\sqrt {1^2} + 1^2$ is what u have

[flat frigate]

Stephen

[signal sonnet]

was just wondering because i was looking at 45 45 90 triangle

because √1 + √1

anyways

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[mortal thicket]

part b

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[mortal thicket]

<@&286206848099549185>

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[raw grail]

I'm not sure your proof for part (a) is adequate too

here's how you should go about this:

if $x^3+px+q=0$ has the roots $\alpha, \beta, \gamma$ then certainly $(x-\alpha)(x-\beta)(x-\gamma)=x^3+px+q$ , expand out the Lefthand side of this and then you'll get three equations, where all the sum of the coefficients $x^2$ terms on the left have to be equal to 0 because it isn't present on the right hand side, similar the sum of all the $x$ terms have to be equal to p because the right is just $px$ and then the sum of all the constant terms have to be equal to $q$ because it's just $q$ on the right hand side.

[flat frigate]

Blue Guilmon

[raw grail]

part (b) once you've established part (a) and using the equations from part (a) is just using part (a) to do induction for $n>3, n \in \mathbb{Z}$

[flat frigate]

Blue Guilmon

[raw grail]

did this help? @mortal thicket

what to do in part (b) will be more obvious once you have done part (a) correctly

if you need help with how to set up an induction proof let me know

sorry about the typos in my latex I wrote it very fast lol

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[tacit yew]

how would we do this

[worthy hemlock]

You deleted your original post. The channel will abruptly close and possibly lock. (This is irreversible). Please claim a new channel and do NOT delete the first message of any future channel you claim.

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[timid goblet]

Is it 8534/15348

<@&286206848099549185>

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[timber crescent]

how so

[timid goblet]

Wdym

Oh nvm

4125+4409

8534

And the total is 15348

Righ

[timber crescent]

no, it says they're picking out of high school only and some college

and out of that how many people is 50 and above

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[main lynx]

I have a doubt regarding the johansen cointegration test

[main lynx]

There is a bit programming involved

I will attach the code below

import glob
import pandas as pd
import numpy as np
from statsmodels.tsa.vector_ar.vecm import coint_johansen

path = "BNKNIFTY/*.csv"
basket_results = []
for fname in glob.glob(path):
    data = pd.read_csv(fname)
    close_prices = data.iloc[:, 4:7]

    close_prices = close_prices.apply(pd.to_numeric, errors='coerce')
    close_prices.dropna(inplace=True)
    johansen_result = coint_johansen(close_prices, det_order=0, k_ar_diff=1)

    cointegrated = np.greater(johansen_result.lr1, johansen_result.cvt[:, 1]).any()

    if cointegrated:
        basket_results.append((fname, johansen_result.lr1))
        sorted_baskets = sorted(basket_results, key=lambda x: np.max(x[1]), reverse=True)[:5]

for basket in sorted_baskets:
    print(f"Basket: {basket[0]}, Trace Test Statistic: {basket[1]}")

This is what I am trying to do

here I am just comparing the magnitude of the trace statistics with critical value, is that the right approach?

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[main lynx]

<@&286206848099549185>

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[wintry sigil]

Can anyone pls tell me how to solve these two equations

[sacred adder]

you have 4 unknowns and 2 equations so there is no single solution

where are these equations coming from?

[vagrant ravine]

Yeah

We need the whole question

[wintry sigil]

Yes no 7)

I tried doing this

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@wintry sigil Has your question been resolved?

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@wintry sigil Has your question been resolved?

[wintry sigil]

Noone is coming to help

[wise blaze]

Is the answer 30

[wise blaze]

anyway i ll just help

correct me if i made some mistakes

thats complicated so i cant tell it by words

i just show you all the steps

tag me if you dont understand smth

[wintry sigil]

I understood

Thankss

[wise blaze]

no problem

I thought you would ask why -10 is rejected

[wintry sigil]

Because it is negative??

i-

[wise blaze]

No

Real number can be negative

They are DISTINCT real number

[wintry sigil]

So distinct real number cannot be negative

@wise blaze

[burnt nest]

@wintry sigil what is the problem?

[stray mountain]

well

what if I tell u you can never?

[stray mountain]

this is precisely the reason

[wintry sigil]

Mr. Mocha already explained me the problem

[wintry sigil]

Hmmm I understood

[stray mountain]

so which question do u want to solve now?

[wintry sigil]

Just this

What does distinct real number mean

[stray mountain]

oh....do worry about those English words😅

Like,

tell me the answer for x+5=7

[wintry sigil]

2

[stray mountain]

good

now tell me for x^2=9

[wintry sigil]

+3 and -3

[stray mountain]

yes!

you can't just say 3

you also have to say -3

3 and -3

[wintry sigil]

Why did he reject -10 over here

[stray mountain]

is 3 a real no.?

[wintry sigil]

Yes

[stray mountain]

and -3

?

[wintry sigil]

Yes

[stray mountain]

so,

tho both are 3 in size,

• sign makes a huge difference

so they both are not the same

3 and -3 are distinct

[wintry sigil]

OoooO

[stray mountain]

which means, the two solutions of
x^2=9 are real and distinct

but look at this,
x^2=0

there is only one solution

[wintry sigil]

Yes

[stray mountain]

so "distinct" doesn't make any sense here

[wintry sigil]

Hmmm

Thanks for explaining

[stray mountain]

any other questions?

[wintry sigil]

This one

No 7 is the question

[stray mountain]

hm...

oh

oh

that seems quite simple

the question is just asking what are all the possible numbers a+b+c+d can have

[wintry sigil]

Yess he got a+c as 15 or -10

But he rejected -10

Why

[stray mountain]

hm...

hm...

i think things just went quite complicated here

so the reason -10 was rejected I guess,

is that a times c is 25

if a times c is 25, I don't think there are any real numbers a and c such that a + c give -10

but if it it is not necessary for a,b,c and d to be real, then -10 can also be considered

then another possible answer can be -20

but the question says distinct and real

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[grizzled shoal]

Two masses are moving on straight frictionless lines with a distance of "a" from each other. The lines are oriented along the x axis.

[grizzled shoal]

the masses are connected by a spring of constant k such that we get a potential energy:
U=0.5 k (r-l)^2

where r is the distance between the masses and l the rest length of the spring

We introduce center of mass and relative coordinates

i would use:
$q_1=x_2-x_1$ and $q_2=\frac{x_1m_1+x_2m_2}{2}$

[flat frigate]

~Martin

[grizzled shoal]

what i am stuck on is getting the kinetic energy T

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.close

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[slim nebula]

Let $\Omega = {1, 2, 3, 4, 5, 6}$, then every of these families $F_1, F_2, F_3$ is a $\sigma$ - body of the subsets of $\Omega$ set:

1. $F_1 = 2^{\Omega}$
2. $F_2 = {\Omega, \emptyset}$
3. $F_3 = {\Omega, \emptyset, {1}, {2, 3, 4, 5, 6}}$

Can you explain what $2^{\Omega}$ and other F's are?

[flat frigate]

Fegres

[broken spoke]

I am 13 and I suck at math please help me

[peak estuary]

2^Omega is the power set

and well the other Fs are given so I'm not sure what you want to hear?

they are sets whose elements are subsets of Omega

also presumably the word you are looking for is sigma-field or sigma-algebra

[slim nebula]

I don't get it

[final halo]

or event space, if that holds any meaning for you

[peak estuary]

the set of all subsets of Omega

[slim nebula]

Like in 3'rd example
Can Omega be in a subset of itself?

[peak estuary]

no

[slim nebula]

Why is it 2?

[peak estuary]

but it is a subset of itself

each element is either in a subset or not

that gives 2 options

which means that the powerset will have 2^|Omega| many elements

which you can see as the origin of that notation

or otherwise see it as the set of functions Omega->{0,1} where that second set is often just called 2 in set theory

[slim nebula]

That makes sense

[peak estuary]

in general the set of functions A->B is called B^A

[slim nebula]

Is sounds unintuitive

[peak estuary]

why

it fits perfectly the definition of subset

A is a subset of Omega if all elements in A are also in Omega

clearly A=Omega works

[slim nebula]

Now I get it

Thanks!

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[lyric galleon]

i need help with part B of this question i don't know what to do with this integration

[glass carbon]

IBP

[lyric galleon]

hello

[glass carbon]

hi

[lyric galleon]

as this ln x is in all brackets squared we cant bring the 2 to the front right?

[glass carbon]

that's true, we can't

[lyric galleon]

i tried doing integration by parts but i didnt understand how to do it

[glass carbon]

what are your u and v (or f and g)

[lyric galleon]

u = (ln x)²
v = x

[glass carbon]

good

[lyric galleon]

becuase v' is supposed to be 1 right??

[glass carbon]

yes

so what's the result after applying IBP?

[lyric galleon]

i dont know what ibp means

[glass carbon]

Integration By Parts

just a shortcut

[lyric galleon]

i dont know how to differentiate (ln x)²

[glass carbon]

Are you familiar with chain rule?

[lyric galleon]

yes

is that when u use the u subtitution?

[glass carbon]

you can, but it's not necessary (might help)

[lyric galleon]

dy/dx = dy/du * du/dx?

[glass carbon]

ye

so here you can do u = ln(x)

[lyric galleon]

ok i will try it

so it is 2 ln x

so does this make u' = 2 ln x

wait

u also need to multiply with the differential of u

so its 2/x lnx

[glass carbon]

yes

[lyric galleon]

i always forget this step wow

why do we need to multiply by the differential?

[glass carbon]

in other words
y = (ln(x))^2 = u^2
u = ln(x)
hence:
dy/du = 2u = 2ln(x)
du/dx = 1/x
dy/du * du/dx = 2ln(x) * 1/x = 2/x ln(x)

Idk if it makes sense?

[lyric galleon]

yes it does

[glass carbon]

that's basically what chain rule says

[lyric galleon]

so when i put it in by parts i get this

x(ln x)² - ∫ 2 lnx dx

[glass carbon]

yeah

I guess you can proceed?

[lyric galleon]

and we can factor out the 2

and integrating ln x we get x ln x - x??

[glass carbon]

sure

[lyric galleon]

these do come with limits

thank you

.close

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[red prism]

hey help in french please

[wheat cave]

que

[lean otter]

vous pouvez simplement utiliser la traduction

[red prism]

tu parles français ?

c'est plus simple pour moi de communiquer en français

[red prism]

?

[lean otter]

alors parler anglais?

[red prism]

je ne parles pas anglais

[lean otter]

Je pensais que tu avais dit que c'était plus facile en anglais pour toi ?

[red prism]

j'ai souvent des personnes qui m'aident en anglais donc j'espere tomber sur ces personnes, les personnes qui ne peuvent pas convenir a mes besoin en maths hors français je les invite a ne pas poluer mon salon merci.

[lean otter]

Ah laisse tomber

[red prism]

mmmdrr mais tu parles français du coup ??

il me faut vraiment de l'aide en urgence

[lean otter]

Quelle est ta question?

[red prism]

en gros c'est sur les fonction composé et matrices jacobienne ça te dit qlq chose ?

[hot thistle]

nous travaillons mieux si vous pouvez nous poser une question plus concrète

[red prism]

j'ai une fonction f(x,y)=(x+4y^4, y-3x²,2x²-3y)

et une autre fonction g(x,y,z)= 2xy-3x-3z

et h= g °f = g [f]

attendez c'est plus simple comme ça

j'ai calculer la matrice jacobienne

[hot thistle]

qu'est-ce que vous obtenez

[red prism]

--

je ne comprend pas comment on a obtenu l'encadré rouge

[hot thistle]

savez-vous ce qu'est une dérivée partielle

[red prism]

oui

[hot thistle]

ils ont fait $\nabla g = \langle \pdv{g}{x}, \pdv{g}{y}, \pdv{g}{z}\rangle$

[flat frigate]

maximo

[red prism]

ahhhhh okkk

purée jsuis bete

c'et vrai

merci bcp

[hot thistle]

pas de probleme

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[lean otter]

How do i convert both of these formulas i just dont get it (if you could answer it in dutch it would be nice)

[lean otter]

Another question how do i write the right-hand side as a fraction and convert it

Like what is 3+x

My brain is just dying atm

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

Can anyone js help

[vague frost]

wdym by convert ?

[lean otter]

Simplify

Reduce

[vague frost]

well for a you can expand the (-3a)^3

and then factor

[lean otter]

Isnt a -27a^3 - 2a^2

[vague frost]

ye

[lean otter]

I just dont know anything abt math i suck at it and i have a test tmrw

But i cant find the answers to these questions anywhere

Cuz like what is 3+x

If you dont even have the value of x how can u know

[vague frost]

x is any value, its a variable

it can be -246 or 65 or 36/87

if the values are included in the domain obviously

[lean otter]

But if they arent

[vague frost]

then x cant be those values

[lean otter]

I just do 18+x if i multiply the 6x3

[vague frost]

for b ?

[lean otter]

Yes

[vague frost]

you distribute the 6

because its 6*(3+x)

[lean otter]

What

[vague frost]

^

[lean otter]

Ye but

Then u get

18+x

For the bottom 12x

[vague frost]

when u multiply 2 fractions, you have to separate the things with + and -

[vague frost]

no, 18+6x

[vague frost]

yes

you can also cross simplify the 6 in the numerator and the 12 in the denominator

[lean otter]

O

Alr

So the answer is 18 top 0,5x bottom

[vague frost]

no no

on top is 3+x

and botton is 2x

[lean otter]

Im just accepting the fact that im boutta fail that test tmrw

[vague frost]

rip

[lean otter]

The 6 just disappears

And 12x turns into 2x

In a magical way

Wtf

[vague frost]

because its 6/12

and u divise both the bottom and top by 6

it gives 1/2

[lean otter]

I get it

You cross multiply them

[vague frost]

yes

[lean otter]

But instead of multiplying

You divide them

[vague frost]

exactly

see ull be fine for tmrw

[lean otter]

Is that even allowed

In the math rules

[lean otter]

I hope so lmao

[lean otter]

Cuz i would just end with 72x

[vague frost]

well if it helps you to see it like this then yes

but u dont multiply top and bottom together

[lean otter]

I see it like this

But we always have to multiply them

But if i just want the bottom

I can divide

Upper left and down right

[vague frost]

no no

thats for addition in between

here you multiply

so you multiply the top with the top

and the bottom with the bottom

[lean otter]

Mhm

[vague frost]

if its + or - you cross

[lean otter]

Okay so cuz of the 3+x

Of allowed to divide the 6 and 12

[vague frost]

you should see them as implicit paratheses

like

[lean otter]

What

[vague frost]

(6)/(x)

[hardy wedge]

this is for when you are dividing

[vague frost]

*(3+x)/(12)

[lean otter]

Alr

[lean otter]

O

[hardy wedge]

$\frac{a}{b} : \frac{c}{d} = \frac{a}{b} \times \frac {d}{c} = \frac{ad}{bc}$

[flat frigate]

fedeCreeper

[hardy wedge]

this is what you were getting confused with I believe

[lean otter]

But

Arent you supposed

To multiply top x top and bottom x bottom

But what i dont understand is

How do i multiply the 6 with 3+x

And after

Simplify it

[vague frost]

if its a multiplication in the middle of the fractions

[hardy wedge]

could you translate the problem btw?

[lean otter]

write the right-hand side as a fraction and simplify it

For this one i dont get question b and it says “simplify the following formulas”

Its 2 am for me rn and i gotta get up at 6:30 for school but i cant sleep cuz i just cant fix these math problems (there for a grade tmrw)

[vague frost]

ok so for b, expand the (3a)^2 and (-3ab)^2

[lean otter]

9a^2 and -9a^2b^2

Right

[vague frost]

theres no -

[lean otter]

There is

Right

[vague frost]

no

[lean otter]

Huh

[vague frost]

not for the bottom

[lean otter]

-3

[vague frost]

-3*-3

is 9

[lean otter]

OO

sh mb

[vague frost]

np

[lean otter]

I tried to do it in my head

Okay so we got that

What do u with the -b^2

[vague frost]

u multiply it with the 9a^2 at the top

and you can simplify with the bottom

[lean otter]

How can u multiply b with 9

Do u just get

9b

[vague frost]

-9a^2b^2

[lean otter]

A^2b^2

[vague frost]

dont forget the -

[lean otter]

Huh

9 just says 9

But

Because it multiplied

With the minus b

[vague frost]

u multiply it with -b^2

[lean otter]

It turns into a minus

9*-b^2 = -9

[vague frost]

yes

*a^2

[lean otter]

Yo

I didnt know u could just multiply em

I asked a diff question in a dutch server and that dude is a math genius

But he was so shit at explaining

I asked a question

He asked me

Do u know what u need to do

So i said obv no

Otherwise i wouldnt ask it

But ye

[vague frost]

¯_(ツ)_/¯

explaining is hard

im also not the best but im trying to get better at it

[lean otter]

You’re good at it what do u study

[lean otter]

Na he was just too lazy to explain it to me cuz its easy as f for him

[vague frost]

well im in college rn and im mostly interested in maths tbh

[lean otter]

I just feel like this is way too easy if i look at other ppl there work

[lean otter]

Cool

You trynna become a math teacher?

[vague frost]

thinking about it

but i dont really have much patience

[lean otter]

Oo that sucks

[lean otter]

I mean if u really like math i would do it if i were you you can pass on your passion on other people and maybe let them know that math isnt as bad as everyone says

[vague frost]

true true

its still an idea

eh who knows

[lean otter]

Js do whatever u like snd you’ll end up in the right place lmao

[vague frost]

hopefully

[lean otter]

Do you maybe have time for one last question if u dont its ok

[vague frost]

sure

[lean otter]

Its b: it says you can also wrote A in the form A=py+q ill let u know what that other dude said but i didnt understand his answer

x = 0,2y-2, A = 0,5y -14

[vague frost]

what is p and q ?

[nimble nimbus]

s set the expressions equal to each other and solve for x and y @lean otter

[lean otter]

Idk it says calculate them

Thats the question

[lean otter]

What are the expressions for b

[nimble nimbus]

To solve the system of equations, we can substitute the value of x from Equation 1 into Equation 2

[nimble nimbus]

b^2 - 3b + 5

[lean otter]

What is the value of x

[nimble nimbus]

I can tell you how, but you have to do it yourself, otherwise its cheating

[lean otter]

What

Yo

I dont know anything abt math💀

Its 2:40

[vague frost]

hes right

[nimble nimbus]

substitute the value of x from Equation 1 into Equation 2

[lean otter]

I spend the last 3 hours trying

[vague frost]

i mean they sry

[lean otter]

And my english is bad but ill try

[vague frost]

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[lean otter]

WTF

thats a weird ah rule

[vague frost]

it is what it is

[lean otter]

Alr

Let me think

[nimble nimbus]

simplify and solve for y

when you have the value of y, we can substitute it back into Equation 1 to find the value of x

[lean otter]

The question says that you have to find the value of p and q

But i dont see p and q

Anywhere

In both of the formula’s

I just see a and y

[vague frost]

p and q are any numbers

[nimble nimbus]

yes

[vague frost]

u can see it as

5x

where p is 5

[lean otter]

A=p(5x+10) + q

Then divide

Right

P(x+2)+q

Wtf

No

This is wrong

Let me try again

[vague frost]

ok

[lean otter]

A=0,1y+2x-10

[vague frost]

yes

then you want to get a form A=ay+b

a and b are any numbers, like p and q

rather, to not confuse u, u want A=py+q

and you have another equation u can use to get to this

[lean otter]

Alr

The equation we’re gonna use is

Y=5x+10

[vague frost]

ok

[lean otter]

A=0,1(5x+10)+2x-10

0,02x+1+2x-10

[vague frost]

why ?

[lean otter]

0,1 * 5 x is 0,02 x and 0,1 * 10 is 1

[vague frost]

0,1*5 is 0,5

and you are in terms of x right now

the question wants in terms of y

A=py+q

[lean otter]

Damn

But

[vague frost]

you had the right idea

[lean otter]

I cant even

Use the equation then

[vague frost]

but the variable change was wrong

[lean otter]

Cuz its gonna remove the y

[vague frost]

well what if instead of replacing y

you find a equation

x=..

?

[lean otter]

How do i find out what x is

[vague frost]

y=5x+10

use this

[lean otter]

Alr

I get it

You divide all by 5

Which equals

X=0,2y+2

[vague frost]

yes

but i suggest you first do -10 on both sides

[lean otter]

Wdym

[vague frost]

for me its easier because its more methodic

but if u can divide first

then do -2

its fine

[lean otter]

Alr

So

A= 0,1y+2((0,2y+2)-5)?

[vague frost]

looks fine to me

you can then simplify

[lean otter]

How do i solve it

2 times 0,2y and 2 times 2 and 2 time -5

[vague frost]

right

you can also simplify inside the brackets first

[lean otter]

How

[vague frost]

(0,2y +2 -5)

[lean otter]

O

[vague frost]

but applying the *2 is still good

[lean otter]

Alr

[vague frost]

youre almost done

[lean otter]

0,1y+0,4y+4-5

[vague frost]

wait wait

[vague frost]

it should be -2 there

not +2

[lean otter]

Huh

Fr?

[vague frost]

y=5x+10, y-10=5x , y/5 -2=x

i completely overlook that -

[vague frost]

so this is (0,2y -2 -5)

[lean otter]

How is it minus if you divide it it comes out plus

[vague frost]

yes but you want in terms of x

so this y=5x+10

you can do -10 on the left and on the right

to get y-10=5x

right ?

[lean otter]

Oo

Ik

Cuz if a number jumps to the other side it becomes the opposite of what it was on the old side

So plus becomes negative

[vague frost]

yes

[lean otter]

Negative plus

[vague frost]

yes yes

[lean otter]

Alr

So

0,2y-2

[vague frost]

yes

[lean otter]

A=0,5y+14

[vague frost]

+14 ?

[lean otter]

He was right

O

Minus

[vague frost]

yep

so here

p is -0,5

and q is -14

[lean otter]

Mhm

Wow

[vague frost]

good job

[lean otter]

Ye thanks

U too for explaining

You got any tips

[vague frost]

glad i could help

[lean otter]

For my text tmrw

[vague frost]

uh

stay calm, dont worry and stay methodic

do things step by step

[lean otter]

Whats methodic

[vague frost]

^ basically

[lean otter]

O

Alr

[vague frost]

relook ur work and avoid making small mistakes

like forgetting a -

or sum annoying like that

[lean otter]

Ye

True

Alr imma still try to get some sleep lmfao

[vague frost]

alr gn man

gl for tmrw

u got this

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[hazy crest]

If (x+h)^2=x^2+88x+y^2, then what does k=

[tulip niche]

Y=h?

[thin bridge]

insufficient info

[twilit spindle]

there's no k in the original expression?

[hazy crest]

My bad

Wrote it completely wrong

[twilit spindle]

looks like it lmao

[hazy crest]

If (x+h)^2=x^2+88x+h^2, then what does h=

[twilit spindle]

first try expanding (x+h)^2

see if anything cancels nicely :))

then Bob's your Uncle!

[hazy crest]

The x^2

[twilit spindle]

but something else does

[hazy crest]

H^2

[twilit spindle]

yes but expand (x+h)^2

[hazy crest]

X^2+xh+xh+h^2

[twilit spindle]

h 👀

there we go :))

[hazy crest]

Keep messing up the variables

[twilit spindle]

ok now we set that equal to our other guy and we get x^2+2xh+h^2=x^2+88x+h^2

what do you notice cancelling out?

[hazy crest]

X^2 and h^2

[twilit spindle]

yep!

now what does that leave us?

[hazy crest]

2xh=88x

[twilit spindle]

now Bob's your Uncle!

[hazy crest]

Ohhh. I see it. K =44. I couldn’t see the x canceling out. Thank you!

[hardy wedge]

well…

I’d argue that we still have insufficient information

because if x is 0, h can be anything

[twilit spindle]

but x is a variable it can be anything

all the x's cancal out when your solving for h

[hardy wedge]

of course, but we can’t divide by x unless we know x is not 0

otherwise we’re losing solutions

so what we could do is provide an answer for x different to 0 and x equal to 0

for x different to 0, h=44
otherwise, h can be anything

[twilit spindle]

Bro is doing Alg I 💀🙏 it's not that deep but yes I agree in normal circumstances but get the basics down before considering the other cases

so I agree but i don't my mans St3phen needs to worry abt that rn

emphasis on the "rn"

[hardy wedge]

no, of course not, but it’s not a good habit to divide by variables unless you know what you’re doing

[hazy crest]

Just act prep

I think it’s assumed it can’t be 0

[twilit spindle]

ofc but that practice comes when Fundamental Theorem of Algebra comes in and students learn abt that stuff

[hardy wedge]

it’s just a very specific case though, if we just assume it’s not 0 like you said, you’re right

[hazy crest]

I’ve got a few more questions if anyone cares to hello further

[twilit spindle]

sure :))

[twilit spindle]

yea I think they'll prob have the instructions x!=0 or smthn of similar nature

but good point nonetheless!

[hazy crest]

Thx. On a typical day at limestone college, 3/5 of all students ride a bicycle to class. Among the rest of the students,1/3 ride the bus and 1/6 walk. On a typical day, what fraction of the students ride the bus to class?

[twilit spindle]

so do you agree that 100% of the students exist?

[hazy crest]

Yes

[twilit spindle]

ok so that is 5/5

[hardy wedge]

suddenly philosophical

[twilit spindle]

if 3/5 of them bike then how many do not bike?

[hazy crest]

2/5

[twilit spindle]

fr ‼️😩

[twilit spindle]

now those are the remaining students now how many of those students ride the bus in the instructions?

[hazy crest]

1/3. So multiplication?

[twilit spindle]

yep :))

[hazy crest]

Okay so 2/15

Great. Thanks

[twilit spindle]

yw!

[hazy crest]

Last question: At 12 midnight the center of a hurricane is 360 miles from the coast of Miami, as shown in the figure below. The hurricane has an approximate radius of 120 miles and is currently approaching the Miami area at 30 miles per hour. If the hurricane keeps its current conditions what time, will the the leading edge of the hurricane first reach Miami

[hardy wedge]

can you show the figure?

[twilit spindle]

think about how many 30 miles chunks are in between the coast and the edge of the hurricane

[hazy crest]

12?

[twilit spindle]

so how many hours?

if it travels 30 miles in an hour

[hardy wedge]

that’s actually not right

since it’s the centre of the hurricane that’s 12 chunks apart

not the edge

[twilit spindle]

oh shoot

yea I didn't read the question

[hardy wedge]

first we need to find how far away the edge is

[twilit spindle]

always read directions on ACT

so the radius of the hurricane is 120mi right?

[hazy crest]

Yep

[twilit spindle]

distance from center of coast is 360mi right?

[hazy crest]

Yeah

[twilit spindle]

so what is the distance from the edge of the hurricane to the coast?

[hazy crest]

120?

[twilit spindle]

radius is 120, diameter is 240

[hardy wedge]

ahhhh i need to practice arithmetic

that sounded right in my head

[hazy crest]

Ahh I see it now

[twilit spindle]

back to basics huh I need to read directions better and you need arithmetic help 😂

[hazy crest]

so 240

[hardy wedge]

yeah I check additions on my calculator even if I’m completely sure they’re right 😭

[twilit spindle]

now how many 30mile chunks are there?

[hazy crest]

8

[twilit spindle]

dude on my BC calc test I had to make sure I was doing my simplifying right for the definite integrals 💀

just had to make sure 5-3 is still 2

[hardy wedge]

IKR maybe the universe changed while I wasn’t looking

[twilit spindle]

yes! :)) so how many hours if there are 30 miles chunks

[twilit spindle]

that what I'm saying bruh

just had to make sure Euler didn't come back from the dead and prove 2+2=5 the day before my test smh

[hazy crest]

8 hours

[twilit spindle]

🎉

[hardy wedge]

so at what time will the hurricane get to miami?

[hazy crest]

So then 8am. Got it. I see the Simplification now. Thank you both so much!

[twilit spindle]

yw! Hope you have a good day :))

now I gotta go to bed myself

[hardy wedge]

gn!

[hazy crest]

.close

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[fallen hound]

hi, can someone explain how to do this? i dont understand why the answer is 1? can someone explain the process into explaining something in terms of months when the original is in years?

[rigid inlet]

Two interest rates are equivalent if they earn the same amount of interest over the same amount of time

So if the annual interest rate is 3% (hence the 1.03), what amount compounded monthly also earns 3% after 1 year?

[fallen hound]

Ohh i see

but what distinguishes the difference between 1 and 2?

[rigid inlet]

1 uses the monthly interest rate, 2 uses the annual

After 1 year, 1 would have earned 3% interest whereas 2 would've earned

,calc 1.03^12 - 1

[flat frigate]

Result:

0.42576088684618

[rigid inlet]

42.5% interest

[fallen hound]

ty

.close

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[safe radish]

Channel closed

Closed due to the original message being deleted

[lean otter]

Woops

[toxic stratus]

[safe radish]

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[mint veldt]

Could someone check my work here?

[mint veldt]

I'm pretty confident that I set up everything correctly

[safe radish]

@mint veldt Has your question been resolved?

[mint veldt]

.close

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[mint quarry]

hm so according to this the third step, while solving a quad. equation we add the square of half of the x coeff on both sides and

[mint quarry]

while solving this

he gets 9/16 instead of 9/4

[quasi bison]

yeah

(3/2)/2 = 3/4

and squaring that gives 9/16

[mint quarry]

Oehh i see yeah

.close

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[lyric galleon]

how do you find the equation for this graph??

[timber crescent]

since it's quadratic we can let y = ax^2 + bx + c

since, at y-axis, x = 0, 3 = c

now we have y = ax^2 + bx + 3

[lyric galleon]

ok

[timber crescent]

and we can use other information given to find a two equations

and find the values of a and b

[lyric galleon]

we have (90,y) and (120,27)

[timber crescent]

yea, try plugging in those values

try with the one where u know both x and y first

[lyric galleon]

a = 1/150

b = -3/5

c = 3

damn

that was so easy

thank you

i have another question

i used the quotient rule

[timber crescent]

do u know quotient rule

what's the problem

[lyric galleon]

and im up to the point where i got ( 4√x + 2x )/ ( 2√x )

i dont know what to do after this

i dont even know if this is right

[timber crescent]

can u show ur working

[lyric galleon]

so im at ( 2 + 2√x ) / (4 + 4√x + x)

my handwriting is so bad wtf 💀

[timber crescent]

give me a sec

im outside rn, lemme find a place to work it out

[lyric galleon]

i think ive made a mistake somehwere

[timber crescent]

mine's worse dw

[lyric galleon]

I HAVE A MATHS EXAM TOMORROW AND IM FAILING WTF

[timber crescent]

,w derivate (x-4)/(2+x^0.5)

[flat frigate]

Results provided by WolframAlpha

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Requested by shik#9660

[lyric galleon]

*cries*

the ( x - 4 ) is the dfference of two squares 💀

and 2 + √x cancelled out with 2 + √x 💀

leaving you with √x - 2 💀

that differentiates to 1/2√x 💀

[timber crescent]

haha right

didnt see that either

[timber crescent]

are you by chance answering igcse

[lyric galleon]

this is A-Level Maths

[timber crescent]

i see

[lyric galleon]

its tomorrow

and i cant even recognise a difference of two squares

[timber crescent]

i have a math exam tmr as well

[lyric galleon]

alevel?

igcse

[timber crescent]

nah o level

[lyric galleon]

o level 💀

cool

good luck

we are done here

[timber crescent]

yea u too

[lyric galleon]

thanks

.close

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[wet cairn]

?

[timber crescent]

#❓how-to-get-help

[safe radish]

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>.
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[cold steppe]

How do i do this?

[lean otter]

3rd law

[cold steppe]

yes but i dont get how it relates

[lean otter]

do u know the 3rd law?

[cold steppe]

how does the equal and opposite reaction make it so that the force is equal?

I thought it was 2nd law with f = ma

and that the force would be double

[lean otter]

m and a varry but f is equal and opposite

specificly f1 = -f2

[lime void]

I squared is -1, I cubed is negative i and I to the fourth power is 1

Then they repeat so I to the fifth is equal to I

[cold steppe]

huh?

[cold steppe]

but if the 10kg objects pushed the 5kg object wouldnt the 5kg object just be pushed back

[lime void]

All action reaction forces are equal

[lean otter]

yes

[cold steppe]

and the 10kg would move forward

[lime void]

The movement is ineqial due to the different masses

[cold steppe]

wouldnt that mean the net force would be forward

and therefore theres a difference in forces

and its not equal

[lean otter]

no

[lime void]

No all pairs of forces are equal

[lean otter]

you are thinking of acceleration, which is not exactly the same

[lime void]

But because of Newton’s second law where acceleration depends on mass the movement of objects is not equal

[cold steppe]

so the magnitude of forces is the same but the reason that the 5kg object moves backwards is beacuse of the varying masses and acceleration?

[lean otter]

alos moving in one direction doesnt mean that the force point in the same direction

[lime void]

Yes

Also momentum plays a role but idk if u have learned that yet

[cold steppe]

Whats that

[lime void]

Yeah basically momentum is equal to mass times velocity and it is always conserved in a collision

If ur taking a physics course you will learn about that later so I wouldn’t worry

About the concept now

But it’s the law that dictates how objects move after collisions

[cold steppe]

oh

Also for this question are the multiple choice answers not displaying the correct answer

[lean otter]

imagine u throw a ball in the air, the momentum/velocity is pointed up, but the force(gravity) is pointed down, so direction of movement doesnt indicate force

[cold steppe]

does the upward force of the ball remain the same even though its falling down

[lime void]

In the air the only force is gravity

Which is always down

[cold steppe]

isnt there like wind resistance or somethin

[lime void]

Yes

U don’t learn that until later physics classes cause it involves calc

For now assume no resistance

[lean otter]

if u consider drag its up but anyways

[cold steppe]

how abt this

[lime void]

This is why objects fall down

[cold steppe]

so does gravity kill the upward force of a ball thats thrown in the air

[lean otter]

what did u get?

[cold steppe]

33

[lean otter]

how did u get it

[lime void]

That’s the thing

[cold steppe]

using the suvat

[lime void]

Once the ball leaves ur hand

There is no upward force

Only grav

[cold steppe]

oh 💀

[lime void]

The ball has initial velocity

Upwards bc u threw it

[cold steppe]

and its on a constant deceleartaion?

[lime void]

Yes

[lime void]

I also get 33

So maybe the choice are wrong

[cold steppe]

so in the force diagrams there would be no upward force shown in the net force of the ball?

[lime void]

Yes that’s right

Cause only thing impacting movement is grav once ball is in the air

[cold steppe]

and then the gravity gets balanced out by an equal force madeby the ground?

[lime void]

?

[cold steppe]

the gravity pulling on the ball

is it balanced out when the ball hits the ground

the equal opposite forcE?

[lime void]

Yes

That balancing force is called the normal force

[lean otter]

same got 33

[cold steppe]

w

[cold steppe]

so sometimes when a ball sinks into the ground why is that

[ionic meteor]

hello

[cold steppe]

u make the help things

[cold steppe]

or like how an indent can be made in the ground if something is heavy enough

[ionic meteor]

was dat

[noble root]

bruh

[lime void]

Those are due to other forces that are outside the scope of the physics u are doing right now

They depend on the material of the floor amongst other things

In ur class those forces will be equal

[ionic meteor]

could you please help me with this question?

[noble root]

i think u open a help ticket idk

[cold steppe]

its fine

i need help with that one anyway

[noble root]

wait whered u get the book

[ionic meteor]

me and eugeen are peers and are ahving trouble with this

the train motion is going left but with the ball, is it swaying right as it resists the change in motion?

so it is in a constant state of inertia?

[noble root]

wait i think i got this

ok so

its clearly

inertia right

so the train must have stopped

as in like

[cold steppe]

it hasnt

[noble root]

it was moving to the right

then ti stopped

[cold steppe]

it didnt stop

[noble root]

so the thimngy moves

[cold steppe]

its in a constant motion

[noble root]

how do u know

[cold steppe]

its asking what constant motion its moving

[noble root]

"describe the train movement that leads to the observation above"

[noble root]

then its on an angle or smth

[ionic meteor]

My apologies, but I was hoping someone else other than you may answer this question

[noble root]

coz that owuld only happen with wind resistance

[cold steppe]

i dont think it would be a sudden stop

[cold steppe]

it says its going on a horizontal flat line

[noble root]

coz no wind res inside a carriage no?

[ionic meteor]

can you please shut your mouth

[cold steppe]

💀

.close

[safe radish]

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