help-23

[lean otter]

Bro i m french il so difficult to understand

😂

[bright carbon]

okay

[ember sphinx]

fixed point iteration method

heard of that?

[lean otter]

I am

[bright carbon]

nope

[ember sphinx]

Than what iterative methods have u learnt

ive glanced at the spec and its not even specific enough

it just says

'Students should be able to solve equations using simple iterative methods'

[lean otter]

Sure

[ember sphinx]

heres what i found online

try this

Rewrite the equation in the form x = g(x), where g(x) is a rearrangement of the equation that isolates x on one side.
Start with an initial guess value for x, let's call it x₀.
Calculate the next approximation, x₁, by evaluating the function g(x) at the previous guess value: x₁ = g(x₀).
Repeat step 3, using the updated guess value, until you reach a desired level of precision or until the iterations converge.
The final value of x obtained through the iterations will be an approximation of the solution to the equation.

[bright carbon]

I think I have learnt fixed point iteration method

[ember sphinx]

but we cant siolate x

u learnt that

[bright carbon]

why not?

I isolated x here

[ember sphinx]

Ahh ok

I was thinking of having no x's on the other side

but it says x=g(x)

yea try that

see if it gets you anywhere

and we got desmos too double check

[fierce umbra]

hi what is this channel for

can i ask any math questions in this??

[ember sphinx]

i hate people who cant read

[bright carbon]

LOL

[fierce umbra]

same bruh

so annoying

[bright carbon]

read the #❓how-to-get-help channel

[fierce umbra]

ty

[bright carbon]

.close

[safe radish]

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[zenith dove]

Does any1 have any idea?

[safe radish]

@zenith dove Has your question been resolved?

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✅

[tardy mango]

steepness represents rate of change, which in this case is the rate at which the cost is changing (same as the ||cost per minute||)

y intercept represents where x=0 (same as when ||minutes = 0 -> initial fee||)

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@zenith dove Has your question been resolved?

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[surreal echo]

could someone tell me why e) is arithmetic?

[surreal echo]

i get that it’s -9 each time but why does it have the plus symbol

like shouldn’t it be 31-22-13-4

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[worthy hemlock]

What exactly are you confused about?

[twilit spindle]

this about how an arc is a fraction of the circumference of a circle

the total circle is 2pi

hence the ratio of how much circle we are covering is theta/2pi

use that with the first intuition and an arc is a fraction of our circumference and Bob's your Uncle! :))

[winter pond]

tysm

.close

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[twilit spindle]

yw!

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[patent mortar]

Can somone help with d pls I don't know which rule to use here

[plucky elk]

,tex .log rules

[flat frigate]

rie.mann

[patent mortar]

there's a square in there so what to do in that

because isn't it different from power rule

[plucky elk]

Apply one of these

[hard crest]

squares are powers, not sure why you think they aren't

[patent mortar]

yes but we're squaring the whole thing

not only x right?

can i use power rule for that?

[hard crest]

no, but look at the next term

[split ether]

You leave (logx)^2 as it is

[patent mortar]

yea that one i can do 10log2x

[split ether]

Yes

So now it's $2(\log_2{x})^2 + 10\log_2{x} - 72 = 0$

[flat frigate]

alonelybean

[patent mortar]

oh we can sub in

[split ether]

Does this not look like a quadratic equation?

Yeah

[patent mortar]

x=log2x

wow

[split ether]

[hard crest]

use a different variable

[split ether]

Pick a new variable

[hard crest]

like L or y or something

[patent mortar]

y

[split ether]

So, you basically need to solve just $y^2 + 5y - 36 = 0$

[flat frigate]

alonelybean

[split ether]

Can you do that?

[patent mortar]

4or -9

we ignore negative in log righ?

[hard crest]

well... log can't take a negative number as input

[split ether]

No, a logarithm can freely be a negative number

[patent mortar]

oh

[split ether]

So you consider both of the cases y = 4 and y = -9

[patent mortar]

oh yes i got it now

thanks (i got 16 and 1/512)

.close

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[blazing roost]

dude

[blazing roost]

pls somebody help me in trigonometry

facing many problems in approach

[pseudo scroll]

do you have a question

[blazing roost]

have a lots

so i want somebody to tell the approach

10 or 5 mins spent will be appriciated

😭

[hard crest]

my approach: have handy or be able to draw the graphs of sin(x), cos(x), and tan(x), and know what a unit circle is and does

[blazing roost]

that does not work

wait

let me send you questions

[pseudo scroll]

how many

[pseudo scroll]

Quite a few indeed

[pseudo scroll]

Which one would you like help with

[blazing roost]

lets start with start

wait

let me send clear one

rotate it pls

[pseudo scroll]

,rotate

[blazing roost]

2nd

[pseudo scroll]

Make an equation purely in terms of $\cos^2 x$

[flat frigate]

neonperseus

[hard crest]

,tex .trig rules

[flat frigate]

Hayley
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hard crest]

[pseudo scroll]

@plucky elk another one

[blazing roost]

you mean the first term

[pseudo scroll]

I mean the entire equation

Can you write cos 2x in terms of cos^2 x

[blazing roost]

yes

2cos ^2 x -1

[hard crest]

,tex .rocket trig

[pseudo scroll]

What about tan^2 x

[flat frigate]

Hayley

[blazing roost]

how

[pseudo scroll]

Look at the third identity under Pythagoras

[blazing roost]

oh my good

yes

[pseudo scroll]

$$\cos^2 x = u$$
$$5\left ( \frac 1u - 1 - u \right ) = 2(2u - 1) + 9$$

[flat frigate]

neonperseus

[blazing roost]

oh yeah

[pseudo scroll]

You can probably solve it from here

[blazing roost]

yes

then ill get the value of

cos x

and then apply cos (2)2x

2 times

and get the ans?

[pseudo scroll]

Yeah seems about right

There might be something better you can do for cos 4x

[blazing roost]

what

!

[pseudo scroll]

Nvm

I was thinking of something else

Write cos 4x in terms of cos 2x and then cos 2x in terms of cos x

You have the value for that

[hard crest]

i mean there is a quad-angle formula but it's easy enough to just apply the double angle formula twice

[blazing roost]

but how did instantly told me to convert it terms of cos ^2 x

[blazing roost]

teacher did not teach quad formula

[hard crest]

almost no one does

[pseudo scroll]

because that's the simplest possible common trig function you can convert everything to

[hard crest]

it's hard to prove without invoking complex numbers

[blazing roost]

hmm ok i see

[pseudo scroll]

it's just something you gain over time through intuition

[blazing roost]

i g you are right

moving on to the 3rd

q

@pseudo scroll sir

[blazing roost]

.

[pseudo scroll]

If you know tan A + tan B and tan A * tan B then can you find tan (A + B)

using the formula

[blazing roost]

ok

[pseudo scroll]

After you find tan (A + B), just find cos (A + B) and sin (A + B)

[pseudo scroll]

It was a question

NO DON'T

[blazing roost]

i saw now

only summ of roots and product

right

[pseudo scroll]

yes exactly

Find the value of tan(A + B)

[blazing roost]

product of tans is 25/3

sum of tans 10/3

[pseudo scroll]

yes

[blazing roost]

tan A+B )= 35 / -241

[pseudo scroll]

Uh

,w 1 - 250/3

[flat frigate]

Results provided by WolframAlpha

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Requested by neonperseus#0

[blazing roost]

OK

SORRY

[pseudo scroll]

what

[blazing roost]

sorry

it was wrong

[pseudo scroll]

,w (25/3 + 10/3)/(1 - 250/3)

[flat frigate]

Results provided by WolframAlpha

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Requested by neonperseus#0

[pseudo scroll]

Now you need to find the sine and cosine with this

Have fun

[blazing roost]

its 10/-22

[pseudo scroll]

What is

[blazing roost]

-5/11

[blazing roost]

tan a+b

[pseudo scroll]

The product is -25/3 smh

[blazing roost]

omg i m so dumb

[pseudo scroll]

I did something completely different

,w (10/3)/(1 + 25/3)

[flat frigate]

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Requested by neonperseus#0

[pseudo scroll]

there we go

[blazing roost]

now its right

ya!

[pseudo scroll]

yes so now fine sin and cos

You're done

And I have stuff to do now

[blazing roost]

thanks a lot bro 🫡
\

may god bless people like you

[safe radish]

@blazing roost Has your question been resolved?

[blazing roost]

.close

[safe radish]

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[lean otter]

Let $m_1,m_2,\hdots, m_n$ be pairwise relatively prime integers greater than or equal to 2. Show that if $a \equiv b ; (\map \bmod {m_i})$ for $i = 1,2,\hdots, n$ then $a\equiv b ; (\map \bmod m)$, where $m= m_1 m_2\hdots m_n$

[peak estuary]

chinese remainder theorem

[lean otter]

the question asks specifically to not use the chinese remainder theorem to prove this

[peak estuary]

ok then do it the slow way with euclids lemma

[lean otter]

whats euclid's lemma 😅

i was thinking we can just use prime decomposition? or is that the same thing?

[peak estuary]

or wait? does that work? not sure but would be my first attempt

[devout shale]

euclid's lemma is used to prove FTA, if you haven't already done that

[lean otter]

we proved that using induction, although idk if that was a part of it lol

[devout shale]

poor text IK

[devout shale]

induction or strong induction?

[lean otter]

strong induction is a dumb name, its induction regardless

oop wrong reply

[devout shale]

soooo, strong induction then

XD

yk what I mean though

that's what you did?

then you used Euclid's lemma as a subsidiary probably without proof or ever even realizing it

I think. I'm familiar with that proof of FTA

[lean otter]

yeah

i mean i can just share it lol

what i wrote in my document

wait

[devout shale]

this part

by Euclid's lemma

[lean otter]

texit kinda butchers my overleaf latex but its okay LOL

its readable

[peak estuary]

euclid is needed for the uniqueness

not existence

[lean otter]

ah i see fair enough

[devout shale]

and Bezout

can't forget about him

(yes we can)

[peak estuary]

I always forget the various implications between all those theorems. Also I wonder which of these hold in other rings

[safe radish]

@lean otter Has your question been resolved?

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[gaunt raptor]

I ve to find imtersection point of line and plane is this the right approach?

[rich tree]

,rotate

[long isle]

yo

[gaunt raptor]

yes

<@&286206848099549185>

[rich tree]

To test you could dot product the direction vector and the normal of the plane

If it equals zero then you know for sure they do not intersect

If it does not equal zero then it intersects

But I believe that is the correct method you have shown

[gaunt raptor]

wdym by this?

so there is no intersection between the line and plane so they r parallel?

[rich tree]

If the dot product is equal to zero, lines and planes do not intersect

So they could be parallel yes

[gaunt raptor]

oh and i had another question do you speak french by any chance?

[rich tree]

I do not speak French

Sadly

[gaunt raptor]

so let me try in english then what is the difference between intersection and percing point of line in plane?

[rich tree]

Here is an example from my textbook btw which could help with future questions like the one above

Also if you ever find an infinite value of intersection then the lines and planes are either similar or they form a sheaf

[rich tree]

Piercing point?

[rich tree]

I have never heard of that term in vectors but I would infer that they are the same

[gaunt raptor]

if wont understand but in q 1 it says find intersection point but again on 2 b) it says find peircing point

[gaunt raptor]

for me intersection and percing point are the same

what is breakthought point tho?

[rich tree]

To me all of those 3 terms sound like they should be the same lmao

[gaunt raptor]

yeah i dont get this question do u know any helper who speaks french?

[rich tree]

I have a friend who did half of further maths and speaks French I could ask

[gaunt raptor]

please it would be helpful

[rich tree]

I’ve asked him

I googled piercing point and it appears that it is when a line intersects a plane that is not parallel or on the line

So basically the intersection point

[gaunt raptor]

so how are 1 and 2 b different?

its the same question

[rich tree]

I believe it is because it is making reference to either a different plane or line

So the intersection is different

<@&286206848099549185> anybody French?

Or can speak it?

[raven heart]

euuh oui

t'en es où?

[gaunt raptor]

je demende la difference entre point de percee et intersection

[raven heart]

la même chose je pense

[gaunt raptor]

difference entre question 1 et 2b

[raven heart]

en même temps ils définissent deux plans \alpha

c'est vraiment sketch ton truc

[gaunt raptor]

de plus le 1 il sont parallels donc pas d intersection

je n oublie jamias jai eu 9/20 dans cet eval

[raven heart]

ah c'est les mêmes nvm

[gaunt raptor]

mais ca me tonnerais qu il pose 2x la meme questions

[raven heart]

point de percé je vois pas ce que c'est à part l'intersection droite et plan

oui c'est probablement l'intersection de d' sur alpha

sinon la question a pas de sens

[gaunt raptor]

nn ca dit point de percee de droite d DANS l alpha

donc le dans c un mistere

[raven heart]

je pense que c'est une typo justement

comme il y avait une typo en 2a

d -> d'

[gaunt raptor]

ah c fort possible

[raven heart]

on te donne un point pas sur le plan

trouve la droite qui passe par ce point et perp au plan

[gaunt raptor]

nn le 2 a jai deja fais

[raven heart]

trouve l'endroit où cette droite tape le plan

2b

[gaunt raptor]

mais le 2 b qui pose probleme

[raven heart]

ouais donc c'est quoi ton d' ?

ah c'est la haut ^^

[gaunt raptor]

En haut c le 1

[raven heart]

,rotate

[raven heart]

ok ok

maintenant c'est facile

t'as ton équation paramétrique

[gaunt raptor]

oui

[raven heart]

tu plug juste x, y, z de ta droite dans l'équation du plan

trouves le bon k qui satisfait l'équation du plan

[gaunt raptor]

de d'?

[raven heart]

tu trouves l'intersection

[raven heart]

quelle autre droite en vrai ?

d' oui

[gaunt raptor]

c ecrit d

normalement

[raven heart]

ouais bha j'y crois pas

le prof a déjà fait la typo en 2a

[gaunt raptor]

la meme question se rrepete dans l autre question

[raven heart]

ça serait pas étonnant qu'il ait continué comme ça

[gaunt raptor]

cet question jai trouver parcontre

[raven heart]

pour moi 2b c'est : "Trouver le point de percé de d**'** sur le plan alpha"

comme tu le dis

d ça n'a aucun sens ici

[gaunt raptor]

tu peux voir mon raisonnement de d si c correct ou pas ? commeca on va etre sur que c un typo

vu qu il n a pas d intersectino

[raven heart]

bha aucun point de percé

c'est bien ça le problème

@gaunt raptor

[gaunt raptor]

jsp quoi faire

[raven heart]

de toute façon si le prof pose deux fois la même question il est complètement con

et je vais supposer qu'il est pas con

[gaunt raptor]

c tres bete ca

[raven heart]

donc il pose pas deux fois la même question

[gaunt raptor]

oue soit on est con ou c le prof 😂

[raven heart]

nan mais on va partir du concept que le prof a de la suite dans ses idées

et que c'est juste des putain de typo

[gaunt raptor]

oue je demende a mon pote

[gaunt raptor]

haha

alr ty @raven heart

.close

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[solemn vault]

Hello

[solemn vault]

I'm stuck on b

[flat frigate]

BasuDev

[solemn vault]

So far I've proved this function is injective, how do I proceed to prove its surjective as well?

What I was thinking was....

since our function is injective, that means that for every q > 0, q € Q there's a unique natural numbers.


And our 2nd and 3rd case gives us a unique natural number for every q. And our Co domain is also Natural number that means our range = co-domain. Which basically proves its surjective..

[peak estuary]

how did you find the q with f(q)=108

[solemn vault]

Prime factorisation

108 = 54×2 = 27×2² =2²×3³

[peak estuary]

and then?

oh wait not you

I am asking the op

[flat frigate]

BasuDev

[solemn vault]

??

[peak estuary]

oh you renamed

sry

got confused between channel name and display name

[solemn vault]

Alr

[peak estuary]

ok

so this process you used for n=108

can you also do that for other numbers?

[solemn vault]

Ye for evry natural number I can

Let's say 124

[peak estuary]

I don't need you to actually do it

[solemn vault]

Alr

[peak estuary]

what does it mean for the function to be surjective

[solemn vault]

That their range and co domain must be equal

[peak estuary]

yes. do you have another more direct definition regarding the elements?

[solemn vault]

Nope

There was one which I currently can't recall

[peak estuary]

f:A->B is surjective if for every b in B there is an a in A with f(a)=b

have you seen that one?

[solemn vault]

Hmm 🤔

OK got it

[peak estuary]

what does that definition mean for our situation

[solemn vault]

That for a natural number there's a q

Such that

f(q)=n

[peak estuary]

and can you answer whether such a q exists?

[solemn vault]

Yes ofc they exists

[peak estuary]

and why?

[solemn vault]

Says right here

[peak estuary]

no. that doesn't show it

you need to show that for a fixed n you can find a q with f(q)=n

you found a q for n=108 and you say you can find one for n=124. can you find a q for every n?

[solemn vault]

But if that doesn't says it then how did I found f(q)=108,

I used the last definition

[solemn vault]

Yes

I can

Cuz evey natural number has unique prime factorisation and by the last definition I can..

And second last as well..

[peak estuary]

now write that down properly

[solemn vault]

Well...

Since, from the uniqueness property of arithmetic, every natural number can be written in the form of prine factorization.... function can give us a unique natural number for every q>0, q € Q we can get q for every n....

That's the best I can do...

[peak estuary]

well you need to explain how to find this q

the way you did it for 108 and would do for 124

give an algorithm to find the q

[solemn vault]

Prime factorisation

Well...

Alr

if n as a prime factorisation that with even powers then you multiply the primes

[flat frigate]

BasuDev

[solemn vault]

These are the algo that I came up with

[peak estuary]

you didn't write down q

[solemn vault]

Wher??

[flat frigate]

BasuDev

$$ q = {p_1}^{2r_1}{p_2}^{2r_2}\cdots{p_N}^{2r_N}$$
If your prime factorisation have even power

$$q={p_1}^{2r_1}{p_2}^{2r_2}\cdots{p_N}^{2r_N}{q_1}^{2s_1-1}\cdots{q_m}^{2s_m-1}$$
If your prime factorisation Consists of both even and odd

[peak estuary]

that's not q

thats n

[solemn vault]

Freak

Oh shit

Hold up...

[flat frigate]

BasuDev

[solemn vault]

Now??

I think that it

*that's

[peak estuary]

small typo but yes

[solemn vault]

Ye that 2 ain't there

Alr is that it?? Did I prove its surjective??

[peak estuary]

yes

[safe radish]

@solemn vault Has your question been resolved?

[solemn vault]

Alr thanks for the help mate

Yes it is

Just in time

[safe radish]

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[safe radish]

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[heavy glade]

is this multiplication or composite?

[near cipher]

probably multiplication

"." is also used in multiplication

[heavy glade]

okay tank you

.close

[safe radish]

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[near cipher]

no worries

[safe radish]

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[sand slate]

i dont know where to start, using the pythagorean theorum to find d

[marsh walrus]

its a right triangle, right

[edgy pendant]

You can use the pythagorean theorem two times

[marsh walrus]

so find 2 of the side lengths

[sand slate]

omg i didnt even see that 😭

.close

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[safe radish]

Please don't occupy multiple help channels.

[final halo]

#help-16

.close

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[manic heart]

what would the constant be?

4 = 57
8 = 64
10 = 67.5

[thin bridge]

the question doesn't make any sense

what constant and
none of those equations are true

[subtle tangle]

is this a pattern finding question

[pastel abyss]

if it's a pattern then it's solved

there's no unknown number

[manic heart]

oh

okay thank you

.close

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[safe radish]

@pine dove Has your question been resolved?

[safe radish]

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[pine dove]

I’m so confused on what to do. I genuinely don’t how I’ll be able to calculate the future performance of the company. I’m supposed to make a table like the one I’ve provided. Do I use the most recent financial statements (2021-2022)? Note: I checked TD Bank and I’m unsure which financial statements I have to use. (Also, for the years I’m forecasting, do I use the past data from 5 years ago or just the most recent data?

[pine dove]

<@&286206848099549185>

<@&286206848099549185>

[safe radish]

@pine dove Has your question been resolved?

[pine dove]

<@&286206848099549185>

[pine dove]

<@&286206848099549185>

[pulsar pecan]

This may not be the best server to ask accounting questions on

[safe radish]

@pine dove Has your question been resolved?

[safe radish]

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[gentle zodiac]

setting y to x is legal right (path 3)

[sweet mica]

Yes, taking y=x is a possible path.

[safe radish]

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[gentle zodiac]

thanks

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[safe radish]

@autumn rock Has your question been resolved?

[safe radish]

@autumn rock Has your question been resolved?

[spring glacier]

do you know where to start?

if so, what do you have?

[autumn rock]

i have no clue... i have all the axioms but i dont have a clear outline or approach to solving this

[spring glacier]

can you list the axioms you have?

[autumn rock]

sure

https://media.discordapp.net/attachments/1021137220985438219/1120172976717971476/image1.png

[spring glacier]

use your "golden rule" of and

on p and not q

[autumn rock]

so (p ^ (~q)) = p = (~q) = (p v (~q))

would my next step be the implication rule?

[spring glacier]

we just want to utilize: p and not q ==> p or not q

from that axiom

then we can use 11

rewrite the disjunction in terms of the implication

it should be straightforward from here

[spring glacier]

actually, its better to use de morgan here instead

[autumn rock]

de morgan 2?

[spring glacier]

okay, lets start over,
given
demorgan 1
implication

you are left with one of your axioms

and thus a tautology

in a hilbert system, the strategy is to try to turn as much into conditionals

show me your proof when you write it out

[autumn rock]

yes im doing it right now

(p ^ (~q)) = (p v (~q)) (axiom (10))
(p ^ (~q)) = ~(~p v ~q) (DM)
(p -> q) = (p v (~q)) (Implication)
(p -> q) v (p ^ (~q)) (Eqn (2, 3))

[spring glacier]

i think axiom 10 is saying
A ^ B ==> A v B

because
A ^ B <==> A v B
isnt necessarily true

i suggest something like this

(p -> q) V (p ^ ~q)
(p -> q) V ~(~p V ~~q) DM1
(p -> q) V ~(~p V q) Double ~

[autumn rock]

isnt axiom 10 only true when p = q?

[spring glacier]

i suppose it could be saying that

the lack of () is strange

i think its better to start with what you want to prove, then reduce to axiom, then the rigorous proof is just the same proof, but bottom to top

[spring glacier]

for that reason i wouldnt use axiom 10, since its too strong to say p = q

[autumn rock]

thanks for the help

[spring glacier]

np

[spring glacier]

you do see what to do from here?

[autumn rock]

yes im starting to see a picture here

.close

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[sand condor]

X(3x+1)-3(x+1)=0

[sand condor]

I’m trying to figure out x

Can I simplify it further

[thin bridge]

yes, expand everything

[sand condor]

Not sure how

[thin bridge]

can you expand
x(3x+1)

[sand condor]

No

[thin bridge]

do you know the distributive property?

this is something you would have been taught before quadratic equations

[sand condor]

I know of it

But I simplified from it to there

[thin bridge]

wdym

[thin bridge]

...

so you went backwards

[sand condor]

No

[thin bridge]

expanding
x(3x+1) gets back what you started with
3x^2 + "

etc

[sand condor]

I was doing pq formula but the square root of 43/9 doesent give me accurate x’s

[thin bridge]

also

[fast gazelle]

...wait how did you get from x(3x+1)-9x-3 to x(3x+1)-3(x+1)?

[thin bridge]

-9x-3 isn't -3(x+1)

[sand condor]

Ah true

Do I divide them all 3x+1

[thin bridge]

no

[sand condor]

I’m not sure what to do

[thin bridge]

if you grouped them properly, factor out, not divide

[sand condor]

I can’t factor out

[thin bridge]

I was doing pq formula but the square root of 43/9 doesent give me accurate x’s
you didn't apply pq formula correctly

can you show what you have after fixing the mistake I mentioned

[thin bridge]

"factor out" the common factor, in this case the (3x+1), the same way
you factored 3x^2 +x to x(3x+1)

(this is not the same as dividing)

[sand condor]

I don’t think we can factor it out more

[thin bridge]

and I'm telling you it can
and involves applying exactly the same thing you just applied

[sand condor]

Unless you want me to -x(-3x-1)?

[thin bridge]

overthinking

how would you factorise
pq - pr

[sand condor]

P(q-r)

[thin bridge]

lowercase p but yes

same idea here

view (3x+1) as the common factor p
and the other x and 3 as the q and r

[sand condor]

Yeah so p=1

1(3x+1)

?

[thin bridge]

yeh, p = (3x+1),
I just said that

[sand condor]

Oh

Okay so we have two of the same p

[thin bridge]

?

[sand condor]

?

[thin bridge]

I merely trying to state that factorising what you have is no different from factorising
pq - pr
which you are able to achieve immediately with little or no difficulty

[flat frigate]

ℝamonov

[sand condor]

(3x+1)(x-3)?

No wait that’s wrong

[thin bridge]

it's right, why do you think it's wring

[sand condor]

Because this would multiply the number invidually

[thin bridge]

wdym

[sand condor]

It should be (3x+1)x(x-3)

[thin bridge]

what's with the extra x

[sand condor]

No I’m wrong

Sorry

3x+1=0

X-3=0

3x=-3
/3 both sides

X=-1

No wait

I’m overthinking

3x+1=0

3(-1/3)+1=0

X-3=0 x=3

X=-1/3
X=3

Yeah that should be right thx

.close

[thin bridge]

your work is very disjointed, but yes those values at the end are the solutions to the equation

[safe radish]

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[thin bridge]

as for the pq formula, if applied properly will get you the same result

[sand condor]

I haven’t done math in years

[safe radish]

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[sand condor]

Like 2-3 years

[sand condor]

Yeah I will perfect it soon

.close

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[cobalt acorn]

I don't get that part

<@&286206848099549185>

[marsh walrus]

factor by grouping

its a trick

[cobalt acorn]

How

[lean otter]

It's like when B x x + b
It goes B(x-1)

[cobalt acorn]

I don't get how they got 2x^2-2x-7x+7 = 0 from 2x^2-9x+7 = 0

[lean otter]

They cutted the 9x

To 2x

And 7x

Example 2x + 3x = 5x
= - 5x
= -2x -3x

[cobalt acorn]

But isn't there multiple numbers that add up to 9x why those 2 is what I don't get

[lean otter]

It's like

a x 1 + a x 2
Doesn't both x a
So we gets a out
And we get a(1 +2)

[lean otter]

We cutted it so we can get two numbers hitted by the same one

[cobalt acorn]

What's this factoring called is there a vid on it

I don't get it

@lean otter

[lean otter]

Ur having problems with why we cutted 9 ?

[lean otter]

Example
5x = 3x + 2x
6x = 3x + 3x
Let's say x =1
5 = 3 + 2
6 = 3 + 3
X = 2
5 x 2 = 3x2 + 2x2
10 = 6 + 4

We cutted the 9 in 2 and 7

So we can get
2x² [[[[[- 2x -7x]]]]]] + 7

And bc its 2x²
Its becomes 2x ( x-1)
Not 2( x-1)
Bc it have ²

[safe radish]

@cobalt acorn Has your question been resolved?

[sacred geyser]

where does the square root of 17 come from I got the square root of 3

[safe radish]

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[prime gyro]

Wrong channel

[safe radish]

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[sacred geyser]

Which channel am I suppose to ask ╮(￣▽￣"")╭

[sacred geyser]

So help

I multiply 3 and 51to get square root of 153

[plucky elk]

,calc 3*51

[flat frigate]

Result:

153

[plucky elk]

,calc sqrt(153)

[flat frigate]

Result:

12.369316876853

[nocturne hazel]

Why the d does not belong to Int(A)

sry

[sacred geyser]

Thanks

[nocturne hazel]

OK

[sacred geyser]

Um is that box 4?

Figured it out thank you

[safe radish]

@sacred geyser Has your question been resolved?

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[solemn vault]

Hi

[solemn vault]

This is my solution... and I'm getting 27 as an answer

Is my solution correct?

[safe radish]

@solemn vault Has your question been resolved?

[solemn vault]

Any help pls??

<@&286206848099549185>

I got it

.close

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[mint veldt]

Don't answer the problem please. I'm only interested in understanding the problem. What are A-E for here?

[loud loom]

arent those the answer choices

like this is a multiple choice question?

[mint veldt]

I wasn't sure.

That was my first thought.

I'll try out the provlem and see. Ty for the reassurance.

.close

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[mint veldt]

From my book that I'm reading, I recall that it is often easier to compute the complement of say A than A. I haven't tried to solve this problem yet, but I'm wondering if anyone would say this is a good idea.

[safe radish]

@mint veldt Has your question been resolved?

[tardy mango]

There’s a lot of stuff in the complement tho

So I wouldn’t bother

[hard crest]

just draw the Venn diagram

[mint veldt]

.close

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[tall hare]

there's debate between my goup on f and i, we keep going back and forth on which one is constant and which one is inflection point. I'm thinking that i should be constant and f should be inflection point

[tall hare]

can someone explain why it is or isnt that

[quasi bison]

(f) should be constant and (i) should be...

wait what?

well, ok, no

if we are to refer to the graph, both (f) and (i) should be "constant".

because there are no intervals where the graph of s is a straight line that isnt horizontal.

[tall hare]

how can they both be constant

[hard crest]

I see a lot of diagonal lines

like the immediate neighborhood of t=4

[safe radish]

@tall hare Has your question been resolved?

[tall hare]

can you elaborate

[hard crest]

if a is zero (acceleration is zero), what's happening to velocity?

[tall hare]

it's constant

i think

[hard crest]

yep! and so position will be increasing linearly

(or decreasing linearly, or constant if v happens to be stuck at 0, but the point is it's linear)

I'm not sure what's going on with the graph vis-á-vis this question because there are no regions on the graph where v is negative

[tall hare]

that's why im thinking it's not an inflection point

s that is

[hard crest]

if it's an interval where a is zero then i'd hesitate to call it an inflection point

[tall hare]

they would both just be constant then

right

[hard crest]

well no, v is constant but s could be increasing, decreasing, or constant

they proooobably want "(at an) inflection point" i guess?? but again it's an interval so that's kind of silly of them

[tall hare]

so if it's at an inflection point that would mean s would also be constant

or otherwise the answer is increasing

still a little confused tho

[hard crest]

s is only constant if v is 0

[tall hare]

so it's increasing then

since the function is only either increasing or constant

[hard crest]

yeah ig

[tall hare]

why unsure

[hard crest]

again this graph is weird because e.g. if you look at (b) it talks about "an interval where v is negative" but that doesn't happen in the graph

[tall hare]

yea but it would always be decreasing in that case so i think that's a hypothetical

[hard crest]

yeah that's the conclusion i draw as well

[tall hare]

wait so where on the function is a zero

[tall hare]

would x=2 be one of them

[hard crest]

any time that v is constant, which means that s is going linearly

so like the area around t = 2.5 looks pretty linear to me

[tall hare]

okay so it has to be increasing

because it's a positive constant

v is

for this graph when a=0, v is a positive constant, which means the function is increasing

does that all check out

[hard crest]

v could be constant 0!

and is, especially around t=6

[tall hare]

is a=0 at t=6?

[hard crest]

I'd say so yeah

since v seems to be 0 in that area

[tall hare]

so s is constant

specifically y=8 at 6

so the answer is constant

[hard crest]

but like there are other intervals where v is constant as well

like the area around t=8

[tall hare]

but is that an interval

(2,3) is clearly an interval where both a is zero and v is constant

[hard crest]

I would argue that, say, $\left(7\frac23, 8\frac13\right)$ is such an interval as well

[flat frigate]

Hayley

[tall hare]

i dont think the problem is like that though

[hard crest]

again i think the answer they want is inflection point

but that's dumb because 1) it's not grammatically correct and 2) they said interval so it's not a point

[safe radish]

@tall hare Has your question been resolved?

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[rancid quail]

how would i go about writing it in that form

[hard crest]

that is a super fun printing error

[rancid quail]

yeah

[plucky elk]

,rotate

[rancid quail]

i just re wrote it

[plucky elk]

when you divide fractions, you multiply by its reciprocal

[hard crest]

so in this case that will be equal to $$\frac{p}{p-7}\cdot\frac{p^2-49}{p^2}$

[flat frigate]

Hayley
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rancid quail]

ah

ok i see

so p^3 - 49 / p^3 - 7 ?

that doesnt seem right though

[plucky elk]

use a(b-c) = ab - ac

you did a(b-c) = ab - c in both numerator and denominator

[rancid quail]

ah right

let me try again

p^3 - 49p / p^3 - 7p?

i assume thats still wrong then

[plucky elk]

it's right. i just led you down the wrong path

[plucky elk]

from here, cancel / simplify before multiplying

you have a factor of p in both the numerator and denominator

and you should factor p^2 - 49 as well

use $a^2 - b^2 = (a+b)(a-b)$

[flat frigate]

rie.mann

[rancid quail]

so p / p - 7 x (p + 7) (p-7) / p^2

which should just simplify after cancelling out to p + 7 / p

if im not wrong

[hard crest]

seems legit

[rancid quail]

so its right?

[hard crest]

well if you parenthesize it as (p + 7) / p yes

[rancid quail]

but how would i write it in the form a + b/p?

where a and b are integers

[plucky elk]

use fraction arithmetic properties

$(a+b) / c = a/c + b/c$

[flat frigate]

rie.mann

[rancid quail]

i dont understand 🥲

how do i make (p + 7) / p into dat

[plucky elk]

(2 + 3) / 5 = 2/5 + 3/5

do you agree with how that simplified?

[rancid quail]

o

yh

so its the same

(p + 7) / p = p/p + 7/p

p + 7/p

right?

[plucky elk]

no

[rancid quail]

oh

[plucky elk]

this was right

what's 2/2 =?

[rancid quail]

1

oh

i see

1 + 7/p

tysm

[plucky elk]

,w simplify p/(p-7) * (p^2 - 49)/p^2

[flat frigate]

Results provided by WolframAlpha

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Requested by rie.mann#0

[hard crest]

what the heck is that last expression

[plucky elk]

me: simplify. wolfie: did you mean un-simplify?

[safe radish]

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[plucky elk]

!show

[safe radish]

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

[lean otter]

No idea of how to start
But it must be solved by integration

[plucky elk]

Did you plug in Psi into the integrand?

[lean otter]

Psi?

[plucky elk]

$\Psi$

[flat frigate]

rie.mann

[plucky elk]

this is a greek letter named Psi

[lean otter]

ah ok yes

[plucky elk]

do you know how to square exponential functions?

[lean otter]

yes

[plucky elk]

and what part of the integral are you stuck on then?

[lean otter]

intergration

[plucky elk]

which part EXACTLY

show your work

[plucky elk]

if you say you can square, you should be able to plug the square into the integral

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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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.

[wheat umbra]

Question: 50 fans are watching a football match in the district league. Of these 50 fans, there is one sports muffle who does not play any sport. How many fans must be randomly selected one after the other, without laying back, so that the probability of a selected sports muffle is 85%?

How can i solve this? I must use the hypergeometric distribution. I came now to h(50; 1; n) := P(X=1) = 0,85 \geq\frac{\binom{49}{n-1}}{50}\ is this correct

[wheat umbra]

$h(50; 1; n) := P(X=1) = 0,85 \geq\frac{\binom{49}{n-1}}{50}$$

but how can i solve for n?

[flat frigate]

octodino

[safe radish]

@wheat umbra Has your question been resolved?

[wheat umbra]

<@&286206848099549185>

[safe radish]

@wheat umbra Has your question been resolved?

[lean otter]

Hello

@wheat umbra

[wheat umbra]

Hey 🙂

[lean otter]

How was your day?

[wheat umbra]

Good, now it is a bit stressfull

i can't find an answer

what about you?

[lean otter]

It was all good thank God

I will help you

[wheat umbra]

Thank you

[lean otter]

Binominal coefficient involved

For the steps

[wheat umbra]

okay

[lean otter]

Define the function

1'

$$
f(n) = \frac{{49 \choose {n-1}}}{50} - 0.85
$$

[flat frigate]

weig

[lean otter]

And you want to find the smallest integer (n) right

[flat frigate]

weig

[lean otter]

such that (f(n) \leq 0).

[flat frigate]

weig

[wheat umbra]

But isn't there a $\geq$

[flat frigate]

octodino

[wheat umbra]

yes

[lean otter]

Weird notation I am confused

Oh no nothing

[wheat umbra]

but it can't be zero, or can it?

[lean otter]

No it cannot

Because the binomial coefficient is an integer

And dividing it by 50 would give you slightly more than 0

Do you understand?

[wheat umbra]

not really sorry can you explain how you get there

[lean otter]

Sure

The original inequality is

$$
0.85 \leq \frac{{49 \choose {n-1}}}{50}
$$

[flat frigate]

weig

[lean otter]

Right?

[wheat umbra]

Yes

[lean otter]

And you can rewrite it as

$$
0 \leq \frac{{49 \choose {n-1}}}{50} - 0.85
$$

[flat frigate]

weig

[wheat umbra]

yes

[lean otter]

I'm moving back and forth from latex sorry haha

[wheat umbra]

ah

yeah making sense

[lean otter]

This is equivalent to finding the smallest (n)

[wheat umbra]

no problem

[flat frigate]

weig

[lean otter]

such that

$$
f(n) = \frac{{49 \choose {n-1}}}{50} - 0.85 \leq 0
$$

[flat frigate]

weig

[wheat umbra]

ah okay now i got it

[lean otter]

So

The function (f(n)) is defined based on the original inequality

[flat frigate]

weig

[lean otter]

The main goal is

To find the smallest (n) that makes (f(n)) non-positive

[flat frigate]

weig

[wheat umbra]

yes

[lean otter]

So back to where we jumped

Defining the function fn as follows

$$
f(n) = \frac{{49 \choose {n-1}}}{50} - 0.85
$$

[flat frigate]

weig

[lean otter]

And you want find the smallest integer (n) such that (f(n) \leq 0)

[flat frigate]

weig

[lean otter]

Do you understand. Let me know if you want me to go back on anything

[wheat umbra]

No everything good to tht point

[lean otter]

I'm chilling in my bed rn tell me anything

[wheat umbra]

hahah

[lean otter]

Ookay

Start with (n = 1) and compute (f(n))

[wheat umbra]

i'm sweating in front of my pc

[flat frigate]

weig

[lean otter]

Me too bro

I swear man what is this heat

[wheat umbra]

is it an approximation of n?

[wheat umbra]

horrible

[lean otter]

No no

It's he starting point of our search for the solution

[wheat umbra]

hahah, "we starting the journey"

[wheat umbra]

Then we got -0,83

[lean otter]

Exactly

[lean otter]

What

[wheat umbra]

1/50 - 0,85 right?