help-23

[midnight hare]

yeah what i stated apparently is the special case

[lament beacon]

this follows immediately if you define g(x) = f(x) - d

[midnight hare]

but my professor told us that the f(a)<Alpha<f(b) is the special case

where f(c) = Alpha

and c e [a, b]

[lament beacon]

it doesn't really matter

[crisp lodge]

yea that's how you prove it lol

[lament beacon]

also doesn't matter

[broken yew]

uhhh

calculations/explaning easier?

plugging in pi is simple

[lament beacon]

yeah fair i suppose

[crisp lodge]

even 0 works

[tall acorn]

Sorry to interrupt, what if f(a) = 0? Does that mean there are no roots?

[crisp lodge]

or just plug infinity

[lament beacon]

but like x = 10000 kinda gets the concept through, ie at large values that function is roughly linear

and since it's continuous as well, you have to go through zero

[midnight hare]

i found this

[lament beacon]

not sure which steps are unclear to you

[midnight hare]

idk how to choose the interval lol

[lament beacon]

so the thing about this function is

it's continuous at all intervals

[midnight hare]

so i can choose any interval like u previously said?

like a rather large one

[lament beacon]

you want an interval where f(a) is negative and f(b) is positive right?

or the other way round -- f(a) is positive and f(b) is negative

[midnight hare]

f(a) is negative

[lament beacon]

yeah well, find such an interval

[lament beacon]

the theorem applies even if this is true

[safe radish]

@midnight hare Has your question been resolved?

[safe radish]

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[safe radish]

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[queen niche]

I asked this question in another channel and tried their advice but couldn't figure it out.

Symbolab tells me that the left side cancels to the right side, but i have no idea how.

I did factor all 4 of the multiples above and got:

(2x+1)(x+2)(2x-1)(x+1)

4(x^2-1)(x+2)(x-1)

the only one that is clearly cancelable is (x+2) but i don't know how the others become what is on the right side of the attached picture

[ancient escarp]

cancel terms

the denominator you sent isn't fully factored

[queen niche]

oh u are right..

the (x^2-1) right?

[ancient escarp]

yep

[queen niche]

yep was able to figure out how to simplify it now

tysm

[ancient escarp]

👍

[queen niche]

ill keep an eye out for (x^2-1) in the future

.close

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[jolly violet]

Hiii uhh is there a discord where i can ask science related questions?

[mint flax]

#old-network

@jolly violet

[safe radish]

@jolly violet Has your question been resolved?

[jolly violet]

Hmm wait

If its abt ionic bonds is it considered biologival science?

<@&286206848099549185>

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[jolly violet]

.reopen

[safe radish]

✅

[jolly violet]

Up

[ancient escarp]

i'd ask in the chemistry discord

though none of the #old-network discords are quite as active lol

[safe radish]

@jolly violet Has your question been resolved?

[jolly violet]

Mind sending a link

[ancient escarp]

should be somewhere in #old-network

[jolly violet]

Thx

.close

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[wise nova]

Boat A is 20km from port on a bearing of 025 degrees and boat B is 25km from port on a bearing of 070 degrees. Boat B is in distress. What bearing should boat A travel on to reach boat B?

[safe radish]

Please don't occupy multiple help channels.

[wise nova]

I need help! It is coming in my test, it is urgent

[inner raptor]

If that's from a test, no help.

[wise nova]

no the question is not coming, just the type of bearing questions that i am practising for

this is practise

and i need help

can somebody solve it

plz help

[lean otter]

lmfao you messed up

should've never said it was for a test

[daring raptor]

● When asking a question, show what you tried to solve the problem. We are not here to do your homework for you, but we are here to help you learn how to do your homework. See ❓how-to-get-help for more info on how to ask questions.

5th rule of guide line maybe read it

[wise nova]

i am showing cuz none were online who was i to show my working out to

i drew a diagram

here is my diagram. happy?

can someone reply

[safe radish]

@wise nova Has your question been resolved?

[inner raptor]

it should be in the direction of the shortest route between boat A and B

So the absolute bearing is FDE, 122.8 degrees

@wise nova

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[wise nova]

reopen

so we just use a protractor right

[inner raptor]

yep

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[wise nova]

thanks

[safe radish]

Please don't occupy multiple help channels.

[wise nova]

close

[inner raptor]

close with the dot prefix: .close

[wise nova]

.close

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[snow oasis]

If

[safe radish]

@snow oasis Has your question been resolved?

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[solar dock]

can someone help me solve this

[solar dock]

i dont need the answer i just need to know whats the beginning steps

[shadow thistle]

Try drawing a triangle and solve for the third side with the Pythagorean theorem

[solar dock]

how can i draw a triangle if there is a pi? do i just include it?
so: y= -2pi , x = 5? @shadow thistle

[shadow thistle]

Nevermind. Sorry. I didn’t see the pi

[solar dock]

i was thinking maybe converting it first pi - (-2pi/5) which gives 3pi/5

because its a tan function

but then what

[shadow thistle]

Maybe try converting it to degrees?

[solar dock]

idk i never did it that way

[deep prism]

Idk if this is true

But

Is arccot(x) = 1/arctan(x)

Is that true

[solar dock]

yes

i was thinking about doing that to eliminate both tans because of tan-1( tan

[deep prism]

Wait no it isnt

I just looked it up

That rule only works for regular tan and cot not arc

[shadow thistle]

Tan-1 does not equal arctan

Yes it does. I meant 1/tan does not equal tan-1

[deep prism]

Pi/2 - arccot(x) = arctan(x)

@solar dock

I just got that from desmos lol

You can rearrange now

Pi/2 - arctan(tan(-2/5pi)

[solar dock]

oh sheesh

nice

okay this was burried in the notes of my teacher, i was wondering when to use it thx xd

[deep prism]

Oh rly

[solar dock]

ok its making sense now, u re arrange and cancel

[deep prism]

I was gonna say idk how to derive that ... if you needed to

But I guess you don't lol

[shadow thistle]

Sorry I couldn’t help. I’m glad Sammy could

[deep prism]

Lol diddnt mean to make you look bad

[shadow thistle]

You. Didn’t. You’re probably smarter than me anyway

[solar dock]

alr thx my gs

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[vapid ridge]

How

[solemn moat]

SOHCAHTOA

for the first one, tan(theta) = 50/75

and then you can do inverse tan of that

and then see if you can figure the second one out

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[vapid ridge]

@solemn moat

.close

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[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

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[rustic kayak]

is this solution correct

[final loom]

....?

a = -1, no?
also, the 2 steps after b = 87/2 is questionable ...? what is 21.75 mentioned there?

btw, somehow your answer is still correct by some god forsaken magic

[safe radish]

@rustic kayak Has your question been resolved?

[rustic kayak]

so its correct

but the steps are wrong

right

[final loom]

solution is questionable at some steps

[rustic kayak]

hmm

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[rustic kayak]

well

thanks ig

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[sacred rose]

What does a finite field of order p^n (n >= 2) look like?

[safe radish]

@sacred rose Has your question been resolved?

[sacred rose]

no

[crisp lodge]

P is some field?

@sacred rose

[sacred rose]

p is prime

Like, for a given prime p and n >= 2, what does the finite field of order p^n look like?

i can clearly see what Z/pZ looks like

but for n >= 2 that field is clearly not Z/(p^nZ) and idk what it looks like

[crisp lodge]

oh nvm then it's out of my reach ehehe

[sacred rose]

And it's clearly not (Z/pZ)^n either

[safe radish]

@sacred rose Has your question been resolved?

[safe radish]

@sacred rose Has your question been resolved?

[sacred rose]

No but I'm going to bed so

.close

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[safe radish]

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[reef dome]

If anyone knows statistics and graphing, how do I show the effect one variable has on another graph?

[ember bough]

maybe a 3d graph idk

[reef dome]

I need to show how the values of studying affect sleep, and how it also correlates to grades

like I know how the value of sleep affects the grades, but I cant show how studying affects sleep separately

[ember bough]

maybe try 2 separate graphs then

[reef dome]

is there a formula that combines the two graphs?

that can create a correlation between them

this is the data I was given

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@reef dome Has your question been resolved?

[safe radish]

@reef dome Has your question been resolved?

[safe radish]

@reef dome Has your question been resolved?

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[pale osprey]

not asking for answer but can anyone explain how to do this. i dont know and have tried youtube and websites and still dont know

[pale osprey]

.reopen

[compact dune]

I could be wrong but what I think you need to do is

a) substitute 1 for all values of x and find the result of dividing g(1) by h(1).

b) find the domain by solving for x in h(x). That is the number that would result in a 0 and therefore, all numbers besides the value(s) that would give a 0 in the denominator would be the domain

[safe radish]

@pale osprey Has your question been resolved?

[pale osprey]

Ty I’ll try that

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[lean otter]

How to solve $\lim_{x\to 0} \frac{\int_0^{x^2} \sqrt{4+t^3} dt}{x^2}$?

[plucky elk]

l'hopital's probably simplest

[lean otter]

I'm having trouble in differentiation of integral

[plucky elk]

no doubt no doubt

1st derivative is FTOC

[lean otter]

FTOC?

[plucky elk]

lemme know when you've calculated that

https://www.khanacademy.org/math/in-in-grade-12-ncert/xd340c21e718214c5:definite-integrals/xd340c21e718214c5:fundamental-theorem-of-calculus-chain-rule/a/fundamental-theorem-of-calculus-review

[lean otter]

Ok

[plucky elk]

FTOC + chain rule i guess

[lean otter]

$\frac{3x^2}{2\sqrt{x^3+4}}$?

[plucky elk]

is this the first derivative of the numerator?

[lean otter]

$$\frac{3t^2}{2\sqrt{4+t^3}}$$

[plucky elk]

you're just applying this

your $f(t) = \sqrt{4 + t^3}$

[flat frigate]

riemann

[plucky elk]

what's the right hand side of the previous image?

for simplicity, assume the upper limit is just x and not x^2

[lean otter]

Right hand side? Where?

[lean otter]

This?

[plucky elk]

yup

[lean otter]

f(x)

f(x) = √(4+x³)?

[plucky elk]

yesssss

okay, but now because it's technically x^2, your right hand side is f(x^2) * d(x^2) / dx because of chain rule

[lean otter]

Yeah

[plucky elk]

now you have a product of functions, with no integrals

[lean otter]

$\sqrt{4 + x^6} 2x$

[plucky elk]

and you can just calculate a derivative again

looks good

[lean otter]

Derivative again?

[plucky elk]

actually you probably don't need to

i think you can take the limit from here?

[lean otter]

I can.

It will be 2

[plucky elk]

[lean otter]

Btw what's partial derivative?

[frigid geyser]

it's when you have a function of a few variables, say for a two-variable case f(x,y) = x^2 + xy^2, and you take derivative with respect to one of the variables

[lean otter]

So differentiating an integral with 2 variables involve partial derivatives?

[frigid geyser]

yes - it's called the Leibniz rule i think

[lean otter]

Ohkay

Thanks

.close

[safe radish]

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[uncut zephyr]

help me answer this thing pls

[uncut zephyr]

Can someone check if my answers are correct

1. {HH,HT,TT,TH}

2. 8

a.HH - 2
b.HT - 1
c.TT - 0
d.TH - 1

[restive creek]

There are 4 elements in the sample space

[safe radish]

@uncut zephyr Has your question been resolved?

[uncut zephyr]

oh i see thanks

was the number 1 and 3 correct?

[restive creek]

1 is correct, not sure what the 3rd question is trying to ask

[uncut zephyr]

OK thanks for the help 😊

[safe radish]

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[flat frigate]

azorfus

[safe radish]

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[final loom]

@magic obsidian you don't You just go visit your calculator

[magic obsidian]

uh no

actually

my question was supposed to be

is there a rule to solve $n^{\sqrt{m}}$

[flat frigate]

azorfus

[final loom]

solve? evaluate? simplify?

which?

[magic obsidian]

simplify?

[final loom]

Yeah in that case, there's no generalization

[magic obsidian]

like how $(x^n)^m = x^{mn}$

[flat frigate]

azorfus

[final loom]

Hmm, there's nothing you can do about $x^{n^m}$ though

[flat frigate]

Ansh

[magic obsidian]

ic

[rich whale]

its just $n^\frac{1}{m}$

[flat frigate]

Mathgeek007

[final loom]

HUH

NO

[magic obsidian]

$n^{\sqrt{m}}$?

bruh how

[flat frigate]

azorfus

[magic obsidian]

isn't it

[rich whale]

ohh sorry

[final loom]

Nvm lmao it's $n^{m^{\frac{1}{2}}}$

[flat frigate]

Ansh

[magic obsidian]

ah i see

i see

[rich whale]

yeah thats what I thought

[magic obsidian]

so how do i solve $5^{\sqrt{x}} + 12^{\sqrt{x}} = 13^{\sqrt{x}}$

[flat frigate]

azorfus

[rich whale]

we know that $5^2+12^2=13^2$ is the only solution

[flat frigate]

Mathgeek007

[magic obsidian]

ah i see

so x = 4?

[rich whale]

ye

[magic obsidian]

what if its not a p.triplet

is there a way to solve?

[safe radish]

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[magic obsidian]

.close

[gritty parrot]

explain how this is the correct answer

its supposed to be 8,5 but 8t says this 8s correct

[quasi bison]

how did you get (8,5)?

[safe radish]

@gritty parrot Has your question been resolved?

[gritty parrot]

4 9 -> 12 9

8 abciss a d8f

add to q

bqm

[quasi bison]

no clue what any of that meant

[gritty parrot]

they are coords

4 being x and y being 9

under a translation 4 being x y being 12

i meant x being 12 and y being 9

so u find the diffrence

which is +8

to abc8ssa

add it to Q

then it should be correct

[quasi bison]

but you aren't translating.

you are reflecting.

[gritty parrot]

whar does what maoe a diffreence

[safe radish]

@gritty parrot Has your question been resolved?

[safe radish]

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[toxic stone]

does anyone knows how can we determine if a set is well ordered ?

[quasi bison]

probably by using the definition of a well-ordered set...

[toxic stone]

is there any quick way?

[quasi bison]

not in general no

you haven't told us what set you're dealing with that you want to show the well-orderedness of, so

[toxic stone]

wait ya

[safe radish]

@toxic stone Has your question been resolved?

[quasi bison]

[toxic stone]

sorry this is the wan

sorry for the wait @quasi bison

[quasi bison]

these answer options look weird but ok

[toxic stone]

why isn't the answer a?

[quasi bison]

is -100 an element of (-100, 200)?

[toxic stone]

no

because exclude it

[quasi bison]

so

[toxic stone]

ah now i get it

[quasi bison]

how can -100 be the least element of your set if it isn't even an element

[toxic stone]

so d should be right ?

because is doesnot have a greatest elemtn as well

because is doesnot have a greatest element as well

or it actually have a largest element?

because the relationship is <=

[quasi bison]

sounds like you don't know what a well-ordered set is

we say an ordered set S is well-ordered if every subset of S has a least element

the presence or lack of greatest elements is completely irrelevant

[toxic stone]

oh now i get it now

thank you man

but do you have any idea why this answer is not E?

arent it using induction?

[quasi bison]

what dumb questions you keep getting assigned...

i would say this is improper though as it reads like asserting the goal at the very start

had it been $\overset?=$ instead of $=$ throughout it would have been a proper (ish) algebraic proof

[flat frigate]

Ann

[toxic stone]

wan't it a modus ponens or law of syllogism?

wasn't it?

[quasi bison]

there are no logical connectives in that proof at all so who knows

it's just a series of equations and nothing else

why the random reacts on my messages

[toxic stone]

or maybe there is mistake on the ans?

[restive creek]

Yes it should be C

what answer was given as correct?

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[flint tinsel]

Hey I'm currently wondering how to formulate a point with maximum distance from a line.
I have points x_i for i = 0, ..., n and a line g: x_0 + t*(x_n - x_0) through the first and last point

And I want like:
max_x_i | .... something with x_i and g | to get the point with the max distance from the line.

[crisp lodge]

x_i are points on the x-axis?

[final loom]

Did the formula for perpendicular distance of a point from the line help?

[flint tinsel]

x_i are points in the 2D space

[final loom]

The perpendicular distance of a point P(m, n) from a line $ax + by = c$ is given as:

$$d = \frac{am+bn+c}{\sqrt{a^2+b^2}}$$

[flat frigate]

Ansh

[final loom]

Did that help you?

[flint tinsel]

helps yes

thank you very much should be able to write it down how I like it

!close

!solved

hmm what to use?

[crisp linden]

.close

[flint tinsel]

.close

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[dawn wagon]

.opzn

.open

[lost lodge]

this book i'm reading (Fraleigh's Abstract Algebra) is telling me that if $G$ is a group and $a \in G$, the cyclic subgroup $H = \left\langle a \right\rangle$ is the smallest subgroup of $G$ such that the element $a$ is contained. how is this correct? if $G = \mathbb{Z}$, and you could take $a = 2$, then you would have $H = \left{2^n | n \in G\right}$, but this subgroup wouldn't even be a group over addition (as an example)! $1, 2 \in H$, but $1+2=3$, and $3 \notin H$ (it isn't a closed function and thus isn't a group). have i severely misread the statement or is the book wrong?

[flat frigate]

alias

[stoic dune]

I think we're assuming finite right now

There's a similar statement for infinite groups, where you include a, and a^(-1)

But if you cycle some element in a finite group, this produces a subgroup.

[lost lodge]

oh lol, makes sense - is there a name for that statement for infinite groups you just mentioned?

[stoic dune]

Oh wait, your example is off. If we're working in Z under addition, then <2> is 0,2,4,6...

And is not 1,2,4,8

That's still not a subgroup, but becomes one if we include -2 and cycle that as well

So <2> is taken as all even integers

[lost lodge]

OHHHH LOL, haha, my mistake

[wild cape]

@stoic dune i dont think we need G be finite

[lost lodge]

i think i mistook the notation from here:

[wild cape]

that notation is for multiplicative groups

the notation for additive groups would be smth like na

[lost lodge]

oh right, thx for letting me know!

.close

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[lost lodge]

.reopen

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✅

[wild cape]

note this def doesnt demand G be finite

[lost lodge]

alright, thx again!

.close

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[wild cape]

also u can take the set H defined above

as ur def of the set generated by a

and show that H is the smallest subgroup containing a

this is a nice short exercise

@lost lodge

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[ripe heart]

This might sound stupid, but I need to know: Is 1+1 always 2?

[lean otter]

ever heard of peano's axioms

there is a function S (or succesor) which returns the natural number right after the input

s(0)=1

and so on

[queen parcel]

s(x) = x + 1, in other words essentially

[lean otter]

this means that 2 is S(S(0)

this is what we need to prove

Use induction

the definition of addition: s+S(m)=S(s+m) and m+0=m

I was going to use induction

so S(0)+S(0)=S(S(0)+0)

another axiom is that m+0=m

so the rhs is equal to S(S(0))

there you go

S(0)+S(0)=S(S(0)

that is your proof

[lean otter]

you could use that as well

@ripe heart , do you understand

[ripe heart]

A little bit.

[wild cape]

@lean otter if ur doing peano then u must define addition

u only defined m+0

[lean otter]

addition is recursion on the second argument

well, actually

i did define addition

[lean otter]

here

[wild cape]

thats the def not a result

but tbh

[lean otter]

it is the definition

i worded my sentence wrong

[wild cape]

u dont need to prove all this if u just wanna say 1+1=2

just use the def

[lean otter]

what def?

[wild cape]

of addition

[lean otter]

whats confusing you?

[lean otter]

i used that

[wild cape]

mb thats for @lean otter

but if u wanna add lots of big numbers then itd help to prove some formulas (indeed by induction)

[lean otter]

yes

but 1+1 is simple

[wild cape]

yes its a tiny recursion depth

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[quaint violet]

Hi all , new here and Im beginning my journey in Applied Mathematics and I was wondering if there was any free resources for Linear algebra textbooks ?

[worthy hemlock]

Ask in #book-recommendations

[quaint violet]

thanks

.close

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[lean otter]

How can I factor $x^3-3xy^2+2y^3$?

[flat frigate]

.doc

[jade gust]

okay I don't know how to explain this properly but maybe consider factoring out (x-y)^2

as you know x^2-2xy+y^2≡(x-y)^2 and looks similar to that form

So then you have (x-y)^2 multiplied by some other polynomial

[lean otter]

i can perform a polynomial division with x-x_0 and get the other factor?

[jade gust]

Idk I guess my way of thinking of that is by letting h(x,y)=x^3-3xy^2+2y^3, and then f(x,y)=(x-y)^2 then necessarily there is some g(x,y) to produce h(x,y) alongside f, i.e. h=fg

[jade gust]

then you'll get the other factor

[lean otter]

Makes sense

[lean otter]

how did u

[jade gust]

how'd i what

[lean otter]

like realise that (x-y)^2 is a factor

[jade gust]

my brain is just too large

[lean otter]

It worked to be $(x-y)^2(x+2y)$

[jade gust]

(x-y)^2*

[lean otter]

I also have same doubt

[flat frigate]

.doc

[lean otter]

if u wanna do it the normal ppl way , split the middle terms
u can easily factorise it to (x-y) and a trinomial, then factorise the trinomial

To be honest, I’m not much exactly sure

This is how I thought i k p(y)=0. So i can perform polynomial division with x-y

yea thats also a fine way of doing it

But that’s tedious

[lean otter]

Can you show this?

$x^3-3xy^2+2y^3//
x^3-xy^2-2xy^2+2y^3//
x(x-y)(x+y)-2(y^2)(x-y)//
(x-y)(x^2+xy-2y^2)$

factor out the x-y part
now its just a trinomial

[lean otter]

tbh its not, if u spot that, then u can use it twice, and get it done instantly

[lean otter]

Let me typeset this real quick

I can’t read that tbh

$x^3-3xy^2+2y^3\
x^3-xy^2-2xy^2+2y^3\
x(x-y)(x+y)-2(y^2)(x-y)\
(x-y)(x^2+xy-2y^2)$

why

It’s okay, i can read now

[flat frigate]

Arkos

[lean otter]

Oh yeah

Yeah now can split and take a factor for the other one too

@lean otter it’s like two numbers multiplies to give -2y^2 and adds to xy.

uhm dont treat it like quadratic , u'll struggle

x^2-xy+2xy-2y^2

now factorise

gotcha

Thanks

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[steady escarp]

could someone pls help me with this question

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@steady escarp Has your question been resolved?

[maiden kelp]

f(g(x)), put in the value of g(x) inside of f and you get your answer

What will 2g(x)+5 equal?

Similar with the second one

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[safe radish]

@compact isle Has your question been resolved?

[plucky elk]

i think you just need to do more example problems to a point where you "trust yourself"

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[sonic galleon]

hi guys, really trivial question

if I have a problem min(-f) s.t. g<0, I can rewrite it as -max(f) s.t. g<0. In this case, if I take Lagrangians, would my lagrangian be L=f- lambda(g-0) or would I have to have a negative in front of the f?

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[sonic galleon]

<@&286206848099549185>

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[safe radish]

@lean otter Has your question been resolved?

[plucky elk]

do you need help setting up a fraction?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

No thanks it’s fine now

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[warm pendant]

this is the question and the second pic is the solution. Can someone help me understand how the circled equations cme please

[broken yew]

(a,b,c) is the normal vector to new plane, from (1)

This normal vector lives on the old plane

as the new and old planes are perpendicular.

[safe radish]

@warm pendant Has your question been resolved?

[warm pendant]

oh i kinda understood the 3a-5b+2c=0 part now

and what about the second one?

a/-11=b/-11=c/-11

[worthy hemlock]

What are you talking about? That question has nothing to do with volts

Still nothing to do with electricity

Why are you trolling?

No one asked about momentum

[wild cape]

@turbid vector stop giving nonsense answers

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[safe radish]

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[clever dust]

hii can someone check if my answers are correct

[clever dust]

please check if its right!!

[lean otter]

yes it's correct.

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[clever dust]

tysm!

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[uncut patrol]

just wondering what the eqaution to find the y-intercept from 2 points was. thanks!

[meager chasm]

wdym

given two points, find y-intercept of line?

[uncut patrol]

yes

[meager chasm]

do you know the slope intercept form of line

[uncut patrol]

y+mx+b

[meager chasm]

uhh no

[uncut patrol]

y=mx+b*

[meager chasm]

yea

b is the y-intercept right

[uncut patrol]

yes

[meager chasm]

given those points, just find the eqn of line in any way

then b = y-intecept

???????????????????????????

someone else is using

you literally have a channel

do you see how this channel is occupied???

<@&268886789983436800>

feel like this guy is in an exam

[wild cape]

@lean otter we're not chegg

also use an unoccupied channel

[meager chasm]

he used

[wild cape]

#❓how-to-get-help

[meager chasm]

like 5 occupied channels

and pinging helpers multiple times

[meager chasm]

alright you know what i mean right

[uncut patrol]

im trying to find the equation to take to points and solve for the y intercpt

[meager chasm]

you don't know how to find eqn of line given 2 points?

[uncut patrol]

no

[meager chasm]

do you know how to find slopes, then?

[uncut patrol]

yes

[meager chasm]

alright so

suppose our points are $$(x_1, y_1), (x_2, y_2)$$

[uncut patrol]

k

[flat frigate]

Chromium

[meager chasm]

their slope is $\frac{y_1 - y_2}{x_1 - x_2}$, correct?

[flat frigate]

Chromium

[uncut patrol]

yeah

[meager chasm]

so

eqn of line is y = mx + b

we know this passes through $(x_1, y_1)$

[flat frigate]

Chromium

[uncut patrol]

ohhhh

[meager chasm]

and this is m

[uncut patrol]

i got it now

[meager chasm]

you can then solve for b

[uncut patrol]

ok

thanks!

.close

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[lethal lagoon]

If you’re changing a percentage to a decimal for a problem for example if it’s 10.4% would it be .104?

[meager chasm]

yea

% literally means /100

[lethal lagoon]

Thanks I was confused for a second

.close

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[lean otter]

Can someone help me with my homework

[plucky elk]

Bots auto-pin your first message so

• Ask your math question in a clear, concise manner.
in the first message so people can find it easily

[quasi bison]

finally someone gets it lmao

that person left tho

.close

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[plucky elk]

#❓how-to-get-help

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[safe radish]

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[novel magnet]

how would i start on this

[fading raft]

im guessing you've not learned about hyperbolic trig functions

right

[novel magnet]

i have actually

infaact

i am in calc 2 and i have completely blanked out of precalc

its been 2 years since i last did this lol

[crisp linden]

then what hyperbolic trig function is this?

[novel magnet]

lol

idk

no idea

[fading raft]

$e^{x} - e^{-x} = 2\sinh(x)$

[novel magnet]

actually

[flat frigate]

azeem321

[novel magnet]

i havent heard of hyperbolic functions tbh

[crisp linden]

what

[fading raft]

[novel magnet]

i think i havent

[fading raft]

probably thought i was mentioning normal trig functions

ok

Start by multiplying both sides by $e^{x} + e^{-x}$

[flat frigate]

azeem321

[novel magnet]

hm ok

wouldnt it just be y(e^x+e^-x) = e^x-e^x

[fading raft]

yup

[novel magnet]

ok

[fading raft]

now multiply it through

and multiply both sides by $e^x$ and see if you notice anything

[flat frigate]

azeem321

[novel magnet]

ye^x+ye^-x right

[novel magnet]

for this

ye^x+ye^-x right

[fading raft]

ye this is the left hand side right

[novel magnet]

it would become ye^2x+y = e^2x-1

[fading raft]

correct

now try to get it in the form

$x=...$

[flat frigate]

azeem321

[novel magnet]

ok

lets see

x=(ln((-1/y-1)-(y/y-1))/2)

damn its a messy one

idk if its right

[fading raft]

yh

looks good

nice

[novel magnet]

really??

lmao no way i did that lgebra right

[fading raft]

Wait

did you square root

[novel magnet]

ye

i did

[fading raft]

oh yes

i just saw the /2

[novel magnet]

oh lol

[fading raft]

nice looks good

need more help?

[safe radish]

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[remote niche]

These are some of the questions i got wrong in my past quiz, can someone teach me how to do it incase questions like these pop up again in my next one?

[worthy hemlock]

For this, it's just knowing the trig ratios, applying the SOH CAH TOA mnemonic

[remote niche]

Which one?

[worthy hemlock]

The bottom picture

With the triangle

And pythagorean theorem

[remote niche]

Can you explain how to do it? Math isn’t my strong subject so its hard for me to get it

It doesnt have to be that exactly, it can be anything

[worthy hemlock]

Using pythagorean theorem, you can find the missing side

Do you recall pythagorean theorem?

[remote niche]

Pythagorean theorem is r2 = x2 + y2?

[worthy hemlock]

That's bad notation

[remote niche]

All I remember about the Pythagorean theorem is that formula given to us by our teacher

[worthy hemlock]

I'm saying that formula is not typed properly

Depending on variable choice, it's a^2 + b^2 = c^2

[remote niche]

But either way is it the same?

[worthy hemlock]

You have it typed poorly, because x2 just looks like a constant, multiplied by x, or 2x

[remote niche]

Ah i just did that since i thought it was a given that it was an exponent in that context

[worthy hemlock]

Do you know how to apply pythagorean theorem to the question?

Here is my suggestion for that question
https://www.khanacademy.org/math/geometry-home/right-triangles-topic/intro-to-the-trig-ratios-geo/v/basic-trigonometry

Watch that, it does everything that question needs

[remote niche]

Alright ill watch it ty.

How about for the first picture though? How do i solve for those?

[worthy hemlock]

I got nothing for that

[remote niche]

Ah

[safe radish]

@remote niche Has your question been resolved?

[safe radish]

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[marsh walrus]

so I'm struggling to explain why the anticipated variance is off by a factor of 4

I'm getting 1/8 theoretical variance

and simulated variance of around .5

its possible I'm just dumb

sample variance for binomial we expect to be pq, right?

Maybe i can ask an easier question?

can someone help me to confirm what the bias of V[xbar] is here?

$X \sim Bin(20, 0.15)$ gives that $Bias(V[\bar X]) =$?

[flat frigate]

jan Niku

[marsh walrus]

we should get that $V[\bar x] = p(1-p)$ i feel like

[flat frigate]

jan Niku

[marsh walrus]

so

,calc .85*.15

[flat frigate]

Result:

0.1275

[marsh walrus]

but then why is it .5

<@&286206848099549185>

[lean otter]

you said prob not stats

[marsh walrus]

im just trying to find bias

im doing something wrong

idk what it is

[lean otter]

jan niku for stats you have to contact chaa

[marsh walrus]

whats their tag

@lean otter

[lean otter]

@thorn valley

[marsh walrus]

[lean otter]

now we wait

https://tenor.com/view/cat-cat-stare-stare-animal-funny-gif-21869355

[marsh walrus]

i feel like this should be easy

[lean otter]

it is

[marsh walrus]

[safe radish]

@marsh walrus Has your question been resolved?

[thorn valley]

uh no

npq

[marsh walrus]

doesnt it cancel?

[thorn valley]

nope

[marsh walrus]

why not

[thorn valley]

why would it cancel?

[marsh walrus]

$V[ \bar X}$, right

[flat frigate]

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

[marsh walrus]

idk why it errors

you get like

\begin{align*}
V[\bar x]
&= \frac{1}{n^2} ( V[X_1 + \dots + X_n]) \
&= \frac{1}{n^2}(n\sigma^2) \
&= \frac{\sigma ^2}{n} \
& = \frac{npq}{n}
\end{align*}

[thorn valley]

uh

[thorn valley]

im not following this

[flat frigate]

jan Niku

[marsh walrus]

so pq

i tried using phat instead but i dont think thats right

and i got lost

[thorn valley]

var(x) = np(1-p)

[marsh walrus]

but its not x its xbar

👀

[thorn valley]

okay

[marsh walrus]

does that not change anything

its an additional calculation inside

[thorn valley]

$var(\bar x) = \frac{var(x)}{n^2}$

[flat frigate]

chaa

[marsh walrus]

oh then it should be pq/n

[thorn valley]

which is the same as $\frac{np(1-p)}{n^2}$

[flat frigate]

chaa

[thorn valley]

_>

oh

wtf

[marsh walrus]

no

var(x) = pq

[thorn valley]

_>

bruuuhuhh

[marsh walrus]

each x is bernoulli

[thorn valley]

var(x) = npq

for binomial

[marsh walrus]

oh

right

[thorn valley]

its like a fact that will never change

smh

like no matter what you're working on

like its a formula

[marsh walrus]

so wait im confused

this doesnt help explain the error

its moving in the wrong direction

[thorn valley]

wrong direction?

variances have direction ?

im confused

[marsh walrus]

as in its shrinking not growing

[thorn valley]

yeah

its supposed to be that way >_>

[marsh walrus]

but the variance i get reported is 4 times larger than the theoretical

[thorn valley]

as sample size increases var decreases

oh

what

[marsh walrus]

thats what im trying to figure out

whats the bias of this estimator?

i havent been able to figure it out

is that whats doing it?

[thorn valley]

wait are u doing this by code

or by hand

[marsh walrus]

both

simulation by code

theoretical by hand

[thorn valley]

hm

and is the simulation right

or are they both wrong

[marsh walrus]

its only 5 lines of code

copied directly from the teacher

i ran it 100 times too

so its like

10 million sample means?

[thorn valley]

your teacher told you that var(xbar) = pq?

[marsh walrus]

no thats what i calculated

i still dont really get why its not true

but thats ok

[thorn valley]

are u using R

im not sure why it wouldnt be wokring if the prof gave u the code

can i see the output

and the code

[marsh walrus]

in a second

my computer is doing something funny

[thorn valley]

maybe cus u used the wrong formula >_>

[marsh walrus]

it hates R

[thorn valley]

LOL

wait Rstudio worked fine on mine

[marsh walrus]

no its my dumb lappy

it struggles with all these apps at once

[thorn valley]

ohh

smh

[marsh walrus]

i guess n is 20

not 5?

thats what my classmate says

[thorn valley]

yeah

its 20

[marsh walrus]

okay lemme see

[thorn valley]

yeah it says each row represents a sample size of 5 but

the simulation you're running is n = 20

[marsh walrus]

I guess this is the answer?

theres 2 two different n's for some reason

[thorn valley]

i mean

n = 5 works

?

ohhh

ok

cus you're trying to find xbar so you use n = 5 and not n = 20 bc you're not doing x

im assuming is why

but yeah his v(xbar) is correct

[marsh walrus]

how dumb

so we take what

im still trying to track

we take 20 samples and track the number of successes

then we take 5 random samples from that collection?

so we have a collection of numbers that are the number of success from a bunch trials of trying 20

then we randomly pick 5 and take the mean

[thorn valley]

no you're using the data to a sample estimate

[marsh walrus]

we do that 100000 times

then we take the mean of that

[thorn valley]

with sample size = 5 and 10000 reps

yeah

[marsh walrus]

thats so complicated

ok

maybe i understand

what a mess

[thorn valley]

like reps = # random sampkes

not

[marsh walrus]

huh?

[thorn valley]

so like 10000 repiittions

oh frick my spelling

is the number of randome samples

[marsh walrus]

repititons of drawing 5 from the original 500000

[thorn valley]

not the sample size

well yeah

[marsh walrus]

i dont get what you mean

[thorn valley]

sample size != # random samples

[marsh walrus]

👀

[thorn valley]

random smaples is the number of times you conduct the experiment

sample size is the size of the experiment

you do each time

[marsh walrus]

so sample size here is 5

[thorn valley]

yes

[marsh walrus]

and # random snapples is 20

ok

i think i understand

[thorn valley]

waht what

[marsh walrus]

thank you 🙇‍♂️

lol what

[thorn valley]

oh wait

[marsh walrus]

we conduct the experiment 20 times

[thorn valley]

yeah

[marsh walrus]

then do that 5 times

[thorn valley]

yey e

sorry mb

[safe radish]

@marsh walrus Has your question been resolved?

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

[signal granite]

Really stupid logics question but i cant seem to grasp it for some reason. If you prove a conditional statement (direct proof) you take the hypothesis P to be true to then "take logical steps" toward proving the conclusion Q. Why do we take P to be true and what are "logical steps"

[broken yew]

Your basic building blocks are axioms.

Without axioms, you cannot prove anything

There is nothing to prove.

In the same way, a proof starts with 'known' theorems, etc from the axioms.

Using these, you prove a new theorem

[signal granite]

How tho? i feel like saying that is equivalent to "taking logical steps" but idk what that means

[broken yew]

Perhaps I misunderstood your original Q

[signal granite]

Also a conditional is true if P is false, so why do we take the hypothesis to be true

[broken yew]

Is there some more context

[signal granite]

uhmmm

Well no not really, im just struggling to understand the meaning of "implies" (=> symbol), so im trying to ask questions that might better help me understand it

[broken yew]

Oh are you saying if we need to prove the statement 'P => Q'

We start by assuming P is true?

[signal granite]

yea

[broken yew]

ok ok.

'P => Q' in words is 'if P is true, Q is true'

ok?

[signal granite]

but isnt that a causal relation. Its possible for P to be true and Q to be false so "If P is true, Q is true" doesnt hold up

[broken yew]

In addition to that, in terms of the basic logic operators 'and', 'or', 'not'

'P => Q' is defined to be '(not P) or Q'

'P implies Q' means

P is true AND Q is false is impossible

[broken yew]

As can be seen from this

$$(P\implies Q):= ((\lnot P)\lor Q)$$

[flat frigate]

Shuri2060

[signal granite]

Yes for the implication to be true but then you're saying that "P implies Q is true if and only if P is true and Q is true"

But then i still dont know what an implication/conditional is

For example, B is a four legged creature => B is a dog