help-23

[safe radish]

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[autumn yoke]

when and where do i apply the reflexive property of equality for writing a proof?

[autumn yoke]

<@&286206848099549185>

[uncut vault]

I dont know

Sorry

[autumn yoke]

its fine thanks

[uncut vault]

You're welcome

[autumn yoke]

.close

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[limpid salmon]

Hi!

[limpid salmon]

I've done this limit

but the result isn't correct, I can't understand why

P.S. I can't use De L'Hopital Rule because the exercise doesn't provide it.

I can only use the "variable changing method"

[gloomy scaffold]

Why this hustle?

Use binomial expansion

You can do it within 3-4 lines myb

[limpid salmon]

ehm... we didn't do that

[gloomy scaffold]

Do you know what binomial expansion is?

[limpid salmon]

yes but no, because we only tauched on two or three years ago

the book wants me to do a variable changing

[gloomy scaffold]

,w expand (3x-1)^(3/2)

[flat frigate]

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[limpid salmon]

I'm in 5th class of High School, we didn't do all this monster-like expansion ahahahah

Is there any easier method to solve it?

[radiant crypt]

try writing it in the form
$(1+\frac{1}{f(x)})^{f(x)}$

[flat frigate]

alihsaas

[safe radish]

@limpid salmon Has your question been resolved?

[gloomy scaffold]

Nvm that wouldn’t have worked anyways

[limpid salmon]

that's what I'm trying to do

but it doesn't work my procedure

I HAVE UNDERSTOOD!

The notable limit is

(x + 1/x)^x

and not

(x - 1/x)^x

So the variable changing is z = -y/3

[safe radish]

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[foggy salmon]

hm

whatve u tried

[frosty estuary]

Did you do steps a and b?

[wheat cave]

Like last time, just posting the question doesn't tell us how to help you
please tell us where exactly you are stuck

[thorn thicket]

i have found the consecutive numbers but i dont understand how to do the number but wht does it mean by double the smller number and add it to the larger number

[quasi bison]

do you know what the verb "to double" means?

[foggy salmon]

for instance, if u choose 1 and 2, u get 1*2 + 2 = 4

[safe radish]

@thorn thicket Has your question been resolved?

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[safe radish]

@lean otter Has your question been resolved?

[static shore]

Please translate the question to English

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

hi all i need help for assiments anyone can help ?

[fiery flint]

you should take a free channel

[lean otter]

how

[safe radish]

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[ruby relic]

Atm i have trigonometric functions like basic part when it is f(x) =asin/cos(b(xc) d and know how to do an curve discussion and get the point where it crosses x but now we need to get the point of x for funcctions like cos(..) =sin(x) and idk how to get or do an discussion. I would just do arcsin/cos and try to replace the x one with other variables and try to somehow get it

[ruby relic]

sin(2/9)=sin(x*pi)
0<x<1; x≠2/9 is a task

[quasi bison]

did you mean sin(2/9) or sin(2pi/9)?

you might be interested in knowing that sin(t) = sin(pi-t) at any rate

[ruby relic]

I just send. Pic

Its the task at the top

[quasi bison]

what language are you translating from?

[ruby relic]

German

[quasi bison]

also yeah that is sin(2pi/9) not just sin(2/9)

you might be interested in knowing that sin(t) = sin(pi-t)

[ruby relic]

Ok

But i still dont know how to get the point on x axis

<@&286206848099549185>

<@&286206848099549185>

[sick zephyr]

it says that sin(2π/9)=sin(xπ)

okay

[sick zephyr]

so we use this

lets convert that pi things to numbers so it looks better

it works like sin(40)=sin(180-40)

so we can find that xπ=140

x=140/180=7/9

as you can see here

ofc its on unit circle

this may help you convert

[safe radish]

@ruby relic Has your question been resolved?

[ruby relic]

@sick zephyr and how do i get to sin(40) etc

[safe radish]

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[lean otter]

Could you help me @sick zephyr. or aren’t you a helper?

[hardy lion]

Do not pinng random people

[lean otter]

Sorry

But could you help me haha

[sick zephyr]

i can

[hardy lion]

No, the channel will close

[wheat cave]

this also isn't your channel anymore

[sick zephyr]

if i can ofc

open it

[lean otter]

How can this be my channel

[hardy lion]

You have to get a new one

[lean otter]

.reopen

[hardy lion]

You have to get a new one

[lean otter]

How

Can’t we just write here

[hardy lion]

It will close

[lean otter]

Oh

[hardy lion]

See this

Get a new one

[timid pasture]

Just get a new channel

[lean otter]

How

[hardy lion]

Go to available

And get a new one

[lean otter]

I have now

[ruby relic]

.close

@lean otter u need to close the channel

[lean otter]

.close

[safe radish]

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[ember sphinx]

https://gyazo.com/2d875801e2980f2948b641c23499456d

[ember sphinx]

bro i swear the teacher just doesnt make sense

[charred crest]

do u want to find the determinant?

ok it's simple

let's take the first row of matrix A

we're expanding

[ember sphinx]

Yea i did it

I got -1 toob

but like i swear

them numbers

came outta no where

[charred crest]

do u understand what i did?

or should i explain

[ember sphinx]

OHHHH

OHHH

HE DID IT with the columns

i always do it withs the rows

so its like (1 3
2 1)

and (2 3
0 1

[flat frigate]

Mehdi_Moulati

$\matr[v]{a&b&c\\d&e&f\\g&h&i} = a\matr[v]{e&f\\h&i} - d\matr[v]{b&c\\h&i} + g\matr[v]{b&c\\e&f}$

[shut inlet]

like this ?

[ember sphinx]

Thats how my teacher does it

i go along the rows

idk why he did it this way

[shut inlet]

you will get the same result

[ember sphinx]

he didnt teach us it this way

Yea i know

but thanks i just thought numbers came outta no where

.close

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[charred crest]

it's the same way

dw

no matter which column/row u do it by

you'll get the same result

[safe radish]

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[stiff vortex]

How do i make a the subject?

[thin bridge]

what have you tried so far?

[stiff vortex]

Nothing, I am confused

[thin bridge]

let's consider something simpler like
$$\frac 1x = 7$$
would you be able to solve this for $x$

[flat frigate]

ℝamonov

[stiff vortex]

Is it x=7?

[thin bridge]

no

are you implying that $\frac17$ is the same as 7?

[flat frigate]

ℝamonov

[stiff vortex]

No

[thin bridge]

because that's what you're saying with

Is it x=7?

[stiff vortex]

Yea

But even that i am confused

[thin bridge]

try solving again

note one of the basics of algebraic manipulation is applying the same operation to both sides of the equation

[stiff vortex]

1/7=x?

[safe radish]

@stiff vortex Has your question been resolved?

[placid kelp]

yes

[stiff vortex]

ohh

[placid kelp]

this is a weird wording tbh. i would phrase it as "solve this equation for a" or "find a formula for a". which i'm like... 90% sure that's what it's asking lol. i dunno if i've ever seen it phrased as "making it the subject of a formula"

[quasi bison]

apparently thats a uk thing or something

[safe radish]

@stiff vortex Has your question been resolved?

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[fallen timber]

If each time you press a button you have a 1.5/100 chance to get money and you press the button 100 times what is the chance that you get money atleast once?

[wind agate]

The chance that you don't get money is (100-1.5)/100 each time

What would it be a 100 times?

[fallen timber]

huh

[safe radish]

@fallen timber Has your question been resolved?

[south epoch]

if the chance that you dont get money for 1 press is (100-1.5)/100 then what would the chance be for 100 press?

[fallen timber]

idk

im stupid

thats why im askling

[south epoch]

think about it on your own

math is about doing everything on your own

[safe radish]

@fallen timber Has your question been resolved?

[safe radish]

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[vital kayak]

comparing coefficients polynomials

[vital kayak]

i don't understand this

can someone explain it to me

[quasi bison]

Q1 or Ex 1?

[vital kayak]

both

ex 1 i think has to do with question 1

i did question 1 but using the synthethic division, idk if it's how i was ment to do it

this is how i go t the answer, not sure if that's how it was ment to be worked out

if you could explain ex1 and maybe after how to use it to work out Q1 i would relly like that 😄

rn im watching a video on equating coefficients to get to know what it means exactly

ok i've understood comparing coefficients, i'm not sure how to use it tho

since i dont have something is equal to something else

[quasi bison]

are you familiar with the concept of degree of a polynomial?

[vital kayak]

im not sure

is it x^2

in this equation

since it's the highest power

[vital kayak]

should i watch a video on this now?

[quasi bison]

if you feel like you would benefit from watching a video then watch a video

i'll be going to sleep then

[vital kayak]

no

if u coudl help me that would mean a lot

i just don't want to be of a nuisance since i don't know what it means

🙏 pls

[quasi bison]

the degree of a polynomial is the highest exponent appearing on x when you expand it fully

for example, deg(5x^11 + 6x^3 - 55x + 90) = 11

[vital kayak]

ok

so the highest power kind of ?

when it has to do with x

[quasi bison]

if you are unable to conceptualize it without reducing it to a two word shorthand...

[vital kayak]

ok sorry yes i understand

[quasi bison]

anyway, polynomials of certain low degrees have special names

polynomials of degree 0 are called constant, those of degree 1 are called linear, those of degree 2 are called quadratic, and so on.

[vital kayak]

alright

[quasi bison]

well, ok, the next ones you may see are quartic for 4 and quintic for 5 and rarely beyond that.

anyway

[vital kayak]

and to the power of 3 i would asume are cubic

i understand

[quasi bison]

why assume

i literally said polynomials of degree 3 are called cubic. why do you need to 'assume' that?

[vital kayak]

sorry i didnt mean to say it like that

[quasi bison]

anyway... the degree function has some nice properties.

of particular interest to us is the property that for any two polynomials P and Q, you have deg(P*Q) = deg(P) + deg(Q).

[vital kayak]

alright

i understand that

[quasi bison]

given this, now turn to ex 1

you are told (x+1) g(x) = f(x), and that f(x) is cubic

find the degree of g(x)

[vital kayak]

x+1 is degree 1

g(x) has a degree of 2

am i mistaken ?

[quasi bison]

no, you are not mistaken.

strange way of asking that question tho

[vital kayak]

i have a question that might sound dumb

can i ask ?

if the degree is 0

so theres only a constant

that's not considered a polynomial right ?

[quasi bison]

did your teacher issue a decree to that effect?

[vital kayak]

i just have anxiety and u r scaring me i don't want to make you mad

sry

[quasi bison]

better to ask a dumb question than act squeamish about it.

[vital kayak]

ok 💪

so now how do i apply it to Q1

[quasi bison]

anyway, no, unless your teacher explicitly tells you that anyone who considers constants to be polynomials will be punished by instant failure of their entire academic year,

there's no reason to exclude constants from being polynomials

[vital kayak]

alright

[quasi bison]

now you know (x-3) is a factor of x^3 - 4x^2 + x + 6

[vital kayak]

yeah

[quasi bison]

this means you know that x^3-4x^2+x+6 is the product of x-3 and a quadratic

[vital kayak]

yeah

[quasi bison]

(x-3)(Ax^2+Bx+C) = x^3 - 4x^2 + x + 6

expand LHS, compare coefficients, solve for A, B and C

[vital kayak]

alright im going to work it out on a piece of paper and send a picture here

at this point what do i do ?

do i input my values of a,b and c to find x ?

input them in here (Ax^2+Bx+C)

so i have the other factor

[vital kayak]

I did this and got (x^2+7x+22) as my other factor

then i use quadratic formula to open it more and i get the answer the teacher gave me

i can't factor it.

i think i made a mistake.

ah i have foudn it

its in comparing coeffs of x^2

yep i got the right answers

thank you ann

.close

[safe radish]

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[safe radish]

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[vale onyx]

horizontal stretch is whenever it's less than 1

[vale onyx]

so would this be √1/2x?

im kind of lost here

[frozen summit]

horizontally stretched means the graph will look like you stretched it by a factor 2

,w plot log(x) and log(2x)

[flat frigate]

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[vale onyx]

ohh wait

am i thinking of a compression

when i put 1/2

[frozen summit]

For instance the blue plot is the red plot horizontally streched by a factor 2

[vale onyx]

less than 1

[frozen summit]

no you are right haha

[vale onyx]

these are the two things i mix up a lot i really need to memorize them

[frozen summit]

No

You are wrong

wait

I'm mixing things up now lol

think of it as "reparametrizing" the x axis as a "z"-axis.
Before we have x, now we have z=2x for instance. When x=1, z=2x=2 so it is indeed "further away". To stretch horizontally by a factor 2 replace all x you see by 2x

[vale onyx]

i see now

[frozen summit]

Harder example:
$x^2+4x+6$ then replace x by 2x gives $(2x)^2+4(2x)+6=4x^2+8x+6$

[vale onyx]

im graphing it in desmos

[flat frigate]

SkyTwX

[frozen summit]

Let's see if what I'm saying makes sense using wolfram

,w plot x^2+4x+6 and 4x^2+8x+6

[flat frigate]

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[frozen summit]

mmmh YEAH not convincing XD

[vale onyx]

so essentially all you really do is put 2 in front of the x

under the square root

i did the square root of x and replaced numbers in front of it

[frozen summit]

yesss!

[vale onyx]

gradually getting higher

[frozen summit]

no

[vale onyx]

yeah i dont know i mixed that up horrendously lol

[frozen summit]

INSIDE of it

[vale onyx]

yeah

under the square root

[frozen summit]

,w plot sqrt(x) and sqrt(2x)

[flat frigate]

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[vale onyx]

yeah

thats how i did it

[frozen summit]

Nice

[vale onyx]

maybe i typed it weird

[frozen summit]

no no I'm just tired, sorry haha

[vale onyx]

its alright lol same ehre

thanks

.close

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[fickle trail]

How would I find the domain of these functions?

[final halo]

how did you arrive at the light blue at the end of your first pic

[fickle trail]

Oops that should say sqrt of -1/3

That tells me no asymptote exists?

[final halo]

yes the denominator is never 0

[fickle trail]

Interesting.,

Alright so (-inf, Inf) for the first one

[final halo]

second one all you need is for the stuff inside the square root to be bigger than or equal to zero

[fickle trail]

2x

The domain for both is (-Inf, Inf) but I’m not sure why for the second one

A variable squared inside of sqrt can never be negative?

[final halo]

who is saying the domain for the second one is (-inf,inf)?

[final halo]

?

[plucky elk]

what is "first one"?

[final halo]

first pic i assume

[fickle trail]

Sorry was afk

Back now.. alright I understand sorry

[fickle trail]

It’s this one that I don’t understand how to find the domain

[final halo]

well this is a completely different problem now

[fickle trail]

On the right track or no?

[final halo]

i mean there really isnt anything to do

[fickle trail]

Ya my bad.. took screenshot of wrong one

[final halo]

im not sure what it is you're trying to do that you think will magically make you realise what the domain is

[plucky elk]

smh logical assumptions

[fickle trail]

Domain is all real numbers because no subtraction and all even powers?

[final halo]

so you think the domain of something like x-1 would not be all real numbers because there a subtration?

[fickle trail]

And because x is odd power

[final halo]

or that the domain of x^3 is not all real numbers because it has an odd power?

[fickle trail]

Yeah

Im confused with domain for this

[final halo]

if you think the domain of x-1 is NOT all real numbers, which numbers are excluded from the domain of x-1?

[final halo]

?

why are you just sending random pics

[fickle trail]

This domain

Confuses me

[final halo]

WHAT domain?

[fickle trail]

Lol

[final halo]

why are we jumping questions here?

[plucky elk]

it won't matter because in 15 seconds avid will send another picture

[fickle trail]

Well, maybe I phrased it wrong

[plucky elk]

feel free to use words such as "okay i got that one. here's my next problem"

words good

[fickle trail]

When there is a variable with even power and even root

[final halo]

come on avid you're better than that middle one

[fickle trail]

Does it always become absolute value?

[final halo]

you know thats not how square roots work

[plucky elk]

how many times have you been told

$(a+b)^n \neq a^n + b^n$

[flat frigate]

riemann

[fickle trail]

My bad..

Ignore middle example

I think first one is correct but not sure about second

Absolute for entire result? Or x only

[final halo]

if you're asking whether $\sqrt{x^2} = |x|$ is true, then yes it is

[flat frigate]

ΣAC

[final halo]

here you're just applying $(ab)^n = a^n\cdot b^n$

[flat frigate]

ΣAC

[fickle trail]

Yeah

But x becomes |x|?

Or it doesn’t need absolute value

In the 2x case

[final halo]

if you're still asking that question, then im not sure what your "yeah" was in relation to

[fickle trail]

To this

[final halo]

okay and then read t his perhaps for the first time

[fickle trail]

So both of these are correct

[final halo]

yes

[fickle trail]

Ty!

.close

[safe radish]

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[peak tendon]

Problem: Factor and simplify the expression. (Type exponential notation with positive exponents)

[peak tendon]

The original expression is beside the bubbled 1.

[final halo]

is your question "i did this, is it correct?", or "ive seen that this is true but i dont know why"

[peak tendon]

The website told me it's wrong but it didn't tell me why.

[final halo]

why did your 3 end up on the bottom?

[peak tendon]

Is it only the x that is supposed to be on the bottom and keep the 3 up top?

In the lecture we never went over any problems exactly like this so I wasn't sure, I was just following the steps I was told to

[final halo]

yeah, its 3*(stuff)

no matter what happens in (stuff)

[peak tendon]

I see, why is it that way instead of how I wrote it may I ask?

[final halo]

well there is just no reason why the 3 should appear on the bottom

things with negative powers can be "moved to the bottom" and the power changed sign

the 3 had no negative power

[peak tendon]

ah I see, its the x that had the negative power so only that should be on the bottom

thank you so much

[final halo]

yep you got it, no worries

[peak tendon]

.close

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[cerulean basin]

Let the consecutive angles be AOB, BOC and COD, such that the largest of them is the angle AOB and the smallest is the angle COD. If m<AOB - m<COD = 28⁰, the measure of the angle formed by the bisectors of the angles AOD and BOC is:

[cerulean basin]

This problem is driving me crazyyy

[final halo]

maybe you should stop ignoring people that are telling/asking you to draw a picture

[cerulean basin]

I've sent a picture already and everyone is ignoring.

[final halo]

people aren't ignoring you on purpose, they either dont know or maybe are thinking

[cerulean basin]

I have not any other data, I don't know if it's even solvable.

The answers could be:

A) 10⁰
B) 15⁰
C) 20⁰
D) 12⁰
E) 14⁰

I drew it again.

<AOB - <COD = 28⁰

I need to find the angle in thenmiddle of the AOD and BOC bisectors.

[safe radish]

@cerulean basin Has your question been resolved?

[cerulean basin]

At least tell me if the problem cannot be solved.

[safe radish]

@cerulean basin Has your question been resolved?

[cerulean basin]

Nevermind , I guess everyone is too dumb to solve it.. thanks for nothing math community

.close

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[tepid hinge]

I need help

[tepid hinge]

Serious help

6t(t+4)=t-20

This question sounds dumb but I can't factor with elimination method the one I know

And I can't factor

Am stuck at the factoring

[trim swan]

What have you done so far?

[tepid hinge]

I got to 6t^2 +15t+8t+20=0

I can't factor that the way I know

Where you get 6t then 15 divided by 6

[pastel briar]

Well 6t*4 should give you 24t and 15t+8t = 23t

[tepid hinge]

The problem is that I don't know where that 6t^4 came from

[pastel briar]

You mean 6t*4 I hope?

[misty bay]

$6t(t+4) = 6t^2 + 24t$

[flat frigate]

Saccharine

[tepid hinge]

I don't understand what the * stands for a multiplication

[tepid hinge]

Hello once again

[misty bay]

hi

[pastel briar]

Yes multiplication

[tepid hinge]

Yes

[tepid hinge]

I am here currently

Because 15 + 8 is 23 and the multiplication of both gives me 120

120 is from the multiplication of 20 and 6

[lean otter]

try breaking up the 6t^2 to help find your factors

should have the form:

$(3t+a)(2t+b)$

[flat frigate]

Stelonis

[lean otter]

where a and b are the other factors

[tepid hinge]

I got those numbers the way I know of doing this type of problems

The thing is with a and B I will send a pic of how I do this

I can't go any further

If I divide 20 by 8 I get 2.5

[tepid hinge]

Bro you still there can you help me out with this?

I believe I am using factoring by grouping

[misty bay]

honestly I probably would do a terrible job of explaining that

the most intuitive methods for me involve polynomial root-finding

factoring by grouping is basically making educated guesses and I don't really know how to explain the intuition behind those guesses

[tepid hinge]

I saw that explanation it is kind of complicated to understand.

[tepid hinge]

That's ok thanks tho

[mortal sandal]

if its too hard to factor you could always use the quadratic formula to find the roots

2t+5 is a factor though

so you just need to find the other one

[tepid hinge]

Yes but I don't know how

I can't work with 8 and 20 I will check out that formula

[mortal sandal]

if you know completing the square that could work too

but grouping like (6t^2 + 15t) + (8t + 20)

what's the biggest common factor of 6t^2 and 15t that we can factor out

[tepid hinge]

I was looking at the square one seemed easy but still didn't gave me the numbers

[mortal sandal]

you tried completing the square?

[tepid hinge]

I tried that square lol

[mortal sandal]

ah i see

thats different then what i was talking about

[misty bay]

that is actually a legitimate way of completing the square is it not

well not exactly that way

but drawing the square

[mortal sandal]

the top two squares work but the bottom two dont

[mortal sandal]

first you'd probably at least have to divide out a 6

or idk

unless you want to start with tsqrt(6) + ... on each side

[tepid hinge]

yes

[tepid hinge]

it is but I don't understand this method I did it wrong

[mortal sandal]

we can go back to the grouping part if that makes sense

like $(6t^2 + 15t) + (8t + 20)$

[tepid hinge]

yes

[flat frigate]

monikanicity

[tepid hinge]

the problem is when am solving for 8 and 20

[misty bay]

well you're stuck with 20 because it's already given

your only choice is in splitting the 23t into parts

[tepid hinge]

so I only have to work with 8

o alr

[misty bay]

yeah you basically have to pick where you want to split the middle

[tepid hinge]

how would that work?

I got 15t and 8t

[tepid hinge]

$4(2t+5)$ is this valid I factored out the gcf

[flat frigate]

(Living in College) GIO9011

[mortal sandal]

yes

[tepid hinge]

I did this already but if I factor out the gcf again using this method gives me a similar answer $3t(2t+5)$

[flat frigate]

(Living in College) GIO9011

[mortal sandal]

good

[tepid hinge]

good

[mortal sandal]

you have to factor each part like that

[tepid hinge]

oohh I see

what do I do with the gcf that I factored out?

[mortal sandal]

Use it to rewrite the polynomial

so rewrite what you already have but with the gcf factored out

[tepid hinge]

alr I will see

$3t(2t+5)+4(2t+5)$

[flat frigate]

(Living in College) GIO9011

[mortal sandal]

yeah good

[tepid hinge]

$(2t+5)(3t+4)$

[flat frigate]

(Living in College) GIO9011

[tepid hinge]

I see now

[mortal sandal]

ye

[tepid hinge]

thank you all for the help

[mortal sandal]

no problem

[tepid hinge]

👍

.close

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[lean otter]

Hello, how do I solve for x here, I’m trying to determine the length? I’m confused as to which formula to apply here?

[lean otter]

Yes

Yes

Okay 1 moment

correct

ive done that

okay

just a little confused, when you say get sin 62, are you asking me to input that into the calculator?

okay, i see

thank you very much!

i see, okay, yeah I was wondering if theres a more efficient way

thanks again, if i have anymore questions ill be back!

take care

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[spiral crescent]

why does this happen

[low canyon]

Because why not?

[spiral crescent]

Can you explain how, its not wrong cuz it does match my answers i found for specific no. Of tosses

[low canyon]

You can condition on the first throw

@spiral crescent

Use the total probability rule

[spiral crescent]

By total probability rule do you mean p(ab)=p(b)p(a/b)

[spiral crescent]

As in introduce a condition?

[low canyon]

I mean that if $\left{F_1, \ldots, F_n\right}$ is a partition, then \begin{align*}
P(E) = \sum_{i=1}^n P(E \mid F_i)P(F_i)
\end{align*}

[flat frigate]

Fέliχ

[low canyon]

Use an adequate partition on the very first throw

(Heads, Tails)

[buoyant shadow]

i think of it as last throw instead

[low canyon]

This is not a good idea

[spiral crescent]

Whats a partition

[buoyant shadow]

wow rude

[spiral crescent]

💀

[low canyon]

How so 😄

A partition of a set are disjoints subsets for which their reunion gives the whole set

[buoyant shadow]

being challenged is perceived as rude, what do you mean

[low canyon]

Basically, a partition here are the two events {The first throw is heads} and {The first throw is tails}

[spiral crescent]

So their sum gives the whole set?

[low canyon]

Their union

[spiral crescent]

But if they are disjoint subsets

Wouldnt their union and sum be the same

[low canyon]

You cannot sum sets

Union is kind of a sum for sets already

[spiral crescent]

How is this an adequate partition

[low canyon]

Because for anything that can happen in the random experiment (throwing a fair coin n times)

Exactly one of these two events ( {The first throw is heads} {The first throw is tails} )

Will happen

[spiral crescent]

And the next time we use partition on the first two throws?

[low canyon]

No, this will be sufficient

The idea is the following:

IF you get heads on the first throw, then you have to get tails on the 2nd throw

And after that, it refreshes everything as you got a tails, so it's kind of like if you restart the whole experience with n-2 throws instead

IF INSTEAD you get tails on the first throw, then good news, it's like refreshing the whole experience but with n-1 throws instead

Maybe I should have started explaining that way

This is why you use the total probability rule

To condition on the first throw

[spiral crescent]

Why does only tails refresh the experience

[low canyon]

Because if you get tails, the whole heads count restart to 0 (in order to get 2 consecutive heads)

So if you get tails on the first throw

it's like if you restart everything

[spiral crescent]

🤔 hm

[low canyon]

but with one throw less

[spiral crescent]

This was def not taught, but tbf you didnt have to actually know all this to solve this

[low canyon]

You do

[spiral crescent]

No no the question was a statement and reasoning type

[low canyon]

You do need to use the total probability rule to get that equation

Trust me on that, no doubt

I could bet you 1 million$ on that

Any other possible ways will have that common point

And I don't see another possible way anyway

[spiral crescent]

I just had to find p2,p3,p4 and for that i dont really need a general expression

[low canyon]

But where did that expression come from then?

[spiral crescent]

But the solution key did it this way so i wanted to know how

[low canyon]

Ok, I understand better now

This is from the total probability rule

[spiral crescent]

Yep thanks i get it now

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[lean otter]

Hi! I've been trying to work out this question for a little bit now. I got to the point that I have ∫(cos(x))/(sin(x) * (ln(sinx))

with U = ln(sinx) and du = dx/(sinx). Just confused on how to proceed from here. Thank you :)

[slow fern]

Do you know integration by parts?

[lean otter]

Yes!

[torn vessel]

Ur derevative is wrong :)

[lean otter]

Thank you!!

[torn vessel]

No prob

[lean otter]

Totally forgot the chain rule 😭

.close

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[torn vessel]

Lol happens

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[lean otter]

<@&286206848099549185>

[dusk vapor]

This is a math server

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

Ahh

I guess I took an L

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[silent brook]

how do i show the latter part about the solution set being a circle?

so far ive tried to make use of mod(a^2)>=4b ineq and relating it to the main equation...?

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@silent brook Has your question been resolved?

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[fast quail]

y = 3x^2 + 2xy x in terms of y?

[obtuse plover]

Get all terms with a y to one side

[fast quail]

i couldn't do it

<@&286206848099549185>

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@fast quail Has your question been resolved?

[fast quail]

thanks

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[lean otter]

Hi im just a bit perplexed on how thee lines follow:

[lean otter]

log11(2x^2+7x-4)=1

11^1=2x^2+7x-4

if both sides have been multiplied by (2x^2+7x-4) i understand how you would get

logbase11(?)=(2x^2+7x-4)

just a bit confused where 11^1 is from

[peak estuary]

remember the definition of log

log_a(b)=c means what?

[lean otter]

11^(2x^2+7x-4)=b?

[dusk vapor]

Mr

[lean otter]

I UNDERSTAND omg thanks

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[glossy rover]

Who can help me:

[cosmic grove]

?

[glossy rover]

I determined that Vn+1 is geometric

[safe radish]

@glossy rover Has your question been resolved?

[glossy rover]

<@&286206848099549185>

Please

Sorry for ping

[young nexus]

can you express v_n as term in n?

[glossy rover]

that is to say? express Vn+1 as vn?

[young nexus]

no, not recursive.

[glossy rover]

I have neither the first term of the sequence, nor the expression Vn, I have to determine it thanks to Vn+1 which is geometric?

OH I CAN

I have the reason

That is 3/2

V_n= (3/2)^(n-p)*v_p

[young nexus]

set p=0

[glossy rover]

I Can Do it ?

[young nexus]

just do it

[glossy rover]

i thought i couldn't

Ok

So

V_n=((3/2)^n)*(v_0)

[young nexus]

exactly, for easier writin, say v_0 = s and q = 3/2

[glossy rover]

Okay i know now

Thanks for help

I Can Do it for the sums

It's easy

Thanks

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[fossil vine]

how do i solve this if x is 4

[fossil vine]

ik 1/2 x is 2

but how do i do 2^-1/2

[faint iron]

almost

[supple shore]

i'm a bit slow in latex

[fossil vine]

whats latex

[south kindle]

a^c=b

[faint iron]

$x^{\frac{a}{b}} = \frac{1}{x^{-\frac{a}{b}}}$

[fossil vine]

im so confused

[faint iron]

its some sort of code to write math with letters

[fossil vine]

why is log here

oh thats for a diff qeustion

[faint iron]

yes

[fossil vine]

oh ok

[faint iron]

lets focus on yours

[faint iron]

this right ?

[fossil vine]

yes

[faint iron]

does this sound familair ?

[fossil vine]

nah havent learnt this yet

[faint iron]

ok

mhm

and its wrong lmao

dont learn it

[fossil vine]

oh lol ok

[flat frigate]

demiryolu mühendisi

[royal breach]

$$x^{-\frac{1}{2}}=\frac{1}{\sqrt{x}}=\frac{1}{\sqrt{4}}=\frac{1}{2}$$

[flat frigate]

Михаил Колесников

[faint iron]

yes

[faint iron]

basically those are formulas

[fossil vine]

if thats the formula and if the power was just -2 instead then would it be like 4^-2/1

then woul;d it be same formula

[faint iron]

ye

pretty much

you dont need the one

[fossil vine]

then what is it

if a number is x

is x^-n always x/n

[faint iron]

like $x^{-2} = \frac{1}{x^2}$

[flat frigate]

demiryolu mühendisi

[faint iron]

no

$x^{-n} = \frac{1}{x^n}$

[flat frigate]

demiryolu mühendisi

[fossil vine]

OHHHHH

thats why x^-1/2 is that

i get it

[faint iron]

ye

[fossil vine]

also howd u put it in latex like did u learn it or what

[faint iron]

power 1/2 is square root

can come handy sometimes

[faint iron]

i know basics

fractions and sums etc

those are simple

it gets tricky when you write whole lines

[fossil vine]

btw im not really learning this in school so what grade or year or idk would u aproximmate this is for

i think i went too ahead

[faint iron]

time consuming

im first year of math degree

[fossil vine]

i mean the questions i asked, what grade would u say its for

or like age

[faint iron]

oh

idk

[fossil vine]

oh cool

[faint iron]

like highschool 1 or 2

[fossil vine]

well ty for help

[faint iron]

no worries

[fossil vine]

oh yeah thats too ahead lol im in middle school

.close

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[lean otter]

can someone explain how -5 is not the answer please?

[royal breach]

9+4=13

[modern fractal]

,w (-3)^2 - 4 \times 1 \times (-1)

[flat frigate]

Results provided by WolframAlpha

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

Requested by Welf#4614

[lean otter]

OHHH

because the -3 needs to be in brackets or else it only ^2 the 3

got it

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[unreal fiber]

<@&268886789983436800>

[harsh shoal]

ty

.close

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[kind hamlet]

hello i'm really having difficulties understanding how to calculate the eigenvectors, i looked at some wirings and some google pages but im having trouble understanding,any help? 😦

[kind hamlet]

i already calculetad the eigenvalues but im having difficulties for the eigenvectors

this is the matrix to be more clear

[broken yew]

ok so first step is to state the definition

Ax = kx
(A - kI)x = 0

Then you solve this equation for each eigenvalue k

This is just an equation in the form Bx = 0 (where B is known)

[kind hamlet]

what is kI?

[broken yew]

kI

I being identity matrix

You start with Ax = kx

Ax - kx= 0

then notice kx is also (kI)x

[kind hamlet]

oh

is x an eigenvalue?

so in my case i found 3

[broken yew]

no, x is a vector

?

[kind hamlet]

oh

[broken yew]

you're familiar with what I wrote or not

Ax = kx

This as the definition of eigenvector and eigenvalue

[kind hamlet]

Yes in the case of eigenvalue

[broken yew]

well no, they're both defined in the same equation

[kind hamlet]

oh

[broken yew]

for a constant matrix A,

Ax = kx

Then k is an eigenvalue and x is an eigenvector

[kind hamlet]

ooooooooh

and to find it i just have to Ax-Kx=0?

where Kx is equal to KIx?

[broken yew]

you have k, solve for x for each k

Each eigenvector corresponds to an eigenvalue

[broken yew]

Notice A - kI is matrix A with k subtracted from each main diagonal entry

[kind hamlet]

yes

i just have to substitute them i guess?

[broken yew]

yes

[kind hamlet]

and then keep going?

oh

wait

dont look at the las 0-lambda im dumb i just changed it

something like this?

[broken yew]

I'm not going to check, but once you have an answer, you can check it works

check the equation Ax = kx holds

[kind hamlet]

ooh i think i got it thanks 😮

.close

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[fiery olive]

Having trouble figuring out where to start for 3c and 3d, here is my work for 3a and 3b

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@fiery olive Has your question been resolved?

[fiery olive]

<@&286206848099549185>

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@fiery olive Has your question been resolved?

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[inner perch]

New topic in math for me

[lean otter]

Oh hello again

[inner perch]

Hi

[lean otter]

What's the question

[inner perch]

I need to calc it

[lean otter]

It's kinda hard to read

[plucky elk]

Complex numbers?

[lean otter]

Is it (x-5)^4=-16

??

[inner perch]

Yeah

[lean otter]

Ok so

-16 is negative

So it will have two complex roots

so

[ember sphinx]

Complex numbers

[lean otter]

x-5=square root(-1)*square root (4)

[inner perch]

Is it complex?

[lean otter]

Solution will be complex

[worthy hemlock]

Don't to the work for people

It doesn't help them learn if you do everything for them

[inner perch]

Where does the i

[lean otter]

You're right

[inner perch]

Coming drom

[lean otter]

Ok

[flat frigate]

dldh06

[lean otter]

Whoa how do u do that

That texit thing

Nvm

So

So now that we know that, what does it become?

[inner perch]

CN

Can we start from beginning

Because i am lost now

.close

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[worthy hemlock]

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

[ember sphinx]

The 16th root of 1 to the power of 7?

Nice.

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[tidal gust]

Situation: Danny Heater set the national high school record for most points scored in a basketball game with 135 points on January 6, 1960. Billy Baller has a chance to break Danny's record at tonight's game. It is half-time and Billy has already made 7 free throw shots worth one point each as well as multiple two point and three point shots. Billy wants to know if he makes more two point shots than three point shots, what is the minimum number of two point shots he can make and break Danny's record.

Product: Determine the minimum number of two point shots that Billy could make during the game to break Danny's record. You must show Billy mathematical proof that you have correctly found the minimum number of two point shots he must score to break Danny's record.

[tidal gust]

okay

so i get that it is like a 3 equation question about system of equations i think

but im stuck and dont know where to start

if anyone could give me tips that is great

please anybody

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[tidal gust]

someone?

please

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✅

[tidal gust]

i don’t know where to start with this word problem can anyone help

[rigid saddle]

@tidal gust u can first set up an equation for this problem
lets assume u need to score greater than or equal to 136 points
we can set the equation equal to 136 for simplicities sake and round up later

So we can get the equation

$7 + 2(x+1) + 3x = 136$

[flat frigate]

Аngеl Оf Неll

[rigid saddle]

7 is the 7 free throw points

[tidal gust]

yes

correct

[rigid saddle]

x is the number of 3 pointer shots

and since we want more 2 pointer shots than 3

we can add 1 to x

so we get 2(x+1) for the 2 pointer shots

and 3x for the 3 pointer shots

then we can solve this equation for x

@tidal gust then u can try solving

[tidal gust]

alright

thank you for this

ill get back to you if I do solve it

[rigid saddle]

yea

just remember take the numbers

[tidal gust]

if not will you proceed to assist me

[rigid saddle]

and force them into an equation

[tidal gust]

got ya

sorry algebra is my weakness

[rigid saddle]

yea

np

[tidal gust]

I think I found x

Is it 25.4

@rigid saddle

[rigid saddle]

alright

thats good

now can u shoot 25.4 balls

or what do we do with this answer

@tidal gust

[tidal gust]

sorry

was eating dinner

[tidal gust]

well no

but you could make 25.4 points right

if you round up the 25.4 to 25

[rigid saddle]

round 25.4 up to 25?

[tidal gust]

or shoot 25.4 3 pointer

[tidal gust]

round down sorry

[rigid saddle]

if u round down do u still get enough points?

[tidal gust]

oof

🤨

[rigid saddle]

so u need to round up

[tidal gust]

ohh

alright

[rigid saddle]

remember u want to get at least 136 points

more is always ok

[tidal gust]

ya that question kinda stumbled me

[rigid saddle]

so then we get 26

for x = 26

[tidal gust]

alright

[rigid saddle]

so how many 2 pointer shots do we need to score

[tidal gust]

well earlier you started x = 3 pointers correct

[rigid saddle]

yes

[tidal gust]

so if I plug in x into the equation you gave me, will that tell me how much 2 pointers i need to score?

oh wait

wait

wait

before you finish typing

im stuoid sorry

[rigid saddle]

np

[tidal gust]

26 three pointers is around 78 points

plus the free throws

+7

so the rest of the points that’s missing

136-78 = y

Y is the 2 pointers?