help-43

[rigid jungle]

i have my x and y

[slate sand]

Not just constants

All lower order terms

[rigid jungle]

i thought constants were not x values

[slate sand]

Here that’s the constants but not always so

Look at this

The 9x and 1x are ignored here

[rigid jungle]

what if there were no exponents

[slate sand]

Because they are lower order than the x² terms

Then you have a fraction

[rigid jungle]

how would my answer change

[slate sand]

Lol

You just have a/b if there are no powers

[rigid jungle]

o add the x

[slate sand]

2x is 2x¹

[rigid jungle]

yea

[slate sand]

There’s always a power

Here “lower order terms” are the constants

I just didn’t want you to think it’s always the constants

[rigid jungle]

so if there was a 2x^3 and a 4x^3 i would ignre the x^2?

[slate sand]

Yes

[rigid jungle]

okay

so how do i determine the end behavior

[slate sand]

The cube will grow much quicker than the square

[rigid jungle]

makes sense

[slate sand]

Here

[rigid jungle]

i dont understand that currently

[slate sand]

Which part

[rigid jungle]

what determines if the first line is positive or negative

if you look at image 1 and 2

[slate sand]

The sign of the highest order coefficient

Divided by

Wait um

You just look at it

Do you know how to draw polynomials

[rigid jungle]

im bad at graphing thats why im asking

[slate sand]

Oh

[rigid jungle]

its 1/1 here

[slate sand]

So on the top and bottom

[rigid jungle]

x+4/x+5

[slate sand]

Let’s look at the top

[scenic forge]

well if its $\frac{2x+1}{1-x}$ then it would be $y=-2$

i.e. 2/-1

[rigid jungle]

there are 2 lines thats why im confused

[slate sand]

Yeah I guess you can just remember that

[boreal girder]

DaveyLovesSocks

[slate sand]

Sign of the Coefficient of the highest order on top times … on bottom

Here it’s + times - because 2x is positive and -x is negative

[rigid jungle]

yea so x/x

1/1

[slate sand]

No no x’s

I only said sign of the coefficients

[rigid jungle]

nonono

[slate sand]

Oh for example

[rigid jungle]

im talking about my equation for this problem lol

[slate sand]

Yeah

[rigid jungle]

x+4/x+1

the x is 1/1

[slate sand]

The end behaviour is yeah

[rigid jungle]

so how does that translate to the graph

thats what im confused on

[slate sand]

It’ll look like an asymptote

[slate sand]

Draw the rest of the features

[slate sand]

Then draw the line y = 1

[rigid jungle]

y = 4

input 0

4/1

4

should be y=4 x=(-4,0)

[slate sand]

The function will tend towards this line at both infinities

[rigid jungle]

is y not 4??

(x+4)/(x+1)

(0+4)/(0+1) = 4/1 = 4

oh im slow

wait what why is y graphed on the x axis

[slate sand]

Divide the coefficient of the highest order

Not the constants

We really don’t care about the lower order terms

At all

Because we’re taking the limit to +- infinity

[rigid jungle]

the end behavior is y?

im more confused now than when i started😭

[lime juniper]

might be helpful to write

x+4=x+1+3

[rigid jungle]

ohhhhhhh

the end behavior is the horizontal asymtote

so i calculate y right

but thats not what i needed

so now that i know

is this not right???

y = 4

x = -4

HA = 1

VA = -1

[lime juniper]

vertical is up down

horizontal side to side

[rigid jungle]

yes

is the dotted line supposed to be -1?

[lime juniper]

its a line, not a number, not sure what you're asking

[rigid jungle]

like the point

of the dotted line

[lime juniper]

what's the question?

[rigid jungle]

is the black ball on the dotted line supposed to be at (-1,0)

[lime juniper]

dont know enough about black balll on dotted line notation to say

:(

[slate sand]

That’s just a vertical asymptote

When the bottom is 0

[rigid jungle]

which is -1

[slate sand]

You’re trying to divide by 0

So you get an asymptote

[rigid jungle]

i have all the numbers

does the graph look correct?

it says my end behavior is wrong

oh

[slate sand]

You’re not posting what the problem is in any of these photos

[rigid jungle]

nah i know what im doing

i figured it out

i was being dumb

the r word is really banned in this server

snowflake stuff

[slate sand]

It’s a big partnered server

[rigid jungle]

oh

if its sponsored and stuff that makes sense then

how tf does the exponent change it

[slate sand]

Change what

[rigid jungle]

is ti x-1/x-2

assuming its x^2-4

and then x+2 x-2

and then GCF cancels x+2

x-1/x-2

does this look right?

WTF IS THIS

nvm

am i supposed to have 2 VA

do i calculate VA after simplifying or before

[plucky rivet]

since the denominator is equal to zero at only one x value, you should have only one VA

[rigid jungle]

so dont simplify at all

[plucky rivet]

can you simplify this? there isn't a common factor in the top and bottom

[compact pewter]

@rigid jungle Has your question been resolved?

[rigid jungle]

i was doing the exponent and then canceling the -4

but im not supposed to

[plucky rivet]

you can't cancel terms that are added or subtracted from the top and bottom, only factors that are multiplied

[rigid jungle]

is there a way to do this without replacing x 4 times

or is that the only way

[plucky rivet]

to solve a nonlinear inequality, you should find the values of x that make the top and bottom equal to zero and put them on a number line. these are the only places your rational function can change sign, so if you try a test nuber in each interval, you'll know the sign of the function on that entire interval

< 0 means you're looking for where the function is negative

[peak kayak]

<@&268886789983436800>

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[rigid jungle]

why mod tag

[peak kayak]

inappropriate post that was deleted by mod

[compact pewter]

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[pearl flume]

Hi everyone,
I'm trying to solve the equation
$$
i z^3 = \overline{z}
$$
where $z$ is a complex number, and I'm only allowed to use the trigonometric form of complex numbers:
$$
z = r(\cos \theta + i \sin \theta)
$$
I cannot use the exponential form like $z = re^{i\theta}$

Could someone help me solve this step by step, staying only within the trigonometric form?

Thanks

[boreal girder]

tommaso

[kind viper]

are you allowed de moivre's

[pearl flume]

yes

[kind viper]

actually first take absolute value of both sides to find that r can only possibly be 0 or 1

r=0 obviously gives z=0, and r=1 requires further investigation

with $r=1$ you get $\overline z = z^{-1}$

[boreal girder]

Ann

[pearl flume]

is that the only solution? apart from r = 0

[kind viper]

i didn't say anything about solutions

well like taking absolute value on both sides gives r^3 = r

so yes r can only be 0 or 1

the r=1 case will lead to more than one solution for z though

and i invited you to try and figure out which ones these could be

[pearl flume]

okay thanks a lot

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[wary mulch]

Is 120 a solution as well

[stark marsh]

yes it is sin(120)=sin(60)=sqrt(3)/2 you could work it out

[wary mulch]

But it’s not apparently

It’s not in the answer

wait nvm

[lavish gull]

wot

[stark marsh]

srry

[stark marsh]

if it messes you up try writing sqrt(3) and 1 as sqrt(3)/1 and 1/1 it may help

ok omit the 1 part but the rest damn my brain is fried

[wary mulch]

ok thanks I get it

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[spice carbon]

Hello, P is directly proportional to Q cube. A change in Q produces a Change in P. When the value of of Q id multiplied by 1/2, the value of P changes by a factor of m. Find m. The answer states m = 1/8 but I don't understand why.

[maiden flicker]

I mean so okay do you know how proportionality works?

[spice carbon]

yes

P =kQ^3

[maiden flicker]

If uhm letss say p was directly proportional to q then what would have been the change in p if you change q by 1/2

[maiden flicker]

Yeah yeah

[spice carbon]

o p would change by 1/2 as well?

[maiden flicker]

Yeah yeah

So now q is cubed what would it change to?

change by*

[spice carbon]

1/2 cube?

[maiden flicker]

Yeah and that is?

[spice carbon]

OOOOOOOOO

1/8

[maiden flicker]

😂😂😭

[spice carbon]

TYSMM

[maiden flicker]

Yeah yeah welcome

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[pearl hound]

can i get help with question 11

a first

i’ve done cos3theta = -1

[placid bridge]

For what values of theta is cos theta= -1?

[orchid moat]

if theta is between -90° and 180°, then what is range is 3 theta in?

[pearl hound]

not to sure can you explain please

[pearl hound]

what do you mean by this

[placid bridge]

When is cos x = -1?

[quiet sentinel]

on the unit circle what angle gives an x value of -1

[pearl hound]

180??

[placid bridge]

Yes

[orchid moat]

like if -90° ≤ θ ≤ 180° can you write that inequality with 3θ in the middle instead

[placid bridge]

So if cos 3theta = -1, what does that tell you about 3theta?

[pearl hound]

uhm

im not to sure

[placid bridge]

Let x = 3theta
Then x = 180 right?

[pearl hound]

yes

[placid bridge]

Replace x by 3theta

$3\theta = 180 \implies \theta = \frac{180}{3}$

[boreal girder]

Sarin

[pearl hound]

so basically since 3theta is doing 3 cycles its going 3 times faster

so u divide by 3??

[placid bridge]

Don't think of theta as angle, just think of it as another variable

If you had 3x = 180, you would solve it by taking 3 to other side to get the value of x. Do the same here

[pearl hound]

ohhh ok I understand, so then we use the unit circle to where else theta = 60

[placid bridge]

Do you mean use the unit circle to see where else cos x is -1 ?

[pearl hound]

yes

that’s what i mean

[placid bridge]

Yes, do that

[pearl hound]

can you explain how to do that exactly please

[placid bridge]

Well, if you think of the unit circle, cos x is -1 when x is 180. To get -1 again you have to rotate another 360 degrees to get back to the same point.

What that means for trigonometric functions(mainly sin and cos) is that their values repeat after adding 360 degrees to their angle

So $\cos x = \cos (360 + x)$

[boreal girder]

Sarin

[pearl hound]

alright that explanation makes sense to me

[placid bridge]

Again, x = 3theta, so substitute that in 360 + x = 180 and solve for theta and finally check whether that value lies in the range they have provided

If it does, that means you have gotten another solution

Similarly try this for x - 360

[pearl hound]

alright i think i got my question explained

thank you so much :))

[placid bridge]

No problem

!done

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[molten rampart]

im getting this, whats wrong?

[rotund sphinx]

They probably just made a typo in E ngl

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@molten rampart Has your question been resolved?

[molten rampart]

ah i see, ty

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[deft tangle]

Domain of 1/(1-tanx)

[deft tangle]

So here clearly tanx=\1

R-(nπ+π/4)

R-π(4n+1)/4

[kind viper]

you need to also exclude points where tan(x) is undefined

slightly fancy way of writing it: $$\bR - \curly{n\pi + \frac{t\pi}{4} : n \in \bZ, t \in {1,2}}$$ (if this makes no sense to you then just ignore it)

[boreal girder]

Ann

[kind viper]

are there answer options? @deft tangle

[deft tangle]

Yeah

[kind viper]

uhhhh

okay hold on

oh i guess they include (2k+1)pi/2 and (4k+1)pi/4 THAT way.

[deft tangle]

It makes clear sense

I didn't understand (4n+2)π/4

I got it

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[deft tangle]

.reopen

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✅

[deft tangle]

Tell me why did you not exclude there are many points

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[deft tangle]

Hold on

.reopen

[compact pewter]

✅

[deft tangle]

@kind viper they wrote wrong n belongs to z

[kind viper]

eh?

[deft tangle]

Here

[kind viper]

no, k goes over Z.

n is 2 or 4 only.

[deft tangle]

Fine

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[rose goblet]

can someone tell me how the s_n formula was found

[civic quartz]

hm

[kind viper]

sum of a geometric progression?

[civic quartz]

Considering
Sn = a + ar + ar^2 +.........+ ar^(n-1)

[civic quartz]

igso

are you here?

[kind crane]

https://math.stackexchange.com/questions/4255628/proof-of-geometric-series-formula>

[rose goblet]

yes but in terms of infinate series

how can we multiply by r

oh its a limit

so we can use n and then take limit nvm

[kind crane]

yes finite sum

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[hardy cedar]

study discussion problem

[chilly basalt]

Hii, show your problem

[hardy cedar]

its a study problem

[idle turtle]

Okay here hit me with it again

[hardy cedar]

okay

[idle turtle]

okay so imagine its like
5x^2x+4=3x^2-2x+5. sometimes i mess up the signs. so this is my result
8x^2+9
instead of
2x^2+4x-1

Here i found it

[hardy cedar]

okay so imagine its like
5x^2x+4=3x^2-2x+5. sometimes i mess up the signs. so this is my result
8x^2+9
instead of
2x^2+4x-1

[idle turtle]

Wait that first polynomial is unclear to me... is that 5x^2 + x + 4?

On the left side

The 2 and x are confusing me

[hardy cedar]

okay so imagine its like
$5x^2x+4=3x^2-2x+5$. sometimes i mess up the signs. so this is my result
8x^2+9
instead of
2x^2+4x-1

[hardy cedar]

$5x^2x+4=3x^2-2x+5$

[boreal girder]

Tan

[hardy cedar]

what the

its

5x^2+2x+4

[idle turtle]

So it's 5x^2 times x?

[idle turtle]

Okay

Tht makes much more sense ty

[bleak dock]

$5x^2+2x+4=3x^2-2x+5$

[boreal girder]

south

[hardy cedar]

btw this isnt a real problem

[idle turtle]

Pulling out my white board and ill. Send some pics

[hardy cedar]

its like a reference to

the factor theorem

[bleak dock]

how so?

[idle turtle]

I would start something like this if you're having trouble with figuring out the signs

Bring the right side over to the left by subtracting the entire right side from both sides

Then you have a negative sign outside the original right side that can be distributed to each individual term

[hardy cedar]

yes

i know that

but when i do it

sometimes i mess up with the signs

[idle turtle]

So then what's the first term 3x^2 gna become?

[hardy cedar]

-3x^2

but sometimes i write it as 3x^2 and end up doing the whole thing wrong

[idle turtle]

Correct. And the second one is "-2x" what is tht gna be?

[hardy cedar]

2x

-5

[idle turtle]

Understandable. There's rly no foolproof way around it. You need to be thoughtful and careful

[hardy cedar]

wait maybe if i do it ur technique

[idle turtle]

Organization of the problem in a way that keeps that in line for you is the best method to it. Other than that, just slow down

[hardy cedar]

then it isnt foolproof

cuz ur technique is like

$5x^2+2x+5-(3x^2-2x+5)=0\2x^2+4x$

[boreal girder]

Tan

[hardy cedar]

as where my technique is

directly doing it

[bleak dock]

well, 2x^2 + 4x = 0

[hardy cedar]

$5x^2+2x+5=3x^2-2x+5\2x^2+4x$

[boreal girder]

Tan

[hardy cedar]

thank you

sm

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[mental cloud]

Hi! I have a question about the following problem (translated)
You buy a car. Write down T for the time that the car will work without defect in years. For every natural number we write down P(T >= n) the chance that T is bigger or equal to n. there is given that (look at the picture). What is the chance that the car will have a defect for the first time in the third year.
I thought it would make sense to just plug in 3 in the equation but that's not what I should do. I have no idea how to do this problem otherwise. Maybe I'm missing some knowledge so please tell me what I need to know to solve this.

[mental cloud]

please ping me when you want to help me

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@mental cloud Has your question been resolved?

[mental cloud]

I'll be back!

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[snow stone]

given that this function, lets call her g, is continuous for g(-1). does it mean that f(-1) must be also continuous?

[snow stone]

i showed that it doesnt necessarily has to

by giving these example ^

ik that f(-1) exists

[crystal wraith]

[winged lion]

It looks good

[snow stone]

cool , cuz f in that example has no limit for x--->-1

but f(-1) exists tho so g(-1) all good

[winged lion]

ya

[snow stone]

but yo know what

[snow stone]

if g(-1) is continous isnt f(-1) also supposed to be?

cuz if g(-1) continuous its limit for both x--->-+1 must exist

[winged lion]

The thing is, the limit of g(x) at -1 is independent of f (given it's not 0) because you get 0

[snow stone]

great thx

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[quartz yoke]

What math should i learn before going to a math career?

[true kiln]

What math career

Research in math in general or any other math related cs, physics,etc

It would be clear if you said what you want to become

[chilly basalt]

Math major?

[quartz yoke]

Ye

[true kiln]

Mb i misunderstood q

[glass turret]

well

you're gonna need to know a lot of math considering you're majoring in math

i think a good foundation of everything up till calculus when you're going into college should be good

and then you learn the rest at college

[soft bobcat]

what country are you from OP

[magic wren]

I think you should reconsider your math career. Majoring in computer science and working a data entry job and studying math in your free time is perfectly valid

[quartz yoke]

Venezuela, i do math for money

[glass turret]

yeah you could go into something such as data science

or if you're really math oriented you can do something like quant

[magic wren]

you should ask yourself why you want to study math

I think you should only go into math if you truly have nothing else better to do, or if you don't trust my word. Both are totally valid reasons

[soft bobcat]

dawg math for money wont get you anywhere

you gotta have a genuine interest

[quartz yoke]

Money, im more interested in programming since i like it and gives money too

[lime juniper]

as someone who majored in math hoping for a math career

it's a bad idea

[soft bobcat]

in whatever you're doing, math or something else

[lime juniper]

go for applied math instead

[quartz yoke]

AI is a good career too?

[magic wren]

If you don't love math with every inch of your soul, you're not gonna make it through a math major mentally intact. If you do love math with every inch of your soul, you're gonna make it through your math major mentally bruised and abused. But at least you have a cool degree or something

[glass turret]

AI uses a good amount of math yea

but i wouldn't say its fully dependent on math

[lime juniper]

I do love math with my soul, made it through my major bruised and abused, but it's a shit degree to get a job with

[glass turret]

nah but there's aura that comes with it

[lime juniper]

so i wouldnt recommend it even for lovers of math

[glass turret]

saying you survived your math major

[lime juniper]

auras dont pay for food and medical care

[winged lion]

The math major survived me

[lime juniper]

and rent

[glass turret]

good point

[quartz yoke]

The point is

[magic wren]

real

I changed course and I'm going into education

[quartz yoke]

I want a career with math that gaves me a remote job

[glass turret]

i would suggest looking into data science

or data analysis

[quartz yoke]

Ai is good too?

Or cibersecurity?

[magic wren]

this is called programming

[quartz yoke]

Yeah but what type of programming

Applied math works too?

[magic wren]

yeah applied math and operations research might be fine

but you'll be on thin ice looking for a job

[glass turret]

i dont think cybersecurity uses a lot of math

AI uses a good amount

machine learning

[soft bobcat]

encoding is all math

[glass turret]

oh shit forgot about that

[winged lion]

Forget jobs, finding internships is hard too, I am applied math major, so I wonder how it's for pure math ppl

[glass turret]

from what you've mentioned I'd probably say data science/machine learning/quant is probably best for you to look at

or cybersecurity too

it's a matter of what you find interest in doing though

i wouldn't suggest going for some job just cause it pays good even if you don't look it

[quartz yoke]

I like those things

[glass turret]

ask yourself whether you wanna be doing that same thing everyday for like 20 years of your life

[quartz yoke]

I want to do a bunch of things

I need resources and money for them

So for starters i have 4 options

[magic wren]

the system is rigged against you

the rich already hold all the wealth

you most likely won't succeed

[quartz yoke]

Cibersecurity, AI, data science, and quant

Whatever quant is

[quartz yoke]

Yeah and?

I know it, im from a poor country

[magic wren]

have you considered becoming a truck driver

[quartz yoke]

Nope

[magic wren]

I heard it's good fun

[quartz yoke]

In my life

Never going to do that

I hate that

Also here the payment is ass

What is quant btw?

[magic wren]

quantum technology

I presume

[tight obsidian]

😭😭

It’s quantitative finance

[magic wren]

oh my bad

[magic wren]

yeah the fact that you speak english as well as you do is gonna be one of your strongest advantages especially since you were born in venezuela (no offense to venezuela but you said it was a poor country)

so one thing you might wanna consider is phonetic training on your accent to make yourself feel more convincing in the anglosphere

[quartz yoke]

Cool

Soooo

[magic wren]

I think you should pick up lots of little skills and some random degree it doesn't really matter which one, like know the basics of programming and matrices and markov chains and all those basic things

[quartz yoke]

The world is doomed and all but im not surrending my life because of that

[quiet sentinel]

This is such a generic and subjective question lol

[magic wren]

Then just try to market yourself as a person who knows how to do stuff and with your excellent attitude you might just make it

[magic wren]

I respect that a lot

[quartz yoke]

Might? I will make it

[tight obsidian]

Venezuela is facing hyperinflation. Best thing to do is leave🥀

[glass turret]

quantitative analysis

[quartz yoke]

Where?

[glass turret]

an example is like the stuff trading firms do to analyze the stock market

[quartz yoke]

Sounds boring

[tight obsidian]

I ain’t telling you that

[glass turret]

well it pays a shit ton

[tight obsidian]

400k base salary

[glass turret]

their interviews are just real analysis and advanced number theory questions

[magic wren]

I was born in Finland, which isn't that bad all things considered but for some reason I've become convinced that I need to find my future spouse in the US so learning and perfecting foreign languages is always a good idea, it might open up cool new opportunities

since this turned into a general life advice thread

[quartz yoke]

I prefer to go to university do networking and taking the jobs they get to me

[magic wren]

Also I think learning languages is good for your brain in general because the way we think is through language

it makes your brain more flexible

just do it right, do it through immersion

[tight obsidian]

Finland is good too.

[magic wren]

don't get too focused on grammar

[glass turret]

yea isn't finland voted to be the world's happiest country

for 5+ years in a row

[quartz yoke]

What about norway?

[magic wren]

this is a good mindset

[glass turret]

honestly

[tight obsidian]

Cmon bruh, what special language did you learn? English? Ain’t that basic requirement ?

[magic wren]

I need to include this in my speech on why I'm the perfect boyfriend

[glass turret]

just do what makes you happy and you'll eventually see a happy life come along your way

[magic wren]

I've also learned Swedish to reasonable fluency

[tight obsidian]

That’s decent

[magic wren]

just to prove a point

I don't even need to speak Swedish tbh

I just enjoy the challenge

[glass turret]

just to flex

[magic wren]

yeah

[quartz yoke]

I dont know about what i love i just need money to live and discover it

[tight obsidian]

That’s what I’m saying.

[glass turret]

well in that case explore your possibilities

try new things

see what you enjoy doing and what you're good at

[quartz yoke]

Should i work in something i love?

[glass turret]

ideally yes

[cerulean bramble]

At this point, then you need to put in the effort to research what is available to you and what you might enjoy

There's not much else that we can suggest beyond this

[glass turret]

damn this just became a life advice channel

[cerulean bramble]

Then, if you decide what you want to do, check what requirements you might need to achieve that

[glass turret]

i'm guessing you aren't in college yet, which means you still have time to explore new things

[cerulean bramble]

Now, if they're maths-based, you definitely need a full school-level amount of maths at the least: most maths-based degrees, it might not shock you, need a decent level of maths to start with

[quartz yoke]

I want to learn math to at least dont feel iletrated

Whatever that means

[cerulean bramble]

"illiterate"

[glass turret]

illiterate?

[quartz yoke]

Illiterate

Yeah

[glass turret]

well

[quartz yoke]

I want my mind to be inteligent

[glass turret]

your school should do a good job of that

math isnt the only way to make your mind "intelligent"

its one of the ways, but not the only way

[magic wren]

Just do intelligent things every day

[cerulean bramble]

https://tenor.com/view/power-rangers-the-way-to-be-cool-is-to-stay-in-school-white-ranger-tommy-oliver-school-gif-26397980

[magic wren]

whatever you do don't ever browse tiktok

and you'll be alright

[glass turret]

speaking from first hand experience i agree with this

[quartz yoke]

The lesson here is i should do something i love and thats all?

[glass turret]

try to get a career in what u love

[cerulean bramble]

...essentially

[glass turret]

first explore your possibilities

you still have time

[magic wren]

@quartz yoke btw chatting on discord is a particularly intelligent activity so you're doing a good rn of improving your chances of having a prosperous life 👍

[cerulean bramble]

Discord is a path to success!? /s

[glass turret]

once you gauge an idea of what you like and what you're good at, you can explore career opportunities in those fields specifically

you guys are sleeping on the discord mod life

[magic wren]

for me it has been like idk where I'd be without discord tbh

Discord allows you to connect with people who are older than you who can give you life advice

that shit's invaluable

[cerulean bramble]

Oh well that's a fair point I take back my /s

[quartz yoke]

How i would try new things if whatever i do is read, eat, doomscroll, hear music and thats all

[glass turret]

well to start off

dont doomscroll

the internet is probably your biggest ally here

you can find pretty much anything and everything on it if you use it properly

you can explore different career opportunities using the internet

see what interests you

[quartz yoke]

I want to be an animator on newgrounds and have a little community

Like jaiden and domics and all those people

[quartz yoke]

How?, sometimes i cant try diferent things

Well, we can finish this here

How i close the thread?

[soft bobcat]

Type .close

[quartz yoke]

Thanks

[soft bobcat]

[quartz yoke]

.close

[compact pewter]

Channel closed

Closed by @near oxide

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

Send your question here to claim the channel.

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

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

[forest token]

how to solve this inequality ?
x-(1+x)ln(1+x)>0 where x is from -1,infinity

[proud halo]

hmm

the left side is the integral of ln(1 + x)

or - of that whatever

[forest token]

u want the actual question?

[proud halo]

yes

[forest token]

we have to tell if it decreases,increases etc

[proud halo]

ln(1 + x)/x

[forest token]

yeah

i differentiated

and did >0 to see where increase

[proud halo]

ln(1 + x) increases, and x also increases

but x increases faster

[proud halo]

Hmm

[forest token]

so ur saying i should do it by intuition?

[proud halo]

Wait

,w graph ln(1 + x)/x

[boreal girder]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by dyxn06

[proud halo]

well I did expect that behaviour

[forest token]

i didnt know it was like this..do i need like more practice or is there a way to prove it mathematically

[proud halo]

let's try it analytically

well you should expect that it's decreasing right?

[forest token]

yeah

for large values of x yes

[proud halo]

did that lead to it

[forest token]

but i couldnt tell for -1,0 interval

i picked option D

[proud halo]

what's the derivative

,w differentiate ln(1 + x)/x

[boreal girder]

Results provided by WolframAlpha

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

Requested by dyxn06

[forest token]

oh wait

one second

[forest token]

yeah

i got same thing

used product rule tho lol

and then i did >0

we can remove x^2

because its always >0

[proud halo]

could probably just analyse it from here

[forest token]

and then i took lcm and removed 1+x

because domain is x>-1

and then i got that expression which i sent initially

[proud halo]

hmm

[forest token]

yeah i was not able to do that

[forest token]

can we take log to other side

and then do e^x?

[proud halo]

maybe

[forest token]

maybe 😭

[proud halo]

[ \frac{x}{1 + x} - \ln (1 + x) ]

[boreal girder]

maison

[proud halo]

for x in (-1, 0) the left term ranges from -infinity to 0

[forest token]

yeah

[proud halo]

and the right goes between infinity and 0

[forest token]

yeah

[proud halo]

yeah it's hard to directly analyze it

maybe sub 1 + x = e^u

[ e^u - 1 - ue^u > 0 ]

[boreal girder]

maison

[proud halo]

since the map is invjective it should be fine

find the new range for u

e^u(1 - u) - 1 > 0

(1 - u) - e^(-u) > 0

(1 - u) > e^(-u)

this looks good now

isn't 1 - u tangent to e^-u

,w plot y = 1 - x and y = e^(-x)

[boreal girder]

Results provided by WolframAlpha

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

Requested by dyxn06

[proud halo]

looks good

@forest token

[forest token]

yea im here

[forest token]

really

[proud halo]

yeah

since 1 - u is tangent to e^-u

we know that e^-u is always above it

[forest token]

brother how do u know that 😭😭

[proud halo]

just looked like it

i knew 1 + x is tangent to e^x

so

[forest token]

oh

[forest token]

okay right

so that means 1-x will always be below it?

meaning it will decrease?

[proud halo]

1 - x but yeah

yeah

I guess you originally stuck a > sign there

to check if it's increasing

[forest token]

yeah

[proud halo]

so your inequality holds for no real value of u

which means the negation =<

is true for all u in R

[forest token]

ohh

okay i got it..but can we do it by putting values somehow?

[proud halo]

sure

you know both ln(1 + x) and x are monotone functions

and that x > ln(1 + x) for all x

so you can probably guess that it's nature won't change in between randomly

and randomly chuck in values and plot it

[forest token]

monotone +- monotone = monotone?

[proud halo]

yeah that is true

[forest token]

ohh okay

so we could have just told from that

by looking at the options

got it

[proud halo]

yeah the options kind of give it away too

also another thing you could do is use the taylor series

[forest token]

😭 dont make me feel bad for picking the wrong one bro

[proud halo]

for ln(1 + x)

[forest token]

1+x+x^2/2

oh yeah

thats a better method

and it could help in other questions as well

[forest token]

wait this is e^x

ln (1+x) is x-x^2/2

okay thanks a lot bro

.close

[compact pewter]

Channel closed

Closed by @forest token

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[rose goblet]

Hello this is kinda weird but what are some ways to make a big multiplication in mind faster/easier

[rose goblet]

Like is there any trick to calculate 9876x5432 in mind or whats the best way i just wanna see how other people would think of it

[solemn matrix]

i got tips for 2 digits

[rose goblet]

Tell me

[solemn matrix]

it makes it faster on paper

so still

[rose goblet]

I meant for in mind

[solemn matrix]

yeah

[rose goblet]

No paper or writting

[solemn matrix]

i think you can still do it in mind

so

[rose goblet]

Yea whats best way to memorize etc

[solemn matrix]

42
56

[rose goblet]

Mhm

[solemn matrix]

you times 4 x 5 and 2 x 6

[rose goblet]

50-8 and 50+6?

Yea

[solemn matrix]

so it's 20 ___ 12

[rose goblet]

Mhm

[solemn matrix]

the blanks is 2 x 5 + 4 x 6

so it should be 20 34 12

[rose goblet]

Oh wtf

[solemn matrix]

it's sum of cross multiplication

dw

[rose goblet]

Doesnt seem to be true

[solemn matrix]

now since 12 > 10

[rose goblet]

This number seems to big

[solemn matrix]

no dw

[rose goblet]

Ok

[solemn matrix]

you carry the 10 from 12 to 34

so it's 20 44 2

carry the 40 from 44 to 20

so it's 24 4 2

the answer is 2442 if you want to try it on the calculator

wait wait

[rose goblet]

Its not though

[solemn matrix]

let me verify it again

oh wait no

[rose goblet]

You did it wrong thats why

[solemn matrix]

yea

so let me clarify it again

[rose goblet]

12 carries on to 35

Not 44

[solemn matrix]

yep

[rose goblet]

Then its 2352

[solemn matrix]

it carries to 35

yeah

[rose goblet]

Idk if this is better though than just multiplying

[solemn matrix]

try 69 x 35

[rose goblet]

Ok wait lets try this

Send a 2x2 and we do it at the same time no paper you with method me without

[solemn matrix]

lol

so imagine on your head that 69 and 35 are in a column

just like how you would do it in elementary school

[rose goblet]

Nah i do differently

Like for this

Id do (70-1)(30+5)

[solemn matrix]

alr

that also works too

[rose goblet]

So its 2100-35 + 350

Basically the minus term times the right side

And the + term times only the 70

[solemn matrix]

lol

[rose goblet]

I think this is the fastest

[solemn matrix]

that's a lot of big calculations

[rose goblet]

Not really

Easy calculations

70x30

[solemn matrix]

69
35

[rose goblet]

-1 x 35

5x70

[solemn matrix]

yeah the part is that you subtract 2100 - 35

[rose goblet]

You can remove 35 from 350

And just add 315

[solemn matrix]

so the numbers are 18 57 45

[rose goblet]

Anyways uhm i didnt quite mean trick

I meant like how yall imagine it

[solemn matrix]

18 61 5

24 1 5

2415

this trick is proven to be correct for every 2 digit number multiplication

[rose goblet]

Give a different

[solemn matrix]

76 x 84

[rose goblet]

6384

Oh damn

[solemn matrix]

that's correct

[rose goblet]

That actually might be faster

[solemn matrix]

did you really do that in your head 😭

[rose goblet]

Yea

[solemn matrix]

i didn't practice that on my head

but doing it on paper is faster than the traditional method

[rose goblet]

Yes obv

Uhm

[solemn matrix]

79 x 46

[rose goblet]

Lemme do this with constants

[solemn matrix]

alr

now i got tricks for numbers like

25 50 and 125

but i want to primarily focus on 25

so take 25 x 12

notice that 25 x 4 = 100

so 25 x 12 can be seperated as 25 x 4 x 3

which is 300

25 x 45

it can be seperated as 25 x 4 x 11 + 25 x 1

which is 1100 + 25 = 1125

now for 50

it's the same

but remember that 50 x 2 = 100

and for 125

remember that 125 x 8 = 1000

this one works for 25, 50, 125 x any number

[rose goblet]

Yea i see

But i was asking for memorizing tricks mostly

Like for 9876x5432

.close

[compact pewter]

Channel closed

Closed by @rose goblet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[blissful carbon]

how does logarithms even workkkkk 😭

[hazy obsidian]

well first of all do you know where the change of base formula comes from

[compact pewter]

@blissful carbon Has your question been resolved?

[blissful carbon]

not rlly

just got into log

[coral halo]

do you have problems with logs specifically for this question or in general

[blissful carbon]

in general

my course didnt rlly explain logs at all i dont know why they kinda just skipped over it

[coral halo]

well guess you got some revision to do then

but to explain it simply, logs allows you to find values of exponents

example

$2^x = 7$

[boreal girder]

Shioshi

[coral halo]

x is the exponent

to find it, you use log

$x = \log_2(7)$

[boreal girder]

Shioshi

[blissful carbon]

that i just plug into a calculator right

[coral halo]

yes

[blissful carbon]

how would i put that in

[coral halo]

depends if your calculator can put a custom log base

if not you're gonna have to change to base 10

[blissful carbon]

mine i click log on 7 and it just gives me a number

its like automatic

[coral halo]

which is the formula given in the question

[coral halo]

then its probably log base 10

[hazy obsidian]

logs is the "opposite" of exponentiation, since exponentiation is basically the amount of times we multiply, logarithms are the amount of times we divide

[blissful carbon]

im just using the microsoft one cuz i dont have a calc they like 50$ lol

so where do we get y and b in this formula

[coral halo]

well you need to change the exponential equation given to a log equation

do you know how to do that

[blissful carbon]

so add log to both sides im guessing

[coral halo]

base?

[blissful carbon]

was responding to this

was just a guess

[coral halo]

yes its correct

but what base

[blissful carbon]

the whole thing

like

log(2x^x+1) =log(9)

[coral halo]

but what base of logarithm are you using

[blissful carbon]

i dont really know what base is but i think 10 is the normal thing right?

[coral halo]

hmm its asking you to use the change of base formula

so i think you'll need to use a different base

[blissful carbon]

oh yeah

[coral halo]

whats the base of the left side

2 right?

[blissful carbon]

yea

[coral halo]

so what logarithm base should you use

[blissful carbon]

10?

[coral halo]

no

[blissful carbon]

2

[coral halo]

yes

[blissful carbon]

im pulling straws here lol

[coral halo]

use log base 2

[blissful carbon]

so i should use base equal to the same base of the equiation?

[coral halo]

yes

[blissful carbon]

ok

[coral halo]

that will give you the exponent directly

since log and exponents are inverse functions of each other

[blissful carbon]

but we need to use base change formula somehow

[coral halo]

what do you get after applying log

[blissful carbon]

i dont know my calculator is being difficult it wont let me put anything besides 2 into the log(

😭

[coral halo]

you havent used the change base formula

now im asking, what equation did you get after applying log on both sides

[blissful carbon]

oh

log2(2^x+1)=log2(9)

[coral halo]

log base 2?

$\log_2(2^{x+1}) = \log_2(9)$

[blissful carbon]

yea

[boreal girder]

Shioshi

[coral halo]

ok so you have log base two and base 2 exponent

what happens to them

[blissful carbon]

i dont know

does

the exponent get divided

[coral halo]

no

they cancel each other

because exponents and logarithms are inverse functions of one another

[blissful carbon]

so x+1 just dissapears?

[coral halo]

not x + 1

2 disappears

[blissful carbon]

oh

that makes more sense lol

[coral halo]

so on the left you are just left with x + 1

$x + 1 = \log_2(9)$

[blissful carbon]

and 0 on the right?

[boreal girder]

Shioshi

[coral halo]

no..

we havent done anything on the right

[blissful carbon]

oh right

im a little slow lol

[coral halo]

its fine

and now we deal with the right

we have this log base 2 of 9

this is where we can use the change of base formula

$\log_b(y) = \frac{\log(y)}{\log(b)}$

[boreal girder]

Shioshi

[coral halo]

can you identify what b and y is

[blissful carbon]

yes b is 2 and y is 9

[coral halo]

good

and our new base is?

[blissful carbon]

log(9)/log(2)

idk

[coral halo]

usually when the base is not specified, its 10

[blissful carbon]

oh ok

[coral halo]

unless you're doing computers then its 2 but thats not relevant

anyways

[blissful carbon]

is it 2 cuz like bianary or somn like that lol

[coral halo]

yea lol

[coral halo]

whats b

[blissful carbon]

2

[coral halo]

good

now you can just type this in your calculator

[blissful carbon]

.301?

[coral halo]

yes

now your equation is just x + 1 = .301

wait lemme check if this is right lol

[blissful carbon]

ok lol

[coral halo]

nvm its wrong

.301 is log(2)

[blissful carbon]

lol

[coral halo]

you need to press the equal sign

should be like 3.1699

[blissful carbon]

oh yeah

lmao

3.1699250014423123629074778878956

so

x=2.169

alright then thanks

and just curious are you a volunteer or does discord like pay you or something

[coral halo]

nah no one gets paid

[blissful carbon]

pretty cool we got people willing to do this for frreee ty

.close

[compact pewter]

Channel closed

Closed by @blissful carbon

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[coral halo]

also this equation works for any base btw

not just base 10

[blissful carbon]

alright

[coral halo]

you can change to base 3, 4, 100 or whatever you like

but just make sure its the same top and bottom

[compact pewter]

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[wispy fossil]

how do i find what the pattern is? is it just guesswork, or is there another way to do it?

[vernal frigate]

do you know arithmetic and geometric sequences?

and what they are

[wispy fossil]

yes

[vernal frigate]

then try to remember the formulas for making a sequence
recursive or not

[wispy fossil]

like a sub 1 *r ^(n-1)?

[vernal frigate]

thats for arithmetic i believe

arithmetic sequence formulas look like this
tn = a + (n - 1)d