precalculus

[warm forum]

Same

[viscid thistle]

thanks for the help

[warm forum]

It’s 1:33 AM now xD

[viscid thistle]

hmm its 12:03 am

here

[warm forum]

,w limit of (sqrt(1-sinx)(tanx-(1/(sqrt2tanx))),x->pi/2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Muzan Jackson#3996

[warm forum]

Hmm

[viscid thistle]

woaj

nice

oh wait

limit does not exist

[warm forum]

Probably

[viscid thistle]

ok bye and thanks

[warm forum]

Ur welc

[viscid thistle]

Well using a+bi, you'll see that a has to be equal to 3 and y has to be equal to -7

I meant x has to be equal to 3 lol

[robust star]

Can someone help me start this?

[robust star]

ty, ig i was overthinking it

[compact isle]

just sketch it in a program

[jaunty portal]

hello anyone pls help

[viscid thistle]

So I need to find all complex solutions for the following equation: 4x^4-25x^2+36=0

From synthetic division I found that -2 is a zero. And I got the following equation: 4x^3-8x^2-9x+18

$(4x^3-8x^2)-(9x+18)$

[obsidian monolith]

caley

[viscid thistle]

$x^2(4x-8)-9(x-2)$

[obsidian monolith]

caley

[viscid thistle]

but i'm struggling to get further from this to find the other solutions

[willow bear]

write $x^2(4x-8)$ as $4x^2(x-2)$

[obsidian monolith]

Ann

[willow bear]

should be of some help

[viscid thistle]

,tex but how did you get this $$ 4x^2(x-2) $$

[obsidian monolith]

caley

[viscid thistle]

nvm

thanks

[plucky perch]

Knowing that:

Show that the expression below is convergent towards a limit gamma in the interval (0, 1)

so basically the harmonic series H(n) - ln(n)

as n goes to infinity

I'm only allowed to use sequences, so all of this is not in a continuous context

[echo wagon]

Do you know monotone convergence theorem?

[plucky perch]

no, can you tell it briefly?

[echo wagon]

A sequence that is bounded and monotone (increasing or decreasing) is convergent

[mild cloud]

https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-series-optional/v/proving-a-sequence-converges

[echo wagon]

How is that relevant to this question?

[plucky perch]

So showing that a(n) is monotone decreasing and finding a lower bound for it is enough to prove it converges

[echo wagon]

I believe it is increasing not decreasing

[plucky perch]

oh yes, the difference is increasing

[echo wagon]

No, I'm lying

It is decreasing

And a lower bound, yeah that suffices

[plucky perch]

oh ok

[plucky perch]

how should we approach that with the starting inequality?

[echo wagon]

There is a clear relationship between terms of the form 1/x and ln(x) with respect to integration

So look at left/right riemann sums that approximates an integral of 1/x that evaluates to ln(n)

[plucky perch]

of couse, knowing that area under ln is 1/x

problem is i cant really use that knowledge into this, im supposed to just use the inequality

[echo wagon]

Oh, I didn't see the given inequality

Can you show it is decreasing using that inequality?

|| Take a_n and use the given inequality to replace ln(n) with something smaller that results in getting a_(n+1)||

[plucky perch]

well using inequality we'd have: ln(n+1) - 1/n < ln(n) < ln(n+1) - 1/(n+1)

so replacing ln(n) to get smth smaller we use ln(n+1) - 1/n+1 and the new series is smaller than a_n and we get a_n > a_n+1 so monotone decreasing

[south summit]

are you doomed to fail if you aren't familiar with trigonometry and algebra formulas? In precalculus.

[devout zinc]

yes

learn them immediately

especially for limits

when u will start limits, knowing how to factor is a must

its essential

wait, limits is precal or cal 1?

limits is cal 1

anyway

you will learn limits anyway so ye you need to know ur trig and algebra

[south summit]

Is there like a AIO formulas sheet preparation

[devout zinc]

well like for the start of precal u need to know that cos^2 + sin^2 = 1 and ur trig identities and also double angles

and also ur factoring formulas

like diff of squres

diff of cubes

sum of cubes

etc etc

how to factor by grouping

u need to know how to deal with abs functions

how to deal with rationals

and square roots

there isnt rlly a formula sheet...

its pre cal

in pre cal u get into limits and derivatives

and u stop there

[south summit]

ALL memorized?

I have a hard time on trig identities without looking at the formulas. Although I do see a very similar relation compared to algebra factoring formulas like a^2 + b^2. Maybe I need to find a way to relate to them easily in my own way.

[devout zinc]

yes

[devout zinc]

technically u just need to memorize the first trig identity

cos^2+sin^2 = 1

the other are derived from dividing by sin^2 and cos^2

[stray shuttle]

Hi, I have a question with regards t setting up a precalc problem
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 6 AM, and walks steadily at 3 miles per hour. Elsie sleeps in, and starts walking west at 3.5 miles per hour starting at 9 AM.
This is supposed to be solved on a two axis coordinate plane
But I see 3 axis
N/S, E/W, and time
How do I set this up?

[south summit]

Damn, these math problems are so dry even the cactus would of died. It's no wonder how the math department isn't able to get anyone interested in mathematics lol.

[sick steppe]

Ok and?

[south summit]

Are you mistaking me for attacking Speedbird48's question where I am only address the concern of dry math problems in general?

[sick steppe]

No, I just dont see a need for a comment like that

[south summit]

There's no need for a comment in search for a better way to learn mathematics?

[sick steppe]

learning and educating are different things, your comment leans more toward a comment on education in my interpretation.

#math-pedagogy is also a more apt place to discuss.. pedagogy

[south summit]

Sure, so what's there a no need of?

and that's determined by you?

respectfully of course.

[hollow lance]

And in what way is your opinion on math problems relevant in any way?

[hollow lance]

Consider setting the place where both are camping at the coordinate point, up would be North, right would be East. Does that help?

[stray shuttle]

I am being helped in another channel but I greatly appreciate you offering help

I was confused about where to put questions

Sorry about that

[hollow lance]

No worries

[south summit]

I am simply pointing out how math can be uninteresting in hopes someone who understands more in math can challenge my idea into a more well-rounded mindset. So that those who share the notion of math not being very interesting can better understand how to learn math in a more fun or productive manner.

In a way you can say I'm also seeking for help, but just not directly correlated to specifics of a math problem.

[hollow lance]

Challenge these views somewhere else, these are question channels and there are rules on how a user must behave. Consider looking into the social channels

[sick steppe]

Again, the pedagogy channel is a place for discussion on pedagogical practices, or any of the discussion channels. I'm not saying I'm the leading figure in pedagogical practices for math, I'm just a teacher candidate.

[stuck lark]

i'd like y'all to drop this. the instigating comment itself was unnecessary but blowing up chat over it is much worse

[open rock]

Hey all!

I wanna learn calculus but not sure what prerequisites I should know

Im good in my algebra, meh in my geometry and have no motherloving clue about trigonometry

What should I learn?

[full pagoda]

definitely trig

geometry doesn't matter too much when starting in calc, but trig is very important

so if you don't know that, i suggest learning trig before you start with calc

[open rock]

So, what good trig books must a high school sophomore student who studies under a mediocre education system get in order to progress?

[full pagoda]

honestly i'd suggest youtube over books

not only is it free but it's probably easier to understand

[viscid thistle]

well in my experience, I just jumped right in lol

[open rock]

Ah, i see

[viscid thistle]

and just learn anything that you need to learn as you go

[open rock]

Well, i have thomas calculus...

[uncut mulch]

you'd need decent knowledge of coordinate geometry

[viscid thistle]

is it one of those huge books?

[open rock]

I heard its one of those introductory books, actually

[viscid thistle]

I mean in size

[open rock]

Nah, im not sure. Ive got a pdf of it and its 800 pages

[viscid thistle]

[open rock]

"introductory"

[viscid thistle]

hmm probably also has stuff like multivariable calc and DE's near the end

[open rock]

😔 Wish i knew what all that meant

[viscid thistle]

me too dude

[open rock]

But is there at least like a list of things to know before I jump in?

[viscid thistle]

[full pagoda]

have you taken precal?

[viscid thistle]

well I mean yea

but I tbh you don't really have to go through all of them

[open rock]

nO

[viscid thistle]

I mean obvious ones being coordinate geometry, and other things you've learnt at school

[open rock]

Yeah... But...

[viscid thistle]

trig is pretty important but I just learned it while learning calculus

[open rock]

Mediocre education and all

Im basically self-taught

[full pagoda]

i'd suggest precal before calculus lmao

[open rock]

huh.

But...

[viscid thistle]

tbh introductory calc really doesn't need that many prereqs ... like the most important would be a good understanding of coordinate geometry and algebra

[open rock]

And forgive me for this

what is precalc

[viscid thistle]

pre-calculus

[open rock]

yeah

What is it about ༼;´༎ຶ ۝ ༎ຶ༽

[viscid thistle]

preparing for calculus

stuff like functions, algebra and all that juicy stuff

[open rock]

So... Is precalc all ill need 😔

[full pagoda]

it will give you a strong foundation, yes

[viscid thistle]

yea but if you feel like jumping right into calculus to test the waters then why not

ofc since you don't have the knowledge from precalc it can be quite hard but the internet is a mans best friend

[full pagoda]

though i definitely don't suggest it

[open rock]

...

Im a man of challenge

but I also take precautions

ill do both

Ill learn just enough that I feel comfortable getting in

But ill also explore the ideas more and interpret what I can from them using my knowledgebase

[full pagoda]

trying to learn calc before getting a foundation isn't much of a challenge, more doing yourself a disservice

[viscid thistle]

Also there's no point in reading books if you don't also practice

you can find many excellent problems to solve on the internet

[open rock]

Oh, no, no. Of course practice is key

I just... Have to practice the right way

[uncut mulch]

if it's a good intro book, the early chapters should give you some decent reciew

[viscid thistle]

yea the book I started out with had a whole chapter on trig and functions and all precalc stuff before beginning

[open rock]

Ive got one last request...

Throighout my high school years we've NEVER dived into graphs

Not one but

Bit*

[viscid thistle]

but if you have no experience in any precalc topic, you're better off finding a resource designated for precalc

[viscid thistle]

oof

[open rock]

So...

Im worried about my algebra

What I already dont know

Im thinking of this

I need to get:

• a good algebra book
• a good precalc book
• a good trig book

Is this a good approach to this?

[full pagoda]

everything you can find in a book you can probably find on either the organic chemistry tutor's youtube channel or on khan academy

but if you really want to buy books, go for it

[uncut mulch]

don't need an algebra book unless you're doing linear algebra (in which case you'll be using a more advanced one)

[open rock]

Buy?

BUY?

BAHAHAHAHAHAHAHA

Zlibrary was my best friend from the day I was born

yeah, im sorry, man. But I just dont have that kind of finances on me

Im trying to gather what I can and honestly, pdfs are the only thing im educated from

[viscid thistle]

khan academy is free

[open rock]

Yeah, but many steer me away from it

[viscid thistle]

and an amazing resource

[full pagoda]

just so you know it's against discord TOS to encourage pirating

[open rock]

is it?

[viscid thistle]

[open rock]

Of course i dont, im sorry

But really, its the only method I have right now

[uncut mulch]

who steers you away from it?

[open rock]

Ive got a friend of mine whos into calc alrsady

He says the calc material in there isnt tip-top

[viscid thistle]

ofc one shouldn't rely solely on khan academy but it's a very great resource

[viscid thistle]

[uncut mulch]

you shouldn't rely on it completely,
but it's decent enough for an intro into the topic

[open rock]

Ah, alright then

So must I really only rely on precalc and trig?

[full pagoda]

rely? no

[uncut mulch]

well precalc covers most of early algebra

[open rock]

༎ຶ‿༎ຶ

[uncut mulch]

those will be extremely important when doing calculus

[open rock]

So, so.

• learn precalc

• learn trig

practice both

And research the topics in calc if I have no idea what theyre on about

[uncut mulch]

pretty much yeh

[open rock]

Will my algebra be sufficient, i wonder

[viscid thistle]

well good luck

if you have any questions, well we're here!

[open rock]

Thank you! Im glad ive found you all

Ill be doing what I can from here on out

[viscid thistle]

6

[viscid thistle]

yoo wtf

how did you do that

can you help with this too

hmm

im not 100% sure about that one

oh

[viscid thistle]

for this question i used rule 7

b=3, k=6

b^something = 6

[viscid thistle]

i got 64 for this but im not 100% sure

it worked

oh

omg

your so good

do you know how to do this one too

legit i simplified it

and it still gives me something with log in it

do you want me to give my working out for q2 or do u want me to do q3

w3

q3

1/4

do u want the working out for q3

yeah can you do these two tho

those 2 first or the working out for previous questions

second one is kinda wierd tho i think it either means 5^3-log_5, 7

[viscid thistle]

those 2

or it means 5^(3-log_5, 7)

[viscid thistle]

40

[viscid thistle]

125/7

damn

yoru smart

do you know if the domain is all real numbers

im pretty sure its allrealnumbers

but it don't work

domain and range is my weakness

oh

im pretty sure x can be all real numbers in any logarithm

the base is >0 and != 1

yes

so doesn't that mean x = allrealnumbers

for domain

my guess would be x=3/2 since log2(2sqrt(2)) = 3/2

im not 100% sure though

yeah i got the answer

i know its x = 3/2

but its asking for domain

it thinks domain is wrong

i think the domain is only x=3/2

i cant do it too hard for me

sorry

oh alright

its okay though

you helped a lot

thanks

no problem

do you still want the working out for the previous questions

or do u want me to skip them

its fine you don't have to do it

im gonna spend some time thinking about the domain

alright

[small tree]

can someone plz help me with this one

[willow bear]

@small tree have you made any progress so far?

[small tree]

no i m working on it

[willow bear]

okay. can you post your attempt once you're done or stuck?

[devout zinc]

use trig

when it gives u degrees, use trig

angle a is 35 deg

u know x = 14

therefore AC = 14 +r

u want to find r therefore we have
$sin(35) = \frac{r}{14+r}$

[obsidian monolith]

IAMTHEFARMER

[devout zinc]

because $sin\theta = \frac{opposite}{hypthenuse}$

[obsidian monolith]

IAMTHEFARMER

[devout zinc]

so basically then you have

$(14+r)sin(35) = r$

[obsidian monolith]

IAMTHEFARMER

Result:

-0.42818266949615

[devout zinc]

^ ignore that

its in rads

$sin35(14+r) = r$

[obsidian monolith]

IAMTHEFARMER

[devout zinc]

then you will have

$sin(35)\times 14 + sin35\times r = r$

[obsidian monolith]

IAMTHEFARMER

[devout zinc]

then u solve

[shy matrix]

Are there no ways to find out the equation of a hyperbola if the only given were the center, the vertices, and the transverse axis length?

[mental pulsar]

Could I get some help on this?

[uncut mulch]

what are you being asked to do with that?

and what's being cut off

[mental pulsar]

oh lmao let me take another

also I'm being asked to simplify

Basically this

I got this far

I’m stuck

[uncut mulch]

consider conjugates and pythagorean trig identities

[mental pulsar]

I'm not very well versed yet lol, we got this hw after a hour session, this is completely new to me

so like

cos^2x + sin^2x = 1 and such?

[uncut mulch]

yes

[mental pulsar]

im still kinda confused

could you elaborate

[uncut mulch]

start by multiplying the numerator and denominator of your initial fraction by
1 + cos(x); which is the conjugate of the denominator

and you can apply cos^2(x) + sin^2(x) = 1
to simplify the denominator after that

[mental pulsar]

So like this ?

[ocean dune]

we can but they should mention the axis of hyperbola are x and y axis!(then we can exactly say the equation of not there exists many hyperbolas with different axis)

[shy matrix]

Yeah a correction was given to us regarding the problem, now I finally solved it

[somber sigil]

yes

[somber sigil]

u can sub tan x=sin x/cos x

[lavish nacelle]

can i check for this qn right, i could come up with three equations

1. cos theta = x / L
2. 1.8/(2.4 - x) = y/ x
3. x^2 + y^2 = L^2

so i can manipulate till it’s left with theta and x in equation 1 or theta and L (with two variables)

doing dL/dtheta = 0 would give the correct ans, but does dx/dtheta work? thanks!

for differentiation optimization qn, the dy/dx, must the y be referring to the actual thing like here since we wanna maximise length so y has to be L

[viscid thistle]

did you survive the squid game?

[devout trail]

Reposting as requested by Ryam.

And at the end you just differentiate L(θ) and find the maximum
You'll end up with something like: tan^3(θ) = 1.8/2.4

Posting as requested by Ryam to copy and paste his image and text.

[manic rampart]

Is this supposed to be + 10 since we reflected over x axis

[unborn blade]

when finding the limit as x->inf (sqrt(x+1)/x) we get a case of inf/inf. so at that point i tried dividing each term by the highest term in the denominator which is x

which gives inf/1 = inf

but this is wrong

because apparently i need to rationalize the numerator first

is there a rule that i basically need to always rationalize the numerator before applying the division by highest power method?

help appreciated

[fierce rain]

can someone help me with a problem

[cunning root]

ye

1.5 hours later tho

[hollow flint]

ye

another 1.5 hours later

@fierce rain

[unborn blade]

can no one answer mine?

[silk summit]

in a polynomial, can the number of points of discontinuity be defined by the degree of the polynomial? example does the function 4-x^2/4x-x^3 have 3 points of discontinuity?

[willow bear]

what did you get after dividing each term by x?

might you have fucked up at that stage?

[ebon fiber]

Think about when this function is undefined. This occurs when the denominator is equal to 0. So find solutions to the equation 4x - x^3=0
you see x(4 - x^2)=0

So the solutions are x =0, and the solution to 4 - x^2 = 0. Isolating for x gives x = 2, x=-2

[upper tundra]

But the problem is after doing that you end up with the same expression again.

You can push that x inside the sqrt making it x^2 and then the whole inside approaches 0 so, the limit of whole expression is 0.

[restive hound]

Hello, I was just wondering. I’m solving a proving trigonometric identities question, it is 1-tan^2x/1+tan^2x= 1-2sin^2x. I took the pythagorean identity for the denominator so it became 1-tan^2x/ sec^2x. Is it right if I separate these to become 1/sec^2x - tan^2x/sec^2x? For it to become cos^2x - sin^2x ➡️ 1-sin^2x-sin^2x ➡️ 1-2sin^2x ?

[willow bear]

parentheses!!!!!!!

but yes, aside from the lack of parentheses with plaintext fractions what you're doing is correct.

[restive hound]

Okay, thank you for the reminder!

[silent cradle]

can someone please help me integrate this

[silk summit]

ohkayy.. thank you very much

[restive hound]

How will I know if two angles are coterminal? I'm given 185 degrees and -545 degrees. Should I subtract 185 to -360 and add 360 to -545?

[willow bear]

subtract your angles from each other

then see if the difference is a multiple of 360°

if it is then your angles are coterminal, if it isnt then they are not

[restive hound]

Oh okay, I got -360°. What if I get negative answers but they're multiples of 360°, they wouldn't be counted?

Like what if I got -720 degrees? it's still wrong?

[echo wagon]

You subtracted 185 and -545 and got -360? Idk how you did it, but no, it doesn't matter

It just means you subtracted the larger one from the smaller one, instead of the other way around

If you did it the other way around, you would get the same number but positive

[restive hound]

Yes, I subtracted 185 and -545 and got -360. Was it supposed to be -545-185?

So if it doesn't matter if I get an answer that is a negative multiple of 360°, it would still be coterminal then?

[restive hound]

Whoops it's supposed to be addition that's why haha

thank you for the help ^^

[willow bear]

,calc 185 - (-545)

[obsidian monolith]

Result:

730

[restive hound]

Thank you!

[cobalt warren]

Can anybody help with this?

[uncut mulch]

have you learned about factor theorem

[earnest hull]

use synthetic division, create the factorable poly, then find the zeros

[trim epoch]

(x-1)(x+2)(cx-d) = Ax^3+Bx^2 +x+6

Expand and compare coefficients

[fresh hearth]

beep boop

[hushed pulsar]

Can someone explains this for me?

(a-2b/a+b) - (2a-b/a+b) = -1

[tiny shoal]

so since the bottom denominators are equivalent, you have: [a-2b -(2a-b)]/a+b

then for the numerator: a-2b-2a+b = -a-b = -(a+b)

bring that back in

-(a+b)/(a+b) = -1

[viscid thistle]

how tf do you graph f(X) = 3x+2 / x-3

i got like some really sus answers

[chrome dove]

anyone know how to do this?

[hushed pulsar]

Wait let me think about that a sec haha

[quick hull]

The y will be whatever the x going through that comes out as so at -2 it is (-6+2/-2-3 -> -6+2/-5 -> -4/-5 -> 0.8) then -1 (-3+2/-1-3 -> -3+2/-4 -> -1/-4 -> 0.25) 0 is (2/0-3 -> 2/-3) 1 is (3+2/1-3 -> 3+2/-2 -> 5/-2 -> -2.5) and I will finally do 2 (6+2/2-3 -> 6+2/-1 -> 8/-1 -> -8) now you may also notice that 3 is undefined for this function if you wish you could try to use a limit to get what happens as x approaches 3, but I am not going to, so to graph that function you would do exactly what I told you with theoretically every x now this is normally what the calculator is supposed to do for you, but for some reason it seems you want to try it yourself? Either way good luck!

[hushed pulsar]

How did you get '-a-b '?

[tiny shoal]

a-2a is -a, b-2b is -b

And since it’s a-2a + b-2b

You collectively get -a-b

[hushed pulsar]

Ah thank you!

[tiny shoal]

No worries

[fathom phoenix]

is the answer to this undefined or 2root3/3?

oh woops i meant this one

[devout zinc]

$csc\theta = \frac{1}{sin\theta}$

[obsidian monolith]

IAMTHEFARMER

[devout zinc]

@fathom phoenix

[fresh hearth]

Hey can someone help me study for my math exam :D

<@&286206848099549185>

Right now I'm struggling with this question

[hushed pulsar]

Can someone explain;
(x^3-3x^2-10x)/(x+2) = x(x-5)

[tiny shoal]

how far have you gone with this problem?

look carefully at the x variables on the numerator

see how you can get stuff to move around on the top

[hushed pulsar]

Yeah i'm trying different things

[tiny shoal]

just to start you off, notice how we have x in each term on the numerator

which allows you to take out x

so you'll have x(x^2 - 3x - 10)

on top

[hushed pulsar]

yes i had that

x(x^2 - 3x - 10)/(x+2)

x(1x1x - 3x - 10)

[tiny shoal]

next step would be to reformulate that expression so a (x+2) can pop out and it cancels out with the bottom

and your leftover would be (x+5)

so you'll have to factor

[hushed pulsar]

Okay i'll let you know

[ebon fiber]

thats just a graph what is the question

[ebon fiber]

.

[viscid thistle]

Can someone show me how to do this?

[trim hemlock]

you would need to determine these things:
Period
Amplitude
An y-intersection

your equation should be in the form Acos(ax+b) or Asin(ax+b)

sometimes the a factored out

but anyway

the period is to find a, a=2pi/Period

the Amplitude is to find A, A=Amplitude

and the y-int is to find b, y-int=Acos(b) or Asin(b), depends on which equation you use

in some cases, you could also use the x-int to find b, but usually y-int is used because its easier, and quicker

[lean hill]

Could someone explain why the below follows from the first equation?

anyone please?

[red tree]

It is merely the result of cross multiplication and collecting it into a polynomial in x

That is what I suspect

no black magic really

[halcyon granite]

how the hell... i dont get it

[lean hill]

OK Thank goodness

[deep barn]

hey, so
For a function f(x), you know that f(3) = -8 and f(4) = 3. One zero of f(x) would be located between x= and x= ___

[uncut mulch]

apply ivt

also the question should really say continuous function

[deep barn]

aight ty

[hearty wolf]

how do you apply the 6 circular functions (e.g., cos, sin, tan, sec, csc, cot) in real life ?

[willow bear]

many ways

as one example, consider a building of some height and some distance from you

it is possible to (relatively easily) measure the angle of elevation to the top of the building

then, if you know either the distance to the building or its height, you can find the other via multiplication by tan(θ) or cot(θ) respectively

@hearty wolf does this answer satisfy you?

[spark glade]

why are radius and meters in the same color

the blue ink went over v= w *r

[silk summit]

in the question - "at what points on the curve x^2 + y^2 - 2x - 4y + 1 = 0, is the tangent parallel to the y - axis?" ; does " when tangent is parallel to y - axis " indicate that the derivative should be found with respect to y?

[willow bear]

no

i mean, you could say that it indicates dx/dy = 0

[somber sigil]

or u can realise that the curve is a circle and centre-coordinates ± radius for x-coordinate is the answer

[green kernel]

How do I solve this? I figured since they were telling us cosΘ is .25, to convert to radians we'd just multiply .25 by (180/pi) but that gives none of the answers in the choices.

[willow bear]

0.25 is not a value in degrees.

cos(θ) = 0.25

not θ = 0.25

[green kernel]

Ah, I see. Duh lol. They would of given the degree symbol or just said degrees. So, I can just use arccos(.25). The answer is D.

Thank you.

[willow bear]

the outputs of trig functions are rarely if ever interpreted as angles in their own right

[trim hemlock]

I think I'm missing the trick here.
Translation: Given y, How many integer m in [-6,6] such that y has 4 asymptotes?
So for sure, y has one asymptote, but now I will have to find a condition for m such that the denominator has 3 unique roots and none of them is x=3. I seem to have hit a roadblock there

I mean i do know there is a discriminant for a cubic but i would really really want to stay away from that

[hollow lance]

The denominator is always zero for x=m, perhaps factor it out and see where that leads

In either case even when you factor it, you will still have to check each factor so you don't have (x-3) at the bottom

[trim hemlock]

oh, how did you obtain that root? rrt?

[hollow lance]

I mean that was the first thing I thought of doing, because of the (2m^2 + 1)x term

[trim hemlock]

oh right

hmmm yeah, did not catch that

alright, so its just factoring and checking, thank you

[hollow lance]

np

[strange flare]

Use rational root theorem

And the factor out polynomial of second degree

[robust star]

I graphed the function and none of these possible roots are true

[willow bear]

are you asked to find the roots?

bc it does seem like you're out of luck. all three roots here are kinda nasty

[robust star]

i had a similar issue from a previous test but this problem is asking for something different

[echo wagon]

You don't need the roots then. You need to know Vieta's formulas @robust star

Which tells you what the sum/product of the roots are in terms of the coefficients

[robust star]

Is there a way to find the roots?

[echo wagon]

Not really a nice systematic way

I mean there are formulas but none that they would expect you to know

So it's possible to find them, but you don't need to

[robust star]

I ran into the same issue during a test where it asked me to find the roots. I guess i have to talk to my teacher about it. ty

[echo wagon]

@robust star you are not asked to find the roots

You can do the question without finding them

That's the point

[robust star]

ik i don't need to find the roots for this problem but in the past I was asked to find the roots.

[echo wagon]

Then possibly there was a way to find them in that question

[robust star]

ill look into it

[echo wagon]

👍

[obsidian monolith]

mechap

[lofty epoch]

How am I supposed to write v_n+1 with v_n

where

[obsidian monolith]

mechap

[lofty epoch]

I figured it out :')

[merry ledge]

(x^m)^n = x^mn

[obsidian monolith]

Aslan

[merry ledge]

Lol

[proud raven]

i dont like this notation

why would you want to do that

idk if i trust mashing together set and interval notation but uhh im just a dumbie so idk 😄

[grand ember]

^

[willow bear]

no braces

your thing is valid as-is but it'll just evaluate to R because (-∞,5) is not a member of R

[nova grove]

y=-f(x+1)-3

the - negative symbol in front of f is reflection across the x axis?

so it would be (-x-1, y-3) for mapping notation?

[red tree]

Did you reason through the meaning of the negative symbol or are you asking because you are seeing if the rule you remembered is right?

[nova grove]

seeing if i remembered the rule right @red tree

[red tree]

Ah well the rule actually follows from the definition of a function and the definition of a graph

without any further memorization

[nova grove]

ok but did i get it right

[red tree]

Not sure, I forgot the rule

[nova grove]

[red tree]

What even is mapping notation?

[bleak lance]

F(x)=(x^2-7x+6)/(x^2-2x+1)

Where is the graph above the x-axis in interval notation?

(-inf,1)?

And below? (1,+inf)?

[echo wagon]

F(x) = (x-6)(x-1)/(x-1)^2 = (x-6)(x-1)

It will be above the x axis if x-6 and x-1 are either both positive or both negative

And it will be below the x axis if the one is positive and the other is negative

So your answers should involve both q and 6, not just 1.

[radiant elm]

guys i dont understand log much but our class almost have a test so can u guys explain for me what is log?

[full pagoda]

inverse of exponent

[red tree]

The definition is

The logarithm to the base $a$ of a number $x$, denoted $\log_a(x)$ is the unique number $y$ such that $a^y=x$.

[obsidian monolith]

Icy001

[red tree]

So like, everything you need to know about what log means is in the definition (that's how math works)

[radiant elm]

ty

[tranquil haven]

Hey

I don't understand this question

[tired axle]

Cool problem. Did you cover the definition of the derivative yet?

[prime steeple]

i just dont understandwhy did we multiply by (n+7)

[full pagoda]

common denominator

[tired axle]

The wiggling emogis on this server are creepy.

[prime steeple]

okay then why did we multiply (3n+8) by (n+8), why not (n+7)?

[full pagoda]

...common denominator

[tired axle]

You're just mixing up what's new, look again

[prime steeple]

r u talking to me

omg pls help i still dont get it

like we multipled everything by n+7 but why did we multiply by n+8

[uncut mulch]

common denominator

recall the basics for combing fractions through addition/subtraction

the LCD is (n+8)(n+7)

[prime steeple]

yep

[uncut mulch]

the frac on the left was multiplied by (n+7)/(n+7) to get that denominator

similarly the frac on the right was multiplied by (n+8)/(n+8) to get that same denominator

[prime steeple]

one sec

lemme show u

@uncut mulch

[uncut mulch]

?

[prime steeple]

im confused like on the right fraction for the numerator we multiplied by (n+8) and for the left one we multiplied by (n+7) why not the right fraction multiplied by n+7?

im sorry man im just forgot the common denominator cuz we didnt take this since grade 7

[uncut mulch]

because the right fraction already had (n+7) in the denominator

[prime steeple]

and forgot it

[uncut mulch]

because (n+7)(n+8) = (n+7)(n+8)

recall the basics for combing fractions through addition/subtraction

starting with something a lot simpler like:
$$\frac 12 + \frac13$$

[prime steeple]

ohhhh

[obsidian monolith]

ℝamonov

[prime steeple]

makes sense now

alr alr thanks

[nova grove]

the domain for f(x)=3(x-2)^2-5

the domain is {x e R } and range is {y e R | y greater or equal to -5}

is this correct?

[tired axle]

yes.

$\forall x\in \mathbb{R}$

[obsidian monolith]

Disorganized

[tired axle]

aka $(-\infty,\infty)$

[obsidian monolith]

Disorganized

[tired axle]

...but you know this, just...I just don't want to do my homework.

[stuck lark]

R doesn't include -inf or inf

[nova grove]

,rotate

[nova grove]

why is this a compression of 2

where did they even get the 2

[red tree]

How sure are you about the order of these things?

[nova grove]

order ? @red tree

[tired axle]

domain.

[viscid thistle]

compression by 0.5

[tired axle]

oh!

yeah, round braces, scuse me
aaaand the LaTeX won't update. My sins on display forever. ~~

[viscid thistle]

wait no

horizontal stretch by a 1/2

all x co ordinates divided by a 1/2

so they are all multiplied by 2

so u can instead say its a compression by 2

[nova grove]

wait

[viscid thistle]

either works

[nova grove]

so i multiply rverything by 2?

[viscid thistle]

yes the x co ordinates

[nova grove]

so 1/2(x +1.5)

[viscid thistle]

so if a point on the curve was (1,5) then itd become (2,5)

[red tree]

Yeah, the order in which you wrote the transformations

[viscid thistle]

why 3 left not 1.5 left

[nova grove]

this

[viscid thistle]

whats the original function that they want to be transformed to this

[viscid thistle]

stretches first then translation

and anyway you wouldn’t multiply 1.5 by 2, one transformation doesn’t affect the other

the transformations only affect the graph you’re transforming

so the compression by 2 wouldn’t affect the other horizontal shift to the left by 1.5

[nova grove]

well that’s what my teacher wrote

[viscid thistle]

whats original graph tho

thats being transformed

[red tree]

Vertical stretch by a <-> left composition with multiplication by a
Vertical shift by a <-> left composition with addition by a
Horizontal stretch by a<-> right composition with multiplication by 1/a
Horizontal shift by a <-> right composition with addition by -a

[viscid thistle]

is the horizontal shift 1.5 units to the left?

[red tree]

I haven't looked at it closely, although I could figure it out myself. Do you know how to figure it out yourself without appealing to remembering what the teacher said?

It's quite possible you never learned how to

[viscid thistle]

ye its whatever is added to x

u go left by x units

and if something is being minused from x then u go right by x units

[viscid thistle]

so for this @red tree is it left 1.5 units

[red tree]

If you figured it out why are you asking me like I have the answer lol

[viscid thistle]

im double checkin if its right

[red tree]

plot the functions on desmos or geogebra to double check

lol

[viscid thistle]

im not the one who asked the question so i dont know what the original function was

bruh keep up

[red tree]

Well then the whole question is not well defined and your teacher needs some reprimanding, isn't that the conclusion

[viscid thistle]

its not my teacher i didnt send the question

[red tree]

Let's say for the sake of the argument that the original function is x^3

[nova grove]

hey

what’s happening

[red tree]

Do you know what the original function was?

[nova grove]

the parent function?

it’s a cubic function so f(x)=x^3

[red tree]

ye

You can't make sense of this problem without that

[nova grove]

what

[red tree]

Translations and dilations are transformations from one shape to another shape

They aren't just properties of a shape

if you ask the same question with parent function (x-1)^3, you'll get a different answer

Lastly, I said that the meaning of the correct answer is visible if you plot the two functions

So consulting the answer key or teacher isn't the main way to check a problem like this

(there could be ambiguity in which a horizontal dilation is equivalent to the inverse vertical dilation but you can readily see the functions are the same in these cases)

[viscid thistle]

what r u trying to say i dont get it

[bleak lance]

I dont see 0 as having anything above the x int

Because 0 isnt greater than 0

[full pagoda]

what

[sick steppe]

one of the roots is 0

[nova grove]

are you telling my match teacher who has a math and teaching degree shouldn’t be consulted for asking for help and getting answers?

i don’t know what you are even saying

[red tree]

No, depends on the problem

This is one of those where you should be able to make sense of how to check your answer independently

[red tree]

actually this isn't even in the ballpark of what I said

I'm talking about problem solving strategy and you're talking about credentials

[kind arrow]

why are trig graphs so insane

[prime steeple]

can anyone help

please

[willow bear]

@prime steeple do you still need help with this?

[prime steeple]

yes

please help

[willow bear]

okay

[prime steeple]

because i have quiz tmr and i cant understand this

[willow bear]

do you know what a geometric sequence is?

[prime steeple]

yes

[willow bear]

okay, what is a geometric sequence?

[prime steeple]

are u questioning me?

i just need the solution so i can understand it

[willow bear]

we don't give out solutions

[prime steeple]

why not?

okay what do we have to do?

[willow bear]

#❓how-to-get-help

[prime steeple]

find a1?

[willow bear]

no, we are not asked to find a1

it's not really necessary for this problem either

[prime steeple]

also

one more thing

need help with this

[willow bear]

anyway, i'm questioning you because i want to find out where exactly you are stuck

or have you decided to forfeit the previous question and will instead demand help with this one first?

[prime steeple]

yes i need help with this

[willow bear]

so you no longer care about the geometric sequence question?

[prime steeple]

i do but i need this

one

first

[willow bear]

.....ok

have you ever seen a diagram before similar to the one shown?

[prime steeple]

yes maybe

[willow bear]

so is that a yes or is that a maybe?

[prime steeple]

maybe

[willow bear]

so you have no recollection of seeing such a diagram before?

[prime steeple]

no

can u just tell me what is this

like

what is the teracher trying to explain

[willow bear]

this looks like a tree diagram

most likely to do with a probability question

[prime steeple]

hm

[willow bear]

maybe those words could remind you of something

[prime steeple]

explain more?

[willow bear]

there's nothing more to explain, really...

[prime steeple]

is it a common multiple?

[willow bear]

your last question makes zero sense lol

[prime steeple]

k

[willow bear]

you're reading too much into this.

with so little detail and such a barebones (literally) diagram there is really nothing more that can be said

[tired axle]

You need to post the complete problem statement if you want help.
You cant drop in on your doctor, show them a picture of the sidewalk, and say "I need help with this". They're not gonna know wtf you are talking about. And neither are we.

BTW the geometric sequence question was solvable, she was just asking what you remembered because she knows what you need to remember to solve that problem

[willow bear]

yeah but somalicock is above such peasant methods

[echo wagon]

I feel like this account is a troll account designed solely to get people to say somalicock

[tired axle]

Lol!
I'm not ready to make that judgement because a disturbing number of students on the internet post incomplete math questions with no context. Asking complete questions is a skill we might take for granted

[tired axle]

You might be right, @LunasongtheSupergay!

We should ask @JoeBiden or @XiJinping

[viscid thistle]

shouldn't it be 2^3 and 2? how did they distrbuite the 3rd power to the 2 and it became 2^2

[hollow lance]

$\left( \frac{\sqrt{2}}{2} \right)^3 =\left( \frac{\sqrt{2}^3}{2^3} \right) =\left( \frac{\sqrt{2}\cdot \sqrt{2}\cdot \sqrt{2}}{2\cdot 2\cdot 2} \right) =\left( \frac{2 \sqrt{2} }{2 \cdot 2^2} \right) = \frac{\sqrt{2}}{2^2}$

[obsidian monolith]

peaceGiant

[clever apex]

how do i graph Quadratic Functions

[ionic fractal]

m(x) = 5x-3 n(x) = x+4

n(m(m(2))) = ?

how do i answer this function

[full pagoda]

m(2)=?

[ionic fractal]

thats everything that was given

[full pagoda]

yes, what is m(2)

[ionic fractal]

7

[full pagoda]

so m(2)=7

what is m(7)

[ionic fractal]

32

[full pagoda]

n(32)?

[ionic fractal]

36

[full pagoda]

congrats

[ionic fractal]

then how come i got that wrong

my module said the answer was 38

thank you very muchhh

[full pagoda]

38 is not right

[ionic fractal]

ill probably just suck it up and understand that the module can be wrong sometimes

thank you very much tho. didnt clearly understand it.

[green kernel]

The graph is in radians of course. I know the formula y = Atrig(Bx-C)+D. Where A is amplitude, B is the Period, C is Phase Shift, and D is vertical shift.

What I don't know, is what x/2 could possibly be.

[uncut mulch]

x/2 is the product of 1/2 and x

[green kernel]

Ah, yeah, that would make sense. Thank you.

[green kernel]

How would I turn 12/sin60 into it's radical form? The answer is 13.856406460551, but I have no idea how to turn this into it's radical form (8sqrt3).

Assuming it's possible because all the answer choices are whole numbers lol.

[red tree]

Did you ever learn what sin(60) is?

[green kernel]

sqrt3 over 2

At least on the Unit Circle it is.

[uncut mulch]

apply that and simplify the fraction

simplify further
$$= \frac{12}{\br{\frac{\sqrt{3}}{2}}}$$

[obsidian monolith]

ℝamonov

[red tree]

Just to ask, is it that you considered doing this but thought it wasn't allowed?

[green kernel]

I considered this, but got stuck on 24/sqrt3.

[red tree]

24/sqrt(3) is progress, and there is a technique called rationalization of the denominator

[green kernel]

Yea :/, so there is.

Forgot all about it because I had to learn it from the internet instead of my teacher.

[red tree]

Teacher didn't teach it?

[green kernel]

Nope. Not a lick. And then decides to toss all whole numbers into the answer choices.

I think she assumed this because most current day calculators tell you 12/sin(60) in radical form already, so I can't blame her.

I personally don't have one of those calculators.

Anyway, I'd get 24sqrt(3) over 3. Then just divide the 24 by the 3 and get 8sqrt(3).

[red tree]

Pretty much

[green kernel]

Thank you.

[dim egret]

Natural draft cooling towers are often shaped as hyperboloids of revolution. Each vertical cross section of these towers is a hyperbola. Suppose that a natural draft cooling tower has the cross section below. Suppose the tower is 450 feet wide at the base, 275 feet wide at the top, and 220 feet at its narrowest point (which occurs 330 feet above the ground.) Determine the height of the tower to the nearest foot.

Need help ^

[spark glade]

someone please answer this

and show work obv

[viscid thistle]

What is the question?

What have you tried?

After you share the original question, please share the work you have completed so far; this will allow someone to help you with wherever you are stuck with the problem.

[narrow oasis]

@viscid thistle is this legal?

Basically I want r to be 6.5 on the second loop

[viscid thistle]

Can we pin this somewhere? lol

[spark glade]

that is the original question

u are supposed to solve and find the answer

crap

i didnt writei t correctly

[spark glade]

here it is

we need to solve

i know the answer is 1

but im not sure how they got 1

[flint phoenix]

I’d put csc and sec in terms of sin and cos and use a sin(90°-x) identity and simplify. And do something similar for the tan and cot thing

I don’t care to work through it but that’s the path I’d take to solving it

[trim hemlock]

another way you could do is to apply product to sum identity and simplify

[spark glade]

we haven't learned that yet

[spark glade]

i'll take a look into this

[cursive imp]

can someone help with this question

[willow bear]

@cursive imp what is giving you trouble here?

is it that the equation of motion as written is actually nonsensical if you think about it physically?

(and also that the precision asked for in part b uses the wrong units?)

[cursive imp]

i think i know how to solve part a but i don’t understand part b.. i got -8.7 as the answer but idk if that’s correct (i substituted x=1 & x=1.01)

[willow bear]

the ball is kicked at t=0, not at t=1.

sounds like the nonsensical nature of the question went over your head huh

[cursive imp]

what .. so u mean i should used h(0) instead of h(1) for iroc

[willow bear]

yes, but

sounds like the nonsensical nature of the question went over your head huh

[cursive imp]

bro shut the fuck up just answer the question next time

[willow bear]

1. there was no need to be this rude. besides, i very clearly gave an answer of 'yes' to your question.
2. please don't call me 'bro'.

[placid knot]

why are you being impolite to people helping you

you get a temporary mute for now, but this type of behavior won't get you very far here

[flint phoenix]

I agree with that decision, but I think saying “the nonsensical nature of the problem went over your head” multiple times can definitely be misinterpreted as condescending. I’m not condoning his response, just saying that I understand why he might have been provoked

[viscid thistle]

How do I go about solving part two of this question? (I don't want the answer; I want guidance)

[red tree]

A good showcase of an effect of “When good teaching leads to bad results” (I just read that paper yesterday!)

[willow bear]

oh? can you link the paper?

[red tree]

Sure give me a couple of minutes

http://jwilson.coe.uga.edu/TiMER/Schoenfeld (1988) Good Teach Bad Results-2.pdf @willow bear got the link

[willow bear]

ty

[civic furnace]

What's the formula for compound interest if the money is withdrawn earlier? I forgot.

say:
5000 for 6 months with 4.4% yearly

i guess i just halve it?

[mild swan]

If there is a withdrawal, I'm pretty sure you can just decrease the balance according to the amount withdrawn

[civic furnace]

see

5000 for 6 months with 4.4% yearly

we have a yearly interest, but the money is withdrawn in 6 months

how do I calculate it?

normally the formula is
A = P(1+r/n)^nt
for:
A = amount
P = principal
r = interest rate in decimal
n = number of times interest is compounded per t
t = time

[mild swan]

If t = 1 year, then n = 2 times

[civic furnace]

there's nothing said about n, though?

we only care about whatever is left at the end of 6 months

i mean

i suppose it is implied that n = 2

but you still have to calculate only the amount that is left at the end of the 6 months

[mild swan]

Oh, if this is a rate at which money is withdrawn, then I imagine the rate would be negative

[civic furnace]

Could you please expalin to me what don't you understand?

The money is deposited for 6 months

The interest rate is 4.4% yearly

You have to calculate how much money will you have given this interest rate after 6 months

I'm asking what's the formula

[mild swan]

A = P(1+r/n)^nt
for:
A = amount
P = principal
r = interest rate in decimal
n = number of times interest is compounded per t
t = time

I think this is right, but idk why you're withdrawing money (usually these types of equations don't involve withdrawal)

Do you have a picture of the original problem?

[civic furnace]

The original problem isn't in English. I have translated it

the principal is 5000
the time is 6 months
the interest rate is 4.4% yearly
calculate the amount after 6 months

[mild swan]

Oh okay

In which case there is no withdrawal

Just compounding interest: no money is being removed from the bank account

If it's compounded yearly, then after 6 months, the balance won't change.

The balance will first change (in other words, be different than the initial amount of 500) after 1 year (or 12 months)

[civic furnace]

in such case the question doesn't make sense

so it must be something else

but regardless

thank you for your help

i'll ask my teacher about it

[willow bear]

simple interest or compound interest?

[bleak lance]

What is 2-x equivalent to?

-x+2?

[sick steppe]

commutativity of addition

$a+b=b+a$

[obsidian monolith]

Mosh

[copper vigil]

$a-b = -(b-a)$

[obsidian monolith]

EndTimes

[copper vigil]

@bleak lance that's how you find the zero

[nova grove]

for the number line

my teacher just plotted random points that’s greater than 4/3 and less than 4/3 ?

then she use points like 2 and 3 using driscrimnate equation?

[red tree]

I would have to say this isn't the best way to present the solution to the problem

even though it is pretty step-by-step

There is too much "process" here and it obscures the logic

[drowsy ledge]

Hi

Could I get help with creating conic sections equations

<@&286206848099549185>

[drowsy ledge]

someone please ;-

For the circle i made the equation

[viscid thistle]

I am actually here to learn calc but good luck

[obsidian monolith]

Key 𐂂

[drowsy ledge]

I got that for the circle

its center is (-1,7)

my bad its supposed to be (x-1)

The r=2

$(x+1)^2+(y-7)^2=4$

[obsidian monolith]

Key 𐂂

[drowsy ledge]

my bad. thats the equation i wrote

or =2^2 but 4 works too

Im pretty sure that is correct, nut i really don't know about the parabola

I don't have to find the directrix or the Focus

<@&286206848099549185>

[drowsy ledge]

Oh wait

0iq

I just have to work backwards

Thanks for helping me

, me

No problem

[viral copper]

Hi can someone tell me what i did wrong pls

[willow bear]

@viral copper your numerator has higher degree than the denominator

so to do a pfd you would need to do long division first

i.e. express (x^3+2x^2-1)/(x^2+x-6) as the sum of a polynomial and a proper fraction

where 'proper fraction' means a fraction where the degree of the top is strictly less than that of the bottom

[viral copper]

ohh ok

tysm appreciate it

[solemn vault]

can someone help me verify this problem?

[jagged glade]

Did you try to find the common denominator?

[viscid thistle]

how do you solve this by hand?

[soft cargo]

That's equal to log2(12^2)+log2(5^3)-log2(15)-log2(150)

which is equal to log2(12^2*5^3) - log2(15/150)

which is equal to log2(10*(12^2 * 5^3))

[viscid thistle]

Apparently not

the answer comes out as 3 on my cas

but that doesn't equal 3

equating the question and your answer returns false

[uncut mulch]

do you know your log laws?

specifically stuff like power law, sum to product, difference to quotient

(the other person messed up the order of operations)

[viscid thistle]

yes

have i gone wrong here?

[raven kindle]

what is the formula of finding chord in a parabola?

[willow bear]

there is no formula and you should not look for one

or are you expected to do problems like this in under 10 seconds?

[raven kindle]

I already graph the parabola

[willow bear]

if you're able to find the focus of the parabola then i fail to see what could trouble you about this

[raven kindle]

my problem is that I could not find the other endpoint of the chord

[willow bear]

have you found the focus?

[raven kindle]

yup

V(0,0)
F(0,3)
D(0,-3)
Q1(6,3)
Q2(-6,3)

[willow bear]

so have you found the equation of the chord?

[raven kindle]

the other endpoint of the chord is (8,16/3)

and i could not find the other endpoint

[willow bear]

answer me

have you found the equation of the chord

yes or no

[raven kindle]

no

[willow bear]

okay why not

it goes through (8, 16/3) and the focus.

and it is a straight line

why were you unable to find the equation of the chord?

[raven kindle]

okay nevermind

thanks for the help

[willow bear]

that sounds like a thinly veiled "fuck off" to me

[civic furnace]

How do I get a formula of a function from a partially filled table, i.e. (lhs is x, rhs is y) 0 = -2, 2 = 0, 3=5 4=9 7=12
Do I just guess or is there some method to it

Function f assigns every natural number n the number of digits required to write it in decimal form, e.g. f(7285) = 4
Give all the arguments n < 3000 for which the following equality holds f(n+1) = f(n) +1

No idea how to do it

Function g assigns every number x in [-5, 6] the smallest integer n such that 3n > x

What's the root of the function?
The answer given by the book is -3, but I think it's also -2 and -1

[civic furnace]

@surreal crest

[willow bear]

you can't, unless you have some more info about the function beyond what the table gives you.

[willow bear]

f(n+1) = f(n) + 1 means that n+1 requires one more digit to write than n. when do you think this happens?

[surreal crest]

You can use lagrange polynomial interpolation.

And just hope

That it's right

(it won't be)

[willow bear]

so the book claims -3 is the only solution of g(x)=0?

[surreal crest]

f is well defined though

There's a function for it

For the first one

[willow bear]

well it's defined on {0, 2, 3, 4, 7} maybe

but nowhere else

[surreal crest]

Idk about the second one

Can't think, all blood in my legs rn

[civic furnace]

it says that
the increasing function f: {0,1 , 2, 3, 4, 5, 6, 7} -> C has been described by the following table.
a) fill it
b) find the roots
c) find the argument a for which f(f(a)) + 2 = 0

[surreal crest]

Also zoosmell pooplord is better than troll

[willow bear]

C?

[civic furnace]

it means Z

[surreal crest]

Polish?

[civic furnace]

yeah

[willow bear]

so you are told that it is increasing.

[civic furnace]

sometimes C is used instead of Z

[surreal crest]

Z is zahlen

German

Why dont they use the standard

C is complex

[civic furnace]

C isn't used for Z anywhere beyond highschool

[surreal crest]

Infuriating

[civic furnace]

so do I jsut guess it?

check Zs

[willow bear]

no you don't guess it

you are missing f(1), f(5) and f(6)

[civic furnace]

oh right

[willow bear]

and you're told the values of f at everything else