precalculus

[tired epoch]

Yeah, in the UK calculus is taught in college, which would be the last two years of American high school

[oblique gazelle]

$$\sum_{a=1}^{4} \sum_{b=1}^{4} \sum_{c=1}^{4} max(a, b, c)$$

[obsidian monolith]

WhatIsSpin

[oblique gazelle]

I'm not sure how to go about solving this

I understand I'll get a lot of 3d points that will make a cube (1, 1, 1) (1, 1, 2) (1, 2, 1) up to (4, 4, 4)

And I think I need to add all those values up (1+1+1+1+1+2+1+2+1, etc.), but I'm not sure how to do that efficiently without manually doing it

[vapid plaza]

4 - max(a,b,c) =
3 if all of a, b, c is 1
2 if otherwise a, b, c, is all 1 or 2
1 if otherwise a, b, c is all 1 or 2 or 3
0 if otherwise (a, b, c is all 1 or 2 or 3 or 4)

= (1 if a, b, c is all 1 or 2 or 3, 0 otherwise) + (1 if a, b, c is all 1 or 2, 0 otherwise) + (1 if a, b, c is all 1, 0 otherwise)

[vapid plaza]

so add up the sum of each of these terms and subtract the overall sum from 64 x 4

answer should be ||64 * 4 - (3^3 + 2^3 + 1^3) = 220||

@oblique gazelle

[oblique gazelle]

Ah ok, that makes sense

And if it was a double integral from 1 to 6 with a and b, I assume it would be 36 * 6 - (5^2 + 4^2 + 3^2 +2^2 + 1^2)

[vapid plaza]

this looks like something that would be in #competition-math actually

[oblique gazelle]

Yeah, it is

Just realized that's a channel, thanks

[coarse kernel]

it seems like you can easily reason the same answer by constructing the points in space

[noble hollow]

do you guys have any modules so that i can practice math specially the junior high school math im already gr.11 and im having a hard time in conic sections and linear equations, i know you guys are thinking that how did i became gr.11 well the answer is the educational system in my country sucks so i really gonna need some help i cant find any module to practice in google so thats why im asking

?

[vocal grotto]

How to solve thiss?😭

Its so hard

[summer ruin]

#linear-algebra

[blissful pewter]

I'm not familiar with your school system, but Khan Academy is a free source to learn/review math that I like. Most of the questions are at a basic level, but they help you understand the concepts.

[viscid thistle]

https://www.toppr.com/

[left oyster]

How do you find the inverse of a function?

and identify the invariant point

Given an equation

[ashen skiff]

To find the inverse, all you have to do is convert f(x) into y, then swap x and y. So for example, the inverse of $f(x) = \sqrt{x}$ is $x = \sqrt{y}$, or $y = x^2$

[obsidian monolith]

🍞 Is Toast Modern? 🍞

[void thorn]

if you wanna find an invariant point, those are points that are just mapped to themselves, so you'd have to solve f(x)=x

[ashen skiff]

Aka the intersection between the graph and y=x, right?

[void thorn]

yeah, you can look at it that way too

[normal sky]

Hey can you guys recommend sites I can use to study trigonometry?

[formal crow]

if this is precalc im done this year

https://tenor.com/view/burying-dying-dead-grave-gif-17189345

[dry wigeon]

need some help and confirmation here
The answer to this would be C correct?

[ashen skiff]

Correct

[dry wigeon]

Then for this one

This would be Yes right?

[ashen skiff]

No

For something to be a function, each input variable can only have one output variable max

The input '10' has two outputs, 2001 and 2003, so the table doesn't describe a function

[dry wigeon]

ohh i see

so then this one would be yes

[ashen skiff]

Yes

[dry wigeon]

awesome, thanks for all the help bro

[dry wigeon]

ok and for this
that would be e right?

for this

is this B?

@ashen skiff if u can help :)

[ashen skiff]

correct

[ashen skiff]

Note that the question is asking for q(y-3), not q(x-3)

[dry wigeon]

so its going to be C theb

right?

or am i missing it hahah

[ashen skiff]

Oh that's my bad, I thought you said C the first time lol

You're right, its B

[dry wigeon]

i gotchu i gotchu

and this is the lasttt one

I got E for that

[ashen skiff]

yup

[dry wigeon]

thanks for all the help!

[viscid thistle]

hello i was wondering if the answer to this would be arccos (-1/3)

i did the process by taking the arccos of the dot product divided by the magnitude, but just wanted to verify

[viscid thistle]

something like 109 degrees apparently

[void thorn]

yeah that's good

[viscid thistle]

alright thank u!

[void thorn]

you're welcome

[brisk pasture]

This has a no removable discontinuity at x=3? Right

Because the vertical asymptote

[coarse kernel]

yes

it's not just not removable, it's a discontinuity of the second kind (or so-called essential discontinuity)

[brisk pasture]

This one would be continuous at x=-4 and a jump discontinuity at x=-1 too right?

[brisk pasture]

A jump?

[coarse kernel]

an (not always) infinite jump

a discontinuity of the second kind is the discontinuity where at least one of the one-sides limits doesn't exist

and both there don't (they are infinities, so they don't exist)

[brisk pasture]

But don't they go on forever? Until x=3?

[coarse kernel]

they do but AT x=3 they are just gone

[brisk pasture]

Ah ok thank you

So they are but aren't finite?

[coarse kernel]

*aren't finite

limits technically exist, but they are infinite so discontinuous

[brisk pasture]

Oh ok thanks

[coarse kernel]

also they are not even equal, one is -infinity and another is infinity

[coarse kernel]

at x=-1 a jump discontinuity, yes

and at x=-4 continuous

[brisk pasture]

Oh ok cool thank you again, my teacher didn't tell me about essential discontinuity

[coarse kernel]

essential discontinuity is the one that you can't do anything about, neither remove or somehow pair the parts of the functions

that's why it's called essential

[brisk pasture]

Ah ok that makes sense

[pale violet]

What went wrong here?

[hushed sphinx]

The exponents in your binomial theorem are off. They ought to sum to 2 in each term.
Also, you seem to be switching variables between "n" and "k" without it really being clear whether they're supposed to be the same, and you also seem to be trying to write both a summation sign and all the terms in the summation separately, which makes it hard to decipher how you thought it would work.

[nova cradle]

I'm evaluating the tan of 13pi/12 and I'm able to simplify down to "2" instead of "2-sqrt3"

I'm using the angles pi/4 in addition to 5pi/6 to represent 13pi/12

[rustic swallow]

need help with this

<@&286206848099549185>

[drowsy lichen]

@rustic swallowruffini

[noble hollow]

9+36+(-3D)+6E+F=0
how can i find the radius with this?

i think there's something wrong with this

or nahh

im not sure

[hazy hollow]

Help

[willow bear]

@hazy hollow 2.8 radians is not 5pi/6 despite any apparent proximity

you should locate the point for 2.8 radians and give its coordinates as it appears on the graph, and rounded to 1dp

[tulip swallow]

$1+1$

[obsidian monolith]

Karter

[hushed sphinx]

No silly trolling, please.

[tulip swallow]

I was just testing something chill

[uncut mulch]

#bots

[hushed sphinx]

#latex-testing, even.

[worn acorn]

Very hard! I tried everything and I got 11!

$699x8034$

[obsidian monolith]

King Tonberry

[worn acorn]

I was testing

[hushed sphinx]

Stop.

[worn acorn]

I'm new...

[sullen saddle]

how do i get the model for this?

[ashen skiff]

First, what is the income equal to?

Really, what is any income equal to?

[sullen saddle]

so (1500-5x)?

[ashen skiff]

The income is how much money they make selling cars. If they sell 200 cars at $1500, their income is going to be 300,000, right?

[sullen saddle]

yes

[ashen skiff]

So for a), since we're trying to find the function, we know that f(x), or the income, is equal to the number of cars being sold multiplied by the price of each car

our beginning number of cars is 200 and our beginning price is $1500

at what rate is amount of cars changing? at what rate is the price changing?

[sullen saddle]

50$ for every 5 cars

[ashen skiff]

right, so if the price goes up by 50, cars decrease by 5. price goes up by 250, cars decrease by 25

so for every x increase of 50, there's also an x decrease of 5 cars

so the price is going to be 1500, plus some value 50x

the car amount is going to be 200, minus some value 5x

[sullen saddle]

so its (200)(1500) + 50(x-5x)?

[ashen skiff]

Income = Price x Cars

The price of each car is (1500 + 50x), where x can be any value

the amount of cars is (200 - 5x), where x can be any value

so the income would be equal to (1500 + 50x) * (200 - 5x)

[sullen saddle]

so -250x^2 + 2500x + 300 000

?

[ashen skiff]

yup

[sullen saddle]

thank uu

i can still simplify it right?

[ashen skiff]

You could pull out a 250 if you wanted to

[sullen saddle]

okk tyy

[ashen skiff]

that would give you -250(x^2 - 10x - 1200) which could be factored to -250(x-40)(x+30) I believe

[sullen saddle]

wait why does the answer key say this

[ashen skiff]

I think they simplified the +50x and -5x to +x and -1x/10

so (1500 + x) * (200 - x/10)

[sullen saddle]

ohh i see

thank you

[sullen saddle]

why do I have to divide 4900 to 100 and 90? for e

[ashen skiff]

Dividing total cost by the price of each kg will give you total kg, right? If the total cost is $1000 and the price of each is $100, you know that there were 10 items because 1000/100=10

Dividing 4900 by 100 gives you 49. That means the total weight would be 49kgs

4900/90 gives you 54.4kg, so that's another possible weight

4900/85 gives you 57.65

The problem with that though is that the price is only ever $85 when the weight is over 200kgs. 57.65 kg at $85 per kg isn't possible, so 57.65 is not a possible weight

[subtle ether]

is anyone here able to help me with a quick problem

[vivid nymph]

if its factoring sure, i enjoy factoring

[ashen skiff]

can anyone explain?

[oblique gazelle]

What have you tried?

I would apply the chain rule and then plug in values

[ashen skiff]

I figured that chain rule wouldn't be needed

if t=7, then i found that g(t) is approximately 6-7

which would leave me with f(6.5) or so

then i took the derivative of that 😅

we aren't given exact values so I can't plug in anything

[oblique gazelle]

Looks like you have fairly accurate graphs to me

Also definitely do not make the mistake of assuming that the derivative of f(g(t)) is the derivative of what g(t) is like you did, you'll get it wrong.

[oblique gazelle]

That's because the derivative of f(g(x)) is f'(g(x)) * g'(x) and that g'(x) is important

[drifting wigeon]

i forgot. when the degree of the numerator is larger than the degree in the denominator, what do we get? (vertical and horizontal asymptotes)

[ashen skiff]

it's more obvious on fullscreen, g(7) is definitely not an easy number to see

it's just slightly less than 6.5

[oblique gazelle]

Yeah, I just approximated it to be 6.5

[lucid trench]

here are some cool precalc notes i took

[velvet fox]

Nice handwriting, do you practice?

[viscid thistle]

yoo I wish I was that neat >w<

[lucid trench]

yes

[lucid trench]

thank you 💚

[viscid thistle]

np

[viscid thistle]

https://www.youtube.com/watch?v=nywVwAhK70M

at least some of you will find this helpful, thank me later

[rapid inlet]

Hello, can someone please check the validity of this proof I wrote please? I'm pretty sure it's fine but a second opinion never hurts

please ping 🙂

[hushed sphinx]

If it's homework and you don't have any particular points in the proof you have doubts about, why not let your teacher/grader do the checking? They get paid for it; we don't -- and it's tedious and boring work.

[rapid inlet]

It's not homework, it's self study

I'm in britsh HS and each time I ask my teachers about any proof based things they just say they can't help me

You don't have to check it if you don't want to tropo, no one is forcing you, just if anyone would like to be a helping hand I would appreciate that - especially given I Don't have anyone to check my understanding against irl

[noble hollow]

can anyone explain what is happening here and why (dont mind the phone brands)
were trying to find the radius with point (3,2) and (2,1)

also dont mind the subconscious thing

[viscid thistle]

lol

[velvet fox]

Do you trace or just write?

[lucid trench]

i don't trace

[velvet fox]

hmm cool, good stuff

[livid dew]

Anyone know of the best online courses for precalculus that do a good job at making the curriculum make sense? Everyone in my class just failed the last test, so I need to figure it out somewhere else

[gusty pasture]

Looking at this reminds me of how much easier life used to be 💀

[lucid trench]

What lol

[gusty pasture]

Calc 1 and 2 are way harder than what pre calc guves

[lucid trench]

ahh yeah i bet

[gusty pasture]

I honestly don’t remember anything from pre calculus because of how much reg calculus is drained into my head

[proper garnet]

hey im reviewing my study guide for the test tomorrow and don’t understand this concept

i dont understanding how the -x^4+12x^3+3x^2 was gotten

could i just add the exponent and call it a day?

[lapis sphinx]

They multiplied the divisor by x^2 to get a leading term of x^4 that would cancel out

[proper garnet]

ok thank you

wait

wouldn’t that mean it should be +11x^2?

[gleaming bane]

se

[gusty pasture]

How can you tell if it’s defined or not

I already did the other parts I’m just confused on the first part

[mellow vigil]

if the denominator is 0 then it is undefined

[obsidian monolith]

NotMyself

[gusty pasture]

So x =3

[mellow vigil]

yes

[gusty pasture]

Wow I’m dumb lmfao

Wait can you help me with the translations

[mellow vigil]

idk translations rn

i am also learn functiond rn

lol

[gusty pasture]

I’m trying to tutor someone pre calc but I don’t remember this

[mellow vigil]

oh

[gusty pasture]

I don’t remember translations with asymptotes lol

[lime torrent]

Sal

Voice call real quick

[bitter sable]

Is there any reason for me to learn "complete the square" or can i just always use the quadratic formula?

[uncut mulch]

it's useful for converting stuff to different forms

helps with graphing, identifying vertex, max and mins

and later on very useful when working with circles,eclipses,conics

and the idea behind it is also quite handy for some questions involving algebraic trickery

note that there should be a distinction between completing the square itself, and solving a quadratic equation using completing the square

i.e for
x^2 +2x = 8
x^2 + 2x + 1 = 8 + 1
(x+1)^2 = 9
CTS only refers to the part up to here

[bitter sable]

Ohhhh thanks, so I shouldn't skip learning CTS right?

@uncut mulch

[uncut mulch]

definitely shouldnt skip

[bitter sable]

alright, thanks, i appreciate it

[uncut mulch]

it's also a good exercise to derive the quadratic formula using completing the square if you haven't already done so

[bitter sable]

Is there a good video(s) that explain all this in good detail?

[gusty pasture]

I cannot rn

[vapid snow]

it only works if the discriminant above or equal to 0

its another method to use if quadratic formula fails

[uncut mulch]

qf doesn't fail

[stuck lark]

it works if discrim<0, u just get complex sols

[vapid snow]

o'

[hallow furnace]

I had a odd question, would anyone know any “assignments” or practice problems for pre calculus that also have a solution sheet that is based around space? Like I would like to practice more of my pre calculus but I thought it would be funner to do if it was based in physics or space

[outer notch]

are there any free websites that have precalculus lectures and practice problems?

[mellow vigil]

Khan Academy

[nova cradle]

Looking for solutions between 0-2pi

Am I missing some useful identity?

[uncut mulch]

tan(k) = sin(k)/cos(k)

[nova cradle]

Thought of that but I don’t see how it’s useful

[summer ruin]

factor sin(x) and now it's an easy equation

should be (x+pi) everywhere though

then also make sure none of the roots turns cosine into 0, if so exclude them

[uncut mulch]

you can factor out sin(x+pi) at the very start

which makes the work considerably less tedious

[nova cradle]

Good idea. Though, Transparent Elemental, what do you mean by "should be (x+pi) everywhere"?

All of the terms with pi were cancelled because of their relation to sines with the input of pi

[summer ruin]

that's only true for tangent here, sin(x+pi) in general isn't equal to sin(x)

[nova cradle]

The graph of sinx isn't identical but the solutions are

The right side of the double angle equation for sin is equal to 0 because it's multiplied by zero (sin of pi)

In the top image it should be -2sinx though

Sorry for the trouble, I just want to understand all aspects of the problem

[viscid thistle]

Can i get help with this, i genuinely attempted it and i don't understand how i'm getting it wrong

[nova cradle]

So, what about between 0 and 1 in the domain...

[summer ruin]

domain is all x, not all positive x

obviously a^(-1) makes perfect sense, it's 1/a

[viscid thistle]

so just uncheck the 1st one from the answer

and i should be good, right

[nova cradle]

yep

[summer ruin]

no, there's one more

which depends on what a is equal to, whether it's greater than 1 or less than 1

[viscid thistle]

its graph always incrases

has to be

[summer ruin]

oh sorry, I thought it was checked for some reason

so it should be unchecked

so you're good

[nova cradle]

Had me confused there for a moment lol

[viscid thistle]

Yessir, we're up

[chilly glade]

How would you find the reference number for t=5pi?

[forest raptor]

confused

where to start

[nova cradle]

I'm not sure what the "width" of the bridge refers to...

Considering the height however, a classical parabola is closest to the x-axis at x=0

If we shift the graph down (-27), the deviation from the x-axis is greatest at x=0

If "h"= height, that would mean (based on the graph of the equation) that the bridge is tallest as x approaches -infinity and +infinity

This however doesn't make sense so I would assume they are talking about the point of maximum deviation (negative) from the x axis which is -27

[nova cradle]

The reference angle (from the unit circle) is the angle between the terminal side of the angle and the closest x axis

[viscid thistle]

how is this wrong

[forest raptor]

yeah the question

is phrased horribly

i thought the same tgunf

[worthy sapphire]

It's semiannual right?

[unborn zenith]

beo

bro*

use I=PRT/100

use that fromula

for*

I am IGCSE O level Student

[viscid thistle]

yes

[unborn zenith]

What do u mean??

[viscid thistle]

add me so we can discuss this in dms

[unborn zenith]

hmm

dude, I am IGCSE o level students

I have Mid term Exam

[viscid thistle]

ok

[potent acorn]

6^n+4 is divisible by 5 for n ≥ 0
Mathematical induction

Can anyone answer this

[vapid plaza]

What have you tried?

[mild swan]

^^

[potent acorn]

@mild swan can you answer this

[mild swan]

.

Doesn’t seem like you’re trying, so why should I?

[unborn zenith]

i think it is inequality

is easy

[mild swan]

“Is easy”

[unborn zenith]

yea

Math is easy for me

[mild swan]

Grammar isn’t, it seems

[unborn zenith]

maybe

[quick aspen]

Hi, what's the fastest method to find the determinant, the inversion , the rank and the singular of a 3x3 matrix matrix?

[sullen saddle]

how do i solve this?

[worldly jewel]

if there's 8 children, the probability of having either a boy and a girl is 50 percent, What's the probability having 6 girls and 2 boys?

Can anyone help to answer this question pls

[willow bear]

f being its own inverse means f(f(x)) = x for all x

[sullen saddle]

and with that Ill be able to find the value of K?

[sullen saddle]

i dont understand this

[willow bear]

(a) I do not understand what "f is its own inverse" means.
(b) I do not understand what "f(f(x)) = x for all x" means.
(c) Both statements in (a) and (b) are beyond my understanding.
(d) I understand both statements in (a) and (b), but not why they mean the same thing.

which of these best describes your confusion?

[sullen saddle]

so if f is its own inverse so the answer would be just 1?

so k=1?

[willow bear]

thank you for not answering my question

[sullen saddle]

d

[limpid moss]

who pinged me here

[willow bear]

right ok so

you understand that when we say two functions are inverses, we mean that their composition is the identity function, yes?

[sullen saddle]

yes

[willow bear]

right

and you understand that when we say a function f is its own inverse, we mean that the composition of f with f is the identity function, yes?

[sullen saddle]

yess slr

[willow bear]

okay, so

does this clear up your confusion

[viscid thistle]

when the function has f(x)

[lucid trench]

you talk like a survey

[willow bear]

how else am i going to discern where exactly the help-seeker is confused if not by giving them a list of options to look through

[lucid trench]

im just saying

[willow bear]

ok yes i did kind of talk like a survey there

what of it

[lucid trench]

nothing

as i said im just saying

[patent trench]

my most unforgiving mistake 😫

[patent trench]

YES

haha professor I am banging your daughter now

[patent trench]

just one more

and I'll be free

professor is rolling in his grave rn

[gusty pasture]

isnt this the u v v' v' thing

like u just flip the sign of the imaginary number

i honestly forgot lmfao

[hushed sphinx]

You mean "complex conjugate"?

[nova cradle]

one think we do know: Shinkansen is absolutely DOMINATING these imaginary division problems

[sterile turret]

why is sum of odd powers factorable but not sum of even powers

[hushed sphinx]

Uh, what?

A polynomial that has only odd powers will always be divisible by x (just by virtue of having no constant term), is that what you're talking about?

[void thorn]

my guess was gonna be that they mean you can factor x+y out x^n+y^n when n is odd

[hushed sphinx]

Oh, that sounds more likely.

[gusty pasture]

Pretty much lmao

[sterile turret]

yes this

[void thorn]

I suppose if that's the question, then one explanation is when you look at x^n-y^n=(x-y)(x^{n-1}+...+y^{n-1}) and replace y with -y, it only changes to x^n+y^n when n is odd, otherwise it squares the -1 away and stays as x^n-y^n

[sterile turret]

like why is x^5+a^5 is factorable

but not

x^4+a^4

[hushed sphinx]

 +.....+       +........+        +......+
x^5   x^4a   x^3a^2   x^2a^3    xa^4    a^5
       -.......-        -........-

Each of the +.....+ or -......- stands for a monomial times x+a possibly times -1.

Becasue positives and negatives alternate, all of the middle terms cancel each other out, so there's just x^5+a^5 left at the end.

But we need the last link to be a +......+, otherwise we would end with x^n-a^n instead.

[vapid plaza]

Another explanation is that x^n+c^n (c nonzero) has a real root (x = -c) exactly when n is odd (and hence we can use factor theorem)

[bitter sable]

https://youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP

If I learn everything from this YouTube Playlist, will I pretty much be set up for Calculus?

[nova cradle]

Knowing math isn't the same thing as being able to do it..

[bitter sable]

Well yeah, I wouldn't just watch the whole playlist with the intention of not being able to apply the information, I'm just saying if I do properly learn everything in that playlist and am able to apply that info properly, would that suffice me of all of the pre requisites I need before taking calc 1

[coarse kernel]

I'd say you don't have to know equations/stuff in polar... well, you'd better do, but it's rather complementary in a way

[serene cargo]

Im not sure if im in the right channel, but is there a simple way to solve that kind of summation ?

i mean j instead of i

[frank vine]

split up the summation and solve indiv parts

[frank vine]

^^

[void thorn]

take the sum $\frac{x^{k+1}-1}{x-1}=\sum_{j=0}^k x^k$, take the derivative of both sides, multiply by $x$, then plug in $x=2^{-1}$.

[obsidian monolith]

Merosity

[void thorn]

just realized this is precalculus channel whoops

[kindred sluice]

how do I find all solutions and the fourth roots of -81i
when 0-81i tan = -81/0 is undefined?
What do you do when you have no angle?

wait i think i got it

if it appears on the axis we just pick the angle for which axis it lands

[trail ledge]

I need this book in pdf

anybody got it?

[viscid thistle]

Do someone know how to find area of this one?

[uneven reef]

does anyone understand proving trigonometric identities?

[visual onyx]

I'm not sure I understand how to do this

[visual onyx]

WHAT IS A NATURAL LOG I DON'T UNDERSTAND

[viscid thistle]

do you know what ln(x) is?

[visual onyx]

Nah, also sorry for posting in all caps, that came off too strong

But yeah I just don't understand, I think its a log with a 10 base always

[viscid thistle]

nah dw about it

oh no

its not that

do you know what the e in that picture is supposed to mean?

[visual onyx]

i think its supposed to be an a, it was in all the other problems but suddenly they changed it

[viscid thistle]

uhh

i believe that's euler's number

it is a constant, like that of pi

[viscid thistle]

How will that work

[viscid thistle]

can i get help with this

[uncut mulch]

you've entered a constant funtion

starting with f(x) = a^x
plug in the given point to determine the value of a

and you'd enter
(whatever you got for the value of a)^x

[viscid thistle]

so plug in 1/3 into f(x)

[uncut mulch]

plug in the whole point into your equation

and/or sub x=-1 into the equation, the point tells you f(-1) = 1/3

[viscid thistle]

ok, the inverse of 3

is 1/3

right

[uncut mulch]

multiplicative inverse yes

[viscid thistle]

so then the answer would be 3

[vapid plaza]

The “reciprocal”, to be precise

[viscid thistle]

oh, alright

[uncut mulch]

well your value of a will be 3

and you'd enter
whatever you got for the value of a^x

[viscid thistle]

ohhhh

3^x

[uncut mulch]

yes

[viscid thistle]

Nah, that makes sense

appreciate it

[paper sand]

Can someone help me with this 😭😭

[restive flame]

I get m=4 and k=1

which is incorrect

could someone help me understand where im going wrong

[restive flame]

@ mods

can i have perms to screenshare

@bright venture

[bright venture]

1. why are you asking in here
2. why did you ping me in particular
3. ok

but I know you were specifically told to DM mod mail

[viscid thistle]

can anyone help with physics queestion?

[olive scarab]

https://dontasktoask.com/

[hushed sphinx]

Also see #old-network to find the dedicated physics server.

[rotund cairn]

can anyone give me tips on getting started learning pre calculus

[mellow vigil]

Khan Academy and Youtube

[light crescent]

organic chemistry tutor

[wide quest]

khan academy explains it better

[surreal berry]

how quickly do mods see it if u dm modmail

[chrome nova]

how do i evaluate the limit of this expression as x approaches 1

(not allowed to use l'hopitals rule 🥲 )

[grave valve]

Ok so first, what is the l'hopitals rule

Cus like, personally I would just multiply by the conjugate

[hushed sphinx]

That might be a good start, but will still leave you with a denominator that approaches 0.

[uncut mulch]

doing some stuff with conjugates should work

[viscid thistle]

split it $\sqrt{x^2-1}/\sqrt{x-1}+(\sqrt{x}-1)/\sqrt{x-1}$ and the other part

[obsidian monolith]

Amer

[viscid thistle]

The first just factor top and cancel

for the second conjugate the top it is double the denominator so it is zero

the limit should appraoch from the right of 1 if not you will be out of the domain

[visual onyx]

I DON't UNDErstand

[nova cradle]

So, do you know what happens when you change x^2 to 2x^2?

Or when you change x^2 to x^2-1?

[obsidian monolith]

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

[leaden parcel]

does anyone have any idea how to solve this?

[formal vapor]

@tall sequoia Question . Im trying to convert -225 into radians. I got -5pi/4 . I know that its going to be -225 * pi/180. I broke down 225(455) and 180 (454), after canceling everything I ended up with -5pi/4. I looked up the answer and its -37/30......where did I go wrong?

[hushed sphinx]

(Pinging modmail does nothing, by the way -- but that's just as well because math help is not a moderator matter).

Who says the answer would be -37/30, or for that matter -37pi/30? Don't trust them.

[fallen whale]

can anyone help me get better at pre cal 12 i have been studying 4 hours a day everyday and i still dont get it i think i have a problem in my fundimentals that need to be pointed out. can anyone help?

[hushed sphinx]

You can try talking about the problems you have here -- but you'll need to bring up the specific things that confuse you; there's not much one can do if you just expect people to take the initiative from scratch.

[fallen whale]

Its pretty hard to give an exact problem because on matter how much i study i keep making mistakes and im hoping somone would be willing to do some questions together and seeing why i am struggling so much

[hushed sphinx]

If you're not willing to say anything more specific than "I keep making mistakes", nobody will be able to help you. Sorry.

[gusty pasture]

What’s the formula for the last one

<@&286206848099549185> pls

I don’t understand what h and k are

[gusty pasture]

Nvm lol

[mellow vigil]

A person has 2 parents. 4 grandparents, 8 great-grandparents, and so on. Find the number of his anscestors during the ten generations preceding his own.

Isn't the above question wrong as there might be someone who had kids with 2 people and then predecessors of those kids married and stuff like that

[amber flicker]

You're correct, but I don't think you need to think about that in order to solve the problem.

[mellow vigil]

will ig but they should have mentioned

[amber flicker]

Well do you need help with the problem itself?

[mellow vigil]

no thnx

[amber flicker]

Alright

[fleet flame]

I need help

[hollow scaffold]

Pictures will do

[hushed sphinx]

How about a rice hat? Not just conic sections, but an actual cone!

[willow bear]

@hollow scaffold don't ping everyone.

[hollow scaffold]

Ok

[obsidian monolith]

NotMyself

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

[mellow vigil]

Is this proof right?

[mellow vigil]

<@&286206848099549185>

[plucky yacht]

ill check it out later

arithmetic progression

i should go back and restudy pre calc

[mellow vigil]

ohk

[viscid thistle]

$S_n = \frac{n}{2}(2 t_1 + (p-1)d)$ I would use another variable for the first term i used $t_1$ instead of $a_1$ because they used $a$ to denote the sum of the first $p$ terms becareful do not sub a in the sum of the first p terms!!

[obsidian monolith]

Amer

[viscid thistle]

so your proof is not correct you assumed first term is equal to the sum of the first p terms

[void gull]

for both questions, try to factorize the denominator and divide the factors from the numerator

[fleet flame]

Ty

[outer notch]

do u guys think it is necessary to memorize the entire unit circle

[void thorn]

depends, once you know 30 and 45 degrees the rest all come from that by symmetry

[shut shore]

Necessary? I don't know.. Worthwhile, yes

[wise spoke]

\text{ For two complex numbers, $z_{1}$ and $z_{2}$, where; } \\
$z_{1} = a_{1} + b_{1}i \\ z_{2} = a_{2} + b_{2} i$ \\
\text{If $a_{1} = a_{2} = 0$ then can we say that $z_{1} \cdot z_{2} \in \mathbf{R}$ ?
}

[obsidian monolith]

∫Inheritanc-e ♦

[tidal bobcat]

yes.

[mellow vigil]

thnx

[mellow vigil]

yes as i^2 = -1

[hushed sphinx]

The entire unit circle is far too much. Textbooks usually list coordinates for points with angles that are multiples of 30° and 45°; as Merosity says these can all be derived by symmetry if you just remember those two base values.
There are other exact facts that could be remembered, such as cos(36°) = (1+sqrt(5))/4 -- but nobody goes around actually memorizing those.

[viscid thistle]

all you need to know is 45 degree triangle and 30-60 triangle, can derive basic stuff from that. for tips you can look up youtube videos, how to memorise it.

[hushed sphinx]

I wouldn't dedicate too much time to memorizing those results. Just remember that there are nice values for 45-45-90 and 30-60-90 triangles and derive the actual values using the pythagorean theorem when you need them, until you've done that often enough that you just remember them anyway.

[safe lion]

Can anyone explain the property log base a^b of x is equal to reciprocal of b times log base a of x

[willow bear]

$\log_{a^b} (x) = \frac{1}{b} \log_a(x)$

[obsidian monolith]

Ann

[willow bear]

this?

[safe lion]

Yes

[uncut mulch]

applying the change of base law
$$=\frac{\log_a(x)}{\log_a(a^b)}$$

[obsidian monolith]

ℝamonov

[uncut mulch]

the denominator will be b

[safe lion]

Oh I got it thanks

[tough parcel]

do u know how when dividing a polynomial; if a term is not there, you have to hold it with a 0?
does that only work with synthetic division or does it also work with long division

[tough parcel]

,tex \polysyntheticdiv{15x^4+10x^3-6x^2+14}{x+2/3}

[obsidian monolith]

babytronfan221

\polysyntheticdiv{15x^4+10x^3-6x^2+14}{x+2/3}
```Compilation error:```! Undefined control sequence.
l.57 \polysyntheticdiv
                      {15x^4+10x^3-6x^2+14}{x+2/3}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```

[uncut mulch]

in polynomial long division you'd write 0x^(the missing power) or leave an appropriate gap to keep stuff aligned properly

[lucid trench]

heres some cool precalc notes i took #2

[ebon blade]

I need help with these

I already have #6 down

I dont want answers please

i just like to understand what I should do to go about solving these

[ebon blade]

its for a project

thanks in advance

[brisk pasture]

How would the black function looked algebraicly?

[brisk pasture]

What would be the transformation from the black to red?

[light crescent]

god damn i wish i had notes like that

[oblique gazelle]

Down five, right three

[light crescent]

wouldnt it be down 5

[brisk pasture]

What would the original function look like? The black one

[feral lake]

the function might be a piece-wise function, like it's split into 2 equations.

maybe something like this

[brisk pasture]

@feral lake like f(x)={x, 0<x<2, and {2, 2<x<5?

Maybe

[feral lake]

yeah

[proven spear]

wtf is sin of -90,

[feral lake]

-1

[proven spear]

thats what i got and someone told me it was wrong

[feral lake]

i guess dont listen to them idk lol

[brisk pasture]

-0.8939966636

[proven spear]

ive been sitting here for 2 hours just dumbfounded, i thought i was the idiot

[feral lake]

did the put it into the calculator?

[brisk pasture]

Or -1

[feral lake]

its -1 on the unit circle

[proven spear]

idk, i just remember the unit circle, but they made me second guess myself

[feral lake]

they prob had their calculator in radian mode and put -90 in

[brisk pasture]

@proven spear it should be -1 or -0.8939966636

[feral lake]

so it thinks its -90 rad

[proven spear]

they wasted so much of my time

[feral lake]

it happens man

but it shouldn't be -0.89

[brisk pasture]

Yeah it happens

[feral lake]

you have your calculator in rad mode so it thinks the -90 is -90 rad

thats where you are getting the -0.983

sin(-90degress) is -1

[brisk pasture]

Yeah lol it's -1, my calculator makes it confusing between rad and deg

[feral lake]

its all good

[viscid thistle]

how do u evaluate tan from unit circles?

[feral lake]

give an example and i will try to help

tan(theta) = y/x

ill give example

[viscid thistle]

so essentially it is the y value over the x value

then simplified?

[feral lake]

yes

[viscid thistle]

kk ty

[feral lake]

remember to keep track of what quadrant you are in

keep track of signs

[viscid thistle]

isnt it the same as a regular graph?

[feral lake]

wdym

[viscid thistle]

like the signs for each quadrant

like quadrant one is all positives, quadrant 2 is x negative y positive and so on?

[feral lake]

yes

[viscid thistle]

kk ty!

how did you memorize the unit circle?

[feral lake]

like the special angles?

[viscid thistle]

yes

[feral lake]

practice

45degree angles are the same

like with sin and cos

sqrt2/2

30 and 60 are harder to remember

[viscid thistle]

hm

[feral lake]

cos60 is 1/2

sin60 is sqrt3/2

[viscid thistle]

right

[feral lake]

just alternate them for 30 degrees

[viscid thistle]

kk ty!

[feral lake]

try to remember which is 1/2

[viscid thistle]

what are coterminal angles?

[feral lake]

and build of that

[viscid thistle]

kk

[feral lake]

its angles that are 360 degrees apart

so you take the original angle and add 360 degrees to it

or subtract it

[viscid thistle]

why?

so its like angles that are the complete opposed of each other?

[feral lake]

no cause its one revolution

think of a circle

and you are facing one way

[viscid thistle]

mhm

so its back to the og position?

[feral lake]

yes

but you make a revolution

[viscid thistle]

what do you mean?

revolution?

[feral lake]

you go counterclockwise 360 degrees

if you add 360

or you go clockwise 360 degrees

if you subtract them

like this

[viscid thistle]

OH okay

could you like give an example?

what would be the coternminal angle for 500 degrees

i'm sorry i keep asking questions

[feral lake]

its ok

im free rn

so

if you are looking for coterminal angles

you add 360 degrees to the angle

[viscid thistle]

so like it would be 860 degrees?

[feral lake]

so 500 + 360

yes

[inner belfry]

I don't want to interrupt yall but can you help me after please

[feral lake]

and you subtract 360 degrees

[viscid thistle]

to find counterclockwise?

[viscid thistle]

whats up

[inner belfry]

do you know anything about the functions of sins and cos? like moving and shifting.

I just learned about coterminals as well but different

f(x)= cos(4x)

I know its moving 4 times as fast as cos (x), just don't know how to find the measure points

[viscid thistle]

oh no we arent there yet

[inner belfry]

oh haha, its okay

[feral lake]

when you add 360 you are going counterclockwise

if you have a negative angle you would move clockwise

[viscid thistle]

add 360 = counter, subtract 360 = clockwise

[feral lake]

yes

[viscid thistle]

that explains a lot tysm!

[feral lake]

np

[hard wigeon]

can someome help me in #help-29 ? it’s based on trig

[feral lake]

the 4 basically makes the wave tighter if that makes any sense

like if you were to graph it

[inner belfry]

yeah, so y stays the same, but x is 4 times shorter?

[honest condor]

Can anyone help with synthetic division when the divisor is prime numbers

[feral lake]

yes

[viscid thistle]

wdym

[feral lake]

yes

[honest condor]

the questions 4x^4 + 5x^3 -10x+8

divided by 3x-2

3x+2*

sorry

[viscid thistle]

okay so

-2/3 woul be the factor i believe

[honest condor]

ya thats what I wrote but I dont think thats it

like your talking about when I do the synthetic?

[viscid thistle]

yes

3x + 2 = 0

x = -2/3

so i would assume that its the factor

[honest condor]

okok yk how I would write it out after synthetic division finding the remainder and quotient

and division statement ?

[viscid thistle]

what is left over (the remainder) over the quotient

i think

like [remainder]/3x+2

can you help @viscid thistle

pls

[honest condor]

wait wym

[viscid thistle]

yes?

wha do u need help w?

[viscid thistle]

#geometry-and-trigonometry

i deadass might die

honestly i don't remember a thing from geometry, did that course over pandemic

i'm sorry i wish i could help!

[honest condor]

Anyone know the end behaviour, turning points and global max/min of a function with a degree of 59 and negative leading coefficent

[quiet veldt]

what pen and whats its longevity

[lucid trench]

it's a pilot precise V5 extra fine pen

my absolute favorite pens

[viral vine]

nice note you got there

[timid falcon]

Can someone explain the difference between closed and open circles? Like if the question is:
lim f(x)
x->-3 from the left, is that 2 or -2? Same for the right

[summer ruin]

the very definition of a limit doesn't care about a circle

the circle represents whether the function is defined at that point or not

if you take any sequence of inputs that converges to -3 then function value would converge (if the function is continuous) to values that should be near that point

so it's 2

[brisk pasture]

What is the black function?

[feral lake]

.

Piecewise

[brisk pasture]

Demos doesn't let me graph like that for some reason

@feral lake do you know what the original function is?

[brisk pasture]

@feral lake oh ok cool thank you

[feral lake]

The brackets are for the interval

[brisk pasture]

Ah ok thanks

[brisk pasture]

How do I graph the red without moving from the orgin?

[viscid thistle]

What do you mean?

[brisk pasture]

For example, the original black function is f(x), how would I graph the red function?

@viscid thistle when I try I'm doing something wrong

[viscid thistle]

Looks like a scaled version of the black function.

Anyways.

Just calculate the slope of the red line for 0<x<2, so you can write the line for that interval.

And when 2<=x<=5 it'll just be y = 1.

[viscid thistle]

Or do you mean how to graph it on Desmos?

The way the other guy did?

[brisk pasture]

@viscid thistle oh wait I got it thank you anyways

[hot brook]

Hello^^ im so sorry ;-; but can someone help me factor this one out im begging

im trying to get the zeroes by using synthetic division and so far i cant get any correct ones from it ;-;

[uncut mulch]

this doesn't have rational zeroes

and has no nice factorisation

[hot brook]

then do i resort to factoring if theres none?

[summer ruin]

you can't factor this most likely

[hot brook]

oh no 😭 how will i graph this then?

[summer ruin]

I guess there's always a quartic roots formula, but you don't want to ever use it

[uncut mulch]

you can use certain methods to approximate roots

you can use derivatives to identify locations of stationary points

[summer ruin]

take the derivative, find local minima, analyze how the derivative behaves i. e. where the function is increasing or decreasing

that should be enough for proper graph

[uncut mulch]

and pug in as many other values of x as you want to get enough points to make your graph look decent

[hot brook]

I actually got one location from it and its -8 but so far for the others i cant-

[hot brook]

im sorry to say this but i dont think i can use that-

[summer ruin]

then you can't do anything about it, besides very long and boring plugging x's in the function and marking the result

[hot brook]

actually theres choices and i know which ones the answer the problem is the problem our wack teacher gave us isnt factorable at all

is this one at least factorable though?

[summer ruin]

I guess not

[hot brook]

god i hope whoever made our worksheets 💀

ig ill just identify it based on the end behaviors

TYSMM THO^^ @summer ruin @uncut mulch

[viscid thistle]

hello, if you had a function f(x), where x is the variable, and f(x) is the function, what does f represent?

is it just a placeholder?

I have questions that are like this

find the domain of $$f \circ g$$

[obsidian monolith]

smoobles

[zinc fulcrum]

well actually f is the function

"f(x)" could used when describing what the function f maps each x to, or it might be used to represent the value that f maps a particular value x to

depending on the context

[viscid thistle]

ah I see

doesn't it get confusing when you have functions and variables in the same field?

like I know f can be either (f)unction or (f)requency in physics

[zinc fulcrum]

it could but I think people are usually good about that when writing things

actually I take that back

it's pretty confusing for people in differential equations

I hope no one in physics names a function f when they are already using f for frequency

[deep marsh]

normally nu is used for frequency tho

[dense depot]

parallel to the line 4x-2y=8 and has the same y-intercept as the line 5x+3y =-15, can someone tell me the point slope form of this?

[granite tinsel]

Of course it is

Use the factor therom

[brisk pasture]

Are the increasing intervals (-infinity, -1)u(-1,1)?

[crisp lynx]

having some problem factoring this expression (x^2+x+6)

It’s one of my roots for linear factorization but I can’t get it as two binomials

[brisk pasture]

I don't think that's factorable

[crisp lynx]

Yeah I know but I need it as a complex root

[late pike]

You can factor it using the quadratic equation

If it is a polynomial with a degree of 2, then you can always rely on the quadratic formula

[crisp lynx]

Lovely thanks so much

And I would just insert that as a factor

Thanks again

[late pike]

Wait just remember to use the opposite sign

[crisp lynx]

Yep

[coarse hemlock]

I have a question if someone can answer pls

For Remainder Theorem…

Am I supposed to plug in the c value to the x??

[sour relic]

Someone explain 4 to me pls :))

[brisk pasture]

I'm confused

How do differentiate a infinite discontinuity from just a continuous function?

[wise rover]

what is an infinite discontinuity?

[brisk pasture]

Theres a infinity at a positive and negative asymptote?@wise rover

I'm not sure 100%

[wise rover]

Read your notes

[brisk pasture]

Bruh

Thanks

@wise rover what are they?

[mellow vigil]

Thats collatz conjecture and its still unproven

tho it has been verified for around 2^60 numbers

[sullen basin]

any canadians here?

what did teach in grade 11?

[viscid thistle]

translate cuz i speak spanish and idk how explain this in english: mira, la discontinuidad de los lomites es algo muy simple, sucede cuando sus evaluaciones laterales del limite, (derecha e izquierda), son diferentes, pues por ejemplo, una función de raíz cuadratica de x, donde x tiende a 0, cuando tiende por la izquierda se forma una raiz cuadrada negativa, lo cual indica numeros imaginarios, por lo cual no se puede representar de forma gráfica, PERO, evaluandolo por la derecha si se puede pues son raices positivas, entonces su limite no existe. También es fácil de ver cuando tienes una función definida o también llamada función a “trozos”, que cuando hay un valor en un intervalo se define valor de la función diferente al del otro intervalo

[unkempt mantle]

Hey everyone, we've recently started learning about limits, but im noticing that no one really understands what a limit is.
I asked my teacher and he didn't give me a definite/clear answer of "What is a limit", i checked on youtube and didn't find many resources.
I first thought it might be the "limit" where we go up the y axis and stop at a certain point (which for me explained why f(x)=x/0 has no limit, because we will go up the y axis and never stop. I'm not sure though.
Where can i find the exact definition of what a limit is?

[stable geyser]

hello, i am starting to learn differentiation (on my own), does anyone have a source where i can get questions from

where i can use things like the chain rule, product rule, quotient rule, etc

[unkempt mantle]

Yea im trying to find questions as well

[vapid plaza]

the limit is formally defined as https://en.wikipedia.org/wiki/Limit_of_a_function#(ε,_δ)-definition_of_limit

(for your purposes)

[viscid gulch]

hello

someone pls

[tawdry trench]

My teacher told me a limit is the study of a function at a certain point, simple and clear lol

And x/0 is non defined because the denominator is 0, so there is no correspondent on the y axis

It's like bargaining at a store, you keep going up and the retailer keeps going down till you both meet at a point

if you dont meet there is no limit

:)

[void cobalt]

how do you find the angle measurement between 0 and 360 with 9cos+7=0

[void cobalt]

But im trying to understand the calculation so the furthest I get is cos=-9/7

[vapid plaza]

What’s where the mistake is

You need to be careful when moving the numbers around

Wouldn’t it be -7/9?

[void cobalt]

Ah yes thats what I meant, apologies. My meaning still stands that I do not know how to find the the angle measurement with this information

[vapid plaza]

You need a calculator

[storm rose]

Need to understand how to do this, as well as many other similar topics before the end of next week.. aha

[plush bane]

do u know abt the power laws? theyre pretty similar

[viscid thistle]

is this accurate?

isn't it like

$-2^{1/2}=\sqrt{-2}$?

[obsidian monolith]

smoobles

[viscid thistle]

why does it give me $-\sqrt{2}$ on the table

[obsidian monolith]

smoobles

[viscid thistle]

I don't think there should be real points in the graph for rational x values

[viscid thistle]

cause the graph is the negative of the exponential function {let say f(X)} and the domain of an exponential function is - (R) and its range is R+ (0,infinty) and you are operating the negative function on f(x) so it would only give you -f(x).

not f(-x)

[vapid plaza]

You typed in -2^x, which is interpreted as -(2^x); instead try typing in (-2)^x.

[viscid thistle]

ah I see thanks

[storm rose]

mhm I got that now

yeah unit test

[slim steppe]

An asymptote

[iron island]

how do i convert 25 into a log with base e??

[mellow vigil]

ig this is how u do it

[obsidian monolith]

NotMyself

[obsidian monolith]

NotMyself

[mellow vigil]

how to solve this?

i added 20 and divided inequality by 25

But idk what to do after this?

[obsidian monolith]

NotMyself

[shut shore]

15 year olds here know trig better than I know the alphabet 😵‍💫

You're an inspiration

[mellow vigil]

lol

[mellow vigil]

btw i wrote [0,pi] 2 times by mistake

[mellow vigil]

nvm got it solved

[spare hatch]

https://media.discordapp.net/attachments/907038223530876951/1035755797076000798/IMG-20221011-WA0021.jpg?width=769&height=671

can i get an answer to this please

[ruby slate]

Hah u must be in 8th grade

i do math 55

lie alg

[spare hatch]

https://media.discordapp.net/attachments/907038223530876951/1035757627398963281/IMG-20221011-WA0024.jpg?width=1193&height=671

yo is this right

[glass wind]

y'all can we use the remainder theorem if a is positive ?

x+a

[vapid plaza]

the statement of the remainder theorem is that (x-b) divides p(x) if and only if p(b) = 0
So if we let a = -b we can equivalently say that (x+a) divides p(x) if and only if p(-a)=0

[spare hatch]

so u cant answer my question?

[void cobalt]

Can anyone explain how to convert a trigonomic function fraction like sin root3/2 to a pi value? I don't understand how the pi values are found

[iron island]

trigonomic function fraction?

[shut shore]

Are you familiar with the unit circle?

I think you're asking about basic inverse trig functions?

[void cobalt]

Yes

I am asking about that

How would I familiarize myself with the unit circle

[willow bear]

are you sure you want to calculate sin(sqrt(3)/2)? and what's a "pi value"?

[lusty sphinx]

i think he meant sin(x) = sqrt(3)/2

you've got unlimited possibilities for x

but we can generalize them into two solutions with an integer parameter

in this case x = pi/3 + 2kpi or x = pi - pi/3 + 2kpi

it's always like this with sine functions

[void cobalt]

how to find reference angle with cosx=-7/9

[lime geode]

Can someone double check these

[hollow galleon]

the last one is a function

it's called a constant function

polynomial of degree 0

y is not defined, so it isn't even in a set (for the last one)

x € R is correct

[hollow galleon]

so it would be ∅

[summer ruin]

for constant function x=4 the range is a set that consists of a single number {4}

and if the function is called x you better not be using x to mean values in the domain

[lime geode]

so what values would i use

[summer ruin]

not values, names

anything else

[lime geode]

? wym

[summer ruin]

this doesn't make much sense if you think about it

[lime geode]

true but can i use yer

for range

[summer ruin]

that wouldn't even be mathematically correct

because the range of constant function is not the entire real line

[lime geode]

true

[lime geode]

guys help?

[hushed sphinx]

You can compute directly what k must be in order to get f(f(k))=2 to be true.

Just expand f(f(k)) using the definition of f, simplify, and then solve for k.

[lime geode]

can someone check if this is right

[willow bear]

seems correct, but does your teacher expect you to write single points as [a,a]? it's a little silly.

[hollow galleon]

seems okay, for a you shouldn't write equations as intervals, only points.

[lime geode]

Im sorry but ive been trying to check my answer all night for this but no one is responding

[lucid trench]

heres some cool precalc notes i took #3 (finally on logs!!)

[viscid thistle]

https://www.studocu.com/en-ca/document/simon-fraser-university/precalculus/samplepractice-exam-june-2019-questions/6027800

I need the document asap

[willow bear]

@sterile turret do you still need help w/ this

[wild adder]

how do i find the domain and range of the square root of a quadratic equation ping me if u know

[sterile turret]

yes

[willow bear]

okay

do you understand that, from what is written, you can directly get the equation of the slant asymptote as y = ax+b?

and that the x coordinates of the intersection points of the graph w/ its own asymptote, if any, are given by the equation ax + b + (cx+d)/(ex^2 + fx + g) = ax + b

@sterile turret

[coarse kernel]

oh god... I accidentally thought that you have a comma after the asymptote and the problem turned into a much harder one

(I thought that the asymptote itself has the form ax + b + (cx + d)/(ex² + fx + g) and N(x) and D(x) are arbitrary polynomials)

[marsh cave]

i know that one of the zeros is 4+i but what is the 5th? and how do i find it

[willow bear]

as stated you cannot even say that 4+i is a zero lol

[marsh cave]

really?

[willow bear]

well who said the polynomial had to have real coefficients?

[marsh cave]

oh i see

i dont quite know how to find the zeros tho

[obsidian monolith]

kunny

[summer ruin]

depends on your interpretation of the right hand side

well you didn't specify what is x and what is y

or which set they come from

right hand side can be interpreted as a constant function

it takes x, doesn't do anything with it and outputs a single number y

while the set notation doesn't even specify what you would do with each input, it just says you take something in X and transform it into an element of set Y

[hexed dock]

circles and parabola? 🥲

anyone? help?

[bitter kayak]

whats the law of sines AAS and ASA about

[arctic oasis]

can anybody help me solve this

the answer key says between 2020-2021 but i just can’t seem to get that answer

[thin kettle]

its an issue with your usage of the rate i believe

convert 1.49% to decimals first

so div by 100

which is 0.0149

and since it said it is increase by that rate

you add 1 to it

otherwise it would be decreasing if you leave it as 0.0149

[thin kettle]

does that help?

[sand plume]

wait

[sand plume]

is this differential equation?

[viscid thistle]

is this a function

[coarse kernel]

yes

[mellow vigil]

in a function every value of x corresponds to only 1 y value so yes

[viscid thistle]

but doesn't it have a single x value for multiple y values at -2 and 2

or is the difference so small in the graph it looks like a straight line

[mighty solstice]

yes it is a function

[mellow vigil]

and that looks like a line

[sudden sleet]

that is allowed

[tribal merlin]

hey

[brisk pasture]

I did synthetic division and got 0, but f(2) didn't give me 0

[summer ruin]

well you clearly did it wrong then

[brisk pasture]

@summer ruin

Did the synthetic division wrong or f(2)?

[summer ruin]

division

[brisk pasture]

No I did that all correct

[summer ruin]

that would imply the theorem is incorrect, which we know that it's true

idk what that synthetic division method is so I can't check if it's valid or not

[brisk pasture]

Bruh

@summer ruin the theorem is true, I got 0, but when f(2) I don't get zero

When I did it synthetic division I got 0, but when I did the remainder Theorem I didn't get 0

[summer ruin]

you would get zero if (x-2) was one of the roots of the polynomial

clearly you have a contradiction

[brisk pasture]

If f(2) you would get -2

[summer ruin]

well what's the question you're trying to ask then?

[brisk pasture]

So it's not a root?

[summer ruin]

you think your result is correct yet it violates the theorem, there's really not much to suggest besides looking for a mistake in your work

[brisk pasture]

If (x-2) is a root of the polynomial

[summer ruin]

clearly x=2 is not a root as f(2) != 0

but you somehow got 0 out of division

which isn't possible

[brisk pasture]

I know

Which doesn't make any sense

[summer ruin]

therefore you made a mistake somewhere

[brisk pasture]

I used synthetic division correctly, but it doesn't work considering f(2)

Which again makes no sense

[summer ruin]

,w synthetic division (3x^5-7x^3-11x^2+2)/(x-2)

[obsidian monolith]

Results provided by WolframAlpha

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Requested by Transparent_Elemental#0874

[summer ruin]

somehow the remainder happens to be -2

[brisk pasture]

I know

[summer ruin]

then it all makes sense now, the remainder is not zero

[brittle shore]

If it is illegal to “cancel” out trig functions in equations, for ex: tanxsecx = -3tanx -> secx=-3 by diving both sides by tan gets rid of a solution. Then why are we allowed to multiply by sinx/sinx? Wouldn’t that also cause domain changes?