precalculus

[stiff sluice]

,calc 180-90-64

[obsidian monolith]

Result:

26

[stiff sluice]

axw = 26

[viscid thistle]

Now you can use the sum of angles in a triangle property

To find the angle WAX

Which is the same as the angle BAC

[stiff sluice]

mmm

[viscid thistle]

mmm

[stiff sluice]

WAX = BAC? how

[viscid thistle]

Mark both the angles in the figure and you will get jt

[stiff sluice]

awx = 64

axw = 26

180 = wax + 64 + 26

,calc 180-64-26

[obsidian monolith]

Result:

90

[stiff sluice]

what? bac is 90?

is linear algebra question

[stiff sluice]

ok i got it, thank you

[viscid thistle]

no

[stiff sluice]

what I mean is that i have a linear algebra question asked in the help channel

[viscid thistle]

no?

nvm

[chrome barn]

$Happy:\left(\sum_{i=1}^9i\right)^2$

[obsidian monolith]

Aestusy

[royal silo]

Can someone please help me understand vectors and how cos and sin is related

[willow skiff]

https://www.youtube.com/watch?v=dC4cudpxVQw

does this help?

[mighty glade]

maybe. what do you need help with?

[lone dove]

Hello all, im stuck on part 2 and cant find a way around it, ive tried to replace sin^2t with 1-cos^2t then use integration by parts but it does not give me a definite answer

[summer ruin]

do integration by parts straight away

[lone dove]

yep i got it , thank you❤️

[royal silo]

I think I got it figured out now but thank you

[mighty glade]

ok ofc

[royal silo]

Thanks!

[wintry pewter]

Hi

[fathom sphinx]

Hi, i'm having trouble with part e : ( How would you solve it?

[winter comet]

the series from r=1 to k of r is (1 + 2 + 3 + 4 + ... + k), and the series from r=k+1 to 80 is ( (k+1) + ... + 79 + 80)
so if you add these, what do u get? :P

[fathom sphinx]

thanks viper

[fathom sphinx]

did it!

[balmy marsh]

Can someone help me understand calculus and how to get into learning it step by step...

[inner topaz]

weird approach but works

[barren jewel]

Can someone explain signing functions

Because I don’t get it

[river drift]

,, \operatorname{sgn}(x) = \begin{cases} +1 & x > 0 \ \hphantom{-}0 & x = 0 \ -1 & x < 0 \end{cases}

[obsidian monolith]

cloud

[river drift]

if that's what you mean

[main temple]

One way to learn calculus is by reading a book about calculus

[winter comet]

no I think the best way is figuring it out on your own with no direction whatsoever

reinvent the integral with no clue that it exists in the first place

[novel nimbus]

BPRP, Professor Leonard, Problem Solving, Organic Chemistry Tutor

For it's basics and main understanding, Professor Leonard and Organic Chemistry Tutor with some Problem Solving on the side is enough

BPRP is for Advanced Calc.

[fading monolith]

[inner topaz]

personally dont like organic chemistry tutor

just hands out formulas and doesnt ely explain

[winter comet]

he helps for how to do basic problems and how to use techniques n stuff

rather than reasoning or rigorous treatment of it n stuff 💀

[inner topaz]

yeah its fine for revising ig after a long time

[willow skiff]

sometimes it's better to be aggressively mid

if 3b1b's production quality goes down for instance, people will definitely notice

and start commenting and downvoting

I guess it's helped a lot of people cause it shows them tons of worked examples

so that people can figure out where they're going wrong on their own

and that's more satisfying than someone lecturing at you

[winter comet]

sometimes the why isn't as important as the what for getting things done as fast as you can :>

[ashen locust]

Do you consider that the topic of intervals is precalculus or calculus?

[winter comet]

just pure intervals themselves? precalc ig

[digital fog]

Can any1 solve this ?

if any1 need solution pls DM

[willow skiff]

does that imply you already know the answer to this question

[digital fog]

wrote it in the wrong channel

i had to be in geom. channel for other question

[kind glade]

Does anybody know what looks like an exponent but it's in the lower left

Looks like this

[green finch]

Note that option A is incorrect bcoz i mistakenly put x= 2 in derivative

[green finch]

Its the limit wdym?

[kind glade]

That 4 is lower

[green finch]

Miss print

[kind glade]

No no I'll show you a regular one

If you compare the two the 4 looks lower

[green finch]

Yup it's Miss print cuz 4^ 9 is indeed 262144

[kind glade]

Really

Could it be online worksheets are shit

I can't trust generated ones?

Ah wait I'm dumb hahaha

[green finch]

U can but u need general knowledge to understand if there is a mistake

[kind glade]

Yeah 4 to the power of 9 is that

Lol I haven't studied for long

I became stupid

[vernal path]

the more i think about it the more i suspect that gaussian elimination is not about matrices at all

[mighty glade]

wdym by this (tbf i bairly know anything about matrices at all so spare me if im wrong)

[green finch]

What the f is gaussian elimination

I don't know names of methods can you demonstrate an example

[summer ruin]

aka solving the linear equations by substitution or by addition of equations

[vernal path]

you take 3 equations with 3 variables, multiplying both sides of some of them and subtracting one equation from another to eliminate terms so you end up with an equation with xyz, one with yz, and one with just z, or any format that lets you do simple substitution

[mighty glade]

😵‍💫 that sounds way too complicated for a simple 3 equation system but you do you booboo

[green finch]

Ahh yes it used frequently in determinants rather than Matrix

[covert forge]

rookies

[green finch]

Well it doesn't take much time to learn limits/continuity upto advance level

[covert forge]

as 14 yo boy these are cookie ez

[green finch]

Yeah bro everyone know its fundamental you don't have to brag about it ..
At a time you have also learnt the fundamentals of limit

[covert forge]

uh i am at contour integrals rn

they are mid

[winter comet]

bro is over here calling everyone else rookie 💀

[covert forge]

cuz these are ez pz

first stage math for asian and middle east dudes

[winter comet]

ur in the precalc channel bro what u expect 💀

[covert forge]

ah yeah

this whole server is rookies

[winter comet]

??

oh

u dont see the other channels

[covert forge]

yes ican

[winter comet]

cuz u have pre-university role

?

[covert forge]

i have crappy english

[covert forge]

i am 9th grade

[winter comet]

you see #get-advanced-access and allat?

[covert forge]

no

[winter comet]

O

theres prolly a channel that explains how to see the rest of the channels

or you can just grab undergrad role that works

💀

[silent prism]

Sheldon negs you

[royal silo]

Can someone pls explain how do do log graphs?

[uncut mulch]

if in doubt, start with a table of values

[river drift]

1/x is continuous yet can't be drawn without picking the pen up

[viscid thistle]

Lol

[slim steppe]

1/x isn't continuous because it isn't differentiable at x=0

I think the terminaology for it is, an "infinite discontinuity"

[inner topaz]

ye

[slim steppe]

A more appropriate example would be the absolute value of x function, |x|, which is drawable, but it's no continuious because it contains a "peak" or upside "peak" at x=0

[inner topaz]

it is continuous but not differentiable*

[winter comet]

to say a function is continuous is to say it is continuous on its domain

1/x is continuous

because it is continuous on its domain

x=0 isn't in its domain

but yea its not continuous at x=0

[river drift]

it's not sensible to consider continuity nor differentiabilityfor points outside a function's domain

[inner topaz]

nah what 1/x isnt continuous

its only continuous in its domain but you cannot say it is continuous

2 different things

[river drift]

what sort of sense does it make to talk about discontinuity outside a function's domain? is sqrt(x) discontinuous at every negative number?

[inner topaz]

thats why we restrain its domain

but you cannot say it is continuous

if i told you that (x+1)/(x+1) is continuous would that be true

ofc not

for sqrt x if we restrain its domain yes it is continuous

[river drift]

it is continuous

[inner topaz]

damn

did i learn it wrong then

[river drift]

in precalc/intro they teach you a notion of continuity which is different than what mathematicians actually use at the higher level

[inner topaz]

you must say it is continuous for some x intervals

[river drift]

without further specification we assume its natural domain

[inner topaz]

wouldnt every function be continuous then

where the point discontinuity is not considered

then it would make no sense

to teach it

[river drift]

no, you can come with any number of discontinuous piecewise functions for example

[inner topaz]

well you can make 1/x a piecewise function too

[river drift]

e.g the function 1/x for x ≠ 0 and 0 for x = 0 would actually be discontinuous (and would be regardless of how you chose a value at 0)

[inner topaz]

mmm

but following the definition of continuity

lim x->a- f(x) = lim x->a+ f(x) = f(a)

1/x

at x=0

has a left and right limit different

therefore it is already discontinuous

[river drift]

the definition of continuity would be something like, the limit exists and equals the function value

[inner topaz]

and the left and right limit must be equal

[river drift]

that's just a prerequisite for the limit to exist

[inner topaz]

well true

[inner topaz]

and the limit doesnt exist for 1/x

you can say its continuous only if x is not 0

but you cant just say its continuous

[river drift]

for that to really make sense as a definition it can only be applied to points in a function's domain

[inner topaz]

damn really

idk i find it weird that only for values in the domain should be considered

[river drift]

i'm not denying that you're taught that it's discontinuous. i just don't agree with it being taught that way

[inner topaz]

goes against what i learnt

[winter comet]

same bro

basically when someone says a function is "continuous", they mean the function is continuous over its domain, not over the real numbers

it sucks but i guess it makes sense at a higher level to do it like that or smthn

[inner topaz]

you dont even need to specify that it is not when x=0?

[winter comet]

nope

not unless you want to

[green finch]

Fr bro people be arguing forever that tan x isn't continuous

[winter comet]

i see where they comin from but nah bruh

XD

[thin cloud]

I really dont understand this

Can someone PLEASE help me

Im having an aneurysm

[quick flume]

nah you got this

[winter comet]

can you solve 6 sin(3x) + 1 = 7 for sin(3x)?

[obtuse loom]

What a motivation

[quick flume]

i try 💪

[obtuse loom]

lol

[winter comet]

hey at least you try keep at it

[thin cloud]

Ah, thanks

[winter comet]

[obtuse loom]

Bombaclate

[quick flume]

no probelmo brotato 😎

[winter comet]

bro + potato?

[obtuse loom]

lol buld is not him tho

[quick flume]

or brochacho

[winter comet]

buld ._.

[winter comet]

bro + muchacho?

[quick flume]

are you still doing the math @thin cloud

[winter comet]

its funny autocorrect wanted me to say mustachio instead

[obtuse loom]

lol

[thin cloud]

Yeah, i did some things and got sin(3x)=1.

From there i made 2 different equations, since Sin(theta)=sin(pi-theta) and sin(theta)=sin(theta+2pi*n)

[obtuse loom]

lol buld tried

that what matters

[winter comet]

do you know when sin(v) = 1?

[thin cloud]

Then it goes downhill from here

[winter comet]

for some v

[quick flume]

yo jacob you know chatgpt exists right

[thin cloud]

I guess

[quick flume]

pretty helpful computer guy

[winter comet]

no way bro is suggesting chat GPT

[obtuse loom]

lol no shit

[winter comet]

😭

[winter comet]

do you know for what v sin(v) = 1?

[thin cloud]

No?

Wym

[winter comet]

do you know what arcsin(1) is?

[thin cloud]

Yes

[winter comet]

the values of v for which sin(v)=1 i meant

[thin cloud]

Yeah, i think i understand

[winter comet]

are you familiar with the unit circle? 💀

[thin cloud]

Yes

[winter comet]

so when y=1, x=0 on the unit circle right

[thin cloud]

Yes sir

[obtuse loom]

Ayo

Nvm

[winter comet]

do you know the angle needed to get there from the positive x-axis

[winter comet]

[thin cloud]

Wouldn't it be 90 degrees

[winter comet]

right

[thin cloud]

Im feeling quite stupid now ;-;

[winter comet]

naw naw

so in your first revolution

the only time the y-coordinate will be 1

is at 90 degrees from the positive x-axis

right

[thin cloud]

Yes

[winter comet]

and for every revolution (clockwise or counterclockwise), you can just add or subtract 360 * (integer)

am I making sense

[thin cloud]

Yes you are

[winter comet]

alr

so if v = 90 +- 360 * (integer) satisfies sin(v) = 1

and v = 3x

[thin cloud]

Thats the sin(theta+360n) yes?

[winter comet]

sure yea

so 3x = 90 + 360 n for some integer n

then whats x

[thin cloud]

30°+120n yes?

[winter comet]

yeah

is that the last option i cant see 💀

[thin cloud]

Yeah that does make sense

[quick flume]

chatgpt told me this x=30
∘
+n⋅120
∘

idk why the spaces

[winter comet]

chat GPT just goated like that fr

[quick flume]

it got it wrong at the start but i corrected it because im him 🧑‍🍳

[winter comet]

[thin cloud]

Generally the method Sal shows in the videos is by using inverse functions. On this specific case we get something like

3x=arcsin(1)

But this solution is only a single solution. From there i was given two formulas

Sin(theta)=sin(theta+360n) which is what you have mentioned, and

Sin(theta)=sin(theta-180).

Then he combined both of them and created sin(theta-180+360) and solved for the rest. My biggest issue is recognizing which of these to use

[winter comet]

you mean sin(theta) = sin(180 - theta)?

[thin cloud]

Oh

[winter comet]

I honestly don't like thinking about it as formulas, I just think of how it makes sense with the unit circle 💀

[thin cloud]

Subtraction aint commutative

Well fuck

That makes sense ;-;

[winter comet]

its supposed to

the second i start mindlessly using formulas it starts not making sense XD

[thin cloud]

Yeah thats what has been happening to me i think

[winter comet]

jus ttry to think it thru and know what you're doing and then ur probably good 🫡

XD

[thin cloud]

Mate, that works

Damn

[winter comet]

in the short run its easy to plug and chug but i think understanding is really good idea

i dont understand half the stuff i see tho

[thin cloud]

I just switched the order and got the same answer twice. I think it really was as simple as (theta-180)=/=(180-theta)

[winter comet]

maybe you were working with the cosine function

because cos(x) = cos(-x)

its an even function, which means negative inputs and their corresponding positive inputs will give the same result

so cos(theta - 180) = cos( -(180 - theta)) -> cos(theta - 180) = cos(theta - 180) actually works with cosine

doesn't work for sine tho

[thin cloud]

Yeah i know

Cosine functions were not giving me any trouble at all

I really think it just boils down to me using the wrong formula on sine function

I was consistently getting cosine functions right and messing up sine ;-;

Because i cant arbitrarily switch placements and preseve order of operations ;-;

But thanks mate

I will see if tbat does it. If i dont i might come back crying here in a minute

[viscid thistle]

Hi, why is the answer not undefined for these two? If the first derivative for this function is just 1 and -1 then how is the answer not undefined? I know f'(0) is undefined here but answer key has different answers for these two

[inner topaz]

the function is not differentiable only at x=0

you can look at the graph of abs x

but basicaly you know that when x>0, f(x) = x and when x<0, f(x) = -x

(definition)

,w graph abs x

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by _rysel_

[inner topaz]

it does have a slope for x>0 and x<0

[glad abyss]

On which intervals is this decreasing?

[jade ledge]

hello

im new here

i just started grade 8

[willow skiff]

hey, welcome and hope you learn some new maths stuff

[willow skiff]

should be clear from the graph honestly

to restate your question, when it stops increasing
that's why the turning points are the endpoints of the inequalities where the function is decreasing

[glad abyss]

I put it in interval notation but I get the wrong answer

[willow skiff]

what answer do you get?

[glad abyss]

Doesn't tell me

[fading monolith]

What was your answer?

[fathom sphinx]

How do i do part b

[winter comet]

2k^2 - 3k > 4850

[fathom sphinx]

😭oh then i just solve it with the quadratic formula

thanks viper...

[thick ridge]

just got an 100 on my trig identities test‼️

[winter comet]

🔥

[plain marten]

whats a cis

[river drift]

,, \operatorname{cis} \theta \coloneq \cos \theta + i\sin\theta

[obsidian monolith]

cloud

[plain marten]

ah

ok

thx

why does this become 2 theta

[winter comet]

cis^2(theta) = (cos(theta) + i sin(theta))^2 = cos^2(theta) + 2i sin(theta)cos(theta) - sin^2(theta) = cos^2(theta) - sin^2(theta) + i sin(2theta) = cos(2theta) + i sin(2theta) = cis(2theta)

[plain marten]

ok so you just change in to duble angles and simplify it fomr there

basicly

[winter comet]

mhm

[river drift]

the cis notation isn't super common because we have by euler's formula that [ \operatorname{cis}\theta = e^{i\theta} ]

[obsidian monolith]

cloud

[jagged patrol]

if there is a point that is between intervals of increase and intervals of staying constant, what is the rate of change at that point. zero, positive or something else

[winter comet]

zero or undefined

[jagged patrol]

so for a question asking me to list subintervals where the output is constant would i use [] or ()

[winter comet]

most likely ()

although

wait you mean the function output is constant?

[jagged patrol]

yes

[winter comet]

it would probably be inclusive then

[jagged patrol]

i see

[winter comet]

because even tho the derivative is 0 or undefined at that point, the function value is still that constant output

as long as there IS a constant output there and theres no discontinuity there or smthn

[jagged patrol]

does this also apply to a point of the same kind but with the constant end not in the interval

[winter comet]

i'm not sure what you mean

[jagged patrol]

let me look for the question

[winter comet]

you mean if there is a hole at the endpoint?

cuz that would exclude the endpoint which would use ()

well

( or ) for that side at least

[jagged patrol]

On which subintervals of [-10,10] is h constant.

a periodic function h has a domain of all real numbers and a period of lenghth 5. 2 periods are shown on the graph

[winter comet]

ah so yeah the sub-intervals would be inclusive

because the endpoints are defined

even though the rate of change is not defined at the endpoints

(endpoints of each sub-interval)

[jagged patrol]

so roc at x=-10 would be constant

and x=-5

[winter comet]

roc?

[jagged patrol]

rate of change

oh wait nvm

[winter comet]

the graph doesn't even show x=-10

[jagged patrol]

thats the wrong word

[winter comet]

💀

[jagged patrol]

its peridoic and i meant the output being constant not the roc

[winter comet]

the output is a constant

[jagged patrol]

.

[winter comet]

i mean at x=-10 idk

the graph doesnt show x=-10

but for certain intervals the output is constant

and i believe thats what they are looking for

[jagged patrol]

and at x=-5?

h is constant there?

[winter comet]

hold up the question is "on which subintervals of [-10,10] is the function h constant"?

[winter comet]

the output is always a constant bro idk what i was talking about 💀

the rate of change is 0 for some intervals () excluding the endpoints

on those intervals h is a constant function

[jagged patrol]

yes that was the exact question that was written

well not with the function

it just said h

but it meant the function

or that the roc is 0

im just confused on whether the left endpoint is considered to have a rate of change of 0

[winter comet]

none of the endpoints in the picture have a defined rate of change

[winter comet]

i think what i said is what they meant

[jagged patrol]

so do i include x=-10 for the answer or not

[winter comet]

x=-10 isn't even in the picture i don't know what ur talkin about 💀

[jagged patrol]

look under the picture

[winter comet]

OH i can't read

hmm

I would guess you'd include x=-10 but i don't know for sure

[jagged patrol]

oh i thought u knew math

how do i get to the smart people

[winter comet]

[winter comet]

idk just hope someone responds fr fr

it makes sense to include x=-10 so i'm pretty sure it is included but it's kind of vague calling part of a function "constant" imo

[formal kestrel]

(-1,0) and (4,5) it's constant.....

[whole void]

just continue the graph it isn’t so hard

[jagged patrol]

Yes I know how the periods work I was only asking about the points that are specially between intervals of positive rate of change and no rate of change

[tight anvil]

hii!! can anyone help me a little bit more w pre calc! i have a mid term tomorrow & i just want to revise w someone a little bit more

[supple sable]

Hello, I just wanted to ask if any one here has revision village, I am struggling with math AA SL and wanted to know if any one could help

[fiery crest]

for this question are the answers 13=f(40) and f(5)=2 means 2 tons made per week by 5000 people?

[formal kestrel]

b) 5000 people produce 2 tons Garbage per week

[willow skiff]

yes

[fresh vigil]

why is precalc so hard

[plain verge]

a lot of theorems, processes, etc

[echo sinew]

It needs a lot of practice, concepts are not hard

[blissful willow]

Which exam is that question part of?

[crimson river]

hey guys how would one factorize this? it doesnt go into squares?

ok thanks its weird it says factorize expression on our assignment

but i thought so too?

how then would i answer?

[willow skiff]

,w expand 2(t+2)(t-2)-3(t-3)^2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[crimson river]

should i answer fully expanded then?

[willow skiff]

,calc 18^2 - 4 * -1 * -35

[obsidian monolith]

Result:

184

[willow skiff]

well it is factorisable in the real numbers

you just need to use the quadratic formula and find the roots first

your factors will have surds, oh well

[crimson river]

isnt it like not a whole integer then

[willow skiff]

yeah that's my point

[crimson river]

i dont think that is expected at this noob level

[willow skiff]

but yeah more likely is that there is some kind of typo in the question

[crimson river]

yes ok thanks man

[willow skiff]

confirm with your teacher then

no worries!

[vagrant nymph]

What is unimodular

[summer ruin]

modulus is one

[vagrant nymph]

Alright thank you

Completely missed it in the question

Idk what was I thinking saw it now

[atomic dragon]

im taking calculus 1 starting february 10th and ive never taken trigonometry before. ik this is a terrible idea but i have no choice as i need to transfer out as soon as possible so... does anyone know any online tools or really anything where i can learn enough trig to do good in calculus 1 in about a month? ive taken college algebra for calc before already

[winter comet]

I don't think its that bad of an idea with that attitude bro if u really tryna do it i bet you could

i don't know any good resources for trig honestly

[atomic dragon]

yeah i mean tbh the calculus class is online so if needs be i could just... google it all

but

i actually want to learn

so

[tame pine]

Yoooo

Entering the precalc zone

[fiery crest]

can i have some help with these?

[rustic yacht]

39. a-iii, b-viii, c-i, d-ii, e- vi, f-iv, g-v, h-vii

[hasty lily]

!noans

[tender quest]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[hasty lily]

!nosols

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[rustic yacht]

Sorry

[inner topaz]

for which ones?

[fiery crest]

i only really know linear idk the others

[inner topaz]

first of all do you know what square and cube mean?

[fiery crest]

x^2 and x^3 correct?

[inner topaz]

ye

what about root

[fiery crest]

eh i kinda understand

its the number divided by itself?

[inner topaz]

not quite

basically the opposite of square

[willow skiff]

if $y = x^3$, then $y^{1/3} = x$ for example

[obsidian monolith]

south

[willow skiff]

so the inverse functions of y = x^2 and y = x^3

[fiery crest]

oh?

[willow skiff]

yeah

[fiery crest]

i still dont really understand whats going on, do i just need to know what each eqaution looks like graphed or do i need to know more than that

[willow skiff]

yes

the main thing is that $x^{1/2} < x < x^2$ for $x > 0$

[obsidian monolith]

south

[willow skiff]

in other words, as x increases towards positive infinity, x^2, x^3.... will keep getting steeper and steeper

they tend towards pointing vertically up

but x^(1/2), x^(1/3)... will keep getting flatter and flatter, and tend towards being perfectly horizontal

also like sqrt(x) = x^(1/2) doesn't exist when x is negative

and the same is true for x^(1/4), x^(1/6) etc.

[fiery crest]

this is exponential growth right?

[willow skiff]

nope!

it's polynomial growth

exponential growth is faster than any polynomial, if you take x large enough

so for example, x^2 grows much, much more slowly than 2^x

[normal raven]

How to find differential Eq by separable method

[willow skiff]

the order makes a huge difference

like the number of multiplications
2 for all x versus x multiplications, and remember x can keep getting as large as you want

the number of multiplications is a nice way of comparing the growth rate

[normal raven]

🙄my Question

[willow skiff]

#odes-and-pdes

or you can open a new help channel

[fiery crest]

oh ok being honest i dont really understand what most of what you said means

[willow skiff]

are you taking precalculus right now? seems like it

[fiery crest]

yeah its the first week

[willow skiff]

ah okay

[fiery crest]

ive been really strugginig with finding domain and range of functions and idk what those graphs mean

[icy jetty]

this is not true, the order is the opposite for 0 < x < 1

[willow skiff]

shit right

[icy jetty]

you meant x to get larger and larger anyway so it doesn't really matter

[willow skiff]

yeah like post-rigorous mathematicians be like in a similar vein

oh well, this local error exists but it cancels out with this local error, and I know the general structure and direction of the proof, so eh

[icy jetty]

so true

[vagrant nymph]

Can some help with q1 z here is a complex number

This is what I tried

[modern valve]

Interesting question. You are correct that z=0 is one solution, and otherwise, |z| has to be 1. To figure out the solutions when |z| = 1, try plugging in something of the form z = e^(i theta).

(Have you learned about e^(i theta) before?)

[vagrant nymph]

Yea I i have I’ll try it

Wait but like we have mod z = 1 so mod re^itheta is basically r

So am not sure how does that help

[echo sinew]

r = mod z

So z = e^(iθ) in your case, since |z| = 1

[vagrant nymph]

Yea exactly so number of solutions of r=1

How do we go about solving this now

[echo sinew]

You know that z = e^(iθ), so you can plug this form of z into the original equation

[vagrant nymph]

Oh okay I’ll try that

So does this suggest we have 4 roots?

[fading monolith]

You can solve from e^(4iθ)=-1

[vagrant nymph]

we dont need to solve just we have to find number of soln

[vagrant nymph]

so my query now is does this suggest we have 4 solution?

[fading monolith]

You could argue from the begining that it does have 4 solutions by Fundamental theorem of algebra

[vagrant nymph]

Ans in my book is given 5

[fading monolith]

Ah well, 4 from e^(4iθ)=-1 and the case z=0

[winter comet]

<@&268886789983436800>

[viscid thistle]

Hey

How does 5/15+6/15=21/15??

[tired pilot]

It doesn't

[viscid thistle]

I’m watching a precalc video and this is one of the questions

WTF

[tired pilot]

It could be a typo?

They are off by a digit

5/15+6/15 = (5+6)/15=11/15

[viscid thistle]

No look bro

[tired pilot]

This seems like they meant to write 11 rather than 21

[fathom temple]

yea but thats wrong

[tired pilot]

Sometimes people just mix symbols up lmao.

[viscid thistle]

😂😂😂ooooh

[viscid thistle]

hello i need some help for no. 8
https://cdn.discordapp.com/attachments/326138737606262786/1327864221316284556/image.png?ex=67849d6c&is=67834bec&hm=70e8b2434bf0d4fae78a0d1c3a68495bb9631d304e96e7f1bdfd82dd3637b8fa&
.
i've got this.. but it only works for half of the equation. (the right half)
https://www.desmos.com/calculator/bjhdyrgbma
1/24x^2 (x+4)(x−3)^3

what am i supposed to do?

[willow skiff]

you're done actually

[winter comet]

nah but the scaling on the left side is way off

[willow skiff]

the end behaviour as well as the roots and the shape of the turning points just needs to match

[winter comet]

it doesn't seem possible to scale it how they scaled it with a quadratic like that

[willow skiff]

agreed but I don't think it's fixable / it's not in their syllabus to know how to fix it

[winter comet]

yeah

thats what i was thinking

i was tryna help but i didnt know how to fix it beyond that

💀

[willow skiff]

that might also mean the scaling is not 1:1

[viscid thistle]

sad

it feels wrong

[winter comet]

yeah so using the point (-2,1) is questionable

but i think she was told to use the point (-2,1) right

[willow skiff]

it's just this

[viscid thistle]

axkyn told me to try that

[winter comet]

oh

[viscid thistle]

and i told you

[winter comet]

💀

[viscid thistle]

😭

is that the problem?

i just don't like how the left side is all weird

[winter comet]

well no the problem is that the scaling is wacky

so using any point to find the scaling isn't really realistic

but i suppose its better than nothing

i'm not sure if you were supposed to scale it in the first place ngl

[viscid thistle]

do you think it's possibly just the graph being not-to-scale on the ws?

[winter comet]

yea thats what we're thinking

[viscid thistle]

still feels wrong 😭

[winter comet]

i mean it kind of is but there isn't a great "correct" answer

[viscid thistle]

yeah

[winter comet]

so your unscaled version is probably fine

ngl

[viscid thistle]

ok time for no.9, the next problem then

one question though, how do you think axkyn got -2, 1 from?

[viscid thistle]

how should i find the point that works best?

[winter comet]

wait mb i mispoke it was (2,-1) 😂

[viscid thistle]

oh 😭

[winter comet]

but uh it was assuming that each box was 1 unit by 1 unit, that looked like a nice point that was on the curve

[viscid thistle]

nice point? what's a nice point?

😭

for 9 should i do -3.5, -1.5 ?

or like 2.5, 2 ?

how am i supposed to pick a point?

[winter comet]

i was explaining where he got it from
for your problems i feel like they don't care about the scaling

💀

i mean you can try to make it accurate but

[viscid thistle]

oh

aw shucks

[fiery crest]

man i hate graphs

[vague totem]

same

[fiery crest]

its so easy to mess up theres so much vocab around it i cant keep track

[fathom sphinx]

Hi, how would I do 8c?

[grizzled current]

I can't fully see the question. Maybe rotate your phone and zoom in?

[fathom sphinx]

Whoops my bad

[grizzled current]

That is an interesting problem. Not sure if I can help with that. Maybe try using one of the math-help channels.

[fathom sphinx]

Ah alr thx Omega

[grizzled current]

You're welcome.

[whole void]

think about what u r subtracting

[acoustic leaf]

What's the best thing to learn pre-calc from the ground up. Cuz im in algebra 2 and i want to test out of calc 1 so i can just go into calc 2

[fresh vigil]

is mathematical induction a part of precalc

my teacher is teaching it and i dont rly get it

part of sequecnes and series unit

[inner topaz]

well basically if you assume that it works for a certain general value and prove that it works for the next value too

you can keep on going

and basically you take the value after the next value because of generality

and you keep on going like that

if you just prove that it works for a specific number for example 1

and do the general proof thing

you will have proven for 2 as well

and then 3 too

4 5 6 and so on

[tame pike]

How do I factor the polynomials?

[summer ruin]

just as usual by factoring out the common factor

if that doesn't work, try to use the square of a sum/difference and sum/difference of squares formulas

[tame pike]

Ok

[willow skiff]

$\frac{f(3 + h) - f(3)}{(3 + h) - 3}$, slope of line segment between $(3, f(3))$ and $(3 + h, f(3 + h))$

[obsidian monolith]

south

[vivid spade]

figured it out thanks

[willow skiff]

np!

[slender rover]

Help me uwu

[winter comet]

no

[slender rover]

I got like a B+

It’s jiever

[winter comet]

jiever

very jiever

[slender rover]

These tests harder than fuxking imosl

[winter comet]

dang

[slender rover]

Like I can get a higher percent on amc probably

[misty whale]

Hi

Would anyone be able to help me with a ph application question?

[winter comet]

what is ph?

[whole void]

Let y = (x + 9). Then it should be clear

For the second one I think it’s even clearer

[misty whale]

Like a chem thing

But might be on our math for application

This is the question, just dm me if you can help. Imma sleep

[hollow widget]

logarithmic stuff

[spring hearth]

hi im new

[winter comet]

hi new

[buoyant ferry]

Hey guys was looking to see if someone could point me in the right direction on what type of problem is this?

At the beach, a rectangular swimming area with dimensions x and y meters and a total area of 4,000 square meters is marked off on three sides with rope and bounded by the fourth side by the beach. Additionally, rope is used to divide the area into three smaller rectangular sections. In term of y, what is the total length, in meters, of the rope that is needed both to bound the three sides of the area and to divide it into sections?

Im looking to have more practice with these types of problems I had a test today and this is the exact question that dunked on me.

[willow skiff]

can you set up an equation for the total length of rope, in terms of x and y?

can you also relate x and y using the fact that area = 4000?

try drawing it, it really helps

[flint kestrel]

Is this equation true or not?
,,\int_{1}^{1}1=1?

[willow skiff]

can you type it out again?

[flint kestrel]

,,\int_{1}^{1}1=1?

[obsidian monolith]

Sapphire (Stacie)

[willow skiff]

that doesn't even make sense, you need the dx

well think about it, you want the area under a single point

so the answer must be 0, no matter what the function being integrated is

[flint kestrel]

So... How am I supposed to answer 1×this=1?

[willow skiff]

can you send the original question?

[flint kestrel]

The one above not the below.

I know it has trigonometry..

But this also has calculus.

[willow skiff]

okay that still doesn't make sense

you are integrating with respect to x

so if one of the limits is also x, you will get a function in x, not a number

[flint kestrel]

Yup I'm not good at integrals.

[hasty lily]

Slop?

[willow skiff]

alphabet soup except it's all maths symbols

[crude elm]

is there somone who understand frensh

[buoyant ferry]

OOh sorry I meant specifically Im trying to solve more problems of THIS type

Edit: I had this question on a test and desire more repetitions.

[forest gull]

can someone please help, chat gpt or mathway cant even give me an answer

I tried three different ways

number 19

[zinc moth]

noooooo i'm in like
the course before 😖

[honest pagoda]

Csc can be rewritten as 1/sin(theta)

So it would be sin(x)/(1/sin(x))+1

1 you can rewrite as

Sin(x)/sin(x)

So it would be sin(x)/((1+sin(x))/sin(x))

Wait hold on I’m sitting in bed rn

Huh

@forest gull

Csc(x)=1/sin(x)

[honest pagoda]

,rccw

[obsidian monolith]

Couldn't find an attached image in the last 10 messages.

Jan 14, 2025, 11:40 PM

[honest pagoda]

I’m pretty sure the answe choices are wrong

I got

Sin(x)^2/1+sinx

,rccw

[obsidian monolith]

Couldn't find an attached image in the last 10 messages.

Jan 14, 2025, 11:46 PM

[honest pagoda]

,rccw

[honest pagoda]

Is this a multi sheet

[winter comet]

multi as in multivariable calc? or wut

its just trig 💀

[fiery crest]

I'm really really struggling with function graphs there's way too much to understand and know. I'm already way behind and it's only been one week

[low yoke]

Can someone explain why h = b * sin(theta)?

I do understand that the equation comes from: sin(theta) = h/b

But I don't get how multiplying the sin of an angle by a side of the triangle can give you the height

thanks in advance

[willow skiff]

great, now multiply both sides by b

$b \sin \theta = \cancel{b} \cdot \frac{h}{\cancel{b}}$

[obsidian monolith]

south

[low yoke]

Yeah, as I said, I know the equation

but I don't understand the relationship between de sin of theta and the side of a triangle

[feral raft]

I am having a problem in the 12th question
I approached it with two ways and from one of the ways I am getting wrong answer
Can someone please tell me where I am wrong (correct answer is [n-1/2])

[willow skiff]

what do you mean, like sin theta = h/b?

sin, cos, tan are all ratios of triangle lengths (in a right triangle)

think about it, say how can sin(45) be the same in one triangle, and another triangle which is 100 times larger

the answer is that all the sides get multiplied by 100

so the 100 cancels out in the fraction

[solid shuttle]

both variants are wrong. The first one has some conceptual and arithmetic oddities. The second one has a mistake in finding of the resulting limit.

Ok, the first one is close to being correct if you say something about the ordering of the roots and explain why the sum of each pair is 1.

[rustic forge]

Alternatively, $f(x) = \ln(x^{n - 1} + x^{n -2} + \cdots + 1) =\sum_{r =1}^{n-1} (x - a_i)$
$f'(1) = \frac{1 + 2 + \cdots (n - 1)}{n} = \sum_{r = 1}^{n-1} \frac{1}{1 - a_i}$

[obsidian monolith]

Arya

[sturdy hound]

can someone please help me with tower of hanoi proof by induction i am really confused

[feral raft]

Bro please tell me how and where I am wrong in second method

[sturdy hound]

https://discord.com/channels/268882317391429632/1329255264741756938 here is my help post here btw where u can help me

or just help me here

[plain marten]

bro these problems hurt my brain. I hate sigma notation

trig is 20 times better than it

[ember meadow]

can someone help with question 10

[willow skiff]

look very carefully at what happens from the 3rd line to the 4th line

for instance, expand the 4th line and compare it to the 3rd line

[ember meadow]

i understood the mistake is in the factoring, that the -7 should have turned positive

but now i am confused on how to actually solve this question

[fathom sphinx]

Hi what did i do wrong for 6d? Answer says 393 825

[summer ruin]

the summation starts at 11, not 1

[fathom sphinx]

i can't split the sum? like say

oh wait im trippin

[fathom sphinx]

thanks Transparent!

[bleak orbit]

Hi all

[bleak orbit]

Can someone help? Or should I go to #prealg-and-algebra ?

[exotic hemlock]

I have to determinate the biggest positive value for δ
|x − 3| < δ ⇒ |f (x) + 2| < 1

[exotic lion]

Could someone help me with No.8

[arctic niche]

do u still need it?

[arctic niche]

i didnt give the answer, i showed u the way

[exotic lion]

Could you kindly explain

[exotic lion]

Why do you consider 16 and 0

[arctic niche]

i numbered it wrongly

so basically uk, for respective of x, what do we do? we use limit 4/3 and -4/3, just like that, look from the y axis

when x=0, y=16 and the area fall between 0to16

as a result it will be 0 to 16

i hope it is clear

@exotic lion

[exotic lion]

And respective for y
@arctic niche

[exotic lion]

Ok

[exotic lion]

No, it's not clear

[arctic niche]

vice versa, look at x axis, in x axis, the curve touches at both point that is -4/3 and 4/3 so the area under the graph is between the interval -4/3 and 4/3 so limit is gonna be that

[exotic lion]

Ok lemme workout and see if I can get the right answer

Thanks man, I got the right answer

@arctic niche

[arctic niche]

ok

welc

[fathom sphinx]

no thx got it

[exotic lion]

I've got another problem, it's No.10, if I get part(a) I may be able to do the rest.

[fathom sphinx]

what topic is this called ☠️

[winter comet]

math

im so helpful

[fathom sphinx]

viper!

I miss when math was simple. Addition, subtraction, multiplication and division (excluding long division), not this integral, matrix ahhh stuff 😔

[winter comet]

💀

[rustic forge]

This comes under the chapter "Quadratic Equations" in High School

[fading monolith]

Basic algebra?

[pseudo tree]

symmetric polynomials maybe?

[rose talon]

What is lim x->0 to 1/x from the left? I thought it was -infinity but my teacher marked it as wrong and said it was DNE

[fading monolith]

From left is when x->0- and its -inf as you said. Maybe you teacher was refering that limit 1/x as x->0 DNE due lateral limits dont coincide

[rose talon]

nah it was a multiple choice question

[wise merlin]

I'm doing scheduling right now and was wondering if I should take AP pre-calc? I'm currently in honors Algebra II but idk if I want to go to an AP math class. Can anyone who's taken it tell me if it's hard compared to algebra II?

[sturdy hound]

u dont have to solve it tho just have to point out the error

[jolly raven]

its been a moment but ill show you the magic of symmetric polynomials

notice how all the variables in the equations you have can be swapped around

and it doesnt change what the equation looks like

that means the polynomial is symmetric and it can be represented in terms of other equations based off a,b,c

ping me if you wanna know more about that / need help if its homework

[fresh vigil]

ok thank you i get it now

[flint kestrel]

May I question what limits are? (Warning:Do not attempt to show limits as it can malfunction my brain and stop it working. Limits are the only concept of mathematics that I cannot understand and will malfunction my brain until someone covers the limit function. Thank you)

When I mean show limits is don't explain limits by doing it visually.

[summer ruin]

a way to reason about function's behaviour in the neighborhood of a particular point

[whole void]

yeah symmetric sums

[jolly raven]

suppose we have a sequence like a_1, a_2, a_3, etc

and suppose that this sequence seems to be approaching something

then a real number L is the limit of that sequence iff for all $\epsilon > 0$ there exists a natural number N such that for all n > N, we have $|a_n - L| < \epsilon$

[obsidian monolith]

hiidostuff

[jolly raven]

basically, no matter how small we choose some number to be, we can find some element of the sequence that is closer to L than that number we chose is small

[queen cargo]

can someone help me in this

i dont understand how to do it

[exotic lion]

I have a question tho, which area I'm I really looking for, the area above the line y=5 or below

@arctic niche

[arctic niche]

area below the line

the area is bounded by line and curve ryt? so that is why it will be that

@exotic lion

[exotic lion]

Where do I multiply the 5

[exotic lion]

Do I multiply it with the final answer or

@arctic niche

[arctic niche]

not multiply it by 5

line - curve

line eqn - curve equation u have to integrate

[exotic lion]

This is what I get but it's wrong

I don't know where I have errored

[viscid thistle]

Does anyone know if this solution is correct?

[kind pagoda]

close

i think it is −6cos^2(2x)sin(2x)

The function involves the chain rule since it's a composite function. The outer function needs to be differentiated first, and then the inner cos(2x) followed by 2x.

[viscid thistle]

But i thought that if the angles are the same u basically add them up? Like for double angle identity

For example, like these ones

[exotic lion]

@arctic niche

[arctic niche]

can u send a clear pic?

it is unclear

can dm the question again

i will solve it in detail

[patent belfry]

hey guys, ive started learning integration and differentiation for a while now, but my trignometry and precalculus is not really the best, so am kinda struggling with it
do any of you have like some kind of pdfs or videos which goes kinda into detail for like the stuffs required for integration and differentiation and stuffs, trignometry aswell
something like with question answers and formulas and cheat sheets
would be really helpful and a lot easier to understand this sem, thank you

[plush pond]

Yoo this may be a dumb question but how do you solve logorithms without a calculator that doesn't have a common base. (or at least not in integer)

For example the following

$\log_{10}(2)=x$

[obsidian monolith]

Your Neighbour Jack

[fading monolith]

a^log_a(x)=x for x>0 and a>0

[exotic lion]

Here

@arctic niche

[arctic niche]

oh i think u made calculation mistake

okay so do it like that

it will be easier for u

wait

i got 32/3

here is the working

1 sec

use this way

@exotic lion

[fathom sphinx]

Hi, did i do part a correctly?

or im i supposed to use the summation formula and sub n=1,2 and 3 respectively into Σr^2 and Σr?

my book doesnt have a ms

gosh and summation hurts my head sometimes

[safe blaze]

$3 \approx \log_{10}(1024) = 10 \log_{10}(2)$

so

$\log_{10}(2) \approx 0.3$

[obsidian monolith]

🤗🤗🤗🤗

[safe blaze]

Finding logarithm without calculator is very fun, and every case needs an individual approach 😃😊

[exotic lion]

Thank you
@arctic niche

[arctic niche]

welc

[crisp bane]

log(😅) = 💧log(😄)

[leaden adder]

hey guys i starting the integrals course this semester does anyone of you could help me out by explaining the basic of it, tips and tricks or just common mistake to avoid. Even links or video i could help myself wiht

[willow skiff]

https://www.youtube.com/watch?v=WDZMjYJyH6k&list=PLHgLUBSREUPki7tCaWsYP3HppRanCdkDH

[viscid thistle]

@viscid thistle

Bro…

[stiff sluice]

<@&268886789983436800>

[viscid thistle]

I mainly need help on 43

I should know how to do 45 we did a problem like it in class

[viscid thistle]

Could you help me with 43?

[stiff sluice]

the triangles are similar?

[stiff sluice]

,rccw

[viscid thistle]

Similar ratio

Yo

[viscid thistle]

Yoo

[viscid thistle]

This?

Yeah

Whats the question

Oh

I see

Yeah

What have you tried

[stiff sluice]

,rotate

[viscid thistle]

So I wont lie

I can really read what you intended to do

Do you mind just telling me

Like you know the triangles are similar

What does that tell you

It tells me that they are both equal

So I should set x= 10.5

Nah

Similar means they share same angles

Oh

I see it now

Thats what those double lines are for

So this doesn’t necessarily mean the angles are the same

But it implies they can be scaled to get the same side lengths

I got some help with a tutor at school and he told me we have to cross divide

Yeah that will get you there but I want you to know why it works fundementally

You know what it means for triangles to be proportional right?

Kinda

Explain as best you can

If a angle is = 1 and the next is = 2

And the next triangle they are 2 and 4 then it is proportional by 2

Yeah thats the idea pretty much

So there is a scaling factor for similar triangles

Because their sides are proportional to one another once you identify the correct sides

So this means if you can identify two known sides between the triangles to be the same

Then you can divide to find the scaling factor

So in this example triangle 1 with side 9.2 is proportional to triangle 2 with side 6.2

So the scaling factor for triangle 1 to 2 is 9.2/6.2

Similarly this tells us that 4.4 * scaling factor = y

Wait what

Or other way around so it should be divides

I thought you divide 9.2 and 6.2 to get the scaling factor

Yeah from triangle 1 to 2 it should be 6.2/9.2

Because you want 9.2(scale)=6.2

Uh

So it would be 6.2/9.2

Yeah it depends on which way youre considering

9.2/6.2 is from triangle 2 to triangle 1.

6.2/9.2 is from triangle 1 to 2

Does it matter which way you divide

Well yeah it tells you which triangle side you would need to scale

So like you saw I made the mistake earlier and you caught it

Phew

4.4(6.2/9.2) = y gives the answer for scaling triangle 1 to triangle 2’s side

Do you see it?

Yes

Because 4.4 is where y is on triangle 2

So y should be 2.97

Yeah I dont know the exact answer but if you calculated it right then nice

And for x I should do the same thing but on the other triangle!

4.4(6.2/9.2) is the answer yes

[viscid thistle]

Yeah

Yup

Now if you know this

The next step is quickly recognizing these problems

And doing cross division

Which is essentially what we did

Woah

If you get the scaling factor you dont need to divide twice and you should be able to do the problems quicker in theory

Like for x you cant apply scaling factor from triangle 1 to 2.

So you need scaling factor from 2 to 1 which was 9.2/6.2

So 10.5 * (9.2/6.2) gives that answer

Oh so 10(9.2/6.2)

10.5

But the quicker calculation is recognizing that division gives you the scaling factor without having to recompute anything

So you can just write 10.5 / (6.2/9.2)

Ooh I kinda see it

This is where you can save time on exams if you are comfortable with this

[viscid thistle]

Because remember that 1/(6.2/9.2)= 9.2/6.2

So the 2 angles that are numbered are going to be constant in the equation

The only thing that changed is what multiplys them

Nvm the 2 angles flip

[viscid thistle]

They arent angles

They are sides

The angles are the things at the corner of the triangle

With the congruent lines

Oooh

@viscid thistle

WTF

Nvm this key might just be messed up

[viscid thistle]

No its right

?

The squiggly lines mean approximately

You got 2.96 for y

If you round to nearest tenth than thats 3

Idk what you got for x

But you are probably right

Well remember what I said before

[viscid thistle]

From here reread

[viscid thistle]

I’m kinda confused

Which part

Since I already divided and got the scaling factor which is 9.2/6.2

Well there are two scaling factors depending on which triangle you scale

You can scale to the bigger triangle or the smaller triangle

And the scaling factors are inverse of each other

OMG

I UNDERSTAND NOW

SMALLER TO BIGGER MULTIPLY AND BIGGER TO SMALLER DIVIDE

Yeah that helps too

Id say what you could do is try more problems though

Its very easy to have false confidence in this stuff

Did I do something wrong?

[viscid thistle]

Yeah i need more practice on this one

[viscid thistle]

Yeah the factor 6.5*9.5

Try to remember where we said the scaling factors come from

Easy way to see it is to apply to one of the known sides

So like 9.2* (6.2/9.2) =6.2

This is clear because it cancels out with denominator

This is also clearly for triangle 1 to 2

But triangle 2 to 1 would be 6.2(9.2/6.2)

Because side 6.2 scales up to 9.2

Oh jeez

@viscid thistle

I’m still confused

Sorry

I tried 6.2*9.2/10.5

And got 5.4

Yeah well remember you multiply a side by the scaling factors

What you dis here was divide a side

Also remember order of operations matters

So keep the scaling factor in parentheses

[viscid thistle]

Dude

10.5(6.2)(9.2)??

Nonono

I’m a little confused