precalculus

[gaunt sand]

facts

[shadow summit]

methods ez, its just a bunch of basic calculus

and probability ig

[verbal rock]

hey i actually prefer living here than nsw i used to live in a crack house now i live in a mansion

[shadow summit]

Average affordable house in NSW:

Dam, nice

Dam even the crack houses cost a fortune

[verbal rock]

ok bye #discussion

[celest nexus]

<@&286206848099549185>

no comprendo

guys is it 12

[spice steeple]

integrals have linearity property you know that right

[celest nexus]

no

i just learned this

like 2 secodns ago

[spice steeple]

integral of f minus g is the same as integral of f minus integral of g

man i wish i knew lateX

[plush sparrow]

yeah

[celest nexus]

what

[plush sparrow]

yk u can copy paste equations from desmos to overleaf right

[celest nexus]

what is goingon

[supple wagon]

Basically, integral of (x+y) is the integral of x + integral of y

[celest nexus]

ok

that

so is it just 18 - 6

its

its over guys

[supple wagon]

No, the integral

[spice steeple]

you need to evaluate the integral of -6 from -2 to 5

also

[plush sparrow]

do u know the constant law in integrals

[celest nexus]

no

i promise i learned this like

actually

a minute ago

[plush sparrow]

integral of c dx = cx

[supple wagon]

https://i.ytimg.com/vi/-QlWEG2j_mM/maxresdefault.jpg

[celest nexus]

ok

so

[celest nexus]

does it equal 0

😭

[shadow summit]

$\int (f(x)+g(x))dx = \int f(x)dx + \int g(x)dx$

[obsidian monolith]

TheLord26

[shadow summit]

so you would do: $ \newline \int^{5}{-2} f(x)dx + \int^{5}{-2}-6dx \newline 18+[-6x]^{5}_{-2} \newline 18-6(5)-6(-2)$

latex?

cmon

work

$\int^{5}{-2} f(x)dx + \int^{5}{-2}-6dx \newline 18+[-6x]^{5}_{-2} \newline 18-6(5)-6(-2)$

[obsidian monolith]

TheLord26

[lavish crystal]

18-6(5-(-2))= 18-42=-24

[lavish crystal]

18-6(5-(-2))= 18-42=-24

[glad widget]

18 - 30 + 12

[ivory mango]

please do not ghost ping others

well

not ghost ping

[glad widget]

Whats a ghost ping

[ivory mango]

if you need help open up a help channel in the help forum

[ivory mango]

its actually different from what he actually did i just confused a ghost ping with what he did which was a cold ping

[glad widget]

Ive never head of either of those before

[ivory mango]

ghost ping = sending a message with the ping and then deleting the message

cold ping is like pinging someone with an issue that the person they pinged has nothing to do with their problem

also on a side note: "18-6(5-(-2))= 18-42=-24" is not precalc

[glad widget]

its 18 - 30 + 12

18 - 6(5) - 6(-2)

if i do what you did instead of straight up simplifying it i will pull out the -6 and get

18 -6(5-2)

= 18 - 6(3)

= 18 - 18

= 0

[ivory mango]

that's not my point anyway

it doesnt belong here as it's algebra

[tender mist]

I was always confused on what is actually considered pre-calc, lol. I know the channel description says trig, logs, and exponents, but my precalc classes back then had like, everything including algebra

[ivory mango]

yeah

precalc is sort of a grey area

[tender mist]

Yeahh, like I know it's normal for math to have a TON of overlap, but it feels like pre-calculus is the only early math subject that doesn't really have explicitly its own direction, it's just a combination of things

[ivory mango]

like right now I was given a notes packet in class and it had "what is e" and "what is a natural log"

and I was the only person in class to not only know the value but what e represents

[river drift]

the weird stuff is when pre-calc classes cover limits, because for me limits are definitionally a calculus topic

[tender mist]

Yeahh, that definitely stumps me as well. Not even just definitionally, but historically limits were conceived with derivatives

so it's a bit odd for sure

Or at least, limits as we know them. Limits were technically informally used in the Greek era, but not the way we use them, and it definitely wasn't a well-researched topic at the time

[shrewd flicker]

Heyy! Is anyone interested in reviewing pre-calc with me for the next 2 weeks? We can be study buddies 😎 I completed pre-calc during my first semester of college and want to make sure that I review the units before starting Calculus.

[shadow summit]

where did you get the 42 from? also it would just be easier to evaluate from the last line

[shadow summit]

the original question is.

i mean, its more like calc than precalc, but eh

[glad widget]

it is the answer for the calc question

[ivory mango]

Where

All I read was that algebra

Oh

It's right above it

I didn't see it at first

[barren finch]

Hey guys, a quick question. I have already done pre-calculus and even tho I am moving to calculus. I don't feel confident moving toward calculus, so can you provide me with some suggestions? Thanks.

[ivory mango]

Do some practice problems

[fleet sinew]

Hi and what?

[tepid timber]

Why not just leave

[uncut mulch]

<@&268886789983436800>

(check logs too)

[analog flower]

@pure oak ^

[swift stone]

The Stewart's book for PreCalculus has been pretty decent so far

[willow bear]

what happen here

[analog flower]

good question

i think it was the logs from them

but they got banned i think

[willow bear]

something something "logs" pun

banned for logs in the precalc channel [vine boom x4]

[uncut mulch]

they were asking to get banned and also try see what happens when you look up messages from them

[fast kiln]

Can anyone explain how, after finding the length of PQ, to do next part ii)

[willow bear]

this pic is very low res

take a better one

The diagram shows part of the curve y = x(9-x^2) and the line y = 5x, intersecting at the origin O and the point R. Point P lies on the line y = 5x between O and R and the coordinate of P is t. Point Q lies on the curve and PQ is parallel to the y-axis.

(i) Express the length of PQ in terms of t, simplifying your answer.

(ii) Given that t can vary, find the maximum value of the length of PQ.

ok i transcribed it

@fast kiln do you know how to find the max value of a function in general

[fast kiln]

Yes

Setting the derivate equal to 0

[willow bear]

well, why don't you do it here?

you've got PQ as a function of t.

maybe before that, it would be nice to find the range in which t can vary. so that you're clear on the domain.

[kindred basin]

i just started exponential functions and logarithms today

its neat

[fast kiln]

Okay but I’m still a little confused on how it works. Isn’t dy/dx a gradient function? Like for a curve I get how you can find the max or min points but how does it work for a vertical line?

[willow bear]

you're overthinking it right now

you should just view 4t - t^3 as a function of t REGARDLESS of where it came from

you have this function and you need to maximize it on the domain 0 ≤ t ≤ 2, that's it.

abstract away from the details, so that they do not cause such confusion.

[fast kiln]

Okay yeah but now I’m curious. Does this change anything about dy/dx being a gradient function and that by setting the derivate of a curve equal to 0, you are simply finding a horizontal part of the curve?

i still dont really get it (i can answer the question now but dont get why/how)

[viscid thistle]

Hello, I'm just new here can someone please help me with my math 🥲

Legit just joined here cause I've been stuck with this math for 2 hours and I haven't made any progress 🙃

[shadow summit]

!da2a

[tender quest]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[willow bear]

well you'll have to show us the thing you're stuck with

we need to see it in order to help you don't we

[viscid thistle]

Mb

[glad widget]

how can i figure out where these 2 equation intersect?

setting them equal gives a linear equation

[glad widget]

nvm i figured it out

[viscid thistle]

hello anyone

im new to these kind of stuff uhh

can i ask

f:x→2x+1
f(x)=2x+1
y=2x+1

are these 3 the same value ?

please ping me because i rarely check servers😭

[worldly marsh]

they all equal to 2x+1

[viscid thistle]

oh okay tysm

[river drift]

2 of those are functions, 1 of those is an equation

[viscid thistle]

sureeeeee

[viscid thistle]

hi, terrible high school, learn almost nothing. Recently bought Axler's pre calc book and im loving it. Do you think someone can learn the entirety of pre calc plus the entirety of calc 1 and 2 in 4 years while studying for 1 hour a day?

[summer ruin]

it's not efficient to study 1 hour a day math subjects

you can learn all of this in under a year

[vapid plaza]

you can learn all of calc 1 and calc 2 in a day if you're really smart

[whole void]

no u cant

[shadow summit]

I don’t think it’s a viable way to learn.

[grim maple]

first of all you have to check if this line represents a pair of straight lines or not, find Delta for it.

if delta = 0 , its represents pair of straight line

if you wanna find the angle between them, you can use tan(theta) = (2(h^2-ab)^1/2)/a+b

[swift stone]

is there a free version of wolfram floating around

something that shows you the result and how it got to it

?

[swift stone]

I would say it's a start, but I would advise 2 things

first off make sure you're stuyding for the 1 hour like no outside distractions nothing just you and the work

second thing I would say if you can try and increase the time as you go along

a little focused studying is better than none / hours of unfocused studying

also if we're giving advice could we like actually add something of use besides saying nah that's kinda dumb

[old pollen]

100% I can testify to this. My goal is like topology in a year or two which is Duable

[old pollen]

Nope

Way to much stuff

[hollow crypt]

uhh

im stuck on how to do this

[old pollen]

Hi rocinate

[viscid thistle]

hi

[old pollen]

Isn’t this like a sinsuodial function

Cause it’s like constant

T-10 obviously but idk

[viscid thistle]

well just off the top of my head, it looks like it covers 180 degrees during 10 minutes (for times less than 10 minutes)

[old pollen]

I think either cos or sin is good?

Idk though

Oh it’s like geometry sort of?

Oh it’s geometry

Ha ha

Unit circle moment

[viscid thistle]

So in 1 minute it should rotate a 1/10th of that. so 18 degrees? maybe

yeah

[old pollen]

If 10 mins=1 dial I could solve it

Idk though

[hollow crypt]

doesnt it look like

a lil more than 180

for 10

[viscid thistle]

yeah maybe, what can we do about it, lol?

[hollow crypt]

soooo whats the asnwr

for 1 i think its

like

20 degrees right

[viscid thistle]

maybe 18 ish

lol right kind of an estimate

[hollow crypt]

ok yeah

[viscid thistle]

yeah maybe 19 or 20

[old pollen]

280 degrees from 0 to 35 mins I think

[hollow crypt]

wait what

wouldnt it be the same

[old pollen]

One circle is equal to 360 degrees

[hollow crypt]

itll be even less tho right

[old pollen]

🤓

[hollow crypt]

cuz now the interval is 5

[viscid thistle]

i think you will need to the any of the ones that involve the "upper" part of the time in pieces

[hollow crypt]

and 1 minute

[viscid thistle]

like split into 2 different problems

[old pollen]

I’m not helping I’ll leave

[hollow crypt]

it would be less than the first answer right

like 5 degrees

cuz its asking in 1 min

so

[viscid thistle]

oh so problem 2... it has a constant rate still (but the other constant rate)... ok let me try

so what do you think, from 35 to 11 minutes on the dial is about 90 degrees?

[hollow crypt]

uh

what does that mean

theres no 11

oh

wait

like about yeah

[viscid thistle]

I got 3.6 degress for teh 2nd problem

[hollow crypt]

ok thanks

wwait thats what the question is asking right

like

its asking to scale it down

[viscid thistle]

it wants to know how many degrees the knob will turn during a certain time period?

well part 3... is kind of like slope.... we divided the change in one quantity by the change in the other

for the first problem: (180 - 0)degrees/(10 - 0)minutes = 18 degrees/minute

in the second one: (90 - 0)degrees /(35 - 10)minutes = 3.6 degrees/minutes

Δy/Δx same idea

[hollow crypt]

ok thanks

[surreal yoke]

anyone got great videos that help you learn linear and quadratic systems (grade 11 Alberta curriculum) to make it easier to understand?

[hard verge]

share the curriculum

our school follows indian system, so we got high level stuff

[spiral sonnet]

What did I do wrong? Given 1/x+6 and the interval [7, 7+h] I was asked to find the rate of change so I plugged them in y1 = 1/13, y2 = 1/h+13 and then did y2-y1 / x2-x1 and ended with h^2 / 13(h+13)

[viscid thistle]

, ask (1/(h+13) - (1/13))/(7 + h - 7)

, ask simplify{(1/(h+13) - (1/13))/(7 + h - 7)}

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by rocinantexyz

[viscid thistle]

not sure where you got h^2 in your numerator; but I'm kind of rusty, heh

double check it maybe

[spiral sonnet]

Uhhh well…. I musta done something either on accident or I just have no idea what I was doing lol

[whole spruce]

is (2x-1, -6y+4) the right mapping notation for this functions?

[lean tundra]

this is really not complicated I would advise you to read more carefully the question

[shadow summit]

$f^{-1}(f(x))=x$ that should help for q1

[obsidian monolith]

TheLord26

[shadow summit]

So you know how to calculate period?

[lethal patrol]

I figured it out already

Thanks for answering though

[arctic sundial]

How do I do this

I’ve tried foiling and factoring but I haven’t gotten anywhere

[shadow summit]

You could try just substituting in the answers.

[arctic sundial]

But I wanna try without substituting

[uncut mulch]

numerator would need to evaluate to 0 when x=k

[arctic sundial]

Why?

Don’t you need to factor so the numerator is the denominator

Oh

Wait

I’m still cpnfused

[uncut mulch]

factor theorem

[arctic sundial]

I found the answer key but I don’t understand

[uncut mulch]

if (x-k) is a factor of the numerator,
the numerator will be 0 when x=k

[arctic sundial]

When x = k its a hole and undefined, no?

You have to factor it before you can find y value of the hole

Oh wait

[arctic sundial]

Yes

So what does that mean

I can create whatever binomial I want?

I’m still confused sorry

I substituted k for x

And x is 3 which means k is 3

But idk how that works still

But then that gives me this

Which is undefined

[uncut mulch]

replace x with k

for the numerator

then solve for when the numerator will be 0

[solemn moss]

Does anyone know where I can learn calculus for free cos I can’t afford university and I can’t take calculus at my school

[spice steeple]

mit ocw, khan academy

[solemn moss]

Thank you🙏

[spiral sonnet]

I’m confused about reflecting the y/x axis when it’s something like 5^x

I thought reflecting the x axis meant flipping it horizontally so -1 would equal 1, etc. but apparently doing -5^x is reflecting the x axis?

[summer ruin]

reflecting along x axis

but yes

[lean jasper]

How do you graph piecewise function?

[shadow summit]

Do you mean piecewise functions?

[lean jasper]

Yes, sorry, it was a typo

[shadow summit]

Npnp

You just graph the functions but cut it off where each of the domains are

[lean jasper]

Okay but where are the domains?

I'm quite new

[shadow summit]

eg 0=<x=<5 means that x can be equal or in between 0 and 5.

[lean jasper]

Okay

And

Probably the last question: when do you need to pluck the number in a domain into f(x) = mx + b ?

I am quite confused at this point

[lunar flame]

Can you guys please share some topic exam questions to practice for Edexcel Further Pure Maths IGCSE: Sequences and Series, Vectors, Binomial Expansion and series, Quadratics, Coordinate Geometry, Exponents and Logarithms, Inequalities and Identities, Sketching Polynomials

[strong epoch]

Does anyone know what I got wrong on these

?

[dense cobalt]

i think this should be in alg

[lean jasper]

Nvm, I finally understand

Anyway thanks @shadow summit

[last pine]

How do you do 64.

Im lost rn

[mystic basalt]

i think change cosx into sin(90 - x)

then apply formula sina + sinb

u get smthin like this
2sinxsiny = 0, from there you can make a general solution

in the next one put sec^2x = tan^2x + 1

[slim crystal]

alr

so how do u even start this problem

ik sec is inverse of cosine

but how do i find secant of pi over 5

without a calculator btw

[summer ruin]

you're not supposed to

use properties of cosine and trig circle

[slim crystal]

what

[marble leaf]

u can use the period of sec and the fact that it’s an even function

[exotic sky]

wait why do they all look equivalent

wait nvm

[stable vessel]

Are all of the properties here true?

Yes they are

[viscid thistle]

x
1⁄2
= 6

i need help

[pure copper]

Does the given answer is c?

[lime lotus]

Am I saying this statement right?

A ↔ B

"A corresponds to B"

[lime lotus]

Like ∠A ↔ ∠B

"Angle A corresponds to Angle B"

[random yoke]

what do you mean by correspond

[lime lotus]

correspondence

A is to B

like that

[random yoke]

the angles are equal in measure?

[lime lotus]

yes like that

[summer ruin]

there is not a unique way to read this

and this is not how mathematicians would read it

[lime lotus]

so how would a mathematician read it?

[vapid plaza]

"correspond" is not a mathematically conventional word afaik

[lime lotus]

What is the correct way?

[summer ruin]

there is not a single correct way

a mathematician would read it as A if and only if B

[lime lotus]

So let's say I saw it on a beginner geometry book

How do i read it?

[summer ruin]

depends on the context

[lime lotus]

Let's say about on congruent angles

How

[summer ruin]

can you post the entire context?

[lime lotus]

like a one-to-one correspondence of vertices of two triangles

wait I'll take the picture

[lime lotus]

Here:

[summer ruin]

read it how your book reads it, a correspondence

[lime lotus]

a correspondence b

like that?

[summer ruin]

a corresponds to b

[lime lotus]

Thank you!

[whole void]

I don’t think explaining it as a bijection is a great way to put it

[willow bear]

do you have something better in mind then @whole void

[whole void]

no I meant simply for two equal angles

but yeah for triangles it makes more sense

[willow bear]

well this is in the context of triangles

[whole void]

yeah sorry i misread i thought it was talking about just two angles

[gentle sapphire]

Guys do you think that the precalculus book by james stewart takes a good approach on trigonometry because i dont think so, its very short and doesnt explain anything in detail, is there a reason for that? Should i go with an alternative?

[shut current]

i have a composite functions test and Rates of Change test on the same day and i cant find a good review sheet. does anyone here have one?

[abstract quarry]

Guyss suggest any good self study (with a good explanation) for precalculus

[abstract quarry]

Plzz anyone

[uncut mulch]

khan can give you a decent intro

[abstract quarry]

did u mean khan academy

if yes then I'll definitely try, I'm learning from this channel called "Bhannat Maths"

But finding it difficult to solve questions on relations

[viscid thistle]

https://tenor.com/view/snusmumriken-snufkin-wind-fly-sad-gif-27295846

[gentle sapphire]

Guys, when it comes to the unit circle in the unit circle, i dont understand how the points in p calculated, like where did we get square root of three over two and 1/2? Is it somethin specific to that triangle or how can these numbers be calculated?

[willow bear]

Is it somethin specific to that triangle
yes
how can these numbers be calculated?
by viewing the 30-60-90 triangle as half of an equilateral

[abstract quarry]

Guyss suggest any good self study (with a good explanation) for precalculus

[gentle sapphire]

Yeah already figured it out, thanks

[shadow summit]

You have literally already asked that and someone has responded with khan academy. Do not repeat questions especially if you are given a good response.

[patent tundra]

please help how can i solve part a of this?

[summer ruin]

"is a solution" means when you plug it in the equation, it turns true

[jolly dew]

Hello! I need some help. How would I find the zeroes of trig functions without a graphing calculator?

ex.f(x)= 1/2 (cos2x)

[summer ruin]

use trig circle

[jolly dew]

Okay I know the trig circle but how?

[summer ruin]

see where on the trig circle the cosine turns to zero

[jolly dew]

Okay but in that case,
1/2 cos2x=0
cos2x=0
and then what should I do?

[summer ruin]

do you see for what inputs the cosine turns to zero on the trig circle?

[jolly dew]

1 or -1

[summer ruin]

there are no such points on the unit circle

remember that the horizontal axis is for cos(x) and vertical axis is for sin(x)

[crisp bluff]

log(a)/log(b)=a/b

is that a rule?

[fading monolith]

No(?

[crisp bluff]

ok

[river drift]

,,\frac{\log (a)}{\log (b)} = \log_b(a)

[obsidian monolith]

cloud

[fading monolith]

That yes

[viscid thistle]

i need some advice regarding studying calculus, before accessing topics like derivatives and integrals, what are the topics i need to study?

[summer ruin]

trig, algebra, learn all the basic functions and their properties

[viscid thistle]

im studying applied maths

( no trig )

does the chapter Relations relate to it?

like calculus

[summer ruin]

all of these are very much applied math

if you don't have solid foundation in trig you're going to suffer a lot in calculus

[viscid thistle]

alright, thanks a lot

[viscid thistle]

may I request you help with this as well ?

[summer ruin]

well how could I know that based off of chapters name

[mossy hound]

i learned the hard way that when i found out that trig is important for some limits

[rough jasper]

Hello I am having trouble with Models and Applications. Can anyone recommend any resources to help me understand the topic better. I am having a problem with verbal expressions in word problems and having to turn it into mathmatical expressions.

[rancid forum]

Why isn't the answer no roots? I got x=-17, but when i plugged x back into 0=... get 8=0. I asked wolfram alpha and it said there's no roots..

[river drift]

if you plug in x = -17 it should give you 0. i think you must have made a mistake when plugging in

[delicate oriole]

someone good with complex numbers?

[rancid forum]

yeah i think i just did something dumb cus i got cube root of -64 = 4 which makes no sense

thx

[tender quest]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[solar olive]

both c and d are correct

[tropic obsidian]

is there anyone that wants to vc and work through math problems? im on exponential and logarithmic functions and kind of have nobody to talk to in my class to sort them through

[rain scroll]

Sorry i am to sleep

[tropic obsidian]

all good!!

[lean tundra]

the logarithm function is the reciprocal function of the exponential which means that if $ln(x)=y$, $e^y=x$, For example $ln(1)=0$, and $e^0=1$
It's a function that is defined in $\mathbb{R}+$
$\lim{x\rightarrow 0} ln(x)=+\infty$ and $\lim_{x\rightarrow +\infty} ln(x)=+\infty$
The derivative of the function is $\frac{1}{x}$
This is the basic of the function ln but I would do reseaches on google because the function has quite a lot of properties TBH and to understand some of the demonstrations for the derivative etc.

[obsidian monolith]

Birby

[willow bear]

are you by any chance french and/or from somewhere that speaks french

[thin dome]

prove continuity of the function $\cos x$

[obsidian monolith]

spdie

[glass dove]

what am i doing wrong here?

the differential quotient should be 2

since it goes up 2 points

someone please help

[willow bear]

it goes up 2 but also right 2

so you are not doing anything wrong @glass dove

[lean tundra]

yep i guess my english betrayed me 😂

[glass dove]

ah ok

thx

[willow bear]

yeah bc what you call réciproque we call inverse

and what you call inverse we call reciprocal

[lean tundra]

well thank you because I didn't know that lol

[rancid bluff]

What exactly is euler's number and how does it relate to logarithm?

I don't really understand. Cause like the log2 8=3 makes sense. But I have no idea what e does or why its even a thing

I hope I explained that well. English is not ny first language

[river drift]

euler's number e is a number with a lot of special properties that makes it show up a lot in calculus. the functions e^x and ln (natural logarithm, log_e) have very nice properties when it comes to calculus. So they show up very naturally in calculus courses. unfortunately i don't think there's much justification to give other than "you'll need it for your calculus course"

[rancid bluff]

Oh I see. Thank you so much for answering my question :))

[spiral sonnet]

To find the regression equation on desmos I input the data then on a separate line do y1 ~ mx1 + b
and then I use the M and B to make my equation right?

[river drift]

if it's a linear regression then yes

[spiral sonnet]

Thats what I thought but it never seems to satisfy the question

[river drift]

what do you mean by that?

[spiral sonnet]

I am asked to find the regression equation to the accurate 2 decimal place using desmos as part of some exercises

This is what I was told to input to find it but when I respond with y = 1.77x - 75.09 it doesn't satisfy the question

Am I doing something wrong?

[river drift]

you didn't round them correctly

[spiral sonnet]

So this is asking me to round it? I figured accurate to two decimals just meant what it is

[river drift]

"accurate to two decimals" means round to two decimals. 1.78 is closer to 1.77915 than 1.77, so it's more accurate

[spiral sonnet]

I hate math in english. That was my problem, thank you

[river drift]

in general if a problem asks for a certain number of decimals, you should always round it

[spiral sonnet]

Somehow I never knew that, thanks for the clarity.

[lean tundra]

do it by resolving linear least square

no jk

[river drift]

that's what the calculator is doing anyway

[viscid thistle]

also because if it is a computer grading you, well they aren't very smart so if it asks what pi and tells you to type in 2 digits after the decimal, and you put in 3.1416 it is prob going to test to see if 3.14 = 3.1415 and when it finds that it doesn't match, it will probably decide the answer was wrong.

,ask 3.14=3.1416

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by rocinantexyz

[viscid thistle]

that is what it is prob gonna do

cuz it is a computer

computer grading has to be hell... I feel so bad for you guys (I'm kind of old so I didn't have to deal with this crap).

[alpine anvil]

can someone help me pass this test

like hop on call and explain the entire test to me

<@&286206848099549185>

[coral pewter]

how do i convert a cartesian equation to a rectangular one i kinda forgot

[river drift]

is that not the same thing?

[toxic jetty]

Chat, I got a precalc exam tmrw, any tips for it?

[honest aurora]

Breathe air

Smile

[uncut jay]

ARE THESE CORRECT?!??!?!?!??!!

its my last attempt and ive been getting these wrong

[willow bear]

you in a test or what?

[uncut jay]

worksheet

[willow bear]

how come you have a limited number of attempts

[uncut jay]

ask my professot

[willow bear]

Q5 appears correct but for Q6 it doesn't say to round so you might want to go for an exact fraction in terms of pi

[uncut jay]

is automatically rounded to that

Im scared to press submit

[velvet iris]

it's not incorrect but the automatic grading might fault you for rounding

[uncut jay]

yep I god faulted

got*

never understood them, fuck this shit

[idle goblet]

Don't know what I did wrong here the answer is -4÷3 but I get -8÷3

[willow bear]

missing dx?

[rough minnow]

Can someone solve this integral for me

Oops

[willow bear]

!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.

[rough minnow]

Hmm i solved it but idk if it's the correct answer

Ok is this correct please tell me

I've solved it but idk if this is correct please verify if any mistakes

[rough minnow]

Now?

[silk needle]

quick question

what is this type of function called?

[half solar]

That looks like a rational function

[shrewd bronze]

I think it’s a cusp something to do with it being differentiable

If something is differentiable it’s continuous, but something continuous is not necessarily differentiable

[silk needle]

idk

[silk needle]

might it be piecewise or composite?

[river drift]

the general class would be an algebraic function, which also includes polynomials and rational functions

[silk needle]

this is the problem im stuck with

its just im unfamiliar with the name of the function itself

[river drift]

note that your graph was entered onto desmos wrong

not every function necessarily has a special category it fits into

[silk needle]

i understand

[idle goblet]

How can I write any quadratic equation as the multiplication of two expressions?
For example 2sin^2(x) + sin(x) - 1

[fading monolith]

Susbtitute sinx=y for example and solve it for y, that is, 2y^2+y-1=0

[brazen valley]

I was doing this integral (integral of cos^3xsinx) the other day, and found something peculiar which I would love for someone to explain to me. Using the substitution ‘u = cosx ‘ the answer I got was -1/4 * cos^4x + C, and using the substitution and some repeated use of the Pythagorean identity I got the answer ‘1/2 - 1/4 * cos^4x + C’

These are both equivalent given the 1/2 can be absorbed into the constant

But I was wondering where exactly the 1/2 came from

I asked my marhs teacher and he said probably the u sub due to a different transformation being carried out, but he couldn’t explain exactly why

Could someone please explain where exactly the 1/2 comes from

I was thinking the pi/2 phase shift between cos(x) and sin(x) has something to do with it but I don’t know exactly

[brazen valley]

It looks like that because you have a modulus in there

the sqrt(3x^2) basically means sqrt(3)|x|

if u swap that out for sqrt3 x u would get a hyperbola I think

some transformation of y = 1/x

[lean tundra]

should be like this tho

[brazen valley]

<@&286206848099549185>

[silk needle]

i know

[fading monolith]

Can you show the process? When you get that 1/2

[brazen valley]

Sry i lost it i had to rewrite

but I got 1/4 this time

Might have made a mistake before

Or now

But it’s the same thing

Where did it come from

And y did the u sub do thay

that

1/4 is 1/4 of their periods maybe smth to do with that

[brazen valley]

Forgot + C at the end

[fading monolith]

Mmmm well I wont care to much about that 1/4, thr integral is a family a functions that differs one constant so

[brazen valley]

Yeah Ik

that’s what i keep getting told

But I just wanna know y the u substitute brings that 1/2 into the equation

It’s a neat number so there must be some good reasoning

related to the substation being a transformation

the actual integral doesn’t matter it’s just interested in what’s happening when you do different substitutions

[willow bear]

just saying... integrals go in #calculus

[fading monolith]

Should be because you are putting cos^2(x) in term of sin(x)

Since your sustitution is with sin and not cos, and is cos^3 whats bothering you

[brazen valley]

Using the Pythagorean identity shouldn’t have done anything #

The only difference is the u sub

[fading monolith]

I know

But did more algebraic manipulation for the second substitution. Again, dont worry about that 1/4

Appears because of getting different substitution and thats it

Notice that arcsin(u)=x and cos(arcsin(u))=sqrt(1-u^2) so if you susbtitute from the begining you will get u(1-u^2)=u-u^3 so its inevitable to get that 1/4

[spiral sonnet]

Given the points (2003, 1483) and (2007, 2239) I use point-slope formula to get the equation y=189x-377084

with this i manage to get every single question I am asked correct (by an automated grader)
but when they ask for the equation for some reason this doesn't satisfy it?

[willow bear]

are you 110% sure that there's no arithmetic fuckup in your work

also show a screenshot of the problem as it appears on your device

[spiral sonnet]

Yes because they ask me to give specific Y's using my equation and I satisfy all the given x's

[willow bear]

so we know there is no input error or anything

,calc 189*2003-377084

[obsidian monolith]

Result:

1483

[willow bear]

,calc 189*2007-377084

[obsidian monolith]

Result:

2239

[willow bear]

ah here's the thing

t years after 2000

t isn't the year itself

it's the number of years since 2000

so you would be using the points (3, 1483) and (7, 2239)

[spiral sonnet]

ooooh

[willow bear]

this is why the !original factoid exists lmao

[spiral sonnet]

idk what that is but now it makes sense lol

thank you

[willow bear]

!original

[tender quest]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[willow bear]

we have a factoid for this exact situation

[spiral sonnet]

wait actually this doesn't solve my problem, because when I calculate for M it's still pretty much 7-3

Or am I just being stupid

[willow bear]

it's not m that is the issue.

the slope is ok

it's the y int that isn't

[spiral sonnet]

oh right

when I do point slope I don't do 2000's

nvm

[lapis bramble]

I'm actually so confused like I know the trig identidys and stuff but how in the world do I do this with no calculater

[summer ruin]

just think about it, you're already given the hint that arccos(-0.65) is a number whose cosine is -0.65

arccos(-0.65) = x -> cos(x) = -0.65

recall what is the range of arccos - that would be the domain of cosine in the equation cos(x) = -0.65

then recall the trig circle and see where you get the cosine to be approximately -0.65

[lapis bramble]

one ces lemme draw out what I'm getting from this

sec

so like this and because 2.28 is closest that whould be right?

[summer ruin]

I don't get what you're trying to say

[lapis bramble]

whoops not -6.5 -0.65

[summer ruin]

try to answer the question on what x is in the equation cos(x) = -0.65 instead of trying to measure arclength

[lapis bramble]

isnt the arc length the same as x?

cuz thats what cosine is

[summer ruin]

sure, but that only complicates the question

you should know at what x you get cos(x) = -1/2

[lapis bramble]

yeah I do but I only remember when I draw out the unit circle so thats why I did 3pi/4

[summer ruin]

well you won't be able to answer the question with that information because you don't know what cos(3pi/4) evaluates to approximately

-sqrt(2)/2 is some difficult to estimate number

[lapis bramble]

so I just think what cos do I need to get aprox -0.65?

so I can do -0.5

[summer ruin]

what x do you need such that cos(x) = -0.65

[lapis bramble]

yeah I get that but like how do I figure that out (also thx so much for helping me with this)

[summer ruin]

just give me a range of values of x such that you can ensure that cos(x) achieves value -0.65 in that range

[summer ruin]

given the restriction

[lapis bramble]

0-pi?

pi/2-pi

not 2-pi

pi/2 throu pi

[summer ruin]

I mean the question is setup in such a way that just saying x belongs to 0 to pi already makes the answer obvious

[summer ruin]

you can make this tighter

[summer ruin]

👆

[lapis bramble]

3pi/4 right

[summer ruin]

no

cos(3pi/4) = -sqrt(2) / 2

[lapis bramble]

oh yeah

i know this one sec lemme get a paper

sqrt(3)/2!?

[summer ruin]

well why suddenly it wouldn't contain any pi? such a value is certainly not on the trig circle

[lapis bramble]

oh yeah duh thats the y-cord

pi/3

[summer ruin]

cos(pi/3) = 1/2, not -1/2

[lapis bramble]

or 4pi/6 I mean

[summer ruin]

yes that's the same thing as 2pi/3

well then you know that 2pi/3 < x < pi

this answers the question

[lapis bramble]

yes

so then whats the answer

like ig 5pi/6 for an aprox and the clossest to that wins

[summer ruin]

you can estimate pi easily and get a bound

and conclude the answer from that

[lapis bramble]

so its 3.28?

[lapis bramble]

here

[summer ruin]

what is

there's no such answer option

[lapis bramble]

2.28 whoops

[summer ruin]

yes

[lapis bramble]

thats what I said up here

ok I understand it now thank you

[rugged ferry]

could anyone solve these

[willow bear]

!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.

[rugged ferry]

help me to learn to how to tackle these types of questions ?

[willow bear]

write out both planes' trajectories as parametric equations in 3D space tbh

like, run the x-axis parallel to one of the planes' courses, the y-axis hoizontally perpendicular to that, and the z-axis upward

also be careful with units (feet for distance vs. mph for speed... one of these gotta get converted at least)

[twilit echo]

can anyone tell me how to solve this?

[river drift]

try substituting the part under the square root

in general integration questions should go in #calculus

[shadow summit]

,,\int 8x(1-x^{2})^{\frac{1}{2}} dx

[obsidian monolith]

TheLord26

[shadow summit]

Now apply the reverse chain rule or use u-substitution

[willow bear]

what are integrals doing in heree

integrals go in #calculus

[shadow summit]

because they posted it here. and its easier to just answer a question than tell them to go to a different channel to post the same question.

[dense hound]

Pre Uni roles don't have access to calculus

[fading monolith]

But the guy have an undergraduate role

[atomic haven]

-8/3 . ( 1-x^2)^3/2

@twilit echo

[willow bear]

!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.

[atomic haven]

you don't need the answer?

[atomic haven]

you need solution?

[uncut mulch]

answers, solutions, same thing
the point is don't give them away like that

[spiral sonnet]

Would have had a 100% on my exam if I didn't accidently give all decimal points instead of reading "to the nearest one decimal" 😦

[viscid thistle]

to me you got 100% 🙏

[shadow summit]

No, that is a valid reason for not getting 100%. It’s harsh but it was also stated in the question. Besides, if you “give all decimals”, especially in a non-calculator exam, you are probably wrong. The standard is rounding to 2 decimal places.

[viscid thistle]

[uncut mulch]

rounding of stated is part of the question after getting a more precise answer

you're essentially missing a step which is cause for deducting marks

much more important if it's stuff related to significant figures

[spiral sonnet]

There were only 4 decimals but I do agree it was my fault.
Sucks though lol

[shadow summit]

sig figs and scientific notation are the best of friends.

[onyx lotus]

hi what is the formula they are using to solve?

[river drift]

that's the formula for the slope of a secant line to the function passing through the specified points

it's a special case of the general formula for the slope of a line passing through two points

[naive tundra]

Need help

[silver dove]

@naive tundra Let's put the second one in the form y = -x-1

and let's make them equal to each other and find the points where they intersect

Then apply integral

[naive tundra]

Umm ok so, if I find the intersection point then I get this coordinate

[naive tundra]

You mean apply integration for both eq of function?

[silver dove]

Well, we learned that they intersect at points 3 and -1

Now we need to find which function is higher than the other in this range

Finding the focus point of the quadratic function may be useful

-x²+x+2

We need to replace -b/2a

b = 1
a = -1

-1/-2 = 1/2

when x = 1/2

the function is at its maximum point

well let's try

-(1/2)²+1/2+2 = -1/4+1/2+2

= 2.25

as you can see

They intersected at (-1,0)

first

If we start from the left

Well, then we know that the polynomial must increase to reach the value 2.25

but they never intersected again until x = 3

So between -1 and 3 the polynomial was larger than the linear function

After 3 the polynomial is smaller

because it reached its focus point at 1/2 and will decrease because the a is negative

ax²+bx+c

This is what is meant by "a"

Now we will subtract the lower function from the higher function in the range -1,3

like -x²+x+2-(-x-1)

= -x²+2x+3

and we will integrate this in the range -1,3

dx of course

So this means, first integrate the polynomial in the range -1,3

you will find an area

but it will be incomplete

Then you will integrate the linear function between -1 and 3

and you will get an area too

but you have to subtract it from the first integral

because it is higher and if you subtract the lower from higher you get a positive value

So think of it as if line segments were drawn between them in the range -1,3

and when you add the lengths of these line segments in the given range, you get the area

The lengths of the line segments are f(x)-g(x) for each x value

where f(x) = -x²+x+2

and g(x) = -x-1

If we were asked to do it in the range -1 to 4, first we would subtract the linear function from the polynomial again since the polynomial is larger in the range -1 to 3.

But since the linear function is larger than the polynomial in the range 3.4, we subtract the linear function from the polynomial

and we take the integral in the range 3,4

and then we would add these two values

Area in range -1,3 and area in range 3,4

It's like dividing a square in half and such as finding the areas of the two rectangles formed by dividing the square in half and adding them together

again you get the area of ​​the square

[naive tundra]

I have a question, why the integration of -x^2+x+2 - (-x-1) have to substract integral -x-1 again? Isn't we have already the area between the line and the curve?

[silver dove]

To prevent the area found from being negative

[silver dove]

and maybe to avoid miscalculation of areas

because there are overlapping areas

if you noticed

If you can find a video about this, maybe you will understand it better

area limited by two functions

[shadow summit]

#calculus

In future have these discussions in the appropriate channels.

[dusky moon]

Hey

I need help with a math homework

but is in spanish

can someone help pls?

[karmic igloo]

where are you blocked?

[shadow summit]

For question 1 you have to cube equation 3. You can do this by just expanding or using the binomial expansion.

For question 2 set make equations 1 and 2 equal, and then solve for x.

For question 3, multiply the top and bottom by the conjugate (1+i). Seperate the fraction, then you can find the real part.

[dusky moon]

yo thanks

[shadow summit]

Do you think you can solve all of the questions with this info? Or do you need me to explain how to do the other ones

[dusky moon]

i think i'm ok

a) is -8

i think

@shadow summit Where are you from, or how did you learn to speak Spanish?

normally on this type of servers nobody speaks other languajes than english

[shadow summit]

I haven’t. I just kinda guessed what each of the questions were.

I mean, most of the key words are pretty similar, so understanding what they wanted was kinda easy.

[dusky moon]

yo your'e a god guesser and also good at math

[sour glade]

How do you use the TeXit bot?

[shadow summit]

Skill.

[sour glade]

Serious answer though.

[shadow summit]

Type “,,” or put latex code in $between solar signs$

[obsidian monolith]

TheLord26

[shadow summit]

I’m not teaching you latex.

[sour glade]

,, \int_{0}^{\frac{1}{e}}\left(\frac{\cos\left(x\right)\sin\left(x\right)^{x}}{\pi x^{\tan\left(x\right)}}-\frac{\int_{0}^{e}\left(x^{a}-60^{a}+9\right)da+\tan\left(x\right)^{\pi x}-68x^{\sin\left(x\right)}e^{e^{x}}+\ln\left(x^{x}\right)}{\int_{0}^{\pi}\left(a^{x}-x^{60}+9\right)da+\tan\left(x\right)-\sec\left(x\right)+68\sin\left(x\right)^{x}e^{x^{e}}+e^{x^{x}}}\right)dx

[obsidian monolith]

Vanouper

[sour glade]

Lol, this equation is so large that it can't even fit it all in.

[shadow summit]

This should either be in #calculus or #latex-testing

[woven ravine]

how the heck does it just become 1/sinx-sinx to 1- sin^2x/sinx?

[solar olive]

do u not know how to combine a fraction

[woven ravine]

wait nah i got it

had a brain fart 💀

[lament glacier]

Csc is the inverse of sin, if sin is equal to (opposite/hypotenuse), csc is equal to (hypotenuse/opposite)

[willow bear]

that doesn't answer op's question

also be careful with the word "inverse"

[lament glacier]

Yes I know, the inverse of sin is actually arcsin

Sorry for my bad english

Sorry, My bad 😑, how did I explain it? 😪

[lean tundra]

"reciprocal" csc is the reciprocal of sin

[dusky moon]

hi

Can someone help?

I need to find the value of Y
is for tomorrow and I just don't undestand

[willow bear]

... this picture looks like the (geometric) definition of a derivative

do you have the exact problem statement in writing? i.e. a written specification of what they want you to do?

[dusky moon]

is just find the value of Y

[fiery creek]

Y or y?

[dusky moon]

using the information of the graphic

[willow bear]

well we don't understand what "Find the value of Y" is supposed to mean here either.

[dusky moon]

y sorry

[fiery creek]

so you want us to find the function?

[willow bear]

even still...

[fiery creek]

there's not enough given information to do that

[willow bear]

^

[dusky moon]

I think that is that

[fiery creek]

what

[dusky moon]

find the function

[willow bear]

you think?

you're the one with the full problem statement, not us

[dusky moon]

yes, beacuse my teacher asked for the value of y but I also think that's impossible with the given info

[willow bear]

did your teacher ask in writing or orally?

[dusky moon]

he just sent that image

[willow bear]

and only that image

and nothing else

zero other instructions

[dusky moon]

He often makes tricky questions

[fiery creek]

your teacher off the perc

[slow dagger]

your teacher is stupid

[willow bear]

"Do this for tomorrow."

"No, I will not elaborate."

"Read my fucking mind or something."

[dusky moon]

absolutely

I hate him

but is for 50% grade

[fiery creek]

no way that's 50% of the grade impossible

[dusky moon]

Yes it is

The whole group is going to fail

[willow bear]

what idiocy

you're being SET UP for failure

[dusky moon]

ok, we all agree about my teacher, but I need to solve the problem

[willow bear]

the problem is unsolvable

[dusky moon]

I think is a tricky question

[slow dagger]

you are fucked up bro

[dusky moon]

i know

[fiery creek]

ok wait

[dusky moon]

find the value of y

[fiery creek]

let me think this through

i've seen similar things before in my calc 1 class

consider tan(theta)

[slow dagger]

u got this!

[fiery creek]

tan(theta) = y/x but you also have similar triangles

triangle QPB also has theta as an angle

[dusky moon]

pitagoras?

[fiery creek]

no, similar triangles

[slow dagger]

nmms

[dusky moon]

tales?

[slow dagger]

...

[dusky moon]

ohhh I get it

srry

I'm just nervous, I don't want to fail

[fiery creek]

can you do what i'm asking

@dusky moon

have you learned similar triangles

and the ratios between the sides

@willow bear am i even on the right track?

i think they just want an expression for y in terms of the other variables

[dusky moon]

I think if you're doing well. because last month we saw that topic

[slow dagger]

...

[dusky moon]

@slow dagger please help

[slow dagger]

why me?

[slow dagger]

@fiery creek is already helping you bro

[dusky moon]

My teacher stated "Find the value of y"

50% final grade

and no calculator but fuck up that, i'm using it

[willow bear]

i don't know

[fiery creek]

Wait till I get home and then I ca. help @dusky moon

[slow dagger]

you are a hero bro

[dusky moon]

okok thanks man

[fiery creek]

Actually nvm you’re on your own I have homework to do

💀💀💀

[slow dagger]

maybe @dusky moon can help you

well, you are helping he

[dusky moon]

I'm solving my problem bro

if I had time I would help @fiery creek

Why don't you help him? @slow dagger you seem to have plenty of free time

[slow dagger]

@dusky moon , we need to be realistic, you are fucked up bro

[slow dagger]

i am also doing homework

im just watching this conversation

[cold gorge]

Would the phase shift of y=-5cos(2x+pi) be -pi/2
because C/B=phase shift so it is pi/2 and flip signs because it is out of the parenthesis

[pastel fossil]

B giving me a difficult time, if anyone knows this stuff better

[cold gorge]

Have you learned the unit circle yet?

[pastel fossil]

Yeah

I have it hold on I don’t have it memorized

[cold gorge]

Think of which quadrant can result in tan being negative

[pastel fossil]

4 and 2

[cold gorge]

yes so how could you get tan to be 1?

if you know tan=sin/cos

[pastel fossil]

If tan was 1 the answer would be 4/pi right?

I mean pi/4

Oh I think I see actually

Pi-pi/4

Then the answer is 3pi/4

[cold gorge]

yeah

[pastel fossil]

Thanks

[cold gorge]

mathway seems to agree with me yet the quiz says I’m wrong

[weary dock]

Gunter borrows $1500 at an annual interest rate of 12% and invests all of it at 1% monthly interest rate. approximate the instantaneous rate of change for gunters net gain in 10 years.

i dont know if this counts as precalculus but im gonna put this here i think its close enough cuz its grade 11 functions

i genuinely dont know how to solve this

its out of my math book and I have the answer but nothing i do is getting me it

[prime venture]

Don’t trust me bro

12 percent of 1500 is 180

[dim orchid]

can i have help with shown work with these

[prime venture]

✌🏽

[rugged crater]

just simplify everything to sin and cos and then its just algebra with a few of the identities

[willow bear]

we won't do your work for you

but if you have an attempt for at least one of these, we can take a look and point you in the right direction

[wind linden]

im not sure if i have to simplify this more

or if my final answer is good

[willow bear]

$\sin\paren{\frac{24}{25}}$ is not a thing you should be writing here at all

[obsidian monolith]

アンナ

[willow bear]

you are not interested in the sine of 0.96 radians

also cos(θ) is negative, since tan(θ) < 0 and sin(θ) > 0.

so your "adj" would have beeen -7 and not 7.

and cos(θ) = -7/25

[wind linden]

ooh u right

[willow bear]

and then cos(θ) + sin(θ) = -7/25 + 24/25, NOT cos(-7/25) + sin(24/25).

[wind linden]

ooh okay that makes sense

so then i would just simplfy those fractions and get my final anwser

[willow bear]

...yes

[wind linden]

thank you! that helped a ton ^-^

i need some guidance on this question

im not rlly sure on what to do without the arc length or without a degree

[willow bear]

without the angle*, you mean?

[wind linden]

ya lmao

i think i can assume that the arc length is 3θ since s=θ(radius) right?

[willow bear]

you don't need to assume that...

[wind linden]

oh ok

[willow bear]

the radius is clearly readable as 3 in the picture

[wind linden]

omg

i didnt even notice the numbers

on the graph cause they were so small

[willow bear]

well there are tick marks

[wind linden]

im not sure if im in the right direction here lmao

[willow bear]

no, you're not

for the formula $A = \frac{1}{2} r^2 \theta$, the angle must be in \textbf{radians}, not in degrees.

[obsidian monolith]

アンナ

[wind linden]

ohh ok

after i convert it into radians

do i just plug it in again and do i get my final answer

or is there still more to it

[willow bear]

no, there's nothing else

[wind linden]

ooh okie thank you very much :)

[low solstice]

yo

help

[viscid thistle]

I hate logarithms goodluck

[thorn creek]

start by taking the exponential of each side of the equation, apply the rule that e^(a-b) = (e^a)/(e^b), then apply the rule that e^(ln x) = x

[willow bear]

show your work

[low solstice]

no need

someone helping mwe

[weak vessel]

31/25

[weak vessel]

u are doing smth wrong

u are taking sin of the answer

but u have to do sin of theta is 24/25

not sin of 24/25

hope it helps

[willow bear]

!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.

[weak vessel]

i didnt knew that sorry

[willow bear]

now you do.

[weak vessel]

ok thanks

[low solstice]

can someone solve this and tell me what the answer u get is

[warped cipher]

have you tried anything yet?

[low solstice]

yeah

i got 4/-5

[warped cipher]

seems correct

[low solstice]

ok tysm

can u just make sure cuz i dont trust myself

[warped cipher]

I am sure

[low solstice]

ok ty

[warped cipher]

check alpha if needed

[willow bear]

you gotta show us how you got it, not only the final answer.

[solar olive]

4 = 2^2
8 = 2^3

[willow bear]

!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.

[solar olive]

So i derived this and i was wondering if theres a way i can also derive a partial fraction decomposition for 1/(1+x^N)

[fading monolith]

I think there is a easy way using complex numbers

For 1/(1+x^N) I would say power series

[solar olive]

I was under the preface of avoiding complex number, hence the need of a piecewise factoring

Though i derived a general case with complex number, i want to try with real numbers

[pastel fossil]

I have to compare the graphs of sin and cos with tan and find the similarities between them, so far I got that all 3 graphs are periodic, exhibit repetitive patterns, and exhibit symmetry, are these bad answers?

[fading monolith]

Mmm i see

[solar olive]

they're not bad perse, though i think the word ur looking for is "periodic" rather than "repetitive patterns"

cos and sin are translations of eachother

due to the fact that cos(pi/2 - x) = sin(x) and sin(pi/2 - x) = cos(x)

etc

[pastel fossil]

Oh I see, so periodic would be a “synonym” of repetitive pattern

[solar olive]

sort of yeah

[fading monolith]

Find the points where sin(x)=cos(x)