help-0

[covert breach]

no calc allowed

[mossy lion]

yeah exactly its just sin(pi/6)

[covert breach]

otherwise i would

fuck man too much work 😂

[mossy lion]

use the unit circle/special triangles

[covert breach]

i gotta remember the trig table too now 😩

so much shit to memorize

and when u go to a job, if u ever need this (probably wont, but if u do), u will use a computer/calculator 😂

sin(60)?

whatever that is

1/2 i think

[warped flower]

yes so sin(x) = sin(pi-x)=cos(pi/2 -x)

[covert breach]

what?

[warped flower]

use all these to get the answer i guess

[covert breach]

didnt get u

lol

it takes long to find it, but at least i know how to find it now

[warped flower]

sin(x)=sin(pi-x)

this is an identity

[covert breach]

i dont wanna remember all the rules tho

[mossy lion]

sin(pi/6) is a well known value

look at the unit circle

[covert breach]

i think its sin(x) = sin(x-2pi)?

maybe both work

[warped flower]

no x-2pi will give u a negative answer

[covert breach]

yeah but i dont memorize all this shit 😂

i use a formula booklet

[warped flower]

becasue sin is an odd fxn

[covert breach]

used to, at least

[mossy lion]

i mean i dont know what to tell you then

[covert breach]

bro when the fuck will i ever use trig anyways

😂

[mossy lion]

im telling you how to solve it

[covert breach]

yeah thnx man

[warped flower]

if ur going into civil eng i guess lol

[covert breach]

basically, i gotta memorize the trig table and the double angle/half angle rules

[covert breach]

im not tho 😂

thats the thing

lol

[warped flower]

its actually pretty useful for buildings and measurements and vectors

[covert breach]

why do u think i havent done, and wont be doing any trig for the next couple years? 😂

the only time i did do trig was for complex numbers

but it didnt need half angle rules and shit

[warped flower]

what are u doing now

[covert breach]

😂

[warped flower]

i mean ok then

[mossy lion]

thats because trig is secretly all just complex numbers 👀

[covert breach]

sorry man

that was too good of an opportunity to pass up

[covert breach]

opposite i think, but eh

[warped flower]

so was ur mom

[covert breach]

same shit more or less

[sleek elbow]

dont you scare me, just started trig in school

[covert breach]

hah nice one

[warped flower]

yea but rs tho

[covert breach]

bro complex numbers + trig is 💀

[warped flower]

are u in school or uni

[covert breach]

add mathematical induction on top

[covert breach]

comp sci

in uni

[warped flower]

ahh

[mossy lion]

trig professors are lying to you and not telling you the easy way to do stuff (eulers formula)

[warped flower]

yea u dont need trig at all lmaoo

[covert breach]

we do linear algebra, probability, discrete math, calculus

thats about it

[covert breach]

yeah

[covert breach]

hmm

no clue what that means

[sleek elbow]

we had tangent and my teacher just told us that the calculator knows all the pairs of the 2 triangle sides :/ I wanna know what tan actually does

like the function

[covert breach]

i havent done trig in years

[warped flower]

makes sense dawg

[covert breach]

this could help

the lines AC and BC are tangent

which is why at 90*, the lines wouldnt intersect

[sleek elbow]

im confused by that

why are there 2 triangles

[covert breach]

no easier way to explain tbh

[covert breach]

forget about the two

one is enough

[mossy lion]

eulers formula simplifies pretty much everything in trig but in trig/precalc classes they give it a different name and basically pretend it doesnt exist or tell you whats really going on. then its an optional topic that people taking calc 2 arent even guaranteed to learn.

[covert breach]

tan is tangent to the circle (slope of the circle at that point)

[covert breach]

whats eulers formula?

he has many

which one u talkin?

e^ipi -1 = 0?

[mossy lion]

$e^{ix}=\cos(x)+i\sin(x)$

[ocean seal]

nix (@ me for the love of euler)

[covert breach]

i have no clue about this one

oh ok

i know this one

yeah we had this

it was 💀

none of us could solve this 😂

and one of the students actually went to cambridge

still couldnt solve

[mossy lion]

thats a cool question

[covert breach]

its fucked

is what it is

💀

[mossy lion]

did people have trouble just with part a or what

[covert breach]

nah

last part

others were easy

d) ii)

[mossy lion]

going to try it now but from a glance it looks like just the geometric series/taking the real part of stuff.

[covert breach]

anyways, im glad i dont have to do much trig other than the occasional numerical analysis

[warped flower]

this looks like a GP

[covert breach]

it is a gp

ofc

i think some of us got a few marks for simplifying it to that

but couldnt actually solve it

[warped flower]

what part couldnt u solve tho

seems pretty ok lemme try it actually

[covert breach]

last one

u guys might be able to

cuz this was in highschool

[warped flower]

true i mean im in uni too

[covert breach]

but none of us were able to

[warped flower]

elec eng

[covert breach]

when we did it in 11th

[warped flower]

true must be hard for 11th

[covert breach]

how do i solve this?

how do i come up with this -8 lol

oh wait, i think i got it

this problems fucked

bruh this ones hella fucked

why cant u just use log rule to take 2log_5(x+3) = 2?

and then log_5(x+3) = 1

[warped flower]

yea u can i think

[mossy lion]

just finished it and yeah its what i thought. just taking the real part

[covert breach]

that would give only one solution

[covert breach]

u proved it?

[mossy lion]

yeah

[covert breach]

using mathematical induction?

[mossy lion]

induction what why

[covert breach]

i mean

[mossy lion]

its just algebra

[covert breach]

thats how the markscheme prooves it afaik

[warped flower]

instead do log(x+3)^2 = log(5) *2

[mossy lion]

its just taking the real part. which becomes what they give when simplified

[covert breach]

oh yeah maybe not, nvm

anyways so

[covert breach]

why is my method wrong?

[covert breach]

what?

[covert breach]

why cant u just do this?

[warped flower]

I mean U can but youll get 1 answer with this I think

in general log 10 is 1

[sleek elbow]

Hmm so what does taking the tan of the far side divided by the close side mean, like lets say the far side is 7 units long and the close side is 2 units long. You would take tan(3.5), but what does tan() do to the 3.5 to find out the angle alpha?

[covert breach]

yeah u only get 1

[mossy lion]

youre applying the rule outside the log

[covert breach]

so why is that incorrect?

[covert breach]

?

[covert breach]

whats far and close side?

[mossy lion]

if it was log(log5(x_3)^2) youd be right

[wraith cairn]

All the solutions for 2log_5(x+3)=2 is in the solutions for log_5(x+3)^2=2, but not all the solutions in log_5(x+3)^2=2 is in 2log_5(x+3)=2

similar to all solutions for x=5 is in x^2 = 25, but not all solutions for x^2=25 is in x=5

[mossy lion]

oh wait

hold on

[sleek elbow]

I didnt know the translation

[covert breach]

yeah but like why the fuck is that applying in logs?

[mossy lion]

is it log5((x+3)^2)

or (log5(x+3))^2

[wraith cairn]

because log_5(-5)^2 = 2 and log_5(5)^2 = 2

[covert breach]

forget those, just think of the alpha and the hypotenuse intersecting the circle, then u can draw a tangent (slope) of the circle at that point

thats your tan

[covert breach]

this is fucked up shit man..

[wraith cairn]

why?

[covert breach]

these trick questions

[covert breach]

cuz if they ask something like this, ill probably fuck it up

[mossy lion]

is the squared inside the log or not

[covert breach]

bro its this

[mossy lion]

because if its log5((x+3)^2) you can do 2log5((x+3))

[covert breach]

yeah its probably that

[mossy lion]

their parentheses are unclear

[covert breach]

but it only gives one solution

[covert breach]

not really

its pretty clear

anyways thnx

ill do another test

[mossy lion]

$\log_5(x+3)^2$ looks like $\left(\log_5(x+3)\right)^2$

[ocean seal]

nix (@ me for the love of euler)

[covert breach]

and lower my motivation even further with another bad grade

[covert breach]

not really, but ok

[wraith cairn]

no it doesn't

[mossy lion]

if its $\log_5\left((x+3)^2\right)$ they should write that

[ocean seal]

nix (@ me for the love of euler)

[wraith cairn]

they do not need to write that

[mossy lion]

its ambiguous

[sleek elbow]

okay but like, I draw this circle, draw the tangent, but how do I get the angle alpha? Like where does that come from

[covert breach]

cos (x+3)^2 = cos ((x+3)^2)

[covert breach]

nop

cuz any one thing after the function is considered as the input of the function

[mossy lion]

[wraith cairn]

ask anyone in the server.

it is a convention.

you absolutely do not need brackets.

also you can't just move down the 2 using the log rule because you'll miss a solution.

[covert breach]

btw, its not even that

[mossy lion]

its not clear if $\log_5(x+3)^2$ means $\left(\log_5(x+3)\right)^2$ or $\log_5\left((x+3)^2\right)$

[ocean seal]

nix (@ me for the love of euler)

[covert breach]

its (log_5(x+3))^2

[mossy lion]

then they should write that

[covert breach]

its obvious tbh

[mossy lion]

it could be either or

[covert breach]

based on conventions

[mossy lion]

$\sin x^2$ is equally ambiguous

[covert breach]

like consider x+3 to be z

[ocean seal]

nix (@ me for the love of euler)

[covert breach]

log z^2 = 2logz

= (logz)^2

[wraith cairn]

you write sin^2(x) if you are trying to do (sinx)^2.

sinx^2 = sin(x^2)

[mossy lion]

there should be no room for mistaking it. if its possible to mistake it then its written poorly

[covert breach]

ok now im confused

ill move on

but i made a whole program on this (shunting yard algorithm)

and that was fun

as i said, now im myself confused mate

[wraith cairn]

nobody would mistake it except for you.

it's written like that everywhere else.

[mossy lion]

LMAO

im sorry but thats just ridiculous

[covert breach]

i think this guy is right but now im confused

so ill let it go

and move on

lol

[wraith cairn]

nix why don't you ask anyone else in the server.

[covert breach]

ok so these two arent equal

[mossy lion]

im not going to ping someone for something so ridiculous. thats just rude

and against the rules im pretty sure

[sleek elbow]

okay but like, I draw this circle, draw the tangent, but how do I get the angle alpha? Like where does that come from?

[covert breach]

@mossy lion

wait ill graph

[sleek elbow]

whats that website btw?

or program

[covert breach]

desmos

[sleek elbow]

is that free?

[covert breach]

yes

[sleek elbow]

oh nice

got it

[mossy lion]

well thats fine but i dont see how the way a website is programmed means anything to a conversation about humans mistaking the meaning when there is a lack of parentheses

[covert breach]

thats your theta/alpha

your degrees/radians

u chose it

its the input

based on that, u get the lengths of the sides/tangent

sin of the angle is the height of the triangle, cos of the angle is the base

[sleek elbow]

wait I dont want the lengths, I want to go from the lengths to the angle

[covert breach]

cuz the website follows order of operations

whether implicit or explicit ones

btw 2^-2 would also be just 2^- * 2

but u have implicit parenthesis added by each program

so it becomes 2^(-2)

its the same here

or similar, at least

[covert breach]

u use inverse trig functions

[sleek elbow]

oh so I was confusing the two 😄

[covert breach]

sin^-1(x) or arcsin(x)

[covert breach]

hmm

so if sinx = 1/2

x = 60*

(i think)

[sleek elbow]

I dont even know about sin and cos yet, so ye

[covert breach]

they taught u tan before sin and cos?

[sleek elbow]

yup

I was kinda confused as I thought sin was the most well known, but I figured well known doesnt mean best to learn first

[covert breach]

it is best to learn them first tbh

they are the most useful too

[mossy lion]

im not going to debate it anymore. the fact is that its ambiguous. i dont really care if youre okay with assuming where parentheses are supposed to be. im not because i think problems should have no room for confusion.

[covert breach]

its not

[sleek elbow]

stop guys 😄

[covert breach]

but it doesnt matter

[sleek elbow]

its fine

[covert breach]

@mossy lion

[mossy lion]

yeah there you go. theyre assuming the square is not on the inside. that was my position from the beginning

[covert breach]

its all the same thing log(x+3)^2 = log^2(x+3) = (log(x+3))^2

[covert breach]

ok lets drop it, imma go study other stuff

but this question was fucked

how do i solve this? (practice test btw)

not an actual test

who knows lol

dont think it would be a

cuz how would denom go to numer

[wraith cairn]

To rationalize the denominator. You have to multiply by 2^(3/4)/2^(3/4)

right now, you have a 2^(1/4) in your denominator.

[wraith cairn]

Also, I want to clarify on the log((x+3)^2) = 2.
To apply the log rule, you need to prove it.
for log(a^n), let a = 10^k so log(a^n) = log(a^(kn)) = kn = nloga
But as you can see in this proof, we assumed a = 10^k so the proof does not hold when a is 0 or negative.
Using the log rule will only find you the solution when x+3 is positive
So you can't apply the log rule to that question and expect to find all the solutions

[covert breach]

bro with the log stuff im utterly confused between everything u said and nix said and shit

[wraith cairn]

Some conventions are different from others. log_5(x+3)^2 almost 100% meant log_5((x+3)^2) because that's the only way it gives nice solutions, but it's best to use brackets.

[lunar zenith]

Imagine a random number generator
between 1-15 numbers
run it 15 times
if 3 or more numbers are between 1-5 than you win
what are the odds of winning?
duplicate numbers allowed ofc

[jagged imp]

including 1 and 5?

and i assume the number generated can be 15 too

[wraith cairn]

You would need 13 cases (probably)

[jagged imp]

if thats all the case, the number of numbers between 1 and 5 in 15 trials is binomially distributed with p=1/3 and n=15

so you can use a calculator to do P(#ofnumbers between 1 and 3>=3) or do it by hand if you like suffering

[covert breach]

i thought it means (log_5(x+3))^2

[wraith cairn]

in this context, it means log_5((x+3)^2)

[covert breach]

wait lemme check on desmos and wolfram one last time

[wraith cairn]

wolfram alpha treats it like (log_5(x+3))^2

[covert breach]

so does desmos

[wraith cairn]

your teacher's notation is ambiguous to some people and most computers, but to solve the problem, just treat it as log_5((x+3)^2)

[covert breach]

its not our teacher

u were saying its not ambiguous

[wraith cairn]

I was wrong. It is ambiguous to some people.

[covert breach]

its not ambiguous afaik, its always (log(x+3))^2

[wraith cairn]

I was familiar with the convention logx^2 = log(x^2), because that's the way I've seen it.

[covert breach]

cuz none of the sites keep log (x+3)^2 = log ((x+3)^2)

[wraith cairn]

yes, but you'll have to do it that way because that's what your teacher meant.

[covert breach]

teachers an idiot

afai can tell, its not ambiguous at all, teachers just an idiot

unless thats not how u solve it

yeah nvm teacher is just an idiot

this is the answer

btw this is an entrance test, so not really homework or anything

(as u can imagine, we dont have trig being taught in comp sci )

[remote heron]

we cant help on tests 👀

[covert breach]

bro

its practice test

chill

[remote heron]

o idk what entrance exam means

[covert breach]

its practice test for an entrance test

nice pfp btw

dm me

gib

@remote heron

[remote heron]

gib what

[tough hatch]

btw this is an entrance test

[covert breach]

how would i solve stuff like this?

[tough hatch]

very sus

[covert breach]

rationalizing the denominator didnt quite work

[covert breach]

bruh

[jagged hemlock]

show ur work

[covert breach]

look here

take a photo? the handwriting is shit tho

[jagged hemlock]

sure

or explain steps in text

what did you get when rationalizing

[covert breach]

jhust tried rationalising the denom

[tough hatch]

the fact that u added not an actual test after saying it's a practical test is sus

[covert breach]

multiply by conjugate

[jagged hemlock]

yea

[covert breach]

ok man

u keep sussing

[jagged hemlock]

what did you get

[covert breach]

26 x root(5) + 13 x 5

whole divided by 31

[covert breach]

a test would last 3 hours + huh?

[jagged hemlock]

how did gou get 31 for denominator?

[covert breach]

and id be playing rocket league mid test too? I assume?

[jagged hemlock]

ok im not helping

[covert breach]

oh sorry

25-6

19

[jagged hemlock]

it isnt 6

[covert breach]

what?

oh yeah

[placid zinc]

Rationalizing the denominator should work

[covert breach]

4*3

12

[jagged hemlock]

show your work again

[covert breach]

13?

[jagged hemlock]

write it out

you have all day

[placid zinc]

I don't know how you got √5 when the question contains √3

[covert breach]

i did

just made a silly mistake i guess

[jagged hemlock]

show picture

[covert breach]

mb

[covert breach]

ok sec

[lusty pewter]

A rectangular sandpit is shown on a map that has a scale of 1:100. On the map the sandpit has an area
of 20 cm2. What is its actual area?

[jagged hemlock]

gou scale it

[lusty pewter]

can i please have some help

[jagged hemlock]

yea what did you attempt

[tough hatch]

channel is busy lol

[lusty pewter]

oh sorry

[jagged hemlock]

i dont mind

[covert breach]

this is what i did

i messed up when squaring 2 root(3)

anyways, thnx for the help

u can ask ur stuff @lusty pewter

[tough hatch]

why did u distribute 13?

[covert breach]

wdym by that?

[tough hatch]

have u tried not distributing 13?

13(5+2sqrt(3))

[covert breach]

yeah yeah i got it

[tough hatch]

don't

[covert breach]

i messed up in squaring 2 root(3) is all

thnx for the help

[lusty pewter]

can i ask my question now ?

[covert breach]

yeah

[lusty pewter]

thans

thanks*

A rectangular sandpit is shown on a map that has a scale of 1:100. On the map the sandpit has an area
of 20 cm2. What is its actual area?

[tough hatch]

sure, just be sure no one else is busy getting their own answered first next time

[lusty pewter]

ok alr

[tough hatch]

the scale is meant to size things down to their respective sizes on the map

emphasis on down

[lusty pewter]

ok

[tough hatch]

so if u want to find the actual area

[lusty pewter]

oh do you times by 100

[tough hatch]

u're gonna have to reverse that

to get a bigger size

[covert breach]

yeah

[tough hatch]

i.e. scaling up

[lusty pewter]

oh ok

so could it be like 5 m x 4m

[tough hatch]

it could be

[lusty pewter]

or 10m x 2m

[covert breach]

basically x/100 = 20

[tough hatch]

but why does it matter lmao

[lusty pewter]

oh wait yeah it doesnt matter

[tough hatch]

u only need the area

[lusty pewter]

so its 20m^2?

[tough hatch]

sure

[lusty pewter]

ohh

thanks for the help

[halcyon nova]

https://cdn.discordapp.com/attachments/269573202018041856/858510406116704276/image0.jpg

<@&286206848099549185>

[remote heron]

,rotate 1

[ocean seal]

Retrieving the previous image failed.

Jun 27, 2021, 1:14 AM

[remote heron]

doesnt load

[lusty pewter]

can i haves some help with a question?/

[vague coral]

[drifting scarab]

Do I ask for help here? I need help with a few Calculus Homework questions.

[vague coral]

[drifting scarab]

Here?

[vague coral]

[drifting scarab]

I need to find the Antiderivative of (2x+3)^3

I tried doing it on the bottom half

[vague coral]

multiply the (2x+3)^3 by 2/2 before

You need this form : u'u^3 to get the antiderivative : 1/4 (u)^4

[drifting scarab]

@vague coral Would it be this?

[lusty pewter]

a / K − y = b / K
[K]
can u help me isolate K

[vague coral]

no

wtf

[lusty pewter]

@vague coral can i have some help with

a / K − y = b / K
[K]
can u help me isolate K

[vague coral]

stop spamming

[lusty pewter]

😦

[vague coral]

$f(x) = (2x+3)^3$
Let $u = 2x+3$, then $u' = 2$. We can multiply $f(x)$ by $\frac{2}{2}=1}$. We just want this form : $u'u^3$ to get the antiderivative in this form : $\frac{1}{4} u^4$
Then $f(x) = \frac{2]{2} u^3$. So The antiderivative $F(x)=\frac{1}{8} (2x+3)^4$

[drifting scarab]

Oh thank you!!!

Btw I dont want to be spammy, but I have another question

Would this be an intergral?

[vague coral]

the antiderivative

[drifting scarab]

Thank YOU! Herels!

Is this the formula I have to use? for this problem?
@vague coral

[leaden seal]

Find the volume of the solid formed by revolving the region bounded by y = sin x, y = cos x, x = 0, and x = π
about the y-axis. Be sure to sketch the region first.

how do you solve this?

[heady gull]

If theres a 0.1% chance of getting one thing and a 0.5% chance of getting another thing, whats the chance of getting both items at once.

[glacial hedge]

Does anyone know why $F_n$ means 2 different thigns in physics and math? what monster is responsible for the naming?

[ocean seal]

Elonmosqito96

[strong furnace]

F_n without context does not mean anything to me -.-

[glacial hedge]

F_n is partial derivative with respect to n in math and normal force in physics

[strong furnace]

both require context

[glacial hedge]

?

[muted pelican]

what changes if 3 balls are selected

[jagged hemlock]

wdym

[muted pelican]

the total number of possibilities are 14C3 rite

[ruby current]

well for (i) you can do 1 - P(no red balls)

[merry willow]

hi guys, how do you read this? probability of 3 intersect odd?

[muted pelican]

o so we can do 1 - 11/14 ?

[merry willow]

from throwing a dice

[ruby current]

P(no red balls) is not 11/14, you have to run through the choices at each step

when picking the first ball it's 11/14

then you have to multiply by 10/13

and then 9/12 for the last ball

to guarantee that you have three non-red balls

[muted pelican]

hmm i see

so the probability of non red balls is 11/14 * 10/13 * 9/12

[ruby current]

three non red balls yep

so it's asking for the complement of that event

[muted pelican]

ah makes sense

[ruby current]

so just subtract from 1

[muted pelican]

for the 2nd one

the total balls are now 13

so we can do 11/13*10/12 ?

[ruby current]

did you learn about bayes' theorem?

[muted pelican]

not yet

[ruby current]

i dont think you can do that

because it doesnt say that the first ball selected is red

only that one ball selected is red

P(at least 1 green | at least 1 red) = P(at least 1 green and at least 1 red) / P (at least 1 red)

this is the definition of conditional probability

[muted pelican]

what does that | mean

[ruby current]

you can just read it as "given"

so probability of at least 1 green given at least 1 red

[muted pelican]

alright

[ruby current]

you calculated the denominator in the first part

[muted pelican]

the P of at least 1 red ball is in the first answer previously yeah?

[ruby current]

yeah

the numerator is tough

[muted pelican]

so the P of at least 1 green ball is 1 - 11/14 x 10/13 x 9/12 x 8/11 x 7/10

[ruby current]

should just be three fractions there, no?

probability of at least 1 green is 1 - 9/14 * 8/13 * 7/12

9/14 for the first non green ball and so on

[muted pelican]

oh

oh yeah 3 multiplicands bc only 3 turns

i got mixed up

so for 1G and 1R, how to do the probability

[ruby current]

we know the probability for at least 1 red, so to find at least 1 green and at least 1 red we can subtract the probability that we have all reds, or red-red-blue, red-blue-red, blue-red-red, red-blue-blue, blue-red-blue, and blue-blue-red

idk if there's a better way of doing this though

[muted pelican]

oh no that is so many probabilities

[thorn kindle]

part b?

the red ball is a given

so you need to just calculate the dependent probability for the next two balls

[muted pelican]

what do you mean by given

[thorn kindle]

you are given that the first ball is red

[muted pelican]

yes

wait is it 100% red

[ruby current]

i thought it doesn't say that the first ball is red, just that at least one is red

so it could be the second one selected for example

[muted pelican]

if the balls are picked without replacement

then what will it be

like the three balls are selected at the same time

for the first part

[ruby current]

i thought we're already assuming we're not replacing them

[muted pelican]

oh

i thought by 11/14 10/13 9/12 they arent selected at once

[ruby current]

thats true

so are you asking what happens if we do replace them

[muted pelican]

i think it is without replacement

[ruby current]

without replacement = not selected at once

with replacement = selected at once

by default we assumed the former

[muted pelican]

yeah without replacement mb

not selected at once

[ruby current]

yeah so thats what we already did

if we're replacing them back in then for part (i) you do 1 - P(no red balls) which becomes 1 - 11/14 * 11/14 * 11/14

[thorn kindle]

P(A and B) = P(A) * P(B given A). P(red and green) = P(red) * P(green given red). P(red) = 3/14. P(green given red) = 5/13. P(red and green) = 15/182

[muted pelican]

i see

[thorn kindle]

probability is a lot less confusing if you actually know the formulas

that was a 5 sec google search lmao

[umbral frigate]

hi does anyone know how I can prove that a cubic is surjective?

[thorn kindle]

so what you're trying to say is that any cubic polynomial y = ax3 + bx2 + cx + d

from R->R

takes on every y value in R?

think about it

@umbral frigate

every cubic polynomial has at least one real root

[umbral frigate]

yep

so can I prove that its continuous

as it approaches -infinity and +infinity

[thorn kindle]

All polynomials are continuous

[umbral frigate]

oh T_T

ok then I should use the intermediate value theorem

[vocal mesa]

IVT + the limiting behavior of cubics sounds good. Note that not every cubic is surjective

[umbral frigate]

ok thanks I think I've got it 👍

[vocal mesa]

sorry, scratch the last sentence

[thorn kindle]

Every cubic is surjective from R to R

[merry willow]

help

i dont understand the implementation of 51-i

and 1/(51-i)

why not just say 50

[alpine sable]

i'm very confused by this question

(from the sat lol)

here's what i did so far

the answer is supposed to be y = 68 but i have no idea how to get there

[gray isle]

the wording in the question is a bit poor

Enrique has 20 more photos than half the photos that Sadie has on her phone

[alpine sable]

oh i see, thank you!

how did you know how to interpret the wording?

[gray isle]

context

[jagged hemlock]

the wording so bad

[drifting scarab]

Guys I have a Question!
I'm not 100% sure if the answer is correct, but I clearly remembered there was a problem similar to this one that would in no way shape or form would, accept it.
Is the answer correct?
If So, I would have to speak to my professor about this glitch.

[slim tangle]

Why is 1 written there

[drifting scarab]

I really can't answer.
The answer has to be written in such a weird way like in the pic. Most of the times it works, but for some reason, this one question just never seems to accept it. Even when I write it different way.

[drifting scarab]

But is the Answer technically right?
(1/9)sin^9(x)?

[slim tangle]

Yes +c

[elder thunder]

what is the sum of a rational number and an undefined e.g : 1+(1/0)

[slim tangle]

Its like what is 1+apple

[elder thunder]

so you cant really have a sum from those 2?

[buoyant kayak]

not sure why that dude said apple, but from my knowledge, your answer will just be undefined

[ionic jewel]

yes it's undefined

the others guys point is that it's equally valid as writing 1+apple

which is also undefined

[lime bronze]

How can 1/3+1/5 result to 1.88?

[gray isle]

its not

[placid stag]

is this channel available?

[lime bronze]

@gray isle

[vale wigeon]

a mistake was made in the third line

they meant to write R_eq = 1.88 Ω, not 1/R_eq = 1.88 Ω

1/3 + 1/5 = 8/15, thus 1/R_eq = 8/15, thus R_eq = 15/8

and 15/8 is 1.875 which they rounded to two decimal places

@lime bronze does that help clarify things?

[elder thunder]

sorry to interrupt, but can I ask physic question here? regarding to the impedance formula of RLC circuit?

[vale wigeon]

there are 10 questions channels specifically so you never have to interrupt

[lime bronze]

So 8/15 got reciprocated?

And turned into 15/8?

[vale wigeon]

yes that's what i said

thus 1/R_eq = 8/15, thus R_eq = 15/8

[lime bronze]

I see thanks

[placid stag]

what is D2?

which one of these?

[elder thunder]

aight sorry bout that, what about my question, can i do that?

[vale wigeon]

yes

@placid stag tbh its not clear to me either

[pliant tundra]

please help

what would be my steps to solve it?

never mind i’m just dumb

[vale wigeon]

you haven't given us any instructions on what to do either

[pliant tundra]

sorry

i have a different question now

finding the focus and directrix of this equation

i narrowed it down to

(y+7)^2=-1/3(x-8)

with my h and k being 8, -7

i’m trying to find the focus

but the thing is confused about is how to find p

they didn’t give me the focus or directrix

so i have no idea what to work with

oh shit i’m fucking stupid again

never mind

i found my p

can someone check my focus and directrix answers

[dawn wraith]

Wait so X is the function, and Y is the variable?

@pliant tundra

I’ll suppose Y is the ‘function’ here, calculate the vertex using -b/2a for the X value of the vertex, then plug that into the ‘function’ to get its y, and you’re done.

Ah, didn’t notice the question

I thought he had wanted the vertex form of this ‘function’

Yeah, but I had thought that he only wanted the vertex form

Anyhow, someone answered his question in another chat, so there’s no use in answering it again

[harsh acorn]

S(n) means the sum of n's digits. For example, $S(1507)=13$.If $S(n)=1274$ what is the possible value of $S(n+1)$? A)1 B)3 C)12 D)1239 E)1265

[ocean seal]

Hyl1s

[harsh acorn]

Hint I need

[vale wigeon]

S(n+1) is either S(n) + 1 (if n ends in anything but 9) or S(n) - 9k + 1 (if n ends in a 9, where k is the number of nines at the very end of n)

[harsh acorn]

tysm

[vale wigeon]

in fact, generally, $$S(n+1) = S(n) + 1 - 9\max{k \in \bN : n/10^k \in \bN}$$

[ocean seal]

Ann

[amber marsh]

where is the

-4x^3 coming from?

i get 4x^3

[placid zinc]

That second term is 4(1)(-x)³

The negative can come out because 3 is odd

[amber marsh]

ohh

ok that makes sense now

i see

thx a lot

[harsh acorn]

If $a_1<a_2<...<a_{2018}$ and $a_1+a_2+...+a_{2018}=2018^{2018}$
Find the remainder when $a^3_1+a^3_2+...+a^3_{2018}$is divided by 6

[ocean seal]

Hyl1s

[harsh acorn]

maybe if we increase the numbers by its cubes, then remainder should be increased by cube of mod 6,

Idk is it right

[vale wigeon]

are the a_k known to be integers?

[harsh acorn]

no

there are no specific information about them

[vale wigeon]

then maybe $\sum_{k=1}^{2018} a_k^3$ is not an integer at all

[ocean seal]

Ann

[vale wigeon]

and it makes no sense to speak of its remainder mod 6

[harsh acorn]

I tried to solve it with assuming numbers are integers, and tried to solve it

I get 4 as the answer

And answer sheet says it is 4
Idk is it coincidence but I get the right answer

[tiny oyster]

How to deal with it🥲

[alpine sable]

i have no clue how to start this one

same as arctan

[vale wigeon]

let t := arctan(x)

12t^2 + πt - π^2 <= 0

[alpine sable]

oh god im stupid

tx

now how do you do this one?

[warped flower]

same

t^2 + 1/t^2 = t

[strong furnace]

this is a trick problem the range of x^2+1/x^2 is [2,inf)

[warped flower]

not really

range is [0,inf)

[alpine sable]

actually

he's right

[warped flower]

hmm true can’t be 0

[alpine sable]

how do you algebraically prove it's always greater than 2?

[strong furnace]

AM-GM

inequality

[alpine sable]

AM GM?

[warped flower]

thing is sinx lies between [-1,1]

so if LHS is [2, inf)

the answer should not exist right ?

[alpine sable]

yes

[strong furnace]

look it up you can also use derivatives for a simpler function x+1/x

[alpine sable]

ok thank you

[strong furnace]

derivatives work for this function as well

[warped flower]

how would derivatives help in solving this tho

am i missing sum

[alpine sable]

derivatives help you find the extreme values

min and max of a function

[warped flower]

yea but we already know the critical points

but we wanna solve for x

[strong furnace]

we have shown that there is no solution to that equation(in reals) he just asked how you would prove range of x^2+1/x^2 is [2,inf)

[warped flower]

ohhh fax yea to show the range u would differentiate

[alpine sable]

tnx

how do you calculate this using only algebra

[warped flower]

tg ?

[vale wigeon]

tan

[warped flower]

ah

i don’t know if u can solve it just using algebra

can u ?

i mean yea that works

[alpine sable]

Hi folks! I'm trying to calculate the characteristic function of the binomial distribution
https://imgur.com/a/NeKlm21

I was trying to plug it into the taylor expansion, but it doesn't seem to work. Could you please provide me with some hints?

[strong furnace]

did you get this right?

[visual furnace]

please help

[alpine sable]

(y-5)^2+y^2=13

Solve this

U will get value of y

Put in eq 2 u get value of x too

[visual furnace]

i dont understand

please help me

im new to this

my teacher just gave me a random A* qu

[harsh acorn]

stop posting this everywere

[visual furnace]

no

im still reading

one sec

kk

i understand it a bit

[ocean seal]

Thk

Hello, I've this problem :\\

“ Determine the polynomial $P \in \mathbb{C}[x]$ of degree 3 satisfying the following conditions:\\

• $-2i$ is a root of $P$.\\

• the other two roots of $P$ are complex conjugates of each other and of modulus equal to 2,\\

• the sum of the roots of $P$ is $1-2i$,\\

• the remainder of dividing $P$ by $x+1$ is $1 + 2i$. "\\

I dont know how to solve it.  I have that the 3 roots are complex, including 2 conjugates, and I have their sum.  how should I reason from there?

[vale wigeon]

you have the roots as -2i, a+bi and a-bi

you know that a^2 + b^2 = 4 and that -2i + a + bi + a - bi = 1 - 2i

[paper parrot]

why is R(3) <= 6 and not just R(3) = 6? Talking about ramsey's theorem

[vale wigeon]

did you read this somewhere? can you show us some context

[uneven garnet]

Okay thanks, I'm trying to solve it

[minor crypt]

@vale wigeon u dutch?

[vale wigeon]

no

why do you ask

[minor crypt]

😳

no particular reason

just thought u were dutch

[vale wigeon]

out of curiosity, what made you think that

[dawn nova]

Hey guys, which function hasn’t got this much immediate growth? I’m basically asking for a more smooth fade-in function, if it makes sense

[boreal sinew]

What's the name of the operation on functions
$$
f: A \to B
$$
$$
g: C \to D
$$
such that
$$
f \times g: (A \times C) \to (B \times D);
f \times g = (a,c) \mapsto (f(a),g(c))
$$

[prisma loom]

Cartesian product?

[ocean seal]

JohnDark

[boreal sinew]

Well, functions are usually defined as triples (D,C,G) where D is a domain, C is a codomain and G is a graph

[dawn nova]

Could you elaborate more, please? The sine seems definitely more smoother than the 4th root, I might go with sine

[spring harbor]

When does a function have no tangent line that's parallel to the first bisector?

[minor crypt]

hmm well first of all, username (although I guess could be german too)

and you use the word 'that' in sentences where it could be left out, e.g. you know that a^2...

In Dutch, the 'that' would be necessary.

My second guess would be you're German. Not like it matters

[spring harbor]

Is this channel taken, perhaps?

[vale wigeon]

i'm neither dutch nor german

[minor crypt]

this is so sad

[minor crypt]

nah go ahead

[spring harbor]

When does a function have no tangent line that's parallel to the first bisector?

[minor crypt]

I wanna say when it's derivative is not f'(x)=x

f'(x)+c

[spring harbor]

Hmm

Well for context, it has given me this function

It's asking for what values a the function has no tangent line(s) parallel to the first bisector

[minor crypt]

[spring harbor]

I thought a<0

but I could be wrong

I don't really have argument to back up my claim

[gray isle]

bisector of what?

[minor crypt]

the first bisector

y=x

[spring harbor]

^^

[placid zinc]

I have also never heard of this haha

[spring harbor]

You mean the term "first bisector"?

[placid zinc]

What's the slope of the first bisector?

[spring harbor]

y=x so 1?

[gray isle]

^ never heard of "first bisector" being used in this context before

[minor crypt]

The derivative of this function is a parabola, so it can never be parallel to the first bissector?

[placid zinc]

Right. Look for tangent lines with slope 1.

Notably, when can f'(x) never be 1?

[spring harbor]

My bad, I translated the question, could be due to that.

[spring harbor]

When the discriminant of x^2 +2x + a + 1 <0?

[minor crypt]

$f'(x)=x^2+2x+a+2$

[ocean seal]

Axhraf

[minor crypt]

oh I think I got it

[placid zinc]

Yes exactly. Didn't need my help at all lol

[spring harbor]

But we get: 4 - 4a -4 < 0 or a>0 ?

[minor crypt]

he was a few steps ahead of us

[spring harbor]

oh shoot I actually thought it gives us something like a>(number) which is not between the options..

[minor crypt]

nvm

[placid zinc]

,w graph x^3/3 + xx + 2x + 1

[ocean seal]

Results provided by WolframAlpha

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

Requested by Kaynex#7520

[minor crypt]

it wouldnt make sense that for all a>0, the tangent line is parallel to y=x

or maybe it would

[spring harbor]

,w graph x^3/3 + xx + 7x + 25

[ocean seal]

Results provided by WolframAlpha

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

Requested by Echo#1357

[spring harbor]

for a =5

Hmm this is weird

[placid zinc]

b² - 4ac < 0
4 - 4(a + 2) < 0
4 - 4a - 8 < 0
a > 1

[spring harbor]

We had to use a+1 cause f'(x) shouldn't equal one

[minor crypt]

a+1

[spring harbor]

Also it's the correct answer thanks.

[placid zinc]

Cool! Glad it works haha

[minor crypt]

DUTCH

[spring harbor]

dutch!

[minor crypt]

[placid zinc]

Just hard to see off the graph

[spring harbor]

yup

[minor crypt]

misschien dat ik daarom wel gelijk wist wat de eerste bissector is

[spring harbor]

hahaha true

bissectrice :v

[minor crypt]

mfw english×dutch

[hardy geyser]

https://gyazo.com/c70bf574fb5063c3bc0e2539fa3562cf

it said to the nearest tenths? do i do something wrong was i not suppose to round?

[gray isle]

nearest tenth means to 1 decimal place

(and should not be confused with nearest multiple of 10)

[minor crypt]

also found 69.8 with calculator

[hardy geyser]

so it wouldnt be 69.8 >>> 70.0?

[gray isle]

no

[minor crypt]

no, a tenth=0.1

[hardy geyser]

what if it was like 69.88 >>> 70? would that be correct?

[minor crypt]

easy way to remember: 1/10=0.1

[gray isle]

no

[hardy geyser]

i thought it was 5 and up you round 4 and below stay the same

[gray isle]

nearest tenth means to 1 decimal place
(and should not be confused with nearest multiple of 10)

[minor crypt]

not if you have to round up to a tenth, then that'd be 69.9

[hardy geyser]

ohhhh

so tenths hundreths are different?

[minor crypt]

a hundreth is 0.01

[gray isle]

hundredths would be to 2dp

[hardy geyser]

0.06 >>> 0.07 yes?

[gray isle]

whut?

[minor crypt]

[gray isle]

no

[hardy geyser]

cause you said 69.8 would be >>> 69.9

[gray isle]

no

noone said that

[minor crypt]

you cant just add a hundreth for no reason

thats not what rounding up means

[hardy geyser]

no like an example

[minor crypt]

a better example would be 0.065>>>0.07

[gray isle]

69.8 is 69.8
it is already to 1dp,
and you don't need to do anything to it

[hardy geyser]

wait how come when u round to the nearest tenths you only add 1 like 69.8 >>> 69.9

[gray isle]

0.065>>>0.07
if you were rounding 0.065 to the nearest hundreth (2dp),
then yes, that would round to 0.07

wait how come when u round to the nearest tenths you only add 1 like 69.8 >>> 69.9
noone said that

[minor crypt]

we said 69.88>>>69.9

[hardy geyser]

oh for the hundreths

wait so shouldnt it be 69.8 >>> 69.9 than if you add 0.1 more or round to the nearest tenths?

[gray isle]

what are you adding 0.1?

[hardy geyser]

wait no i didnt mean to say that i mean to say 70

[gray isle]

69.8 is 69.8
it is already to 1dp, (inherently it is already to the nearest tenth)
and you don't need to do anything to it

[hardy geyser]

what if it was like 69.4

[gray isle]

it is already to 1dp, (inherently it is already to the nearest tenth)

and you don't need to do anything to it

[hardy geyser]

inherently? what does that word mean

ohhh i searched it up ok

numbers after the decimil like ones, tens is it the same logic so i wouldnt round up anything in the ones right

[gray isle]

whut?

[hardy geyser]

like u know how u have ones tens hundreds after the decimil point

[gray isle]

before or after

[hardy geyser]

after the decimil

https://gyazo.com/b72ec45c1ad7eeb65503830346afd9c7

like i wouldnt round up the ones right?

its the same logic on both sides?

[gray isle]

the ths are important

tens is different from tenths

round appropriately depending on what they ask for

[hardy geyser]

round to the nearest tens 34 >>>> 30? right?

[gray isle]

yes

[hardy geyser]

round to the nearest ones 7 >>> 7?

[gray isle]

yes

[hardy geyser]

oh ok i see the difference and similiarties thank you sensei ramonov

[twin condor]

To my understanding since it said at x = 0 i can remove absoulte value and write it as x ² since 0 is not a negative number and then i would get 2 as the second derrivitave am i right?

[shell heron]

yes

[twin condor]

Kk thx

[shell heron]

no worries

[ancient creek]

wait but shouldn't this be indeterminate? cuz x*|x| can be written in piecewise form as:

f(x) = { x^2 x => 0
{ -x^2 x <= 0

thus,

f''(x) = { 2 x => 0
{ -2 x <= 0

lim x-> 0 of f''(x) should thus be indeterminate

(pls confirm my answer with others also)

[fringe yoke]

That's smart

I never thought about dealing with absolute values like that

[wise sigil]

This shows that f'' can no tbe continuous at x = 0
But really f' isn't even differentiable there

[twin condor]

But it said at x = 0 ?

[wise sigil]

What you have is f'(x) = 2|x| and from this the whole situation should be pretty clear

[twin condor]

So no soultion here ???

So 2 ??

[ancient creek]

ah I see, thx

[ancient creek]

no there is no solution

[fringe yoke]

@ancient creek

What do you mean?

It is continuous

and differentiable

at x=0

[ancient creek]

it is not differentiable at x = 0 for f'(x)

[fringe yoke]

oh for f'(x) ?

one sec

[ancient creek]

yes

[fringe yoke]

Ohhhh

It's continous

but non differentbaible

I get it

[twin condor]

So no solution for f’ and f’’ ?

[fringe yoke]

f'(0)=0
f''(0) = DNE ( f'(0) is non differentiable at x=0)

[ancient creek]

Yup

[fringe yoke]

That's a great problem to think about

[twin condor]

Kk also just checking f’ of absolute value of x at x = 2017 is 1?

[fringe yoke]

??

[twin condor]

Anthor question unrelated to the one above

Wuts the 1st derrivitave of Absolute value of x at x =2017

Is it 1??

[fringe yoke]

f(x) = |x|
f(x) = {x for x>=0}
{-x for x<=0}

f'(x) = {1 for x>=0}
{-1 for x<=0

2017 >= 0. Yes
So:
f'(2017) = 1

f'(1241284180294812094812) = 1

f'(0.00001) = 1

[twin condor]

Kk thx alot

[fringe yoke]

In my calculus class we never learned about absolute values like this

this is so interesting

[twin condor]

Neither did we XDDD

First time seeing this

[fringe yoke]

But for that one you just sent, f''(0) = DNE

Yeah I am not comfortable with absolute values

I see them sometimes on harder problems

and I just give up

Problems like this are good to become more comfortable with them

Than kyou

[twin condor]

Bwt when i change absolute value to piece wise do i always do
{ blah blah. X>=blah
{blah blah x<= blah

Like the = i put on both ?

I used to only put on 1 so just cheacking

[fringe yoke]

XD

Idk either

I just graphed it

and messed around with it

Hmm let me think

[twin condor]

Me during math class XD
thanks aloooot tho really helped me understand

[fringe yoke]

|x| = -x for negative values of x
= x for positive values of x

x|x| = -x^2 for negative values of x
= x^2 for positive values of x

[fringe yoke]

This is probably more complicated than it seems

What grade math is this btw?

[twin condor]

12 ( finaly year of highschool)

My teacher taught us everything and even stuff outside of book but never seen this at all XD

[noble sinew]

Only do on one

[fringe yoke]

Wait you are done with high school

why are you still doing this ?XD

[twin condor]

I have something like a goverment exam done after u finsh highschool

[fringe yoke]

oh

best of luck to you

[twin condor]

Kinda like a 3rd semester exept u only do exams and have 1month holiday to prepare

Pretty similare to gaoka (china college exam thingy)

Name probably wrong

[shut elk]

hi guys, can someone elucidate differentiation for me? the kind folks of the discord have already helped me out a little but there's something i want to confirm/disconfirm

so for example, the first derivative of say.. the volume of a sphere is it's surface area.

and, a more appropriate example for my question is that of $d = 4.9t^2$

[ocean seal]

ex

[shut elk]

which i believe has first derivative of a linear proportionality $y=9.8x$

[ocean seal]

ex

[shut elk]

so the above was the freefall equation and its first derivative is this straight line passing through the origin with gradient 9.8

does this mean that.. the rate of change of d=4.9t^2 is the 9.8?

it's likely i am thinking about this all wrong, thank you for your patience in advance lol.

[fringe yoke]

Would you mind watching a youtube video about it?

This guy does a great job

[shut elk]

i'd be very happy to

[fringe yoke]

Let me find it

[shut elk]

much obliged.

[fringe yoke]

@shut elk

here is the entire playlist of calculus intuition videos

https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

it takes around 4hrs

Here are some derivative specific ones

[shut elk]

many thanks, i was hoping it would be "Differentiation by Tim O'Brien"

[fringe yoke]

https://www.youtube.com/watch?v=9vKqVkMQHKk&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=2

https://www.youtube.com/watch?v=S0_qX4VJhMQ&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=3

https://www.youtube.com/watch?v=CfW845LNObM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=12

[shut elk]

thanks again!

[fringe yoke]

Yeah make sure you watch them

If you want to UNDERSTAND

If something doesn't click immediately, you can rewatch a few times

[alpine sable]

Is the channel free now?

[fringe yoke]

go

[alpine sable]

So I have an arithemtic progression a1,a2,a3... and i got an equation a1+a3+...+a2019+a2021 = 2022 (this is a sum of elements with odd indexes) and now I need to calculate a2+a10+a1000+a2021+a2022. How do I do this?

[strong furnace]

Did you get the trig question from earlier correct?

[alpine sable]

yes

i used the tan sum formulas

ty

[strong furnace]

I would want to know how that worked out(in DMs) but let's get rid of this one first

[alpine sable]

actually I really need to do some other math problems

If you really want to I can tell you how it worked out tomorrow

[strong furnace]

I don't want the whole solution I solved it myself I just want your first few steps

Since my solution was a little iffy

[strong furnace]

The first expression is an AP with common difference 2d

2nd expression is a multiple of first expression

Just write it down in the form a_1+b*d for some b

[chrome monolith]

Can i get help

[humble ore]

What is the definition of modulus?

[chrome monolith]

Sqrt a^2 + b^2

Idk y in the ans key they have a half outside the bracket

[glass lichen]

yeah, cause you have 1/2(something on the unit circle of the complex plane)

[chrome monolith]

Uh

[glass lichen]

and unit circle is defined as |z|=1

[chrome monolith]

Does it have anything to do with the i