precalculus

[proud raven]

lemme screw with it for a sec

[surreal crest]

k(k+3)/2(k+1)

[bronze sandal]

i see

[velvet blade]

Also another doubt, give me a sec

[bronze sandal]

would i be able to apply the sum of an arithmetic series here

[surreal crest]

yep

lemme show a hint on how

wait

lemme see maybe

[velvet blade]

Did he just ask to plot it all out one number at a time?

[bronze sandal]

when are you not able to apply the sum of an arithmetic series

[surreal crest]

$\sum_{k=1}^{n-1} \frac{k(k+3)}{2(k+1)}$

[obsidian monolith]

gristle:

[surreal crest]

you cant apply it here

[bronze sandal]

:(why not

[surreal crest]

cuz u cant

theres no use for it

[bronze sandal]

wait so if i wanted to rewrite in terms of n

i cant?

[surreal crest]

maybe

but it isnt gonna use n(n+1)/2

[bronze sandal]

ahh i see

uhh

is there any way to rearrange that? maybe using the harmonic number?

[surreal crest]

hmm?

[bronze sandal]

im trying to find the average number of comparisons in insertion sort

ive seen other people simplify their summations using the harmonic number

[surreal crest]

my algos memory is weak, havent studied that topic in a long time

[bronze sandal]

its all good the context isnt too important

[proud raven]

@velvet blade https://mathinsight.org/applet/polar_coordinates_map_rectangle

check out this applet

[surreal crest]

but no you cant really simplify it

even with harmonic series

[bronze sandal]

aw man i guess im just gonna submit the summation lol

[surreal crest]

well lets see if we cant derive anything

set n=2

[proud raven]

do you see how the inequalities are present in the polar form?

[surreal crest]

you get 4/4 = 1

[velvet blade]

Yes I'm getting it

[proud raven]

then say like r=0=r_1, and r_2 = r, and 0=theta_1 and 2pi=theta_2

[surreal crest]

set n=3, you get 1 + 10/6 = 1 + 5/3

[proud raven]

then the "rectangle" is just a circle

with radius r

[surreal crest]

= 8/3

[bronze sandal]

im sorry, but what are we trying to derive

[proud raven]

you can also sort of understand this is in like

[surreal crest]

the sum in terms of n

[bronze sandal]

ahh ok

[surreal crest]

set n=4

[proud raven]

try writing those inequalities in a similar way for rectangular coordinates

[bronze sandal]

i know the sum works if thats what youre trying to show

[proud raven]

so you see that a washer/disc,section of circle whatever you wanna call it

[bronze sandal]

and i dont need to show work deriving it

[surreal crest]

we get 8/3 + 18/8 = 8/3 + 9/4

[proud raven]

is the rectangle of polar coordinates

[surreal crest]

,wolf 8/3 + 9/4

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by gristle#9192

[surreal crest]

n = 4 -> 59/12

so yeah it isnt simplifiable

in any obvious way

[bronze sandal]

rip

thanks for helping tho

[surreal crest]

np

[bronze sandal]

i didnt realize it wasnt simplifiable

[tough thicket]

When you’re in calculus ab and can’t follow a precalculus conversation

[surreal crest]

@exotic hollow very cute

[tough thicket]

😭

[velvet blade]

@proud raven is there any way I plot this on desmos?

[proud raven]

hmm ill have to remember

you need to switch the axes

[tough thicket]

I don’t like sigmas

[proud raven]

instead of x,y to r,theta

[bronze sandal]

o lol this is a little bit beyond precalc, it just uses precalc material

should i have not posted here>?

[tough thicket]

I don’t know, I dont remember any sort of precalc class

Or if I’ve ever even taken one

[bronze sandal]

rip:(

is there a dedicated channel for more CS related stuff

[tough thicket]

I did algebra 1-2

CS?

[bronze sandal]

comp sci

[tough thicket]

Computer science?

Is that a class?

Computational something?

[bronze sandal]

huh ok

[proud raven]

yea im not sure researcher

[tough thicket]

Idk what comp sci is

[bronze sandal]

oh sorry its computer science

[tough thicket]

I didn’t even know that was a class

I’ve learned a lot today

[surreal crest]

just drop computer science lol

do pure math

[bronze sandal]

that sounds kinda scary lol

[surreal crest]

it is

[bronze sandal]

i think the avg gpa for math majors is like 2.4

[surreal crest]

but its so rewarding

eh

[tough thicket]

Unfiltered math

[surreal crest]

i got a 5.0 math gpa

and

[bronze sandal]

shoot

[surreal crest]

i hardly even try

u can breeze thru it if ur serious about it

[tough thicket]

I feel like after 11 years of schooling I’m only just now tickling the surface of math

[bronze sandal]

i heard theres no numbers in the upper divs?

[surreal crest]

what do u mean no numbers

like

[bronze sandal]

im not sure tbh

[surreal crest]

you dont work with numeric calculations

thats true

[bronze sandal]

is it all letters

[surreal crest]

no its algebra mostly

[bronze sandal]

ahh i see

i dont like algebra

[surreal crest]

thats not the algebra ur used to

[tough thicket]

Lol

[surreal crest]

u have actually never seen this algebra

[bronze sandal]

what kinda algebra are we talking about

[tough thicket]

Does math

[surreal crest]

abstract algebra

[tough thicket]

doesn’t like algebra

[bronze sandal]

oh:(

[tough thicket]

[surreal crest]

group theory rep theory galois theory blah blah blah

rings fields

blah blah blah

[bronze sandal]

glad i dont need to take those things

[surreal crest]

u should

they'd make you a better computer scientist

[bronze sandal]

it prob would:(

[surreal crest]

and i say that as someone who hates algebra

[tough thicket]

Can math be a hobby

[surreal crest]

yep

[bronze sandal]

yeah i dont understand a lot of the math theory in some of my classes lol

[tough thicket]

How does one hate algebra

[proud raven]

on the second one im like

on #6

[tough thicket]

Isn’t that the basis on which most math is founded upon

[bronze sandal]

@tough thicket algebra gets harder lol

[surreal crest]

not really

[tough thicket]

What other direction can math go before algebra

[surreal crest]

(yes but no)

well

generally theres like

4 main fields u can really go into

[proud raven]

@velvet blade what were you confused about on #6

[surreal crest]

algebra, analysis, topology, and maybe u can tack on number theory

i just do analysis

the others suck

[bronze sandal]

wait @surreal crest do you know stats i kinda need help on that too lol

[surreal crest]

but analytic number theory kinda cool tho

yes

[bronze sandal]

or welll its just algebra i guess but in stats class

[surreal crest]

ask in appropriate channel tho

brb water

[tough thicket]

Isn’t topology the place for sociopaths

[surreal crest]

topology isnt too terribly tough

analysis can be nastier

[tough thicket]

And number theory is for masochists

[surreal crest]

number theory is for people who dont need to pay rent

[tough thicket]

The philosophical equivalent to math

Got it

[velvet blade]

@proud raven Sorry for late reply. I was confused on what to do in that problem

[proud raven]

i think its just asking like

what the shape of each of those things are

can you repost

[proud raven]

how do you feel about a

not that it should immediately jump out at you, but if you try out a number of points or recognize the form you should see the shape

[velvet blade]

is it just 8 cosx, 8 sinx?

[proud raven]

yea

[velvet blade]

seems like a circle thing

[tough thicket]

Is a problem that involves trig functions truly a precalc problem?

[velvet blade]

I guess

Is a problem that involves trig functions truly a precalc problem?
yes

[proud raven]

so yea, thats what i think this is

[tough thicket]

Shit I’m stupid I was thinking pre algebra

[proud raven]

if youre comfortable with the whole

like image thing

so you see how y=3 is a line

then this transformation turns a line into a circle

[velvet blade]

Like I was thinking how x= rcos(theta) and y=r sin(theta)

[proud raven]

which is really just a line i guess

but a line has different forms in different coordinate systems

how about b

[velvet blade]

Okay, so mapping is all about association

[proud raven]

i think in the context of this problem, its more about letting you see what these forms look like in different coordinate systems

[velvet blade]

how each point morphs into another through a function?

[proud raven]

like do you see how a circle is really just a line?

or a rectangle can be a circle

like not so much that theyre the same, but that circle is the polar form of a rectangle

and a circle is the polar form of a line

in a way theyre the same thing

its just the system thats changed

[velvet blade]

ohh...

wait is this something related to topology in UG?

changing maps?

[proud raven]

oh idk

im also like

since i never took precalc i dont want to abstract the purpose or stuff too much

because i still am sorta worried im misinterpreting

[velvet blade]

Ohh

[proud raven]

but like

i mean on b

you see how that vertical line in rectangular

when you move it over with that map

it kind of removes the thing that should give you that circular behavior

because x is constant

[velvet blade]

in the website?

[proud raven]

i mean on problem b

see how if you fix y, you just end up with a circle of radius 2^y

but if you fix x, you get exponential type behavior (i think)

[velvet blade]

No if you fix x you'll get a line

[proud raven]

in the preimage yea

[velvet blade]

it's just plotting points at the same angle

but different r

[proud raven]

in the image i think its exponential?

lmc

i think if youre moving from rectangular to rectangular as seems to be the case

hmm but im not really certain maybe i should play with it more

[velvet blade]

Yeah I screwed with it on the website

you'll get a ray travelling away from the origin

You're not changing the angle. Only it's radius

[proud raven]

oh

yea i guess youre right

since x always is y

so its a ray leaving at the angle theta

[velvet blade]

Yeah

[proud raven]

where theta is equal to what you fixed x as

[velvet blade]

yeah

[proud raven]

cool

[velvet blade]

[proud raven]

yea this stuff is a bit of a mindwarp without computer tools sorry lol

[velvet blade]

bruh only thing that bothers me is I'm not able to figure it out how to do it in desmos

[proud raven]

yea im not sure im not very good with desmos

i think youd have better luck with python or something

[velvet blade]

Yeah I downloaded VS code yesterday. I should start with learning today

[proud raven]

@velvet blade i guess also this is a good chance to do the like

maybe screw with one or two concrete values

but once you see the pattern

just solve it like

what is the form of (2^y cos x, 2^y sin x) where x=c with c in R

type of thing

[velvet blade]

Yeah I got that

I got the idea, so I got the jist of those special cases in my head

Moving to next topic

[proud raven]

[willow bear]

mumble mumble this map will come back in a slightly different form to haunt you later

[bronze sandal]

Yeah I downloaded VS code yesterday. I should start with learning today
@velvet blade idk too much about ur math problem but if u wanna plot stuff in python, matplotlib might be useful

[velvet blade]

mumble mumble this map will come back in a slightly different form to haunt you later
did I do something

like screw something up?

[willow bear]

no

[velvet blade]

@bronze sandal I don't know anything about python, I should start learning today

[willow bear]

i mean, you should have gotten the result of "circle of radius 4 centered at the origin"

[velvet blade]

if y=2

yes I got that

I understood that concept

[willow bear]

you may or may not see something very similar way later on

i'm not gonna spoil

[velvet blade]

i'm not gonna spoil
Bruh is this going to be a horror movie or something

[willow bear]

no

[velvet blade]

okay

[bronze sandal]

if you have 0 experience with python, it might be kinda hard to install packages and run programs in the terminal. youve gotta use this thing called pip to install stuff. you can try writing code in a google colab notebook. you will have access to matplotlib and a ton of other nice things and from there u just have to learn the syntax

[velvet blade]

Is google colab better than VS code?

[bronze sandal]

uhh depends what ur doing. i dont rly use google colab, but you dont have to set up ur coding environment. i personally like vscode better just bc im more familiar with it but google colab might be easier to use if ur just getting started

youd be making 'notebooks' which are can contain little python code snippits as well as text explaining what its for. its pretty useful for data science stuff. its also all run on the cloud:)

[velvet blade]

Oh okay, so colab does compiling in cloud?

[bronze sandal]

yup. it doesnt rly make a difference for u but for more computationally challenging machine learning problems, you can run things with google colab without shredding ur own computer

[velvet blade]

Okay thanks

[viscid thistle]

Where do probability questions go?

#probability-statistics or any #question channels if they are free

Ah

Thanks

[glossy trench]

anybody know how to do this??

[maiden pelican]

Find the sum and the product of the roots (real and complex) of x^3 + 3x^2 + 7x − 11 = 0.

How do you do this

[bold meadow]

Vieta's formula

[maiden pelican]

Oh, thanks. I didn't know that existed

[crisp crystal]

I'm trying to understand how to graph this equation, y=sin2 theta but i just can't wrap my head around it

[wintry yacht]

Is there any way to know that a function is one-to-one without graphing this function?

Not sure if there was a way of checking if a function is one-to-one without using the horizontal line test

[blissful ridge]

If f(x)=f(y)

Then if you could show that x=y

Then it is an one to one function

[uncut mulch]

first derivative

consider strictly increasing/decreasing continuous functions

[wintry yacht]

How do I do this by derivative?> first derivative
@uncut mulch

[uncut mulch]

calculus

[misty ocean]

cos2a (sin a=5/13 cos a=-12/13)

someone help?

[sour hemlock]

do you know the trig identity for cos2a

[misty ocean]

its cos^2 a- sin^2 a right?

[sour hemlock]

yes

[misty ocean]

but like idk how to find that

[sour hemlock]

there you go

solved

ok, so you are asking us the derivation of that trig identity?

[misty ocean]

yes

[sour hemlock]

well, plenty of online resources for that

you could do cos(a + a)

write it out

and see for yourself

[fading lodge]

can anybody help with mathematical inductions

[misty ocean]

ohh ok

thx

[fading lodge]

how do i solve 2^n+1 is divisible by 3

[sour hemlock]

so, for what values of n is (2^n) + 1 divisible by 3?

[fading lodge]

uhm it says that for all n is the element of Z^+

so does that mean for all values of n?

[sick steppe]

all positive integers n

[viscid thistle]

you can probably do it with a proof of induction i'd think

idk

[sick steppe]

$\mathbb Z^+ = {1,2,3,...}$

and yeah it's an induction question

[fading lodge]

wait

[viscid thistle]

ah pog

[fading lodge]

i’ll send

what ive done so far

[viscid thistle]

base case is super easy

👍

proving the n + 1 th case is true is something i cannot do in my head

[obsidian monolith]

moshill1:

[fading lodge]

so basically 2^1+1 is 3 which is divisible by 3

then step 2 is inductive?

[sick steppe]

2^1 + 1 = 3 = 3(1)

then yeah inductive hypothesis

[fading lodge]

2^(k+1)+1 should also be divisible by 3

[viscid thistle]

2^(k+1) + 1 = 2*2^k + 1

[sick steppe]

dont do the question for them

[viscid thistle]

oh

ok

[sick steppe]

@viscid thistle

it's math help not math solve

[viscid thistle]

good point

👍

[fading lodge]

yeah im up to that point

i dont know what to do anymore

from what i researched i need to split up 2x?

[sick steppe]

there's no x

only variable is k

[fading lodge]

so what does this mean?

[sick steppe]

that's 2 times

if you type math you use * for multiply

[fading lodge]

oh sorry

i forgot

my bad

[sick steppe]

it's fine lol

[fading lodge]

so i have to split up 2*?

but how do i do it

1* and 1*?

[viscid thistle]

What are you talking about?

Im lost

[sick steppe]

2^n + 1 divisible by 3

n is pos integers

[viscid thistle]

How about n=2

[sick steppe]

yeah i just did it, it's not true

[fading lodge]

yeah but i also have to prove that 2^(n+1) +1 is true right?

or disprove

[viscid thistle]

You cannot prove this

[sick steppe]

if it's disprove then any even n works to disprove

[fading lodge]

okk i see

it says to either prove or disprove

and since it said that n is all elements of

positive integers

[sick steppe]

that would've been nice to know lol

[fading lodge]

then its wrong right?

[sick steppe]

you have to disprove it

[viscid thistle]

if n = 2k+1 then the equality holds

[void cave]

Does anyone know how to solve this

[fading lodge]

in this example why did it split 3*

?

[void cave]

If u know ping

[cobalt swallow]

@fading lodge 3 = 1 mod2, 3^2 = 1 mod 2 , 3^3 = 1 mod2 ...... 3^k = 1 mod 2 where k belongs to N.

[fading lodge]

whats mod2?

[cobalt swallow]

when you divide 3 by 2 you get remainder 1

https://brilliant.org/wiki/modular-arithmetic/#:~:text=Modular arithmetic is a system,modulus)%20to%20leave%20a%20remainder.

[sick steppe]

@cobalt swallow just use the word divide, we dont need modulo arithmatic

[cobalt swallow]

@sick steppe why are you so anti for a thing, mod works fine. Just because you don't like that doesn't mean it isn't a solution.

[sick steppe]

Im not anti

[viscid thistle]

Modular arithmetic is unnecessary

[sick steppe]

you just dont learn modulo until uni, not high school

[viscid thistle]

Especially if you are not used to it

[fading lodge]

yeah im only gr11 hehe

[cobalt swallow]

@void cave you can use binomial theorem as well expand 3^k = (1+2)^ k

[viscid thistle]

...

[sick steppe]

what

[void cave]

@void cave you can use binomial theorem as well expand 3^k = (1+2)^ k
@cobalt swallow how exactly

[fading lodge]

i think he meant to ping me

[viscid thistle]

Let the guy use induction

[void cave]

I think that i should just make all the roots n

[fading lodge]

i think i got the answer

[void cave]

Or 2n

[sick steppe]

@void cave that wasnt for your question

[void cave]

@void cave that wasnt for your question
@sick steppe that guy pinged me

[sick steppe]

yeah, your question has nothing to do with 3^k, it's radicals

[cobalt swallow]

@void cave you get all powers of 2 when you expand (1+2)^k except there is one 1 when you subtract it by 1, you get even number

[sick steppe]

why must you insist on over-complicating things?

[viscid thistle]

This is so unnecessaryyyyyyy

[cobalt swallow]

Ok! I am done . People don't really appreciate help in this precalculus section Pity!!. They are standard techniques always used in number theory.

[void cave]

@void cave you get all powers of 2 when you expand (1+2)^k except there is one 1 when you subtract it by 1, you get even number
@cobalt swallow even if i do that , the other side still makes a problem , how about we have the same root power n or 2n

Ok! I am done . People don't really appreciate help in this precalculus section Pity!!. They are standard techniques always used in number theory.
@cobalt swallow no don't go

[sick steppe]

@cobalt swallow this is high school, not uni. when did you learn number theory in high school?

[sick steppe]

,rotate

[viscid thistle]

$3^{k+1}-1=3\cdot 3^k-1=3(3^k-1)+2$

[fading lodge]

oh wait a sec

[void cave]

Damn now i have no one to help me

[fading lodge]

oh there

[sick steppe]

yeah @fading lodge you need to disprove the statement

n=2 will suffice

[obsidian monolith]

HoboSas:

[fading lodge]

did i disprove it rigjt

[cobalt swallow]

@void cave sorry!! It was mahat's question

[fading lodge]

right*

[sick steppe]

just write out n=2 case and you're done

[void cave]

So em

[fading lodge]

kk thanks

[cobalt swallow]

@void cave sorry

[fading lodge]

no worries @cobalt swallow i got the answer

[void cave]

Damn u wrong pinged me

Right ?

[fading lodge]

i was overcomplicating things for myself

[obsidian monolith]

HoboSas:

[fading lodge]

how am i supposed to answer mathematical induction when there is no “n”?

[cobalt swallow]

@void cave since I disturbed you, see here 4- x^2 = (2+x )(2-x) . Use this . Bye! Good night

[void cave]

@void cave since I disturbed you, see here 4- x^2 = (2+x )(2-x) . Use this . Bye! Good night
@cobalt swallow i did and yet no way out but okay peace

[viscid thistle]

Maybe square both sides

[fading lodge]

how am i supposed to solve this when there is no n

[viscid thistle]

Can you send the task?

[fading lodge]

the whole task?

[viscid thistle]

Prove or disprove

How about b=1 a=2

[fading lodge]

but i think i need to use mathematical induction

[viscid thistle]

Prove or ** disprove**

How about b=1 a=2

[fading lodge]

yeah then its wrong

[viscid thistle]

Yes

Same thing for 2nd

[fading lodge]

how do i solve it through mathematical induction?

like the

k+1 thingy

cuz its telling me to prove/disprove it using mathematical induction 😐

oh wait

i dont need to

since step 1 is already a fallacy

YES

Thanks @viscid thistle

[viscid thistle]

I dont think you need induction to disprove

[sick steppe]

proving something isnt true is just find a counterexample

[fading lodge]

yeah i just realized that

thankss

how do i do number 1 tho

[viscid thistle]

wtf

i j in R??

what are even x and y

[fading lodge]

idrk it doesnt state it in the problem

[ripe adder]

I need help on a systems of equations problem

this woman has 25000$, she invested it in 2 companys

one at 10% interest, one at 8% interest

she received 2200$ in interest after 1 year

how much did she lend to each buisness?

Idk how to find the answer as I dont know how to formulate it as a system of equations

[fading lodge]

I =prt right?

[ripe adder]

I thought so

but how do use that equation in context of a system of equations

[fading lodge]

divide both sides by rt and u get the formula for p

[ripe adder]

so

2200 = P0.08t

[fading lodge]

yeah

[ripe adder]

2200=(p)(0.08)(1)

that doesnt make sense because 2200 is the total return

so idk how to split that

into two "cases"

or equations

[fading lodge]

ohh i see

i also dont know how to split them

[ripe adder]

same

[fading lodge]

lets wait for a grade higher than us

xd

[ripe adder]

<@&286206848099549185>

[viscid thistle]

anyone willing to help me on the question tan(arccos(-6/7))
need to find the value

what have you tried

wdym

have you tried doing anything before posting this here

like tried to solve the question?

or did you just find the problem and directly posted it here with no attempt at solving it

like tried to solve the question?
uh yeah

no why would i do that

some people do unfortunately

but what did you try anyways

wdym

do you know how to solve it?

uh, yeah i do?

mind if u help me in a vc then?

i'd prefer not to

?

are u going to help me?

yes, but here?

wdym "but here?"

where else should i ask

lmao

what

by here, i mean i'm helping you here

can you answer my question

so why add the question mark?

i added it as an interpretation to as why are you asking such

and tbh i am looking to vc since text is too slow

.....

bruh

tbh u are kinda weird man

oh wow?

[ripe adder]

I need help on a systems of equations problem
this woman has 25000$, she invested it in 2 companys
one at 10% interest, one at 8% interest
she received 2200$ in interest after 1 year
how much did she lend to each buisness?
Idk how to find the answer as I dont know how to formulate it as a system of equations

[viscid thistle]

is it weird to assume that if you ask help here and i answer, then i'm weird for you being reluctant to cooperate with me?

i am looking at your chat history

and so far i havent seen you help anyone

[ripe adder]

lmao

[obsidian monolith]

Ronert XII:

[viscid thistle]

other than questioning them if they actually need help or to cheat

idk how u even got the helpers role lmao

[ripe adder]

@viscid thistle has helped me with math for 2 years now

if not more

I think tbh they have helped me more 1 on 1 than any math teacher individually

[viscid thistle]

show me one message in this server where he helped u with math

[ripe adder]

im not the one making the claim

you also dont seem to understand that these people are tutoring for free

[viscid thistle]

oh so, first off, you judge overgeneralising by looking at a chat history of one day, and you'd rather help someone being reluctant to cooperate?

[ripe adder]

its a resource, not a service

[viscid thistle]

like that's just messed up

i asked for help

don't assume genders

and he just keeps asking questions

that's bad

and putting question marks after every sentence

BECAUSE YOU DON'T WANT TO COOPERATE

like some philosophical weirdo

[ripe adder]

lmao

[viscid thistle]

and i ask if he can vc to help me

[ripe adder]

this guy is a troll

[viscid thistle]

then he just says ....

like what

i'm trying to establish a help system where i build intuition and you were rejecting it

[ripe adder]

nully nobody does VC tutoring in this server

[viscid thistle]

don't manipulate my words

[ripe adder]

or its rather rare

[viscid thistle]

that's not what i said

[ripe adder]

well

he should understand that

[viscid thistle]

obviously there was misinterpretation here

since we are texting

this is why id rather vc

yeah and you started the misinterpretation

look at you

like a 5 year-old pointing fingers

how mature

yes keep going hold up

can you stop being so inmature and leave this channel if you aren't asking for help

[sick steppe]

Probably could've had the answer by now

[viscid thistle]

indeed

[ripe adder]

i doubt he is looking for the answer truly

[viscid thistle]

bruh

you guys are weird

looks like a troll

[ripe adder]

my thoughts exactly

[sick steppe]

Ok good luck on your endeavours Nully \s

[viscid thistle]

lmao

thank you

moshill

@ripe adder can you repost your question after this non-sensical and ilogical conversation just ended

[sick steppe]

forgot the \s

[ripe adder]

wait nvm

nvm

I need help on a systems of equations problem
this woman has 25000$, she invested it in 2 companys
one at 10% interest, one at 8% interest
she received 2200$ in interest after 1 year
how much did she lend to each buisness?
Idk how to find the answer as I dont know how to formulate it as a system of equations

@viscid thistle

[obsidian monolith]

Ronert XII:

[ripe adder]

ill post a picture of the problem so its clearer

#61

[tough thicket]

What do you know and don’t know

[ripe adder]

Uhh

[viscid thistle]

as i'd love to help you rn @ripe adder , i'll leave this to Mau, my motivation kind of went away after that

[ripe adder]

I am stuck on how I can turn this into two equations

sounds good @viscid thistle i understand

[tough thicket]

Actually @viscid thistle I misinterpreted this

I’m not great at system of equations

But I’m pretty sure interest is an exponential function

[ripe adder]

I was using I = (p)(r)(t)

but I can see how it may use a different formula

i am confused on which one though

[tough thicket]

So I mean

You have 25000

I’d set that equal to profit as x with the percentage as an exponential rate

Like 10 percent would be

x^0.1

And 8 as x^0.08

[ripe adder]

I see

[tough thicket]

That’s where I’d start but

I’m not the best at these kinds of things

[ripe adder]

But how do I use the 2200 to create two equations

Because those have to be equal to something right?

[tough thicket]

2200 is split between 10 percent interest and 8 percent interest

[ripe adder]

Yrs

But I don't think it's even

ly split

[tough thicket]

Yeah I wouldn’t think so either

[ripe adder]

How do I find the split I guess would be my question

[tough thicket]

I feel like it would start off with writing profit in terms of p

And splitting that somehow between a system of equations

I’d be just as lost as you are, and would also like to know how to go about this

[ripe adder]

Well we know that p1 + p2 = 2200

[tough thicket]

No

[fading lodge]

can i ask a q?

[tough thicket]

We know that p1^0.1 + p2^0.08 = 2200

[ripe adder]

Yes yes

So if we know that

I will try this on my own

[tough thicket]

You can also say that p1 + p2 = 25000

There’s two equations now lol

@fading lodge what’s up

[ripe adder]

Perfect

[fading lodge]

how do i express this as a sum or diff

[ripe adder]

Thanks @tough thicket

[fading lodge]

of a simpler logarithm

[tough thicket]

@ripe adder did that actually help lol

[ripe adder]

I have to math it out but it's a better start than I had before

[tough thicket]

Simpler?

[fading lodge]

wait i will send the directions

[tough thicket]

Aren’t you just splitting them up?

[fading lodge]

im not really sure how to do that

[sick steppe]

log laws

[fading lodge]

oh wait

i just found it

thanks

how about if its a fraction

is it difference?

[ripe adder]

@tough thicket i found it: 2200=(x)(0.08) + (y)(0.1), 25000 = x+y, x = 15000, y = 10000

[tough thicket]

Good job man that was all you @ripe adder

[ripe adder]

1 minute after solving it my professor gets back to me

[tough thicket]

Oh wow it didn’t involve exponential?

That makes a lot of sense though

@ripe adder

[fading lodge]

how do i solve a logarithm of a number if b=2^1/2

[whole vessel]

Same thing @fading lodge . sqrt 2 to the what is 16? Except we know that it needs to be squared twice as much, since sqrt 2 squared is just two. So sqrt2 to the power of 8 would be 16

so x = 8

@fading lodge Also yes, a fraction is difference.

[fading lodge]

so it’ll be sqrt2^x=16 right

[whole vessel]

yeah

And 2^x = 16 would be 4, we can do that in our head.

But since it needs to be squared twice as much, it is 8.

[fading lodge]

kkk thanks

[whole vessel]

You can think of it like:
for every sqrt2 squared, it is only 2

[fading lodge]

btw how can i isolate x from that equation

[whole vessel]

Sorry I didn't see your message until now. You can ping me, since I have this server muted. @fading lodge

x is already isolated here

[fading lodge]

ohh okk

[daring dew]

U could also square both sides and then u get 2^x = 256 so x is 8

[fading lodge]

how about this one?

im so confused of logs

@whole vessel

do i distribute the log

wait so its x^1

i think i got it

nvm

[whole vessel]

Ok, so do you know the property that you can raise the entire log term above the base, and it cancels it out?

Yeah exactly.

[fading lodge]

then its x=3

[whole vessel]

x^(logx(2x-3) = x^1

Yep, 3

[fading lodge]

wait what gets cancelled out?

the log itself?

[whole vessel]

yep, it just turns into what you were taking the log of.

[fading lodge]

ohhh okk

i think im starting to get it

[obsidian monolith]

TB:

[whole vessel]

ahhh there we go @fading lodge

Trying to figure out how TeXit works.

LaTeX

[fading lodge]

am i doing this right

1/4

x is 1/4?

[whole vessel]

Do they want the exact answer or a rounded one? Because x is already isolated.

[daring dew]

Idk cant read it properly

[fading lodge]

rounded one

[whole vessel]

Ok than just to the left side of the equation on a calculator.

[fading lodge]

the teacher wants solutions so as much as i just want to use my calcu

i cant

[whole vessel]

wait

She wants you to do fourth root of 27 in your head?

[fading lodge]

wait

i typed it wrong

its 4th root of 27

[whole vessel]

wait nvm

lol

[daring dew]

....

[whole vessel]

ok that actually makes sense

if it were cube root

[daring dew]

Idk why u would use a pencil

[whole vessel]

u sure its not cube root?

[daring dew]

Makes shit super unclear

[fading lodge]

nah its not cuberoot

its a ballpen but the ink faddd away

my only ballpen

[whole vessel]

4th root you can't really do exactly in your head.

Does your teacher want you to reverse the process and end up with a log equation?

Because that's weird.

[fading lodge]

oh its neg 1/4

nah

they want me to find x

i did it in a calcu and its -1/4

why is mine 1/4 what

[whole vessel]

good luck lol... you kinda need a calc for that

[fading lodge]

yeah

last question

[whole vessel]

I guess just round all the values lol?

[fading lodge]

how am i supposed to do this

with them having different uhm

idk what u call it

[daring dew]

Bases

[fading lodge]

bases

yeah

[whole vessel]

that is a great question

send pic of instrucitons

[fading lodge]

solve for x

those are the instructions

[daring dew]

rewrite first log ig

[fading lodge]

so is it gonna be log(x^2-1)-log(x+1)=9^3?

[tough thicket]

aren't log and log10 the same

[whole vessel]

yeah

[tough thicket]

because everything is in base 10

[whole vessel]

common log

[fading lodge]

oh wait i didnt know that

kkk

[whole vessel]

If not specified it is common log which = base 10

and natural log, or ln is base e

those are the two that are standardized

[tough thicket]

very pretty, e is

[whole vessel]

And that is coming from and avid banana eater.

[tough thicket]

is that a euphemism for being gay

[whole vessel]

No.

[fading lodge]

,rotate

[whole vessel]

I just like bananas.

[fading lodge]

is this correct

[tough thicket]

@fading lodge there's one last step lol

i'm pretty sure

[fading lodge]

is it to factor

[whole vessel]

do quadratic formula

[tough thicket]

actually nah nvm

does it require you to do that?

[fading lodge]

it wants me to find x

[whole vessel]

so yeah

[fading lodge]

so im assuming yeah

[whole vessel]

you have to solve completely

[fading lodge]

factored is

[tough thicket]

yeah subtract the 1000 over first

xd

[fading lodge]

oh ok wait

[tough thicket]

i'm not confident in that statement being a good idea

[sick steppe]

. . .

Log(a)-Log(b) = log(a/b)

just

gonna put this here

[tough thicket]

what's that gonna do for him there

[sick steppe]

x^2 -1 = (x+1)(x-1)

$\frac{x^2-1}{x+1}$

[fading lodge]

oh wait so is it (x^2-1)/(x+1)

[sick steppe]

log(fraction) = 3

yeah

[tough thicket]

what

[sick steppe]

log(x-1) = 3

[tough thicket]

wasn't it just x^2 - x - 1

[sick steppe]

x-1 = 1000

x=1001

[fading lodge]

yeah but

he made me realize something

since the log bases are the same anyway

i can just subtract first

[tough thicket]

is there still no formatting shortcut to add subtext

log(subtext "a")

[fading lodge]

ty everybody for the help

[tough thicket]

[fading lodge]

can i still use compound interest formula even if n=40 mins

nvm i think its better to just multiply

[viscid thistle]

how do i find the derivative of the inverse function given f(x)=4x^3

[fading lodge]

cube roots?

f(y)=4x^3
x=4y^3
cuberoot of x = 4y
cuberoot of x/4=y

correct me if im wrong

[viscid thistle]

shouldn't x be divided by 4 first?

[fading lodge]

i mean u would still have the same answer

[viscid thistle]

if we did it your way it would (cuberoot of x)/4, not cuberoot of (x/4)

[sick steppe]

y= 4x^3
x=4y^3
y^3 = x/4

[fading lodge]

how do i solve 10000 = 3200 * 2^x

solve for x

[sick steppe]

isolate for 2^x

then take logs of both sides

Unless it's a common base problem (which this isnt)

[fading lodge]

natural log right?

[sick steppe]

any log works

[fading lodge]

do i subtract the 2 numbers first or get the logs first

[sick steppe]

subtract what?

[fading lodge]

10k and 3200

[sick steppe]

why would you subtract them?

3200 * 2^k

[tough thicket]

you're not subtracting 3200 over

you can't

[fading lodge]

ohhh

so im just

putting it there?

[bold venture]

can someone go to general and help me plssss

[sick steppe]

putting it there?
@fading lodge what??

[tough thicket]

how would you isolate 2^k

[bold venture]

it’s due in 20 mins

[tough thicket]

hey invisible spy are you in precalc

[sick steppe]

@bold venture we dont help w/ exams/tests

[tough thicket]

hey invisible spy is it a precalc question

[fading lodge]

i have to isolate 2^x right

[sick steppe]

yeah

[fading lodge]

how would i isolate it?

[sick steppe]

. . .

[fading lodge]

oh

[sick steppe]

divide?

[fading lodge]

divide both sides

yea

[sick steppe]

yeah

[fading lodge]

sorry

im feeling extra dumb today

[bold venture]

@bold venture we dont help w/ exams/tests
@sick steppe it’s hw it’s due in 20 mins

[sick steppe]

if it has a due date/time not buying it

[tough thicket]

bro you're not entitled to our help anyway, and you sure are acting like it

[fading lodge]

wait so after i divide it i just take the logs of both sides rigjt

tyty

[bold venture]

bruh what did I even do

all im asking is for help

[tough thicket]

this is not you asking

i gave you help by saying it's a slope formula problem

you can google slope formula

[bold venture]

I didn’t see ur message @tough thicket

[viscid thistle]

what does it mean by 'restricing f(x) to a monotonic increasing domain'

[bold meadow]

That means if $x_2>x_1$, then $f(x_2)>f(x_1)$.

[obsidian monolith]

usernamephobic:

[viscid thistle]

#9, theres no number that add to 64 and multiply to 4

how do i do this

[bold meadow]

Quadratic equation solution.

[viscid thistle]

we haven't been taught that, is there a way to do it without it or

[bold meadow]

Completing the square then

[whole vessel]

take out 4 first though

so it is easier

[mystic umbra]

how to get from this to this?

the guy in the video said you can rewrite it first then fill in the + - signs later. so I guess there are 2^4 permutations of + and - signs?

[gentle vigil]

You have to complete the square and then factorize it

[mystic umbra]

completing the square is for degree 2 so I need to substitute out the A^2 to u first right?

that after all that I replace u with a^2

?

[gentle vigil]

Yes

[mystic umbra]

I working through it

I never learned this in school but now I'm teaching myself

[mystic umbra]

how do you use tex?

$\lefta^2-4\right^2=0$

[obsidian monolith]

galois:

[mystic umbra]

I don't see how to factor this into that final step

I did it again this time I got $\left(a^2-4\right)^2=12$

[obsidian monolith]

galois:

[mystic umbra]

maybe $\left(a^2-4\right)^2-12=0$ is better to factor?

[obsidian monolith]

galois:

[gentle vigil]

Are you sure about your simplification?

[limber compass]

Is that correct?

[mystic umbra]

@gentle vigil I am reading this from a website. my first time completing the square

two different tutorial two different answers

😦

none of them show the process of getting it into 3 terms (ax^2+bx+c)(ax^2+bx+c)=0

ok I checked again definitely $\left(a^2-4\right)^2-12=0$

[obsidian monolith]

galois:

[gentle vigil]

Yes that’s correct

But you don’t want to do it like that

Change the middle term to complete the square

[mystic umbra]

Change the middle term to complete the square
@gentle vigil I don't understand. what would I change it to?

oh i see

[tough thicket]

i always hated completing the square

[limber compass]

please help with my q ^ as well

[gentle vigil]

oh i see
@mystic umbra you got it?

please help with my q ^ as well
@limber compass sure, what is it?

[mystic umbra]

yes I do now

took me some time to work it out

all my books out here

[limber compass]

@gentle vigil scroll up

[mystic umbra]

using this book https://www.amazon.com/Schaums-Outline-Mathematical-Handbook-Formulas/dp/0071795375

page 2 special products and factors. all the identities right there.

I think x^3-12px>=R

@limber compass

[limber compass]

is what I did wrong?

please help 🙂

[gentle vigil]

@gentle vigil scroll up
@limber compass
I think your solution is correct, just you wrote the wrong sign at the end

[limber compass]

how is that?

[gentle vigil]

It should be >, not <

[limber compass]

why is that?

i had that but then I changed it

to <

because I thought since we want 3 roots.

that must be less than 0

when u minus both

do you get me?

[gentle vigil]

No it must be greater than 0

[limber compass]

why is that?

because

if you do

length of max - R = red.

then that will give u when it touches the line correct?

but we want it so that the ORANGE line is greater than the blue

and for that to be true

[gentle vigil]

@limber compass

[limber compass]

why did you square them?

[gentle vigil]

Because in question it’s written that exponent should be integer

Did you understand why t should be greater than R in order to get three roots?

[limber compass]

@gentle vigil Yes i understood : )

Can you help with this as well please?

[cobalt swallow]

@limber compass what is the condition of a quadratic equation to have two distinct real roots?

[daring dew]

Discriminant has to be positive

[cobalt swallow]

then the solution stares right at you Catherine

[vast ravine]

So uh.. i have a question, i'm doing double angle formulas and my teacher didn't go over what to do in this situation,

i need to find the double angles of sin2theta, cos2theta and tan2theta

theta is in qIV

i'm gien sectheta = 37/12

given*

soo since it's the reciprocal of cos, would cos be 1/37/12 or 12/37

man even typing that seems messed up

anyone here?

[fervent night]

@vast ravine so now that you have cos@ you can calcuate sin@ using √(1-cos^2@) which will be 35/37

sin2@ = 2 × sin@ × cos@
cos2@ = cos^2@ - sin^2@

[vast ravine]

i don't think i'm getting cos correctly

am i?

the fraction is confusing me

nvm it's making sense

cool yeah thank you

i appreciate it :]

[fervent night]

[ashen skiff]

How would you find cos(11pi/12) using sum and difference formula? I keep getting a weird answer

[tame mango]

Activities
With sets A and B. Determine the relations:

• R = (a, b); a is a multiple of b
• R = (b, a); b is power of a
• R = (a, b); a is a divisor of b
  A = {2, 4, 6, 8, 10} B = {4, 8, 16, 32}
  helpe

[glass venture]

@ashen skiff i would try to figure out cos(pi/12) first

which you can do using the half angle formula on cos(pi/3) a bunch of times

then do pi - pi/12

[viscid thistle]

which you can do using the half angle formula on cos(pi/3) a bunch of times

• one time on cos(pi/6)

[glass venture]

ok yeah true lol

[ashen skiff]

@glass venture we have to solve it using sum and difference formula

[uncut mulch]

consider 11 = 3 + 8

[viscid thistle]

consider 1 + 1 = 2

I am serious btw

[ashen skiff]

11pi/24 then...?

[viscid thistle]

why 24?

11/12 = 1 - 1/12 = 1 - (1/3 - 1/4) = 1 + 1/4 - 1/3

or $\cos(\frac{11\pi}{12})=\cos(\frac{8\pi}{12}+\frac{3\pi}{12})$

i ?

[uncut mulch]

where tf the i coming from

[viscid thistle]

wtf is that

that was a slipped-finger

it's edited

but the bot is lagging

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

see

damn I kinda liked it

[ashen skiff]

Oh ((-radical2)/4) (1+radical3) was right

[viscid thistle]

??

[sick steppe]

Oh ((-radical2)/4) (1+radical3) was right
🤔

[viscid thistle]

I guess radical = root

so $-\frac{\sqrt{2}}{4}(1+\sqrt{3})$

[obsidian monolith]

HoboSas:

[sick steppe]

no i know what they mean by radical

[viscid thistle]

radical is square root

[sick steppe]

ik

[edgy blaze]

question. It's been a while since i've done a lower level math class. If they want you to write quadratic equations you're given roots say, 2 and 5

you just (x-2)(x-5) and then foil right?

[sick steppe]

That'll give the family of quadratics w/ those roots, yes

[steel tulip]

how do I solve ln(ln(x)) = a?

Wait is it just e^(e^a)?

[viscid thistle]

Solve for x i assume?

[steel tulip]

yeah

[viscid thistle]

Then yes

[steel tulip]

ty

[vast ravine]

2sinϴ ≠ sin2ϴ right?

i have 2sin(π/12)cos(π/12)