precalculus

[midnight summit]

you can now see difference of squares

$(x-4)((x-1)-i)((x-1)+i)$

[obsidian monolith]

mohad12211:

[midnight summit]

you see it?

(x-1) represents a

and i represents b

is it clear? @kind pier

[kind pier]

im trying to understand that concept more.

[midnight summit]

it it's x+4 my bad

[kind pier]

so this crosses the imaginary plane at 1,0 twice?

but even if I don't get that 100% it's not super important I don't understand how to distribute all those terms together to get the polynomial

whenever I do it I wind up with i's that didnt cancel

[midnight summit]

the zeroes are 1+i and 1-i

on the complex plane they are (1,1)(1,-1)

$(x+4)((x-1)^{2}-i^2)$

[obsidian monolith]

mohad12211:

[midnight summit]

$(x+4)(x^2-2x+1)-i^2)$

[obsidian monolith]

mohad12211:

[midnight summit]

i^2 = -1

then it's -(-1)

= +1

$(x+4)(x^2-2x+2)$

[obsidian monolith]

mohad12211:

[kind pier]

so you have to do the imaginary ones first

[midnight summit]

yeah

it's easier

[kind pier]

calc 1 starts tomorrow

may jesus have mercy on my soul

[midnight summit]

don't worry calc 1 is not that hard lol

[viscid thistle]

,help

[obsidian monolith]

A brief description and guide on how to use me was sent to your DMs! Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[willow bear]

yeah... the hard part of calculus is algebra 😂

[wise salmon]

id say the hardest part of calculus is the word problems

"application" problems that is

[potent pulsar]

^

[spark cliff]

this might sound like a dumb question but if you’re writing the inequality w >= -8 in interval notation i know it’s (-8,infinity) but how do you know which parenthesis would be a bracket

whichever it’s pointing to?

[willow bear]

no, it'd be [-8, +∞).

square brackets mean the endpoint is included

round brackets mean the endpoint is not included

[spark cliff]

but why is it not infinity]

[willow bear]

because infinity isn't a real number

[spark cliff]

oh

[spark cliff]

is (x^-3y^4/5)^-2 simplified 25x^6/y^8

[willow bear]

do you mean $\left( \frac{x^{-3}y^4}{5} \right)^{-2}$

[obsidian monolith]

Ann:

[willow bear]

if so, yes

[spark cliff]

yeah wrong parenthesis whoops thank you

[vernal rapids]

Ehem

$[-8; +\infty[$

[obsidian monolith]

DarK:

[vernal rapids]

Is looks bizzare with one bracket being [ and the other being )

Like a bullet

[willow bear]

it also looks bizarre with the bracket pointing outwards

it looks like something you could impale yourself on

[viscid thistle]

[frozen needle]

reverse brackets

[spring thunder]

so french are sadists @willow bear

[vernal rapids]

$\big]-\infty;+\infty\big[$

[obsidian monolith]

DarK:

[vernal rapids]

Impale yourself on both infinities

[kind pier]

when you're doing synthetic division

of lets say a 6th degree polynomial by a third degree polynomial that is factorable

can I factor the third degree and synthetically divide using each of the two factors one at a time?

or does it not work like that

[fleet granite]

wdym

[willow bear]

it does not work like that i'm afraid

[kind pier]

okay if I have $2x^4-x^3+9x^2 divided by x^2-4

oh dam

[willow bear]

$\frac{2x^4 - x^3 + 9x^2}{x^2 - 4}$

[obsidian monolith]

Ann:

[kind pier]

i cant just run synthetic divison with 2 and negative 2

[willow bear]

no

[kind pier]

one by one then right?

ah ok

I noticed that when they were factors it was working out

[spark cliff]

$x<18/{x-3}$

[obsidian monolith]

burnt toast:

[spark cliff]

we’ll go with it

so can you multiply by x-3 to eliminate the denominator

and then divide by 3

[willow bear]

did you mean $x < \frac{18}{x-3}$

[obsidian monolith]

Ann:

[spark cliff]

yes

i have no idea how to use this

[willow bear]

if so, no, you cannot multiply both sides by x-3, because x-3 is not sign-constant.

the very first thing you should do whenever you encounter a rational inequality is to bring everything to one side and write it as a single fraction

then factor everything as far as possible

then make a sign table

[spark cliff]

what if you can’t factor anything lmao

sign table what

[willow bear]

ok have you ever solved any rational inequalities before

[spark cliff]

no cause i have zero idea what i’m doing

i’m so list right now

[willow bear]

ok have you ever solved any polynomial inequalities before

[spark cliff]

yeah

[willow bear]

https://www.youtube.com/watch?v=gfnVHwhEe6U here i found you a video

[spark cliff]

thank you

[tropic crown]

Is this right?

Solving for the indefinite integral

[rare galleon]

Yea

you forgot the -2/3

but yea is correct

[white schooner]

can someone help me find the center and radius of the function x^2 +y^2 -6x=7

[native sequoia]

complete the square on x^2-6x

[white schooner]

hmmmm y^2 isnt included?

[native sequoia]

no that separate if we are trying to get into a form like
(x-h)^2+y^2=r^2

[white schooner]

yes the standard equation

im stuck in here

what will i do in the y^2

[native sequoia]

not sure how you got 5

[white schooner]

oooohhh sorry

typo error

[native sequoia]

ignore the y^2 it's already in the form (y-b)^2

you want to convert x^2-6x into a form (x-a)^2

and you are allowed to add/subtract numbers

have you learnt completing the square

[white schooner]

i do

but i havent mastered it yet

x(x-6)

[native sequoia]

nah

well we can add numbers to both sides of the equation x^2-6x+y^2=7

expand (x-a)^2 and try equate it to x^2-6x

to get started

[white schooner]

ohh thanks ill try

huh i dont get it

wait

i literally lose because of the y^2

[native sequoia]

y^2 is already in the form (y-b)^2, you don't need to work on it, why is it giving you trouble

a circle with centre (a,b) and radius r has the equation (x-a)^2+(y-b)^2=r^2

[white schooner]

so i can also write it down as (y-0)^2

inb order to avoid confusion

sorry if im to slow 😦

[spark cliff]

i’m confused

can you multiply by 4

and then get like 3/x + 2/x

[willow bear]

you \textit{can} multiply both sides by $4$, but you will \textbf{not} get $\frac{3}{x} + \frac{2}{x} = 5$.

[obsidian monolith]

Ann:

[spark cliff]

yeah i realized that

so then multiply both sides by (x-1)(x+2)

right?

[willow bear]

yes

[spark cliff]

to get 8 = 5x^2-5x-10

?

and then just subtract the 8 and then factor it

[willow bear]

sure

[spark cliff]

is that ‘sure’ you’re wrong but i’m gonna let you realize it’s wrong so you learn or ‘sure’ that’s correct lol

it’s +5x whoops

[deft crow]

without using a calculator, how would you know 351 is a multiple of 3?

is there some clever way to check for something like this when reducing fractions?

[frozen needle]

there are theorems about that

3+5+1 = 9, which is divisible by 3
so 351 is divisible by 3

[short sorrel]

^^

If the sum of a number's digits is divisible by 3, then the number is divisible by 3

Same with divisibility by 9

[deft crow]

wow thank you

[frozen needle]

it's an iff

[short sorrel]

Hush

[frozen needle]

it's a very cool thing

[native sequoia]

if is fine

[shrewd urchin]

,w factor 2y^2-28y+98

[obsidian monolith]

Display results online and refine query

Requested by Krishna#4971

[autumn sonnet]

Why does it hold for a polynomial f(x) that it is divisible by (x-1)^3 only if f(1)=f'(1)=f''(1)=0?

[willow bear]

well

which direction do you want first

divisible by (x-1)^3 implies condition on derivatives

or condition on derivatives implies divisible by (x-1)^3?

[autumn sonnet]

divisibility implies the derivative zeros

[willow bear]

ok

well

let f(x) = g(x)(x-1)^3

for g a polynomial

i invite you to differentiate this twice and verify that f(1), f'(1) and f''(1) are all zero

while i disappear for about 15 minutes

@autumn sonnet have you done what i invited you to do? and does that direction of your iff statement require any further clarification?

...

[autumn sonnet]

Yeah I saw why it works, thanks. I wonder if this is the case with any polynomial divisible by (x-n)^m

[willow bear]

yes, a polynomial $P(x)$ is divisible by $(x-r)^m$ iff $P^{(k)}(r) = 0$ for $0 \leq k \leq m-1$. this works for any real (or complex) number $r$ and positive integer $m$

[obsidian monolith]

Ann:

[tropic crown]

can someone help me understand why its 1/ln5 and not just ln5?

[valid flint]

this is more appropriate for #calculus

also, taking the deravative of 5^t would give = ln(5) 5^t . and you have that 1/ln(5) to cancel the extra factor out essentially

[uncut lake]

can someone solve that

<@&286206848099549185>

[pale kettle]

Read the rules in #❓how-to-get-help

Tell me what rule you broke and I'll help you

[uncut lake]

ok

@pale kettle not 15min

[pale kettle]

Okay, now is there some way we can make the left side simpler?

[uncut lake]

no

i dont see any way possible n o p e 😡

[pale kettle]

think harder

[uncut lake]

what even is this qn

is this trig identities

🤔

[spring thunder]

[uncut lake]

suspicious

[spring thunder]

no not even trig identities needed

[pale kettle]

think about the left side

can you maybe factor something?

[uncut lake]

um yea sinx but it doesnt help 😡

i tried it

i thought this was trig identites bruh idk what to even do rip

[spring thunder]

hint : it helps very much

if i tell you the product of two numbers ab equals 0

[pale kettle]

What are the solutions to the equation x(2-x)=0?

[spring thunder]

what can you say about a and b?

[uncut lake]

0 2

👀

[pale kettle]

So then what are the solutions to your equation

[uncut lake]

um

0 2

👀

[pale kettle]

no

[fallen swallow]

h(t) = cot t
find the slope at the interval pi/4 to 3pi/4

is it undefined

cuz cot pi/4 is N/A no?

[willow bear]

no, cot(π/4) is defined.

as is cot(3π/4).

[fallen swallow]

ah i confused pi/4 w/ pi/2

thanks

[willow bear]

cot(pi/2) is also defined.

[fallen swallow]

lolwhat

i followed this?

[kind pier]

@fallen swallow did you figure it out?

[fallen swallow]

figure what out

the question?

[kind pier]

that cot is reciprocal

so if it tan is undef at pi/2 which is 1/0

the recip 0/1 is defined

because were not diving by 0 anymore

[fallen swallow]

ohhh

so the image was wrong and N/A should be 0?

[kind pier]

yes the image is wrong

[fallen swallow]

well thanks

[kind pier]

do the recip of all the tan values

thats your cot

[fallen swallow]

👌

thanks dude

[fallen swallow]

limit as h goes to 0

tried but had no luck at all

any help?

[echo plaza]

multiply by the conjugate

$\frac{\sqrt{5h+4}+2}{\sqrt{5h+4}+2}$

[obsidian monolith]

CaptainLightning:

[karmic topaz]

^

[fallen swallow]

sorry is the conjugate here sqrt5h +4 +2?

[karmic topaz]

yes

[fallen swallow]

oh thanks!

[vapid cave]

Can someone help me with a trig problem. I can't figure it out. I have to find all answers between [0, 2pi) for the equation cos2x - sinx = 0

I have narrowed this down to -sin^2x - sinx + 1 = 0

But I can't factor this for the life of me

<@&286206848099549185> I'm sorry to ping you but I need to finish this question before I can finally sleep

I think I might have gotten it

[torn swift]

Call sin(x) a new variable, y
y^2 + y - 1 = 0
You’ll need to use quadratic formula to get the roots

[vapid cave]

I solved it

I was too tired to realize how factoring works

it is -(2sinθ-1)(sinθ+1) = 0

[torn swift]

Oh lol

That’s fine as well then

[vapid cave]

Thanks anyways

gn

[deft crow]

is this intermediate step correct or is there a different way I should be thinking about this

the solution went from one the top to the bottom so maybe there's another way to look at it?

[karmic topaz]

thats the right way

youre good

[deft crow]

cool ty

[olive star]

imma go watch evangelion @viscid thistle baiiii

👋

[torn swift]

Wrong channel

[viscid thistle]

@olive star bye

I will watch later too @olive star

[autumn sonnet]

How do I find an arithmetic progression difference? I've tried using negative the first and last term in the sum formula, but that didn't work.

[prisma scroll]

@autumn sonnet common difference is just the difference between two consecutive terms. You can find it depending on what you're given with. Do you have a problem or something where you are stuck at?

[autumn sonnet]

I meant the difference of the entire progression

As in each term subtracted from the next

[short sorrel]

Yes, the common difference

So like if we have 1, 3, 5, 7, 9

The common difference is 2

As 3-1=2, and 5-3=2, and 7-5=2...

Is that what you mean?

Oh wait, do you mean

If we like take a series and convert it from addition to subtraction?

[autumn sonnet]

Yes

[wanton jewel]

can someone help with break equation?

[viscid thistle]

Just a question, I am going to go pre-calculus H next year and was wondering what topics I should review or learn to be prepared

[torn swift]

trig will be a big focus of the course

[viscid thistle]

Isn’t it more like limits and continuity, derivatives, integrals, etc

[torn swift]

that's calc

[viscid thistle]

That’s the first chapter in our textbook

Limits and continuity

[short sorrel]

(although limits and basic derivatives are sometimes introduced in precalc.)

hmm, the first chapter? are you sure this is a precalc book?

[viscid thistle]

This year we did mainly transformations, logs, trig(unit circle, identities)

[short sorrel]

that sounds like precalc.

[viscid thistle]

Oh

It was called Algebra 2H

[short sorrel]

¯_(ツ)_/¯

[viscid thistle]

I heard people in precalc learn the same

[short sorrel]

the names i'm using are the north american names

[viscid thistle]

Same here

Wait so limits/derivatives are calculated

Calc**

[torn swift]

yes

at least typically they are

[viscid thistle]

Alright

[torn swift]

no idea what you are going to learn in calc if you call this precal

[viscid thistle]

I heard it’s like integrals and stuff

Then comes multi variable calc

[short sorrel]

calculus in the US is traditionally split into

calc 1 and calc 2

then multivariable and diff eqs

calc 1 is limits, derivatives, and basic integrals

calc 2 is more integrals, solids of rotation, etc

and both have applications.

[viscid thistle]

I think in my school
Precal=cal 1
Cal= cal 2

Same thing just different names

[short sorrel]

thats a bit weird

but i can see it

[viscid thistle]

Does calc 1 expand from algebra 2

[short sorrel]

it builds off it, yes

they're generally considered separate subjects, but

calc uses algebraic techniques heavily

many students comment that the algebra is the hardest part of calculus.

(or maybe the trig)

[viscid thistle]

Oh

I found trig to be generally straight forward

[short sorrel]

yeah, it comes to everyone differently; trig in calc mainly comes up in using identities in integration

[viscid thistle]

Isn’t integration like area under curve and between 2 curves

[short sorrel]

thats the geometric intuition, yeah

the nice bit - and the part that ties it to differential calculus - is that the integral is the inverse of the derivative

[viscid thistle]

Is differential calc the same as multi

[short sorrel]

no, "differential" means "regarding derivatives"

so calc 1

[viscid thistle]

Ok

[royal aspen]

i know in AP calculus, at least for calc BC, there isn't much of a distinction between calc 1 in 2, but that may have just been my class

[vapid cave]

Calc bc covers both

[limber bone]

more integration techniques , series and i think polar coord

[autumn sonnet]

Any idea where I should begin in this?

[obsidian monolith]

memes:

[obsidian monolith]

Whoever:

[delicate sequoia]

hey how could i find the asymptotes of x.(e to the 1/x)

[blazing solar]

isn't it (ln b)/(ln a)?

[short sorrel]

yes.

[wraith idol]

Yes I was on my phone

I typed it wrong

God i should be ashamed sorry

[viscid thistle]

lol

[violet ember]

who else is a highschool precalc yeet?

[hazy crown]

Yeet

[shrewd urchin]

[willow bear]

n is an arbitrary integer

[violet ember]

?

[split cave]

n is any whole number

[willow bear]

this says that the graph of y = cot(x) has asymptotes
...
x = -3pi
x = -2pi
x = -pi
x = 0
x = pi
x = 2pi
x = 3pi
...

and so on

[violet ember]

ahhh

thank you

[rugged ice]

I know how to do this, I'm just fried beyond belief and can'r work anymore. Someone mind helping out?

[frozen needle]

Do things slowly, step by step

[rugged ice]

Just give it to me, I can barely remember my name at this point

[prisma marten]

Use your log rules

Then raise everything by b

[rugged ice]

I'm fried

I can't do anything

My entire head is numb

I'm shaking

[prisma marten]

Probably should take a break from math then

[rugged ice]

It’s literally just this problem then I’m done

[prisma marten]

I’ll walk you through it but I won’t give you the answer

[rugged ice]

That’s fair

[prisma marten]

Let’s start with Left and go right

What can we do with that 3

[rugged ice]

Move it to be the exponent of the 5

[prisma marten]

Perfect

Let’s make that log(b)125 then

On the Right side, what can we do when we have two logs subtracting

[rugged ice]

Turn them into a fraction

[prisma marten]

Good

So logb 125 = logb (4/y)

What can we do if everything has the same base?

[rugged ice]

A bit too fried for that one, chief. But, I’m assuming we can simply divide or multiply to simplify?

[prisma marten]

Hmmm let’s take an extra step then

Let’s move the right side to the left to make it equal 0

So logb 125 - logb (4/y) = 0

You tell me the next step

[rugged ice]

Turn the subtracting logs into a fraction again?

[prisma marten]

Yep

It’s gonna be a bit ugly, but keep it organized and it will work out

Can you tell me what we get after you make the newest fraction

[rugged ice]

logb(125/(4/7)

[prisma marten]

= 0

Okay, let’s raise both sides by ___?

[rugged ice]

b?

[prisma marten]

Yep

(125/(4/7)) = b^0

Hopefully you know anything to ^0 = 1, after that it’s just algebra which I know you can do

Also that 7 is a y

[rugged ice]

0.032 or 4/125

[prisma marten]

Perfect! good job man

[rugged ice]

I honestly regret deciding to take this class this summer. I’m already loaded with ap summer work for us history and lang

I don’t know how to give myself a break

[prisma marten]

Is this preAP Calc?

[warped badger]

i need help with a math problem

[prisma marten]

Sadly I cannot read your mind 😔

What’s the problem bud

[warped badger]

i nned to find out the displacement spped of a new yorker falling out of the world trade center

it is very important

[rugged ice]

It’s honors pre cal

[prisma marten]

Ah Canadian here so not quite sure your system but I have a good idea

Well best of luck to you man :)

[fallen swallow]

displacement speed of a NYer falling off WTC?

what

[spring thunder]

we won't assist manslaughter in here

letting you know

[violet ember]

just to make sure

π is always an asymptote of any tan function right

[prisma marten]

Pi/2?

Tanx = sinx/cosx

So what values of x will make it go to infinity, well the numerator never goes to infinity, only -1 to 1, so we want the denominator to approach 0

Cos x is 0 at Pi/2

[violet ember]

is that a yes?

[prisma marten]

It is an asymptote at Pi/2

Tan(Pi) = 0

[violet ember]

sorry i mean is π always an asymptote of any cotangent function

[prisma marten]

Do the same reasoning I did and try and prove it to yourself

[autumn sonnet]

If the formula for a single term in binomial progression (x+y)^n is (n k) * x^n-y * y^k is the formula for (x-y)^n = (n k) * x^k * y^n-k?

[willow bear]

ok first off

the terms in the expansion of $(x+y)^n$ are given by $\binom{n}{k} x^{n-k}y^k$, not by $\binom{n}{k} x^{n-y} y^k$

[obsidian monolith]

Ann:

[willow bear]

and second, no, the terms in the expansion of $(x-y)^n$ are given by $(-1)^k \binom{n}{k} x^{n-k} y^k$. the expression you gave still gives the terms of $(x+y)^n$ just in reverse order

[obsidian monolith]

Ann:

[full garden]

hey guys

if a question is asking me to find how long the ball will stay in the air for

and they are giving me a quadratic equation

do I solve for roots or find the vertex

[prisma marten]

What’s the equation

[full garden]

h(t)= -4.9t^2+19.6t+2

[prisma marten]

So we input times to and it outputs the height

What would h=0 represent?

[full garden]

I dont know time?

[prisma marten]

The time the ball is on the ground

[full garden]

oh

[prisma marten]

So if we can find both times the ball is on the ground

[full garden]

but like if I find the t intercept it gives me when it was lauched

oh

@prisma marten so if I find the t intercept i'll be the tottal time?

[prisma marten]

The positive one, yes

Draw a diagram/graph if it helps

[full garden]

what does negative time mean @prisma marten

[prisma marten]

That would be before he throws it, which is nonsensical

[full garden]

alright thank you so much @prisma marten

[prisma marten]

No worries:)

[rugged ice]

GOD I regret taking this class online

All of the notes are in video form and I can't retain anything from videos, even if I write it down

[viscid thistle]

?

Dr. Grimes and I flew aboard the NASA SOFIA mission in October 2016. We gathered
cosmic ray data on our way up. Here are a few data points:
Elevation Cosmic Ray Hits per Minute
33,164 ft 283
42,998 ft 549
We will pretend that at sea level the count is zero. That isn’t true, but we will use that for
this problem.
A] Use this data to determine the
rt y Pe^rt
equation where y is hits per minute, and t is
altitude.
B] If Baldwin’s cross-sectional area is 400 times that of the Geiger counter sensor, then what
would be his equation?

[short sorrel]

"rt y Pe ^ rt"

how was this formatted

$y = Pe^{rt}$?

[viscid thistle]

there

[obsidian monolith]

Namington:

[viscid thistle]

yes

[short sorrel]

right, so y is hits per minute, t is altitude

[viscid thistle]

yes

[short sorrel]

we have two data points

[viscid thistle]

yes sir

[short sorrel]

(33164, 283) and (44998, 549)

if you were to substitute one of these data points in

$283 = Pe^{33164r}$

[obsidian monolith]

Namington:

[short sorrel]

you'll notice that we have two unknowns

[viscid thistle]

yes

i dont know how to get p

[short sorrel]

oh, correction: we actually have 3 data points

"We will pretend that at sea level the count is zero. That isn’t true, but we will use that for
this problem."

so we also have (0,0)

[viscid thistle]

yes

[short sorrel]

but yeah

anyway, we cant solve an equation with 2 unknowns... alone

but what we can do

is establish a system of equations

[viscid thistle]

ok

so we will have 2 equations

[short sorrel]

inputting another data point, we get $539 = Pe^{44998r}$

[obsidian monolith]

Namington:

[viscid thistle]

ok

[short sorrel]

and our last point, $0 = Pe^0$

[obsidian monolith]

Namington:

[short sorrel]

buuuut thats a bit weird

so i'm gonna disregard it where possible

since it would suggest P = 0 is a valid solution.

[echo plaza]

[viscid thistle]

wouldnt that be like p=0

[short sorrel]

yeah, which makes that solution extrenuous

[viscid thistle]

ok so ignore that

[short sorrel]

so our system is:\
\
$283 = Pe^{33164r} \
539 = Pe^{44998r}$

[obsidian monolith]

Namington:

[short sorrel]

can you solve this?

[viscid thistle]

yes

can we isolate p and make the equations equal each other

[short sorrel]

sure.

[viscid thistle]

can u keep going?

[short sorrel]

well, isolating each for P

$283 = Pe^{33164r} \ \implies P = \frac{283}{e^{33164r}}$

[obsidian monolith]

Namington:

[viscid thistle]

yes i got that im at

them equaling eachother in fraction form

[short sorrel]

$\frac{283}{e^{33164r}} = \frac{539}{e^{44998r}}$?

[echo plaza]

}}

[obsidian monolith]

Namington:

[viscid thistle]

ok

then i just multiply

[short sorrel]

again, sure

technically we have to make sure the denominator will never equal 0, buuuut

e^x is never 0

for any real x

so in this case, that doesnt matter

$539e^{33164r} = 283e^{44998r}$

[obsidian monolith]

Namington:

[short sorrel]

the problem here is that

r is up in the exponent

do you know how to bring that down?

[viscid thistle]

natural log?

[short sorrel]

yes, but do be careful

[viscid thistle]

first divide?

[short sorrel]

you can do that, or use log laws to break the logs up first

either works

[viscid thistle]

what do i do with the 539 and 283

[echo plaza]

ln(ab)=ln(a)+ln(b)

[viscid thistle]

im confused

[short sorrel]

let's take the ln of both sides

$\ln(539e^{33164r}) = \ln(283e^{44998r})$

[obsidian monolith]

Namington:

[short sorrel]

the trick is that

the exponents arent applied to the entire thing

so we cant just take them down or anything

what we can do

is break up these logs

note $\ln(ab) = \ln(a) + \ln(b)$

[obsidian monolith]

Namington:

[short sorrel]

soo, breaking up these logs

[viscid thistle]

ln(539)

ln(e^33164r)

[short sorrel]

right, and similar for the other side

what can we do for the ln(e^stuff)?

[viscid thistle]

I know e is like 2.3

[short sorrel]

...a couple decimal places off, there, but either way, that's not really relevant here

I'm asking you to simplify $\ln(e^{33164r})$ and $\ln(e^{44998})$

[obsidian monolith]

Namington:

[short sorrel]

recall that ln means log with base e

[viscid thistle]

i dont know what to do

[willow bear]

do you know what ln is

[viscid thistle]

natural log

my fault

[willow bear]

ok do you know what the natural log of a number is

as in

the definition

[viscid thistle]

its a log with base

e

[willow bear]

no, this is circular and gets you exactly nowhere. when asked "what is the definition of log", you cannot just answer "it's a log"

[viscid thistle]

isnt it like the function of a exponetitial graph

[willow bear]

no

the natural log of a positive number x is the answer to the question "e raised to what power equals x?"

[viscid thistle]

ok

What’s $\log_e{e}$

[obsidian monolith]

∂u/∂x = ∂v/∂y & ∂u/∂y = - ∂v/∂x:

[viscid thistle]

1

?

and that is $\ln{e^1}$ right

[obsidian monolith]

∂u/∂x = ∂v/∂y & ∂u/∂y = - ∂v/∂x:

[viscid thistle]

yes

excuse my latex I’m on a overcrowded train

nah ur good

i understood

what would ln(e^2) be then?

wouldnt it be 2

🤔

So if that’s right

What does ln(e^33164r) simplify to

okok

i get it

it cancels out

33164r

not quite

the ln(e^33164r)=33164

log(x^n)=nlog(x)

but this isnt log

i found r

then what do i do

But ln is log base e

i got it

thank you so much

what do i do for b

just multiply by 4 right

huh b?

If Baldwin’s cross-sectional area is 400 times that of the Geiger counter sensor, then what
would be his equation?

[viscid thistle]

On our SOFIA flight we also took air pressure data. Here are a few data points:
Altitude Pressure
2,366 ft 27.448 inHg.
16,813 ft 15.606 inHg.
43,003 ft 4.782 inHg.
A] What is the pressure at sea level inHg based on this data?
B] Based on this data, at what elevation will the pressure be half that of sea level?
C] What will be the air pressure at 100,000 ft based on this data?

can some help with this

[past glade]

how do you find out if a piecewise function is injective/surjective

like this one for example

[willow bear]

prob try to graph it and see if anything jumps out at you

[viscid thistle]

On our SOFIA flight we also took air pressure data. Here are a few data points:
Altitude Pressure
2,366 ft 27.448 inHg.
16,813 ft 15.606 inHg.
43,003 ft 4.782 inHg.
A] What is the pressure at sea level inHg based on this data?
B] Based on this data, at what elevation will the pressure be half that of sea level?
C] What will be the air pressure at 100,000 ft based on this data?
can some help with this?

[split cave]

Do you have a calculator with statistics functions ? @viscid thistle

[viscid thistle]

I believe so

[narrow hawk]

@past glade that doesnt look like preuniversity to me

in fact that doesnt look like calc either

[prisma marten]

looks like precalc? like creating functions based off of data points

[viscid thistle]

This is the precalculus chat

This is my teachers notes

What I dont understand is that when I put arctan(-1) in a calculator I get -pi/4. What he said is that -pi/4 is just a reference angle. I don't really get why it's a reference angle and not just an angle.

[willow bear]

it is likely that the convention in your class is to take the argument of a complex number to be between 0 and 2pi

[viscid thistle]

Yes forgot to say that

[willow bear]

that said

2pi is exactly what -pi/4 and 7pi/4 differ by

[viscid thistle]

I think I dont understand what the argument is

[willow bear]

you know how complex numbers can be thought of as vectors?

the argument of a complex number is the angle, measured counterclockwise, that the vector representing said number makes with the positive real axis

[prisma marten]

This isn’t precalc

But, find r and find theta would be your first step

[short sorrel]

eh, i could see an advanced precalc class covering it

de moivre's isnt like

conceptually difficult or anything

once you get past the initial barrier of manipulating complex numbers, that is

[prisma marten]

I first encountered it in Lin Alg, but I also have no idea the US Curriculum, half these channels are weirdly named to me

[hard hornet]

Wouldn't you convert it to

cis first

and then demoivre's comes super nicely

[kind pier]

it is precalc

its the cis part I'm having trouble understanding

i did 2[cos(11pi/6)+isin(11pi/6)]

then 2^-10 or 1/2^10[cos(-55pi/3)+isin(-55pi/3)]

@prisma marten

[willow bear]

yeah well you're almost done

[kind pier]

it didnt take that though

i tried leaving everything squared also

[willow bear]

weird... that sounds like the correct answer to me

,w (sqrt(3)-i)^(-10)

ugh

[obsidian monolith]

Display results online and refine query

Requested by Ann#0413

[kind pier]

omg

how are you able to do that

[willow bear]

do what

[kind pier]

LOL

just casually pull up all this info

[willow bear]

there was a "MORE" react on the original message

i clicked it

[kind pier]

oh wait

it says my stuffs backwards

that was it

my stuff was backwards

thanks

[fervent lagoon]

does it look like i did this right?

[toxic prairie]

Anyone around to help with some simple precalc?

[prisma marten]

[limber bone]

cos(a) =4/5 thats a

then cos(a+pi/6) thats c

cos(b+pi/6) = 4/5 thats b

then cos(b) = d

[fervent lagoon]

yo could someone help me out with this

[spark cliff]

It’s the first answer right?

[willow bear]

no

[steel granite]

if you know that x=1 is a root you can do synthetic division

and then it is just a power of 2

which means you can use quadratic formula

to find the other 2 roots

[fervent lagoon]

yo please helpppp
https://cdn.discordapp.com/attachments/509460208737845248/594342880232079380/helppp.PNG
I need to find cos(a+b) in terms of trigonometric functions of alpha and beta
im basically proving the angle addition identities

these are the side lengths I found
I already found sin(a+b) but I cant find cos(a+b)!!!!

https://cdn.discordapp.com/attachments/509460208737845248/594343370999201812/lengths.PNG

[native sequoia]

FB=EC

AE=AC-EC

@fervent lagoon

[fervent lagoon]

yeah i just realized lmao

[earnest barn]

Are we able to simplify $\cos^2(x) + i\sin^2(x)$ using Euler's identity?

[obsidian monolith]

Daniel Cann:

[willow bear]

nope

[viscid thistle]

@earnest barn think about how the identities are generated

do you know?

[gusty spade]

Hey guys Uni student here and starting a Pre-Calculus course tomorrow and I'm not very good at Math (though I do like the subject) was wondering if I could get some help?

[willow bear]

with what?

[heady jewel]

so you want help with the things in your pre calc course

[gusty spade]

Yeah I do. If that's not a problem?

[willow bear]

well like

do you have a problem you're stuck on or what

if you do, post it and someone will help you\

[gusty spade]

I don't have any today. My class starts tomorrow. If I have enough time though I will post it.

[fervent lagoon]

is cos(40)cos(80) different than cos(80)cos(40)

[cursive estuary]

No, since it's just multiplication between two numbers

[willow bear]

multiplication is commutative

[shrewd urchin]

Order doesn't matter

[native sequoia]

it's written differently

[white schooner]

help me find the standard equation of the parabola with focus (0,-3.5) directrix y=-3.5

where is the opening 😦

?

im confused

[pale kettle]

What do you mean where's the opening?

[kind pier]

I need to turn this into polar (x^2+y^2-2x)=4(x^2+y^2)

[karmic topaz]

x^2 + y^2

[rugged ice]

I’m not wrong, though?

The three vertices you get from this are (0,0), (0,6.5) and (1.733,0)

(0,6.5) leaves you with the greatest answer

Wait

I’m dumb

Just read it says minimum, ignore me

[patent beacon]

@kind pier
x² + y² = r²
x = rcosθ

And in case you ever need it,
y = rsinθ
But it's not useful here

[errant garden]

i was wondering for 3d vectors, whats the fastest way to find the shortest distance from a point A(x1, y1, z1), from a line r = (x2, y2, z2) + k(x3, y3, z3)

[civic plaza]

Choose 2 points p and q on the line

Let b be a vector pq and let c be a vector pA

|b x c|/|b| is the distance

[errant garden]

yep that works, thanks. i was thinking of using projection, but it is quite slow and probably only used when the vector is needed

[fringe lintel]

is the domain: all real numbers?

[timber plinth]

well, is there any scenario where it would be undefined over the reals?

[fringe lintel]

isnt odd root all real numbers and even will be need to set it >/= 0

[timber plinth]

Well, not always >= 0, since you might have it shifted, but uh yeah

[fringe lintel]

it say in my book "odd roots are defined for both positive and negative values... so (neg infinity, positive infinity)"

[native sequoia]

If the codomain is $\mathbb R$ and that is the principle 3rd root, then the maximal domain is [1, inf).

[obsidian monolith]

EpicGuy4227:

[native sequoia]

but if it is the real 3rd root, the maximal domain is R

[willow bear]

principal*

also, [0, +∞)

[native sequoia]

ty

x-1?

[willow bear]

ah

mb

[willow bear]

what is giving you trouble here

make a picture

[fringe lintel]

im finding the vertext of K

but that number is high

[rugged ice]

you guys, i’m desperate and exhausted. i have two assignments due in an hour that i thought were due tomorrow. i don’t know how to find the ordered pair of angles and the notes the teacher provides are vague, please help

[glacial island]

if it's not one of those unit circle angles, you need to use sin/cos/tan etc. pythagorean rules

[rugged ice]

I don’t know rules, I don’t retain information from online classes, I just take them for the credit.

[glacial island]

oof

[pale kettle]

Then figure out some way that you do retain them?

Like figure out how you learn?

[glacial island]

i take precalc online too, but u should try to learn it

[pale kettle]

We're not here to feed you answers

[prisma marten]

Don’t do assignments last min if you know you need extra help

[glacial island]

pain in the ass but each module is built on the last module

[rugged ice]

I didn’t know it was due today

Assignments are typically due Thursdays

[glacial island]

as for this rule
the pattern goes 1,2,3,4 and then 4,3,2,1 divided by 2

you should be able to memorize the ordered pairs that way

[rugged ice]

My life is too shit right now for my memory and my mental health is awful so learning has been hard for me as of late

[prisma marten]

May want to reduce your course load then

[rugged ice]

I don’t even know why I bother anymore

Honors and AP courses? Sure, they look good on an application, but I’ve never had dreams or wanted to be anything, so why take them?

God I’m in an awful state h

[glacial island]

just finish up the courses u have then dont take them anymore

[rugged ice]

I'm signed up for college psyc and soc along with ap lang and ap us history next year

I do have a bit much but I don't have anything else to do with my time

[pale kettle]

You really should just get your life sorted out

[glacial island]

ask to drop them before they start if you really think ur mental state is bad

[pale kettle]

Like sure your grades might suffer

But in the long run, it's a lot more important for you to be in a good place

[glacial island]

and for ur time, find a hobby, figure yourself out

[pale kettle]

And your grades and your learning will be much better in the future because of it

[rugged ice]

I literally can't be in a good place with my situation. My family could care less for me, I live in a ghetto farm town with no one I can talk to or relate to.

I'm just me trapped in my room

Also, what would I do for a negative angle on the circle?

[glacial island]

the ordered pairs work the same for negative angles

[rugged ice]

I'm assuming flip the quadrant since you'd be going backwards, yes?

[glacial island]

yes, it's going counterclockwise

[rugged ice]

And, as an example, say you have an angle over 360 degrees, would it just fall into the same position of another angle +360

Like, say you have an angle of 400. Would that be in the place of 40?

[prisma marten]

Yes

[rugged ice]

Thanks!

so -pi/6 (-30 degrees) would be in the same place as 330?

[prisma marten]

Yes

[willow bear]

they differ by 2pi, a full turn

[rugged ice]

Thanks guys, those assignments are done and I can rest easy.

[gusty spade]

Need help with the PreCal assignment.

[pale kettle]

What have you tried? Or what are you stuck on?

[gusty spade]

I just posted the screenshot.

[pale kettle]

I know

[limber bone]

assume dollors per ONE hour for first mechanic is x and the same for second mechanic is y

[rugged ice]

Ax + By = 1000

x + y = 110

it’s quite simple to solve, i just plugged in two values and got the answer

[gusty spade]

Just plugged in the variables?

[rugged ice]

Well I just chose two simple, reasonable numbers that would add up to 110, plugged them into the 15x + 5y equation and it all worked out.

[gusty spade]

Is it 110 for both or the second one?

[grizzled orchid]

oh my fucking god aleks

i pity

$15x + 5y = 1100$

oh latex is down oof

[grizzled orchid]

@gusty spade You've probably already solved this problem but I feel like I should point out that you don't need to "choose values" in this case

Solving for one of the variables (in this case y) and treating it like a system of equations is generally easier and works in most cases

[viscid thistle]

can someone help me with this

[willow bear]

what is giving you trouble here

[viscid thistle]

i dont think it equals

[willow bear]

what's making you think that this equality does not hold, then?

[viscid thistle]

to me its like 2x3=6 but 2+3=5 so that shouldnt equal either

[willow bear]

well ok the thing is, yes, IN GENERAL the product of two numbers isn't the same as their sum

but that doesn't mean that x+y NEVER equals xy

for example, 2 + 2 = 2 * 2

another example, 25/9 * 25/16 = 25/9 + 25/16

so it is entirely possible to have two well-picked numbers whose sum equals their product.

have you ever proved any trigonometric identities before?

@viscid thistle

[viscid thistle]

i just got it, i saw what i was doing wrong

[gusty spade]

@grizzled orchid You've worked with Aleks?

[grizzled orchid]

oh have i

fucking kill me

[short sorrel]

recall the definition of a function

[minor osprey]

hey hey hey

so when given a quadratic function of f(x)=-490x^2 + 75x + 12

how do we find the x intercept

you cannot factor it

(as far as I can see)

and when you put it in the quadratic formula

it returns the wrong answer

the correct answer stated in the textbook is 0.3

[prisma marten]

Can you show your work please?

[minor osprey]

for factoring or quadratic formula?

[short sorrel]

quadratic formula

[minor osprey]

I may or may not have madea mistake when using the quadratic formula

[prisma marten]

Quadratic

[minor osprey]

so Im checking it once again

[short sorrel]

make sure to consider both the + and - solutions

[minor osprey]

is a = 490 or -490

[prisma marten]

-490

[minor osprey]

maybe it is my calculator?

here is what I plug in

perhaps I should do more in hand

[prisma marten]

Do more steps

Use calculator to do the multiplication sure, but make sure you write out your steps

also Learn Quadratic formula button on your calculator

[minor osprey]

just want to make sure

this is all correct?

[karmic topaz]

plus minus

but yes

[minor osprey]

ok lets see

nvm nvm

It seemed that the problem was

that I got the + value

but I did not switch it to -

I have it now with the work

so thank you guys

Ive now realized my mistakes

[fervent lagoon]

could someone plz help me

I have no clue what to do

[native sequoia]

use double angle formulas on cos(2b) and cos(2a)

@fervent lagoon

[fervent lagoon]

how does that help?

if i used cos(2b) then I get cos(2b)=24/25

[minor osprey]

Terrorist scum

[fervent lagoon]

and 24/25=cos^2b-sin^2b

lel t-side forever

[native sequoia]

you should know the forms 1-2sin^2(b) and 2cos^2(b)-1

[fervent lagoon]

i solved for cos(b) but now im stuck

[native sequoia]

you should be trying to get CE

[fervent lagoon]

do i solve for tan(2b)

[native sequoia]

no

[fervent lagoon]

and use half angle formula

[native sequoia]

tan(b)

oh ye you could use half angle formula for tan

[fervent lagoon]

i got tan(2b)=24/7

and tan(b)=24/32

is CE 5.25?

[native sequoia]

yah

[fervent lagoon]

is CD 24/7

yeah its correct

thanks dude

[native sequoia]

np

[willow bear]

ok, what's giving you trouble here?

[gusty spade]

On the instructions it says to identify the center and radius. however I'm having trouble doing that. Like starting the equation to get the answer basically.

[willow bear]

you don't need to do anything to the equation. it is almost a matter of reading off the required details.

do you know what the general equation of a circle is?

[gusty spade]

No. Or at least I don't remember.

[willow bear]

then you should go and consult your notes or your textbook.

[shrewd urchin]

Circle is a set of all point equidistant form a given distance .

I.e distance between these points is always a constant

Let's say h,k is the centr of the circle and r is the radius of circle

We wish to find all point (x,y) such that it is r units away from (h,k)

$\sqrt{(x-h)^2+(y-k)^2}=r$

[obsidian monolith]

Krishna 🙎:

[shrewd urchin]

$(x-h)^2+(y-k)^2=r^2$

[obsidian monolith]

Krishna 🙎:

[shrewd urchin]

$(x+1)^2+(y+2)^2=2^2$ (h,k)=(-1,-2) and r=2 .

[obsidian monolith]

Krishna 🙎:

[shrewd urchin]

You need to plot the point -1,-2) on plane then take 2unit measure on the compas. and take (-1,-2) as centre and draw that circle

@gusty spade

[prisma prairie]

can someone verify if this is correct

[next willow]

It is, it seems to me

[prisma prairie]

@next willow can you explain the 2nd line

where does a^(4/6) come from and for the denominator, why is a^(5/6) + a^(1/6) = a^(5/6)?

[next willow]

They didn't sum the denominators, let's say they manipulated the fractions so that they had the same denominator and then summed them (notice that a^(5/6)=(a^(1/6))^5=
=a^(1/6)(a^(1/6))^4 )

Or you can say that they collected 1/a^(5/6) from those two terms
x+y = 1/a^(5/6) (a^(5/6) x + a^(5/6) y )

The following steps weren't possibly necessary also, since twose two terms can be observed to be equal: a^(-1/6)/a^(5/6) + a^(-5/6)/a^(1/6) =
= 2* a^(-1/6)/a^(5/6)

[prisma prairie]

what lol

i understood your first little sentence

but like i still dont get where that a^(4/6) came from

[next willow]

I'll write the steps in LaTex

[prisma prairie]

ok thanks bro

[next willow]

It'll take me some time

[prisma prairie]

ok np

[next willow]

$\frac{a^{-\frac{1}{6}}}{a^{\frac{5}{6}}} + \frac{a^{-\frac{5}{6}}}{a^{\frac{1}{6}}} = \frac{a^{-\frac{1}{6}}}{a^{\frac{5}{6}}} + \frac{a^{\frac{4}{6}}a^{-\frac{5}{6}}}{a^{\frac{4}{6}} a^{\frac{1}{6}}} =
\frac{a^{-\frac{1}{6}}}{a^{\frac{5}{6}}} + \frac{a^{\frac{4}{6}}a^{-\frac{5}{6}}}{a^{\frac{5}{6}}} =
\frac{a^{-\frac{1}{6}} + a^{\frac{4}{6}} a^{-\frac{5}{6}}}{a^{\frac{5}{6}}} $

[obsidian monolith]

Mat:

[prisma prairie]

ohh

okay lol

how did you even figure that out

i wouldn't have if i had 1000 hours

just seems so hidden

[next willow]

As I tried to say before, this is just one of the many possible paths

If you get more comfortable summing fractions you'll see the paths quickly

[prisma prairie]

@next willow so i tried doing this my way but not sure what i’m doing wrong

[willow bear]

yikes

skyscraper fractions

[prisma prairie]

so the answer is supposed to be 2/a

and it's question 9

[earnest nymph]

The first fraction in the second lime seems off

[prisma prairie]

can you help @earnest nymph

[earnest nymph]

Change in to fraction first

[prisma prairie]

change what into a fraction

the quesuton?

question*

[earnest nymph]

The exponent

[prisma prairie]

like that?

[earnest nymph]

No

[prisma prairie]

then?

[earnest nymph]

I mean like sqrt (a) = a^(1/2)

[heady jewel]

which grade are you in

[earnest nymph]

Don't change the negative exponent

[heady jewel]

oh youre in the US

[earnest nymph]

So like just remain a^(-2/3)

[heady jewel]

and whys this in precalc lul

[prisma prairie]

like that?

[earnest nymph]

Yeah I think it's more suitable in #prealg-and-algebra @heady jewel

[heady jewel]

yes

[earnest nymph]

Yes but like I say don't change negative exponent

[heady jewel]

a^3/6=a^1/2

they get cancelled

in the first term

[earnest nymph]

@prisma prairie Something like this

[prisma prairie]

oh ok

[heady jewel]

so elite what was your question

[prisma prairie]

i dont know how to get the answer

[heady jewel]

like were you trying to solve it

oh

did you get it now?

[prisma prairie]

the answer is 2/a

but i get something else

no i still can’t

i need help still

[heady jewel]

maybe you did a mistake

but ill solve it for you

in #prealg-and-algebra

[prisma prairie]

im in college btww

[heady jewel]

WTF

lol

[prisma prairie]

ok ill be in that chat

[earnest nymph]

I got this?

[prisma prairie]

answer is 2/a

[earnest nymph]

I know

[prisma prairie]

oh

so how come you got that

other answer

[heady jewel]

OMG

you copied the question wrong

bruh

in the first term

denominator is a^5/6

lol

@prisma prairie

@earnest nymph

[prisma prairie]

no tis not

question 9

@heady jewel

[heady jewel]

the solutions whih you gave above