precalculus

[potent remnant]

help please

<@&286206848099549185>

[woeful galleon]

What does concave Down mean

I think a) -8<x<5 as the slope= rate of change

Not sure about b but I think c) -infinity < x < -8 as it increases to 0 at -8 it means that the slope itself was negative initially so it fits

Just joined the server so hope that helps

[red crane]

It means the curve bends downwards

[woeful galleon]

Ok

Sorry I don’t do the American curriculum so I don’t understand much terms

[red crane]

The tangent line has to be above the graph in the vicinity of the point

Just like imagine x^2

But inverse

It’s curving down

Y=-x^2

[woeful galleon]

Ah gotcha

[red crane]

Is concaving down

[woeful galleon]

Ok then it’s increasing -> 0 -> decreasing

[hallow pilot]

Has anyone taken AP calc BC?

And if so, how fast did it go?

[red crane]

Very fast

You do calc 1 and 2

Albeit generally most schools have you take it all 180 days

But it’s a lot every day

What grade are you in?

@hallow pilot

[proud crescent]

<@&268886789983436800>

[visual minnow]

hi, any tips for studying precal?

[north cloud]

Use khan academy

[viscid thistle]

can anyone teach me the basics? i have tons of question when i study so ill need someone who has a patience and can answer my questions😅

calc 1

im struggling please help the poor man

help me solve this

[summer ruin]

have you computed g(f(x))?

[viscid thistle]

idk how

my past teacher didnt have enough time to teach us that

[summer ruin]

replace every appearence of x in g(x) with f(x)

[viscid thistle]

f[g(x)]

?

[merry goblet]

g(f(x))

[summer ruin]

that's the opposite of what I said

[merry goblet]

so take f(x) and plug it into g(x)

[viscid thistle]

oh okay

[viscid thistle]

is it all parenthesis?

no bracket?

[merry goblet]

no brackets

[viscid thistle]

so the result will be g(1/x-2) = (1/x-2)^2+2

[merry goblet]

right

[viscid thistle]

what is next

wait

can u guys wait for like 10mins

my moms complaining that im using my phone while eating

so that later ill just write it on my paper

[merry goblet]

next just simplify it. turn it into one fraction.

that should give you values for alpha, beta, and gamma

[viscid thistle]

is the y called gamma

[merry goblet]

yes

they're some of the most commonly used greek letters

[viscid thistle]

@merry goblet

[viscid thistle]

all x here will change to 1/x-2?

like a(1/x-2)^a?

[junior plover]

you dont need to sub f(x) in there

your final answer will look like that after solving.

g(f(x)) is f(x) subbed in place of x in g(x).

[merry goblet]

square what's inside the parentheses

then add the 2 to that fraction

dont plug in any greek letters

just simplify the expression
[1/(x-2)^2]+2 so that it's only one fraction

from there you can figure out what each greek letter is equal to just by looking at it

[viscid thistle]

2 right?

[merry goblet]

what

what is 2

[viscid thistle]

wait

why did i type that

nvm that

what should i do next

[merry goblet]

well where are you

what have you got

[viscid thistle]

do i have to solve the denominator?

the (x-2)^2

or it stays like that

[merry goblet]

yeah expand it

[viscid thistle]

is the answer (x-2) (x+2)?

[viscid thistle]

if this is the answer so the result will be
[1/(x-2)(x+2)]+2

[merry goblet]

what no

you're squaring it

so (x-2)(x-2)

[summer ruin]

it is not and doing anything with the denominator doesn't bring you any closer to actually answering the question

why not just combine 2 and 1/(x-2)^2

[merry goblet]

you're gonna have to expand it regardless

[summer ruin]

no, denominator contains no gamma

[merry goblet]

i mean yeah i guess, but it's probably good to expand it and make sure the greek letters line up

[viscid thistle]

where did the 2 come from?

from the denominator?

[summer ruin]

.

[viscid thistle]

can u guys give me another problem like this

and help me solve it

i kinda understand it more when i look at another same problem

[merry goblet]

what exactly are you having difficulty understanding?

then maybe we can tailor a problem around that

[viscid thistle]

honestly, at this part i find it hard already i dont know what greek letter is equal to just by looking at it

[merry goblet]

you need to just simplify the expression so that it's one fraction

only then can you see what a, b, and y are

you won't be able to see it otherwise

it will line up, like if i have 2x+3 and ax+b, then i know that a is 2 and b is 3

[viscid thistle]

oohhhhh

okay

[merry goblet]

yeah, you just need to finish up the expression. that's it

[viscid thistle]

waittt

[merry goblet]

so add 2 to 1/(x-2)^2

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

[obsidian monolith]

Wumbo

[viscid thistle]

oh okayyy

waitt

[merry goblet]

yes. just make it one single fraction

[viscid thistle]

let ne resend the problem so that i dojt have to scroll up again

will the answer be 2x^2 - 8x +9 / (x-2)^2

[viscid thistle]

here

[merry goblet]

yes?

[viscid thistle]

can u teach me how to add it

i probably forgot it

i want to recall

[merry goblet]

so to add fractions you need common denominators right?

[viscid thistle]

yes

[merry goblet]

so multiply 2/1 by (x-2)^2/(x-2)^2

then both fractions will have the same denominator

[viscid thistle]

can u show this in picture

[viscid thistle]

like this

[merry goblet]

yeah one sec

[viscid thistle]

okie

[merry goblet]

$\frac{2}{1}*\frac{(x-2)^2}{(x-2)^2}$

[obsidian monolith]

Wumbo

[viscid thistle]

so y said

u said

in order to add fractions i need common dnominators first

[merry goblet]

right

and here we're multiplying

[viscid thistle]

wait a sec

where did u get the

fraction

that

(x-2)^2

over (x-2)^2

[merry goblet]

well we're adding 1/(x-2)^2 and 2 right

[viscid thistle]

yes

[merry goblet]

so i want my 2 to have the same denominator has 1/(x-2)^2

so i'm going to multiply my 2 by (x-2)^2/(x-2)^2

which is the same thing as multiplying by 1

any expression or number divided by itself is equal to 1

[viscid thistle]

okayyy

okay okay

[merry goblet]

so right now we have $\frac{1}{(x-2)^2}+\frac{2}{1}*\frac{(x-2)^2}{(x-2)^2}$

[obsidian monolith]

Wumbo

[viscid thistle]

okayy

[merry goblet]

which is the same as $\frac{1}{(x-2)^2}+\frac{2}{1}$

[obsidian monolith]

Wumbo

[merry goblet]

i just multiplied 2/1 by 1

[viscid thistle]

okay

since the last part is equal to 1

[merry goblet]

since the last part is equal to 1 it doesnt change the expression

[viscid thistle]

yes

[merry goblet]

but it makes it so that i can now add the 2 to the fraction 1/(x-2)^2

so it becomes$\frac{1}{(x-2)^2}+\frac{2*(x-2)^2}{(x-2)^2}$

[obsidian monolith]

Wumbo

[viscid thistle]

yehhh

[merry goblet]

and since both fractions have the same denominator i can now add them together

[viscid thistle]

yeahhhh

so what is next

[merry goblet]

so now we add the numerators together to make 1 fraction

[viscid thistle]

okay

[merry goblet]

$\frac{1+2*(x-2)^2}{(x-2)^2}$

[obsidian monolith]

Wumbo

[merry goblet]

does that make sense how i did that

[viscid thistle]

3•(x-2)^2/(x-2)^2

[viscid thistle]

yes

[merry goblet]

no

[viscid thistle]

wait

so whats going to happen

i thought we are adding

both constant no.

[merry goblet]

yes but for example 1+5y does not equal 6y

just expand the (x-2)^2 and then multiply it by 2

[viscid thistle]

(x-2) (x-2)2?

[merry goblet]

yes

what does that equal

[viscid thistle]

2x - 4 + 2x - 4?

[merry goblet]

you remember pemdas yeah? you gotta do the exponent first, then multiply

so do (x-2)^2, then multiply by 2

[viscid thistle]

in pemdas
parenthesis first

[merry goblet]

there is nothing in the parentheses you can do to simplify it, so we move to exponent

[viscid thistle]

can u show me the answer

[merry goblet]

so (x-2)^2=(x-2)(x-2)

[viscid thistle]

yes

[merry goblet]

which is x^2-2x-2x+4

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

[obsidian monolith]

Wumbo

[merry goblet]

and now we have to multiply by 2, because we have 2*(x-2)^2

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

[obsidian monolith]

Wumbo

[merry goblet]

so $2*(x-2)^2=2x^2-8x+8$

[obsidian monolith]

Wumbo

[merry goblet]

does that make sense?

[viscid thistle]

waittt

[viscid thistle]

where did u get the 4x here

[merry goblet]

(x-2)*(x-2)

you FOIL it out right?

[viscid thistle]

yeah

[merry goblet]

and we got x^2 - 2x - 2x +4

i added the 2x's together to get 4x

[viscid thistle]

OHHHH

okayyyy

i get it now

[merry goblet]

so it simplifies to x^2-4x+4

[viscid thistle]

okayy

[merry goblet]

okay so now

[viscid thistle]

wait

[merry goblet]

yea?

[viscid thistle]

waitt im trying to understand this

oh okayy

[viscid thistle]

now that we have this

[merry goblet]

mhm

[viscid thistle]

the next thing we have to do is to multiply 2 to (x-2)^2 which will give us 2x - 4

[merry goblet]

no we just did 2*(x-2)^2

[merry goblet]

.

[viscid thistle]

oh thats the final answer?

[merry goblet]

no

remember the big fraction we had

[viscid thistle]

OHHHH

OKAY

[merry goblet]

okay so here's where we're at

$\frac{1+2x^2-8x+8}{(x-2)^2}$

[obsidian monolith]

Wumbo

[viscid thistle]

yow dude im sorry i thouht it was different from the other

[merry goblet]

no you're good. it's tough stuff. i get it

[viscid thistle]

thank you so much man for helping me

okay move on

[merry goblet]

okay so you see how we got to this point yea?

[viscid thistle]

yesss

[merry goblet]

perfect. okay so now we add the 1 and 8

[viscid thistle]

so 9?

[merry goblet]

$\frac{2x^2-8x+9}{(x-2)^2}$

right

[obsidian monolith]

Wumbo

[viscid thistle]

2x^2 - 8x + 9

OH YEAHHH

okay

[merry goblet]

yes perfect

[viscid thistle]

so back to the provlem

says that i have to find these letters

[merry goblet]

so we're really close to finding alpha, beta, and gamma

if we expand the denomintor we will see it clearly

[viscid thistle]

what do you call that again

greek

[merry goblet]

those are greek letters

[viscid thistle]

oh yeah greek

[merry goblet]

yea

okay so expand the bottom

foil it out

[viscid thistle]

so the a is 2 then the 8 is b and y is 9

[merry goblet]

almost

a and y are correct

[viscid thistle]

mhm

[merry goblet]

so you have a -8x and a +2Bx

so then -8=2B

you see where i got that?

[viscid thistle]

what made the 8 turn negative

[merry goblet]

it's being subtracted. it's the same thing as saying 2x^2+(-8)x+9

did that make sense

$2x^2-8x+9=2x^2+(-8)x+9$

[obsidian monolith]

Wumbo

[viscid thistle]

what number before it turns -8

[merry goblet]

could you rephrase that

[viscid thistle]

i mean like

did 8 change another number

like

aaa let me translate it

YEAH

what replaced -8

WAIT

no nvm it sorry

[viscid thistle]

i forgot we have 8 here

what the heck is wrong with me

[merry goblet]

lol

i was like uh how do i explain this

[viscid thistle]

im sorry dude LOL

[merry goblet]

no you're good lol

[viscid thistle]

so yeahh

[merry goblet]

do you see why -8=2B though?

[viscid thistle]

yes

its the same place

[merry goblet]

right. okay so what is beta then

[viscid thistle]

16?

wait

its 8

[merry goblet]

no.

[viscid thistle]

the beta is -8

[merry goblet]

$-8=2{\beta}$

[obsidian monolith]

Wumbo

[merry goblet]

divide both sides by 2

[viscid thistle]

-4

[merry goblet]

right

[viscid thistle]

OHHHH

WAIT

so

if it only find the b

we get -4

but if its 2b

we have to multiply it by 2

??

[merry goblet]

and it would give us back the -8 that we started with yes

[viscid thistle]

OKAYYY

but wait

[merry goblet]

but b=-4

which is all we needed

since we already have a and y

so a=2, b=-4, and y=9

now solve a+2b+y

[viscid thistle]

2-8b+9

is that correct

since its 2b

[merry goblet]

2b=-8 right?

[viscid thistle]

yeah

[merry goblet]

so a+2b+y=(2)+(-8)+(9)

[viscid thistle]

oh okay

i have to put it in a parentheses

[merry goblet]

no i just did that to make it clear

so what is a+2b+y equal to

[viscid thistle]

2+(-8)+9

[merry goblet]

which is

what

[viscid thistle]

i still have to do the pemdas righ

t

or no

[merry goblet]

if you add a negative, it's the same as subtracting the positive

so $2+(-8)+9=2-8+9$

[viscid thistle]

11 - 8 is 3

[obsidian monolith]

Wumbo

[viscid thistle]

so the answer is 3

[merry goblet]

yep!

ironically i added this incorrectly originally and got 1 lol

[viscid thistle]

LOL

[merry goblet]

yeah idk man

good job tho!

[viscid thistle]

MAN

WAIT

i feel like i wanna solve it now

even tho it only wants to find the greek letters

wait

is it even solvable

[merry goblet]

it's not something you solve. it's just a function

you could graph it if you wanted, but that's about it

[viscid thistle]

oh okayy

okayyy

MAN

[merry goblet]

the final form is $\frac{2x^2-8x+9}{x^2-4x+8}$

[viscid thistle]

why is hard math for me then for someone like u guys find it easy

[obsidian monolith]

Wumbo

[viscid thistle]

yesh

[merry goblet]

i've been doing math for like 20+ years at this point so

[viscid thistle]

woah

[merry goblet]

that helps

[viscid thistle]

you must be a prof

[merry goblet]

no just a degree

[viscid thistle]

why dont u get masteral

[merry goblet]

oh i plan to

[viscid thistle]

mhmmm

i hope u get higher

what is next to masteral again

[merry goblet]

and i hope you do well in school!

[viscid thistle]

i forgot

[merry goblet]

after master's is phd

[viscid thistle]

YEAH

i hope you get that also

[merry goblet]

haha. ty

[thorn creek]

the masters is optional in some programs

[viscid thistle]

you know man actually im in college and im studying electrical engineering, when we were in senior high school.. our school system is bad so our subject in pre-calculus that we only took for 1 semester is not enough for us

[thorn creek]

at my alma mater the masters degree is what you get as a consolation prize for failing quals

[merry goblet]

oof

[viscid thistle]

im freshman btw

do you guys have senior high

like grade 11 and 12

[merry goblet]

yeah.

highest math class in my high school was calc

[viscid thistle]

whattt

we dont even have calc in highschool

we only had mathematics thats all

[merry goblet]

but i've heard other schools teach calc in like sophomore/junior year

[viscid thistle]

and when i turn gr11 we had general mathematics then gr12 pre cal

[merry goblet]

yeah just depends on the area

[viscid thistle]

its really bad for me to study this course not knowing the basics of calculus

[merry goblet]

yeah that's tough. i wish you luck.

it's like 4:30 here though so i'm headed off

[viscid thistle]

you know man my classmates here in college are from stem strand that focuses on science,tech,engineering, math

thats why they adv than me

aaa

i picked other strand

i picked gas that focuses on generals

thats why

i kinda luck ỉn knowledge compare to them

yeah enough with the story

i just wanna learn math cause the relief when you finish it solving is a very good feeling

anywayss

THANK YOU SO MUCH MAN @merry goblet thank you for helping me and the other guy earlier that also helped me

Anyone know what main parts of geometry are used in Pre-calc like major points and like HAVE to knows? cause my geometry level is kinda weak so i wanna know what to focus on so I don't get stuck behind

[viscid thistle]

isnt the 8 on the denominator supposed to be -8

[leaden flint]

can someone please help me with this question 🙏

[summer crag]

||7.5cos(2π(x)/365-14π/365)+21.5||

[summer crag]

what should be the amplitude and period of T(d) ?

Also notice that the avg. temp is max at d=7

[leaden flint]

ah i solved it, thank you

🙏

[violet belfry]

does anybody know about "The idiots guide to calculus. "

[tired holly]

i got fed up with the byu double angle stuff in unit 3 so i wrote some super simple python code to solve all double angle identities based on original angle measure which you can get from arc sin/tan/cos: here it is if anyone would like it:
import math
angle = float(input('input theta'))/180*math.pi

cos2_val = str(math.cos(angle2))
sin2_val = str(math.sin(angle2))
tan2_val = str(math.tan(angle*2))

print('cos2theta = ' + cos2_val, 'sin2theta = ' + sin2_val, 'tan2theta = ' + tan2_val)

sorry it should say angle*2 for cos2val sin2val tan2val if u want it to work

[violet belfry]

ok

[scenic coral]

Lmao

Btw \* to cancel discord * for *italics*

also consider using
```python
code
```
which gives

print("hello world")

[frigid trout]

Does anyone have any YouTube video recommendations to learn pre calc from the beginning

[thorn creek]

the beginning of what, time?

i generally recommend khan for precalc

[frigid trout]

Just like from start without any previous knowledge I meant

Thank you will check it out!

[storm lodge]

#include <bits/stdc++.h>
using namespace std;

int main()
{
  cout << "it actually works\n";
}

[scenic coral]

#include <stdio>

int main() {
  std::cout << "fr\n";
}```

[storm lodge]

just realized you in usaco server

[scenic coral]

xd

[viscid thistle]

Hi, can someone explain the given solution to me?

[spare wharf]

How come 0.1 became 10? Thanks.

[summer crag]

0.1 = 1/10

[polar meadow]

divide by 0.1 and multiply by 10 is the same thing. See for yourself: 5 : 0.1=50 5*10=50

[spare wharf]

Aghh

Thank you!

[quasi brook]

could someone pls explain why the fundamental theorem of calculus is true?

like WHY can the antiderivative of a function be used to calculate the area under the curve

i'm not understanding the wiki page

[summer ruin]

if you want a proof - you can just search for it

[velvet sequoia]

Let F(x) be the area under f from 0 to x. Then increasing the value of x means shifting the right-side boundary of the area more towards the right. If f is high up at the right boundary, then shifting the boundary leads to a quick increase in area. If f is close to the x-axis at the right boundary, then shifting the boundary leads to almost no change in area. So as you shift the right boundary, you would expect the rate of increase of the area F(x) to be proportional to the value of f at the right boundary (that is, f(x)).

And it turns out that you have F'(x) = f(x) for "nice enough" functions

[quasi brook]

yep I'm reading the wiki page rn

but I didn't understand some parts of it

[quasi brook]

continuous functions right?

[quasi brook]

intuitively, i get that

[velvet sequoia]

Ye

[quasi brook]

but i didn't get the proof

like

here's an img

I got this so far

but I didn't understand this

like i didn't understand after h1 and h2 are introduced

[velvet sequoia]

It's more or less the same reasoning but written in equations and in more detail

You'll start approaching #real-complex-analysis territory when you look into it further

[quasi brook]

💀

so someone who's still in hs, the actual proof is too advanced?

rip

[velvet sequoia]

If by an "actual proof" you mean properly defining stuff like limits, continuity, integration instead of using pictures and vague wording

Then it's analysis

[quasi brook]

oh rip

ty for the explanation!

[velvet sequoia]

But there's nothing stopping you from studying it if you're interested

[quasi brook]

hm

what kind of prior knowledge would be required?

like for calculus you need to have a good grasp of trig/algebra

anything like that needed for real analysis?

[velvet sequoia]

Sets and experience in working with rather abstract stuff

The most basic parts of analysis are just making calculus rigorous so knowing calculus beforehand would let you know what it's trying to do

[summer ruin]

you basically can't properly do any math without acing everything in high school math, basic calculus knowledge includes sequences, limits and continuity

[quasi brook]

goti t

[quasi brook]

cool, thanks for all the advice!

prob won't be studiyng it any time soon though 💀

[viscid thistle]

Anyone?

[mellow vigil]

watch 3b1b calculus series

its one of the best playlist for UNDERSTANDING Calculus

[viscid thistle]

GUY
i have an exam on monday
MATHS - indefinite integration and conics
PHYSICS - magnetic effects of current, magnetism and mattter, current electricity, heating effects and instruments
CHEM - amines, carbonyl compounds, carboxylic acids and chemical kinetics
(tips pls_
i did complete most of it but im scared of chem and conics

guys i mean

[hallow pilot]

Im going into 12th grade this year

I have done studying of calculus over the summer

I have gotten currently up to curve sketching, but I am going to start integrals before I start school on Tuesday

I have not come across anything that is very difficult so far

And I have been able to work through a lot of it on my own

[viscid thistle]

Can someone help me here?

[queen cargo]

heyy can someone help me on a question

[frigid crag]

yes

im scared but lets see ^^

[warped cipher]

Do you still need help?

[viscid thistle]

Yes

[warped cipher]

just realized this is a probability question

i think you got a wrong channel

[viscid thistle]

Oh

Well can you help me anywho

In dms?

[warped cipher]

no, this is exam

I can't help sorry

your question belongs in #probability-statistics

[queen cargo]

can someone still help me

[radiant kite]

with what

[queen cargo]

lIf the domain of f is all real numbers in the interval​ [0,8] and the domain of g is all real numbers in the interval ​[-​3,4], the domain of f+g is all real numbers in the interval​ _______.

i know the answer is [0,4] but how do I get that answer

no worries i got it

[ebon moat]

yo guys how do I solve num 3? I'm done with 1 and 2 but I don't know what to do on num 3

[willow bear]

to cut away the black bands about 1.5 times as tall as the image itself...

@ebon moat you're given the equations of some circles, you're asked to read off their centers and radii

[ebon moat]

how do I do that

[willow bear]

do you know in general what the equation of a circle looks like?

[ebon moat]

is it the
x²+y²=r²? or is it some other variation of it?

[willow bear]

$(x - h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

[obsidian monolith]

Ann

[willow bear]

you need to massage your equations to look like this form, though

[ebon moat]

how do I do that

[junior plover]

<@&268886789983436800> urgent!

[hollow hedge]

got it

[junior plover]

these shits are increasing

[hollow hedge]

they're just hacked accounts

[junior plover]

oh

[solar olive]

3x^2 + 3y^2 = 48
x^2 + y^2 = 16
center = (0, 0) radius = 4

x^2/2 + y^2/2 = 18
x^2 + y^2 = 36

center = (0, 0) radius = 6

[viscid thistle]

can anyone help me

[solar olive]

f(g(x)) = 2(x+2)^2-(x+2) -2

g(f(x)) = (2x^2-x-2) +2

[thorn creek]

i do not like questions like that

[feral halo]

would it be 6xh + 3h^2 + 4?

I'm really confused can someone help me on this

[late geyser]

an h should cancel out of every term, not just the last one.

[versed vapor]

I am confused 🆘

[feral halo]

thanks

[queen cargo]

can someone help me

quickly

this things due in like 10 minutes

I have no idea

how to do this

[queen cargo]

no worries

[viscid thistle]

hello chat

[radiant kite]

help

[radiant kite]

please guys help 😩

[untold spindle]

<@&268886789983436800>

[obsidian monolith]

Dyssrupt

[timber spindle]

Will I be ok in Calc 1-2 if I’m not good with conic sections?

[severe moat]

how long, realistically ofc, would it take to learn college level calculus if the most advanced math class ive taken is algebra 2 with statistics?( looked into trigonometry by last unit)

[short saffron]

Can I ask a basic topology question here?

[deft cypress]

ur an opp

[tawdry viper]

@everyone

I need a tutor

for precalc

I can play

pay

[untold spindle]

use khan academy, its free

[tawdry viper]

oh okay, but its not that good at explaining

[untold spindle]

also dont ping everyone, it doesnt even work

[tawdry viper]

oh nvm

sorrry

for the troubles

[untold spindle]

if you need elaboration upon a topic you can always ask in this server

[tawdry viper]

ok

what math are you in?

[untold spindle]

college algebra, but it hasnt started yet

[tawdry viper]

what grade?

[untold spindle]

11th

[tawdry viper]

ah I see

im a freshman lol

I need help

[untold spindle]

with?

[tawdry viper]

2^x=(.0625)^-14

Solve for x

@untold spindle

[fresh agate]

once i know more math ill probably understand what this sever is talking about

[rough birch]

2.46

[tawdry viper]

huh

[rough birch]

lme double check

[untold spindle]

!nosols

[tender quest]

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

[rough birch]

@tawdry viper

[tawdry viper]

yah

I think thats right

[rough birch]

it is

[untold spindle]

i just told you not to give out solutions

[rough birch]

one time dude chill out

I'll explain

First, simplify (.0625)^-14

it becomes

2^x = 16^14

To solve for x, take the logarithm base 2 of both sides

x * log2(2) = 14 * log2(16)

[untold spindle]

still, its better to have them work through the problem themselves with you guiding them along the way, instead of having an explanation handed to them on a silver platter.

[viscid thistle]

how does it simplify to 16^14?

[rough birch]

simplification

?

[warm frost]

does anyone have the pdf version of this book? thanks

[viscid thistle]

Author? I can't see it

[thorn creek]

there ar efour listed authors but they're illegible in that image

first one looks like demora maybe

and an image search surfaces this: https://www.amazon.com/Precalculus-Graphical-Numerical-Franklin-Demana/dp/013227650X

so itr's demana, not demora

[viscid thistle]

Found the 8th edition lol

[thorn creek]

the 7th edition is from 2006, not that precalc has materially changed in the past 50 or 60 years

[viscid thistle]

Yeah I think someone did a sweep on it and took down all the sites with it for free .-. pair that with premium pdf .com or something that spammed sites tryna grab your credit card

You can find other editions (namely 8 and I think 10) and there are quite a few sites that tell you the exact answer to every problem in the book, but yeah I don't think you can find edition 7

[warm frost]

Hmm okay

Thank you

I found edition 8

[shy sonnet]

Does anyone know how to solve this?

[zenith stirrup]

If it is true for all x then simply put x equal to 2 you will get b and then put x equal to -3 u will get a

[pine light]

Can someone help me? I don't understand the last part, how does plugging in the x-coordinate of min prove B^2<AC? Like, shouldn't it be independent from x?

Proof of Cauchy-Schwarz btw

[ornate lion]

whats pie

[zenith stirrup]

Imaginary roots, discriminant negative, rest all follows

[short saffron]

Can a continuous function that is strictly increasing and strictly decreasing on an interval have an inverse? If not, why?

[willow bear]

vacuous truth go brrr

but also how are you gonna have a function be both strictly inc and strictly dec at the same time...

[pine light]

Sorry, but I'm too dumb for your explanations. Can you be more particular?

[radiant kite]

ping me

[pine light]

I got it, thanks!

[prime peak]

can someone help pls 😭

i forgot how to do these

[untold spindle]

You got the factored form already so that's good, now all you need to do is set each of the factors equal to 0

And solve for x

[prime peak]

yeah i did that

but for some reason its wrong

[untold spindle]

Well how did you get -1?

[prime peak]

oh shoot

wait that still wrong tho

[untold spindle]

Ohh I see, "enter all answers including repetitions"

[prime peak]

yeah i get it you write the double 0 twice

[untold spindle]

The double 0?

[prime peak]

yeah

answer is

1/2, -2, 4, 4

[untold spindle]

Ah yes good job👍

!nosols

[tender quest]

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

[queen cargo]

heyy can some help me

[void thorn]

hint: you can rewrite this in terms of the definition of derivative of e^(-cos x) at x=0

[queen cargo]

please help me 😭😭

im dying here

[queen cargo]

no worries

[tawny veldt]

i can’t tell which i disliked more pre cal or trig

they’re very fun when not for school

[quiet falcon]

going into precalc this year, anything i should be prepared for?

[warped cipher]

Check pinned messages for important stuff

[scenic coral]

It's just trig identities? Or is discord not showing the other pins?

[warped cipher]

Well I mean to say Trig identities important in precalc so you could prepare for that

You could also do graphs iirc

[zenith stirrup]

Lhspital rule laga le

[radiant kite]

yea im trying to solve it without using derivatives

or taylor series

or l'hopitals rule

[void thorn]

your funeral

[radiant kite]

there has to be a way

[void thorn]

there is depending on what you're willing to allow

[radiant kite]

just nothing that involves derivative

[void thorn]

is this allowed $$\ln(x)=\lim_{h \to 0} \frac{x^h-1}{h}$$

[obsidian monolith]

Merosity

[radiant kite]

how did u get that

but yea sure that is allowed

[vapid plaza]

[ \frac{e^{- \cos x} - e^{-1}}{x} = e^{-1} \frac{e^{1 - \cos x} -1 }{1 - \cos x} \frac{1 - \cos x}{x^2} x]

[void thorn]

basically the limit definition for e^x but turned inside-out

[obsidian monolith]

elon mask

[vapid plaza]

Oh it looks ugly bruh

[void thorn]

you can then substitute h=1-cosx

[vapid plaza]

The rhs can evaluate limit quite easily using some “elementary results” about limits

[void thorn]

since as x->0 in 1-cos x you have h->0 that turns it into lim_{h->0} (e^h-1) / h which...

[radiant kite]

how did u get 1-cosx in the denominator?

@vapid plaza

[vapid plaza]

Bro I wrote that whole thing

[radiant kite]

oh its multiplied nvm

[vapid plaza]

Limit of (1-cos x) /x^2 can be found by using elementary methods and the fact that limit of sin x / x is 1

[vapid plaza]

For example this post
https://math.stackexchange.com/questions/1334164/finding-the-limit-of-1-cos-x-x2

[radiant kite]

but how can u just replace the x in the denominator with h?
if h=1-cosx then shouldnt the denominator be cos^-1(1-h)?

arccos(1-h)

[vapid plaza]

No, we are solving for the limit of just $\frac{e^{1 - \cos x} -1 }{1 - \cos x}$ right now

[obsidian monolith]

elon mask

[void thorn]

the denominator is 1-cos x, so just replace that entire denominator with h

[vapid plaza]

After this we can multiply it with the other limits to arrive at the answer

[radiant kite]

oh ok

then just basic limits stuff from there

[mental ridge]

i need help studying for precalc test tmrw

dm me looking to go in a voice call so you can help in depth

[radiant kite]

what is the test about?

[mental ridge]

rates of change

[radiant kite]

average rates of change?

[mental ridge]

change in tangent

yes

[radiant kite]

alr

[mental ridge]

and a couple more topics

[radiant kite]

i guess i can try to help you a bit

in like 15 mins

[mental ridge]

bet

just message me

[radiant kite]

alr

[mental ridge]

yo

[radiant kite]

yea

@mental ridge

im here

sorry it took this long

[short saffron]

If $p(x)$ is a polynomial function, then what is $p'(1/x)$?

[obsidian monolith]

sunside

[radiant kite]

if p(x) was ax^n+bx^n-1+cxn^-2... and so on

then derivative of p(1/x) would be

nax^n-2+nbx^n-3... and so on

[short saffron]

hmm, are you sure? why n-2 in the exponent of the first term?

[radiant kite]

because when u do the power rule the exponent becomes n-1

and then u divide by x

so it becomes n-2

oh wait

nvm

[short saffron]

The derivative of p(x) would be nax^n-1+nbx^n-2... and so on. So plugging in 1/x, we get na(1/x)^n-1+nb(1/x)^n-2+... what am I missing?

[radiant kite]

it is ax^1-n+ax^2-n... and so on

right?

[short saffron]

maybe, I'm unsure 🙂

we need to work some examples probably

like p(x)=1+x^2

I think it's like this @radiant kite : if p(x) is a polynomial function, then we can apply the chain rule for (p(1/x))'=-1/x^2 p'(1/x). Of course, this leaves us with p'(1/x).

[frigid trout]

im just starting out pre calc ex. for z= 8i−172 the imaginary number will always be whats before i so 8 and real -172

so if its -9i +8 imaginary would be -9 and real 8?

[summer ruin]

yes

[frigid trout]

thank you, will those type of questions be formatted like that always and will there be more complex versions?

[uncut mulch]

imaginary part

[frigid trout]

oh yea sorry

[summer ruin]

you should be relying on understanding instead of question formatting

[rotund remnant]

Hey guys, I want to study pre calc and gen math 1 in advance. What should I study first?

[uncut mulch]

basic algebra

geo

[viscid thistle]

quick question

how do i get 24x there again

i forgot

from expanding (4-3x)^2

yeah

but how

is it foil method?

= (4-3x)(4-3x)

doing FOIL

16 - 12x -12x + 9x^2
collect like terms
16-24x+9x^2

YEAHHH

okay

thank u

im just used to x^2 always at first

anyone interested in number theories

[viscid thistle]

This is right, right?

differentiating gets me 2sqrt(x)

[viscid thistle]

Is this correct?

ah ive multiplied wrong as well anyway should be x^0 not x^1

[fresh kindle]

dude someone be my study buddy have help me with math i love it and i am terrible at it 🥲

[radiant kite]

no lhopitals

[charred frigate]

please don't post questions in multiple channels, especially in a channel that the question is unrelated to

[untold spindle]

the sin function gives different output depending on if your calculator is in degrees or radians

[uneven oxide]

the one on the right is in rads?

[untold spindle]

no, the left one is in radians, the right one is in degrees

check your desmos settings

[uneven oxide]

ok thank you

[untold spindle]

np

[analog flower]

these don't feel like they should be equal, and yet they are

[north cloud]

Woooah

How

Impossible

My eyes and brain hurt

[obsidian monolith]

Dyssrupt

[viscid thistle]

W property

[viscid thistle]

well they're going to be in product form when you ln them on both sides

[weary karma]

could someone help me with online pre-calc?

[slim steppe]

You could rewrite that as ln(x^x), and numerically test it

[smoky nexus]

Divide numerator & denominator by x?

Also simplify e^-1 & e^-cosx

[tropic obsidian]

Why does this work?

[obsidian monolith]

Şêro

Şêro

[tropic obsidian]

which would make sense, but I guess my question then is where the cube came from?

[obsidian monolith]

Şêro

[tropic obsidian]

oooh okay, thank you!

[floral horizon]

I’m finally able to understand messages in this channel now W

[desert socket]

im confused. shouldnt the 2nd part of the numerator be sinb/cosb...?

[uncut mulch]

yes

[tropic obsidian]

LITERALLY

[silver elk]

probably a typo?

[raw sinew]

omg hi

[shadow jay]

i dont get this

can somebody please explain it for me? thank u sm :D

[thorny cypress]

you have a second order equation

do you know the geenral form of a circle?

[floral horizon]

you learn this in geometry

[proven spear]

we need to convert it to the form (x-x_0)^2+(y-y_0)^2=r^2

just some basic algebra

the center would have the coordinated (x_0, y_0)

and the radius is r

[hallow lodge]

anyone know why they wrote vertices as that

[summer ruin]

as what?

these are coordinates of the vertices

[hallow lodge]

why the 1 and the -3?

[summer ruin]

(1, -3) is the center of the ellipse

[hallow lodge]

why did the order chhange for co vertex?

[summer ruin]

it didn't change, (1,-3) is still the center of the ellipse

now you're adding or subtracting some number to x instead of y because coverticies are located along other axis

[hallow lodge]

so do i always write them in that order?

with b^2 in the middle

[summer ruin]

what order?

[hallow lodge]

vertex has a^2 on the last part

while co vertex has b^2 in the middle

[summer ruin]

they don't, these are roots of a^2 and b^2

and obviously your question reduces to whether (1,-1) is the same point as (-1,1)

it isn't

the order in which you write coordinates depends on what point you're trying to describe

[hallow lodge]

is this always the formula of vertices and coverts?

[summer ruin]

see this picture

[hallow lodge]

ive done horizontal and vertical equations. they seen to have the same formula being, square rooting a^2 for vertex and b^2 for covert

[candid jetty]

I know it’s kinda sudden but I need some help with some Precalc

We have a quiz tomorrow and I’m struggling to understand. Has to do with functions

I can be more in depth, just give me a minute

Here’s a good example for one of the things I’m struggling with

I can answer the simpler ones, but this one I can’t figure out

There’s some other things but that was the first question I saw when I opened my MacBook

Just ping if anyone responds so I know to check here

Yes, but please don’t ask me to define it

Basically it’s a relationship between x and y. Usually I see them put on a table, with x on the left and y on the right. These points are used on a graph

I tried my best, but defining things is not my specialty

It’s ok if I use the usua f(x) right?

[verbal garnet]

so long as there is only one function named f at the same time

[obsidian monolith]

kebesque integral

[candid jetty]

And when you’re given an x value, you can plug it into those x spots

40?

I’m struggling to describe it, but I’ll make an attempt

I need to plug it into the equation 4xpixr squared

I can’t find the pic symbol in my phone

Pi

Ohhhhhhh I see what I was doing wrong

[obsidian monolith]

kebesque integral

[candid jetty]

I know pemdas, but I kept plugging it into parenthesis for some reason

I did the math for the first problem in the picture

I got 113 after rounding

It doesn’t tell me where to round to

Just to simplify

Squaring a fraction

I take 1 over 3

And square it

What would I be looking for?

Ah ok

I got 4 times pi over 9 for the second one

Only got the second one right

5-2(s+3)

Would I do distribution here?

Or whatever it’s called

Where I multiply both by 2

I got it!

Just have one more thing on this HW then I’ll be good to study

[candid jetty]

I got them all except for the last one, which is definitely tricky

Wait I may have found my issue

[obsidian monolith]

Şêro

Şêro

[candid jetty]

7 plus 4 plus 6

Because -1 squared is positive 1

And two negatives make a positive

And 6 is 6

PEMDAS and all that

You end up with 17

Yeah I had gotten that one right

The only one I hadn’t gotten was the third one

I did that

Lemme type it out

[obsidian monolith]

Şêro

[candid jetty]

Ok this is where I got confused

[obsidian monolith]

Şêro

[candid jetty]

Wait what?

How did you get to that step?

That process in the middle is what stumped me

[obsidian monolith]

Şêro

Şêro

Şêro

[candid jetty]

Kinda? We’re in a part that I struggle with now

Well

I can see what you’re doing

But I can’t replicate it when given different numbers

I struggle to read deeper into math

[obsidian monolith]

Şêro

[candid jetty]

$y^2+2xyx6+12

Huh

Weird

Just try and read that I guess

So

y^2+12y+36

[obsidian monolith]

Şêro

[candid jetty]

Ah ok

Can I have another?

[obsidian monolith]

Şêro

[candid jetty]

Alright

Would I distribute first?

Hm

4z+12^2

4z^2+2xz+9?

That’s wrong, I know it

4z^2+2xZ+2x3+3^2

4z^2+2z+15

Is that right?

[whole island]

@candid jetty remember first, inner, outer last.

[candid jetty]

Sucks it can’t be FOIL

[whole island]

yes, foil.

if you follow these steps, include order of operations, you will get the answer

[candid jetty]

Ah ok

[candid jetty]

So I can do that now

I can determine what a function is

I know how to find intercepts

Y intercept, make xs 0

X intercepts, make y zero

I can determine symmetry of a line

Actually

I may need to work on determining symmetry with an equation instead of a graph

There’s other things I think

We only did half the chapter

[dry sparrow]

hey

[untold spindle]

,rccw

[untold spindle]

Have you done anything yet?

[dry sparrow]

i think i got it actually

-9x+3 after i used PEMDAS

[untold spindle]

Ok 👍

Could I see your work?

It doesn't sound quite right

[untold spindle]

Oh that's not how you multiply binomials, what you should be evaluating is
(5x-7)*(2x+3)

!nosols

[tender quest]

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

[digital valve]

sorry

new to the sertver

[untold spindle]

It would be better for her to work it out herself rather than given the answer on a silver platter.

[untold spindle]

All good, please do delete the answer though

[dry sparrow]

thanks

yes thank you

cashapp?

[untold spindle]

Umm <@&268886789983436800> isn't this against the rules?

[dry sparrow]

was the answer he provided right tho?

[digital valve]

?

[untold spindle]

Work it out yourself and you'll see

[digital valve]

10x^2-9x-18

[untold spindle]

[digital valve]

this is correct

[untold spindle]

I just told you not to give out answers

[digital valve]

she asked

if the answer was right

is the asnwr correct @raven lark

[untold spindle]

<@&268886789983436800> srry for second ping btw

[digital valve]

ur spamming the moderators?

why

[dry sparrow]

10x^2+x-21

this is uit

after working it out i got this not that @digital valve

[modern valve]

sorry for late response, banned relevant users

[untold spindle]

It's all good, thanks

[warped cipher]

how did you get active role with 10 messages

[untold spindle]

You don't want to know ;-;

[warped cipher]

sadge

but im surprised tho

[remote dune]

could be deleted messages

[viscid thistle]

oh dam my dad made me do more math 😐 😐

[short knot]

How do I simplify this

I’ve been trying too but I’m confused bc you can only at like terms

[odd yew]

it is multiplying -9 with sqrt(-36)

so you have -9*6i

which equals to -54i

which can be expressed in the standard form of a + bi

a = 0

b = -54

[short knot]

thank you

[cloud flower]

I just started learning about functions in precalc and i forgot everything from algebra

And i have no idea what im doing

How would you solve y=x^2 +-3

For example

[scenic coral]

Can you clarify your use of +-

[cloud flower]

Either or

[scenic coral]

Ok

[scenic coral]

That's not a function

[cloud flower]

Oh

[scenic coral]

A function must satisfy the vertical line test

Meaning a unique y must exist for every x in the domain

[cloud flower]

Okay well how would i solve a function without a number on x

Thats what i dont really get

Like for example

[scenic coral]

plus or minus would make it not a function due to it yielding 2 y values

[cloud flower]

F(x)=x+4

[scenic coral]

wdym by solve?

[cloud flower]

Like what would be my value

Or my output

[scenic coral]

x + 4 ...

[cloud flower]

Is that literally it

Is the output just x+4

Okay if thats the case would x=2y^2 be 4y

[chrome galleon]

How would i get x? I dont understand what I am looking at exactly.

[cloud flower]

Or 4x2 making thr output 8