precalculus

[harsh smelt]

btw, here is another crosscheck

[gloomy mortar]

That’s what you do for everything else

Plug it into the equation

[harsh smelt]

,w 52.31/sin(86deg)-45/sqrt(1-16.5649)

[obsidian monolith]

Display results online and refine query

Requested by Commander Vimes#7532

[viscid thistle]

Welp we assumed that if you are taking cosine law or trig you had some good base on algebra

[gloomy mortar]

So would you say then that I should’ve taken a and isolated it before doing all this?

Yeah I did and you plugged in stuff into your equation

[harsh smelt]

here everything is fine

[gloomy mortar]

It would still give the same result as if you isolated the cosC if you do the math right and yeah I didn’t divide the cosC but that’s the thing I didn’t divide cosC I don’t have to isolate it all first I’m gonna get the same thing right?

Just like in that equation

I didn’t isolate a, I plugged it into my equation

[remote veldt]

The two will give the same final result, if you do it correctly. Plugging in numbers is more error prone though - for example, you took 3633 and 3138cosC, and you subtracted 3138 from 3633

[gloomy mortar]

Like how you get the same thing doing x+4=0 as having x=-4

[remote veldt]

this is an error that's far less likely to occur when you're working strictly with variables

[gloomy mortar]

Okay well I’m saying that’s not how I’ve been taught. I’ve been taught to plug things into my equations. I would’ve made this same mistake with variables

[remote veldt]

do you know why 3633 - 3138cos(C) isn't the same as (3633 - 3138) * cos(C)

[gloomy mortar]

I don’t get how I’m supposed to get cosC by itself with so much multiplication

[remote veldt]

division is what undoes multiplication. I'm going to work with only variables, because I don't want to type in the numbers. I'll be as detailed as I can be

[gloomy mortar]

Hold on

Yeah I know what undoes multiplication

Doing it in the variables confuse me with it even more though

[remote veldt]

$$c^2 = a^2 + b^2 - 2ab\cos(C)$$

$$c^2 + 2ab\cos(C) = a^2 + b^2 - 2ab\cos(C) + 2ab\cos(C)$$

$$c^2 + 2ab\cos(C) = a^2 + b^2$$

$$2ab\cos(C) = a^2 + b^2 - c^2$$

$$\frac{2ab\cos(C)}{2} = \frac{a^2 + b^2 - c^2}{2}$$

$$ab\cos(C) = \frac{a^2 + b^2 - c^2}{2}$$

$$\frac{ab\cos(C)}{ab} = \frac{a^2 + b^2 - c^2}{2ab}$$

$$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$$

[obsidian monolith]

Nicholas:

[gloomy mortar]

Yeah I figured it out but I told you it confuses me more

[remote veldt]

why?

[gloomy mortar]

See I already did this when I said hold on

Because I had to do it many times since there’s so many letters

That confuses me having so many variables

Which is why plugging it in (if I did the math right) works better for me

[remote veldt]

if you do it with numbers, you have just as many numbers as letters

and the numbers are longer to write

[gloomy mortar]

It’s just easier to me seeing the numbers, idk, just how my brain works

I was originally making the same mistakes with the variables as I did with the numbers

I had to redo it several times

[remote veldt]

alright; if you've found somethign that works, leave it there. Leave your mind open to the possibility of working with variables however - it really will end up simpler

[gloomy mortar]

Variables confuse me because of all the letters. I think the reason numbers are easier is because I can simplify them as I go

How’s this

[inner karma]

just imagine that the letter is a number

just without giving it the number properties

like the property of 1 that any number times it equals the number itself

[gloomy mortar]

It’s just easier for me to do the numbers, I just separated cosC from the rest of the multiplication and that messed it up but I would’ve done the same with variables

Is that question right now

Also what about this one? Is this correct?

[inner karma]

yes

correct

but my question is

why derive it all over

when you could've just known what side is opposite the angle you wanna find(which is the length 20 side)

then use $$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$$

[obsidian monolith]

TheDucc:

[inner karma]

where the lowercase c is the side opposite the angle you want to find

a and b are the other 2

sides

that's it

[gloomy mortar]

For 2, I didn’t have a originally, I had to find it

And like I said, numbers are just easier for me to keep track of since I can simplify them as I go instead of having tons of letters in there constantly

Just how my brain works idk

[velvet garden]

Here goes a set of exercises from our last assignment

About exponential, logarithmic and trigonometric equations.

[vague jewel]

any tips to get x alone

[velvet garden]

Factor x

[vague jewel]

OMG

i feel stupid

i was so focused at the constant

[velvet garden]

Yea happened to me in a chem exam, didn't even think about factoring a var in order to get it alone

[vague jewel]

yes my bad

here can u confirm if theyre the same?

[viscid thistle]

@vague jewel do you have to prove that they are the equal?

[vague jewel]

no

[viscid thistle]

Then?

[vague jewel]

my prof wrote this and idk why he put e in the bottom

[viscid thistle]

Where

[vague jewel]

or take out an e

highlighted

[serene heath]

x=e^(ln(x))

[vague jewel]

AH

so u can put e as long as u put the whole thing in ln(....)?

[steep fox]

what is the point in #geometry-and-trigonometry if trigonometry can also exist here

[gloomy mortar]

Calculus is also in here, and precalc is a specific subject in the US

[vague jewel]

was that about my qs?

[steep fox]

my message was about mythical's

[vivid nebula]

pog

im here ngl

[zinc raft]

Is that -2 + 2/5 ??

[past meadow]

yes

[viscid thistle]

can someone help me with number 1?

[uncut mulch]

@zinc raft @past meadow actually no. it implies - (2 + 2/5) = -2 - 2/5

mixed fractions

[past meadow]

oh you're right. didn't see the -

[austere zinc]

is there anyway i could get some help with this? i am having trouble with it

[harsh smelt]

you are liuterally given answer in the matrix

look on row where 4th entry is not zero

and on constants vector column

[austere zinc]

is the answer literally just 1?

ive never seen this before

[harsh smelt]

yes

[austere zinc]

ok thank you

[harsh smelt]

in general in rref you get 1 and some A in constant's vector and it means that x_i is A

[harsh cipher]

Hello

I have a question

[past meadow]

[harsh cipher]

how can e= 0

e cannot equal 0

[willow bear]

who wrote the thing in purple?

[harsh cipher]

the guy in the video

not me

[harsh smelt]

why you say it is parabola and draw hyperbola?

[willow bear]

can you fast forward a few seconds

[harsh cipher]

that's the end of the video

[willow bear]

it just cuts out at this point?

anyway yeah it should be E ≠ 0

[harsh cipher]

that's the whole video

[willow bear]

can i have a link to the video

[harsh cipher]

you need to log in to watch

😦

http://bclearningnetwork.com/LOR/media/cc_math/Math12_PC/Unit7/Lesson5/ConicsL5q4a.html

or try that

[willow bear]

urgh

[harsh cipher]

lol

exposed my school damn it

whatever though you I'm cool with that

[willow bear]

ok yeah lmfao this guy fucked up

the y term must stay so E must equal 0

bruh

[harsh cipher]

huh?

e must = 0?

[willow bear]

no i'm just quoting what the guy in the vid said

[harsh cipher]

oh

lol kk

[harsh smelt]

why you say it is parabola and draw hyperbola?

[willow bear]

those are meant to be two parabolas

[sterile notch]

http://bclearningnetwork.com/LOR/media/cc_math/Math12_PC/Unit1/Lesson1/

damn we have full access to the course now

too bad its just precalc

[silver matrix]

Hello, I have no clue on how to do this. Any help would be appreciated.

[lilac pier]

@silver matrix In my opinion, it would be easier if you think about this question in terms of probability. That is, the probability that a student purchases tickets to a play is 0.65 and the probability that a student purchases a ticket to a football game is 0.6. Now think about P(A∩B)

[silver matrix]

The maximum would be 0.60 from that intersection but I don't know how to calculate the minimum.

Maybe Baye's Theorem?

[willow bear]

no

[silver matrix]

Ok

[willow bear]

inclusion-exclusion

let A be the event that a randomly selected student purchased a play ticket and let B be the same for the football game

we're given that P(A) = 0.65 and P(B) = 0.60

inclusion-exclusion gives $P(A \cap B) = P(A) + P(B) - P(A \cup B) = 1.25 - P(A \cup B)$

[obsidian monolith]

Ann:

[willow bear]

so $P(A \cap B)$ is minimized when $P(A \cup B)$ is highest, and in this case it can go all the way up to 1

[obsidian monolith]

Ann:

[willow bear]

which leaves you with 0.25 for the minimum

[silver matrix]

Wow, thanks for the answer. I didn't know about this principle. It makes a lot of sense.

Thanks.

[silver matrix]

What I've done so far is
f(4) = 3 · 4^2 - 4 · 4
= 3 · 16 - 16
= 32

So if I substitute on the formula, it gives me:

,align
\frac{(4+h) - f(4)}{h} \
&= \frac{32 + h - 32}{h} \
&= \frac h h \
&= 1

[obsidian monolith]

Pa_u_los:

[silver matrix]

Which it's incorrect.

So I don't know how to approach it in a correct way.

[obsidian monolith]

Publius:

[silver matrix]

Why?

[pale bison]

substitute x to be 4 + h as required

[willow bear]

$f(x) = 3x^2 - 4x$

[obsidian monolith]

Ann:

[willow bear]

$f(\thonk) = 3(\thonk)^2 - 4(\thonk)$

[obsidian monolith]

Ann:

[willow bear]

did i make myself clear enough

[pale bison]

not quite ann, what about f(🥒 )?

[willow bear]

f(🥒) = 3(🥒)^2 - 4(🥒)

f(🍆) = 3(🍆)^2 - 4(🍆)

[sour eagle]

what about f( ) = ?

[silver matrix]

,align
&=3(4+h)^2 - 4(4+h) \
&=3(16+8h+h^2) - 16 - 4h \
&=48 + 24h + 3h^2 - 16 - 4h \
&=\frac{3h^2 + 20h + 32}{h} \
&=3h + 20 + 32 \
&=3h + 52

[obsidian monolith]

Pa_u_los:

[silver matrix]

What am I doing wrong?

[sour eagle]

why are you dividing by h

[pale bison]

1. line 3 and line 4 are NOT EQUAL, so don't put an equal sign
2. you forgot to minus f(4)

[silver matrix]

No, I did not forget to minus f(4), it's -16 and -4h with the minus in front.

[pale bison]

no, you did

double check again

[sour eagle]

that's -4(4+h) but there is also f(4) = 32

[pale bison]

this entire thing is f(4+h)

btw Dan, f( ) = 3( )^2 - 4( ), it's just algebra bro

[silver matrix]

Ok, thanks for the answers.

[sour eagle]

😭

f(f(f(f(f(...))))) = ? 😳

[obsidian monolith]

Publius:

[viscid thistle]

guys, may I get help with this?

@viscid thistle lol

dude, im lost

@viscid thistle

@viscid thistle what was your grade last week

for the written problem

let me check

wait

are you in AoPS too?

no i am psychic

what?

nvm what was your grade last week

like overall?

polynomial: for the written problem

ah

6.6

[fossil crown]

From

#❓how-to-get-help

Rule 6

Do not ask for help on tests. Any violation of this will lead to appropriate action being taken at mod discretion.

[viscid thistle]

6.6?? wtf lol

its not a test 🙂

out of 8

now you are lying

show a screenshot

prove it 🙂

how about

i send it after the due date?

send the week b4 that one then

lol

ah fs

nice screenshot dude

wrong one

yeah 6.6

lol

lmao, dude their grading is so ass

why

the overall explaining it, for example, I can understand the problems fine its just putting them in words are very diffucult

i think thats the point

lol

just a guess tho.

yea probably

im still very confused about that question though

protip

get rid of the parameters

smart

lmao your tabs @viscid thistle

"interval notation latex"

dude i didnt even learn it

its so wack

[gloomy mortar]

Could someone help me with how to start this problem?

[viscid thistle]

@gloomy mortar its a triangle

draw the triangle

[gloomy mortar]

Yes, I know it’s going to be a triangle but there are all these speeds and stuff, I’m confused what would be what and where on the triangle

I tried earlier but I ended up getting confused where each value would go

[viscid thistle]

what do you mean

you have the length of the triangles sides in miles

@gloomy mortar bruh i already told you guidance

[gloomy mortar]

This is the next problem we just did the other

[viscid thistle]

I know.

Don't you remember the big text i made

[gloomy mortar]

Yes and I have it saved I’m still confused what’s what though

[viscid thistle]

lol

You dont know what motion eqn are

[remote veldt]

@robust rover your selection is definitely wrong. Anything squared is positive, so how would it be possible for csc^2(x) to be negative?

We also know that sin(x) is between -1 and 1; this means that csc(x) can't be between -1 and 1, so that exclused the second option.

To decide between the other three, you need to know some special angles. I would suggest simplifying csc^2(x) and cot(x), and see if you recognize any special angles/ratios

I kinda figured; it's still important to know why those first two are wrong

guessing between 3 is much more likely to be correct than guessing between 5

https://www.khanacademy.org/math/trigonometry khan academy has a whole bunch on this stuff. The entire first section should be relevant

[gloomy mortar]

Did I set this up right?

Because I feel like the triangle should be flipped but then there isn’t two angles

Unless I were to make two triangles in one?

[viscid thistle]

looks right, remember to put arrows tho

[uncut mulch]

its recommended you actually draw a diagram with at least N↑

when bearings are involved

and no, the diagram looks wrong

[gloomy mortar]

I still feel like it should be flipped but how would there be two angles if it were flipped

[uncut mulch]

draw axes with NESW, and denote the airport at the center

diagram's still wrong

[viscid thistle]

@uncut mulch are you available?

[uncut mulch]

maybe. use an open channel. i'm im unable, someone else will

[viscid thistle]

yea no worries

[uncut mulch]

@gloomy mortar still there?

[gloomy mortar]

Yes

[uncut mulch]

did you follow the initial instruction?

[gloomy mortar]

Wdym

Wait

Let me try

Like that?

[uncut mulch]

better approach than before, but not accurately representing the bearings

N18°E is 18° East of North

and S62°E is 62° East of South

[gloomy mortar]

What

OH WAIT

[uncut mulch]

eg

18° measured from North towards East

[gloomy mortar]

So that?

[uncut mulch]

the angles are right now. but you mixed up the planes

[gloomy mortar]

N18°E and S62°E

[uncut mulch]

the plane going S62E and travelled 570mi/3 = 190mi

[gloomy mortar]

Oh whoops yep

[uncut mulch]

the plane going N18E and travelled 525mi/3 = 175mi

[gloomy mortar]

Okay so is that right now?

[uncut mulch]

and you should apprpriately label those points as A and B

yep

[uncut mulch]

perfect

[gloomy mortar]

So then would I want to find <C? That would be 100°

[uncut mulch]

try to refer to it as <BCA since there;s other things mixed in the diagram

but yes

[gloomy mortar]

Yeah

Is this right?

[uncut mulch]

yeh

[keen sigil]

could someone help me out with this? im not sure how to do it

[willow bear]

"exact multiple"

did they mean rational multiple

[keen sigil]

i would assume so

oh is it csc^2(x) = 4/3

i worked it out and got pi/3 as the reference angle

[willow bear]

yup

[keen sigil]

oh, ok

thanks

[remote veldt]

wait this exact question was posted a little bit earlier

choices rearranged though

interesting

[hallow belfry]

can anyone help me with this

[viscid thistle]

use sine law

@hallow belfry

[hallow belfry]

ohh

ok

ty

[viscid thistle]

np

🙂

@viscid thistle isnt it cosine law

You prolly meant cosine law not sine law

@hallow belfry its cosine law not sine

[hallow belfry]

ok ty

was a bit ocnfused trying to flip the triangle and stuff

[viscid thistle]

Np

[hallow belfry]

how do i find c tho

[viscid thistle]

@viscid thistle yah cosine law my b

use cosine law to find C

big brain working overtime

This'll help :)

@hallow belfry

[hallow belfry]

ye i got it but ty

[viscid thistle]

np 🙂

[sinful viper]

find the number of possible pathways, u can move in any direction as long as it spells “level”

probably related to Pascal’s triangle but I’m not sure how to apply it

[sinful viper]

would it still work if you can do the puzzle backwards? ie bottom up

if it was like a word that wasn’t level I can just add up the sum of the 5th row

[viscid thistle]

i found 11

[full garden]

Hey guys i have a very quick question please

For all values of x, let f(x)=4. Calcluate f(3)

I think it should be 4 but idont think question can be that simple

can someone please clarify it for me

[past meadow]

4 seems to be correct. thats an odd question

[full garden]

EXACTLLYY

EXACTLLYYY

[full garden]

can someone please clarify it for me

[viscid thistle]

well if for all values of x gives a f(x) = 4, and 3 is an example of x , then f(3) must be 4

[full garden]

okay thank u bro

[viscid thistle]

np 🙂

[full garden]

I don't know if I should pick C or D

I really don't know because they both seem to be correct

can someone please clarify for me

[viscid thistle]

i'd guess C if iwere u

[full garden]

😅 okay bro thank u ❤️ very very much

[somber thicket]

im in pre calc 11

[full garden]

nice me too bro

grade 11 right?

[somber thicket]

yea

[smoky needle]

Can someone help me with this?

[viscid thistle]

http://home.windstream.net/okrebs/page102.html

[rigid beacon]

@smoky needle double angle formula

for tangent

[viscid thistle]

What?

No. Its sum of angles formula

@rigid beacon you prolly mean it, didn't you

[rigid beacon]

yea that's what I meant

my bad

[full garden]

This is the question and that is my answer

Is this correct 😅 ?

[modern wolf]

I think so... Every 5 days it multiplies the number of bacteria by 2

[full garden]

okay thank u so so much buddy

[modern wolf]

Np

[full garden]

Here it defines a function so one input and one output

so it cannot be 4, or 2

but I think it can be -2 and also 1 and the function would still be defined

cansomeone please please clarify this question for me

[harsh smelt]

@full garden why do you think -2 is not needed

and 1 is not?

[full garden]

okay

so -2, 1 is a repeated point

that's why

[harsh smelt]

that's true

[full garden]

oh

[harsh smelt]

now what is the reason for 1?

like why did you decide it is not needed

[full garden]

i think 1 is valid 😅

because I think two inputs can have the same output if the numbers are different

[harsh smelt]

yep

x^2 is trivial example

[full garden]

❤️ thank u bro

so a can be 1

okay thank u bro

[harsh cipher]

Hello

question

can someone show me their work after they factor (3x^2-2x+1)

[viscid thistle]

@harsh cipher they did a process called complete the square

I suggest you to watch some videos about it

[sinful viper]

I’m stuck on this question again

[viscid thistle]

I guess every term is a sum of a geometric sequence

[sinful viper]

ah yeah, I did some work and term 2 (0.11) is equal to 1/10 + 1/100, and 0.111 is equal to 1/10 + 1/100 + 1/000

how should I apply that to determine the general/explicit term?

[viscid thistle]

the n'th term is the sum from i = 1 to n of 10^-i

not 100% sure

[sinful viper]

what is i?

[viscid thistle]

is just a variable

hold on

[stuck lark]

$\sum_{i=1}^n10^{-i}$

[obsidian monolith]

RokettoJanpu:

[stuck lark]

seen smth like this?

[viscid thistle]

I didnt know you could do that

[stuck lark]

not you

[sinful viper]

I have but quarantine happened so teacher didn’t go in depth whatsoever x_x

or go into any detail into what it is LOL

[stuck lark]

it's summation notation, a way to shortly write sums. use google

[sinful viper]

ah ok, I googled it and got the gist of it

[harsh cipher]

@viscid thistle the +1 is complete the square part.

in order to find the centre I need to factor that

[warm grail]

Anyone remember the details of half angle identities?

I think that it's simple, but it's been awhile since I've touched the subject so I forget most of what I knew!

[warm grail]

Yes exactly

[viscid thistle]

does this help:

[warm grail]

So if I have sin^4x set equal to a phrase, where do I go from there?;

Well I have this stuff in my notes, I just can't remember what to do with the info if that makes sense

I forget how the whole interval thing works, too

Should I watch a Khan academy vid? Maybe that's the strategy here

[viscid thistle]

nice arm

[warm grail]

Oops

That's a leg but okay bro

Shouldve tried to crop picture lol

[viscid thistle]

that was my initial thought but it looked like you were wearing a shirt

[warm grail]

Haha yeah

Weird pic

[viscid thistle]

looks to thin to be a leg imo

[warm grail]

Haha well

Idk dude

[viscid thistle]

i think for the first question you should expand the fraction on the outside of the brackets with the stuff inside the brackets

[warm grail]

Think so?

Then it would all be over 8

Maybe I replace cos2x and cos4x with they're identities

Like another form of the phrase

[viscid thistle]

yah maybe

[warm grail]

I'm lost

Imma watch Khan academy lol

Sorry bout that

[viscid thistle]

no worries haha

i think you should make everything on the right side in terms of sinx

for 6)

[viscid thistle]

can someone help me with two questions i have for my online precalc class please im genuely stumped

[tawny nacelle]

[hardy galleon]

Ok so I'm not sure if this goes here or in algebra but

I'm minimizing an expression with AM-GM inequality and I can't figure out how to do it

The question goes

a>b>0, a + 1/[(a-b)b]

The farthest I got with this is that

[viscid thistle]

AM-GM?

[hardy galleon]

a + 1/[(a-b)b] - b + b > (a-b) + 1/[(a-b)b] > 1/2 * [(a-b) + 1/[(a-b)b]] > sqrt(1/b)

arithmetic geometric mean inequality

=tex \sum_{k=1}^{n} \frac{a_k}{n} >= \sqrt[^n]{\prod_{k=1}^{n} a_k}

.help

[viscid thistle]

,tex

[obsidian monolith]

Please give me something to compile! See ,help and ,help tex for usage!

[hardy galleon]

,tex

[obsidian monolith]

Please give me something to compile! See ,help and ,help tex for usage!

[hardy galleon]

,tex \sum_{k=1}^{n} \frac{a_k}{n} >= \sqrt[^n]{\prod_{k=1}^{n} a_k}

[obsidian monolith]

Jasper:
Compile Error! Click the reaction for details. (You may edit your message)

[hardy galleon]

this is the am gm inequality

[viscid thistle]

jesus

is this whats waiting for me

[hardy galleon]

so I need to somehow apply this to minimizing

a + 1/(a-b) * 1/b

Does anybody have any idea

[viscid thistle]

you might wanna ask in #❓how-to-get-help people come here less and its more for discussion

[hazy geyser]

Can some hero here show me that

prove this?

[viscid thistle]

just expand it

and simplify

[hazy geyser]

then wha

ah ok

solved it

[smoky needle]

Can someone help me with this?

[viscid thistle]

https://socratic.org/questions/how-do-you-simplify-the-expression-sin-arctan-x

[smoky needle]

@viscid thistle thank you!

[viscid thistle]

np 🙂

[drowsy karma]

When you're converting a slope y-intercept equation into a general form, how do you know which terms to bring over to the other side? Does Y always stay?

[muted granite]

Why is y=(.30/2)(x)+1.30 not the proper equation for the table of values?

[drowsy karma]

Like I'm looked at some answers in the key. Equation was 3y = 21x -8, then they brought Y over so it became 21x - 3y - 8 = 0 . But in another equation 3y = -5x + 10, they brought the right hand over so it became 5x + 3y - 10 = 0

[viscid thistle]

bc as your x increases your y decreases

[drowsy karma]

So like how would you know which side would you bring over

[viscid thistle]

plus, 1 - .84 isn't .15, it's .16

[muted granite]

So, how do I find the equation?

[viscid thistle]

are you sure the numbers for the y-value are correct?

[muted granite]

yes

@drowsy karma I think for general form you have to make both variables positive terms. That decides what crosses.

[drowsy karma]

But it made 3y a negative

in the first example

[muted granite]

oh nvm then.

[drowsy karma]

Yeah idk

[viscid thistle]

it doesnt matter

[drowsy karma]

Apparently it needs X to be positive all the time

Thats how it decides

according to megan on youtube

[muted granite]

@viscid thistle Do you know how to derive the equation from that table of values? Any two points I always get a different slope. im at a lost.

[viscid thistle]

@muted granite your slope should be -0.3, not 0.3

[muted granite]

-0.3/2?

[viscid thistle]

also, since its in a decimal form, you might wanna convert it into a whole number

[muted granite]

y=(-0.30/2)+1.30 is not correct.

[viscid thistle]

well thats bc you can't have a decimal in a fraction

[muted granite]

that didn't work either.

[viscid thistle]

what did u try

@muted granite

[muted granite]

y=-0.15x+1.30

the issue is the slope. because the value of y is not decreasing at a constant rate.

[viscid thistle]

maybe they want the equation of the slope from x= 0 to x = 5?

so (.56 - 1.3) / (5 - 0)

[muted granite]

I tried that. Did not work either.

i dont get it. You should be able to find slope viz. slope formula, and the y intercept, and call it a day.

[viscid thistle]

maybe the answer in N/A

[muted granite]

@viscid thistle the answer is y=-.148x+1.30. But Idk why.

[viscid thistle]

@muted granite its bc (.56 - 1.3) / (5 - 0) = -.148

you said you tried that but it didn't work

[fluid sable]

Hi,

I have a question

[past meadow]

[fluid sable]

How would you go about solving this ?

o is this not precalc

I feel like I'm slowly

[uncut mulch]

it is

[fluid sable]

becoming worse at maths

its actually annoying lol

[willow bear]

this is precalc alright

it might help to express 27, 9 and 243 as powers of 3

[fluid sable]

I've thought of that yeah

9^3/9^3p-1=no^3

[willow bear]

27 is not 9^3

[fluid sable]

no

[willow bear]

and 243 is not 27^3

[fluid sable]

no

hello maths ?

[willow bear]

$\frac{3^3}{3^{2(3p-1)}} = 3^5$

[obsidian monolith]

Ann:

[fluid sable]

3^3*

yes

[past meadow]

so now how can we simplify that?

[fluid sable]

$\frac{3^3}{3^(3p-1)}} = 3^5$

[obsidian monolith]

Saveable:
Compile Error! Click the reaction for details. (You may edit your message)

[fluid sable]

Wait

why 2(3p-1) ?

like the power

[uncut mulch]

9 = 3^2

[fluid sable]

Oh my god

im actually

so tired

let me get some coffee and come back

[pale bison]

$3^{2(3p-1)}=(3^2)^{3p-1}$

[fluid sable]

hold up

:p

[pale bison]

nvm

[fluid sable]

what is that

im p sure

its something to do w getting the same denominators

and then life becomes easier

[past meadow]

not quite. think index laws maybe

[obsidian monolith]

Publius:

[fluid sable]

alright i think

I have to review those before trying to answer this

I haven't done so in a while

How old are you sneaky out of curiosity lol

you seem much better than me

[past meadow]

whats gonna be useful here might be $\frac{a^{b}}{a^{c}}=a^{b-c}$

[obsidian monolith]

Sneaky:

[fluid sable]

Oh my god

[past meadow]

thats an odd question

[fluid sable]

I remember that

How come ?

I'm 15.

[past meadow]

16 myself... back to the maths.

[fluid sable]

Alright,

Well

[past meadow]

can you see how to apply that rule here?

[fluid sable]

I can

one sec

let me apply it

$\frac{3^{3}}{3^{3p-1}}=3^{3-3p-1}$

[obsidian monolith]

Saveable:

[fluid sable]

im trying lol

ignore idk how to do the ()

[viscid thistle]

you forgot a + I think

[fluid sable]

a+I ?

In what sense

[viscid thistle]

-3p+1

[past meadow]

im assuming you mean $3^{3-(3p-1)}$

[viscid thistle]

exactly

[fluid sable]

Oh you meant that

[past meadow]

[fluid sable]

One question

Why does it become positive ?

my bad

[obsidian monolith]

Sneaky:

[fluid sable]

my bad

[past meadow]

sorry typo above. its --1, which is +1

[viscid thistle]

• times -

[past meadow]

^

[fluid sable]

i just realized

yeah

quarantine school

doesnt really help you understand

[past meadow]

hang on

we've lost

a 2 somewhere

[fluid sable]

xD we have

$\frac{3^{3}}{3^{3p-1}}=3^{3-2(3p+1)}$

[obsidian monolith]

Saveable:

[willow bear]

no

[fluid sable]

No?

[willow bear]

left-hand side fucked up

[fluid sable]

theres supposed to be a 2

before the 3p-1

cause its 9 ?

9=3^2

$\frac{3^{3}}{3^2{(3p-1)}}=3^{3-2(3p+1)}$

[obsidian monolith]

Saveable:

[fluid sable]

Something like that ?

[past meadow]

}{ around the exponent

[fluid sable]

O my bad

$\frac{3^{3}}{3^{2(3p-1)}}=3^{3-2(3p+1)}$

[obsidian monolith]

Saveable:

[past meadow]

theres an error in there

[fluid sable]

like with the latex ?

[viscid thistle]

$\frac{3^{3}}{3^{2(3p-1)}}=3^{3-2(3p-1)}$

[obsidian monolith]

HoboSas:

[fluid sable]

Dude its my first time using it lol

Wait

[past meadow]

you seem to have learnt it pretty fast so nw

[fluid sable]

Ah you meant mathematically

[past meadow]

but yeah you changed the sign

what hobo typed is correct

[viscid thistle]

you just forgot a +

[fluid sable]

Oh yeah

accidental

ny bad

I'm currently studying alg 2 but i genuinely hate maths now

[viscid thistle]

nothing important

😦

[fluid sable]

after being introduced to logs and stuff

i've just lost all hope

xD

[past meadow]

ok, so now we have $3^{3-6p+2}=3^5$

[obsidian monolith]

Sneaky:

[fluid sable]

Yes

Wait

[past meadow]

I'm waiting

[fluid sable]

I have a feeling the answer is 0

[viscid thistle]

I guess p=0

[fluid sable]

^

I plugged the points in and got 243=243

[past meadow]

still worth going through the memes of equating exponents or using logs to solve it more analytically

[fluid sable]

yeah lets try

to use logs

xD

[past meadow]

sure, so lets take log_3 of both sides

[fluid sable]

isnt it just the log

log(3)(exponenthere) ?

[past meadow]

$\log_3(3^{3-6p+2})=log(3^5)$

[obsidian monolith]

Sneaky:

[fluid sable]

yeah

[past meadow]

so we can hit em with the log laws and we get what?

[viscid thistle]

hit em hard

[fluid sable]

Is it the property of equality or something

[past meadow]

$\log(a^b)=b\log(a)$

[obsidian monolith]

Sneaky:

[fluid sable]

h

thats what my teacher likes calling it

[past meadow]

h?

[fluid sable]

hm*

well in that case

I'm screwed with logs too

I completely forgot the laws also

[past meadow]

just using the one i posted above here

[fluid sable]

Isnt the equation already

log(b)(a)

[past meadow]

$(3-6p+2)\log_3(3)=5\log_3(3)$

[fluid sable]

huh

[obsidian monolith]

Sneaky:

[fluid sable]

Yes

That

[past meadow]

oh if that doesnt make sense we can just equate exponents from

here:$3^{3-6p+2}=3^5$

[obsidian monolith]

Sneaky:

[viscid thistle]

you can divide by log_3(3) because it's !=0

i mean it's just

1

[past meadow]

log_3(3) is just 1 was more my approach

[viscid thistle]

yes im stupid

[fluid sable]

Cant we do

3-6p+2 = 5 or something

since they have the same base

Idk

[past meadow]

yes

[fluid sable]

-6p = 4 ?

[past meadow]

nope

[fluid sable]

wait what

-6p = 5-3+2 ?

[past meadow]

check your signs

[fluid sable]

-2*

-6p=-10

[past meadow]

you're telling me 5-3-2 is -10?

[fluid sable]

lmfao

wait

wait

5-3 = 2, 2-2=0

[past meadow]

poggers yes

so -6p=0

[fluid sable]

xD

p=0

[past meadow]

yeah nice work

[fluid sable]

lol

more like awful work

xD

[past meadow]

well you solved it so

[fluid sable]

see this is the reason

i hate maths

just cause im bad xD

[past meadow]

you picked up everything i said very quickly

you're not bad at all

the speed at which you picked up latex was impressive as well

[fluid sable]

Thank you for your kind words

but in actuality

logs, radicals, fractional radicals and stuff

they're all extremely hard for me

[past meadow]

well feel free to come back here and ask whenever you get stuck

[fluid sable]

will do :))

and you guys respond so fast haha

At least i have today and tomorrow to study, so hopefully it'll work out.

If I study logs today and the rest tomorrow

[narrow peak]

a curve is such that $\frac{d²y}{dx²}=6x-2$ and P$(2,8)$is a point on the curve. The gradient of the normal at $P$ is $-\frac{1}{2}$. Find the equation of the curve.

[obsidian monolith]

Hmm:

[narrow peak]

do i integrate

sub in 2

wait let me latex my solution

$\frac{d²y}{dx²}=6x-2\\frac{dy}{dx}=\int{6x-2dx}\=3x²-2x+c=2\3(4)-4+c=2\8+c=2\c=-6\\int{3x²-2x-6dx}=x³-x²-6x+c$

[obsidian monolith]

Hmm:

[rigid beacon]

wrong channel?

should be in #multivariable-calculus

[narrow peak]

FUCK I THOUGHT

IT WAS CALCULUS

IM SO STUPID

[rigid beacon]

F

[narrow peak]

LOL

[uncut mulch]

nah just regular calculus or general questions

[narrow peak]

anyway…

[rigid beacon]

o u right

[uncut mulch]

questionable 3rd line

[narrow peak]

i put it in #calculus

[uncut mulch]

the slope isn't 2 for all values of x

[narrow peak]

yeah i got lazy to put in latex am on phone rn

[rigid beacon]

why is 3rd line bad?

[uncut mulch]

the slope isn't 2 for all values of x

[rigid beacon]

oh yea

[narrow peak]

should have capitalized the c as well to make it clearer

[rigid beacon]

I think they subbed in the point and slope over 2 lines

[narrow peak]

bad presentation on my part

[uncut mulch]

just ditch writing =2 in that line and put all details in the line after

[rigid beacon]

^

[narrow peak]

o

[uncut mulch]

if you started it here and were already getting help, might as well finish it here

[narrow peak]

sure

[rigid beacon]

yea so after you're done with that bottom line

[uncut mulch]

used a different constant for the second integral

[rigid beacon]

you have info to solve for the new constant

[uncut mulch]

like d

[narrow peak]

should have capitalized the c as well to make it clearer

[uncut mulch]

and use the given point to determine it

[narrow peak]

yes

[rigid beacon]

or c with a subscript

[narrow peak]

i am on the right track tho?

[rigid beacon]

looks like it to me

[uncut mulch]

yeh. justify that you determined the slope is 2 at x=2 though.

[narrow peak]

cuz

[uncut mulch]

which i assumed you did on your side

[narrow peak]

normal at P=-1/2

stated in question

so dy/dx=2

then solve for that constant

then integrate again

[uncut mulch]

might be good to put y = in that last line
and then determine your new constant by using the given point

[narrow peak]

i did on my paper

presentation is hard on latex ngl

[uncut mulch]

just some pedantry, but overall pretty good.

[narrow peak]

ok ima ask my next qn in calculus channel

nvm this is simple factoring which idk im dumb as fuck

nvm i figured it out

[viscid thistle]

hey does anyone know examples of transformations that dont require to go in order

[austere cloud]

if you ask for non commutative operations, division works

[harsh cipher]

Hi

I cannot solve this question

I got it down to (3(y^2-4y+4))/(40)= 1

[uncut mulch]

express it in the form:

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$

[obsidian monolith]

ramonov:

[vague aurora]

what does it mean when the trig function has a number next to it?: Like tan54°37'

i dont understand the extra 37'

[past meadow]

the 37' is minutes. there are 60 minutes in a degree

[vague aurora]

ohhhh, thanks

[harsh cipher]

hmm ok let me check

so I did get it down to (2(x^2-6x+9))/40) + (3(y^2-4y+4))/(40)= 1

couldn't solve the (y-2)^2 where it had 3 infront

[uncut mulch]

p/q = 1/ (q/p)

[harsh cipher]

rationalize?

[uncut mulch]

not rationalising

just expressing in in the above form

[harsh cipher]

then it becomes p/q

that's the same thing

[uncut mulch]

rearrange it so that the coefficient of the numerators are 1

and a and b will be your radii of the ellipse

e.g.

[harsh cipher]

I couldn't figure it out for the y^2. I'm looking on google for examples

sigh

[uncut mulch]

$\frac{py^2}{q} = \frac{y^2}{q/p} = \frac{y^2}{ \sqrt{q/p}^2}$

[obsidian monolith]

ramonov:

[harsh cipher]

ok that makes sense

okay still didn't get 4 root 30 over 3

[uncut mulch]

what are you getting?

[harsh cipher]

4 root 10 over 3

I think im truly stupid

[uncut mulch]

the whole thing is rooted

(not just the 40)

[harsh cipher]

so root 9 in the denom is simplified to root 3

[uncut mulch]

there is no 9 in the denom

[harsh cipher]

root 3 ^ 2?

[uncut mulch]

oh, during rationalisation

sqrt(9) would simplify to just 3

[harsh cipher]

yes

but the top root 40

[uncut mulch]

or get sqrt(3) *sqrt(3)= 3 directly

[harsh cipher]

oh its root 1600

[uncut mulch]

huh?

[harsh cipher]

root 40 ^ 2

[uncut mulch]

doing too much extra stuff

[harsh cipher]

okay

[uncut mulch]

your y terms: $\frac{3(y^2-4y+4))}{40} = \frac{(y-2)^2}{40/3} = \frac{(y-2)^2}{\sqrt{40}{3})^2}$

[harsh cipher]

how the hell did it get a 4

[uncut mulch]

$\frac{3(y^2-4y+4))}{40} = \frac{(y-2)^2}{40/3} = \frac{(y-2)^2}{\left(\sqrt{\frac{40}{3}}\right)^2}$

[obsidian monolith]

ramonov:

[uncut mulch]

where your minor radius is sqrt(40/3)

[harsh cipher]

you mean 3?

[uncut mulch]

yeh

[harsh cipher]

simplifying sqrt(40/3)^2

[uncut mulch]

$=\frac{\sqrt{40}}{\sqrt{3}} = \frac{2\sqrt{10}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \ \
\frac{2\sqrt{30}}{3}$

[obsidian monolith]

ramonov:

[uncut mulch]

and then multiple that 2 to get the length of the whole (minor) axis

[harsh cipher]

yep

got it now

thanks for the help..

when I see this question on the test I will not get it wrong lol

[uncut mulch]

np

[sterile notch]

Is there an easy way to tell whether a polynomial is easily factorizable or not?
Like x^3-x^2+9x-9 looks kinda difficult, but turns out to be (x-1)(x^2+9)
But x^4+2x+8 looks easy but seems difficult to factorize

Is there a way to identify if one is difficult?

As much as I've noticed (x-1) seems to be the usual one you can try factorize, but idk.

[willow bear]

a polynomial's factorization difficulty depends on how many techniques it takes before it budges

rational root thm is pretty powerful but even that won't get them all

[viscid thistle]

Hmm idk about figuring out if a polynomial is easily factored... but just try all the normal methods. Rat root theorem is good, but If those don’t work, brute force your way into finding the zeroes.

[tawny nacelle]

wolfram ftw

[viscid thistle]

lol

[past meadow]

just use the cubic formula

[viscid thistle]

What if 4th degree poly?

[sterile notch]

Wolfram broke for some of them for me.

[fluid shore]

yes cubic formula for a quartic

[past meadow]

quartic formula

[viscid thistle]

aAa ima try to derive those before I use them.

[fluid shore]

Use the sextic formula

whoops sorry that doesn't exist

[viscid thistle]

Then I’ll invent it

Or someone will idk

[sterile notch]

I've been using synthetic division, but it seems to break every now and then.

[past meadow]

you arent gonna have much luck with deriving the quartic formula squid

as it looks like this

[tawny nacelle]

something something galois

[viscid thistle]

That’s perfectly fine.

[past meadow]

soap sometimes polynomials arent gonna have real roots

[viscid thistle]

that too

[past meadow]

the quartic one you posted above does not, as a matter of fact

[tawny nacelle]

which soap are you talking to

[sterile notch]

I'm going to try look into rational root theorem hopefully it elps.

[tawny nacelle]

[sterile notch]

lol i frgot to change name lel

[tawny nacelle]

yes wth man

[viscid thistle]

multiple sOaps

[fluid shore]

i mean

[viscid thistle]

Don’t drop it

[past meadow]

other soap lol

[sterile notch]

i'll just change it to soup

[tawny nacelle]

nice

[fluid shore]

factorizing these things, honestly, can also just be a matter of cleverly adding 0s to the given polynomial

[sterile notch]

wth, i cant change nicknames here lol

[tawny nacelle]

[viscid thistle]

@sterile notch rational root theorem is powerful. I happen to use it a lot when doing polynomials.

[fluid shore]

you gotta play around and see what works and what doesn't

[past meadow]

^

[sterile notch]

Okey, this should do lol

[viscid thistle]

Agreed.

[sterile notch]

Thanks, ill give em a go.

[viscid thistle]

If all else fails, plug it into graphing calculator and see if the zeroes have weird decimals and such. If so, it’s most likely not easily factored.

If looking for zeroes as a question and not easily factored, rational root theorem or brute force it.

[fluid shore]

urm i'm against brute forcing. Usually, there is a clever trick with adding 0s in the right places

depends on the polynomial

play with it and see what you get, i suppose

[viscid thistle]

hMm well you’re the boss. I’m still studying the subject so I should listen to more qualified advice before administering my own.

[fluid shore]

Nah, brute forcing is fine as a method. I just don't like to do if i can help it.

You are free to give advice, no one here should be stopping you from doing that.

[viscid thistle]

Well thank you for the reinforcement, but I agree, it’s a taxing process in some cases, and some of the other methods should be explored first.

[viscid thistle]

if you understand a certain derivation of the quadratic formula very well you also, in principle, know how to derive the quartic equation

And could do it by hand even, given a lot of time

[harsh smelt]

find amount off all combinations of 4 out of 60

and 1/divided by ^ is the answer

because to win he has only one combination

{3, 15, 46, 49}

but he may get {1, 2, 12, 48} as well

or {4, 5, 6, 7}

in general he can get 60C4 combinations

with only one winning

[viscid thistle]

Hey guys! Quick question! what double angle identity should I use to turn cos(4w) into sine?

[uncut mulch]

that's an ambiguous question

[viscid thistle]

completely solvable though, right?

[uncut mulch]

there are many ways to express cos(4w) in terms of the sine of something

[harsh smelt]

well, the most obvious is

cos2x = 1 - 2sin^2x

[uncut mulch]

and it is unclear what you actually want, and/or whether double angle identities are actually needed

[viscid thistle]

cant u just turn it into sin(4w + pi/2) ?

[uncut mulch]

yes

[viscid thistle]

well there u go then

@viscid thistle hey can you tell me howyo ucame to that?

sin is just cos, but pushed pi/2 units to the right

https://www.desmos.com/calculator/b7u2cvfc9u

[desert kiln]

for any value of w, sin(4w+pi/2) will equal to cos(4w)

[viscid thistle]

look at the graphs for sin and cos

[desert kiln]

oops I was too late

[viscid thistle]

no worries

yea i get that

wow i should have not have fixated on the double angle part of that

and thought more out of the box

yah

[uncut mulch]

and it is unclear what you actually want, and/or whether double angle identities are actually needed

[viscid thistle]

yikes on me

the double angle thing is kinda unnecessary

[uncut mulch]

it should tell you specifically that the want it in terms of sin(what they want)

[viscid thistle]

my hw specifically asked for double angle, but that answer was accepted

[sterile notch]

If I'm given some points say: (1,2), (3,4), (5,6), and asked to make a parabola which crosses all these points
It can be turned into a linear algebra problem since applying: ax^2 + bx + c = 0,
to each point lets me create a system of linear equations (x^2, converted to coefficients since they are known)
Can these kind of problems be only solved with linear algebra?

Or are there different or better methods?

[past meadow]

(1,2), (3,4), (5,6) does not define a parabola. those 3 points are colinear

[sterile notch]

yea, idk i was just thinkin of random numbers

[past meadow]

but there are ways to solve systems of equations in 3 variables without linear algebra

[sterile notch]

(1,2),(2,1),(3,4)

Here's one that does make a graph

And the first thing I did was, put it in the parabola thingo

a1 + b1 + c = 2
a4 + b2 + c = 1
a9 + b3 + c = 4

Got a matrix:

1 1 1 2
4 2 1 1
9 3 1 4

And solved for a,b,c (2, -7, 7)
So 2x^2-7x+7 will *touch* those points

How would you do it without linalg?

Or solving a bunch of linear equations.

[lilac pier]

solve them simultaneously

lol

[sterile notch]

Thats linalg bruh

[lilac pier]

is it? 😮

[sterile notch]

Yea?

[lilac pier]

Hm I dont think there is any other way

[sterile notch]

Gonna bet u there is another way

[sterile notch]

Okay, I think there is a way, it's pretty gross, but it's by using the two points with the highest gradient, and approximating the vertex, then exhaustively checking it's neighbours until it works.

I think theres a better way using some basic geometry

[fluid sable]

This is exponential right ?

[pale bison]

can't be too sure just by looking at the graph

[fluid sable]

Hm?

That's all you're given usually?

[pale bison]

then yeah, exponential i guess

but keep in mind you can approximate that graph with a polynomial very well

[fluid sable]

Hm

How can i find the equation

[pale bison]

you can probably get a good guess by finding some nice integer value points

[fluid sable]

I did but like

[pale bison]

and assume the function has the form y = ae^(bx)

[fluid sable]

(2,3) (3,9)

[uncut mulch]

+c

[pale bison]

fair point but it seems to have a horizonal asy. at y = 0

in any case, plug those points into the equation and solve

[uncut mulch]

also consider (1,1)

[fluid sable]

Hm?