precalculus

[fluid sable]

I really dont know how to :/

Hm

I did 3^x for some reason

Have any idea where i went wrong ? :p

[pale bison]

3^x wouldn't work because it doesn't pass the point (1, 1)

[fluid sable]

Yeah

[uncut mulch]

the base you choose doesn't really matter

[fluid sable]

Hm?

[pale bison]

take it over Ramonov, i dip, ty

[uncut mulch]

since the constant in the power adjusts for that

[fluid sable]

So

x^3x?

because they're multiplied by 3 each time

like

1 , 1x3, 3x3

[native sequoia]

3^x was pretty close because of that reasoning

[fluid sable]

Right?

But idk

how to get it right

Its wrong ik for sure

@native sequoia any clue ?

On what it is

[uncut mulch]

if you determined a constant ratio of 3 as x increases by 1,
you'd get something like:
y = a * 3^x
and then sub in any of the points to determine a.

[fluid sable]

a=3/3^x

xD

[uncut mulch]

what are you subbing?

[fluid sable]

3

oh wait

a3/9?

[uncut mulch]

a point involves and x and y coordinate

what's:

a3/9
supposed to be?

[fluid sable]

1/3

[uncut mulch]

did you mean
a = 3/9

(a3/9 is something completely different)

but yes, a = 1/3

[fluid sable]

Alright

Thank you ❤️

[normal crown]

Hi guys, I'm not exactly in an English speaking country so a lot of terms are plain alien to me

but if I wanna ask about the monotony of a function, should I ask here ?

whit this sorta function, grade 2 I guess it's called

[willow bear]

degree 2

or quadratic

[normal crown]

I'm having a problem with the monotony table

tthanks

so the way I learned in school

is to diferentiate* f(x) to f'(x)

then do f'(x)=0

and get two x values

pretty much this style of table, values are very weird here

so let's say x1 = -1

and x2 = 1

the sign between them is the opposite sign of a

so if a is for example 6

then the sign in the table is minus, no ?

[muted granite]

When I multiply AB I get the same answer as multiplying AC. But it says that I am getting the product wrong for AC. Any idea why?

[drowsy karma]

Write an equation of the line passing through point (-6, 5) and parallel to the x axis.

what does it mean by parallel to the x axis?

[viscid thistle]

@muted granite https://www.symbolab.com/solver/matrix-multiply-calculator/\begin{pmatrix}0%263%260\\ 1%260%261\\ 0%262%260\end{pmatrix}\begin{pmatrix}6%265%267\\ 4%26-2%26-5\\ 5%263%268\end{pmatrix}

@drowsy karma parallel to x-axis means a straight horizontal line

[drowsy karma]

ah thanks

so its just 0?

[viscid thistle]

yah

slope is 0

[muted granite]

@viscid thistle thats the same calculator I used. And AB=AC but the homework im practicing on says otherwise.

[drowsy karma]

Given the line joining the points (2,5) and (8, -q) where q is a whole number, is parallel to the line 3x-2y-5=0, then the value of q is ___

So I understand finding the parallel slope to the equation part

But I don't understand what it wants me to do with the points?

Parallel slope is 3/2 and for the points I have -q -5 / 6

so I'm kinda stuck

[viscid thistle]

@drowsy karma general concept, if two lines are parallel, their slope MUST BE EQUIVALENT

After having both slopes, set them equal and solve for q

[viscid thistle]

you got A right tho

[spark cliff]

can I have help

[viscid thistle]

https://www.slader.com/discussion/question/transform-each-polar-equation-to-an-equation-in-rectangular-coordinates-then-identify-and-graph-the-equation-0c730a33/

[spark cliff]

bruh

is r=12+12sin(theta) a limacon without a loop or a cardioid graph?

[viscid thistle]

cardoid

[spark cliff]

yeah whoops

What are the polar coordinates of (-5, 3pi/4) in rectangular coordinates?

is it

wait

ok i got it im too lazy to type out

[viscid thistle]

i got it too

here

[spark cliff]

yeah we good lol

oh

never mind

i got it lmao

no i didn't get it how do you do that lmao

is it legit the same thing? @viscid thistle

oh angle measures

i have no idea then lol

[viscid thistle]

This is what I got for the other question

[spark cliff]

yeah im not gonna lie i just plugged it itno mathway

[viscid thistle]

https://socratic.org/questions/how-do-you-convert-6-0-to-polar-form

[spark cliff]

-6, pi?

[viscid thistle]

actually this is better

https://socratic.org/questions/how-do-you-convert-6-0-to-polar-form-1

[spark cliff]

its still 6,0?

im confused

[viscid thistle]

yah i think so

according to mathway

[spark cliff]

thats dumb

af

[viscid thistle]

its (6, 0*)

• being degrees

[spark cliff]

yea

wait i dont get the thing where r has to be negatibe

negative

[viscid thistle]

https://www.slader.com/discussion/question/the-rectangular-coordinates-of-a-point-are-given-find-polar-coordinates-of-each-point-express-thet-8/

[spark cliff]

what lol

12, 5pi/6?

uhhh wait r has to be negative

then i have no idea lol

wait

[viscid thistle]

Here the answers

[spark cliff]

I WAS COECT

CORRE CT

COORECT

bruh i cant spell

correct

[viscid thistle]

CORRECT

thats good

[spark cliff]

so -12, -5pi/6

?

[viscid thistle]

what about that?

[spark cliff]

that's the answer right lol

[viscid thistle]

yah

[spark cliff]

bruh okay not the answer???

[viscid thistle]

uh what?

[spark cliff]

i dont know

the explanations dont help AT all

[viscid thistle]

its -12, -pi/6

[spark cliff]

i put 5

why

why is there no 5

[viscid thistle]

idk

[spark cliff]

ok wait

im stupid

LMFAO

bruh

wait

wtf

they're both positive???

12,5pi/6

what the fuck

[viscid thistle]

whatsthe other answer

[spark cliff]

it was 12,5pi/6

bRUH

im so

dumb

i thought it said less than zero

not greater than

lmfao

okay well then

[viscid thistle]

where does it say greater than

[spark cliff]

Let r > 0

At the end lol

its obviously not A and im pretty sure its not C but idk about B or D lol

[lilac pier]

Recall that x^2 + y^2 = r^2

you can factor out the 3 so you have 3(x^2 + y^2)

[spark cliff]

i dont know where you're going with this tbh

i dont see it

i'd guess B but im not sure lol

@lilac pier sorry lol

[viscid thistle]

https://www.slader.com/discussion/question/the-letters-x-and-y-represent-rectangular-coordinates-write-each-equation-using-polar-coordinates-r/

[spark cliff]

so b?

imma roll with it

[viscid thistle]

the answers always C

[spark cliff]

what kek

[viscid thistle]

lol its a meme

[spark cliff]

its not A!

i know which one it isn't but idk which one it is lol

[viscid thistle]

lol

[spark cliff]

bruh how is it equal to zero now what

lmao

o wait

[spark cliff]

uhhh its wrong

hmm

[viscid thistle]

its not the exact same question

[lilac pier]

x^2 = 6y or 19y?

[viscid thistle]

^

[lilac pier]

dude you're asking multiple questions

[spark cliff]

i mean i posted the exact question lmao

[viscid thistle]

it has x^2 = 6y bc i didn't bother to look for x^2 = 19 when i saw this

[spark cliff]

f

[viscid thistle]

its C

[spark cliff]

yeah i got it lol

[viscid thistle]

good

[spark cliff]

2 more and then im going to bed lol

so

yeah i really dont know how to do this one lmao

[viscid thistle]

this looks hella similar to a question we did earlier

https://www.wyzant.com/resources/answers/757828/the-letters-r-and-theta-represent-polar-coordinates-write-the-given-equatio

[spark cliff]

which lol

bruh

ur googling skills are A1

[viscid thistle]

thx 🙂

[spark cliff]

wait so (x^2+y)/9 = 0?

[viscid thistle]

what?

[spark cliff]

since its equal to zero lol

wha

t

[viscid thistle]

isn't it x^2 + y^2 - 9y = 0

?

[spark cliff]

oh

shit

yeah

just subtract omg

[viscid thistle]

lmaooooo

[spark cliff]

wait bruh

this one is even harder

im gonna stba myself

i legit havent learned this in over a year lmfao

[viscid thistle]

bring it

theres nothing google cant handle

lmao

[spark cliff]

true lmao

i feel bad

even tho its the whole purpose of this discord

[lilac pier]

try it yourself first

[spark cliff]

r^2=x^2+y^2
y=rsin(theta)
x=rcos(theta)

thats all i know kek

[lilac pier]

apply it

[spark cliff]

bruh do you really have to square that whole thing

[viscid thistle]

i dont think so

[spark cliff]

oh

well that's what i would've done kek

[viscid thistle]

@spark cliff

here u go

[spark cliff]

wait bruh

how'd you get the thing under saying y=rsin(theta)
x=rcos(theta)

im blind af sorry

[viscid thistle]

idek

[harsh cipher]

Hi

question

how can the answer be (x^2)/4 ?

it should just be x^2

[willow bear]

why should it be just x^2

[harsh cipher]

because the length is 2 meaning

[willow bear]

aight hold on

[harsh cipher]

okay

[willow bear]

yeah you're right

as written there is no correct answer and it should be $x^2 + \frac{y^2}{9} = 1$

[obsidian monolith]

Ann:

[willow bear]

if they wanted $\frac{x^2}{4} + \frac{y^2}{9} = 1$ they should've made the semi-minor axis be 2 units long

[obsidian monolith]

Ann:

[harsh cipher]

thanks

🙂

[prime prawn]

is there an explicit formula for something of the form:

$t_{n+1} = a + b*t_n$

a and b are constants

[obsidian monolith]

Linguist = Trash:

[prime prawn]

must be parabolic

edit cubic

edit i fucked up, but the differences between the terms are exponential

[harsh smelt]

@prime prawn yes there is

it is called recurrence relation

[viscid thistle]

hi

i need help

height of a rock thrown off a cliff can be modelled with h(t)=-4.9t^2+12t+50

t is time in seconds and h(t) is height in meters

a) find speed at 4 seconds
b) find avg speed over the first 4 seconds
c) when would speed be 0

@viscid thistle t is time, so time at 4 seconds is h(4)

ok

do i do the derivative?

this is on a derivative ws

ok so at 4 seconds

h(4)=19.6m

19.6m/4s

?

4.9 m/s

is that my answer for a?

@viscid thistle

,calc -4.9(4)^2+12(4)+50

[obsidian monolith]

Result:

19.6

[viscid thistle]

19.6m/4s
@viscid thistle HECK NO

?

1. This is NOT a constant acceleration movement
2. This is not the typical motion problem $x=vt$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

oh ok

So

$\begin{cases} x=x_0+v_0\cdot t-\frac{1}{2}\cdot g\cdot t² \ v=v_0-g\cdot t \end{cases}$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

@viscid thistle you should know these

ok

Its physics-oriented

alright

So

Which of both do you think we gotta use

hm

bottom/?

One is velocity

Yeah

And $v_0$ is the initial velocity, which is the velocity at t=0

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

ok

so how do we find v at t=0?

and what is g

h(0)

ok

g is the gravitational acceration

so h(0)=50

$g≈9.8m/s²$

ohh and thats some constant

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

ok yeah

Yeah

ok h(0)=50-9.8t

Plug those in and you have a

ok h(0)=50-9.8t
@viscid thistle ?

Oh wait

shit

h(0)=50

yeah

Okok

ok

ok

Lol

so yeah h(0)=50

and noww

v=50-g*t

?

Yeah

t is obviously 4s

g is what i said before

ok i got 10.8

And you have a

,calc 50-9.8*4

[obsidian monolith]

Result:

10.8

[viscid thistle]

Aight cool

ok awesome

now avg speed over 4 sec

Well

Do you know the eqn of average speed

no

$\text{average speed}=\frac{\text{total displacement}}{\text{total time}}$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

oh ok

so h(4) i need to find ya?

$\text{average speed}=\frac{\text{total displacement}{\text{total time}}$ is applied to our problem $\text{average speed}=\frac{h(4)}{4}$

Hmm...?

$\text{average speed}=\frac{h(4)}{4}$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

@viscid thistle

nah

a isnt right

u take the derivative

h(t)

h'(4)=-27.2m/sec

Excusez moi

ah yeah u heard me bro

ur wrong

wrong

No

Thats another approach

Wtf

Wait

@viscid thistle maybe physics approach isn't what you want so keep looking for help

Repost it

Bruh you are just annoying smh

Im out

------free channel--------

[uncut mulch]

speed isn't displacement/time

that's velocity

[viscid thistle]

No one said that

@uncut mulch this was what i said

$\begin{cases} x=x_0+v_0\cdot t-\frac{1}{2}\cdot g\cdot t² \ v=v_0-g\cdot t \end{cases}$

[obsidian monolith]

Al𝟛dium:

[uncut mulch]

20 minutes ago-ish

[viscid thistle]

?

Oh is speed ≠ velocity

Im not native so i used them the same way

[uncut mulch]

yeh, they're different

[viscid thistle]

Oh jeez

So speed is the derivative of s(t)?

Nice to know

[uncut mulch]

I didn't check the graph here. 1 sec

,w graph y= -4.9t^2 +12t +50 from x = 0 to 6

[obsidian monolith]

Display results online and refine query

Requested by ramonov#0921

[uncut mulch]

yeh definitely different here

[viscid thistle]

Aight, wasn't noticed of that detail at all

So speed is the derivative of s(t)?
?

[uncut mulch]

what's s(t)?

[viscid thistle]

Displacement in the function of time

[uncut mulch]

no

[viscid thistle]

We use displacement for s :(

[uncut mulch]

velocity is displacement/time

speed is total distance travelled/time

[viscid thistle]

When a=0

And its not falling

we use d(t) for displacement

Each country uses another letter so im not learning yours :( lol

[viscid thistle]

😦

Big brain ❤️ @viscid thistle

😘

[spark cliff]

idk what to do after this lmao

[viscid thistle]

ight hol up

[uncut mulch]

arccos both sides to see if you get a nice value

[viscid thistle]

@spark cliff

[spark cliff]

how did you get 105

what

f answer was 75

Would’ve gotten it wrong if I did it myself too so LMAO

I got like 30 lmao

[uncut mulch]

rent mistranscribed w

[spark cliff]

oh i see where lol

[uncut mulch]

,w arccos (( sqrt(3)-1)/ (2sqrt(2))

[spark cliff]

f

[obsidian monolith]

Display results online and refine query

Requested by ramonov#0921

[uncut mulch]

,w 5pi/12 * 180/pi

[obsidian monolith]

Display results online and refine query

Requested by ramonov#0921

[uncut mulch]

wolfram hates degrees

[spark cliff]

hmm i see that lol

,w arccos (10/sqrt(26)sqrt(21))

[obsidian monolith]

Display results online and refine query

Requested by burnt toast#0001

[spark cliff]

,w arccos (10/(sqrt(26)sqrt(21)))

[obsidian monolith]

Display results online and refine query

Requested by burnt toast#0001

[spark cliff]

ummm

[uncut mulch]

,w arccos (10/(sqrt(26)sqrt(21))) * 180/pi

[spark cliff]

well

[obsidian monolith]

Display results online and refine query

Requested by ramonov#0921

[spark cliff]

o

whut

[uncut mulch]

what was the question

[spark cliff]

i just need it in degrees kek

and this is possibly what I have gotten

[uncut mulch]

should be -10

when applying arccos

,w arccos (-10/(sqrt(26)sqrt(21))) * 180/pi

[obsidian monolith]

Display results online and refine query

Requested by ramonov#0921

[spark cliff]

uhhh

it said it was wrong apparently

idk

i tried 10 and -10 lol

oh

wait

wait

no i see what ur saying im dumb

so its 115.3 degrees?

[uncut mulch]

yeh

[spark cliff]

dang

[spark cliff]

don't remember the equation of ellipses either kek

the vertices are obviously (-4,2) and (4,2) but idk the foci

[viscid thistle]

@spark cliff

[spark cliff]

how

DO YOU DO THAT

[viscid thistle]

imma genius

🙂

[spark cliff]

ok its wrong

hmm

imma just mess around with it till its right and ball kek

[viscid thistle]

the numbers aren't exactly the same tbh

[spark cliff]

ic

[viscid thistle]

the process is right though

[spark cliff]

ah

where'd you get -6 for the horizontal radius

and 4 for vertical

lol

like what if it isn't exactly on the line in the graph given kek

i dont really see how you got half those numbers lmfao

[viscid thistle]

@spark cliff imma link the diagram

this should help u

so your horizontal radius should be -5

[spark cliff]

either way your equation isn't right lol

graph it in desmos

[viscid thistle]

you have to apply the steps from the solutions onto your ellipse

[prime crypt]

#3 please, kind of lost 😔

[snow iris]

Good evening, im having a bit of trouble with this:

Due to an unexpected heavy storm the water level in a dam must be lowered one foot. The output of gate A manages to reduce the level in 4 hours. If we open the A&B gates simultaneously, the desired level is achieved in 2 hours and 24 minutes. In how long will only gate B succeed? Hint: The output of gate B is smaller than that of A

[patent beacon]

That's a pretty useless hint lol

[viscid thistle]

@prime crypt

[patent beacon]

Think in terms of rates.
A lowers at 0.25 ft/hr.
A and B lower at 0.41666 ft/hr

[prime crypt]

Damn it’s blurry

[patent beacon]

So clearly, B alone has a rate of their difference

[prime crypt]

@viscid thistle thanks, very similar but you got a better quality shot of it?

[rich flint]

For spruce I got between 150 and 250 and for cedar I got between 180 and 300 planks

Oh I see your getting help

[prime crypt]

yeah, not sure how to approach it

[rich flint]

You see the inequalities that you solved for earlier? You use the same concept but this time use compound inequalities. Meaning it will look something like this 1800<x< 3000

[prime crypt]

ohh gotcha, never done compound work lol

ib man

[prime crypt]

🐐thank you!

[viscid thistle]

np 🙂

always here to help

[patent beacon]

Note you can keep the weight constant by replacing 6 cedar planks with 5 spruce. As well, doing so is always cost saving. It looks like the strategy then is to get as many spruce in as possible

[rich flint]

Cute dog

[patent beacon]

My Suki is the best dog! Thx.

[prime crypt]

@viscid thistle how’d you find that so fast btw? was working so didn’t ask then lol

[viscid thistle]

I have my ways 😉

[violet quail]

any idea on how to begin?

should i substitute the exponents somehow?

[willow bear]

multiply through by e^(3x) lol

[harsh cipher]

Hi question

[pale bison]

what's up?

[harsh cipher]

in this video around 0:58. He says if one of them move to the other side it would become negative

lol naisu

what is "one of them" ?

http://bclearningnetwork.com/LOR/media/cc_math/Math12_PC/Unit7/Lesson5/ConicsL5q4d.html

[harsh cipher]

okay..but how does that relate to writing the restriction

[pale bison]

so like, Ax^2 + Ey = 0
then Ax^2 = -Ey, and RHS is surely going to be negative, since E is positive

[harsh cipher]

(A)(E) must be greater than zero

[pale bison]

huh?

[harsh cipher]

okay

[pale bison]

if AE > 0
then both must be non zero, and share the same sign

[harsh cipher]

e represents vertical translation

I mean Ey

[pale bison]

E doesn't represent any translation, it scales the function parallel to the y axis

[harsh cipher]

ok I don't understand why AE must be greater than zero

[pale bison]

the parabola opens down

so ignoring all other terms, if you write
Ax^2 + Ey = 0

then that simplifies to y = (-Ax^2)/E

if they're less than 0, then it opens up

ok bad wording there sorry

the coefficient of x^2 is -A/E

so if A/E > 0, then -A/E is negative, hence the parabola opens down

so then the question becomes, when is A/E > 0?

it's when AE > 0

[harsh cipher]

ok I need to think about that

I don't understand things right away lol

[pale bison]

if red > 0, then it opens up

if red < 0, it opens down

your goal is to get red < 0
i.e.
-A/E < 0
multiply both sides by -1 (remember that flips the sign)
A/E > 0

you can then multiply by E^2, which is surely positive, since square of any number is positive

this yields AE > 0

i'm excluding the possibilities of either of them being 0 for the sake of simplicity

let me know if anything confuses you

[harsh cipher]

okay thanks for the detailed explanation

[rustic quest]

hello please help me i got the answer 1 and im not sure how to solve this

[brittle fable]

What does the 'interval u = 0' mean?

[stuck lark]

presumably a poor rewriting of R\{0}

[brittle fable]

But he says 0 < u < 2 pi

Im not sure if u = 0 means the open ray (-,0) or something else

[stuck lark]

full context?

[brittle fable]

this is the first time i've seen this notation, and the context is not appropriate for this channel

but its about the mobius strip

I'm going to move it to topology-geometry

[stuck lark]

@brittle fable oh you're looking at a region in the uv plane. the open interval u=0 likely refers to {0}xR

[brittle fable]

ah that makes sense

[split bay]

I am not sure how to find the exact value of theta here

[lilac pier]

It would help to first find sin(theta) and cos(theta) and then use double angle identities.

[vague aurora]

I understand Sine and cosine, but why do the other functions work together in this neat pattern?

Why can cot be represented as a segment from csc to cos and tan as from sec to sin? The others I more or less understand

[blazing parrot]

say for tangent, it means O/A right

if we had the radius be A, then O would be where tangent is

[vague aurora]

If the radius was A, wouldn’t O be 0?

[sour eagle]

@vague aurora So tangent is defined as O/A in a right triangle, right? In right triangle ABC, with A = 90 degrees, tan(ABC) = AC / AB
But AB is the radius of the unit circle ( which is 1 ), so AC = tan(ABC)
So the segment AC is defined as the tangent of the angle.

Also this could be taken to #geometry-and-trigonometry

[rich flint]

@viscid thistle if you plug in 0 what do you get?

If you plug in the angle 45 what do you get?

Yes you do get 15 I just want you to see that if you plug in those angles for alpha it will tell you those values

If you plug in 90 it will be undefined

@viscid thistle check 30,60,45, and 0 and look at the behavior of the numbers

[still yew]

Idk if this is the right area, but I have a question regarding Eulars formula (or just trying to derive it from its power series)

[rich flint]

@still yew just post the question so people can see if they can answer

[still yew]

Ok

Hold on

This is currently my work, but I dont know if I am doing it right.

[rich flint]

What class is that?

[still yew]

Nvm

I found out

[frigid sapphire]

https://i.imgur.com/QSXGAN1.png

how can I simplify the fraction like this?

[willow bear]

??

whoever wrote this multiplied both sides of the equation by pqf.

[uncut mulch]

that's an "f"?

[frigid sapphire]

it's my math teacher sorry

I know I didn't even know it was an f at first

haha

[misty heath]

what does it mean to solve 1/p + 1/q = 1/p for f

oh wait

[willow bear]

the right-hand side is 1/f

[frigid sapphire]

ok I see that now Ann, thank you

yeah isn't that wrong? solving for f is isolating f

[willow bear]

what do you mean by "wrong"

presumably you just aren't done yet

[frigid sapphire]

ah yes wtf

ahah I had it paused but...

[willow bear]

unless, of course, you believe that every single equation can and should be solved in a single step with a single algebraic trick, and that multi-step solutions are invalid and """wrong"""!

[frigid sapphire]

now I wonder why she did that other than to teach us how to do that.

[misty heath]

you could multiply through by pqf then distribute to take out the f, or divide over each side

[frigid sapphire]

she isolated f afterwards lol

I guess I forgot or didn't know that I can just multiply something random like that

[willow bear]

you could multiply through by pqf
that's what was done

[frigid sapphire]

I know for example multiplying by 2/2 would be equivalent to 1

but pqf isn't so obvious

[willow bear]

it's the lowest common multiple of all the denoms

so the motivation is that you wanna get rid of the fractions

bc equations without fractions are generally less complex than those with

[frigid sapphire]

https://i.imgur.com/d8tG2R7.png

this in interval notation is (-5, 2) right?

[uncut mulch]

what's that interval supposed to represent?

[frigid sapphire]

the domain , sorry

someone else told me it

(-inf, -5) U (-5, 2) U (2, inf)

only thing I don't get now is why exclude -inf and inf?

[rich flint]

@frigid sapphire solve for y then find the domain

[frigid sapphire]

yeah (-5, 2)

obviously there's more

[rich flint]

What did you get for y ?

[frigid sapphire]

wait solve for y?

why?

if u can just do

y - 2 != 0

y != 2

etc.

right?

[rich flint]

Yes solve for y remember the domain is of x

@frigid sapphire let me check

[frigid sapphire]

the domain is of x?

[rich flint]

Yes I see. When I thought I saw the x variable in there when it wasn’t. So you will see you will have a polynomial meaning what?

[uncut mulch]

do you have the original question?

since its a bit weird to be asked for the 'domain' of something like this

[frigid sapphire]

it's ok, someone else helped me. thanks a lot

[uncut mulch]

and deals with something that seems to be called the "implied domain"

that seems much more appropriate as a solve question

[frigid sapphire]

@rich flint so a quadratic equation

nope

idk man :/

too tired and busy

[rich flint]

@frigid sapphire yes a quadratic equation which is a polynomial. Therefore the domain is -inf to positive inf. Ramanov is right you may want to go ahead and post the original question to make sure that is what is being asked the presentation threw me off cause I see no x variable only a y.

[frigid sapphire]

I'm stuck on this one now https://i.imgur.com/ekytBE8.png

I tried doing 1188/0.2 but nope

1188 * 0.2 also nope

[viscid thistle]

@frigid sapphire the strat is making up a system of eqn

Call x the solded tickets on July and y the solded tickets on August

[frigid sapphire]

damn really

[viscid thistle]

?

Yeah

lmao

What did you expect lmao

lolol

[frigid sapphire]

only an x

[viscid thistle]

You don't know how to solve a system of 2 eqn

Do you?

@frigid sapphire hello?

[frigid sapphire]

I don't sorry I was looking at my book

[viscid thistle]

Do you know how to solve a system of 2 eqn?

👻

@frigid sapphire ...

[frigid sapphire]

sorry

I'm so tired

no I don't

[viscid thistle]

Do you wanna take a rest and continue later

You can tag me when so

[frigid sapphire]

I can do this right now

I'm not looking at the book now

[viscid thistle]

R u sure?

[frigid sapphire]

yeah

[viscid thistle]

Ok so first i suggest to watch some videos about system of 2 eqn

[frigid sapphire]

ok

oh that I kinda remember how to do it

[viscid thistle]

https://youtu.be/-mZZ6iPwQpE

Re-watch in case

[frigid sapphire]

2 variable systems of equations are very simple from what I remember

it's the 3 digit that's hard

I just need to formulate it into a system of eqn

[viscid thistle]

So for first eqn: we have the info that x and y adds up to 1188

Translate this onto mathematical language for our first eqn

[frigid sapphire]

yes I got that one right somehow

[viscid thistle]

So it is....?

(The first eqn)

[frigid sapphire]

x + y = 1188

[viscid thistle]

Cool

[frigid sapphire]

and second one is soemthing like 1.2x + .2y = 1188

not sure

[viscid thistle]

For the second one its a lil bit more adv

Wait

So if we say that y (August) had 20% more of sold tickets than x, considering that the expression: 20% more means to multiply by 1.2

Try again for the 2nd eqn

[frigid sapphire]

x + 1.2y = 1188?

[viscid thistle]

Nono, forget the 1188

[frigid sapphire]

x + 1.2y =

ehh

[viscid thistle]

For the second eqn we want an equivalence between x and y

x + 1.2y =
@frigid sapphire not literally

You almost got it

So if we say that y (August) had 20% more of sold tickets than x, considering that the expression: 20% more means to multiply by 1.2
@viscid thistle consider this again

[frigid sapphire]

1.2y - x

damn idk

[viscid thistle]

Almost

Thats not an eqn

Its an expression

Uhh

I gtg for some time so ill leave the second eqn here, DON'T SPOIL IT BEFORE TRYING ||1.2x=y||

[frigid sapphire]

ok thanks

[viscid thistle]

Np

[frigid sapphire]

thank god, no class today, I can sleep

lmao

[viscid thistle]

Lol

Have fun

[tepid basin]

Hello, does anyone know how to rotate i by 40 degrees. I don’t know the formula

[viscid thistle]

https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-rotations/v/rotating-points

[frigid sapphire]

https://i.imgur.com/JQRSeuC.png

I'm having trouble writing this as a system of eqn

one sec, gonna write my stuff down

0.08x + 0.04y = 1400

that's the only one I think is right

[cyan kernel]

There's a couple ways to define an x and y, but I'll say x + y = 1, where x and y are the percents (as decimals) of the year that they were invested at; obviously they need to add to 1 = 100%

[frigid sapphire]

ah

it's not a system of eqn

(29000 - x) = amount invested

0.08x + 0.04(29000 - x) = 1400

so they just turn "y" into that pretty cool

[cyan kernel]

It is a system there too

They said x + y = 29000 and made that substitution y = 29000 - x that you see

x and y mean different things there but it's perfectly fine to do it that way

[frigid sapphire]

yeah

ok

[thin sky]

how do you prepare for putnam

[pale kettle]

@thin sky are you in college?

[honest radish]

How to check if function increases on <a,b> where a and b are some real numbers.

f(b) - f(a)  > 0
or
f`(a) > 0 and f'(b) >0

[willow bear]

neither

a function can satisfy one of these - hell, even both - yet fail to be increasing on [a,b]

you need (∀x, y ∈ R)(a ≤ x < y ≤ b -> f(x) < f(y))

[honest radish]

(∀x, y) what is it?

[willow bear]

sorry, forgot the R

∀x,y ∈ R means "for all real x and y"

[winged breach]

okay so im doing differentiation now and i need to find the derivative of $3√x^2 - 1/√x$

[obsidian monolith]

Ross:

[willow bear]

$3 \cdot \sqrt{x^2} - \frac{1}{\sqrt{x}}$?

[obsidian monolith]

Ann:

[winged breach]

yes

[willow bear]

not $\sqrt[3]{x^2} - \frac{1}{\sqrt{x}}$?

[obsidian monolith]

Ann:

[willow bear]

just to make 100% sure we're on the same page

[winged breach]

okay sorry 2nd one

[willow bear]

:|

okay, so that's $x^{2/3} - x^{-1/2}$... how familiar are you with the power rule?

[obsidian monolith]

Ann:

[winged breach]

yeah i got that far

now simplifying that

[willow bear]

no

what i just did was a simplification

[winged breach]

oh okay so thats the final answer

[willow bear]

no it's not.

and you also avoided my question of

how familiar are you with the power rule?

[winged breach]

not that well then

so its 2/3x^1/3 for the first part right?

[willow bear]

no it's not.

$\frac{2}{3} - 1 \neq \frac{1}{3}$

[obsidian monolith]

Ann:

[winged breach]

-1/3 >

?

[willow bear]

yes

the derivative of $x^{2/3}$ is $\frac{2}{3} x^{-1/3}$. glad we could get that sorted out.

[obsidian monolith]

Ann:

[winged breach]

yes thank you

[obsidian monolith]

Ross:

[winged breach]

and now $\frac{2}{3} x^{-1/3} +\frac{1}{2}x^\frac{3}{2}$ ?

[obsidian monolith]

Ross:

[willow bear]

no, $-\frac12 - 1 \neq \frac{3}{2}$

[obsidian monolith]

Ann:

[winged breach]

ohh $-\frac{3}{2}$

[obsidian monolith]

Ross:

[willow bear]

go review your fraction arithmetic

[fluid sable]

If we had

$8/5 x = 58/5$

[obsidian monolith]

Saveable:

[fluid sable]

Could we potentially remove the denominators ?

Since they're essentially the same ?

[uncut mulch]

$\frac85x =\frac{58}{5}$?

[obsidian monolith]

ramonov:

[viscid thistle]

@fluid sable if its what Ram wrote, yes.

[fluid sable]

^

We wrote the same thing

It's just I don't quite understand latex that much yet

[viscid thistle]

ok

[uncut mulch]

use sufficient parentheses in plain text.
practice with latex in bots
there's a cheat sheet in #resources

(not much point in latex if the ambiguity is still there)

[vague aurora]

@sour eagle but isn’t triangle ABC in your example different from the triangle in the circle?

[thin sky]

@pale kettle No; I am doing my first semester at college this fall

but I heard about the putnam competition and was curious about it

[sour eagle]

@vague aurora The triangle ABC has the same angle ABC that defines the sine and cosine

[willow bear]

#calculus

[sour eagle]

😔

[willow bear]

that was in reference to a now deleted message, dan

[viscid thistle]

Can someone help me with that

[willow bear]

with what

[paper pecan]

with that, of course. pftt

[uncut mulch]

that was in reference to a now deleted message

[viscid thistle]

if you have like a

matrix multiplication sequence like

ABCDD^(-1)BC

can you like ignore the order you multiply them in

and turn the DD^(-1) into the identity matrix

in other words

is ABCDD^(-1)BC = ABCBC?

no u can't ignore the order you multiply them in

that doesn't answer my question tho

why does what i wrote seem to be true

your question and what i answered are different

you aren't ignoring the order in your question

polynomial: is ABCDD^(-1)BC = ABCBC?

is what i asked

yes thats correct

oh i thought u meant u were asking can u rearrange them

no but i mean can you just ignore the DD^(-1) in the middle of a matrix multiplication like that

why is that

since you haven't mulitplied it out yet

like you still have BC

on the right

yah u can just ignore it bc you can get back to it later. it's not going anywhere.

its usually done first though because it's the easiest to solve

ok so what about

ABCCBD

can you make that into

ABC^2BD

or are you now ignoring order

u can make that into C^2

why tho

idk if i understand matrix multiplication properly lol

i know that AB is not BA in almost all cases

but why can you do that

well bc C * C = C^2.

yes but dont you need to compute BD first

and then C(BD)

and only then C(C(BD))

no

matrix multiplication is associative.

oh

i didn't know that

wtf

lol

my education has failed me

damn

[paper pecan]

dman

damn

danm

[viscid thistle]

danm

[paper pecan]

namd

[viscid thistle]

jinx

mand

[paper pecan]

lol

[willow bear]

is ABCDD^(-1)BC = ABCBC?

yes

$DD^{-1} = I$

[obsidian monolith]

Ann:

[viscid thistle]

Has anyone used an especially commendable resource for understanding trig identities? (Using OpenStax but looking for others too).

[rich flint]

@viscid thistle ask in book discussion as well

[weak sierra]

can someone help me out with this question

ping me if you can help

yea

[viscid thistle]

@weak sierra any issues still?

[frank flame]

<@&286206848099549185>

[smoky pagoda]

?

[frank flame]

can I ask a limits question

:x

[fossil crown]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[north crescent]

Ask the q @frank flame I can probs help with limits

[frank flame]

#help-1 @north crescent

[north crescent]

Ann is helping, she’ll do better than I could ever do

[frank flame]

uh it's been an hour

I don't think she is

[coarse storm]

@frank flame I can try helping you

[frank flame]

thank you so much!! Ann helped me

[coarse storm]

Ohh, so you are all good?

[weak sierra]

can someone help with this question

i got the first part but i cant figure out the second

ping me if you can help

[coarse storm]

@weak sierra

Ok

This is fairly easy

For part I you know p has to be in the direction of -10i+24j

[weak sierra]

yep

for part i i got

-15i + 36j

using magnitude of the -10i +24j and comparing

@coarse storm

[coarse storm]

Yep

That is right

[weak sierra]

so how do i do ii

[coarse storm]

What you did in case you were confused is you calculated the length of the given vector and divided the vector by it's length

Giving you a vector of length one in the same direction

[weak sierra]

yep

[coarse storm]

And then you multiplied that by 39

Cool

Now for 2p + q being parallel of the positive y-axis and mag of 12 units

What is the vector that is 12 units long and in the positive y direction going to be?

Well i is in that direction but only is one unit long

[weak sierra]

mhm

[coarse storm]

And so 12i is going to be the resulting vector

Right

[weak sierra]

yea

[coarse storm]

So we can say that 12i = 2p+q

Right

So 12i-2p = q

And you know what p is

so just sub in p and do the calculation and you should be done

[weak sierra]

oh ok

@coarse storm could you dm me the written process if possible

i dont quite get it

[coarse storm]

Sure

Just give me a few minutes to write it out

[weak sierra]

alright thanks

[coarse storm]

@weak sierra

[weak sierra]

alr thx

[coarse storm]

Does it all make sense?

[weak sierra]

yep

[coarse storm]

Glad I could help

[weak sierra]

wait one more thing

im using my calc for the third part

where we have to find the magnitude of q in the form k root5

im getting a completely different answer

@coarse storm

so im getting 6root 193

idk why

[coarse storm]

Ohh

[weak sierra]

yea

[coarse storm]

Ohh

I see

My stupidity

[weak sierra]

?

[coarse storm]

I accidentally wrote i instead of j in my working out

[weak sierra]

where

ohhhhh

well its alright

[coarse storm]

I think that is all good now

[weak sierra]

yep got it

lemme just check

thanks man

got it

[coarse storm]

Wait, you got answers!?

[weak sierra]

?

[coarse storm]

You said "lemme just check" as if you have the correct answers.

[weak sierra]

i got the answer with root 5

[coarse storm]

Ohh right

Yep

Cool

[weak sierra]

nah like lemme check on my calculator

its fine

[coarse storm]

Yep

All good

[maiden pebble]

I believe that I have forgot how to take the derivative of logs

is the derivative of 5lnx --> 5ln(1) times x

[willow bear]

no

ln(1) is 0 for a start so that sort of thing would mean 5ln(x) is constant which it isn't

$\dv{x} \ln(x) = \frac{1}{x}$

[obsidian monolith]

Ann:

[maiden pebble]

Ooh, is this like when you said that in sinx, x isnt a constant

[willow bear]

...

when did i say that

you're probably twisting my words here

[maiden pebble]

huh, didnt mean to sorry

[willow bear]

i mean of course x isn't a constant, you're differentiating with respect to x

so how can x be a constant

[maiden pebble]

idk, thats why im asking for hlep

So, since lnx = 1/x, would 5lnx be 5/x

[willow bear]

lnx = 1/x

do you really think the equals sign means "next step"

because it doesn't, and what you said right there is some bullshit

[maiden pebble]

chill

[willow bear]

ln(x) is not the same thing as 1/x

[maiden pebble]

Idk what I said to put you off but im just trying to get some help

[willow bear]

i pointed out EXACTLY what you said to "put me off"

so if you still don't know then you must not have paid attention to the message i sent nearly a minute ago, and i cannot be blamed for that

what you probably MEANT to say is
"so since the derivative of ln(x) is 1/x, would the derivative of 5ln(x) be 5/x?"
to which the answer would be that yes, the derivative of 5ln(x) is 5/x.

[maiden pebble]

well I am confused, so that could be one reason as to why I dont understand what your talking about

[willow bear]

to which the answer is yes.

what part of

do you really think the equals sign means "next step"
because it doesn't, and what you said right there is some bullshit
do you not understand

[maiden pebble]

https://i.imgur.com/P9hLCwE.png

Lost me there

[willow bear]

and then you just chose not to read any of what follows?

[maiden pebble]

I have read everything you said

[willow bear]

what part of me pointing out your improper use of mathematical notation in "lnx = 1/x" do you not understand then?

[maiden pebble]

I understand that you were pointing out my notation

but my questions so far have not involved notation

[willow bear]

again

what you probably MEANT to say is
"so since the derivative of ln(x) is 1/x, would the derivative of 5ln(x) be 5/x?"
to which the answer would be that yes, the derivative of 5ln(x) is 5/x.

[maiden pebble]

Cool, glad we got the answer in the end

[willow bear]

i'm not entirely happy i only got a half-assed acknowledgment from you of your own misuse of notation

ie writing one thing while intending to say another

but w/e i guess i'm not gonna get that out of you any time soon

and you'll keep writing things like "x^2 = 2x" or "1 = 0" without caring for the actual meaning of the equals sign and one day you'll fuck up in a problem and spend a fuckload of time trying to hunt it down

but hey who am i to stop you