help-0

[harsh nimbus]

I did this idk if it’s right

[undone dock]

$x^{-n} = \frac{1}{x^n}$

[ocean seal]

K.

[alpine sable]

oh

damn ok

Thanks guys

[west hearth]

How would the figure look like for this?

[wet path]

for the first term, it wwould be 1/2 x^-1/2

[west hearth]

Would any part of the trapezoid be in the second quadrant

[harsh nimbus]

Oh yeah my bad

[wet path]

yeah

[harsh nimbus]

Updated

Thanks

[harsh nimbus]

What do you have so far

[west hearth]

.

Just wanted to ask that

[harsh nimbus]

It could be

That doesn’t matter as it only says one base is on x axis and other is above x

[silver current]

what do i expand sec x to?

[harsh nimbus]

So your trapezoid is in first or/and second quadrant

[winter rock]

Wassap

[harsh nimbus]

But can’t be in third or fourth

[winter rock]

Someone can help me for an ex (level 16yo-17yo Europe)

The sixteenth

[crystal crag]

To integrate, multiply and divide by (secx+tanx) then move on with substitution

[west hearth]

Doesn’t part of the trapezoid being in the second quadrant

Change our answer

Compared to like, being entirely in the first quadrant

[harsh nimbus]

No because the y stays still in positive

[west hearth]

True but we have to find the y coordinate of the Center of mass and for that we need the moment along the x axis

So like if part of it is in the second quadrant then 🤔

[harsh nimbus]

All three possible cases I guess

[west hearth]

Huh

Isn’t the side opposite to the base along the x axis

Cos our bounds of integration would change

In all three cases

[harsh nimbus]

Wait I am confused

Let me re try

[harsh nimbus]

Yeah you right no it wouldn’t my bad I read the second part as y axis instead of x

[west hearth]

Actually nvm

It would be the shape shape regardless of where it was

The distance from each segment to the x axis remains the same

[rocky spindle]

any idea how to start this ?

[hazy parcel]

how do i do a question if it says "show that x+4y = 24"

[tall kayak]

by plotting a grph

[hazy parcel]

by using equations

not graphs

[tall kayak]

you need 2 equations for if there are 2 variables in your equation

[ancient obsidian]

Am i right ?

[tall kayak]

ys

[tall kayak]

2nd one is incorrect

[ancient obsidian]

Can u explain what I done wrong

[tall kayak]

addition

[ancient obsidian]

Bruh

[tall kayak]

oh sorry

its correct

[ancient obsidian]

My bad

[tall kayak]

i didnt see that 10^-5

[ancient obsidian]

Oh ok

So it's correct right ?

[tall kayak]

wait lemme calculate it by myself I am doing it in my mind right now

[ancient obsidian]

K

[tall kayak]

yes

its correct

[ancient obsidian]

Alright

Thx

[tall kayak]

🙂

[ancient obsidian]

Now I have a question on this one

[runic flower]

@rocky spindle

[ancient obsidian]

What do I do with the power of 10

[runic flower]

Im sure about the first method
But the second , not sure 100%

[runic flower]

2.46 × 10^-3 = 0.0246

no

0.00246

[ancient obsidian]

So u move the decimal 2 places

?

[runic flower]

3 places

cause the power is -3

So you move the decimal 3 places to the left

if it was power 3 then to the right

[ancient obsidian]

Ok so then u add 5 x10^5

Which will equal 5.0246

Right ?

[runic flower]

No !

[ancient obsidian]

Hmm

[runic flower]

You have 3(5×..) + ...

[warm wind]

Can someone solve this without Hospital or Taylor?

[runic flower]

so its 15×

[ancient obsidian]

Ok

Then what ?

[runic flower]

then add simply

[ancient obsidian]

Alright

Thx

[winter rock]

Pls

[tall kayak]

The photo is not clear though

[winter rock]

Can someone tell me why we went from

[tall kayak]

what?

[winter rock]

AR -rAR = AB - rAC

To

AR - (1-r) = AB - rAC

@tall kayak

I have to say that r=all the reel expect 1

[wary stream]

That's not even the proper statement, but you just factor

[winter rock]

Could u show me how pls😭

[wary stream]

The GCF

Factor the GCF

[wary stream]

From that line

[winter rock]

Man

I swear

I don't understood how u factorized it

[wary stream]

All you do is factor the common term

AR is the common term

So you factor that out

[winter rock]

but it's AR - (r × AR) isn't?

[tawdry sphinx]

you factor out AR on the left side so it becomes AR * (1-r)

[winter rock]

How?

[wary stream]

Yes, it's that, but each term has a common factor of AR

[tawdry sphinx]

you have 1*AR - r*AR

and now you factor out AR

[winter rock]

A yeahhhhh

[wary stream]

So divide the terms by AR

[winter rock]

Wait

[tawdry sphinx]

no just factor it out

[wary stream]

You're left with AR(1 - r)

[tawdry sphinx]

don't divide

[winter rock]

I delete one AR

[wary stream]

When you factor, pull that common factor out and divide all those terms by that common factor

It's the same

[tawdry sphinx]

So let me show all of the steps:

AR - r*AR = 1*AR - r*AR = AR * (1 - r)

[tawdry sphinx]

yeah but saying divide it by that is quite confusing, I know what you mean but it just sounds a little confusing

[wary stream]

You are dividing though

[tawdry sphinx]

let's discuss that afterwards

[wary stream]

Factoring is pretty much dividing all the terms by that common factor and having that common factor outside

[tawdry sphinx]

@winter rock did you understand it now?

[tawdry sphinx]

yes I know

I know what factorization is haha

[wary stream]

Me too, but that's how to explain that last step

Common term gets pulled out, divide all terms by common term

[tawdry sphinx]

now it makes more sense because if you don't specify pulling it out then it sounds confusing

[wary stream]

That's why I said pulling out common term

[wary stream]

See, here, pull out common term

[tawdry sphinx]

yeah i meant that one but who cares anyway

if she/he gets the point it's fine i guess

[stable gazelle]

Hi

I don’t understand how to factorise that :

Anyone can help me please

[tired axle]

which one are you talking about @stable gazelle

[sleek quest]

I am trying to understand something about (a+b)(a-b)

I need to expand (x^2+2x+1)^2(x^2-2x+1)^2 and I get it wrong, can someone explain what's wrong

Is it even in the form of (a+b)(a-b)?

It's a^2-b^2

That's a known identity

Question is can I use it to expand the above

That was not my question

It's fine

[eager fern]

I have no idea

[sleek quest]

I want to solve it in the most efficient way, I can always expand each trinomial and multiply together, but I don't think that's necessary

@eager fern system of equations?

[eager fern]

Idk

I swear my teacher gives hw that we haven’t done in class

Every single math class does it

[ancient obsidian]

Is this correct?

The answer as to be in scientific notation

<@&286206848099549185>

[eager fern]

Do I substitute

[tawdry sphinx]

can't you just plug in 9 and 1 for f(x)?

as long as x isn't equal to 4 this should be possible

[robust aurora]

What do I plug in for (x) ?

Just any value?

[eager fern]

Idk what I’m doing

We haven’t done this in class and ik that for a fact

[tawdry sphinx]

did you read my answer?

[tawdry sphinx]

the result of g(x)

[eager fern]

Yeah idk what it means

I see this problem and I’m absolutely lost

No idea

[robust aurora]

Wait what?

[tawdry sphinx]

@robust aurora#help-1 is open i can help you there

[robust aurora]

Alright

[eager fern]

U a bitch

[robust aurora]

😭

[tawdry sphinx]

calm down

[tawdry sphinx]

man

ok you can wait now wtf

[eager fern]

Lmao

Not like u were going to

[tawdry sphinx]

i will help

just calm down a bit ok?

[eager fern]

^^

U funny man

My teacher a dumb

Every math teacher is

I might become one just to be the only good one

[tawdry sphinx]

ook?

so anyway

[winter rock]

@tawdry sphinx this man is high

Could u help me please

[tawdry sphinx]

i think so xD

gimme a minute

[winter rock]

Np

[tawdry sphinx]

i'll try and help him

[winter rock]

Its something really easy😭

The two things I linked in green

I know I have to link them and make the B disapear

But idk if I should make an addition or something else

[tawdry sphinx]

so @eager fern for the first one you have $9=\frac{a*3^2-b}{3^2-4}$ then solve for a and b with the other equation

[ocean seal]

NoRysq

[wary stream]

Don't be rude

[tawdry sphinx]

ok @winter rock can you post it with a bit higher quality in #help-8? I think I only have you and Litto now

[glacial shore]

15^2+x^2=20^2
Whats x?

[eager fern]

Why would I use the other equation when it had c and d in it

[tawdry sphinx]

this channel is busy rn @glacial shore sry

[alpine sable]

$x=\pm\sqrt{20^2-15^2}$?

[glacial shore]

k should i try another one?

[ocean seal]

jswatj

[tawdry sphinx]

no not that one i mean you have f(1)=1

[alpine sable]

U can also say that a^2-b^2=(a-b)(a+b)

[tawdry sphinx]

guys?

can you maybe move to discuss this?

[winter rock]

@tawdry sphinx

Yh I moved to qs 8 thx

[tawdry sphinx]

$9=\frac{a*3^2-b}{3^2-4}$ and $1=\frac{a*1^2-b}{1^2-4}$

[tawdry sphinx]

i saw it

[ocean seal]

NoRysq

[eager fern]

Idk

[tawdry sphinx]

then you get a system of equations

[alpine sable]

you have two equations and two unknowns just use substitution

[winter rock]

Take your time brother

^^

[jolly hearth]

Is this channel open or not yet

[alpine sable]

I guess now it is

[jolly hearth]

ok nice

Would you guys consider laws of logic math

Like is it ok to post here

[tawdry sphinx]

as far as I know any math questions

[jolly hearth]

Oh ok

Cause this one is more logic based so i was just wondering

[tawdry sphinx]

logic is still maths

[jolly hearth]

"f the weather is nice, then you go for a walk.
You did not go for a walk."

[alpine sable]

then the weather is not nice

[wary stream]

Ask in #discrete-math

[tawdry sphinx]

oh i know that one

[wary stream]

For logic help

[jolly hearth]

Oh thanks dude

[feral cobalt]

p --> q ; ~q then implies ~p

Think about the truth table for an if then statement

[jolly hearth]

Oh ok thanks

[eager fern]

Idk what I’m doing

Ik it’s not right

Wait nvm is it

A = 6 b =9

[tawdry sphinx]

you got those 2 equations and you now you solve one for a and plug that into the other to get b

then plug in b to get a

wait you did that actually

[zinc roost]

If i wanted a expression to show the quotient of x and 3 how would i put it?

[tawdry sphinx]

then it should be right

[eager fern]

K thanks

Sorry for being rude

[tawdry sphinx]

you mean in latex?

[tawdry sphinx]

i already forgot but you need to understand that there are other people here too

[zinc roost]

ye options are 3x 3/4 or x - 3

x/3*

[hard flume]

Hi i am new

👍

[wary stream]

#rules and #❓how-to-get-help

[tawdry sphinx]

you mean doing this $\frac{x}{3}$?

[ocean seal]

NoRysq

[hard flume]

o thanks

[robust crow]

can anyone tell me if this modular equation is correct?? the equation is x²-4x>0

[tawdry sphinx]

i can hardly read that sry, I'll try though

[slender girder]

Is this occupied?

[tawdry sphinx]

yes

[robust crow]

Do you need me to send you another photo?

with better quality

[tawdry sphinx]

#help-8 is open

would be nice

[slender girder]

I asked

[robust crow]

Ok

[covert mist]

wait dont u mean start both timers together when 3 minute is up flip it again and wait for the 4 minute timer to run out then flip the 3 minute timer and since its 1 minute at the top now its 5 minutes

[robust crow]

@tawdry sphinx I did it

[tawdry sphinx]

I need to fresh up my mind real quick that is not my favorite topic haha

[robust crow]

ok

So I will ask it in other channel

[tawdry sphinx]

i guess you can leave it here but I am so confused about that triangular symbol there

didn't see that in ages

wait is that delta?

[winter rock]

Hey wassap

I need help for the eleventh

I have to verify if they are parallel

@tawdry sphinx could u help me brother

[tawdry sphinx]

I'll be with you shortly

[winter rock]

Thxx

[tawdry sphinx]

which one of these?

[winter rock]

The eleventh

I have to verify if those points are parallel or not

I remember I had made it in class it was easy but I forgot how to do it

[tawdry sphinx]

construct a vector from M to N

[alpine sable]

hi

[tawdry sphinx]

multiply that vector with a scalar (any number call it k). If there is a k to reach point P the points M N P are colinear

[winter rock]

How long should the vector be?

Like 2cm

Or we don't care abt that

Lemme show u what I'm doing and send u a pic

[tawdry sphinx]

just the vector from M to N

we don't care or know how long that is

[tawdry sphinx]

ok

i gtg soon though

[winter rock]

Don't worry Im doing fast hehe

Thx for ur help tho

[tawdry sphinx]

you just need to do vector M - vector N

actually the other way around to get from M to N

[winter rock]

Look

What is in the parenthese () is the result of N-M for MN

[tawdry sphinx]

N-M will give you a vector MN

[winter rock]

Yh

[tawdry sphinx]

if you can extend that vector or retract it and by that touch point P , then P is on a line with M and N right?

that is what colinear means the points are on a "line"

[winter rock]

Yh

[tawdry sphinx]

so to adjust the magnitude of the vectorwe can multiply by k

we do not need to multiply P by k

P should stay where it is

so basically you have: $k * \vec{MN} = \vec{P}$

if you can find a k that works then there is a line connecting these 3 points, if not there isn't

[ocean seal]

NoRysq

[tawdry sphinx]

@winter rock hope this helps but I really need to go soon

[winter rock]

Thx

Np

I understood

[tawdry sphinx]

ok perfect

[high lintel]

can i get assistance actually im dumb, i dont need help

[rich kraken]

<@&286206848099549185> could you assist me with this problem my professor

Actual problem given to me by my professor

[quiet basin]

can someone plssss help me with this

its about the sin formula

[rich kraken]

@quiet basin so you know sohcahtoa right?

[quiet basin]

yes

[rich kraken]

So what does sohcahtoa say about sin(theta)?

[quiet basin]

thats where im stuck i dont get it my teacher explained it in a super confusing way

[rich kraken]

This might help

[quiet basin]

yes

thx

ill try it

[rich kraken]

So the hypotenuse is the longest side. And then you have two shorter sides sometimes called “legs” that make a right angle with each other see?

[quiet basin]

so kinda like this

[rich kraken]

Yup!

[fierce frigate]

just remember soh cah toa

[rich kraken]

But just wanna make sure you remember what hypotenuse, adjacent, and opposite are

[snow nest]

crap i was just about to say that

[rich kraken]

So you can remember

[quiet basin]

kkk thx

[fierce frigate]

soh cah toa will make ur life eaasier

[snow nest]

^^^

[rich kraken]

@quiet basin So the hypotenuse is the longest side. Then you have those two shorter sides sometimes called “legs”. You should see that the two “legs” make a right angle with each other right?

[quiet basin]

yes

[fierce frigate]

soh is Sin Appossite Hypothenus
cah is Cos Adjacent Hypothenuss
toa is Tan Opposit Adjecnt

took me so long to type HAHAHAH

[quiet basin]

lol

that helped tho thx

[rich kraken]

@quiet basin Now “adjacent” means next to so when we talk about the “adjacent” leg we mean the leg adjacent or next to the angle. And when we say “opposite” leg we mean the leg that’s on the other side from where the angle is

[fierce frigate]

opposite is infront of the acute angle

adjacent is below the acute angle

hypothnus is basicall the vertical lin

[rich kraken]

@quiet basin You see how on the diagram the adjacent leg is right next to the angle theta and the opposite is opposite the angle theta?

[pine rose]

I need help plz

[rich kraken]

Hypotenuse isn’t vertical

[fierce frigate]

idk th name

i forgot

[rich kraken]

Or at least not necessarily

[fierce frigate]

what is it call

[quiet basin]

o

yes

yea i see

it

[fierce frigate]

diagonal right

[pine rose]

Who is the helper?

[fierce frigate]

not me im stupid

im just learning about soh cah toa rn

[pine rose]

I mean who is the persono that helps with matheamticas

[fierce frigate]

for my aaddmaths today

quiz

[quiet basin]

bam so i get x/5 then i use algebra right

to solve it right

[fierce frigate]

what

oh

that

ok

so

[cloud widget]

Does anyone know a powerful differential equations calculator that can show all the steps? like these steps for example?

[snow nest]

we'll all do our best to help, but if the problem isn't solved within 15 minutes, you can ping helpers role

[fierce frigate]

u do
for exampl u uss sin
sin theta = op/ hypo

[rich kraken]

Yup! If the hypotenuse is 5 and the opposite is x then sin(theta)=x/5 and then you just need to solve for x!

[quiet basin]

yes yes i get it now thxxx

[fierce frigate]

sin theta x hypo (if we look for opposite)

[quiet basin]

thank you all of u who helped me

[rich kraken]

Np have a good one!

[quiet basin]

ur rlly smart

[rich kraken]

Before you go, wanna see one cool kinda more advanced thing? I think you can handle it :)

[quiet basin]

if u dont mind me asking how old are u

[quiet basin]

sure

[rich kraken]

I’m 18 lol

[quiet basin]

lol

[keen wasp]

ive spent like 30 mins on this q i dont really know what to do i thought the answer was b, f

[rich kraken]

@quiet basin so you know about a coordinate plane right? Where you have an x-axis and a y-axis?

[quiet basin]

ye

[rich kraken]

And you can plot points on the coordinate plane?

[quiet basin]

yes

[fierce frigate]

just a little fun fact if u want to look for the adjacent of something, u do algebra like
tan theta= (opposite)/x
tan theta * x = (opposite)
X= opposite/tan theta

idk if its tan tho

[cloud widget]

any help on a good diff eq calc/ 🙂

[keen wasp]

sry im only in 11th grade, we cant take that until next year 😦

[fierce frigate]

yea its tan

[rich kraken]

@quiet basin imagine you’re given the distance r between a point on the plane and the origin and you’re also given the angle theta it makes with the x-axis

[fierce frigate]

whats thta? myy teaacher haavent taught us about that

[quiet basin]

kkk

[fierce frigate]

oh

basicaly thaat

isnt that bassically norml soh cah toa?

but the numbeers is in the graph

[rich kraken]

You can find the x-coordinate by doing r*cos(theta) and the y-coordinate by doing r*sin(theta). See if you can understand why?

[fierce frigate]

r u gonna leearn about other trigonometr things @quiet basin

[rich kraken]

@quiet basin So x=r*cos(theta) and y=r*sin(theta) see if you can understand why

[quiet basin]

kk give me a sec

[rich kraken]

Think about sohcahtoa when you do it

[quiet basin]

k

[tight locust]

a good way to understand this is that polar equations are literally just parametric equations

[fierce frigate]

soh cah toa

[tight locust]

they are literally the same thing.

[fierce frigate]

ust memorize that, mk ur life easier, dont be like me, not payying aattention in class

HAHHA

in return i leearn for 9 houts

hours

to understand

[quiet basin]

wait wait wait

[fierce frigate]

algbra m8

[quiet basin]

x=rcos(theta) y=rsin(thet

then

[fierce frigate]

u wnt mee to explin?

[quiet basin]

sure

why am i doing this

wait

[rich kraken]

Sorry you gotta do \* to get * to show up like normal

[quiet basin]

thats ok

[rich kraken]

But ye I think you can understand it

[quiet basin]

@fierce frigate are u 18 aswell

[fierce frigate]

no hHAhah

im not even 18 yet

but im sure as hell going to collegge at 16

[quiet basin]

how old

angle

[fierce frigate]

14

[quiet basin]

tri

[quiet basin]

o

im 11

[fierce frigate]

how r u leaarningn this aat 11

[wary stream]

True?

[quiet basin]

ye

[fierce frigate]

ur not allowed to be here

[wary stream]

Because that's against discord's TOS

[snow nest]

discords TOS

[fierce frigate]

isnt that against the TOS

[quiet basin]

im not

[ionic jewel]

it's 13

[keen wasp]

lmao

[quiet basin]

finished

[tight locust]

\\

[keen wasp]

if anyone knows linear algebra please check out #help-1 if u have time

[quiet basin]

11-10+11-1+1+1

thats my age

figure it out

hehehehe

[fierce frigate]

ur 12

[quiet basin]

no

[fierce frigate]

or 13

[quiet basin]

no

[fierce frigate]

idk

lazy

[quiet basin]

kk

[fierce frigate]

ur 12

my calc says it

[wary stream]

Still against TOS

Also that math is 12

[fierce frigate]

13

[wary stream]

Now it's edited

[quiet basin]

im 13

im in yesr 9

year 9

[fierce frigate]

how ar u in year 9 when u r 13

[quiet basin]

if u look at my problem ull see the grade

[fierce frigate]

im 14 and in year 9

im IGCSE

idk

[quiet basin]

i live in nz

[fierce frigate]

if its called yar9

anyyways havee u figured it our?

out

[quiet basin]

ye

i have

[fierce frigate]

what uss adjcent and hypo

[quiet basin]

4.7

[fierce frigate]

how did u ggt number

[quiet basin]

o no im talking about my work

wat u talking about

[fierce frigate]

the question bam madee???

gave*

[quiet basin]

o

[fierce frigate]

this

[quiet basin]

yes coz u need them to caluclate the answer

[fierce frigate]

ill make ur lif easier
cos= adjacnt/hypothenus

which one is adjaceent which one is opposite

x or r

[fierce frigate]

mr answer it

[quiet basin]

r is hypotuse

i cant spell

[fierce frigate]

ah whatver x is adjacent r is hypothenus

just fill it in

[quiet basin]

y is oppsite

[fierce frigate]

cos = X * R
cos*R = X

thats how u geet that

and thn just switcharoo

[quiet basin]

kk

im dumb

[fierce frigate]

X= cos*r

hav eu learn the tan^-1 thing

i forgot what its called

[quiet basin]

netive numbers

?

[fierce frigate]

No

@rich kraken I forgot what is it called again

[rich kraken]

What thing?

[fierce frigate]

The one where u do tan^-1

[rich kraken]

You mean arctan?

[fierce frigate]

Or cos^-1

[rich kraken]

arccos?

[fierce frigate]

No

The

The

One

[rich kraken]

What are you asking for in reference to them?

[fierce frigate]

Where u press shift and press tan

In the calculator

[rich kraken]

tan inverse or arctan same name for what tan^-1 is

[fierce frigate]

ohh

Yes inverse

Thank you

Memory is broken

[rich kraken]

arguably more accurate to say arctan but ye

Different name for the same thing

[fierce frigate]

@quiet basin try doing this in your spare time

or this HAHAAH no dont do this if u havent learn about the sine rule

[warm wind]

Lim of x-x²(ln(1+1/x)) as x approaches infinity

But without using Hospital or Taylor series

[fierce frigate]

i need helpo

@rich kraken

this

[alpine sable]

Calculate the two momentum of two bird-system above us

Help

Pls

Turtoro

[fierce frigate]

i odnt know

im confusd about omething rn

[alpine sable]

Someone help me

[wary stream]

Ask in the physics server, linked in #old-network

[alpine sable]

I got banned from it because I “talked during a chess discussion”

lol

[fallow pagoda]

help?

[glass lichen]

what have you tried?

[fallow pagoda]

i tried to factorise it to try find t but im kind of confused

like i made h = 0

@glass lichen

[glass lichen]

that's correct

$0=16t-t^2$

[ocean seal]

Mosh

[glass lichen]

what's common to both terms?

[fallow pagoda]

t

and theyre both square numbers

[glass lichen]

16t isnt a square number cause of the t

but yes, factor a t

$0=t(16-t)$

[ocean seal]

Mosh

[glass lichen]

so you can read off the solutions

[fallow pagoda]

so t=0, t=-16?

im kinda confused how to convert that to time too

[glass lichen]

16-t=0 means t= what?

[fallow pagoda]

t=16

ohh thats the answer?

[glass lichen]

yes, so at t=0 and t=16, the height was 0

[fallow pagoda]

oooh thank you!!

[glass lichen]

so it hits the ground after 16s

[fallow pagoda]

wait then it says What is the greatest height the ball reaches above the ground?

[tranquil saddle]

I was wondering if I should write it out as 3 (4-1) + or If i'm just doing it completely wrong

[rich kraken]

@fierce frigate I’m walking rn so I can’t help too much but what I will suggest is that you draw a line that intersects point A and is perpendicular to line DC and then you also draw a line that intersects B and is perpendicular to AC and that should help you out quite a bit

[tranquil saddle]

or should I just subtract 1 from my final anwser?

[glass lichen]

yeah, so give it an attempt first

[rich kraken]

Will help out more with this problem once I’m done walking but it’s easier to explain when I also have a paper I can draw on lol

@fierce frigate But I’m hoping you can figure it out from the hint I gave you

Esp if you’re gonna go to college at age 16 ;)

You got it

[fallow pagoda]

do you sub 60 into t?

[glass lichen]

why 60.. when you know after t=16 the ball is on the ground?

[fallow pagoda]

ohh loll i thought cuz 60 seconds in a minute

[glass lichen]

???

[fallow pagoda]

i see now my bad thank you

idk i didnt understand it

so wait do u sub in 16?

[glass lichen]

No, you know the height when t=16

we just found that..

[fallow pagoda]

yeah

im really confused LOL

[glass lichen]

you know the 2 roots of the parabola right? what are they?

[fallow pagoda]

wait whats the parabola?

[glass lichen]

16t-t^2....

[fallow pagoda]

oh

[glass lichen]

the function the question is talking about?

[fallow pagoda]

okay

bro im really lost im so sorry

can someone help with this instead

[quiet basin]

hii im back

[alpine sable]

it is the same as a $f(x)=5x^2$ except $x=x-3$ and we subtract 8 from y

we have $5(x-3)^2-8$

[ocean seal]

Euclid

Euclid

[fallow pagoda]

ooooh yeah okay i see thank you

wait i have one more cna u help?

[alpine sable]

sure

[fallow pagoda]

what rule is used?

[alpine sable]

law of cosines

i think

[fierce frigate]

already understood it lol

[rich kraken]

Nice!

[fierce frigate]

took me a whilel

[quiet basin]

hi backk

[fierce frigate]

to understand

[fallow pagoda]

but with cosine doesnt it have to be the length around the angle ? @alpine sable

[fierce frigate]

wish me luck for my addmaths quiz today :)

[alpine sable]

with law of cosines you can have $33^2=87^2+87^2-2\cdot87^2cosx$

[ocean seal]

Euclid

[quiet basin]

@rich kraken sin formula actually turned out to be easy thanks to u

[rich kraken]

Nice! You can @ me if you need some help in the future!

[fallow pagoda]

@alpine sable but what do i do with that cosx if i cant put it in the calculator like that>

[quiet basin]

o thx

[fallow pagoda]

wdym?

i get that to find an angle u have to do shift cos or whatnot

but yeah im a little confused where i put that and stuff

[quiet basin]

Annual sales (in millions of units) of a certain brand of tablet computers are expected to grow in accordance with the function

f(t) = 0.18t2 + 0.16t + 2.64 (0 ≤ t ≤ 8)

Per year, where t is measured in years, with t = 0 corresponding to 1997. How many tablet computers will be sold over the 8 year period between the beginning of 1997 and the end of 2004? (Round your answer to two decimal places.)

?= million units

[alpine sable]

or actually you can do $x=cos^{-1}\frac{33^2-2\cdot87^2}{2\cdot87^2}$

[ocean seal]

Euclid

[fallow pagoda]

thank you ahh

[alpine sable]

because you can put the non cos terms on one side

and then divide by the coef in front of the cos x

[quiet basin]

do You take the definite integral of f(t) from 0 to 8 and you get 56.96 as your answer. (When you take the integral of the function, f(t) = 0.18t2 + 0.16t + 2.64 , use the power rule.) or am i just wrong

[fallow pagoda]

@alpine sable hmm it says its wrong?

[quiet basin]

wats ur question

[fallow pagoda]

because for the cosine rule to find an angle you need to know all sides

i think?

[alpine sable]

yes

[fallow pagoda]

and there we dont know all sides

[alpine sable]

its isosceles cause the right side of the triangle is just a rotation of the left

[fallow pagoda]

ohh thank you!

i got it

[alpine sable]

o

i saw my mistake

you need the radius of the circle

to get the sides

[fallow pagoda]

well we can just put it in as 87^2+87^2

and bla bla bla

[alpine sable]

also it says to round

[fallow pagoda]

i got the answer it was a practice exam so the time ran out, i literally had 1 minute left but for some reason didnt let me put it in lol

so i guess we'll never know whether it was right or not

but thanks anyways! i think i understand it now cuz the other side was the same

[alpine sable]

im not that good at trig so it was probably wrong

[lapis valley]

is this sqrt(2)/2+cis(225 or 5pi/4)

[lean night]

can someone help me answer this question, i got stuck whit this :((

[worthy bear]

so i have a question im trying to do math homework right now and im all honestly just lost as i wasn't there in class to be taught it and my teacher legit won't help me so does anyone mind helping me with my math segment homework? i need to see how a few questions are done for me to understand it

[lapis valley]

bruh

why u all posting in here

go somewhere else after someone has posted a question and yet to recieve a reply

[worthy bear]

sorry

[fringe spindle]

6P5 = 720 for no digit used more than once per number. and assuming even numbers mean you can use all 6 again, this is equal to 5! for the arrangement of the other digits not including the last even digit, multiplied by 2 for the 2 even digits = 240

oh wait sorry there's 3 even digits

so 5! x 3 = 360

that's it

[versed violet]

hey, can someone help me with a problem? I dont know much about integrals...

I have to code a program to do this

cna someone help me with the sum part?

[glass lichen]

what about it..?

[dawn charm]

To prove that it's closed you just have to take any two elements from the group and prove that you get another element from the group. For instance, in the first point (a), the group is defined as the set {2n | n in Z}. Let a, b be any integers, and let n = 2a and m = 2b. n and m are clearly in the group of even integers. To prove that it's closed under multiplication, just multiply n and m. So you get n * m = 2a * 2b = 4ab = 2 * 2ab. And if you let 2ab = c (which is clearly in the even set too), you get n*m = 2c, which is in the group of even numbers. So the set/group is closed. You can apply the same procedure for point(b)

[versed violet]

well, I need help with the integral too

what is the sum summing

[glass lichen]

function values

at your test points x_i on the interval [x_0,x_n]

[versed violet]

damn I guess I am fucked up

[jade holly]

had 2 exams and watched 5 lectures td lol. can someone lead in me in the right direction for setting up this algebra question so i can code the function lol.

[rich basin]

Thanks

[jade holly]

5.8m x efficiency... then?

[glass lichen]

The eqn you have posted is called a riemann sum. What it does is it takes an interval and partitions (splits) it into smaller intervals.
On these partitions we pick a point x_i and find the function value. Then consider the area of the rectangle formed by f(x_i) and the length of the partition. Then sum all those up and slowly make more and more partitions

@versed violet

[tranquil plinth]

Im partaking in year 6 division, anyone tutor?

[stoic lintel]

Guys how do u find trigonometry

[jade holly]

42 x input # of barrels

[dawn charm]

Think of the summation (and the coefficient) as the formula for the area of a rectangle. (x_n - x_0)/n is just the "base" of the rectangle and the summation (or f(x_i)) is just the height of every rectangle at the point x_i. So you're just summing areas of rectangles. As the limit goes to infinity you get a more accurate estimate

[uneven cave]

how am i supposed to find the area of the triangle

[tranquil plinth]

soh cah toa

[stoic lintel]

Depending on the triangle

[tranquil plinth]

i think

[uneven cave]

my triangle is small

[stoic lintel]

There are 3 methods!

[tranquil plinth]

which type

[uneven cave]

3 sided

[tranquil plinth]

duh!

[stoic lintel]

First method is the height x base

Second is the heron formula

3 one if the triangle ain’t right angled, using the formula 1/2 x a x b x sin (c)

Hood dat helped!

[tranquil plinth]

dope

[kind parcel]

What equation should i use here?

[lean night]

thankyou it really helpfull, hope the best for you

[dawn charm]

I'm glad and thank you! 😄

[tranquil saddle]

hey wondering if someone can hop in a vc and help me out with some problems?

[supple prairie]

can someone help me?
Dad wants to make a cabinet frame out of rectangular plywood. The perimeter of the plywood is 60 m and the area is 216 m². Dad's plan is to cut the plywood into 2 large and small rectangles in a ratio of 1: 3. Determine the length and width of the small rectangle! *

[stoic lintel]

Can someone help@me

[lean night]

so in b point, i can use same prosedur?, a,b is any integer, and n = 1a and m =1b, and multiply n*m, = 1 a * 1 b = 2 ab = 1 * 1ab, sorry, correct if im wrong please

[uneven cave]

yes

[uneven cave]

it would be 2 to the n1a multiplied by the root from the ab squared

[tranquil saddle]

I am confusion

[fathom sequoia]

is there any way to simplify this $2^{2x}-3\cdot2^{x}$

[ocean seal]

TJ89899889

[fringe spindle]

np, thinking about that more, if they still meant only 5 digit numbers for even, it should be like 3C2 x 4! x 3 (this is for each set of 5 digits using all the 3 even numbers; 3C2 for the selections of 2 of the remaining odd number times 4! for the arrangements of the preceding digits times 3 for the 3 possible end digits, + 3C2 x 4! x 2 (this is for each set of 5 formed using exactly 2 of the odd digits, we can select each set of 2 odd digits in 3C2 ways, again 4! for the preceding numbers, but now only 2 possibilities for the end digit and add these up just gives 360 again

[wispy sorrel]

just plug in a number

[dawn charm]

You should choose two odd numbers, so like n= 2a+1 and m = 2b + 1. So by multiplying them you get n*m = (2a+1)(2b+1) = 4ab + 2a + 2b + 1 = 2(2ab + a + b) + 1 which is an odd number 🙂

[tranquil saddle]

you see I don't understand how to do functions

[wary stream]

Just plug in the values for x, from the table

No

We're not here to give answers

Don't care, we don't give answers

No

That is not the point of this server

People are here to help you, not give answers

[fierce frigate]

ayo thee quiz waas so easy

[supple prairie]

can someone help me,my teacher didnt teach me this

Dad wants to make a cabinet frame out of rectangular plywood. The perimeter of the plywood is 60 m and the area is 216 m². Dad's plan is to plywood the square into 2 parts, large and small, in a ratio of 1: 3. Determine the length and width of the small rectangle! *

[wary stream]

If you don't understand a concept, we will help you understand it

<@&268886789983436800>

[supple prairie]

stop

[wary stream]

Stop

[supple prairie]

its your own

[sly mantle]

b&

[fierce frigate]

@rich kraken the quiz i talked about

[supple prairie]

i dont understand the concept

[fierce frigate]

was so easy

[supple prairie]

[wispy sorrel]

how do you roughly graph a polynomial that doesnt have any real zeroes in order to find the amount of turning points?

[placid zinc]

Know any calculus?

[wispy sorrel]

no Im in pre calculus

[placid zinc]

Oof. Yeah you don't have an amazing option

What's the poly?

[wispy sorrel]

5x^4 + 15x^2 + 10

and by roughly graph I mean just using multiplicity for the zeroes and the leading coefficient test

[placid zinc]

I don't think you can have a turning point, since all three terms increase as you get away from 0

(Other than the turning point at 0)

[wispy sorrel]

so do I just guess for these problems

[placid zinc]

Like I said, no roots means no amazing points of reference

A turning point is caused by two terms fighting for dominance. That just isn't happening with the above function

[harsh nimbus]

isnt there one turning point
0,10

or is that not considered a turnign point

[placid zinc]

Yeye, other than that one

[harsh nimbus]

which question?

[pure grove]

11

[wispy sorrel]

but how do I determine if theres just that one

[harsh nimbus]

i assume bdc

[placid zinc]

6x - 1 has no turning points

[harsh nimbus]

oh wait

[wispy sorrel]

thats max number of turning points

[harsh nimbus]

my bad let me doub.e check

oh i see i forgot

[wispy sorrel]

for example x^3 has 0 turning points

[placid zinc]

Max possible is "degree - 1"
I don't even know how you'd include leading coefficient

[wispy sorrel]

the leading coefficient test includes both degree and the actual coefficient apparently

[vapid herald]

could i get some help with this problem

[alpine nacelle]

@vapid herald still here ?

[vapid herald]

yes I am

[alpine nacelle]

First, you need to find the vector V

[teal vessel]

idk how to solve this question

can u solve it for me too plz

[alpine nacelle]

From which point does the vector V start ? (what are its coordinates)

[alpine nacelle]

go in an other chan

[vapid herald]

it would be (0,0,0) right?

[alpine nacelle]

no, (0, 0, 0) is the origin, where you can see the i, j and k vector starting from

the vector V starts to an other point here

[vapid herald]

ah okay I see

[alpine nacelle]

so, can you give the coordinates of starting and ending points ?

[fathom sequoia]

Given the rational expression:

$\frac{x-2}{3}-\frac{x}{x+2}$

Would you say the following is a fully simplified version of it:

$\frac{\left(x+2\right)\left(x-2\right)-3x}{3\left(x+6\right)}$

Or is there still more work to do

[vapid herald]

so it would be (2,0,0)

[alpine nacelle]

DUDE, learn how to read

can't you see people are already talking here ?

seriously there are at least 6 other chan without messages

[fathom sequoia]

Wait a sec made a mistake

in the

tex

[alpine nacelle]

nobody cares, just go in an other chan

[alpine nacelle]

yes, it is the starting point

now, find the ending point, and so you find V

[ocean seal]

TJ89899889

[wary stream]

If you have read #rules and #❓how-to-get-help, you should know that you should not ask your question in a channel that is busy

[fathom sequoia]

Dude you are rude

[dark granite]

They weren't being rude. You are the one who barged in

[vapid herald]

so when you say find "V" do you mean the magnitude

[alpine nacelle]

you need to find the vector first, so you can find the magnitude

[quiet basin]

hi im backk

[alpine nacelle]

if you have the starting and ending points, you can find the vector V = (a, b, c) and then the magnitude is sqrt(a²+b²+c²)

[fathom sequoia]

k

[vapid herald]

well technically a vector doesnt "end" right but you are talking about inside the bounds of the prism correct

so the end points would be (0,1,1)

[alpine nacelle]

yes

so what is the vector V equal to ?

[vapid herald]

V = (-2,1,1)

[alpine nacelle]

yes

and what is its magnitude ?

[vapid herald]

sqrt(6)

[alpine nacelle]

yes

now you need to find the angle between the vector and the base of the prism

[vapid herald]

so are we considering the base to be

[alpine sable]

@frozen vortex

@frozen vortex

[vapid herald]

that corner?

[alpine nacelle]

yes, the angle between the vector and the plane that the base is

[vapid herald]

okay how would I go about calculating that

I assume

it would be

let me draw it

[alpine nacelle]

first, can you see that the vector (-2, 1, 0) is the "same" as V but within the plane ? (a projection)

plane which is the base

[vapid herald]

yes correct

oh wait so it would be

[alpine nacelle]

so what is asked is the angle between V and (-2, 1, 0)

[alpine nacelle]

you want the angle between V and your blue vector

[vapid herald]

okay the magnitdues are the same

so it would just simply be sin(theta) = 1/sqrt(6)

or theta = sin^-1(1/sqrt(6)))

[alpine nacelle]

which formula did you use ?

[vapid herald]

just sin operation right

[alpine nacelle]

oh ok

mb

[vapid herald]

does that work?

[alpine nacelle]

first, V and (-2, 1, 0) don't have the same magnitude, but yeah you can work in the right triangle

[vapid herald]

oh wait youre right

its not 1,1

[alpine nacelle]

V is the hypothenuse

[vapid herald]

-2,1,1*

yeah exactly

[alpine nacelle]

and your opposite side is 1

so sin(theta) is indeed 1/sqrt(6)

[vapid herald]

1/sqrt(6) though right

[alpine nacelle]

yes

[vapid herald]

so thats simply it?

[alpine nacelle]

indeed

[vapid herald]

awesome thank you very much i didnt know it was that simple i couldve figured that out haha

[neon bramble]

hey is my answer right?
-10n^3 - 15n^4 = -5n^3(-2 - 3n)

[wary stream]

What's the context?

Wait, I see

[fathom sequoia]

yes that's right 😄

👍

[neon bramble]

aight thanks

[fathom sequoia]

Wait nvm

[neon bramble]

what

[wary stream]

It's not right

[neon bramble]

oh

[wary stream]

You have sign errors

[fathom sequoia]

yeahh

your negative should be a positive

[neon bramble]

oh

[fathom sequoia]

$-5n^{3}(2+3n)$ is the answer

[neon bramble]

oh

[ocean seal]

TJ89899889

[wary stream]

Come on, why'd you give the answer? I wanted the person to discover the mistake

[neon bramble]

oh wait i see know

lmao

[fathom sequoia]

they already know the mistake

it can also be $5n^{3}(-2-3n)$ if u want doesn't matter really

[ocean seal]

TJ89899889

[wary stream]

They know it was a sign error, I wanted them to determine how the signs were wrong

[fathom sequoia]

k do u know why the signs are wrong @neon bramble

[neon bramble]

yeah i get it now

[dark granite]

no point in asking now

you already gave em the answer

[fathom sequoia]

k so next time should I not

[neon bramble]

is it because negative divided by negative is positive

or no

[fathom sequoia]

yes

[grim delta]

how should I solve this problem
specifically the last part where it says “find the plane determined by these lines”
i got the point from the first part

[dark granite]

I mean, next time if someone else is already helping them, let them help them and don't interfere. And yea def don't just spew out the answer lmao

[fathom sequoia]

$-a\cdot-b=+b$
$a\cdot-b=-b$
$-a\cdot b=-b$

How do I do spaces

[dark granite]

with \

[wary stream]

By using the space bar?

[dark granite]

and spaces on either side of em

no

within the dollar signs

[ocean seal]

TJ89899889
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[wary stream]

$$-a \cdot -b=+b$$
$$a \cdot -b=-b$$
$$-a \cdot b=-b$$

[fathom sequoia]

ok theres no nwe line

[dark granite]

do you want a newline or just a space?

[fathom sequoia]

but there's th erule I guess @neon bramble

[fathom sequoia]

newline

[ocean seal]

dldh06

[dark granite]

ohhhh

then do two backslashes after the last dollar sign of the each line

[wary stream]

Do double dollar signs

I prefer that

[fathom sequoia]

ok theres the rule

[neon bramble]

thanks

[fathom sequoia]

obviously you know positive times positive is positive so I wont tell you

but with negatives its confusing

[grim delta]

that and division is just multiplication by a fraction @neon bramble

[neon bramble]

aight

[grim delta]

$\frac{a}{b} = a \cdot \frac{1}{b}$

[ocean seal]

Dogecode

[grim delta]

and the same rules apply to that

[kind parcel]

guys im so lost

[alpine sable]

standard deviation is range, right?

[kind parcel]

its like a variation thing from the mean

[blazing rose]

i use riemann sum for this right

[pastel kiln]

How do i find a slope?

pls help i have a test tmmr and idk anything

[blazing rose]

(y2-y1)/(x2-x1)

[runic canopy]

What should i do first when approaching this problem? Should i distribute top?

[blazing rose]

you always plug in first but in this case you see that u get 0/0

[grim delta]

l hopitals rule

[blazing rose]

so you need to figure out what u can do to simplify

[feral cobalt]

First thing I'd do is see what makes your answer be complex/invalid for the function. But for x= -3 you divide by 0, so thats a gap in your function

[grim delta]

l hopitals is where you take the derivative of the numerator and the denominator

[runic canopy]

I feel like everytime i get an x in the bottom, ill get it invalid

[blazing rose]

you could factor the top

[grim delta]

that’s equal to the original equation

[runic canopy]

Ohh ok ok i didnt learn that

[blazing rose]

u dont need it

[grim delta]

It looks like that would get rid of division by 0

[grim delta]

You probably will at some point

[feral cobalt]

No. If x is 4, you'll get something over / 7, and thats valid

[runic canopy]

Oh damn ;-;

[feral cobalt]

Anything except -3

[runic canopy]

But if i factor top it, should i plug?

[blazing rose]

factor top out

keep bottom

[runic canopy]

Ok ok

[blazing rose]

you will see what u gotta do after that

[runic canopy]

Kinda just cross out the top and bottom

[grim delta]

yeah that seems good

[blazing rose]

yeeeaa buddy

[blazing rose]

can someone help

[runic canopy]

😂 thx i hate limits and all, i had covid so i missed alot of the lectures

[sly timber]

Is this physics ?

[blazing rose]

calc

[sly timber]

Can’t help sorry ):

[grim delta]

Factoring is good too in this case, id say both ways were good approaches to this problem

[blazing rose]

darn

[grim delta]

Once you learn lhopitals it comes up a lot though

[runic canopy]

Ill keep that in mind

[sly timber]

How do I factor 8x^3 -12x^2+6x-1?

[feral cobalt]

How do you say it. I've been saying it like "le' hospitals" like some french name

[grim delta]

In this case for lhopitals it would’ve become $\frac{2x+1}{1}$ after you derive which you can then plug -3 into and get -5