help-0

[willow wadi]

For this question do u get
**
Resolve a force of 200N in the direction S 22 degree E into its regular componets
do u get **
East = 200 cos (68) and South = 200 sin (68)

<@&286206848099549185>

[wary stream]

If that force is Southeast, then that angle you used is technically wrong

[willow wadi]

oh if not

then its right

[wary stream]

You used the proper trig functions for each direction

[bitter sage]

hey anyone know how to solve this question?

[tight locust]

what is B?

[noble sinew]

Only 1 value of B possible such that LHS limit equal to RHS limit

But not rly required to even calc RHS limit

Just calc LHS limit and set A equal to that

[bitter sage]

wdym calc lhs limit?

can you show what u mean?

[noble sinew]

Calculate limit as x approaches 1 from the left

[bitter sage]

so i use the x^2 + 2x - 3/x - 1 and lim x-> 1

[noble sinew]

Yes

[bitter sage]

and that gives me a?

[silk veldt]

Is this the correct process for the algebraic question?

[bitter sage]

so a = 4?

[noble sinew]

Si

[bitter sage]

Ok

[noble sinew]

You didn’t multiply probably when multiplying both sides by 2

[bitter sage]

The question seems like it would be a lot harder

[silk veldt]

Maybe I missed the 18

[noble sinew]

Yep

[silk veldt]

Thanks for the help

[ashen plaza]

Oooooooo

[spice imp]

So me and my mate were talking about how fast you would need to move to stay the same spot under the moon at all times. I said 1670km/h, since its just moving the circumference of the earth in 24hrs. He isnt satisfied, and we want to know if the moons orbit would factor into this in any meaningful way

[ionic jewel]

it's about the right answer, but for the wrong reason

it actually takes 27 days for the moon to orbit the earth

you just get to use the earths rotation to help

[spice imp]

So could i make it more accurate? Nvm dont tell me, ill try figure it out and come back

So, if the earth didnt rotate to start, you would need to go 24.7km/h to stay under the moon. The earth rotating seems the complicated bit now, considering youd add or subtract(not sure) the relative velocity of the rotation at whatever point on earth youre at, right?

[normal hazel]

Lmao are these kindergarten questions?

[ionic jewel]

I'm pretty sure your first answer was mostly accurate, but i was just pointing out how it could be more complex if you wanted to look more into it

[glass lichen]

clearly not, dont be a dick

[ionic jewel]

of courses, the moon's orbit isn't a perfect circle either, so there's plenty of other things that could be a problem

[spice imp]

Yeah, unfortunately i dont have the know how or patience to factor the moons orbit or earths rotation into it

[ionic jewel]

your approximation is about right

[modern wren]

IS anyone Familiar with Ramsey Theory?

I found a Transform Function for base 3

It generalizes but ill be doing that tonight

[modern wren]

?

[alpine sable]

<@&268886789983436800>

[sly mantle]

ty

[wary stream]

Just to confirm, people can't promote other servers? I was gonna ping mods but I had to look at the rules to double check and didn't see anything so I was hesitant

[heavy otter]

The rule is against unsolicited advertisement

there's no problem with linking a server if it's relevant to the conversation and/or the other person asked for it

[wary stream]

Ah, I see, thanks for clearing that up

[elfin talon]

Don’t be a snitch bro

[wary stream]

I didn't snitch the first time but it is a rule that is enforced, so if a mod needs to be called, then they'll be called

[elfin talon]

Ok

[sly mantle]

not a fan of this comment

[elfin talon]

Me too brother, me too

I disappoint my self sometimes lol

[alpine sable]

If you can't swim with the sharks you aren't a titan.

one thing that I can't wrap my head around is that we always say that subtraction does not share the same properties that addition does (i.e commutative and associative) yet subtraction can be written as addition? e.g 4-5 = 4+(-5), a+b-c= a+(-c)+b

hey guys what's the difference between sin and |sin|? what does | mean?

I believe it is the absolute value? https://en.wikipedia.org/wiki/Absolute_value

thanks

np

is that clojure?

your avatar

or some other lisp dialect

that's the DeepMind logo

[unkempt tulip]

aaaaaaaa

[honest hawk]

Do you mind if i get some help on this one?

The formula in question is this:

But, I guessed the right answer due to the difference of 80 and 30 being 50.
How would one mathematically apply this to show proof though?

[astral dagger]

but this difference may have nothign to do with the answer

[honest hawk]

ah

[astral dagger]

also, this logarithm is base 10

[honest hawk]

For reference, it gives me the explanation, but it isnt the best:

[ocean seal]

SubGui

SubGui

[honest hawk]

(thanks for the assistance, by the way. Im a bit all over the place today.)

[astral dagger]

such that you just need to put 80 and 30 on the left side of the equation and solve for the maximum and minimum intensities

[ocean seal]

SubGui

[honest hawk]

ah. that makes sense. Ive always been murky with reverse engineering logarithms

[north hemlock]

Hello! I am trying to write an analysis of this histrogram and boxplot but I don't know what more there is to discuss about these

I need 2 slides but I only have one so far with what seems to be all the relevant information

is there anything I am missing or things I can talk more about?

[north hemlock]

<@&286206848099549185>

👀

[queen nova]

what is it called when a line on the graph is horizontal and straight

<@&286206848099549185>

[plucky radish]

the function is a constant - i.e. y=4 would be a straight line with an intercep at (0, 4) and a gradient of 0

you could say it's parallel to the x-axis, you could say it has no gradient, or just say that "y is constant"

[queen nova]

got it thank you

I'm trying to write a function for the following problem: Jeania’s parents have given her a interest-free loan of $100 to buy a new pair of running shoes. She plans to pay back the loan with monthly payments of $20 each.

I put P = b(p) = -20m + 100 is that right?

[topaz scaffold]

It should be b(m)

[queen nova]

the question said to set it to b(p)

Write a function rule for the balance of the function B(p), where p represents the number of payments Jeania has made.

[topaz scaffold]

Then you gotta use p instead of m

Since it's a function of p

[queen nova]

oh ok

so -20p + 100?

[topaz scaffold]

Yea

[lucid beacon]

Could anyone help point out the errors in my solution? Also I'm not sure if this is the correct channel

[queen nova]

ok got it tysm

[lucid beacon]

Question: 2log(x+3) = log(ax) has only one solution. Find the value of a

I assume that's it is an integer solution but it isn't specified

[ionic jewel]

slap the 2 into the log using the relevent log rule, then remove the logs

[topaz scaffold]

Bring the 2 inside the log

Oh

[lucid beacon]

I managed to get a = (x+3)^2/x

[ionic jewel]

,w (x+3)^2 = ax, a > 0

:thonk:

[topaz scaffold]

Expand and move over the ax

Then solve the quadratic

[glass lichen]

why the hell did I think it was a cubic

[topaz scaffold]

a has to be positive

So a = 12

[ocean seal]

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[lucid beacon]

Yeah I thought a trivial solution was a = 0, lol

[glass lichen]

no

cause then you'd have log(0)

[lucid beacon]

Yeah

[glass lichen]

so a clearly cant be 0

[ionic jewel]

i mean there's multiple integer solution pairs for (x,a)

there's no global a that works for all x

so idk what they want

[glass lichen]

they want the quadratic you get to only have 1 solution

so ||discriminant of 0||

[lucid beacon]

Okay thanks guys

[north hemlock]

Hello! I am trying to write an analysis of this histrogram and boxplot but I don't know what more there is to discuss about these. I need 2 slides but I only have one so far with what seems to be all the relevant information. is there anything I am missing or things I can talk more about?

[snow nest]

oh my god

is that an AMC question

holy shit that gave me chills for some reason

[north hemlock]

<@&286206848099549185>

[frosty jungle]

Guys what is 1 + 1 ?

[north hemlock]

pain

[topaz scaffold]

10 in base 2

[wanton orbit]

hello friends. i'm trying to wrap my head around this one, but how do i calculate a percentage increase to another percentage? (x% rises / falls to y% , the difference measured in a percentage)

i hope it's not too much of a dumb question

[alpine sable]

@wanton orbit do you mean for example: x is increased by y% to z%, where you know y and z but not x?

[wanton orbit]

i think not,

lemme try rephrase it

x% of a random number rises to y%, and i need the difference in a percentage?

[alpine sable]

i'm not really sure what you mean, sorry

[wanton orbit]

it's ok man

[queen nova]

what is the constant term in this equation: -8x2 + 54x + 140

[ionic jewel]

140

it's the one without the variable

[queen nova]

ah ok

ty

[topaz scaffold]

y%/x% -1 should be the percent increase

[wanton orbit]

oki doki

minus one?

[topaz scaffold]

Yea

[wanton orbit]

okay

thank u

[north hemlock]

pog

[wanton orbit]

hold on, man. i don't know if this is the right one. the calculus isn't adding up.

[topaz scaffold]

Oof

[north hemlock]

calculus on percentages

[wanton orbit]

a 15.4% of the population claimed to be evangelical, in ten years, it rose to 22.2%, this news article claims it has risen in 61%, i'm trying to get the formula of this thing so i can continue with this assignment

[north hemlock]

imagine if the news is fake xd

[wanton orbit]

it's probably not, it's has data from the national demographics center

which have (presumably) better mathematicians than me

[north hemlock]

well 15.4% to 22.2% is a 44.2% increase

44.15584415584415

[wanton orbit]

[north hemlock]

,w ((22.2 - 15.4)*100)/15.4

[ocean seal]

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[north hemlock]

yep

or u can do ,w ((22.2)/(15.4))-1

,w ((22.2)/(15.4))-1

[ocean seal]

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[north hemlock]

which is the same but not as a percent (yet)

to get that to be a percent, just *100

[ionic jewel]

,calc 1.61*15.4

[ocean seal]

Result:

24.794

[ionic jewel]

definitely not 22.2

[north hemlock]

true

"news article claims it has risen in 61%," #FakeNews ggwp

[wanton orbit]

,w ((22.2)/(9)-1

[ocean seal]

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[wanton orbit]

seems legit

[north hemlock]

hm

[wanton orbit]

gosh darn it

[north hemlock]

what're you trying to do exactly

[wanton orbit]

calculate percentage growth

from 22.2% to 31%

[ionic jewel]

we already did that didn't we

,w .31/.222-1

[ocean seal]

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[wanton orbit]

that makes it a

39% increase?

from 22.2% to 31%?

is that it?

[unborn dome]

can someone help me with this?

[alpine sable]

Hey guys need some help checking this... I think I did it right? But I got slight different numbers for the solutions. I know the end result is the same because there are no solutions but... not sure if I messed up somewhere ?

[alpine sable]

I could be very very wrong, but from what I remember you just pick some random number ( in between the constraint) as your "w" and then solve for all those possible solutions... which If I remember correctly means you just say + 1/2pi... or whatever to resemble all solutions in that range

So basically you need to come up with a formula that works for all solutions in that range

[undone dock]

i think its just a quadratic in terms of cos(w)no?

[alpine sable]

Yeah its a quadratic

But it wants every solution for every possible angle between 0 and 2pi

I remember it was pretty easy I just forgot exactly how you do the notation

[alpine sable]

Im pretty sure this is the exact same problem with just a quadratic

https://www.youtube.com/watch?v=h7trDHjKCYc

[unborn dome]

hm

ill have to watch that

[alpine sable]

Yw lol

[unborn dome]

ty

[alpine sable]

I remember alot of geometry.. since I took it THREE FREAKING TIMES. If you need the DL lemme know

[azure forge]

hello can someone help me with this word problem arithmetic sequence?

[ionic jewel]

for which one

[azure forge]

both hopefully

[ionic jewel]

well lets do the first one

so lets say it has 1 unit of air it in it start

then after 1 second, it loses 1/20 of it

so how much air does it have now? @azure forge

[azure forge]

0.95?

[tight locust]

(1 - 1/20)^6

400000(1.052)^6

[glass lichen]

have you ever tried.. helping?

[tight locust]

have you? i've clearly helped him more than you have

[jade kestrel]

Been dealing with modular arithmetic a lot lately and I wanted to find an easy algorithm for computing exponents.

So I figure out that
I could simply reduce the output after each operation using mod. Quite obvious solution.
So then
2^5 mod 5

2*2 = 4
4*2 = 8 = 3
3*2 = 6 = 1
1*2 = 2

But what if I do
2^5 mod 4

2*2 = 4 = 0
0*2 = 0
0*2 = 0

This is problematic.

[glass lichen]

You didnt help them at all but ok

[ionic jewel]

this isnt right

it would be A(.95)^6 for an original amount A

[azure forge]

what does ^ mean?

[tight locust]

it asks for the percentage

[glass lichen]

exponent

$a^b$

[ocean seal]

Mosh

[ionic jewel]

exponent

[azure forge]

oh okay thanks

[tight locust]

A doesn't matter

[ionic jewel]

i mean its still a different number

,w 1 - 1/20^6 = 1(.95)^6

[tight locust]

and it asks for the amount remaining. hence the subtraction from 1

[ocean seal]

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[tight locust]

learn to read

[glass lichen]

dont be a dick

[tight locust]

i'm not

i'm exercising great restraint

[ionic jewel]

also ur still not right

ur telling me that despite the fact it loses 1/20 of the air just on the first second, it still has 99.999999% left?

if you absolutely need the disparaging comments at least be correct

[alpine sable]

Can I get help on this problem on which I am stuck at from yesterday night?

[glass lichen]

Also given b was about exponential growth and decay, and they're both from the same sheet of questions, you can safely guess that a is also about exponential growth and decay

aside from the fact the wording implies 1/20 of the air in the containter per second

[unborn dome]

uh

can someone help out with this question https://media.discordapp.net/attachments/803057978277888020/873020142945173504/unknown.png

i know one of the answers is 0.666 so i rounded that to 0.67 and got partial creddit

[tight locust]

my bad you're right. i forgot my parantheses. (1-1/20)^6. sorry for doubting your reading ability

[ionic jewel]

fair enough, in that case its the same thing 👍

[lusty plaza]

stay in terms of pi

[unborn dome]

but its accepting 0.67

[lusty plaza]

weird

[unborn dome]

not so sure how 5.61 is wrong tho

i converted 0.67 into degrees

subtracted that by 360

then turned that answer into radians again to get 5.61

[azure forge]

what should i do?

idk who to follow 😳

[alpine sable]

(1-1/20)^6

[glass lichen]

$1-\sin^2(w)-\sin(w)=0$

[ocean seal]

Mosh

[alpine sable]

Becomes a quadratic 😳

[unborn dome]

yea

one of the solutions gets crossed out because it goes below the limit in the inequality

the other one that doesn't get crossed out is

sqrt5 - 1 / 2

arcsin(sqrt5 -1 / 2) = 0.666 or 0.67

[glass lichen]

,w solve x^2+x-1=0

[ocean seal]

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[tight locust]

not quite golden

[unborn dome]

cant you re-order it

[glass lichen]

yeah so you're solving $\sin(w)=\frac{\sqrt{5}-1}{2}$

[ocean seal]

Mosh

[unborn dome]

yep

[tight locust]

plus or minus

[glass lichen]

already been accounted for...

[unborn dome]

the minus gives u a negative answer which is below the limit

so yu take postiive

arcsin of that

thats 0.67

after that i convert this into degrees

so

[glass lichen]

does it just want the exact answers...?

[unborn dome]

yea.

its taking in the 0.67

[glass lichen]

yeah cause that's an approximate answer

im asking does it want the exact answers

[unborn dome]

tried it with pi o na previous question and it made it incorrect so im not sure

for now i'd assume decimal is the safe route

okay hear me out @glass lichen , 0.67 into degrees thats 38.39

360 - 38.39 thats 321.61

i then converted 321.61 back into radians

[glass lichen]

that's wrong

that's why

it's sine not cosine

sine is negative in quad 4

[unborn dome]

oooooooooooooooooooooooooooooooooooooooh

[glass lichen]

you want pi-(reference angle)

[unborn dome]

aaaahhhhh that hurts

so pi - 38.39 ?

or pi - 321.61

[glass lichen]

no...

$\pi -\arcsin(\frac{\sqrt{5}-1}{2})$

[ocean seal]

Mosh

[unborn dome]

wow

I feel like a complete jackass 😦

for overseeing that sin thing aaaah

[void hearth]

I tried finding some way to express RM in other vectors, and came up with RM - RS = SM <=> RM - b = SM

then I tried finding some way to express SM in other vectors, and came up with SM + MQ = SQ <=> SM = SQ - a

sub the 2nd equation into the first, I get

RM - b = SQ - a

I cant figure out what to do next

[unborn dome]

can someone help me out with this question btw

this is cancerous

[void hearth]

use double angle formulae

[strong furnace]

if you look at the diagram you have kind of only used the quadrilateral SQRM for the equations you have right now , doing similar things with the other quadrilateral would help you get there

[unborn dome]

im assuming i do something like this @void hearth

[void hearth]

sin2x = 2sinxcosx, you can use pythagorean to solve for cosx

x is the angle, not the side

but youre on the right track

[unborn dome]

yea

so

x^2+7^2 = 8^2 @void hearth

[void hearth]

yeah

[unborn dome]

x = sqrt 15

[void hearth]

cosx = sqrt(15)/8

and you have double angle formula so

[void hearth]

alright, ill see what i can do

[unborn dome]

wait what...

where di d u bring cos from

[alpine sable]

A plank of wood 24m long has an 8m long piece cut off it. Express, in simplest form the ratio of the length remaining to the length cut off?

[void hearth]

sin(2x) = 2sin(x)cos(x)

[main zephyr]

is this correct?

[charred flint]

,rotate cw

[charred flint]

nah, you found BA

[main zephyr]

oh

so i need to sub 5

aight thanks

[charred flint]

yup

[unborn dome]

wait

for sin wouldnt that just be for sin thats 2/1 * 7/8 * 7/8? @void hearth

cuz they're already giving me sin

oh shoot that cos(x)

adjacent over hypotneuse

[void hearth]

yeah you have to find cos(x), ratio of adjacent and hypotenuse and plug that in

[unborn dome]

i mean

yea

whoops

sqrt 15 / 8

[void hearth]

so

[unborn dome]

2/1 * 7/8 * sqrt 15/8

[void hearth]

sin(2x) = 2sin(x)cos(x) = 2(7/8)(sqrt(15)/8)

yeah

and you simplify

[unborn dome]

thats 7sqrt15/32

[void hearth]

yeah

[unborn dome]

LETS GOOOOO

now its tangent time boi

uh

[void hearth]

tan(2x) = sin(2x)/cos(2x) so you can figure something out

[unborn dome]

thats 2tan a

[void hearth]

by dividing the first 2 results you get

[unborn dome]

wait really

thats it?

[void hearth]

yeah

[unborn dome]

wow... im really...

[void hearth]

comes from tan(x) = sin(x)/cos(x), same idea

[unborn dome]

its -7sqrt15 /17

pog

got it right

[void hearth]

yeah

just remember whenever you see 2x, x/2, or something involving 2 double angle formula helps

[unborn dome]

got it

thank you chief

and now I'm confused again @void hearth pepehands

[void hearth]

cos^2(x) - sin^2(x) = cos(2x)

you see the first terms, they have the same number right

[unborn dome]

wait

isnt that just 74 degrees

[void hearth]

yeah

youve got it

[unborn dome]

wow....

[void hearth]

just multiply or divide by 2

mindblown

[unborn dome]

i feel so...

well i got it right

thanks man

[tame horizon]

Help please

I don't understand the question

[unborn dome]

can someone help me on this please

for sin this is what I got

[rigid smelt]

the half-angle formula for sine is $\sin(x/2)=\pm \sqrt{\frac{1-\cos(x)}{2}}$

[ocean seal]

waler

[rigid smelt]

you messed up your sign

oh wait nvm cos(x) is negative

and cos(x) is not -sqrt(35)/4

you probably miscalculated somewhere

[unborn dome]

oh shoot

its

sqrt 35/6

wtf.

[rigid smelt]

-sqrt(35)/6 but yeah

[unborn dome]

yes

wait no

wouldnt it become a positive

because 2 negatives

make a positive sign

if its 1 - (-sqrt35/6 / 2

[rigid smelt]

yeah i know

[rigid smelt]

thats why i said

i was implying that cos(x)=- sqrt(35)/6 not the the number in the square root

[unborn dome]

AH i got it

LETS GOO

and for tan i can just divide the two right @rigid smelt White

[rigid smelt]

yeah

[unborn dome]

https://media.discordapp.net/attachments/791699984495935508/823363968193134652/7482_WalterFaint.gif

[rigid smelt]

and im not walter white

[unborn dome]

you are now Waler White from now on

[rigid smelt]

...

[unborn dome]

say my namee...

anyways thanks for the help

[sudden tulip]

How do I solve iii

[gray isle]

Consider that a rhombus is a special type of parallelogram

[slate heron]

$\overline{PQ}=\overline{QR}=\overline{RS}=\overline{SP}$

[ocean seal]

Louis

[sudden tulip]

Hmm

[slate heron]

all sides of the rhombus are equal

just prove that

[sudden tulip]

Ok thanka

9 how do I do

[rigid smelt]

when two graphs of two functions meet, they equate each other

but before doing that, i'd suggest finding y

[sudden tulip]

Ok how do I find y ?

[rigid smelt]

algebra?

if i gave you xy + 2 = x, can you find y?

[sudden tulip]

Yep

[frosty notch]

is pi = 4

[rigid smelt]

idk man, i wish there is some kind of tool for us to type in our simple and probably very frequently-asked question so we can get the answer

[slate heron]

π=C/d

[slate heron]

Symbolab.com lol

[topaz scaffold]

Ew

[rigid smelt]

yeah but who am i to create such a thing

[slate heron]

What

[topaz scaffold]

Obviously the best is $π = 4 \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1}$

[ocean seal]

RipeOrange

[carmine lion]

uh what

anyways,

how do i know if this is unique

$f(x)=-x[(x+4)(x-3)]^2$

[ocean seal]

abe

[astral dagger]

the sum evaluates to arctan(1), beautiful

[carmine lion]

the only way for the function to be not unique

would be if i didn't know its y-int

so what i gave is correct right?

oh nvm

the function can be compressed

or expanded

nvm

[astral dagger]

I think that as you're talking about polynomials, compressing or expanding would mean multiplying by some factor in front of the equation

[carmine lion]

yes

[astral dagger]

so it'd still be the same function?

[carmine lion]

so it would be unique only if i knew the y-coordinate of at least 1 turning point

here the turning points have no listed value

so its not unique

¯_(ツ)_/¯

[astral dagger]

being a poly'al, its derivatives are 0 at some point, so maybe there's such behavior on it's critical points and concavity but..

maybe it doesn't answer your question

[carmine lion]

if you know where dP(x)/dx=0

then its unique

that should be enough reasoning

[astral dagger]

it is a 5th degree polynomial

[carmine lion]

yes

look

if i change the value of a

[astral dagger]

doesn't look the same

[carmine lion]

the turning point y-coordinates change

so that means the function ain't unique

because it doesn't give enough information

[astral dagger]

indeed

[carmine lion]

alr

👍

just wanted to clarify

ty

[astral dagger]

If I was of some help

well, am going sleep, have a good night

[topaz scaffold]

Gn

[deft stirrup]

hey guys i have a question about courses, im going to be a junior next year and have the choice between pre-calc and stats, what is the difference and which do you recommend

[ionic jewel]

difference: they are completely different classes with literally no overlap

advice: depends what you want to do, but if you have literally any interest in a STEM field of any kind you will need both eventually

most people do the pre-calc into calculus route first though

[deft stirrup]

what if im interested in finance

ive heard stats is more useful for that

[ionic jewel]

you will want both still

[topaz scaffold]

I would say do precalc

[ionic jewel]

if you plan on doing a college degree you can look at the finance graduation requirements, iirc at my university you need up to calc 2 and one stat class

[deft stirrup]

ah ok

[ionic jewel]

i would recommend pre-calc as well

[topaz scaffold]

Helps build the fundamentals

[deft stirrup]

awesome this was really helpful thanks

[topaz scaffold]

What's up with the exclamation mark?

[main escarp]

hey I need help,
With this question am i the stupid one or is my teacher

here when she take -2 away from -12 isnt that -10 not -14?
(-12)-(-2) = 10?

^ the question

its during the first butterfly step

ping me pls

(might be confusing due to annotations but ignoring x3

[slate heron]

Taking away a negative number adds it. imagine if someone takes away a parking ticket from you - you dont have to pay the parking ticket so you sort of "gain" money

wait one sec

ive read your thing wrong

[main escarp]

?

[slate heron]

why is she wrong?

[main escarp]

idk

im confused

[slate heron]

shes subtracting 2 from -12

[main escarp]

yes

waot

[slate heron]

-12-2

[main escarp]

i did wrong

[slate heron]

not -12-(-2)

[main escarp]

yeah

i see now

i read inccorrectly

thanks for help

lol

[manic glade]

this is wrong right? the 1/1 shouldnt be there(?)

[placid zinc]

That's sus. Is there a context?

[manic glade]

its part of a longer proof but its self contained

thats the only other part relevant to and preceding it, but its the same issue

(0,1) doesnt include 1 right?

[placid zinc]

True

Yeah you're right, so the subset symbol is a lie

Likely just a printing mistake, and it is hard to gauge how important the mistake is

[ionic jewel]

the first screenshot is correct though, isn't it?

wait $\frac11 \subset \bQ$

[ocean seal]

bunny

[ionic jewel]

so it's fine i can't read, it's not fine

[manic glade]

yeah i guess the cardinal is the same anyway

should have screenshoted the subset part

but still, shouldnt be there since they reach that conclusion by starting with the subset claim

[slate heron]

Do you know the package that allows \bQ ? It's a lot shorter than \mathbb(Q)

[placid zinc]

Does making it [0,1] break everything?

[manic glade]

the question is specifically about (0,1)

just starting with 1/2 should be fine though i reckon

[ionic jewel]

i believe it's just set up automatically in the preamble of this bot, you can find it somehow, but go to #bots to test

[manic glade]

btw anyone know a good math editor addon for googledocs?

currently using hypatia and its pretty terrible

everything is a struggle and it bugs out a lot

also no colors

[slate heron]

use latex lmao

[manic glade]

well it is latex but you need an addon to add it to docs

afaik

theres no built in options it adds math as images

[slate heron]

must you use docs

[ionic jewel]

hes saying using latex instead of google docs

like literally worst case you can use latex for your equations in a different program then screenshot and add to google docs lmao

[slate heron]

lol. go on #bots, render latex with the bot, copy image, paste

[manic glade]

but i can already do that within the doc using any of the addons, thats literally what they are for

its just latex editors

[halcyon pulsar]

What would be Exterior angle of pentagon?

[manic glade]

theres just a bunch of them was wondering if anyone has experience with a nice one

[halcyon pulsar]

Shouldnt it be 108°

?

Or 72°

[manic glade]

72

assuming its a regular one, it can vary otherwise

[ionic jewel]

I've tried a handful and they all suck compared to something like overleaf or this discord bot

[manic glade]

rip

[halcyon pulsar]

How u conclude that🤔

[manic glade]

i googled the question tbh

[halcyon pulsar]

Hmm

Shouldnt interior angle be 72• insteat of exterior angle being 72°

[manic glade]

https://www.cuemath.com/questions/the-measure-of-each-exterior-angle-of-a-regular-pentagon-is/

360 / sides

[opal pier]

What is the mathematical chance a portion land in my yard

[woeful pulsar]

Pigeon? Well it depends on how you model the situation

[opal pier]

3 pigeons in my neighborhood

~ 100 other yards

[placid zinc]

Depends on how much bird seed you own

[woeful pulsar]

Do you assume each pigeon selects a yard uniformly at random?

[opal pier]

No

[woeful pulsar]

Then how do the pigeons select yards

[placid zinc]

In order to predict a pigeon, we gotta think like a pigeon

[woeful pulsar]

coo

[alpine sable]

is the ans tan-1(x) ?

[pure hill]

I thinks its arctan(sqrt(x))

try substituting x with tan^2t and you will get your answer

[alpine sable]

ok

[tribal geyser]

Hey guys can someone help me with 9a)? I don’t get where L came from in the answer

Like I worked it out but instead of L I got dB

[ionic jewel]

you are right, it is the books mistake

(or L = dB)

[tribal geyser]

Oh because I literally don’t see L anywhere haha

but thank you for the confirmation

@ionic jewel

[alpine sable]

i think i am stuck

can you help

[pure hill]

yeah go on

[alpine sable]

i tried, but dont kno

i think i am doing some mistake

i get a wierd ans

[pure hill]

see when you substitute x with tan^2t then in denominator you can write 1+ tan^2 t as sec^2 t

then its all done

[alpine sable]

oh, i substituted as tan2t

instead of tan sq t

[pure hill]

ohh that explains the weird answer

[alpine sable]

ya

thx bro

[pure hill]

✌

[alpine sable]

"the equation 3x
2

• kx − x + 3 = 0 has real roots."

Help

[vale wigeon]

did you mean 3x^2 + kx - x + 3 = 0?

[alpine sable]

Yes

[vale wigeon]

and what is the question? are you asked to find the values of k which make this true?

[vale wigeon]

yeah, ok, so you are asked to find the values of k that make this true

have you been able to do parts a through i?

[alpine sable]

Yeah

[vale wigeon]

then what's troubling you with part j?

it's much the same as all the otehrs

[alpine sable]

J, I need to do by myself

The A to I were done by others

[vale wigeon]

.-.

[alpine sable]

In class

[vale wigeon]

okay so then why did you answer "yes" to my question of "have you been able to do parts a through i?"

[alpine sable]

Cause I write 😎

[vale wigeon]

"i have done them myself" and "they were done in class and i copied them down without understanding" are two very different things.

anyway, whatever.

tell me, does the word "discriminant" ring any bells to you?

[alpine sable]

Idk

Me is too dumb

🍞

[vale wigeon]

so that's a no?

[alpine sable]

Ye

[vale wigeon]

does the expression b^2 - 4ac sound familiar at all?

[alpine sable]

No

[vale wigeon]

no? then how did you do it in class?

[royal magnet]

the difference between two numbers is 4 and six times the smaller is equal to four times the greater. find the numbers

can somebody help me in this? ⬆️

[alpine sable]

Nvm I got ot

[split citrus]

This channel is occupied, ask the question in another channel

[royal magnet]

um ok

[alpine sable]

@vale wigeon

?

Just wanted to do some trolling

[plucky radish]

S = Small
L = Large
establish rules6S = 4L
S+4 = L
multiply by 66S+24 = 6L
remove previously established '6S = 4L24 = 2L
solveL=12
S=8

[royal magnet]

THNXXX

[vale wigeon]

...

[brave thicket]

hello, i need help in adding 1^2 + 2^2 + ... + 50^2

does anyone know a fast way on solving this and how?

[vale wigeon]

there happens to be a convenient readymade formula for the sum of the first n squares, actually.

[brave thicket]

i found a way of solving this, with this formula:

n(n+1)(2n+1) / 6

[vale wigeon]

yeah, that's what i was going to share now

[brave thicket]

however, idrk how that formula came to be

do you know how that formula was made?

[vale wigeon]

there are many ways to arrive at it

are you comfortable with big sigma notation? i might be able to show you one way to derive it.

[brave thicket]

yes

[vale wigeon]

excellent

so what we're looking for is an expression for $\sum_{k=1}^n k^2$

[ocean seal]

Ann

[vale wigeon]

what i will start with is this: $\sum_{k=1}^n (k^3 - (k-1)^3) = n^3$

[ocean seal]

Ann

[vale wigeon]

does this require explanation?

[brave thicket]

yes

[vale wigeon]

i'm writing out the following sum:
1^3 - 0^3

• 2^3 - 1^3
• 3^3 - 2^3
• ...
• (n-1)^3 - (n-2)^3
• n^3 - (n-1)^3

notice how, when the sum is written out this way, a lot of terms cancel out

this is deliberate, of course

after you cancel everything out, all that remains is n^3 - 0^3, or just n^3.

does this make sense?

[brave thicket]

yes

[vale wigeon]

okay, great

now if you expand and simplify k^3 - (k-1)^3, you get 3k^2 - 3k + 1

let me just double-check that...

,w simplify k^3 - (k-1)^3

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ann#0413

[vale wigeon]

okay yeah

so we have $\sum_{k=1}^n (3k^2 - 3k + 1) = n^3$

[ocean seal]

Ann

[vale wigeon]

in other words, $3 \sum_{k=1}^n k^2 - 3 \sum_{k=1}^n k + \sum_{k=1}^n 1 = n^3$

[ocean seal]

Ann

[vale wigeon]

do i need to continue or can you see it already?

[brave thicket]

i havent seen what you mean yet

[vale wigeon]

alright

you know that $\sum_{k=1}^n k = \frac12 n(n+1)$, right?

[ocean seal]

Ann

[brave thicket]

yes

[vale wigeon]

and $\sum_{k=1}^n 1 = n$, of course.

[ocean seal]

Ann

[vale wigeon]

so now we have: $$3 \sum_{k=1}^n k^2 - \frac{3}{2} n(n+1) + n = n^3$$

[ocean seal]

Ann

[vale wigeon]

it's a matter of simple algebra from here on out.

@brave thicket

[brave thicket]

alright, i think i understand now, thanks

any other simpler way of arriving to the formula? i might need an easy way to explain the formula to a friend

[vale wigeon]

hmm

i remember seeing a geometric demonstration somewhere but idr what it was

[brave thicket]

alright then, thanks for the help once again

[alpine sable]

@pure hill

@vale wigeon

<@&286206848099549185>

how to prove onto?

[vale wigeon]

@alpine sable you should not ping random people out of the blue like this

[alpine sable]

kk

pls help tho

[hexed viper]

Graph it

[alpine sable]

?

we r supposed to prove that it is invertable

[hexed viper]

It’s obvious if you graph it

[noble sinew]

You need to show that for all x and y that f(x)=f(y) implies x=y. So start with suppose f(x)=f(y) and then try to deduce x=y

its not a proof to graph it

[hexed viper]

Graphing makes how to prove it obvious

[alpine sable]

how to prove onto?

[noble sinew]

Need to show for every y there is an x such that g(x)=y. So let y be arbitrary (in (-1,1)) and try to find a correct x

[alpine sable]

i get x=-y/1-y

[hexed viper]

You can either use a continuity argument with intermediate value theorem and limits or split it into cases of x being positive and negative and manually invert it in those cases

[alpine sable]

and x=-y/y-1

what am i to do then?

@noble sinew

[noble sinew]

not sure how you got x=-y/(1-y)

but once you get the correct 2nd solution then you have a correct value for x when y>=0 from one equation and another equation for when y<0

and you have proven onto

[barren plover]

is this correct

pls ping w answer

[wary stream]

Looks right

[barren plover]

just cuz it loosk right doesnt mean it is

ru sure

@wary stream

[wary stream]

Are you sure it's right?

[barren plover]

im not

thats why im asking u

obv

[wary stream]

Well, what's the formula?

[barren plover]

i have no idea lol

i guessed

[alpine sable]

A tangent and a secant

[wary stream]

It's a tangent and chord

[alpine sable]

its a secant

[wary stream]

Secant is a line, in that diagram, it's a line segment, therefore chord

[slate heron]

is that a question on a test? are you trying to cheat the right answer

[alpine sable]

I think so, that's why I am not helping lol

[barren plover]

a secant is a line that intersects it twice ykyk

bro why does everyone in this servr

think that

i am not cheater 😠

[alpine sable]

because it looks like that

[slate heron]

because youre afraid of inputting any answer without 100% confidence

[alpine sable]

I mean it has been enough time I dont think it is a test anymore

[wary stream]

Well, if you're not a cheater, use the formula

And submit it

[barren plover]

yea bcuz its like a practice test before i take my final test tomorrow

if i score below an 80 on it

i dont get access to the final

until 6 hours before it closes

[slate heron]

practice for the next 5 hours, take the test in the final 1 hour

if you cant do the practice test without help online, it probably wont get you a much better grade for the final

[wary stream]

And if you have to confirm your answers, it proves that you're not confident in your knowledge of that concept meaning more studying

[alpine sable]

in that case I guess its fair

[barren plover]

i looked through my notes to get the answer to this but theres nothing for a question like this

i juts used a protractor and guessed

[alpine sable]

Its a secant and a tangent intersecting

I guess you must have learnt something relating to that

what happens when 2 chords of a circle intersect?

[barren plover]

i thought i remembered problems that look like that but they r nowhere in my notes so idk

[alpine sable]

what is the angle formed at the point of intersection?

[barren plover]

uhh

i am sutpid

[alpine sable]

well go through your notes again then

tommorrow is your exam

[wary stream]

Read the question

It's there

[alpine sable]

it would be safe to assume SR as a chord tbh

tangent chord is what you need

@wary stream you were right

[wary stream]

Told you it's a chord

[barren plover]

its not doe

[alpine sable]

it is a chord too and a secant too

[barren plover]

i guess so

yea

[alpine sable]

i guess you have the answer now

[barren plover]

huh

how lol

[wary stream]

Secants are lines

[alpine sable]

Angle formed by a chord and a tangent intersecting is 1/2 of the arc

[wary stream]

Chords are line segments

That is a line segment

Therefore is a chord

[alpine sable]

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc

[barren plover]

wait so was i right

i think im right

yes

[alpine sable]

Yes

[barren plover]

YAYAY

OKAY

TY

[alpine sable]

all secants contain a chord @wary stream and all chords are secants

[wary stream]

Well guess it's a secant that's a chord

[alpine sable]

you can't just say that because its a line segment on a circle, its a chord

[alpine sable]

all secants contain a chord

[slate heron]

yeah i think it's a tangent and a secant

[pure hill]

the answer to this problem is given -10 can someone explain why it will not be |10| instead?

[gray gorge]

If x is negative, can the expression be positive?

[pure hill]

but it gets cancelled out won't that mean there will be no effect of the sign on the answer?

[copper gust]

1/(1+x^2) ≤ a. ; what happens to the inequality when i sqrt

[gray gorge]

I'm not sure what you mean

[pure hill]

I am saying that x will not have any influence over final value, i suppose

can you tell me the procedure you used for this problem?

[gray gorge]

Well, how did you arrive at an answer of +10?

[pure hill]

I took x^2 from the numerator and cancelled it with x in the denominator

[alpine sable]

$n_{1}(2n_{1}-1)+n_{2}(2n_{2}-1)+n_{3}(2n_{3}-1)+n_{4}(2n_{4}-1)+...+n_{i-2}(2n_{i-2}-1)+n_{i-1}(2n_{i-1}-1)+n_{i}(2n_{i}-1)$

And,
$n_{i}=n_{i-1}+1$

Say,
$n_{1}=1$

Can we somehow formulate this in terms of $n$?

[ocean seal]

IDrinkWine

[alpine sable]

And, $n_{i}=10$

[ocean seal]

IDrinkWine

[gray gorge]

So I assume you set x = sqrt(x²) to achieve this?

[pure hill]

oh okay I got it

thanks a lot

[gray gorge]

Np

[eager badger]

Hello, I'm not sure how best to describe this but I'm looking for algorithm to find an optimal bijection between two sets of 2D points, I have tried something with munkres-kuhn hungarian algorithm and fiddled around with the norm i used for the distance between points, but it doesn't look clean for, say, more than 500 points. Here's my result so far

i want my result to have "no intersections"

you can tell this version is working because some clusters move together, and the shape is still rectangular during the transition

also there may be somewhere better for this sort of question but I didn't really know where else to go

[robust phoenix]

x=9-3÷1÷3+1 how do we solve it ?

x-1=9-3÷1÷3
=3x-3=9-3÷1
=3x-3=6
=3x=9
x=3
I know i have a problem i just don't know what is it

[vale wigeon]

you're completely ignoring the order of operations here

x-1=9-3÷1÷3
=3x-3=9-3÷1

this move is illegal and also unnecessary

[robust phoenix]

oh yeah you are right

[vale wigeon]

$9 - \frac{3/1}{3} + 1$ can and should be just evaluated as normal.

[ocean seal]

Ann

[robust phoenix]

so how should i solve it

x-1=9-((3/1)/3)

[vale wigeon]

no

you're overthinking it again

are you not able to calculate 9 - (3/1)/3 + 1

by doing arithmetic

step by step?

[robust phoenix]

i am

[vale wigeon]

so what's the problem?

[robust phoenix]

no i am but i want to solve it in steps like the one above

[vale wigeon]

not worth the effort.

[robust phoenix]

Yeah

[robust phoenix]

can i ask another question ?

[vale wigeon]

sure...

[vale wigeon]

what is the goal here? to find the area of the region marked with S?

[robust phoenix]

yes

[vale wigeon]

okay

have you made any progress so far?

[robust phoenix]

yeah

[vale wigeon]

would you mind sharing?

[robust phoenix]

sure but it's not that great

i was just expanding my field of view

[vale wigeon]

i have to say, this problem looks nasty

maybe it is possible to do it by coordinate-bashing

[robust phoenix]

what do you mean by nasty, nasty as good or bad lol

[vale wigeon]

i thought 'nasty' was an unambiguously negative descriptor...

[robust phoenix]

well yeah but sometimes it isnt i like nasty problems

oh i think i got it

idk if it may help but sure

[vale wigeon]

that 4.72 is almost certainly inexact.

[robust phoenix]

why though ?

i used the pythagorean theorem

[vale wigeon]

and you took the root of something.

and your calculator gave you a decimal approximation.

anyway, idk about you, but this is how i would begin.

[robust phoenix]

yeah its 4.71 something

but i did it by my mind tbh

[golden arch]

What am I doing wrong?

[robust phoenix]

sure

[vale wigeon]

@golden arch channel busy please move

the process that springs to mind right now is:

• write down the coordinates of every point i can
• write down the equations of lines OF and CE
• find the coordinates of K and L
• use the above data to find the length of LF and the altitude of triangle KFL originating from K

[robust phoenix]

OF is about 5.4

[vale wigeon]

why are you so insistent on decimal approximations?

also i didnt say to find the length of OF

i said to find the equation of the straight line going through O and F

[robust phoenix]

ohhh

[vale wigeon]

which in this case will be $y = \frac{2}{3}x$

[ocean seal]

Ann

[robust phoenix]

idk tbh i'm not that great in mathematics

and i don't use a calculator i use my mind

[alpine sable]

Hi, i need help from a question from calculus 3. Its about directional derivatives and finding the gradient of f.
This is the question from webassign, and couldn't understand what i did wrong.

I took the partial derivative for x and y respectively and plugged it into the calculator and got the unit vectors of <-48,72>, but somehow its wrong?

[vale wigeon]

<-48, 72> is not a unit vector.

they ask for a unit vector, i.e. a vector whose length is 1.

[alpine sable]

i forgot, what was the formula for the unit vector?

[vale wigeon]

...divide the vector by its own length

that's how you scale it down to length 1

how else?

[novel lintel]

a <= b means a < b or a = b

[alpine sable]

oh i got it

[robust phoenix]

yeah

[novel lintel]

So if I know a < b, can I conclude that a <= b

[vale wigeon]

yes

[novel lintel]

but

ikd

seems odd

idk*

I mean a neq b but it is smaller

seems like cheating lol

[alpine sable]

basically its u = a/|a| right?

[robust phoenix]

no if you know a<b then it's a<b, until you can prove that a can be equal to b or get datum

[vale wigeon]

@alpine sable yes, that's what i said.

[novel lintel]

got it

[vale wigeon]

muhannad is misleading you a bit here.

yes, you can conclude a ≤ b if you know a < b.

it doesn't work the other way around, of course.

[robust phoenix]

how can you know that it a might equal b ?

[vale wigeon]

nobody says that

[robust phoenix]

huh

[vale wigeon]

a ≤ b doesn't mean "there is a scenario in which a = b"

[robust phoenix]

it means or

[vale wigeon]

yes, it means "a < b or a = b"

[robust phoenix]

oh i think you are correct

OR gate

[vale wigeon]

yes.

[robust phoenix]

how did you know the basics of math

[vale wigeon]

????

[robust phoenix]

your math level is great

[vale wigeon]

i mean... thanks ig

i'm not going to share my entire life story here lmao

[robust phoenix]

it's ok i understand

[vale wigeon]

please don't reply-ping me so much.

it's a bit annoying.

[robust phoenix]

say less

[flat vale]

What do we call a particular character in an equation?
e.x

2 * x + 5

is there a word for 2, x and 5?

same word

not coefficient, pronumeral

[dawn bison]

terms?

[flat vale]

ahhh i see

thanks!

what about + and *

can that be term as well?

not operator?

[dawn bison]

2 * x is 2x. so 2x is a term. the terms of the expression you gave would be : 2x and +5

[novel lintel]

oh so if a < b then a <= b

[short turtle]

quick question, is sin4x the same as 2sin2x?

okok i just suddenly forgot thinking it can be 2sin2x

[ocean seal]

balance

[alpine sable]

very simple question, but

is 2-(5*(the square root of 9) )considered a perfect square?

[vale wigeon]

$2 - 5 \sqrt{9}$?

[ocean seal]

Ann

[vale wigeon]

...why isn't the bot here

[alpine sable]

2-(5*sqrt9)

[vale wigeon]

so... -13

[alpine sable]

technically you can fully simplify it

but does that make it a perfect square

or no, because if you reverse factor it

[vale wigeon]

no, hiding it behind obfuscation like this does not change whether or not your number is a perfect square.

being a perfect square isn't a matter of 'consideration' either.

there is no integer that gives -13 when squared.

[alpine sable]

well thats why its i

but while sqrt(25*9) might be a perfect square

[vale wigeon]

it isn't.

sqrt(25*9) = 15

[alpine sable]

25*9 is 225

[vale wigeon]

sqrt(25*9) = 15

15 is not a perfect square.

[alpine sable]

wait im so confused

what makes it a perfect square

[vale wigeon]

what makes what a perfect square?

[alpine sable]

2-5*sqrt9 is a perrfect square

[vale wigeon]

what?

[alpine sable]

is it?

[vale wigeon]

no it's not.

[alpine sable]

why not

[vale wigeon]

-13 isn't a perfect square!

[alpine sable]

oh

its what you get at the fully simplified version of the equation

[alpine sable]

squares aren't negative?

nothing squared is negative

[vale wigeon]

you're acting as if 2 - 5*sqrt(9) and -13 aren't one and the same...

[vale wigeon]

did i ever contradict that?