help-0

[alpine sable]

All together?

[agile compass]

What is 800?

I don't know what """its""" is

[alpine sable]

48 x 50

Times

1/2

[agile compass]

That's our area of the base

[alpine sable]

Yes

Now what do i do

[agile compass]

Volume = area base * hight

[alpine sable]

But

I still

Dont get that

For an answer

[agile compass]

,w 48501/2

[ocean seal]

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Requested by Tiessie#7180

[agile compass]

So thats our base

And the hight is given in the picture

[alpine sable]

mhm

So 192,00

Would it still be the same

As this

I got 19200

But the answer is

[agile compass]

,w 1200*80

[alpine sable]

192,000

[ocean seal]

Results provided by WolframAlpha

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

Requested by Tiessie#7180

[alpine sable]

Wait how did u get

80

O

But now

1/3

[wanton otter]

I see an alternate angle shape (aka Z pattern) where the angle below c and the angle to the right of b are equal (so theyre both 22 degrees). an angle across a straight like = 180 degrees so angle b = 180 - 22

the entire shape = 360 degrees so take each angle, subtract them from 360 and the remaining angle is angle a

hope this helps 🙂

[spring harbor]

can someone rephrase this so that it makes sense

its referring to the p value being 0.003

[uneven fulcrum]

@spring harbor could you send the whole question?

[spring harbor]

@uneven fulcrum

[uneven fulcrum]

@spring harbor i dont want to give you the wrong answer so i would just @ a helper as im not 100% sure of my answer

however i would also say its C just not sure as the questions i get on my exam board are very different

[loud barn]

So the word PARIS, the first letter must be a vowel (This is for permutations)

Can someone explain how it would be 2 x 4 x 3 x 2 x 1 = 48

Why did we put the 2 first which is I

When we could also use A which would be 4 x 4 x 3 x 2 x 1

unless im doing this wrong

Is it because theres 2 vowels

[shell widget]

suppose we put A as the first vowel. Then we have 1 * (4 * 3 * 2 * 1) for total arrangements. then suppose you put I as the first vowel. We still have 1 * (4 * 3 * 2 * 1) for total arrangements, add them you get 2 * ( 4 * 3 * 2 * 1 )

And yes, the 2 at the start is for the 2 choices we have for the vowels

[loud barn]

Ooooh i get it thank you

[mossy cedar]

anyone know 9?

[alpine sable]

anyone who can help me over basic category theory definition of slice category?

[woeful pulsar]

just ask

[real forum]

What is 2+2?

[alpine sable]

oh, sure

[onyx bridge]

@real forum do you want help with that?

if anyone needs help with honors pre calc or below i can help

[real forum]

Lol im kidding

Sorry

[woeful pulsar]

intensively studies definition okay I got this

[alpine sable]

I'm reading Aluffi's Algebra, and it introduces slice category C/c of C, in which objects are morphisms of C and morphisms are "commutative diagrams" in C.

my que is:

1. why it needs to be commutative diagram?
2. if f1 and f2 are two objects of C/c then how to make sense of morphisms between them? what's the domain and codomain of morphism between f1 and f2?

[woeful pulsar]

1. commutative diagrams are just another way to represent of a bunch of relations

For objects in C/c, they are simply (A, f) such that f: A->c

that you got so far?

[alpine sable]

yeah

[alpine sable]

not this though!

[woeful pulsar]

a commutative diagram is just a bunch of relations that says "which arrows compose to make which arrows"

[alpine sable]

Someone plspls help

[woeful pulsar]

In particular if g: A->A' in C, then there is an arrow g: (A, fg)->(A', f) @alpine sable

[alpine sable]

yeah i get that. but how is it connected to slice category?

Are the first 2 answers

Correct

[woeful pulsar]

you need to use the "which arrows compose to form which arrows" in a slice category

[alpine sable]

ah i see, to satisfy the definition of category, right?

[woeful pulsar]

yeah, the commutative diagram is another way of showing the definition of slice category

[alpine sable]

i'll need to think over this

and 2nd que? @woeful pulsar

[woeful pulsar]

Hmm... let me check if there are any good examples of slice categories

[alpine sable]

that would be great

[woeful pulsar]

https://ncatlab.org/nlab/show/over+category

yeah for example, the first two are more familiar to me

[alpine sable]

it includes down set, which is new to me!
any example which is only based on sets?

[woeful pulsar]

well, you can construct a poset out of the powerset of a set

by inclusion

then you can construct a down set from there

[south wing]

I could use some help with 4 and 5

[alpine sable]

ah okay let me think about it

[glass lichen]

for 4, how many ways can you re-arrange the letters excluding Y?

[south wing]

ohhhhhh

would it be 6 times 5 times 4 times 3 times 2 times 1?

[glass lichen]

yes, 6!

[south wing]

and what about 5?

[glass lichen]

how many ways if I fix the last 2 letters to be CK (in that order)?

[south wing]

so would that be 5!

[glass lichen]

yes, but if I swap the C and K, it's still 5! ways

so it's 2*5!

[south wing]

ah okay thank you

[alpine sable]

help

Pls

Is number 2 right or no

[woeful pulsar]

hmm looks off

[alpine sable]

Pls help me

What do i do

[woeful pulsar]

do you remember formula for volume of pyramid?

[alpine sable]

V=1/3bh

[woeful pulsar]

looks okay, can you substitute in the values?

[alpine sable]

uh

V=1/3x12x25.2

[woeful pulsar]

what happened to 4?

and where did you get 25.2 from?

[alpine sable]

6.3x4

[woeful pulsar]

and that 6.3 x 4 is?

[alpine sable]

25.2

[woeful pulsar]

yeah but what does this number represent?

what quantity are you trying to calculate here?

[alpine sable]

Base

[woeful pulsar]

is that how you calculate the area of the base?

look at the shape of the base

[south wing]

for 3 would you do 4! times 1?

[alpine sable]

Yhh

[woeful pulsar]

remember the base is a right triangle

[glass lichen]

yes

[south wing]

ty

[alpine sable]

oh?

Determine the equation of the polynomial function that has the following zeros and passes through the point
(7, 5000): x = 2 (order 1), x = -3 (order 2), and x = 5 (order 1)

[onyx bridge]

@alpine sable yo i can help i dm

[glass lichen]

do you know what order of a root is?

[alpine sable]

Which tho

[woeful pulsar]

what do you mean?

you need to find the area of the base, right?

[alpine sable]

Yes

[woeful pulsar]

the base is of the shape of a right triangle

do you know the formula for the area of that?

[south wing]

i’m confused on how you would set up 6 and 7?

[alpine sable]

I don't understand why this is coming up as wrong

[patent burrow]

it's probably the symbol

you put 0 instead of theta

[worthy verge]

Theta

[glacial pier]

I dun know how to do it with change of variable

[patent burrow]

isn't that a test?

[glacial pier]

It's assigment

[patent burrow]

oh alright

[woeful pulsar]

x^(1/4) is kinda trippy to work with isn't it

[alpine sable]

its big ideas hw and yeah i put theta

same with this idk

both showing up as wrong

[south wing]

^

[patent burrow]

can you repeat letters?

like use a single letter multiple times

XXXX or TTTT

[full walrus]

hello

can somebody help with this

How from this can i get pi^4/15

/15 is not in the exponent

[ionic jackal]

Shape of the Base?

[woeful pulsar]

erm... have you seen any other integrals like this before?

[full walrus]

no not like this the engines like wolfram alpha give me some kind of a mix of polylogatithm fucntions but I know for a fact that the solution is pi^4/15 cause im trying to understand planck distribution of body radiance as a function of wavelength and temperature and I found this

[woeful pulsar]

hmm strange

,w integrate x^3/(e^x-1) from x=0 to infinity

[ocean seal]

Results provided by WolframAlpha

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

Requested by Element118#2437

[woeful pulsar]

yeah wolfram alpha is giving the exact value here

@full walrus

[full walrus]

oh so the solution is correct but for some reason it gave me some kind of a crazy function maybe i didnt set the boundaries

[woeful pulsar]

yeah

[full walrus]

thank you very much

[full walrus]

yes i was lacking boundaries thank you<3

[alpine sable]

Hello, so I used the alternating series test to prove that it is converging, i just have two things I want toclear up

1. If you want to find the maximum amount of error of a nth partial sum, would you just have to do 1/(n+1)^(4/3) in this case?

2. This series would be absolute convergence as the absolute value of the series is still converging right?

[woeful pulsar]

that is an upper bound for the error yeah

[woeful pulsar]

yeah the series absolutely converges, because sum 1/n^(4/3) converges

[alpine sable]

@woeful pulsar

Can u check my answers

For me?

[woeful pulsar]

why not ask wolfram alpha

[alpine sable]

Who is that

[lost steeple]

It's an online calculator

[alpine sable]

Can someone help me with this. Just dm me ig

could sm1 explain

this for me

i dont understand what the question is saying

and how get got 48/16

[glass lichen]

ok well you have a vertex of (-4,12)

so $y=a(x+4)^2+12$

[ocean seal]

moshill1

[glass lichen]

then you have a point to determine a

$60=a(0+4)^2+12$

[ocean seal]

moshill1

[alpine sable]

yeah i got that

thats what i have

wait

its x +4

or no

since we dont have x

@glass lichen

[glass lichen]

what do you mean?

[rocky kite]

Could anyone review this proof?

[alpine sable]

@glass lichen 60 = a(x+4)^2 + 12

isnt it that

[glass lichen]

you cant plug in half a point

[alpine sable]

wdym?

@glass lichen ?

[glass lichen]

you plugged in y=60, but not the x value of the point

[alpine sable]

ohhhh

i see

ok i get it

[rough sky]

can someone explain solids of revolution to me?

[charred flint]

@rough sky for an integral you add a bunch of vertical lines from x=a to x=b

if you spin a shape around, these lines correspond to circles with the radius of that line

so for a solid of revolution, you add circles instead, and integral of f(x) turns into integral of pi*f(x)^2, the formula for the area of a circle

[grim mango]

how do i do number 12

[vestal hollow]

https://cdn.discordapp.com/attachments/821535367136149527/836792360935358525/unknown.png

This diverges right?

As n -> infinity

Here it is in Desmos

I'm not sure how I'm supposed to evaluate this lol, L'Hopital's rule won't give me anything

Or actually

Hm

If I apply it 2020 times I just get 0/e^n

but how could the limit be zero?

if the function just keeps climbing as we approach infinity

[vestal hollow]

Yeah I forgot it would come back down 😛

[opal shell]

Can someone help me with this

[vestal hollow]

Is there any way to evaluate the limit (approaching infinity) algebraically or am I just supposed to know that it goes to 0 when the constant is <1?

[alpine sable]

why is -sinxtanx+cosxsec^2x=cosx?

[alpine sable]

substitute tan(x)=sin(x)/cos(x), sec(x)=1/cos(x), and add the two fractions

[rocky kite]

Could someone verify this?

[alpine sable]

do you know where I could find a list with all the trig equivalents? it is extremely annoying trying to do calculus without knowing trig

[gray isle]

there's a pinned list in every channel

[alpine sable]

thanks..................... DANG! are we really expected to know all of that? D':

I am in need of a math tutor for a specific subject

Pre-calculus, the professor, nor the textbook explains clearly enough for me to understand, and I'm pretty sure I flunked my first exam, and I only have 2 more exams of the quarter.

[crystal cape]

The function f is defined by f ( )x=x2−4x+7 forx<k, wherekis a constant.(ii)State the largest value ofkfor which f is a decreasing function.

how do i do this

[alpine sable]

well in the server you can ask for help with specific problems or concepts but i don't think this would the right place to look for a subject tutor

[vestal hollow]

No you're not, don't worry!!

You only need to know a couple

[alpine sable]

Gotcha

[alpine sable]

think about what the graph of a parabola looks like, this is an upwards-facing parabola so the function will decrease until it gets to the minimum value at the vertex, and then increase after that

[alpine sable]

which ones should I learn?

first you need to know these definitions

[vestal hollow]

Defining relations, Pythagorean, and double angle

Those are most common

The others can be useful though

[crystal cape]

i havent done these type of questions

[alpine sable]

you only need to know the first one here, as you can get the bottom two from the first one by dividing by sin^2 (x) and cos^2 (x)

[vestal hollow]

Yup

[alpine sable]

k, yeah, thought as much.

@vestal hollow should I be fine with that for advanced calculus BC?

[vestal hollow]

Should be, yeah

[alpine sable]

i suggest you play around with the graph on desmos to help you visualize it, the key thing to notice is that the function is decreasing on the interval (-infinity, x-coordinate of vertex)

[alpine sable]

no you'll need to know some others as well

tbh, I barely survived and I don't know how I managed to get an A

[vestal hollow]

The Pythagorean and double angle ones are really useful for polar integration

[alpine sable]

know sine/cosine addition identities

[crystal cape]

for now can u show how to solve this. i have this as my hw

[alpine sable]

on the interval (-inf, 2), the function is decreasing

but after you get to the turning point the function will start increasing

so the largest k that works is k=2

because when x<2 the function is decreasing

@vestal hollow @alpine sable thank you very much fellas

[royal veldt]

Hi, would anyone want to help me do this math equation?

[crystal cape]

whats the formula for volume obtained by rotating a curve

[alpine sable]

solids of revolution?

[crystal cape]

yes

[alpine sable]

guys

I need help with my math homework

I don't understand how to graph inequality

[alpine sable]

formula for the solid of revolution rotating the region under a curve around the x-axis bounded by the lines x=a and x=b

dont just memorize the formulas you should understand why they work

also be familiar with disk/washer method

[crystal cape]

ohk

[crystal cape]

thats definite integration right

[alpine sable]

yeah its a definite integral

[crystal cape]

thx

[thorn tulip]

Could anyone help with this stats problem?

[crystal cape]

how do i get the limits

the limits are 3 and 0 here right?

[alpine sable]

yeah

lower bound is 0 upper bound is 3

[thorn tulip]

oh, my bad

[crystal cape]

how do i solve this

its part of the solid revolutions question

[rough sky]

is that it? thanks

[vivid kayak]

How do I even find Q?

for iii)

nvm

[lusty charm]

Okay guys

So this is related to the polynomial thing, we just learned it today

I have two questions; but my first one is this

How do I do this question?

[stuck kestrel]

ok

since side is x

then side of the shaded square is x-3

area of the shaded square is (x-3)^2

[lusty charm]

what is ^?

[stuck kestrel]

the black part inside the bigger square

[limber fable]

what a wonderfully confusing question. I'm pretty sure they just want you to notice that the x^2 square consists of 4 parts - two squares of area(x-3)^2, 3^2, and two rectangles of area (x-3)*3. Hence, x^2 = (x-3)^2 + 3^2 + 2*(x-3)*3, and therefore (x-3)^2 = x^2 - 2*(x-3)*3 - 3^2.

[lusty charm]

i still dont understand what ^ is lol

[limber fable]

exponentiation

[stuck kestrel]

to the power

yes

[lusty charm]

OH

[alpine sable]

raised to

[stuck kestrel]

true

so it says that area of the entire square is area of black square + area of rectangles

[lusty charm]

uhm

[stuck kestrel]

which is x^2=(x-3)^2+(x-3)*3+(x-3)*3+9

good

[lusty charm]

Im still confused ill ask my teacher tmr

[stuck kestrel]

ohk

which grade are you in?

[paper wave]

I need halp

[stuck kestrel]

can you send a pic of the question

or diagram

[valid bone]

sure

[lusty charm]

8

[stuck kestrel]

integral of the solid?

volume?

ok

what figure do you get after rotation

yes

wait

let me do it

basic question

yeh it is correct

ans = 81pi/2

same here

ok then

bye

[verbal ermine]

can someone tell me how they got from the top line to there

[stuck kestrel]

ok

NM^-1 IS N/M

(N/M)^-1

=M/N

=M*N^-1

[verbal ermine]

mhm

[stuck kestrel]

Umm

[verbal ermine]

and i get M = M lol

[stuck kestrel]

hah

i dont know how they got m^2=n

[verbal ermine]

lemme see the mark scheme

[stuck kestrel]

yeh

ok so (NM^-1)^-1 = N^-1 * M^1

=MN^-1

AGAIN!!!!

[verbal ermine]

ikr

how did they get M^2?

[stuck kestrel]

hmmmmm

[lilac kestrel]

yo sm1 help with c

[stuck kestrel]

did you factor b?

[lilac kestrel]

wdym

[stuck kestrel]

i mean did you factorise b

hi

um

[ionic jewel]

what did you get for b is his question

[stuck kestrel]

YEZ

[lilac kestrel]

im sorry if the answer completely missed the mark

i took the vid on the lesson the same day

@stuck kestrel

[valid bone]

@compact flax I dont know sorry

[ionic jewel]

what does this even mean

which number are you doing

[alpine sable]

<@&286206848099549185>

[vale wigeon]

there is none, and if there is, it's arbitrary.

and subjective.

im tempted to say that the intended answer for #10 is a 2×2 grid of squares but honestly who knows

[ionic jewel]

ah yes deleting all your posts

a classic

[gray isle]

magic

[alpine sable]

Should I not

[vale wigeon]

bruh

yeah you should not

it leaves the other half of the convo just hanging there

simply acknowledge the question is fucked up / unanswerable and move on

[alpine sable]

Ok but is no one is working on the problem , how's there a problem in deleting it ?
I mean you don't want others to spend time on a problem like that
?
I'm new on discord..

@ionic jewel

[ionic jewel]

why

did you ping me

[alpine sable]

Do u wanna explain me ?

[alpine sable]

.

[ionic jewel]

don't delete posts, it's generally annoying at best and rude at worst

[alpine sable]

Okay.

[alpine sable]

If A={<1,1,2>,<2,1,2>,<3,2,1>}
What values can b take to be a member of the span of A for <b,1,2>

[woeful pulsar]

like, vectors, or continued fractions

[proud bough]

Find all functions f: R -> R satisfying the following condition:
F(x+y) = f(x)*f(y)*f(xy), for all x, y in R.

[ionic jewel]

find the span of A first, although it looks like R3 initially

[proud bough]

I tried the only method I knew which was sub but I cannot get anything

Please help &-&

[fallow epoch]

guys

i need help

quic

this assignement is due

in like 1 hour

anyone help?

[woeful pulsar]

what have you tried?

c and a are quite similar, and I suppose b and d uses the same ideas too

[fallow epoch]

well for C i did the quotient of 500/8 over 500

theoretically they're all equal

but in the spinner's context

they're different

[woeful pulsar]

actually, the problem with this is we don't know if the spinner is biased, and how it is biased

[fallow epoch]

if its theoretical, it probably wont be biased

[woeful pulsar]

since we don't know how it is biased, the experimental evidence gives some information how the spinner is biased.

[fallow epoch]

because you cant calculate which nimber it'll go to

[woeful pulsar]

but it might also be affected by random error

[fallow epoch]

what i've come to for C

is 62.5/500

but the thing is i cant decided whether to round up or down

[solid schooner]

Anyone willing to help?

[woeful pulsar]

what is r?

[solid schooner]

no clue this is parametric equations. I have no clue how to solve this

[woeful pulsar]

looks sus, I think there's a mistake in this question

[indigo jetty]

@solid schooner probably just a printing mistake for y, so just treat it as y = 3sin2t

notice that sin t = x/2?

find an expression for cos t based on this

[tawdry urchin]

hey guys

[indigo jetty]

also, 3 sin2t = 6 sin t cos t

[tawdry urchin]

I have a final problem that i am struggling with can someone please help me with this?

ignore the bottom text

[left spear]

You have a product whose cost depends on how many are sold I guess

If you try toying around with different values of q you can see how it affects p and in turn the total revenue (which is the price per unit times the number of units sold)

[tawdry urchin]

these word problems got me trippin xD

[left spear]

To be fair it's badly phrased

[tawdry urchin]

it is

wouldnt first derivative be a solution to this?

[noble sinew]

it would but you have to rewrite the expression given

p=200-q is price for 1 unit

so what is total price for all units sold then?

[tawdry urchin]

Im stupid

[noble sinew]

what do they say q is?

[tawdry urchin]

price per unit

but has no value

[noble sinew]

q

[tawdry urchin]

oh demanded

units demanded

[noble sinew]

so if q was 10 we would be selling 10 units for a price of 200-10 each, agree?

[tawdry urchin]

yeah..

[noble sinew]

so we would be selling for (200-10)*10

does that make sense

[tawdry urchin]

a little bit

i wish i was better at math

[noble sinew]

so the total amount we sell for is then (200-q)*q

[tawdry urchin]

i see

200q - q^2

?

[solid schooner]

Yh i agree it is T instead of R

[noble sinew]

yep

now we want to find maximum of money made

[tawdry urchin]

-2q + 200?

[noble sinew]

that is the derivative yes

[tawdry urchin]

god this is awful xD

[noble sinew]

why? you need 1 step more and you are done

what do we do after finding the derivative?

[tawdry urchin]

i forgot... havent done this in llike a year 😢

[noble sinew]

so the derivative tells us where a function is increasing or decreasing. So a maximum (and minimum) must be where the function stops increasing (decreasing), which it does when the derivative is equal to 0.

[tawdry urchin]

ahhhhhh..... now it makes sense

q = 100?

[noble sinew]

yep

[tawdry urchin]

final answer?

xD

[noble sinew]

now plug in q=100 in the equation we made

to find money made

[tawdry urchin]

the one we made? the q^2 +200q?

[noble sinew]

yep

200q-q^2 but yes

[tawdry urchin]

10k

[noble sinew]

indeed

[tawdry urchin]

Thanks so much <3

Do you have any source of like a video where i can fully understand the concept of what i just did ?

[noble sinew]

if its the derivative thing then can prob google finding min/max of a function and find something

[lost creek]

so i have this function, i've determined that it has a pole of order 3 at z =0. I'm having trouble finding the residue at z = 0

used series expansion instead

[sour cypress]

Hey, in the formula (see attached image) the result is 1.08. My question is, is it possible for me to figure out the S and F values if i only know the RESULT value, for example if my RESULT is 5.2 what would S and F have to be in order for the formula to be valid?

[gray gorge]

You've got one equation and two unknowns S and F, so no

Unless you have an additional, different equation relating S and F to each other

[sour cypress]

Ok thanks

[carmine lion]

how do i eliminate the parameter

$x=a\cos \theta - b\sin \theta \$
$y=a\sin \theta + b\cos \theta$

[ocean seal]

abe

[light dagger]

Hey guys can u guys help me? my question is: how can i divide N items into M groups with as near equal size as possible

[carmine lion]

bruh i took the channel

[noble sinew]

Divide it into N groups :))

[carmine lion]

can you help me

[gray gorge]

What parameter

[carmine lion]

theta

basically just a direct relationship between x & y

no theta

[light dagger]

for example: I have 39 runners and I need to split them into equal groups with those groups being as big as they can (up to 8 runners per group) while still being near equal.

[carmine lion]

so yea

[loud barn]

Wal first figure out what numbers from 1-39 can be divided into 39

[noble sinew]

But okay I asumme 1<M<N? Then find common divisor of N (39), which is 3,13. So we can have 3 runners in each group

[light dagger]

but in that case i will have 13 groups, i want to have the small number of groups but they had to have the max size as possible

for example 4 groups of 8 and one of 7

and i want my algorithm to work with every number

[gray gorge]

the idea is that you wanna write sin(theta) and cos(theta) in terms of a, b, x, and y
so here's a hint: calculate ay - bx, and also calculate ax + by

[noble sinew]

define near equal then

[carmine lion]

im confused

[alpine sable]

The volume of the sphere is

You can use 3 as an approximate value for π

No calculator allowed

[light dagger]

for example 90 runners and i want them to be in groups of 8. u can do 90/8= 11.25, 11 groups of 8 runners and the last one will only have 2

i want the groups to be the max size possible but near equal.

[noble sinew]

Yes so it is to make it into as few groups as possible then minimise length of group i from group i+1?

[light dagger]

i know that i can just take one member of witch group until i fill the last group

I thought there could be some possible mathematical calculation

[alpine sable]

how are you weighting the two factors

average size of a group and standard deviation of the sizes of all the groups

[noble sinew]

So in the example with 90 the best solution would be 6 groups of 7 and 6 groups of 8?

or what

[light dagger]

YES

8+8+8+8+6+4
8+8+8+7+7+5
8+8+7+7+7+6
8+7+7+7+7+7

something that does this.

[alpine sable]

so start with 12 groups of 8, then remove one from each group until you get to 90 total

[knotty garnet]

Or start with 11 groups of 8 and add one to each group

[noble sinew]

Your top one is 42 and the other ones are 43 total btw from what you posted

[light dagger]

yeah that's the way i will program this, but i thought that was a possible math equation to know the answer

[knotty garnet]

Yeah you already did it

90/8

N/m

[light dagger]

thats sound smart. i will try this. thank you

[knotty garnet]

Then floor it and give the remainder to some of the groups

[light dagger]

that way will exceed the max number per group (8). but its something similar to that. Thank youu

[gray gorge]

tfw you want to make groups of 8 and in the end you only end up with one group of 8

[knotty garnet]

Er 12 groups of 7

My bad

[light dagger]

i said that the max number per group should be 8 but i never said that my group had to be 8. xD

[gray gorge]

o

[light dagger]

i only want the number per group be the biggest possible in each group.

[karmic spoke]

Is this 27.86 or 25?

the answer was 25 but I got 27.86 idk what I got wrong

😔

[tidal badge]

what is that in the bracket

0-12.30?

[tidal badge]

What does it say inside the bracket?

[karmic spoke]

yeh

12:30

sorry for answering late

@tidal badge

[tidal badge]

as in, time?

or 12.30, decimal

@karmic spoke

[alpine sable]

looks like a colon

[tidal badge]

yea thats what i was thinking

[alpine sable]

some people use that ratio for division

[tidal badge]

ahhhh

makes sense

[alpine sable]

which is not wrong

A:B is A/B

[tidal badge]

yea ive just never seen it written like that in a solution

in that case 12/3=4 but the square cancels with the root? and 25^2 is 625 so 625+4

but

[alpine sable]

if it's a distance between two points, make sure to put the (0-25)^2 under the root as well. And if that's the case then yes, it's 27.86

[tidal badge]

does that mean the entire thing is under the root then?

[violet loom]

Guys I need help

This question, dafuq

[tidal badge]

yea thats what i was looking at like you cant get close to 25 with out the whole thing being rooted

[alpine sable]

yesss exactly, but it still doesn't equal 25 so idk

[tidal badge]

i wonder if they wanted them to round?

so then 4^2+25^ = 641, if you root that, you get 25.31

which rounds to 25

oh nvm its divided by 30

u right

[alpine sable]

ohhh, I interpreted it as 0-12.3

[tidal badge]

its 0-0.4

which is still

625.16

[alpine sable]

no you're correct with this then

[tidal badge]

so root that and yea u get 25.00

ye ye

lol had a field day with that ratio

[alpine sable]

ahahahaa my dumbass wasn't even able to read it 😃

[tidal badge]

same tho phew lets look at this parametric question

ahh i believe this is a further topic on polar coordinates since theres that 2r for the y

[violet loom]

It should just be regular A level parametric

[tidal badge]

hmm okay lemme see

the whole thing with parametrics is equating your equations for t

[violet loom]

I get that bit but the y parametric doesn’t have a t in it

[tidal badge]

yea and they haven't defined r at all

it could be a misprint, let me solve and suppose r = t

yea okay so

i think its a misprint because it works

k= 9/4 and you will obtain the given form

try solving it and assume r=t

@violet loom

[violet loom]

Thank you @tidal badge

[tidal badge]

no problem

[junior magnet]

could anyone explain how the summation on the left is simplified to the formula on the right? I can't seem to see it

[gray isle]

seems to be applying the formula for the sum of the first n squares

[junior magnet]

oh okay, thanks! I'll look that up

[carmine lion]

hey gy

[ocean seal]

abe

[carmine lion]

how do i simplify this

[tough ether]

If I have a complete directed simple graph on n vertices where between any pair there exists a edge in both directions, why is that thing edge transitive? This was trivially stated, but what is the explicit automorphism?

[karmic spoke]

@tidal badge oh I see

Thanks

But would that ratio thing still hold up since 12:30 is fine

Time*

Not ratio

Sorry for not being clear

And sorry for not being here

I was doing something rq

[shell widget]

@carmine lion try multiplying/dividing by 1 + cos(theta) + sin(theta)

[carmine lion]

i did

https://cdn.discordapp.com/attachments/409596215697866773/836956469106704424/473221703418511360.png

[shell widget]

you got that?

[carmine lion]

yes

[shell widget]

lemme check

[carmine lion]

im aiming to get to this last step

cuz its a proof question

$\frac{1+\sin\theta}{\cos\theta}$

[ocean seal]

abe

[nocturne wolf]

I need help

[carmine lion]

this channel

is taken

please go to another channel

[nocturne wolf]

Wht

Oh okay

[carmine lion]

did you check?

[shell widget]

im getting something else

[carmine lion]

huh

what are u geting

[shell widget]

can u show ur working

[carmine lion]

ok

[carmine lion]

sending it now

[shell widget]

idk what uve done

the numerator becomes $( 1 + cos\theta + \sin\theta )^2$ and the denominator becomes $( 1 + \cos\theta )^2 - \sin^2 \theta$

[ocean seal]

Sup?

[shell widget]

using (a+b)(a-b) = a^2 - b^2 identity for the denominator

now expand the numerator using (a+b)^2

same for denominator, expand (1 + cos(theta))^2 using a^ + b^2

[carmine lion]

$\frac{[(1+\cos\theta)+\sin\theta]^2}{[(1+\cos\theta)+\sin\theta][(1+\cos\theta)-\sin\theta]}$

[ocean seal]

abe

[shell widget]

yes

[carmine lion]

did i do something wrong here

[shell widget]

thats right

[carmine lion]

so?

[shell widget]

now expand the numerator using (a+b)^2

and for denominator, you have (a+b)(a-b) = a^2 - b^2

[carmine lion]

yea

so shouldn't u get what i wrote

[shell widget]

no

try again

[neon tinsel]

Can I send an image here?

[shell widget]

$\frac{1 + 2\cos\theta + \cos^2 \theta + 2( 1 + \cos\theta )( \sin\theta ) + \sin^2 \theta}{1 + 2\cos\theta + \cos^2 \theta - \sin^2 \theta}$

[carmine lion]

is that right

so far

[ocean seal]

Sup?

[shell widget]

This is what you should get

[carmine lion]

yes

then what

[shell widget]

cos^2 + sin^2 = 1

1 + 1 =2

[candid torrent]

this trig is disgusting

[neon tinsel]

I am thinking you should use half angle properties if we are still talking about this one

[carmine lion]

haven't learned those yet

[shell widget]

$\frac{2 + 2\cos\theta + 2\sin\theta + 2\cos\theta \sin\theta}{2\cos\theta ( \cos\theta + 1 )}$

[ocean seal]

Sup?

[carmine lion]

yes

i got there

[carmine lion]

divide by 2?

[neon tinsel]

Try this maybe?

[gaunt ember]

probably a very stupid question but, if there isn't a number near the 1st Y, how can divide?

equations system btw

[gray isle]

um you really need to improve your handwriting

i'm finding it extremely hard telling your ys and 4s apart (which also look somewhat like Gs and lightning bolts)

[gaunt ember]

wait i'll rewrite it

[gray isle]

,rcw

[gaunt ember]

those "lighting bolts" are 4

[alpine sable]

why would u divide?

[gray isle]

if you insist on doing some stuff like that, consider y = 1y

[gaunt ember]

substitution method

[gray isle]

if you wanted to solve using substitution, you could add 4 to both sides of the first equation

to isolate y

which you could then sub into the second

[alpine sable]

or divide by 4 in the second one

[gray isle]

^

[gaunt ember]

got it

thanks

[alpine sable]

would this be A?

<@&286206848099549185>

[noble sinew]

Yes

[native temple]

Hello

Can rational expressions not have a common demoniator

[raw valve]

@native temple yes I'm pretty sure

[native temple]

oh

[oak chasm]

@native temple Do you mean within a single rational expression or two or more rational expressions?

[native temple]

2 or more

is it because some polynomials aren’t factorable

by any method?

[oak chasm]

Polynomials are always factorable over the complex numbers.

[native temple]

what do you mean over the complex numbers

[ocean seal]

Chai T. Rex

[native temple]

is that by p/q?

in the complex plane

how would you even find those numbers....?

[oak chasm]

No, it's because the complex numbers are a splitting field.

I don't know all the methods, but, for example, Wolfram Alpha can compute the roots.

[native temple]

ohh

[oak chasm]

Some polynomials can't be factored over the real numbers, though.

[alpine sable]

but all polynomials can be written by linear and quadratic factors

[rare lotus]

how do i go about answering this

mostly i

[oak chasm]

@rare lotus Which discrete probability distributions do you know?

[rare lotus]

none that i know off, my teacher sent us and said to "try it"

[oak chasm]

Try what?

Here's a list of discrete distributions: https://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions.

[rare lotus]

try the question

[oak chasm]

See if one of the descriptions matches.

[rare lotus]

ight jn

[oak chasm]

@alpine sable Sorry, channel is busy.

[alpine sable]

unfrrtdyoof

understood*

[oak chasm]

Try #help-8.

[alpine sable]

i think im in the wrong server as well

[oak chasm]

Oh, OK.

[rare lotus]

i think binomial

[oak chasm]

Yes, I think you're right.

What parameters does the Wikipedia article for binomial distribution list?

[rare lotus]

yes/no

[oak chasm]

No, that's the decision or something, what numeric parameters does it list?

[rare lotus]

"It is a discrete probability distribution with two parameters, traditionally indicated by n , the number of trials, and p , the probability of success."

[oak chasm]

OK, so that should answer part i.

[ocean seal]

Chai T. Rex

[oak chasm]

That's also part of part i.

[ocean seal]

Chai T. Rex

[rare lotus]

ohh

[oak chasm]

@rare lotus Please keep reading past that 🙂

[rare lotus]

yea ll go read thank you

i think i have somewhat an idea what to do now thank you

[oak chasm]

You're welcome.

[oblique charm]

hey i have a combinatorics question and i have no clue which formula to use

[oak chasm]

@oblique charm How far have you gotten?

[oblique charm]

i've gone as far as having k = 2 and n = 12

if that makes any sense

i'm not entirely sure if i'm supposed to use k-selection formula or k-combinations

[sudden patrol]

i need help

[oak chasm]

@sudden patrol Sorry, channel busy.

There's only one pear left, but enough of each of the other fruits to satisfy the two you have to pick.

So, separate it into a sum where one term has you picking the remaining pear and one term has you leaving the one pear.

[oblique charm]

uhhh

i'm sorry i'm going in clueless but i get what you mean

i do know i have to use one of these formulas, unless i'm wrong

[oak chasm]

You have to choose one fruit from banana, apple, and kiwi + you have to choose two fruits from banana, apple, and kiwi.

You can use stars and bars for both: https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics).

[oblique charm]

okay okay, i'll see what i can do for thatt

[jovial adder]

Determine the convergence or divergence of the following improper integrals. If an improper integral converges, evaluate it. $\int xe^(-x^2) dx$ Where the limits of integration are 0 to $\infty$

[ocean seal]

RudyTheButler

[alpine sable]

Help

Google confused me with the formula lol

assuming its a half circle

calculate the area of one of the half circles

and multiply by lenght to get volume

So i have to calculate the area of the half circles then multiply by 15 and that gives me volume

of one

just one half circle

how would u do that

A = 3.14 x r^2/2

= 3.14 x 36 /2

= 56.52

use pi

3.14 right

so pi*r^2/2

to get 18pi

What

$\frac{\pi\cdot r^2}{2}=\frac{\pi\cdot6^2}{2}=\pi\cdot18=18\pi$

[ocean seal]

Delta

[alpine sable]

to have an exact value

u can round up at the end, not in the middle

ok thx

[glacial pelican]

pls

[alpine sable]

how do i get sa though

occupied

the area (halfcircle) is 18pi so what is the volume

847.8

or 18*15 *pi

and u get that correct

oh yeah i have to round

yeah underestandaple

im not a human calculator tho so cant tell

ye

then the area

of the entire figure

This is what i did

thats fine

u should use the pi symbol

and round up at the end

o

now u rounded up in the middle assuming pi=3.14 even tho it is not

my teacher says just make pi = 3.14

i dont think it matters here but generally that is the case

k

how do I find sa now?

the area of the entire figure

how I find that

what sides does it have

er

like it has 2 half circles

[crude root]

isnt this half a cylinder?

[alpine sable]

one in both ends

ye

[crude root]

its a half a cylinder so do half the formula

[alpine sable]

no

so

[crude root]

semicircle area x height

then

[alpine sable]

k

we already did volume

ye we need sa

we are doing surface area now

[crude root]

1/2 the cylinder plus the rectangle

in the cross section

[alpine sable]

pls

let me explain

[crude root]

o

ok

[alpine sable]

hmm

using formulas does no good if u dont know where they come from

ye

[crude root]

o

[alpine sable]

ok so we have 2 half circles

and the rectangle in the back

and that curvy bit

SA of Cylinder = 2x3.14xrxh + 2x3.14xrx2

do i jus do that then divide the answer by 2

no

then get sa of rectangle and add those two together to get the total surface area

waht

u know the area of the half circles

[buoyant anchor]

I need help solving my hw problem

[alpine sable]

they are 18pi as we calculated'

occupied

oh

so we have 2 half circles

the rectangle

yes

which is how much?

3

whar

show how did u get that

uh 2 half circles = 2

• the rectangle is 3 shapes lol

[buoyant anchor]

I don't know where to start

[alpine sable]

nvm

how do u calculate the area of a rectangle

l*w

what is the lenght and what is height

and pls use * if you could

[oak chasm]

@buoyant anchor Sorry, channel busy.

[alpine sable]

15*6

that x is throwing me off

is it 6?

yes

look carefully

12

good

so 12*15

or 180

yes

then the curvy bit

how would u do that

I dnt know

imagine straightening it up

what shape would it have

Rectanglular right

yeah

we know one of its sides

correct

yes

what is the other side

equal to

umm

Is it 12

why

6

why

will it be longer than the bottom rectangle

no

oh 15

why

because bottom one is 15

and side is 6*2 would be 12

yeah that was the one we knew

but when u straighten it it gets longer

like if u have a string

and u straighten it

it gets longer

yes

so

the other side is equal to what side

in the diagram

Bottom?

it is longer than the 12 in the bottom

o

its equal to the half circles side

can u see it now?

no bro

i stll dont get it

wait a sec

k

i mean this

of the half circle

s

[spice tendon]

What is the answer to this?

[alpine sable]

idk

[nova slate]

Lol

Idk

[ionic jewel]

probably 4 for both

[alpine sable]

occupied

[ionic jewel]

i think it wants you to complete the square?

[nova slate]

Yes

I think same

[ionic jewel]

oh sorry delta

[alpine sable]

#rules

[alpine sable]

so the half circle is equal to the other side

ill try and find a video so u can see why

k thank you

when u fold a paper to a cylinder

one of its sides will be equal to the circles cirumference

@alpine sable

Ohh

[potent knoll]

Zero ? lol

[alpine sable]

no

y+14+0 isnt 0

[alpine sable]

can u see now

hanh yeah i know

[potent knoll]

I even don't understand the question lol don't mind my nonsense

[alpine sable]

but it is not 0

i just fucked up my explanation

[dire wren]

lmao its 4

because you can complete the square into (x+2)^2

just as bunny said

[alpine sable]

Tysm @alpine sable

did u get it

[static pasture]

Hi! could someone please help with this

[ionic jewel]

You want one of the trig functions

[static pasture]

im still lost lol

[ionic jewel]

alright lets use angle C

[ionic jewel]

what is tan(27) in terms of the sides of the triangle?

soh cah toa

[static pasture]

To be honest I have no clue...

[ionic jewel]

tan(x) = opposite side divided by adjacent side

[static pasture]

so would it be 27 divided by 6?

[ionic jewel]

opposite side

27 is an angle not a side

what side is opposite the 27 degree angle?

[static pasture]

its a triangle... there is none? Sorry im really bad at math.

does the right angle have somethingn to do with it?

[ionic jewel]

trig only works because its a right angle

[ionic jewel]

its not math

look at the triangle

what side is far away from angle C

the only sides that isnt part of making angle C

[static pasture]

a

[ionic jewel]

a??

there is no side named a

[static pasture]

sorry im lost

[ionic jewel]

the triangle is made of 3 lines

AB, BC, and AC

one of them is oppsite of angle C

the one on the other side of the triangle