help-0

[marsh wren]

nice

[alpine sable]

Can anyone help with what to with this question

[vale wigeon]

have you heard of riemann sums before

[lean stone]

hey can anyone help me solve this question

[vale wigeon]

@lean stone please don't multipost, and also don't post in occupied channels.

@alpine sable are you still here?

[lean stone]

occupied channels? and yeah sorry about that, i just assumed this chat died mb

[vale wigeon]

it's been only 4 minutes

[lean stone]

i didnt see the timestamp yeah

[vale wigeon]

i'm waiting for a response from bobbyrobson

[alpine sable]

@vale wigeon yes

I am

I know what riemann sums are

[vale wigeon]

great

you can rewrite your summation slightly to make it look more like a riemann sum

[alpine sable]

I'm kind of getting confused on where to start because there are 2 variables and I'm not used to it

[vale wigeon]

consider splitting the 1/n^2 into 1/n * 1/n

you'll have $\sum_{i=1}^n \frac1n \sqrt{1 - (i/n)^2}$

[ocean seal]

Ann

[vale wigeon]

which, as $n \to \infty$, will approach $\int_0^1 \sqrt{1-x^2} \dd{x}$

[ocean seal]

Ann

[mystic sinew]

the displacement would just be the area of the top half minus the area of the bottom half right

[marsh wren]

i believe so

[mystic sinew]

I counted it many times it doesn't accept 210

[marsh wren]

$v = \frac{ds}{dt} \implies s = \int v dt$

[ocean seal]

iBoughtWinrar

[mystic sinew]

10(2.5 +0.5 + 6) - 20 (1+1.5+3)

which calculates to -30

aaaaaaaaaaa

why can't I get this right

so many time I got this wrong

[marsh wren]

its 45-55 no?

[mystic sinew]

-10 does not work

[marsh wren]

its 45 above

nvm

its not equal axes

so its 90 above

and then its gotta be 110 below

so -20

[gray isle]

,calc 10(2.5 +0.5 + 6) - 20(1+1.5+3)

[ocean seal]

Result:

-20

[static saffron]

show that the norm $$||(x,y)|| = |x+y| + 2|y-x|$$ is equivalent to the euklidean norm by finding values $A,B > 0$ such that $$ A||\cdot|| \le ||\cdot||_2 \le B||\cdot||$$ is true

[ocean seal]

derdotte

[static saffron]

i dont really know where to start here

[molten vector]

can someone explain the two solutions? what is the delta?

[marsh wren]

https://cdn.discordapp.com/attachments/310848513489502228/830241656904613938/unknown.png

probably this

i forgot the name

kronecker delta

[molten vector]

how come the kronecker delta is included in the solution for kn(t) and ln(t)?

[woeful pulsar]

sin/cos are orthogonal vectors wrt to the integral inner product

[elfin ibex]

BRO IM GONNA KMS

DOES ANYONE KNOW HOW TO SIPLIFY THIS THING

im friking crying 😭

[woeful pulsar]

how about show your work for each of them

then we can check out where you are stuck

[elfin ibex]

i dont know how to start

:C

[woeful pulsar]

start with the first question

what's one apple + 6 apples

[elfin ibex]

how

7

[woeful pulsar]

now look at question 1

[woeful pulsar]

7 whats?

[elfin ibex]

how is this helping

[wind aurora]

@woeful pulsar just use Mathway.com

and simplify

[vale wigeon]

ew mathway

[elfin ibex]

bro screw this im gonna die

[wind aurora]

why is that like a quiz

[elfin ibex]

its homework

[woeful pulsar]

you can do 1 apple + 6 apples, how is Q1 any different

[elfin ibex]

im gonna fail math

[elfin ibex]

so just 7sqrt5?

[woeful pulsar]

yeah

[elfin ibex]

but 3 is confusing af its odd numbers

[woeful pulsar]

sometimes it can't be simplified further

53 is a prime number

[elfin ibex]

do u still need the sqrt or ust leave it as 53

[woeful pulsar]

you can't simplify it any further

so the best you can do is $7\sqrt{3}+\sqrt{53}$

[ocean seal]

Element118

[woeful pulsar]

sometimes you can, sometimes, you can't

[elfin ibex]

okay

[woeful pulsar]

you need to learn how to tell the difference

[elfin ibex]

well what abt 5

what do you do with numbers outside

[woeful pulsar]

well, think about how you can factorise 63

to simplify

there's nothing to it really (for question 5)

[elfin ibex]

21*3?

[woeful pulsar]

factorise more?

[elfin ibex]

7* 3 * 3?

[woeful pulsar]

thus how can you simplify sqrt(63)?

[surreal sierra]

When you are doing all of these radicals , just remember that is the square root of both are same, then you can just add up the numbers like normal and add the square root at the end.

[elfin ibex]

what?

[woeful pulsar]

$\sqrt{63}=\sqrt{7\times3\times3}$. Can you pull any factors out of the square root?

[ocean seal]

Element118

[elfin ibex]

3?

[woeful pulsar]

yeah

what does that give you?

[elfin ibex]

um.. sqrt(63) 3sqrt(7)?

idk..

:C

[woeful pulsar]

yeah that's all to it

[elfin ibex]

oh

[woeful pulsar]

now look at the question and see if you can simplify anything else

[surreal sierra]

Listen me me bro, I am going to take number 3 as an example. One of the factors of 63 is 9, so split the equation into sort(9) x sqrt(7)

[elfin ibex]

uh huh

[surreal sierra]

The square root of 9 is 3, so sqrt(63) is 3sqrt(7)

[woeful pulsar]

that's another way to think about it too

[elfin ibex]

but wher'd you get 7 from

[woeful pulsar]

factor from 63

[elfin ibex]

oh

ohh

i see

here lemme go quickly make my own problem

[surreal sierra]

You would split the 63 into 9 and 7, the sqare root of 9 is 3, and you leave 7 alone

[elfin ibex]

actually ill brb gotta do this class work

[surreal sierra]

Ok sure!

[elfin ibex]

can someone explain this in simpler words

[surreal sierra]

Remember how I showed you to split the 63 into 9 and 7 and to take the square root of 9 to make 3? This is basically saying to do that

Whenever you have a number in a square root, try and find out if it has any perfect squares as factors, find the square root of the perfect square, and leave the non-perfect square in a square root.

[elfin ibex]

oh ok

lemme make a problem and try myself

[alpine sable]

you can also just find the prime factorization of the number inside the square root

[elfin ibex]

like the factor that cant be factored anymore?

[alpine sable]

you know what the prime factorization of a number is?

for example of 24

[elfin ibex]

i think

[alpine sable]

ok so you're familiar with prime/composite numbers right

[elfin ibex]

i think...

;-;

sry big words make me confused

might be dyslexia

[alpine sable]

ok ill do my best to explain

so examples of prime numbers incluse 2,3,5,7,11, ...

these numbers have no factors except 1 and themselves

[elfin ibex]

oh

okay

yeah i remember

[alpine sable]

a composite number is just a number that isn't prime

[elfin ibex]

so like 4

8

[alpine sable]

like 6, which has factors of 1,2,3,6

[elfin ibex]

12

[alpine sable]

yeah 4 is also composit

[elfin ibex]

okay

[hasty quail]

2

[alpine sable]

we can write every composite number as a bunch of primes multiplied together

for example 4=2*2 and 6=2*3

[elfin ibex]

i have a problem ill like to try

[alpine sable]

so lets try to write 90 as a product of primes

[elfin ibex]

you can correct me if i get stuck

[hasty quail]

think of the factors of 90

[surreal sierra]

No worries! Hope you understood what I said as many people say that in math I am really vague and complicated

[elfin ibex]

well the prime is 5

right?

[elfin ibex]

yeah

and thanks!!

[alpine sable]

5 is one prime that is a factor of 90, correct

but we can break it down further

[elfin ibex]

we can?

[alpine sable]

we need to break it down all the way until we just have a bunch of primes multiplied together

[elfin ibex]

hmmm

[surreal sierra]

Do you want a practice problem in case you need some further explaination?

[alpine sable]

so taking out the 5, we have 90=5*18

[elfin ibex]

5

9

[alpine sable]

now lets break down the 18

[hasty quail]

90/10

[elfin ibex]

9

wait

oops

3

[hasty quail]

6

[alpine sable]

18=3 times what?

[elfin ibex]

2,9,3?

are factors

ughhhh

they aint prime

mb

[alpine sable]

18=3*6 is what i was looking for

so now we just break down the 6, which is 2*3

[elfin ibex]

but 6 isnt prime-

yeah

okay

[alpine sable]

so 18=2*6=2*2*3

[surreal sierra]

Do you want to go into Vc for a minute? It might be a bit easier to explain.

[elfin ibex]

sure but i cant talk

[surreal sierra]

Ok

Try and solve this problem using what I showed you. Tell me is you are confused with anything.

[elfin ibex]

okay

well

[surreal sierra]

It is showing 75 btw

[elfin ibex]

4sqrt(5) is simple right?

so its just 75

[surreal sierra]

No

[elfin ibex]

oh-

[surreal sierra]

Forget about the 4sqrt5 for a minute and first simplify the 75

[elfin ibex]

okay

do yk how to use a calculator?

[surreal sierra]

Are there any perfect squares that are factors of 75?

[elfin ibex]

cuz my teacher said we were supposed to find the factors by using a calculator

[surreal sierra]

Oh

[woeful pulsar]

well, grab a calculator and test the squares you know

[surreal sierra]

Ok

I tried to make this one simple, so first try without a calculator

[elfin ibex]

are the prime factors- 5, 3 and 5?

[surreal sierra]

?

Are there any perfect squares that are factors of 75? That’s the first step

[elfin ibex]

how do you find perfect squares-?

;-;

cuz when i keep simplifying i get 5

[woeful pulsar]

well they are just two factors that are the same

just pair up the factors

[elfin ibex]

5 and 3?

[surreal sierra]

Perfect squares are 1,4,9,16,25,36,49,64,81,100

[elfin ibex]

oh

[surreal sierra]

Those are the first few perfect squares

Are any of those factors of 75?

[elfin ibex]

1?

[surreal sierra]

There is one more

It is 25

[elfin ibex]

ohh

[woeful pulsar]

you want to search for the biggest one

[surreal sierra]

Yes

[elfin ibex]

alright kk

brb gotta speedrun this quiz

[surreal sierra]

So just split the 75 into 3 and 25

Find the sqrt of 25 which is 5, and you are left with 5sqrt(3)

[elfin ibex]

how do you know which factor goes in the sqrt

[surreal sierra]

Now add 4sqrt(5) and 5sqrt(3). Since you cannot simplify it further, thatvis your answer

[surreal sierra]

3 isn’t a perfect square, so you know it goes in the square root

The 25 was too, but you could just simplify it into 5

Also, I have to go, just DM me if you are still not understanding. I could be able to explain it to you at 12: 15 New York Time Zonr

[elfin ibex]

we in the same time zone

alrighty

cya and tysm!

[surreal sierra]

Ok. Is there any time you are free?

[elfin ibex]

im free 7:30-2

[surreal sierra]

I can explain it in more depth there

[elfin ibex]

or around 5

[surreal sierra]

Cool. I am free at 12:15, so I will meet talk in DM’s there. If not, I should be able to talk at 5.

[elfin ibex]

kk

[alpine sable]

for #12 do you notice any factoring patterns?

difference of squares should come to mind

for #14, you should recognize 2(sina)^2-1 as a form of the double angle identity for cosine

[woeful pulsar]

as well as the other identities for cos

[alpine sable]

2(sina)^2-1=(sina)^2+(sina)^2-1=(sina)^2+(1-(cosa)^2)-1=(sina)^2-(cosa)^2

then just use difference of squares

[elfin ibex]

we havent learned sin and cos yet

must be hard ;-;

[woeful pulsar]

those are functions which can be defined with the unit circle

https://www.solidangl.es/2021/02/spr21-mat130-circular-functions.html @elfin ibex if you want to read up

written by another person on this server

[elfin ibex]

hmmm sounds cool

ima use that for quantum physics one day

[alpine sable]

how would i solve these

[woeful pulsar]

construct an equation, solve the equation

[alpine sable]

how do i construct a equation

for the first one

x+3x+10?

@woeful pulsar

[woeful pulsar]

you need to make the equation

so far you have an expression

what is this expression equal to?

[alpine sable]

90?

x+(3x+10)=90 right

i get 20

x = 20

thanks

[woeful pulsar]

you can do the same with the other one

[alpine sable]

yes

[elfin ibex]

Element188 deserves a rank up

[woeful pulsar]

and I shall hide in the shadow of Element188

[elfin ibex]

xD

nahh

[alpine sable]

secret angel

[elfin ibex]

Element gonna get promoted sooooon

[woeful pulsar]

and then I'll hide in the shadow of Element

by having 3 extra digits at the end

[alpine sable]

element "188"

[woeful pulsar]

probably should context

[vagrant sphinx]

Trigonometry I think

Was asking for that too

He hasn't replied yet

[woeful pulsar]

hmm, you can continued fraction it until it stops

[brave cairn]

can someone explain why this is true?
assume B & C are angles of a triangle

[vale wigeon]

are B and C acute

[brave cairn]

B is, idk about C @vale wigeon

[nocturne wolf]

Can someone help me with this one im confused

[brave cairn]

99, but idk how to explain it to you in English, not sure what term you use for that kind of angle

198/2

[nocturne wolf]

ALRIght thank you!! I was just making sure

[elfin ibex]

bro this server teaches things faster than me teacher

[brave cairn]

@vale wigeon did it just cross out sin
from sin(90-C)=sin(B)

[vale wigeon]

well

you can do that if you know both your angles are acute

[brave cairn]

really?

[vale wigeon]

yes

if two acute angles have the same sine they are the same angle

[elfin ibex]

big brain comeback

[magic tusk]

also if two acute angles have the same sine it means they are compatible as a couple 🙂

[magic tusk]

If your class has a textbook, ask the teacher where in the textbook you all are working on, and read the section of the textbook and you can learn it super fast. It'll be like reading 4 pages in the book that would take the teacher 4 days to teach, but you 30 minutes to read.

[elfin ibex]

such a smart idea

[magic tusk]

Yeah it's also 100% what you do in college.

[elfin ibex]

;-;

cant wait-

im alr getting paid tho :))

just gotta save up a bit

invest

then make more money

then invest

more

more

more

more

!!

[sullen nova]

Hello

[elfin ibex]

wasabi

[magic tusk]

Stop.

[elfin ibex]

?

[sullen nova]

So you’re recieving ur first pay check?

[magic tusk]

@sage lynx If f(x) = x^2, f(x+3) = (x+3)^2

Take it to #discussion

[sage lynx]

Great thanks

[magic tusk]

Then try and distribute everything and factor out an x somewhere so you no longer have an x at the bottom (can't divide by 0) and direct sub in for your answer

[sage lynx]

alr i'll do that thank you

[elfin ibex]

not a job. im only 14

i do yt

i couldve been payed at 11 if my parents supported me though

[sullen nova]

Ur channel?

[elfin ibex]

its linked to my discord profile

or just search up Murple and find the first channel

[spare hill]

is this channel open now?

[woeful pulsar]

ig so

because there's no math talk here

[spare hill]

ok. i'm trying to find approximation of vector V in R3 using two other vectors U and Z.

i know how to do it

but i want to be able to explain the process

like, (<V,Z>/<Z,Z>)*Z is part of the linear combination to approximate that vector

but

how would i explain the logic of using dot product to approximate?

[woeful pulsar]

bilinear forms? probably?

are U and Z orthogonal?

[spare hill]

yes

what does bilinear form mean?

i'm trying to explain it in simpler terms

like, what does (<V,Z>/<Z,Z>) do exactly

[woeful pulsar]

it's a special function that takes in two vectors

[spare hill]

it seems to find out the scale between V and Z

[woeful pulsar]

but all symmetric positive definite bilinear forms are essentially dot products

[spare hill]

yes but i want to understand the intuition of this, not explain it using jargon

[woeful pulsar]

Ever heard of a projection?

[spare hill]

yes

[woeful pulsar]

we are essentially projecting V onto Z

[spare hill]

still i wish to explain it along the lines of "the (<V,Z>/<Z,Z>) portion of the equation calculates the ________ relationship between V and Z before applying that scale onto vector Z"

i understand the projection thing

it's just i want to explain the equation itself

in micro level, not macro

i guess, even in the projection, what would (<V,Z>/<Z,Z>) intuitively mean?

[woeful pulsar]

the dot product is the product of lengths * cos angle

if that helps

[spare hill]

hmm i guess it could be a relation of lengths but it's a little more complex than that

hard to grasp the words for it

[woeful pulsar]

maybe you can share what you want to say exactly, and we can try to break that down

do you want to say "using the dot product here will give the best approximation"?

[spare hill]

no, it's the same as above

"the (<V,Z>/<Z,Z>) portion of the equation calculates the __ relationship between V and Z before applying that scale onto vector Z"

the blank is where i dont know what type of relationship to describte it as

[woeful pulsar]

maybe if you normalise it into unit vectors it might be better?

you want to use that exact phrasing?

[spare hill]

maybe

idk, i think i'll just call it "relation" with the quotes intact to emphasize the obscurity

ty tho

[dusky notch]

hey does anyone know how to figure out if these are convergent/divergent? the endpoints from a ratio test were -1/3 and 1/3 and now im trying to test them but im currently stuck. Any help is appreciated. Thanks!

[glass lichen]

simiplify the numerators

[dusky notch]

can i just multiply them by each other so it ends up being -1^n

in num?

[glass lichen]

(-1)^n for the top one, yes

[dusky notch]

so what does that tell us

i want to say alternating harmonic series but its not quite there yet

since it has a square in denom

[glass lichen]

top one you can use alternating series test for convergence

bottom one is the Basel Problem, which is known to converge

or use p-series if you didnt know that

[dusky notch]

ohh ok

[glass lichen]

they should both converge

so the interval of convergence is inclusive on both ends

[dusky notch]

how do we do alternating series test again

[glass lichen]

$\sum (-1)^na_n$ converges if $\lim_{n\to\infty}a_n=0$

[ocean seal]

moshill1

[dusky notch]

so in this case wouldnt our an be n^2?

so it would diverge to infinity?

since (-1)^n* 1/n^2

oh it would be 1/n^2

which the limit would be 0

[glass lichen]

a_n = 1/n^2

and lim is 0

so it converges by alternating series test

[dusky notch]

oh that makes sense, thank you!

I appreciate your help

[south marsh]

can someone help me with this?
Find three consecutive integers such that the sum of the first and half of the
third is 16 more than the second.
my answer for the value of x is 30

[glass lichen]

what's x?

[south marsh]

there's none in the given

[glass lichen]

You said x, I am asking you what x is

cause the question as you have it written has no x

[south marsh]

here's the equation i used to get x = 30 but i'm not sure with this
x + 1/2x + 2 = x + 1 + 16

[glass lichen]

You still have yet to say what x is

[south marsh]

i'm tryna find the x

so i can get the three consecutive integers

[stable dune]

The top of a ladder rests at a height of 18 feet against the side of a house. If the base of the ladder is 5 feet from the house, what is the length of the ladder? Round to the nearest foot. Just type the number and round to the nearest tenth.

can someone help me out?

[muted raft]

@south marsh How did you get 30? It should be 32.

show your steps.

[south marsh]

sorry i got it wrong w my equation

the equation should be
x + 1/2(x+2) = x + 1 + 16

right?

[muted raft]

if you meant (x+2)/2 then yes.

However, like moshill said, before you begin doing any of this, you must first define what x stands for.

[south marsh]

ok i'll take note of that

[muted raft]

So you would say, let x be the first integer in the three consecutive integers. Then x+1 is the second integer and x+2 is the third integer.

[south marsh]

ohh i thought s/he was asking for the value of x already sorry for that

thank u btw

[halcyon cloud]

can anyone help me with this

[spring harbor]

Given that the median is either 16 or 17, how can we find x?

Well I am looking for the average of that given the median is 16 or 17.

not sure how to do it.

[real briar]

are u taking a test? LoL

[muted raft]

What does median mean? @spring harbor

[spring harbor]

The median is the value separating the higher half from the lower half

[muted raft]

Basically median is the "middle value" in the sorted list.

If you were to sort your above list, what would you get?

[spring harbor]

6 8 10 x 20 32 40?

[muted raft]

don't forget you have 2 20.

[alpine sable]

Vibe

Don’t forget to become a business man you must skip math.

[muted raft]

But, we see that the list is even.

[spring harbor]

Oh I thought I only count one.

6 8 10 x 20 20 32 40?

My apologies

[muted raft]

so then the median of this list is (x+20)/2 = 16

since the length of the list is even.

If it was odd, we would have simply "picked" that element.

[spring harbor]

Ohh I see

So x = 12

Alright I got it, thanks

[noble sinew]

Well them saying median is either 16 or 17 implies that the value of (x+20)/2 is a number between 16 and 17

so it isn't x=12

[spring harbor]

Yeah 12=<x=<14

The question was to find the average

and the answer is that it lies between 18.5 and 19

[noble sinew]

Yes and since it seems like it can only be integer solutions for the list

it means x=13

[spring harbor]

14*?

[noble sinew]

since that will give (13+20)/2=16.5

hence the median is either 16 or 17

[spring harbor]

Oh yeah just the average of the two

that also works

[sleek osprey]

i got 6

.425

[final crest]

Does anybody know 8 queen problem here?

[fresh sedge]

Hey there,

1. Given that, sin(x)=7/25 since u got a hint u have to draw a picture u can draw a right angled triangle and since we know that sin(x)= perpendicular/hypotenuse= 7/25. put the values on the diagram and u will observe that the adjacent side is missing so the answer to (1) is ADJACENT.
2. the length of the missing side can be calculated by pythagoras theorem, so the length of the missing side will be 24.
3. they asked the value for tan(x) which is equal to perpendicular/adjacent = 7/24.
4. Now, the value for cos(X)= adjacent/hypotenuse= 24/25.

Due to network issues I am not able to upload the picture But If u have any doubt do ask me.

Thank you!

[hybrid steeple]

What is the perimeter of the​ polygon

[pallid smelt]

hi! hi can you help me solve a problem pls?

i have been stuck with it for hours

and

to find the last 5 digits of

[solar cargo]

Okay so when it comes to the first equation I'm pretty sure you would just get the cube root

[pallid smelt]

how?

[solar cargo]

A³ + B³ = 48

so

[pallid smelt]

the cube root of 48?

[solar cargo]

basically put a square root over it, but instead of it being a square root, make it a cube root.
What that means is ∛.

∛

It's literally a square root with a 3

[pallid smelt]

oh ok

[spring harbor]

and?

You can't just cancel the power like that

[solar cargo]

Put it over everything then you have a + b = 16

[spring harbor]

woow wowo calm, first of all cube root of 48 is not 16

[pallid smelt]

really? thx

[spring harbor]

@pallid smelt No

[solar cargo]

wait holup

I'm an idiot

holup holup

cube root 48 mb

[pallid smelt]

is 3.63

[solar cargo]

oh im an idiot

[spring harbor]

you're wrong on both

cuberoot of (a^3 + b^3) is not a + b

[solar cargo]

it removes the cube homes

[spring harbor]

No it doesn't

[solar cargo]

whenever you have a cubed, to get rid of the cubed you put a cubed root over it that's what i was taught

[spring harbor]

@pallid smelt Ill try to think of a solution one second

[solar cargo]

Then you repeat it on each side

[spring harbor]

@solar cargo not if you have a plus sign

[pallid smelt]

oh thx

[solar cargo]

okay see, there's a lot of different things here, and tbh I'm prolly wrong ngl
I'm just doing what my teacher told me, but I can't remember every single detail
There goes my chance at actually helping

[spring harbor]

thanks for trying but you're doing it wrong xD

[solar cargo]

well frick

[spring harbor]

@pallid smelt don't do what he said

[pallid smelt]

ok

[solar cargo]

yeaaaa I'm what we like to call teacher in trAinING

[pallid smelt]

then what should i do

[final crest]

Is this correct

[solar cargo]

already working on a question here

@final crest prolly move to a different area cuz we're already helpin someone

[spring harbor]

@final crest Go to some other channel

[solar cargo]

or rather someone else is helping

[pallid smelt]

ok

so

[final crest]

Okay

[velvet pelican]

These are not solvable (atleast in the real numbers)

[pallid smelt]

really?

ill have to tell the teacher

[velvet pelican]

You can graph them

[pallid smelt]

oh

hiow?

[spring harbor]

what does the exact question say?

Does it say solve for a and b?

[pallid smelt]

no, to tell the vaule of a+b

[spring harbor]

Ohhhh

[pallid smelt]

and the 2nd one to get the las 5 digits of

[gray isle]

consider the expansion of (a+b)^3

[solar cargo]

Yo echo

[cerulean glade]

u guys ever heard of mathway?

[oak chasm]

@pallid smelt Do you know about modular arithmetic?

[pastel mauve]

how do i get the asnwer

[alpine sable]

There are three padlocks with associated keys: red key, black key and for the last lock both green and yellow keys fit.

You must take one key up at a time with your eyes closed. What is the chance that you choose the right keys, in the right order, in the first attempt?
The answer must be written in percent to 2 decimal places

My presumption was 1/4 then + 1/3 then after its a certain win.
But it's wrong.

<@&286206848099549185> ^

[pastel mauve]

dont ping helpers unless it has been 15 minutes

besides i already asked a question :(

[gray isle]

the question implies that you have a geometric sequence. divide the appropriate terms to get the common ratio

[alpine sable]

No idea

ooh it's about his.

[pastel mauve]

anyone know mine?

[cold roost]

He responded to your question

[alpine sable]

Well,

then I surely have no idea.

[gray isle]

the question implies that you have a geometric sequence. divide the appropriate terms to get the common ratio

[cold roost]

You can do a process of elimination to find the ratio for the sequence @pastel mauve

[pastel mauve]

how

[alpine sable]

I repeat, I don't know what you mean. Maybe give me an explanation.

[pastel mauve]

i think its A

[alpine sable]

Or like an example.

[pastel mauve]

@cold roost is m ine A

[gray isle]

yes

[pastel mauve]

how about this

[cold roost]

yo you better chill

[pastel mauve]

its the last one im asking.

[alpine sable]

Ryan sold 60 shares of A stock. The value of each share has decreased by $2.50 since he bought the stock. Express the amount Ryan gained or lost as an integer.

can someone help please?

[alpine sable]

Seriously?

[pastel mauve]

2.5*60

[alpine sable]

No

[pastel mauve]

what

how

[alpine sable]

It's decreased, isnt it?

[cold roost]

It's pretty obvious you're taking a test or quiz and no point in giving an answer if you're just cheating. It seems like you don't know the material already.

[pastel mauve]

yeah they want how much he lost

so 2.5$*60stocks gives you amount he lost

[ionic jewel]

$-2.5\times60$

[ocean seal]

bunny

[alpine sable]

Yeah so why use addition

[pastel mauve]

i said multiplication

[alpine sable]

I meant multiplication,

[alpine sable]

This is right I believe,

not addition.

[pastel mauve]

yeah

okay

[alpine sable]

You don't get less by multiplying.

ohhh I get it now

[unkempt umbra]

Can someone explain to me why every integer in base 10 modulo 7 is equal to its value in base 3 modulo 7? I think it's a property I've seen somewhere online but with no explanation.

To be more clear
say we have 19 (in base 10)
19 modulo 7 = 5

19 = 201 (in base 3)

201 modulo 7 = 5

This is true for absolutely every number but i don't know the reason. Can someone explain?

[alpine sable]

write both numbers out in their expanded form

19 base 10=201 base 3= 2*3^2+0*3^1+1*3^0, which is congruent to 2*10^2+0*10^1+1*10^0=201 base 10 in mod 7

you can do this for any two numbers

and they'll be congruent modulo 7

[vale wigeon]

this has to do with the fact that $3^n \equiv 10^n \pmod{7}$ for all natural $n$

[ocean seal]

Ann

[abstract sundial]

Help immediately

[pale river]

Is (a) just F(15)?

[stoic hound]

Yep

[abstract sundial]

Can someone help

[pale river]

Isn't F(15) mean less than or equal to 15 oz though?

not strictly less than

[stoic hound]

This is a continuous probability distribution

So there's basically zero chance that it'll be exactly 15 oz

[dawn wraith]

Don’t repost the same question in different channels.

[pale river]

okay got it. thanks

[abstract sundial]

Are you going to help me or no

[dawn wraith]

Bud, the first number says whether you go to the right or the left, and the other number is up or down.

I’m sure you can figure it out

[abstract sundial]

@rose quiver you got something to say pussy?

[alpine sable]

dunno why 969.12 was wrong for the first part

and the second part is also wrong

so im clearly lost

[alpine sable]

No idea

What this is asking me to do

[lament lintel]

does anybody know the answer

[untold wharf]

@lament lintel first

you need to isolate x

distribute the 6 to the equation on left

which is 6x + 6 is > or equal to 7

subtract 6 on both sides

6x = 1

divide 6 on both sides

x = 1/6

mb sorry

i meant x > or equal to 1/65

1/6*

[alpine sable]

guys

Z=X/2-3t

To make x I found 2 ways

2Z+3t=X

or

2(Z+3t)=x

What is the correct answer pls tell me

actually

pls answer quick

I really have a test tmr

PLS

[stoic hound]

Can you show how you got both of these answers, step by step?

[alpine sable]

well

The first one

I did this

Z=X/2-3t=>2Z+3T=X

Then

for the second

I did Z+3T=X/2

2(Z+3T)=X

[stoic hound]

Please elaborate

[alpine sable]

Z=(2/x)-3t

I put 2 to Z

X/2

Then I plused 3t to 2z+3t=x

[stoic hound]

How can you put 2 to z?

You can only perform an operation on the whole right side and whole left side at once

So for example you can multiply both sides with 2

[alpine sable]

yea

[stoic hound]

Then you get 2z=x-6t

So x=2z+6t=2(z+3t)

[alpine sable]

Oh so wait

You can't put 2 to z

Cuz

Like

In equations especially this one z=x/2-3t=> z+3t=x/2-3t+3t

So 3t cancels from the right and goes to left

But here I can't since z=x/2-3t

If I times it by 2 I get another answer

[stoic hound]

You can times it by 2

But that times 2 will also affect t

[alpine sable]

Yea

That's what I meant

Thanks

[stoic hound]

This can get confusing at first

Try not to think "I'm taking this term and putting it here", instead think "I am performing some operation on both sides"

[alpine sable]

yea

[stoic hound]

Hopefully that will make it easier to think about

[alpine sable]

Thanks a lot

[untold wharf]

you guys done?

cause me have question too

[lament lintel]

thx

[stoic hound]

Yes

[untold wharf]

I normally would know what to do if the angle was 90

but tis 89

its 89

so idk waht to do

[stoic hound]

How would you do it if it was 90?

[untold wharf]

if it was 90, that would mean that the height would be 16

find the area of the triangle

then i find area of sector

which is 90/360 times pi (16) squared

and whatever that equals

u minus it by the area of triangle

idrk

[stoic hound]

That's the segment area

You just want the length of the arc

[untold wharf]

oh

mb

LMAo

wait hmm

is this trying to trick me

[stoic hound]

No

[untold wharf]

if it was arc

then id do 90/360 times 32pi

cause two times 16 is 32

[stoic hound]

Precisely

Now all you gotta do is use 89 instead of 90

[untold wharf]

oh wow

was the triangle a decoy

[stoic hound]

Huh I guess it was

[stoic hound]

Mb

[alpine sable]

@vale wigeon sorry I was just confused with how you got rid of the other 1/n?

[abstract sundial]

<@&286206848099549185>

[alpine sable]

you need to plot those points on a graph?

also don't ping helpers right away

[abstract sundial]

I been waited for more than a hour

[untold wharf]

@abstract sundial what do u do with those points

[abstract sundial]

I plotted them

[untold wharf]

oh wait what math are you doing?

[abstract sundial]

Inverse functions

[worthy crescent]

can someone help me on my test?

[untold wharf]

@worthy crescent #rules

[abstract sundial]

You'll get banned

[tidal gate]

are there things that are true but can't be proved?

in mathematics

[untold wharf]

pretty sure no

idrk

theres usually a theorem or a reason behind every right answer

[wild shard]

[stoic hound]

Yes! You should check out Godel's incompleteness theorem

[abstract sundial]

@untold wharf do I find the slope and y intercept next and just find the inverse?

[tidal gate]

so it's possible that some conjectures people are working on the proof may not even be provable

that's sad

[lost steeple]

How can I solve these?

Can someone tell me the steps

[wild shard]

take inverse sin for first one

[tidal gate]

can you prove that a statement can't be proven?

[wild shard]

in the second one

secant is recipricol of cosine

[stoic hound]

Yeah

[stoic hound]

It's very rare, but possible

[lost steeple]

@wild shard How could I do it withhout a calculator

I'd love to use a calculator but I can't

[wild shard]

do you know your unit circle?

[lost steeple]

Kind of

-1/root(2) belongs to the

30-60-90 triangle

https://gyazo.com/fdd7bbaab9e953c0ddda090a889782a3

Is this correct?

Oh wait it belongs to the 45-45-90 one

[wild shard]

ya

[lost steeple]

how do I

know if it's positive or negative

[wild shard]

well sine is positive in the first and second quadrant

[lost steeple]

is there suppose to be 2 answers?

https://gyazo.com/2007bf88467d8261c7fceedc9843732e

[wild shard]

Only 1 ans

[tidal gate]

solution in red

[vale wigeon]

@alpine sable what do you mean?

the 1/n that appears there is the subinterval width

[tidal gate]

@stoic hound

how?

do you have an example of a statement that I can prove to be unprovable even if it's true

[stoic hound]

Godel's incompleteness theorem gives one example

[tidal gate]

in other words, it would be impossible to know whether it's true or not right?

[lost steeple]

https://gyazo.com/c2adbc45713ad50e4976b8544936695a
Wouldn't it be right in here too?

[tidal gate]

yes

[lost steeple]

so there are more than one answers

[tidal gate]

there are 2 answers

within the interval [0,2pu]

2pi*

I gave you where one of them is and you got the other one, now it's easy

[zealous crypt]

what is the function if the slope is -1 and the constant term is -3

[stoic hound]

Sorry, I spoke in haste. You can prove, with Common Sense, that certain statements are unprovable within a particular logical system

[tidal gate]

hm... proving with common sense doesn't sound very convincing honestly

[stoic hound]

Lemme give a simple example

[tidal gate]

maybe I'll buy that with an example

[stoic hound]

Suppose you have a system of axioms, X. You can construct all sorts of theorems out of these axioms

[tidal gate]

ok, you can't prove that my mom is gay using math

[stoic hound]

Suppose you make the claim: "This theorem cannot be proved true by using the axioms in X"

If the theorem is not true, then that means you can prove it to be true. Contradiction

[zealous crypt]

what is the function if the slope is -1 and the constant term is -3?

[stoic hound]

Which means it must be true, I.e. You can't prove it to be true 🤯

[stoic hound]

Y=-x-3

y=mx+b is the general form where slope is m and constant is b

[zealous crypt]

that's why it was flagging it as false

i kept writing -1x-3

😂

[tidal gate]

bro but you just proved it to be true. what if I change "axioms in X" by "using logic", then the universe must explode

[stoic hound]

"using logic" is a very vague term

Anyways I don't know half the story myself

[lament lintel]

does anybody know the answer

[tidal gate]

just replace it by ""This theorem cannot be proved true. period"

[stoic hound]

Just trying to show that there's more to it than might seem at first glance. You should probably read more about this to get a better idea

[stoic hound]

Good point actually, I'm not sure how to respond to that 😅

[tidal gate]

if it's true, it can't be proved true, so contradiction

so it must be false

[alpine sable]

when yall finish can i get some help in #help-1

[lament lintel]

i need help

[stoic hound]

What methods have you learnt for solving this sort of thing?

[lament lintel]

idk i missed a whole class of algebra

i just need the answer or the whole solution if you want

[stoic hound]

One thing you can try is this

Use the first equation and put y on one side and put everything else including x, on the other side

So you have y in terms of x

Then plug this value of y into the second equation

Now you have an equation in just x

Which you can easily solve

[lament lintel]

so what the answer ?

nvm gtg dm me the answer if you have it

[narrow vector]

does anyone know how to find time given force mass and velocity

cant find the formula

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[alpine sable]

wouldn't it simplify to (1/n*1/n) (1-(i/n)^2)

[narrow vector]

thanks for explaining it now I can solve this problem I was stuck on

[oak chasm]

No problem.

[alpine sable]

how do i get MPT

[oak chasm]

@alpine sable Please don't post to multiple channels.

[alpine sable]

no one is using this channel so I switched to it is that really a problem?

[oak chasm]

Yes, from #❓how-to-get-help:

3. Stick to one channel and don't post the same question in multiple channels. Please don't ask for help in other channels if no one is responding in the one you have posted your question in.

[alpine sable]

if no one is using this and i move my question here and delete the question in the other room it doesnt break the rules

:/

[oak chasm]

No, it still does. People can, for example, be looking up something to help you and then the question disappears.

This is understandably not ideal.

[alpine sable]

bro drop it, it didnt hurt you so calm dowm

[oak chasm]

You probably shouldn't incite other people by telling them to "calm down" when you've broken the rules.

[alpine sable]

why does it require a whole conversation with someone that has a trex as a pfp

[oak chasm]

<@&268886789983436800>

[alpine sable]

bro where did you come from, you can only make things blow up by stepping in something that doesnt mean shi

like in no way were you involved

[toxic crow]

isnt it just 60 though?

[sly mantle]

@alpine sable please familiarize yourself with the server rules in #❓how-to-get-help. in particular, don't multipost

[alpine sable]

now thats your job

not some trex dude -_-

[toxic crow]

@alpine sable isnt the answer to MPT 60 degrees?

[alpine sable]

that is what i was askin

[toxic crow]

intuitively it makes sense, you can prove it using arc lengths

[alpine sable]

k

[ocean carbon]

How can I calculate the initial velocity needed to fire a projectile such that it will fly in a straight line towards a given target?

[lament lintel]

can somebody tell me the answer

[spring harbor]

maybe go to a physic server you'd get more appropriate help there

[spring harbor]

no we can't tell you the answer

[ocean carbon]

do you know one?

[spring harbor]

#old-network

[lament lintel]

why

[spring harbor]

because you're supposed to solve it not us

[lament lintel]

kk

[spring harbor]

we can help you learn how to do it though

[alpine sable]

im pretty sure you can more 3 on the right side of the equals and y on the right side of the equals sign switch the value of it like make 3 negative and y negative

not 100% sure tho havnt done that in 2 years

[sturdy rapids]

Yo can someone help me out with my homework?

When this channel is done being used?

[oak chasm]

@sturdy rapids Is it the same question you asked in #help-5?

[sturdy rapids]

yeh

But, I need someone else to help me on it

[lament lintel]

idk what that means but whatever

[oak chasm]

Please don't repost the question to multiple channels. From #❓how-to-get-help:

3. Stick to one channel and don't post the same question in multiple channels. Please don't ask for help in other channels if no one is responding in the one you have posted your question in.

[lament lintel]

i can't even multiply

[sturdy rapids]

well you learn something new everyday

[lament lintel]

idk how i made it to algebra without multiplying

[prisma crest]

Is someone able to help me with some Stats Questions?
If so, please PM me !

[marsh olive]

How should I factor this trinomial?

(2x^2)+x-28

[narrow vector]

begin by using the x method

[marsh olive]

I tried, I can't find the two factors of -56.

[narrow vector]

you multiply-28•2

okey

[marsh olive]

Mhm, but then what would the factors of -56 be that equal 1?

[narrow vector]

let me explain

so the sum of -28 times 2 is -56

we want to find one that is equal to 1

that would be -56/7=8

[marsh olive]

Oh I did an unsmart

Ok I got the rest from here lol thanks

[upbeat isle]

can someone help me solve 2theta=arccsc 2root3/3?

[alpine sable]

how would u calculate the surface of the intersection of 2 circles of radius 1, one on the origin and the other on x=1, y = 0?

Help plz

[spring harbor]

@alpine sable probability to select a white ball from urn A is the amount of white balls in urn A divided by the sum of all balls in that urn

[oak chasm]

@alpine sable Sorry, this channel is currently busy.

[alpine sable]

can anyone expand this? (2x^3)^4

[misty roost]

I'm sure, but the important part is that you know how to do so yourself

do you know exponent rules?

[alpine sable]

Can anyone help me out with some group theory? This question has given me a shape A, and has asked me to select three permutations from a list of permutations that correspond to non-trivial symmetries of A

Not only have I never heard of non trivial symmetries, but I've also not seen it in the context of a shape before and I'm pretty stuck. Would appreciate it 😅

[snow tundra]

hey is anyone in here familiar with math that is used in realestate? id say im very good at non calculus or heavy algebra based math like most people ig but the terms they use are a bit confusing for what im supposed to do with them. im doing my best to catch up on my work while im free this week

[thorn kindle]

You have x shirts and y pants. How many combinations?

Wait nvm thatd just be xy

And i guess you could extend that to hats as well

Xyz?

[solemn tartan]

Whats a singularity?

[ionic jewel]

yep

[woeful pulsar]

the trivial symmetry is the symmetry that leaves it in place

firstly you need to determine a way the group acts on the shape

[nimble elk]

how do I solve problems like this

[woeful pulsar]

make some equations to solve for x

[snow tundra]

What is the monthly tax liability on a property assessed at $133,000 if the published tax rate is $1.50 per $100 of assessed value? The sales price of the property was $150,500. The vacancy rate in the area is 6%. The market capitalization rate is 8%.

[nimble elk]

like 4x+5=65?

[woeful pulsar]

but that's not really true, you need to find an equation which you can conclude from the diagram

[snow tundra]

so the sale cost is not relevant im just confused as to if the vacancy rate or the market capitalization is relevant

[nimble elk]

65+4x+5=180?

[woeful pulsar]

still not true

[woeful pulsar]

hmm, I'm just guessing only the published tax rate and $133000 is relevant

[snow tundra]

yeah thats what it feels like to me

[woeful pulsar]

since idk the specifics but it doesn't seem likely that the other factors should influence it in any way

[snow tundra]

im really not like a math idiot but sometimes i get a bit to caught up in the extras

[woeful pulsar]

if it does, there's a lot of missing context on how they influence it

[snow tundra]

ill tryt o solve it and lyk and I agree the missing context was a red flag to me as well

yeah it seems they arent relevant by any means. just distraction

[upbeat isle]

hi ca i get some help with this problem?

so i got to 2theta=+- 2root3/3

Am i just supposed to know what that fraction is or can i do more to solve/simplify it

[woeful pulsar]

where did the cos go

[upbeat isle]

srry 2theta= arccsc(+-2root3/3)

[ionic jewel]

i think ur just supposed to know it

it's on the unit circle

[ashen wave]

Is anyone here good with quadratic functions?

[normal jasper]

Could someone help me with this question

[slender marten]

If x = -1, x = 1 and x = 3 are zeroes of the polynomial then the cubic must have the factors (x+1), (x-1) and (x-3).

[alpine sable]

Hello, just had a quick question. Is there a way to solve this question without calculators as it's mentioning?

[alpine sable]

I can't think of a way that is particularly fast or fun

[charred flint]

when that's question 1 of 10 for an hour long test

[alpine sable]

writing out the primes less than or equal to sqrt(2021) and some of their powers, and then counting some stuff is pretty slow but I think it'd work fine

wait no you'd need more primes than that

primes less than 1010

[sly coral]

how would you solve this ?

[alpine sable]

Right, that's what I did. The question's conceptually easy, except, the fact that there's computation restrictions make it insanely hard. Especially since I can't compute anything larger than 10x10

So I was just wondering, if I was missing out on some insane theorems that would simplify this problem, and I haven't been able to find any

After trying to figure out the number manually, I gave up and just wrote some code

def P(n: int, k: int) -> Set[int]:
    """returns a set of integers that can be exponentiated with n to get a number less than k//2"""

    S = set()
    x = 1

    while n < k ** (1/x) \
        and (v := n**x) <= k/2 \
        and k // v != n:
        
        S.add(x)
        x += 1
    
    return S

def get_primes(s: int, e: int) -> Iterable[int]:
    """returns an iterable of all primes in [s, e]"""
    
    s = 2 if s == 1 else s
    
    for i in range(s, e + 1):
        pred = True
        for n in range(2, i):
            if i % n == 0:
                pred = False
                break
        if pred:
            yield i

data = Tuple[int, Set[int]]
def _C(g: data, h: data, k: int) -> int:
    """
    returns the number of integers in g and h 
    that when exponentiated with their bases and multiplied give a number less than k
    """
    
    a, b = g[0], h[0]
    g, h = g[1], h[1]

    count = 0

    for x in g:
        for y in h:
            if (a**x)*(b**y) <= k:
                count += 1
    return count

def solve_math(D: Dict[int, Set[int]], k: int) -> int:
    count = 0
    filteredD = [(n, ns) for n, ns in D.items()]

    for i in range(t := len(filteredD)):
        for j in range(i + 1, t):
            count += _C(filteredD[i], filteredD[j], k)
    
    return count

count_math = solve_math( {n: P(n, 2021) for n in get_primes(1, 2021//2)}, 2021 )

I wrote the code in a way that follows exactly what I'd be doing mathematically, except since it's computerized it makes the process of computation much easier

The answer's 966, and I can confirm that with a completely computerized solution

But I just want to know if there's another way

does "be able to reach your answer without any calculator or computer" just mean you need to explain what you would do without a computer, even if the process takes a while?

and you don't actually have to do it?

[alpine sable]

I don't know myself either, this question is a series of 5 that I have to submit to join a math club. And the questions are very vague as well

I don't have their contacts either to clarify what they're saying

So I have no idea myself

I wouldn't count on there being a nice way to do this by hand lol

Yeah, same

[sly coral]

how would you do 5b?

im a bit stuck on how to solve it

[fringe rose]

whats the asnwer

[slender marten]

What have you tired?

[fringe rose]

nvm

[alpine sable]

Hey, can anyone explain this to me.

[woeful pulsar]

the solid line implies it is part of the solution set

the dotted line implies it is not part of the solution set

the darker region is implied to be in the solution set

[alpine sable]

So after that I got A, do you know if thats correct?

[slender marten]

I'd recommend solving for y explicitly then if you have y >= ... this means the shaded area needs to be above the line and if y <= .. the shaded area is below the line.

[woeful pulsar]

I can evaluate points on the line, just above and just below to check

[slender marten]

To avoid errors, Desmos can also plot inequalities.

[alpine sable]

desmos?

[slender marten]

It seems A is correct.

[alpine sable]

oh the caculator

[slender marten]

https://www.desmos.com/calculator/hxtjuun9ez

[alpine sable]

Ahhh, I 100% forgot desmos existed thank you so much both of you :)

[gilded rampart]

Find the point that extends the line from (-2,-7) to (2,-3) in the ratio -7/3

[raw inlet]

would this be like a inflection point like i drew

or would it be a x -int?

im trying to draw a graph based on some conditions and this is one of them

[ionic jewel]

assuming you are trying to graph f(x) and not f'(x) it's an inflection point

it would be an x intercept on f'(x)

[raw inlet]

this is my question

x -int?

okok basically i move everything down

[ionic jewel]

which one are you doing?

or does it have to do all of them?

[raw inlet]

yea

all of them combined

but its just c) im consufed about

[ionic jewel]

f(x) has inflection points at x=2 and x=5

[raw inlet]

so how my graph looks would be right i assume then if they are inflection points

[ionic jewel]

hmm yeah

assuming the slope is 0 at x=2 then yes

but it looks like it is

[alpine sable]

is anyone here capable of answering a physics question?

based on density

[raw inlet]

ty very much

so im a bit confused 💀