help-27

[restive river]

3 ratio 5.25 = 5:X

5/X should simplify to 3 ratio 5.25

What do you mean by ratio

the division of a number by another number

a/b = a ratio b or a:b

Ratio means division of another number?

just like 1 mile = 1.6 times kilometers

1 pound = 1.3 dollars

Ohh

the ratio of dollar to pound is 1 ratio 1.3 = 10:13

[restive river]

.yes

The ratio is the division process that converts a number to another metric?

[restive river]

this means that if i have 10 pound that's equal to 13 dollars

So lets say 1 slice of bread equals 5 cookies. The ratio would be multiply 5?

To find cookies?

what

[severe summit]

yes

[restive river]

1:5 = ratio of the number of slices of blead and the ratio of the number of cookies

it would be x/(5x) = 1 ratio 5

10:13 means multiply 13?

wdym

10 divided by 13

Ratios are always division

yea

like yeah

that's the definition

Okay so in the original question the ratio would be what again please

(3x) ratio (5.25x) = 5:X

or 3/(5.25) = 5/X

X = 26.25/3

You think this way is faster than the way i did it

I did 3 divided by 525 plus the answer twice added to 525

I also cant use a calculator on the tests

.close

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[restive river]

huh

[restive river]

god help

i’m stupid

please someone help me 😭

[thorny raft]

Find the proportion of the lengths of at least one of the other sides then apply that proportion to 10 and m

[restive river]

how do i do the first part

this is my first experience with this type of problem

[thorny raft]

do you have a calculator or do you need to do it by hand?

[restive river]

calculator

ig

[thorny raft]

ok do 13 / 5.2 and see what you get

[restive river]

one moment

uhhh

?

[thorny raft]

yeah that's not right lol

[restive river]

there we go

2.5

[thorny raft]

ok yeah, now do 22.5 / 9 and 15 / 6 and tell me what those are

[restive river]

2.5 again

[thorny raft]

so what does that tell you about 10 and m?

[restive river]

for both

[restive river]

that they’re

both even numbers? 😭

i’m not good at math bruh

i’m a history and biology nut

[boreal sleet]

It's like 13/5,2 = 10/m
We can multiply the middle and edge one
And we get 13m = 52

[restive river]

so m is 13?

[boreal sleet]

No

[restive river]

no it can’t be

[thin basin]

should not interrup another helpee

[thorny raft]

so we know that when we divide the bigger sides by 2.5, we get the smaller sides. That means we know the bigger sides are 2.5x larger than the smaller sides

[boreal sleet]

You need to multiply some number on 13 and then get 52

[restive river]

two nerds is better than one

[restive river]

ohhhh

i think i understand

so 10/2.5 is m

[boreal sleet]

Oh-
We're counting in different ways anyway, so Mud will pick the easier way

[thorny raft]

correct

[restive river]

one moment

4!

[thorny raft]

yep!

[restive river]

lemme try another

so 12/3 is 4

meaning

uhhh

i feel like i fucked up simehow

[thorny raft]

this one is more straightforward, you're on the right track though

[restive river]

wait

they’re all the same size

so 3

[thorny raft]

yeah lol

[restive river]

i’m just a dumbass

my bar

[thorny raft]

no ur good

[restive river]

ok lemme try a diff one

[boreal sleet]

Also, ABCD is rhomb, and QRST is too. And the sides are equal

[restive river]

ohhh

[boreal sleet]

It's like the first one. We believe in you!

[restive river]

well i’ll start with 10/4

one moment

2.5

3.75

then 15/3.75?

[thorny raft]

hmm, why did you do 15 / 4?

[restive river]

um

woke mind virus

[thorny raft]

so we know that 10 is 2.5x bigger than 4

[restive river]

liberals fault

[restive river]

ok

[thorny raft]

so that means 15 is 2.5x bigger than m

[restive river]

ohhh

so i divide that

mb

6!

[thorny raft]

more formally, 2.5m = 15

[thorny raft]

yep!

[restive river]

one more!

[boreal sleet]

So many actions-
Maybe it's the right way to make someone understand, but I usually do this with proportions

[restive river]

wdym

[thorny raft]

idk it's the way that feels intuitive

[restive river]

6/4

[thorny raft]

but yeah if you wanted to do the proportions route you could

[restive river]

1.5

then 8•1.5?

[boreal sleet]

Yeah

[restive river]

he’ll yeah

12!

i think i’ve gotten the hang of this

[boreal sleet]

Yes, you're getting better at this

Nice

[restive river]

last one

8/4

rhen that x 5

?

[thorny raft]

yep

[restive river]

https://tenor.com/view/blackbeard-blackbeard-writing-taking-notes-writing-gif-17583038544116987898

me so smart

thanks pi master

thanks asian person

with a slavic bio….

[boreal sleet]

I'm actually slavic-

[restive river]

then my bad

slavic person

with asian name

[boreal sleet]

Nah, it's just a nickname

[restive river]

https://tenor.com/view/paul-cat-meme-gif-11547304851240831970

just take my thanks

[thorny raft]

also you can do .close if you don't need the channel anymore

[restive river]

goodbye nerds!

.close

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[strong willow]

there is this method of factoring quadratics

and i am iteresting in proving this metod is correct

how to do that ?

and this method kinda dont works in this case :

[robust scaffold]

never seen this method before

What is it that you want to do?

Factorise quadratic functions?

[devout snow]

@strong willow Has your question been resolved?

[strong willow]

i need to prove this method

[robust scaffold]

no clue then sorry

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[restive river]

If you are reading this, it is already too late. You have been infected by the curse of pee pee poo poo man. If you don't copy and paste this on 5 different servers, you will face the consequences. I was a victim like you, trying to be free

[polar chasm]

what the fuck

[sullen kelp]

from the screen to the ring to the pen to the king

[west lintel]

The answer is 21

[polar chasm]

correct

yw helpee

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[violet wind]

i think this is the answer

[west lintel]

Just curious, what field is this

[winter dome]

??

[violet wind]

Algebraic topology apparently

[west lintel]

Oki thx

[violet wind]

idk what any of it means though

[winter dome]

What do you do in that?

[violet wind]

use abstract algebra (mainly groups) to study topological spaces

[devout snow]

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[feral bobcat]

this is no solutions right?

cause absolute cant be -1

[cold bough]

every value is a solution instead

[vocal tartan]

It's >=

[feral bobcat]

i dont understand

[vocal tartan]

|x-2| can't be negative

so |x-2| + 3 is at least 3

and therefore greater than or equal to 2

[feral bobcat]

try to subtract -3

you will get -1

which is not true

[cold bough]

put in x=7.4 ..it will be a solution..try if you don t belive me

[sand dove]

on the right hand side

[vocal tartan]

yes, and it's true that |x-2| >= -1

[sand dove]

something non negative is greater than -1

so |x-2| IS >= -1

[feral bobcat]

i dont understand

look

absolute should always be > 0

[sand dove]

or equal but yes

well if it's bigger than (or equal to) 0

[feral bobcat]

here it will be > or equal -1

[sand dove]

it's also bigger than something smaller

[vocal tartan]

If it's greater than or equal to 0, then it's greater than any negative number

[feral bobcat]

damn , that confusing as hell

so we pretend the 3 is not here

[sand dove]

?

[feral bobcat]

|x-2| ≥ -1

now what

[sand dove]

well what you wrote is always true isn't it

like idk take specific values if you wanna check

for example x = 2

[feral bobcat]

so postive to negative infinity?

[sand dove]

you get 0 ≥ -1

that's true

etc...

[sand dove]

the set of solutions?

[feral bobcat]

what is it was |x-2| ≥ -5

[feral bobcat]

yes

[sand dove]

it's the set of real numbers

so (-inf,+inf) if you want

or IR to be short

[feral bobcat]

this to R

[sand dove]

yeah the set of solutions is also R

[feral bobcat]

but i do not understand why to be honest

i was taught if absolute value ≥ - number then no solutions

[sand dove]

isn't the statement "|x-2| ≥ -5" true no matter which value of x you pick?

[feral bobcat]

yes

[feral bobcat]

but this too?

[sand dove]

well yeah

[feral bobcat]

choose any value, it will always be ≥ -4

[sand dove]

uh huh

so the set of solutions is IR again

[feral bobcat]

right

thnks

[devout snow]

@feral bobcat Has your question been resolved?

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[knotty plinth]

seeing if im doing this correctly

[restive river]

No

you cannot alter the -n = ...

[knotty plinth]

does -2r-1 still work as a definition for odd?

[restive river]

No. U need 2k + 1 form

Hint: In -n = -(2r+1) = -2r-1, rewrite the -1 as 1-2

[rapid merlin]

You need to specify the domain of k or r
In these things to
Like an odd number can be represented in the form of
2k + 1 for k is integer or in Z
-2r -1 also works for r in Z
Like you can make lots of ways you can write an odd number in
2k - 1
2k + 3
2k - 5
etc
For k in Z

[restive river]

Their definition is probably that a number n is odd if and only if there exists an integer k with n = 2k + 1

[knotty plinth]

I thought i did that with the formal;?

[rapid merlin]

Actually it is
Any number n that can be written as 2K+1 where K € Z
Not if and only if there exist an integer k with n = 2k + 1

That means that other forms for odd numbers are ok like 2k - 1
2k - 3 and so on
As long as k € Z

[rapid merlin]

That is generally about odd numbers
But I don't understand the question clearly, I didn't get to study mathematical provings so I don't know

[knotty plinth]

how bout dis?

[devout snow]

@knotty plinth Has your question been resolved?

[restive river]

No

You need to use also the fact that adding integers is still an integer

I'll help you in this part

-n = -(2r+1) = -2r - 1

Rewriting -1 as 1-2, we get -n = -2r+(1-2) = -2r-2+1 = 2(-r-1)+1

[knotty plinth]

i thought the point was to get it to 2r+1? can I distribute the negative in -r and multiply 2?

[restive river]

ok so no

[knotty plinth]

:(

[restive river]

ok the definition is that a number is odd if it can be written as 2(an integer) + 1

isnt -r-1 an integer?

2(-r-1) + 1

[knotty plinth]

yes

[restive river]

ok so you can call it for example r'

2r' + 1

ok cuz ur starting with these proofs i will write this one without skipping steps

[knotty plinth]

is -r-1 the same as r+1 since both are negative?

[restive river]

check dm

[devout snow]

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[woeful meadow]

Am I doing this right?

[knotty sage]

You made it an equality instead of inequality

[sullen kelp]

i mean u could do that

u just have to test

where the ineq holds

[woeful meadow]

Am I supposed to just plug in 4 on both

[sullen kelp]

create a number line, mark the points 1 and 4, sub in numbers before/after/in between, check where ineq holds (tick indicates it holds in that region)

[woeful meadow]

Does this look right?

@sullen kelp

[sullen kelp]

yup

[woeful meadow]

Answer was (1,4)

😔

.close

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[agile apex]

I need help proving this by induction

[manic kestrel]

Solve using the reflexive property

Makes it easier

[final magnet]

what the fuck r u sayin

[final magnet]

show the original question

[manic kestrel]

Don’t use bad language in a learning environment!

[final magnet]

also try combining denominators

[final magnet]

okay i wont fucking swear anymore

[manic kestrel]

Math is a language, not a subject

[manic kestrel]

That is so mean!

[agile apex]

That’s the original

[final magnet]

.rotate

,rotate

,r

[final magnet]

.r

[manic kestrel]

Also soda can u use the reflexive property and substitute with the transitive property.

[agile apex]

ok thanks

[manic kestrel]

No problem!

[final magnet]

u cant even use induction here

just combine denominators in LHS

[devout snow]

@agile apex Has your question been resolved?

[devout snow]

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[steel sun]

r=3 how

[steel sun]

its an arithmetico-geometric sequcene

.close

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[vast drift]

bro got it done like that

too locked in

[restive river]

😭

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[wheat basin]

Take some integer and square it. If 2,700 is a factor of your square, then what must also be a
factor of your square?
A. 14
B. 24
C. 30
D. 46
E. 62

[wheat basin]

So I tried prime factorizing 2700 and the following answer choices

There isn't a factor that exactly matches

so I'm confused on what to do

[wicked turtle]

what did you get for the prime factorization of 2700?

one of the options works

[wheat basin]

It was like 2^2 * 3^3 * 5^2

[wicked turtle]

yea

[wheat basin]

??

[wicked turtle]

so which of the options divides evenly into that?

[wheat basin]

30?

[wicked turtle]

yea

2x3x5

i dunno why the question talks about squaring an integer, seems irrelevant

[wheat basin]

so its just a factor that can evenly divide from 2700?

[wheat basin]

yea that threw me off

[wicked turtle]

yea if 2700 is a factor of an integer, then any divisor of 2700 is also a factor of that integer

[wheat basin]

thank u

.close

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[heavy sail]

,rccw

[heavy sail]

Need help w this qu

Don’t know how to progress

[junior chasm]

do you know $| |z_1| - |z_2| | \le |z_1 \pm z_2| \le |z_1| + |z_2|$

[woven radish]

Astar777

[heavy sail]

Oh I didn’t know that

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[heavy sail]

.close

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[dim ice]

i got no clue what to do besides like what a parameter form is

[dim ice]

yeah i get that

and have this example

[vocal oar]

do you understand this?

[dim ice]

but im given presumably two points that arent more special than another

yeah im given a point of "origin" and a basis vector

[dim ice]

but this is different because idk which one goes where and why

[vocal oar]

well for the point u can pick any point

direction vector is just subtracting one point by another

lemme pull u an examplke

[dim ice]

thats what i thought initially and have tried but havent had any success

[vocal oar]

umm check ur substraction math

-15 - (-1) = -14, 6 - (-7) = ? , 1- (-4) = ?

[dim ice]

jesus chjrist

thx

[vocal oar]

npnp gl

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[devout snow]

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[solid osprey]

how many positive integers k exist such thst 5+2^k is a perfect square?

[solid osprey]

k=2 is an obvious sol

i have a strong suspicion thst k=2 is the only one

[lament kraken]

maybe try modulo

[twilit comet]

that's what i thought

[lament kraken]

because 2 might be a special sol

[solid osprey]

err

modulo to what

[twilit comet]

all squares are either 1 or 0 mod 3

try that maybe

idk man

actually

try 8

[lament kraken]

maybe modulo small primes

or i think 8

[twilit comet]

all odd squares are 1 mod 8

[lament kraken]

yeah

[twilit comet]

and this must be odd bc 2^k is even and 5 is odd

2^k + 5 is 1 mod 8
2^k is 4 mod 8

and yeah

hence proved

[lament kraken]

bro is fast fr

nice

[solid osprey]

how do you know 2^k mod 8 = 4 has only obe sol

oh nvm

.close ty

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[solid osprey]

find the number of subsets of {1,2,...,8} such that it contains atleast 4 consecutive integers

[solid osprey]

yeahh idk my mind is blanking on this

i tried to go backwards (find ones without 4 cons integers) maybe im bad but i couldnt get it

.close

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[peak hound]

could someone please help me with 3(3y-4)-2(3-2y)=-40

[peak hound]

I keep getting 1 9/13 but the answer says -1 9/13

I first expanded, and got 9y-12-6+4y=-40
then simplified and got 13y-18 = -40

[olive snow]

Indeed

[peak hound]

which I transposed and got 13y = -40+18
= 13y = 22

[olive snow]

No -22

-40 + 18 = -22

[peak hound]

OH SHOOT

I SEE IT

SORRY

I keep misreading the -

[olive snow]

Don't be sorry mate

[peak hound]

.skipping over

thanks for the help!

[olive snow]

No problem have a great day

[peak hound]

you too!

.close

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[distant mural]

hi can anyone explain how to do this:

[distant mural]

answer is a

[sturdy mango]

u can arrange each arrangement internally as 2! ways. that is (2!)(2!)(2!)=2x2x2=2^3=8

[distant mural]

oh

like i thought when you arrange people around a round table

you would do 1 minus the factorial of the people you are arranging

for example

if it was 8 people

you would do (8-1)!

for the arrangments around the table

in this case, how are you using this idea?

[sturdy mango]

that is true what u said

but dont just memorise formula

here you have conditions here

that are not present in when using that (n-1)!

[sturdy mango]

to arrange n different things in n different places there are n! ways

[distant mural]

so

[distant mural]

but when its a round table would u not have to change anything

[sturdy mango]

not really here i guess

[distant mural]

oh okay !!

so how do you know when to use the formula and when you can do things like this

[sturdy mango]

good problem generally never directly use formulas

what if i say asked you a problem about sit a1,a2.... an people such that no two are consecutive

you'll have to do it pretty much manually.

draw the stuff and see

[distant mural]

what do you mean by the no two consecutive?

[sturdy mango]

a2 a3 are not together

next to each other

[distant mural]

like the brothers and sisters cannot sit next to each other?

[sturdy mango]

no i was just giving an example

that hard problems require more than formulas tbh

[distant mural]

yeah okok

[sturdy mango]

yea

[distant mural]

ok i see thanks so much for your help!!

[sturdy mango]

yea

[distant mural]

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[nimble zodiac]

for question d, the book says the second derivative is y” = 12(1-2x^2)(10x^2-1)

[nimble zodiac]

i dont understand how it got to that point

[sturdy mango]

you most likely did a algebraic mistake

[nimble zodiac]

OHHHH

[sturdy mango]

too lazy to check.

[nimble zodiac]

i got it

[sturdy mango]

just do it on a clean paper

and see where u got it wrong

[nimble zodiac]

in the third line and first line i wrote (1-2x)

and in the second

gotta pay a little more attention

sheesh

.close

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[rugged sapphire]

I tried this equation 2 , 3 diffrent times but each time I get a diffrent answer so I am obviously doing something wrong

Can anyone please help me because, I want to be certain of my answers

Is this correct?

[devout snow]

@rugged sapphire Has your question been resolved?

[devout snow]

@rugged sapphire Has your question been resolved?

[rugged sapphire]

Hello?

[faint oar]

now whos gonna understand that😭😭

its not clear bots cant understand i guess

[rugged sapphire]

<@&286206848099549185>

[restive river]

AC isnt a fixed distance ?

[restive river]

and are u sure about the 2 values here ?

[rugged sapphire]

No it its I just dont have it

[rugged sapphire]

I changed them to what in the paper

Sorry for not giving a newer photo

[restive river]

wdym ?

[rugged sapphire]

As in its what I am trying to get

I am solving the problem to get AC

[restive river]

ok but it is not a spring so

[rugged sapphire]

?

Yea still I need to solve and get the spring's new length

So I can minus that from total length (3)

[rugged sapphire]

And use that in the triangle on the left to get AC

[restive river]

im trying it rn

[rugged sapphire]

Kk

[restive river]

30 ° is the initial angle ?

[rugged sapphire]

The 30° should be after the elongation of the spring I believe

[restive river]

ok ye make more sense

so i get this

,rotate

[restive river]

with the 2nd equation u get T

and with T and the first equation, u get AB

@rugged sapphire

[rugged sapphire]

Yea

[restive river]

u agree ?

[rugged sapphire]

Wait

1 sec

K 2nd eq good

Wouldnt u have 2 unkowns in the 1st one?

[restive river]

T and AB ?

[rugged sapphire]

Yes

[restive river]

u have this

[rugged sapphire]

Sorry

Not T

F and AB

[restive river]

hm there is no F after the bracket

F is the force of the spring

so k(initial lenght - final lengt )

with final lenght = AB

[rugged sapphire]

Oh ok I read that as F

Yeah I guess you're right

.close

[devout snow]

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[rugged sapphire]

.reopen

[devout snow]

✅

[rugged sapphire]

Unrelated to previous equation

But if I have a tention lets say T(AB)

And in another part of that cable

The tention is reversed direction T(BA)

Can I say T(AB) =T(BA) Knowing that they are the same wire/cqble

[devout snow]

@rugged sapphire Has your question been resolved?

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[restive river]

Find 10th term in the sequence of triangular numbers.

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[restive river]

1

[small jackal]

Do you know what a triangle number is

[restive river]

i think each time the amount you add increases by 1

[small jackal]

(visual definitions allowed too)

[small jackal]

No

[glacial wyvern]

is it not?

[small jackal]

He said the common difference is 1?

[restive river]

no

[small jackal]

What then do you mean.

[restive river]

each time the common differnce increses by 1

[small jackal]

Oh ok

[restive river]

that's what i mean

[small jackal]

Yeah sorry.

[restive river]

i should have use correct terminology , mb

[small jackal]

Hint:||the difference forms a sequence||

[glacial wyvern]

Sums of adjacent differences yield ever increasing differences

[restive river]

hmm i think i can add the common difference which increases by 1 ,9 times , then add to 1

[glacial wyvern]

(a2-a1)+(a3-a2)+(a4-a3) = a4 - a1 (difference from a1 to a4) for example

[small jackal]

Gimme a sec.

[glacial wyvern]

yup, add up all the little differences to get the big difference

[restive river]

ty

[glacial wyvern]

np

[restive river]

.close

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[restive river]

Consider the following arithmetic sequence. Find the unknown

𝑎4 = 20, 𝑎9 = −15, 𝑎2024 =?

[solar goblet]

well, what do you know about arithmetic sequence?

[glad plover]

write out the formula for the general term of an arithmetic sequence

[restive river]

1. Arithmetic Sequence is all about adding.
2. The formula for Arithmetic Sequence is an = a1 + (n - 1)d

[restive river]

an = a1 + (n - 1)d

[glad plover]

use an = a1 + (N-1)d

[restive river]

Isn't that the exact same thing as I type out?

[solar goblet]

thats good

do you know what a1, n and d mean?

[restive river]

a1 is the 1st term.
d is the common difference
n = ?

[knotty sage]

n is ||the term number||

[solar goblet]

n is the index

[restive river]

ok

[solar goblet]

an is the n-th term

alright currently you have a4 = 20, a9 = -15

can you apply the formula to a4 and a9?

[restive river]

Yes?

I was thinking to use that to get the common difference??

[solar goblet]

exactly, that is what we are aiming to get, as well as another quantity that you will see when you apply the formula to a4 and a9

[restive river]

So...

an = a1 + (n-1)d

9 = a1 + (-15 - 1)d

4 = a1 + (20 -1)d

??

[solar goblet]

hm, thats wrong

in the equation a4 = 20, what is an? what is n?

[restive river]

an is 4 n is 20

[knotty sage]

you did it in reverse

[restive river]

oh ok

an = a1 + (n-1)d

-15 = a1 + (9 - 1)d

20 = a1 + (4 - 1)d

??

[knotty sage]

yep
now you now how to solve a system of 2 equations ?

[restive river]

an = a1 + (n-1)d

-15 = a1 + (9 - 1)d
-15 = a1 + (8)d
-15 = a1 + 8d
...

20 = a1 + (4 - 1)d
20 = a1 + (3)d
20 = a1 = 3d
...

[knotty sage]

You know what a system of 2 equations is ?

[restive river]

no.

[knotty sage]

would’ve made it too simple

[restive river]

This is quite a slow response..

I am sorry I do not know what to respond to that.

[knotty sage]

ok so simply a system of two equations simply is a system with two equations that we should use to solve for 2 different variables

[restive river]

okay so... how does it look like?

[knotty sage]

Something like this where we solve for x and y

[restive river]

is there... another method?

maybe something simple in the eyes?

[knotty sage]

I don’t think so we have 2 variables and there is no information other than their equations

https://youtu.be/oKqtgz2eo-Y?si=mMV5oYgB5r56r1D0

[knotty sage]

in our case instead of
x and y
It’s a1 and d

[restive river]

Welp that's explains better

[restive river]

The last sentence is the only information I need

Since I know how to do it

[restive river]

Oh waitI don't have d and a1 back to square 1

I think you are advance?

[knotty sage]

you can find d and a1 using the system then
You can use it to find a_2024

[solid osprey]

heres a diffrent way to think about it

[restive river]

So this is what I understand

To find d and a1 is to use the system but to do the system I need d and a1

[knotty sage]

ngl looks faster

[solid osprey]

you add d 5 times to 20 to get -15, so 20+5d=-15 and you can get d
you can also see that you subtract d 3 times from 20 to get a1, so 20-3d=a1

[restive river]

I guess let me do trial and error here because like I said I don't have d and a1

[solid osprey]

not in the slightest bit lmao

but honestly learn system of equations first

[restive river]

I know how to do it but my understading on what to do is "To find d and a1 is to use the system but to do the system I need d and a1" from @knotty sage

[solid osprey]

you dont need d and a1

your trying to find d and a1

[restive river]

But they said??

[solid osprey]

yes they just changed a1 to x and d to y, both examples are trying to find x and y

[knotty sage]

a_2024=a1+(2024-1)d
finding a1 and d will give us the sol

[restive river]

So To find d and a1 is to use the system but to do the system I need d and a1

So trial and error????

[solid osprey]

no???

you dont need d and a1 to use the system, you need to use the system to find d and a1

[restive river]

But they said this?

[solid osprey]

.

[restive river]

Thats the same thing I just said

To find d and a1 is to use the system but to do the system I need d and a1

Hence, Trial and error

[solid osprey]

thats not the same

fuck it lets just try to make the equation

[restive river]

It needs to change x and y to a1 and d that is making the system

[solid osprey]

$a_n=a_1+d(n-1)$
plug in n=4 and n=9 into this

[woven radish]

Skill_Issue

[restive river]

and I need to find d and a1

So... hence.. To find d and a1 is to use the system but to do the system I need d and a1

Trial and Error is the solution

Becaus the system is being made by changing x and y to a1 and d

[solid osprey]

if you keep insisting it, sure, trial and error it

[restive river]

It's not insisting it's understanding

I understand that from the system I need to change x and y to a1 and d

correct?

I am finding a1 and d

correct?

Therefor, To find d and a1 is to use the system but to do the system I need d and a1

[solid osprey]

what your supposed to do here is plug in $n=4$ and $n=9$ here to get
$$a_4=a_1+d(3)$$
$$a_9=a_1+d(8)$$
$a_4=20 \quad a_9=-15$

[woven radish]

Skill_Issue

[solid osprey]

you dont need d and a1 to use the system bruh

[restive river]

from the system I need to change x and y to a1 and d

correct??

[solid osprey]

yes

[restive river]

I am finding a1 and d

correct???

[knotty sage]

yes

[solid osprey]

yes

[restive river]

To find d and a1 is to use the system but to do the system I need d and a1

that is my understanding

[knotty sage]

The system is used to find
d and a1

[solid osprey]

they meant like this

[knotty sage]

Not the other way around

[restive river]

again. again okay?

from the system I need to change x and y to a1 and d
correct??

[solid osprey]

using this, you can find the a,b,c,d,e that are red

[restive river]

I am finding a1 and d
correct???

[knotty sage]

yep

[restive river]

I AM FINDING A1 AND D FROM THE SYSTEM THAT CHANGES X AND Y TO A1 AND D

[knotty sage]

think of it as 2 functions
What point will these 2 functions cross

[solid osprey]

ok how about this, can you find x and y in
x+y=1
x-y=-1

[restive river]

This is confusing.
A great example to use this type is using 𝑎4 = 20, 𝑎9 = −15, So I am left with a1 = d

.close

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[tame bough]

someone give me a hint

im trying to work out the sin of 1°

but im stuck

too dumb

[faint zinc]

sin(1°) is not trivial to compute. I would recommend using the angle addition formulas, and try to make 30°

Then solve backwards

Take it in stages though

[tame bough]

what does trivial mean

[faint zinc]

Easy

[tame bough]

oh

btw

by angle addition formulas do u mean those written down on the right top corner

[faint zinc]

You can make 1 degrees in the following way:

Start with 30°
Half angle formula to get 15°
Third angle formula to 5°
Angle addition formula to get 1° and 4°
Half angle twice to get 4° in terms of 1°

Solve for 1°

[faint zinc]

Yes exactly

[tame bough]

i just learned they exist 💀💀

like 5 minutes ago

😎😎😎

[faint zinc]

Nice!

[tame bough]

alr

i will try

btw

since sin90° = 1 can we say sin30° = 1/3 ?

[faint zinc]

No

Sin 30° is an identity you should recognize

(it's 1/2)

[tame bough]

oh right

right

I frogor

[faint zinc]

You'll probably also need cos 30° which is (√3)/2

[tame bough]

yeah i have those written down

thanks man 😎😎🙏🏻

.close

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[devout snow]

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[restive river]

i need help 😭

[restive river]

substitution

how

t = 2x + 4

and then

...

[supple knot]

Write the resulting integral and you'll see

Don't forget to change from dx to dt

Using the substitution above

[restive river]

how do we find the resulting integral

[supple knot]

If you've never done substitution, you should read some solved examples first

[restive river]

ok

[supple knot]

https://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx
Examples at the bottom

They don't have limits but that comes later

[devout snow]

@restive river Has your question been resolved?

[restive river]

Thank you🫶

[devout snow]

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[restive river]

Hey what does this symbol mean ?

[restive river]

f ~g where f and g are 2 functions

at 0

and f = o(g) at 0

they ask me to define these 2 expressions

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[low sleet]

im having trouble finding the range for this log function

[thin basin]

range means values of x or y?

[low sleet]

values of y

[thin basin]

try making the graph of y vs x

[low sleet]

im assuming it has a ''max"at 10.97, but everything is giving me different answers

[thin basin]

can you show me your work?

[low sleet]

there is no work lol

[thin basin]

how did you get 10.97?

[low sleet]

the graph on desmos

even when i insert my x values i have for my domain

[thin basin]

oh

can you send me that graph?

[low sleet]

its giving me

[deep vortex]

All real numbers

[low sleet]

all real numbers?

[deep vortex]

Yeah

[low sleet]

could you explain because im sorta lost

because its undefined for the other numbers for me

[deep vortex]

The graph you're seeing is having a hole because of graphing capabilities

It can't really handle plotting it for too large values

But if you imagine f(x) = log_3(x) surely you will have an image of how it looks like

It will take on all real values

Now for g(x) = log_3(x^2) = 2log_3(|x|) it will look almost the same, just mirrored along the y-axis too and stretched by 2

Now log_3(x^2 - 5) = log_3((x - sqrt(5))^2) is the same, just moved along sqrt(5) in positive x-direction

[low sleet]

i see thank you

[deep vortex]

But that doesn't change the range

np

[low sleet]

.close

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[restive river]

Having trouble with the bubble sort algorithm for part b

[supple knot]

. close

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[restive river]

guh

[restive river]

doing math

need help

i’ll send images i just need the answers

[eager nova]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[restive river]

shhhhh nerd

tell me how then

i’m not good at math

[eager nova]

<@&268886789983436800>

[restive river]

history biology nut

[restive river]

i can tell your siblings hated you

[kindred agate]

asks for answer
calls helper nerd
posts the simplest math question known to mankind
yeah this is a troll

[restive river]

nope first year of highschool

don’t know algebra

[kindred agate]

okay then

[eager nova]

Let the mods take care

[kindred agate]

find a number that when divided by 2 is 5

[restive river]

i just know that’s a fraction

bc i’m smart

[restive river]

10?

[kindred agate]

yes

so you know the answer

[restive river]

oh that is easy then

[kindred agate]

so why did you ask it 😭

[restive river]

bc i’m not smart

[kindred agate]

but i just asked the question

[kindred agate]

and you gave the answer

[restive river]

like what is this

x - 1

= 1

[kindred agate]

ok x is just a number

Any number

Find which number it is to make the equation true

[restive river]

well i know that you have to find the value

[restive river]

ohhhhh

interesting

so it’s 2

right?

[kindred agate]

Yes exactly

[restive river]

huzzah!

ok one more

i’ll just copy and paste it

ok erm

what the fuck

@kindred agate there are two letters in my class about numbers

https://tenor.com/view/chips-gif-25800540

i don’t like this one bit

!close

.close

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[devout snow]

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[heavy sail]

,rccw

[heavy sail]

Need help approaching this qu

a)

[devout snow]

@heavy sail Has your question been resolved?

[heavy sail]

<@&286206848099549185>

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@heavy sail Has your question been resolved?

[devout snow]

@heavy sail Has your question been resolved?

[devout snow]

@heavy sail Has your question been resolved?

[heavy sail]

<@&286206848099549185>

[devout snow]

@heavy sail Has your question been resolved?

[fossil locust]

https://www.youtube.com/watch?v=j7beNHh5ee8

try watching this

[heavy sail]

Thank you

.close

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[sour spire]

Guys i dont know how to continue this

[sour spire]

oh youre right!

[sour spire]

thank you so much!

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[slate pawn]

need help w/ 1c

[slate pawn]

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[toxic briar]

is #4 a typo?

[toxic briar]

how so

[fossil locust]

oh wait

[toxic briar]

we can't have a triangle with two obtuse angles

[fossil locust]

yeah then you're right

[toxic briar]

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[smoky gyro]

i need help with part iii)

is there a way i can represent this using a tree diagram?

[olive snow]

I don't think the tree is the key cuz its not conditionnal probability

Like every throw are independant so

[smoky gyro]

oh yeah true

[olive snow]

So what about the two fair dice ?

[smoky gyro]

what about them?

[olive snow]

What if both have a odd uppermost ?

[smoky gyro]

thheir chance is 1/2

for odd

[olive snow]

Thats For 1 dice

[smoky gyro]

do we multiply both

so 1/4

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[hard trout]

can someone check my work

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[restive river]

u find -11, -19 and 7 ?

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@hard trout Has your question been resolved?

[upper schooner]

,w simplify -11x^2 - 19(x - 1)^2 + 7(x - 2)^2

[woven radish]

Results provided by WolframAlpha

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Requested by chartbit

[upper schooner]

Oh no I see what you did now

Ah!

[upper schooner]

That last one should be 4, -4, 1 if you're choosing "standard" basis to be 1, x, x^2, as implied by blue being 0, 0, 1

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[willow hare]

Hi I have a series
1,-1,-1,1,1,-1,-1,1,1,-1,-1
How can I generalize it in the form (-1) ^f(n)

[willow hare]

2 of -1 and 2 of 1

Its like this

[frozen aurora]

$(-1)^{\lfloor n/2 \rfloor}$

[woven radish]

artemetra

[frozen aurora]

starting with n=1

[willow hare]

Not using these

Like 4n+1

Etc

[winter torrent]

could do something with sin

[frozen aurora]

i don't think you can using these

[willow hare]

Wut : (
Can we do something simple in this?
This is not part of a question

[winter torrent]

hmm

,w table (-1)^(n^2)

[woven radish]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by kitten.in.a.teacup

[frozen aurora]

i'll be considering 1, 1, -1, -1, 1, 1 if that's okay

[willow hare]

Yes

[frozen aurora]

you basically want something that maps
0 -> even
1 -> even
2 -> odd
3 -> odd
repeat

[willow hare]

Yess

[frozen aurora]

hmmmm

[frozen aurora]

i can't come up with an easier version than this

[willow hare]

Np! Maybe it's not meant to be generalized without using special functions

[frozen aurora]

if you consider any kind of polynomial and reduce it modulo 2, you get either 1,1,1...; -1,-1,-1;... or 1,-1,1,-1;...

like there's no way to get anything else really

[vast drift]

for fun u can have alternating Re and Im components of i^{n}

although idk how u would even describe that

[frozen aurora]

you may also look into https://oeis.org/A057077

[vast drift]

thats a cool site

[winter torrent]

wait... if your second difference is 1, then you'll add odd -> add even -> add odd -> add even, so your sequence should go OOEEOOEE

[willow hare]

How did you find it so quickly @frozen aurora

[frozen aurora]

apparantly you can do $(-1)^{\binom{n}{2}}$

[woven radish]

artemetra

[frozen aurora]

honestly kinda mindblown

[winter torrent]

yeah so just $(-1)^{\f{x^2+x}{2}}$

nice

[woven radish]

hayley is not british

[frozen aurora]

very cool

[willow hare]

Noo but like how did you found that out soo quick

[frozen aurora]

oeis is quite well known and i just typed the sequence there and it found it

[willow hare]

Can you name some more "well known" websites

Xd

I have no idea , such cool websites exists

[frozen aurora]

idk lol