help-0

[pallid scarab]

Remember what $a² - b² = ...$

[ocean seal]

rafilou2003

[raven girder]

not sure

I only know a formula for (a-b)^2

oh wait

(a+b)(a-b)

[pallid scarab]

Yes

[raven girder]

3rd formula

(I always google these feels bad)

[pallid scarab]

Apply to this

1-x² = ...

[raven girder]

then I end up with

[ocean seal]

madmike

[pallid scarab]

What?

Let's do this step by step

[raven girder]

(1-x)^2 cancels out

wait

I did a mistake

[pallid scarab]

Yes

[raven girder]

it's + not -

[pallid scarab]

Not just + either

[raven girder]

ok sec

[pallid scarab]

What is 1-x²? You didn't reply

[raven girder]

(1+x^2)(1-x^2) ?

oh

(1+x)(1-x)

[pallid scarab]

This

[raven girder]

I see oops

so then (1-x) / (1+x)

[pallid scarab]

Yes

[raven girder]

and now I can insert x=1

0 / 2 = 0

[pallid scarab]

Yes

[raven girder]

Thanks 😄

Would you recommend to learn the binomial formulas? I always look them up

despite knowing them since high school

I can't memorize formulas well

[pallid scarab]

At least know (a+b)^n and a^n - b^n for n = 2

Bare minimum

[raven girder]

Alright

[pallid scarab]

If you want to learn :

$(a+b)^n = \sum_{k=0}^n\binom{n}{k}a^kb^{n-k}$

[ocean seal]

rafilou2003

[pallid scarab]

And $a^n-b^n = (a-b)\sum_{k=0}^{n-1}a^kb^{n-k-1}$

[ocean seal]

rafilou2003

[raven girder]

do you actually have this in your head?

[pallid scarab]

Yes

The second one is easy to remember with this trick

It's just a sum of terms, many of which cancel out with the previous/the next one

[raven girder]

ok^^

$x^2+x-12 = (x-3)(...)$

[ocean seal]

madmike

[raven girder]

Is this possible?

yes it is

$x^2+x-12 = (x-3)(x+4)$

[ocean seal]

madmike

[raven girder]

I just did this with experimentation lol

Is there any trick to figure out stuff like that?

Seems useful to pull out the denominator if it would result in dividing by 0

which is often a sum

[pallid scarab]

Giving an example

If you have x² + ax + b

And you find that k² + ak + b = 0 for some k

Then you will be able to write x²+ax+b = (x-k)(...)

Here for the generalized theorem :

https://en.m.wikipedia.org/wiki/Polynomial_remainder_theorem

[raven girder]

so in my case k=3

but I was looking for the (x+4)

see the exercise was

[ocean seal]

madmike

[raven girder]

3-3 would divide by 0 so I tried factoring out (x-3)/(x-3)

now I had to find the (x+4)

is there a trick for that?

or am I misunderstanding

I guess what you said means that this is possible at all

but not a recipe to find the other factor

which is probably some binomial formula again right

[pallid scarab]

I'm just saying that if $a$ is a root of a polynomial $f(x)$, then $f(x) = (x-a)g(x)$ where g(x) is a polynomial of smaller degree

[ocean seal]

rafilou2003

[pallid scarab]

Here, x²+x-12 = (x-3)(ax+b), because it has to be of degree 1 + 1 = 2

Because of the coefficient in x², a = 1

Because of the constant, b = +4

Another example :

[raven girder]

so it's (ax+b) but only if the highest degree x is x^2 ?

[pallid scarab]

Yes

If the highest degree were x³, then it's (ax²+bx + c)

Another example to check if you understood :

x² + 10x + 9

You can check that (-1)² -10 + 9 = 0, so -1 is a root of x²+10x+9

From what we said, we can factor : x² + 10x + 9 = ...

Try it

[raven girder]

sec

ah you already have k=-1

and now

ax+b

which means

(x-1)(10x+9) ?

Sorry not sure if I understood

[pallid scarab]

We have a few problems with your factorization

1. we subtract the root from x. So (x- (-1)) (...) = (x+1)(...)

[raven girder]

ahh

[pallid scarab]

Then, we write x² + 10x + 9 = (x+1)(ax+b)

What's the coefficient in x²?

[raven girder]

1

[pallid scarab]

So a =?

[raven girder]

1

[pallid scarab]

Yes

[raven girder]

oh sorry I thought it's x^2 + ax + b

[pallid scarab]

No prob

Then, the constant coefficient is?

[raven girder]

9

[pallid scarab]

So the value of b?

[raven girder]

9

(x+1)(x+9)

[pallid scarab]

Yes, but be careful, b will not always be equal to the constant

Let's take another example

[raven girder]

ok

[pallid scarab]

x² - 5x + 6

2 is a root

So we write x²-5x+6 = (x-2)(ax+b)

What's the term in x²?

[raven girder]

you mean 1?

[pallid scarab]

Yes

So a = ?

[raven girder]

1

and I'd think b=6

[pallid scarab]

Let's see why b is not equal to 6

[raven girder]

😄

[pallid scarab]

How do you compute the constant term from (x-2)(x+b)

Just from this expression

[raven girder]

not sure what you mean, should I expand it?

[pallid scarab]

Yes

[raven girder]

x^2 + bx -2x -2b

[pallid scarab]

So what's the constant term?

[raven girder]

-2b ?

[pallid scarab]

Yes!

[pallid scarab]

But it's also 6

So b = ?

[raven girder]

-12 ?

[pallid scarab]

-2b = 6

[raven girder]

oh

-3

[pallid scarab]

Yes!

[raven girder]

so I can't actually use this trick

this will trip me up lol

or actually

I find the root k

and then I write (x-k)(x+b), expand it and then figure out the actual b I guess?

[pallid scarab]

Yes

[raven girder]

Thanks a lot

I will write this down and it'll help me in the future

they should teach this in school lol

[pallid scarab]

Always remember that a is the x² coefficient, so don't forget it

For example, 2x² - 3x + 1 = (x-1)(2x-1)

[lone heart]

@raven girder Has your question been resolved?

[lone heart]

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[finite vortex]

the train can go in both directions it must take block a and place it in block b's position and vice versa and the train cant perform a U turn and the train should go back to its original position and both block a and block B can't pass through the tunnel but only the train can pass

[lone heart]

@finite vortex Has your question been resolved?

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[gentle prism]

Angles are a measurement of rotation about a point. Are two coterminal angles the same rotation? Explain your answer.

[nimble fern]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[gentle prism]

4

[nimble fern]

!Show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[gentle prism]

I said Two Coterminal angles are not the same rotation because one rotates clockwise and the other rotates counterclockwise so the rotation is different

I don't think its correct

[nimble fern]

Do you have definition for "rotation"?

[gentle prism]

no

Its referencing this

Not specifically this

[nimble fern]

,rotate

[nimble fern]

hmmm

[gentle prism]

someone on brainly says
Coterminal angles are two or more angles that have their initial and terminal sides in the same positions. However, the angle measures differ either because: One angle is measured clockwise and the other is measured counterclockwise. The angles' terminal sides completed different complete rotations.

[nimble fern]

2 things

1. supplementary angles at a point

2. rotations for more than one whole circle

[gentle prism]

ok

[nimble fern]

first one, that's what you explains

[gentle prism]

right

[nimble fern]

second one, consider 30° and 390°

they looks the same, but one rotate way more than the other

[gentle prism]

mhm

[nimble fern]

does that answer your question?

[gentle prism]

I guess, how would I write it out though

[nimble fern]

that will be an English problem lol

and I am not that good in English

[gentle prism]

ok. I think I can do it

.close

[lone heart]

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[candid sparrow]

does anyone know how to do algebra 2 w statistics

[ivory pendant]

I am here first g

Take another channel

[ivory pendant]

Stuck

[lone heart]

@ivory pendant Has your question been resolved?

[lone heart]

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[fickle lotus]

can someone please help me?

i got v=7.59

[viral oracle]

what's 6m

[fickle lotus]

i got this but i dont understand where the 90 came from

[viral oracle]

bruh mane

that's a rectangle

that's why 90 degree

[fickle lotus]

idk

its from the answer key

[viral oracle]

let h be point on cd such that ch = 4

abch is a rectangle

angle hab is 90

[fickle lotus]

so it should be like wl?

[viral oracle]

what

[fickle lotus]

like length times width?

[viral oracle]

you need to find the angle

[fickle lotus]

angle is 90

so its 90 + 7.6 = 97.6?

[viral oracle]

yes

[fickle lotus]

ah ok thanks

.close

[lone heart]

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[prisma badger]

.reopen

[lone heart]

✅

[prisma badger]

.close

[lone heart]

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[chrome field]

hi

[chrome field]

i have a question

im only 13 years old so its maybe very simple to you

is this good?

[lone heart]

@chrome field Has your question been resolved?

[alpine sable]

At step 3 you made a mistake

You made the second fraction negative

[chrome field]

then what should i do ?

@alpine sable

[alpine sable]

A negative exponent moves it to the denominator

[chrome field]

k

[alpine sable]

$x^{-1} = \dfrac{1}{x}$

[ocean seal]

CWolf

[chrome field]

ohh ok

[alpine sable]

so you should switch the entire thing around

$\dfrac{1}{a^2} = a^{-2}$

[ocean seal]

CWolf

[alpine sable]

$(a^{-2})^{-1} = a^2$

[ocean seal]

CWolf

[chrome field]

i dont learn that rn in class

but tysm

[alpine sable]

Np 🙂

[lone heart]

@chrome field Has your question been resolved?

[lone heart]

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[quartz mango]

How do i substitute or transitive?

[zenith cypress]

easy

you have x

[quartz mango]

Yes...?

[zenith cypress]

you just plug x in the second equation

that's substitution

[quartz mango]

So x - 6y = 4?

[zenith cypress]

no i mean you have x= 3y +2

[quartz mango]

Oh

[zenith cypress]

you plug that in the second equation

so you replace x with ...

[quartz mango]

So then it'll become a systems of equations?

Then I can solve it

[quartz mango]

2?

[zenith cypress]

it is already a system of equations

[quartz mango]

Oh

[zenith cypress]

no because x is not 2 it's 3y +2

[quartz mango]

Oh ok

I think I can solve it

I'll try

[zenith cypress]

of course you can

you're smart

bye

[quartz mango]

Am I though?

Bye

.close

[lone heart]

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[spare fern]

.close

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[mellow ore]

is this correct? Idk how continue

[worn fox]

what the original statement of the question?

[mellow ore]

just calculate the double integral

[worn fox]

maybe you wanna try swapping the order of integration

[mellow ore]

I knew it could be done when it is a rectangle

idk how to do that

[worn fox]

try drawing the region of integration

[lone heart]

@mellow ore Has your question been resolved?

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[alpine sable]

Help

[fierce prairie]

I recommend you make a new channel

it’s gonna be deleted cuz you deleted the message

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[outer steppe]

If a bacteria population doubles in 5 days; when will it be 16 times as large & when was it 1/4 of its present population?

[alpine sable]

Okay so if every 5 days it doubles lets say you start with one, its been 5 days so it doubles so 2, you continue this until you reach 16 times, do you understand?

and just times the days into that

@outer steppe

[outer steppe]

Yes, but how would I write this as an exponential equation?

[alpine sable]

hold on a second

for the x-axis i would write days, and for y do bacteria for the math part on x do it in 5's and show it doubling every 5 days

if you dont get it I can see if I can write it out

[outer steppe]

Thanks but I'm not graphing it, I mean like this

r is the rate in that question

[alpine sable]

I'm not 100% sure then

[outer steppe]

Okay, thanks though

[outer steppe]

So an x=y^2 graph?

[alpine sable]

sounds reasonable

[outer steppe]

Okay, from the way I'm solving it, I did this

Thanks I got it now

[alpine sable]

well I hope its right!

[outer steppe]

Bye ty

.close

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[shut parcel]

Anyone know how to solve this question? Literally stuck

[shut parcel]

I tried solving it by this way: 500 + 1500 = 2,000 and then 20,000 + 1500 = 21,500

21,500 - 2,000 = $19,500

But I know it’s wrong since it’s not in one of the options lmao

[mellow zodiac]

i can't read what is on the screen

[shut parcel]

@mellow zodiac What does the pic look like for you

[mellow zodiac]

it's too small try getting a better pic

unreadable basically

[shut parcel]

What about now

Have you tried zooming in? @mellow zodiac

[last ether]

Find the required reserve ratio

It has no excess reserves

The cash I'm assuming is the reserves

[slate monolith]

@last etheryou also took econ?

[last ether]

I'm taking AP macro rn

Lol

[shut parcel]

Target reserve ratio = Target reserves/Total deposits… but I’m unsure if if I should add the 1500 to the cash and deposits (which I think is correct)

[last ether]

The reserve ratio is always (requires reserves)/(deposit)

[last ether]

No don't add 1500 yet

You need to find the reserve ratio first

[shut parcel]

Target reserve ratio = 500/20,000*100% which is 2.5%

[last ether]

Yeah

So when they deceive a deposit of 1500, how much is in the excess reserve?

[shut parcel]

Does excess reserves refer to the cash or the deposits

Cash: 500+1500 = $2,000 and Deposits: 20,000 + 1500 = $21,500. So then, Target Reserves = Actual Reserves - Excess Reserves

[last ether]

Cash is total reserves

Gotta eat I'll brb

[shut parcel]

I don’t think I have the formula for Total reserves

[last ether]

There's only two types of reserves

[shut parcel]

Take your time!😊

[last ether]

Required and excess

From the get go, you have 500 in required and 0 in excess

You don't need the formulas, you just need to understand the concepts and components. Not everything will be formulaic

[shut parcel]

I hope I’ll understand when you get back😭

[shut parcel]

2,000/21,500 = 9.3%

[shut parcel]

No wonder you’re a pro at Econ😭

[shut parcel]

Actual Reserves = Reserve ratio x Deposits. So, Actual Reserves = 0.025*20,000. Thus, Actual Reserves = $500. Is this correct

[shut parcel]

Total reserves = Cash + Deposits

I think the final answer is 1,500 lmao

I was overthinking and thought I had to solve the question

[last ether]

That's definitely not right

[last ether]

No this is way, way too small

It would also make no sense

If your reserve rate is 2.5%, how can a deposit of 1500 result in 1500 in maximum total loan returns? That doesn't even make any sense

You started, before the depsoit, with:

500 in Required ; 0 in Excess

Find how much is in the Required and Excess after the 1500 deposit

[lone heart]

@shut parcel Has your question been resolved?

[last ether]

_ _

[shut parcel]

Target reserve ratio = 2,000/21,500 x 100%. Target reserve ratio = 9.30%. Actual reserves = reserve ratio x deposits. So, Actual reserves = 0.093…. x 21,500. Thus, actual reserves = $186.05. Excess reserves = Actual reserves- target reserves. Excess reserves = 186.05 - ?

[shut parcel]

I have no idea if I’m doing it right

[last ether]

Where is the 2000 coming from

The ratio stays the same

You found it was 2.5%

[shut parcel]

500+1500

[last ether]

Doesn't work like that

The "cash" is total reserves

[shut parcel]

Oh so, we don’t add the deposits to cash

[last ether]

Total reserves is Required Reserves + Excess

[last ether]

Well ultimately you do but remember that Cash/Total Reserves = Required + Excess

The thing is that you need to find how much cash is in required and how much cash is in excess reserves AFTER the 1500 deposit

The reserve ratio always stays the same unless the central bank changes it, which rarely happens

[shut parcel]

Do we do 500/21,500 instead

[last ether]

... you just found earlier that the reserve ratio was 2.5%

[last ether]

IT STAYS THE SAME

[shut parcel]

Omg I’m sorry

[last ether]

You started, before the depsoit, with:

500 in Required ; 0 in Excess

Find how much is in the Required and Excess after the 1500 deposit.

Remember that your ratio is 2.5%

[shut parcel]

This is probably wrong but.. I got 37.5

Target reserve ratio = Target reserves/Total deposits. 0.025 = x/1,500. So, x = 37.5😭

[last ether]

That doesn't answer anything. 37.5 is 2.5% of 1500, but that doesn't answer any of my questions. You just did a step in the process of solving what I asked you to solve

I want you to solve how much money is in the Required Reserves, and how much money is in the Excess, AFTER the 1500 deposit

You did find the change in required reserves, but again, that's not what I ultimately am looking for

[shut parcel]

1500/0.025 = $60,000

[last ether]

That's not anything

I'm looking for two answers

[shut parcel]

I don’t know how to solve it😭

[last ether]

If the deposit is 1500, how much of that 1500 becomes reserved money and how much becomes excess?

If the ratio is 2.5%

[shut parcel]

I’m confused with the formulas and which to use

[last ether]

You already found that $37.50 of the $1500 becomes reserved. This implies how much becomes excess?

[shut parcel]

37.50 = 500 - excess reserves

Excess reserves = 462.50

[last ether]

No

Whenever someone makes a deposit, some of that money becomes required reserves. Whatever's left of that deposit is excess

If 37.50 dollars of the 1500 dollars becomes required, then whatever's left is excess

So 1462.50 dollars becomes excess

That's the change in reserves

This means AFTER the 1500 deposit, there will be 537.50 dollars in reserved and 1462.50 dollars in excess

[shut parcel]

1500 - 37.50 = 1462.50

[last ether]

If you have a reserve ratio of 2.5% and 1462.50 in excess reserves, what's the maximum change in money they can get as a result of loaning all their excess reserves?

[shut parcel]

This question got me stuck lol

[last ether]

What's the money multiplier

[shut parcel]

1/reserve ratio

[last ether]

2.5% is your reserve ratio

Find the money multiplier

[shut parcel]

40

[last ether]

So maximum change in money = excess reserves • money multiplier

[shut parcel]

58,500

[last ether]

Honestly I think you're just confused on where the deposit money goes to

Every time someone makes a deposit, that money gets split into required reserves, and if there's any left, it becomes excess reserves

The more you do these you'll notice a pattern

[shut parcel]

Thank you so much for your patience

[lone heart]

@shut parcel Has your question been resolved?

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[heavy vigil]

can anyone please explain to me how to do these type of questions? or like just help me understand this problem and what to do.

[lone heart]

@heavy vigil Has your question been resolved?

[heavy vigil]

<@&286206848099549185>

[surreal crystal]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[heavy vigil]

1

[surreal crystal]

okay

first we need to consider the period of the sine

and identify where the arcsin is defined

since the sine only goes from -1 to 1, arcsine can only take -1 to 1

this means we lose most of our solutions

like this

we only get half the period of the sine wave

and since sin(0)=0, arcsin(0)=0, so we have (0,0)

the period of sin is 2pi (because 2pi=0 in radians)

so half is pi

so here is how we can get our solutions back

we know 2pi=0 in radians

that means we can add 2pi however many times we want and this will fit the sine wave

because we are essentially adding 0

so we need to figure out what sin will be from pi/2 to 2pi-pi/2=1.5pi

intuitively from the graph, we can just do pi-arcsin(x) to extend this function

we know the interval this solution exists

pi/2 <= a < pi

we know this solution has to be in the pi-arcsin(x) term

so, intuitively, we can solve this problem by just applying a=pi-arcsin(8/11)

although in this problem there is a more methodic approach

[surreal crystal]

this is just a good rule to remember

to extend our sin easily we can add 2pi any number of times, or do pi-arcsin and add 2pi to this any number of times

does this make sense?

[surreal crystal]

i can get into a more straightforward approach to solving this as well, i just felt explaining this was important to this type of problem

but i do want this method to make sense to you, since it is much more efficient than algebra

[heavy vigil]

Yeah i think i mostly get it, im srry if this is a dumb question but arcsin is inveter sine right?

[surreal crystal]

yeah

its a good question rather

very important

[heavy vigil]

Would it be alright if i got more straightforward approach?

Okay just making sure

[surreal crystal]

alright

so in this problem there is tan(2a)

basically the goal here is to rewrite this term using trig identities and end up with sin(a) terms because we know they are 8/11

this way, we ignore where arcsin is defined entirely

do you know of any trig identities that would help with expanding tan(2a)?

[heavy vigil]

Double angle identities?

[surreal crystal]

right

i suggest applying this identity, so we can use more familiar double angles

$\tan{2a}=\frac{\sin{2a}}{\cos{2a}}$

[ocean seal]

Cycadellic

[surreal crystal]

do you remember the double angle formulae for sin and cos?

[heavy vigil]

Yes i do

[surreal crystal]

apply them here, what do we get?

[heavy vigil]

Sorry quick question, i got the sin parts for solving the double angle formula for sin and cos but what do i fill in for the cos(a) parts?

Like when i was trying to expand sin 2(a), for 2sin(a) i got 0.752 but i dont know what to fill in for cos(a)

[surreal crystal]

can you send a picture of what you did?

[heavy vigil]

Yea give me a sec

Apologies for the messy writing, but yea im kinda stuck on what to write for cos(a)

[surreal crystal]

,rotate

[surreal crystal]

okay, so, lets write 8/11 so we dont get cluttered

now

$\tan{2a}=\frac{2\cdot 8\cos{a}}{11(\cos^2{a}-\sin^2{a})}$

[ocean seal]

Cycadellic

[surreal crystal]

what does $\sin^2{a}$ mean?

[ocean seal]

Cycadellic

[heavy vigil]

Like when i expand it?

[surreal crystal]

hint:||sine "squared" of a||

[heavy vigil]

2 sin (a) cos (a)?

[surreal crystal]

this one is important

we do $\sin^2{a}$ to avoid confusion with $\sin{a}^2$

[ocean seal]

Cycadellic

[surreal crystal]

$\sin^2{a}=(\sin{a})^2$

[ocean seal]

Cycadellic

[surreal crystal]

well, whats sin(a)?

[heavy vigil]

1/csc (a)?

[surreal crystal]

well, yeah, but we are given sin(a)

remember

$\sin{a}=\frac{8}{11}$

[ocean seal]

Cycadellic

[heavy vigil]

OH

[surreal crystal]

yeah

so

send me a pic of what we have for tan(2a) so far

if its not tedious to send one

[heavy vigil]

Sorry you gotta rotate it im not sure why it keeps rotating

[surreal crystal]

,rotate

[surreal crystal]

good

how can i get cos^2 into terms of sin

[heavy vigil]

Cos^2 (a) - Sin^2 (a)?

[surreal crystal]

thats double angle

but its close

consider

$\sin^2{a}+\cos^2{a}=1$

[ocean seal]

Cycadellic

[surreal crystal]

the pythagorean identity

[heavy vigil]

Ohh okay

[surreal crystal]

okay

that just leaves the cos(a)

i say

oh waity

we shouldnt do the sqrt i did cause we dont want to figure out which is the right one

so we can use sin angle sum on this one

because $\cos{x}=\sin{(x+\frac{\pi}{2})}$

ugh

[ocean seal]

Cycadellic

[surreal crystal]

there we go

[heavy vigil]

Ohhhhhh

[surreal crystal]

yeah

and whats $\sin{\frac{\pi}{2}}$?

[ocean seal]

Cycadellic

[heavy vigil]

0.027

[surreal crystal]

thats in degrees

we want radians

its 1

in radians

[heavy vigil]

Yea sorry i forgot to putt my calc in rad

[surreal crystal]

okay, once you apply all that you can sub 8/11=sin(a)

send me a pic so i can verify when youre done

after that, you can just plug it into your calculator to get a solution for tan(2a)

@heavy vigil i lied

[heavy vigil]

Oh 😭

[surreal crystal]

using sin sum will give us cos terms

didnt realize

so far

$\tan{2a}=\frac{16\cos{a}}{11((1-\frac{8^2}{11^2})-\frac{8}{11})}$

[ocean seal]

Cycadellic

[surreal crystal]

just to write it out

so, it simplifies to

$\tan{2a}=\frac{-176\cos{a}}{31}$

[ocean seal]

Cycadellic

[surreal crystal]

actually

we do have sin(a)=8/11

so we can check our a to get the right one with this formula

hm

this problem has a niche trick to it

lets see

ah!

we are given $\frac{\pi}{2}\leq a <\pi$

[ocean seal]

Cycadellic

[surreal crystal]

okay

so now we can make this work

cosine is negative on pi/2<=x<pi

so we know

$\cos{a}=-\sqrt{1-\sin^2{a}}$

[ocean seal]

Cycadellic

[surreal crystal]

good

now you can just sub in sin(a)=8/11

[surreal crystal]

and solve this with it

[heavy vigil]

Does this make cos(a)= -0.687?

[surreal crystal]

yeah

then just *(-176/31) gives you your answer

is everything clear about this?

[heavy vigil]

Yea i believe so, all i gotta do is this now?

Idk why its cropped like that... but it gives u the full image when u tap it

[surreal crystal]

all good

i see the whole thing on pc

[heavy vigil]

I got 3.9

[surreal crystal]

yeah

although, your math teacher might want closed form

something like this maybe

at least mine always did

[heavy vigil]

Alright got it

[surreal crystal]

good

any other questions about this?

remember the method that we can add 2pi to arcsin or to pi-arcsin

much faster on tests and such

[heavy vigil]

Ill put that into my notes

Thank you sooo much for this

[surreal crystal]

np

[lone heart]

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[stray estuary]

I'm looking at rings for the first time, and we were given some multiplicative properties. Do my proofs for them look good?

[lone heart]

@stray estuary Has your question been resolved?

[stray estuary]

<@&286206848099549185>

[nimble fern]

hello blanket!

i have been reading this since you post, but since i am not very familiar with rings and abstract algebra (because i nearly failed that course lol) i am not confident that i can help

do you mind if i ask along when i help?

[stray estuary]

oh ye sure nw

[nimble fern]

1. is a(0+0) = a0+a0 defined for a and 0 in ring R?

[stray estuary]

yeah, part of the definition given for rings was that a(b + c) = ab + ac

[nimble fern]

good, just as i expected, thanks!

[stray estuary]

lemme send that rq too

[nimble fern]

sure!

[nimble fern]

much better

[gentle creek]

Very much doable

[nimble fern]

oh, Bee33 wanna continue, imma gonna eat

[stray estuary]

yeah im dippin my toe into our next part of abstract algebra before i take it and i was just trying my hand at some of the more basic proofs we're gonna encounter

[nimble fern]

sorry, Blanket, i gotta eat first

[stray estuary]

nah nw

[stray estuary]

.close

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[proper nebula]

Not sure if I did the problem right and if not wanted some pointers into the right direction

[proper nebula]

And I guess also this I’m super rusty lol

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[mortal fox]

Hi, i don't understand how to do these limits, i see the teacher done this but idk how to do it

[frank apex]

plug it in directly
you get something on top
0 on bottom
if x = pi/3 - 0.0001 then cos(x) will just be barelyyy bigger than 1/2
and denom will be barely > 0

[mortal fox]

So that does infinite?

[mortal fox]

It works so?

[frank apex]

300/0+ = +infinity

[mortal fox]

And 300/0-= -infinity?

@frank apex

[frank apex]

yes

[mortal fox]

i see, thank you very much

.close

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[prime agate]

if you flip a coin until you get Heads what are the odds to flip the coin 4 times?

[cinder spindle]

in other words, you flip 3 tails ?

$\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}$

[ocean seal]

chromium

[prime agate]

mhm yea I guess I overthink that maybe

[golden canyon]

Don't forget that you have to flip a heads at the end

[cinder spindle]

ah yea true

but

that's if the question means precisely 4 times

idk

it should probably be 1/16

[golden canyon]

yeah

there is a fixed sequence of 4 flips you have to throw

[prime agate]

u stop only when u flip heads

its infinite

[golden canyon]

TTTH

[prime agate]

until heads

now if we define X as the number of the coin flips (unknown) what is the Expected value of X?

E[x]

what im thinking of is :

1*\frac{1}{2}+2(\frac{1}{2}\frac{1}{2})+3(\frac{1}{2}\frac{1}{2}*\frac{1}{2})+4(\frac{1}{2})^{4}+....+n(\frac{1}{2})^{n}

$1*\frac{1}{2}+2(\frac{1}{2}\frac{1}{2})+3(\frac{1}{2}\frac{1}{2}*\frac{1}{2})+4(\frac{1}{2})^{4}+....+n(\frac{1}{2})^{n}$

[ocean seal]

bon

[prime agate]

$E(X)=\underset{\omega\in\Omega}{\sum}X(\omega)P(\omega)=1*\frac{1}{2}+2(\frac{1}{2}\frac{1}{2})+3(\frac{1}{2}\frac{1}{2}*\frac{1}{2})+4(\frac{1}{2})^{4}+....+n(\frac{1}{2})^{n}$

[ocean seal]

bon

[prime agate]

@golden canyon @cinder spindle

basically I need to calculate the average numbers of flips

<@&286206848099549185>

[frank apex]

you can write this as
1/2

• 1/4 + 1/4
• 1/8 + 1/8 + 1/8
• 1/16 + 1/16 + 1/16 + 1/16
• 1/32 + 1/32 + 1/32 + 1/32 + 1/32
  now look at the columns

[prime agate]

its like $\frac{1}{2}+\frac{1}{2}+\frac{3}{8}+\frac{4}{16}+...+\frac{n}{2^{n}}$

[ocean seal]

bon

[prime agate]

ok I look at them

[frank apex]

what's this

[prime agate]

mhm like almost 1

[frank apex]

assuming you continued the column down it would approach 1

what's the sum of the next column?

[prime agate]

oh

0.5

0.25

0.125

etc

[frank apex]

yes

[prime agate]

so I need to calculate like q series

with 0.5=q

[frank apex]

pretty much

[prime agate]

so its 2 right

[frank apex]

yep

[prime agate]

there is a name for that right? telescopic series or something

[frank apex]

geometric series?

[prime agate]

ye ty

[lone heart]

@prime agate Has your question been resolved?

[lone heart]

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[orchid parrot]

https://media.discordapp.net/attachments/1097186756534747276/1097749338064703539/image.png

[orchid parrot]

I tried equation

-b/2a

But couldnt match

[main kraken]

-b/2a = x val of vertex
f(-b/2a) = y val of vertex

[vale wigeon]

sketch a graph

[main kraken]

also note that discriminant > 0 since two x-ints

then consider c/a = product of roots

@orchid parrot

[orchid parrot]

Nope

It doesnt have

Happen

[orchid parrot]

I dont understand what to do

I mayched my

Equation

But two sides gets equal

@vale wigeon

[lone heart]

@orchid parrot Has your question been resolved?

[orchid parrot]

<@&286206848099549185>

[alpine sable]

y=-a(x-4)^2+2

you can try to use vertex form

[orchid parrot]

By vertex form i will get to know

Only the y point

[alpine sable]

c is the ordinate of the intersection of parabola and y-axis

[lone heart]

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[dusk vapor]

the first 3 terms in the expansion of (a + x)^3(1-(x/3))^5, in ascending powers of x, can be written in the form 27 + bx + cx^2, where a,b and c are intergers. Find the value of a,b and c

[chrome salmon]

Where's a?

Oh in the binomial

[dusk vapor]

(a + x)^3(1-(x/3))^5

yeah

[chrome salmon]

This is like $(a+x)³(1-\frac{x}3)⁵$ right

[ocean seal]

fäf

[dusk vapor]

yup

[chrome salmon]

You know the general formula of binomial expansion?

[dusk vapor]

yeah

[chrome salmon]

Make cases then

[dusk vapor]

huh

cases?

[chrome salmon]

For x , you can get the coefficient by getting the coefficient of x from first expansion and constant terms from other expansion added to the constant of first expansion multiplied to coefficient of x from second expansion

[dusk vapor]

wait

so like

[chrome salmon]

Like if we have $(a_0 + a_1 x + a_2 x²)(b_0 + b_1x + b_2 x²) = a_0b_0 + (a_1 b_0 + a_0 b_1) x + (a_0b_2 + a_1b_1 + a_2 b_0) x²$

[ocean seal]

fäf

[chrome salmon]

I haven't written the whole product

[dusk vapor]

why is it equal to?

wait

no nvm

[chrome salmon]

I just multiplied

[dusk vapor]

i got it

yeah

[chrome salmon]

So if you generally want $n$th term then you can get it by $\sum_{i=0}^{n} a_i b_{n-i}$

[ocean seal]

fäf

[dusk vapor]

i haven't covered that yet

[chrome salmon]

You don't need to

Thus just needs logical thinking

[dusk vapor]

mm

[chrome salmon]

Like what are the types to two powers of x that give x³

It's x² and x , 1 and x³

[dusk vapor]

x^2 x x?

yeah

[chrome salmon]

So just multiply their coefficient aswell

[dusk vapor]

ok so

i need help

shit

[lone heart]

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[tall pebble]

Howd they get 5pi/6

[lone heart]

@tall pebble Has your question been resolved?

[tall pebble]

<@&286206848099549185>

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@tall pebble Has your question been resolved?

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[jaunty token]

i need help with geometry similar triangles

[hard patio]

Post your question

[jaunty token]

the picture may be to big but its number 8

[hard patio]

That’s really blurry

[jaunty token]

ill try taking another

there we go?

im having trouble finding the sacle factor k and the rest

hello

[jaunty token]

scale factor *

[hard patio]

Okay you know what OM is

And you know what OP is

[jaunty token]

yea from O to M?

[hard patio]

Yes

[jaunty token]

yea]

[hard patio]

Yes?

[jaunty token]

yea

[hard patio]

You know the definition of scale factor?

[jaunty token]

uh no not rlly

[hard patio]

You should look it up, it will clear things up for you

[jaunty token]

oh wait i know which yea

i know how to find the scale factors is just i have trouble with midline triangles

[hard patio]

Wdym by midline triangles?

Calamity?

Why’d you delete it?

[rocky atlas]

I looked up Google and it seems midline is a legit word

While it's true midline triangle doesn't exit but midline is a thing that exist in triangle

And I uttered middle line instead of midline

So I reflected on myself and thought it's better deleted

[hard patio]

Ahh

[lone heart]

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[lone heart]

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[hard patio]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[alpine sable]

@twilit karma what’s your question

[twilit karma]

I've sent the question

[cinder tundra]

You sent the exercise, not your question.

We don't do homework, we help you to understand how to do it if you're stuck in a specific step.

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@twilit karma Has your question been resolved?

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[uneven palm]

i did some computation and my results is that dimU =4

idk if that is correct

[loud bramble]

no

[ocean hawk]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[uneven palm]

i tried computing x1 from the first equation

then x4 from the second equation

then by setting 0 first x1 then x2 and so on so forth

i obtained 4 tuples

no it should be 5 so

[loud bramble]

do you know that each linearly independent equation reduces the dimension of your set by 1?

[uneven palm]

no

[heady pollen]

you can think about it like this:
x1 is already fixed if we know x2 and x3
that kinda "removed" one dimension of freedom

[uneven palm]

so my approach is not correct

[uneven palm]

which means we have 3 degrees of freedom

[uneven palm]

doing the same for x4

[heady pollen]

👍

[uneven palm]

but what was wrong with my approach

[heady pollen]

wait, one second

[loud bramble]

its not clear what is your approach

[loud bramble]

what does it mean

[uneven palm]

after you found x1 and x4

if you set 0 x2

you get this tuple(1/2,0,1,1,1)

right

[loud bramble]

i dont understand but no

this vector isnt in U

[uneven palm]

but how do you find the answer so

[heady pollen]

what might help is:
think about a general vector in that vectorspace V
then look at how many degrees of freedom you have
for example here we can say:
2x1=x2+x3
x2=a, x3=b => x1=(a+b)/2
x4=3x5
x5=c => x4=3c
thus we get the general vector
v=( (a+b)/2, a, b, 3c, c )
as you can see, we have 3 variables = 3 degrees of freedom

[loud bramble]

since it doesnt satisfy 2nd equation

[uneven palm]

exactly what i did

only that i didn't substitute a,b,c

but i think that's the same

but now i think i got what you mean

[loud bramble]

you can also think about it geometrically

[uneven palm]

how so

[heady pollen]

if you can think in 5d 🙂

[uneven palm]

thanks a lot Martin

[uneven palm]

ugh

a bit difficult

[heady pollen]

skill issue

[loud bramble]

well by analogy to 2d,3d its clear what happens

each equation gives you a 4-dimensional plane in R^5. Intersection of such (independent) planes is 3-dimensional, just like intersection of 2d planes is 1d plane - a line

[uneven palm]

oh so interestion of 2 4d planes give a signle one ine 3d

which means dimension 3

bcs its on 3d space

[lone heart]

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[crisp fulcrum]

hi

[crisp fulcrum]

i'm trying to solve this integral

the actual solution is -πγ/2

but i keep getting πγ and idk why

[quartz beacon]

Can u send the question?

[ocean hawk]

what integral?

[crisp fulcrum]

here's the integral

um the funky L is supposed to be a $\mathcal{L}$

[ocean seal]

what is an σ-algebra

[crisp fulcrum]

please help me i'm desperate

[karmic rapids]

,, \log(x) = \int \limits_0^\infty \frac{e^{-t} - e^{-xt}}t dt

[karmic rapids]

@crisp fulcrum

[crisp fulcrum]

what am i supposed to do with this information

[slow hound]

[karmic rapids]

plug it in

into the original integral

[crisp fulcrum]

why

[crisp fulcrum]

why would i do that

[lone heart]

@crisp fulcrum Has your question been resolved?

[lone heart]

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[ocean hawk]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[ocean hawk]

you could write a recursive definition

similar to what you had, you'd just need a_0 and a_n and a_{n-1} instead of x and y

or f(0), f(n), f(n - 1)

[lone heart]

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[alpine sable]

what about it?

[ocean hawk]

what do you need help with

[alpine sable]

right with respect to what?

if you want to troll with a conjecture, at least be more specific

[gray isle]

if you want to troll with a conjecture, resist the urge to

just don't do it period

[keen plinth]

why is it always the same picture

[ f\left(n\right) , = , \begin{cases} \frac n2 & if ~ n ~ is ~ even \ 3n + 1 & if ~ n ~ is ~ odd \end{cases} ]

[gray isle]

.close

[lone heart]

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[ocean hawk]

<@&268886789983436800> obvious troll

[night geyser]

Stop shitposting in help channels

.close

[lone heart]

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✅

[vale wigeon]

you say you need help but you cannot clearly formulate a problem.

you have given us a function. nothing else. we cannot tell you if that is "right" or "wrong" any more than we could tell you if the number 37 suspended in a vacuum is "right" or "wrong".

okay, so that is a linear equation, and you are tasked with solving for x. yes?

is that a yes or a no

okay

do you know in general how to solve linear equations?

6th grade...?

hold on.

before we continue, i must ask you this for legal reasons.

are you over 13 years of age?

of what year...?

alright then.

okay, so.

do words such as "distributive property" and "expanding the parentheses" and "collecting like terms" ring any bells to you

okay, so in that case

your equation is

5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13

what happens when you expand everything out?

write it out on paper.

and send a pic here

that is one line and the way you've wrapped it around is going to make it tricky to read back your work

(or to write multiple lines)

so youre gonna need to (a) get a wider sheet of paper or (b) write narrower

anyway if you know how the distributive law works then you should have no problem expanding, say, 5(-3x-2) as -15x - 10

no, it is not.

4x+5 isn't 9x

[rocky atlas]

4x and 5 are unlike terms, and you can't add unlike terms

You can only add like terms

If it were given 4x and 5x then yes, on adding them it's 9x

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[silk pewter]

im doing the The Continuum Hypothesis

[silk pewter]

can anyone help

[tired harness]

Just ask the question. Don't ask to ask

[silk pewter]

ok

idk if it even a question

[nimble fern]

i forgot what's that flipped C sign called 🥲

[silk pewter]

bet

its hebrew number

[nimble fern]

tyty

[silk pewter]

np

[nimble fern]

looks clear to me, which part do you not understand?

[lone heart]

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[sudden fulcrum]

okay guys... please tell me if stupid but i dont get how do you get from picture 1 to picture 2 ...why I get 2*sqrt((H-h)h)

[sudden fulcrum]

nice

[carmine reef]

It's just algebraic manipulation

isolate s

In the last step, both sides get square rooted

[sudden fulcrum]

yeah but isnt 4 inside square root and after tossing it out i gets reduced to 2

[carmine reef]

Though I can't see why the 4 would be outside of the square root, maybe that's a mistake

yeah

[sudden fulcrum]

yeah...i just came here to see if i am really that stupid or my professors are

[carmine reef]

looks like a mistake yeah

[sudden fulcrum]

cause today alone i found like 5 of mistakes from materials that were given to us by professors to learn for midterm

ok thanks

[carmine reef]

Oof