help-26

[normal tapir]

sinh and cosh?

[pine sonnet]

idk man

i never seen it represented with e

[outer laurel]

you know eulers identity/formula

[pine sonnet]

no

[outer laurel]

oh well

[pine sonnet]

we have not gone over that

[outer laurel]

uh i dont really see how ur supposed to do this then

[normal tapir]

it's just the definitions

[outer laurel]

i guess

[normal tapir]

cosh = 1/2(e^x + e^-x)

[outer laurel]

https://math.stackexchange.com/questions/2853279/the-interconnection-between-hyperbolic-functions-and-eulers-formula

[normal tapir]

ans sinh = 1/2(e^x - e^-x)

[pine sonnet]

i got no clue what all of that means

but i was able to finish the problems thanks

.close

[topaz sinew]

Channel closed

Closed by @pine sonnet

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tender musk]

what is injective and surjective

[frank tide]

do you need the specific definition or just an idea

[tender musk]

uhhh

can I have an example?

[frank tide]

A function f: X -> Y is injective if for all f(x) in Y, f(a) = f(b) implies a = b

Surjective if for all y = f(x) in Y there exists some a in X such that f(a) = y

[tender musk]

o-o

ok so...

64^0.5

= sqrt(64)?

and that is

... injective?

[frank tide]

is your function sqrt(x)? or sqrt (64)?

[tender musk]

uhm

I'm not sure

but

ok

so what if f(x) = 2x

[frank tide]

What do you think

[tender musk]

well

f(1) != f(2)

so.... surjective?

[frank tide]

that’s the property for infective

does that line hit every y value?

[tender musk]

yes

right?

[frank tide]

yes

so it is injective and subjective

[tender musk]

they can be both???

[frank tide]

you can think of injective as passing the horizontal line test and surjective as reaching every y value

yes when it’s surjective and injective it’s called bijective

[tender musk]

so x^2 is only injective?

[frank tide]

f(2) = f(-2) so it’s not injective

[tender musk]

oh I see

[frank tide]

also we don’t reach any of the negative numbers when you aren’t using complex numbers

so it’s neither

[tender musk]

mhm

so

if a function has more than 1 input with the same output it is not injective

[frank tide]

yes

[tender musk]

and if a function can't output every value then it is surjective?

[frank tide]

yes

[tender musk]

k thanks

a lot

.close

[topaz sinew]

Channel closed

Closed by @tender musk

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[oblique ivy]

How would I go about this. Don't know where to start

[mint crescent]

https://tutorial.math.lamar.edu/classes/calcii/taylorseries.aspx

[oblique ivy]

so for c_0 I would just plug -1 in for x in x^3?

[mint crescent]

[oblique ivy]

thank you

.close

[topaz sinew]

Channel closed

Closed by @oblique ivy

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[honest ember]

can you see these are rationalising factors of each other

?

[honest ember]

hey I need to leave so please reply if you want me to explain

[half edge]

Fellow JEE aspirant, Hello!!

[honest ember]

hi

[half edge]

This year I believe I will easily get AIR 5

[honest ember]

oh damn

you joking?

[half edge]

How can I jest? My ability is inherent.

[honest ember]

okay

I don't really care

( this doesn't apply if you can help me 🙂 )

[inner dove]

What what

Jee??

[inner dove]

Yes they are

[honest ember]

okay so

if

[inner dove]

Which topic is this actually related to?

[inner dove]

Inequality in jee

[honest ember]

no

okay so

[inner dove]

So

[honest ember]

if this is t

[inner dove]

t+1/t=14

[honest ember]

yes exactly

[inner dove]

Opps

[honest ember]

then solve quadratic

you'll get 2 roots

equate it

[inner dove]

Rationalization works for square only?

[honest ember]

equate the powers and you'll get the answer

[honest ember]

what?

yeah

you can rationalise terms which looks like conjugates in complex numbers

[honest ember]

Idk honestly

[honest ember]

now equate it

with this

[inner dove]

I see

I see both plus and minus

Clearly 4 roots

[honest ember]

yes

[inner dove]

Thank you very much

.close

[topaz sinew]

Channel closed

Closed by @inner dove

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

<@&286206848099549185> I need help reading this, all I need to know is how many boys are anxious

[topaz sinew]

Please don't occupy multiple help channels.

[neon iron]

.close

[topaz sinew]

Channel closed

Closed by @waxen solar

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[nocturne oracle]

how did they get the x intercepts of the derivative

[eternal cave]

x intercepts of the derivative?

[nocturne oracle]

i mean like zeros i guess

of the cubic function

[eternal cave]

The root of the cubic function?

Use calculator is the fastest way

[nocturne oracle]

is there a function on the calculator that solves polynomials

[outer laurel]

graph it and trace or calc

if it doesnt have that function then you're out of luck

[topaz sinew]

@nocturne oracle Has your question been resolved?

Channel closed

Closed by @nocturne oracle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hazy dirge]

so i need help figuring out which type of functions f(x) and g(x) are

is f(x) a cubic polynomial function or cubic function

and is g(x) a logarithmic function?

[outer laurel]

yes

is cubic not the same as cubic poly?

[hazy dirge]

uhh i think it is i just saw someone say cubic poly online and another say cubic

it has to be the same right

[robust ocean]

F(x) is a polynomial of degree 3
G(x) is a logarithmic function

[hazy dirge]

thank you for this

[robust ocean]

Do you want B too?

[hazy dirge]

please if u can

im working on that now and i know ill need help

[robust ocean]

You find the value for x in f(x) that do not exist but for polynomial is exist for all real number so f(x) domain is all real numbers.
G(x) is also defined for all positive real numbers except 0. Since log (0) does not exist. G(x) is all real number > 0

[hazy dirge]

okay so is this correct

[hazy dirge]

also for this how do i explain g(x) is a logarithmic function

[robust ocean]

Yes.

[hazy dirge]

so how would i explain it

like g(x) is a logarithmic function because..

@robust ocean

<@&286206848099549185>

[robust ocean]

If has log in it

[rustic pewter]

It's a logarithmic function if it is

So basically

If it's logarithmic it's a logarithmic function

[hazy dirge]

would i even have to explain why its a logarithmic function

i explained the last one thats why

[rustic pewter]

It's logarithmic because is has a logarithmic term

[hazy dirge]

okay okay

is that all i would write about that

[rustic pewter]

Idk

[topaz sinew]

@hazy dirge Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[candid cape]

Hello, can anyone help explain how i can answer this

[rain patio]

the sine rule

20/sin(20°)=x/sin(39°)

[rain patio]

if you can use a calculator

[candid cape]

yes i can use one

can i send you my work?

[rain patio]

sure

[candid cape]

so i got right so far...

[rain patio]

uhm

[candid cape]

or not... 😭

[rain patio]

Isn't the formula= A/sina=B=sinb

the side on top

the degree in the bottom

and you don't need the 59 (which is wrong)

it's 180-39-20

[candid cape]

oh

[rain patio]

a triangle is always 180 degrees together

[candid cape]

gotcha

[candid cape]

im not sure :,))

[rain patio]

try it

[candid cape]

im just learning about this

[rain patio]

Ah I thought you maybe had a variant

then I'm sure

It's A/sin(a)=B/sin(b)

And to decide what the couple A,a is, you need to choose the opposite side of the angle

[candid cape]

sin a?

wait wait

I think I did this wrong

[rain patio]

noo

it's sin(20°)

never ever scratch it like that

you have to calculate the sin of 20° on your calculator

Wait

I'll indicate everything

second

[candid cape]

o

[rain patio]

Then with the calculator you see

Sin(20°)=0,3420.....

Sin(30°)=1/2 or 0,5

And then it's just filling it in and letting the calculator do the rest of the work

So X=29,2380

[rain patio]

I would do the calculation 20/sin(20°) in your calculator because it has a lot of decimals

[candid cape]

okok lemme read what you just said

[candid cape]

what do you mean by this?

oh no wonder

i need to set my calculator to uhh

degrees?

[rain patio]

The equation to solve x

[rain patio]

Yes

Or you could convert the degrees to radials 😅

But I'd indeed set it on degrees

[candid cape]

uhh

i dont know how to do this

lemme google

im dumb

[candid cape]

yes

[candid cape]

yes

[candid cape]

how do i fill it in or what do you mean?

[rain patio]

You need to add the °

[rain patio]

Just calculate it

[candid cape]

i found how to turn it into deg

calculate it by adding it?

[rain patio]

You still need to add the ° after the 20 and 30

In the sin

[rain patio]

No calculate it by doing the equation I sent you -> 2/sin(20°)=x/sin(39°)

[candid cape]

ohh

[rain patio]

I was wrong btw I thought the question said

30 degrees, it's 39

Now it's correvt

Ct

[rain patio]

Ah nice yea normally now you should be able to calculate it

[candid cape]

I do this by hand?

[rain patio]

With your calculator ofc

2/0,34202

And then multiply it by sin(39°)

And that's your x

A simple equation

[candid cape]

wait wait

how can i put the equal sign on my calculator?

im so confused

[rain patio]

No the equal sign is the equation in your formula

[rain patio]

Yes correvt

Correct

Do you know how to solve equations?

[candid cape]

no i have trouble with them

is it 2sin(39)/sin(30)

?

[rain patio]

Yes!

[candid cape]

yaaaaaaaaay

ok i kinda know 😎

2.517?

YOO

wait i understand now

big brain moment

[rain patio]

No

It's along 3,6800

[candid cape]

wait wait

lemme show yu

here is a similar question

here is my work

i put that in the cal

it said 64.387 which was right

🥳

[rain patio]

Aaah

It was 24?

Congrats!

Ah this is another exercise

[candid cape]

i did a similar question

[rain patio]

Yes I see

[candid cape]

so its a different one

yee

I GOT IT

THANK YOUU

[rain patio]

Yw!

[candid cape]

this is so coolm i love math

🤍 🙂 may god bless you, you cool mathematician

thank you again, i will close this channel

:>

.close

[topaz sinew]

Channel closed

Closed by @candid cape

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[raven cove]

Can someone well versed in discrete math tell me why this is a time complexity of N and not N^2 ?

[raven cove]

Or tell me why the summations lead to N summations not not N^2?

[kindred linden]

You have to notice one thing for that

Do you agree that a step is equivalent to k increasing of 1 ?

[raven cove]

Like induction?

[kindred linden]

What do you mean ?

[raven cove]

Nvm forget what i said

So the outer loop runs from 1 -> N

and inner loop goes from k < 9i

[kindred linden]

Yes

[raven cove]

I guess a better question is how do you write a summation for a while loop

[cursive mango]

Ohh

[kindred linden]

You don’t have to here

[cursive mango]

It’s because the k=1 is outside the for loop

I was so confused

[kindred linden]

Because to evaluate the complexity here

[raven cove]

Pls elaborate

[cursive mango]

k is never reset to 1 it’s just incremented

[raven cove]

Correct

[kindred linden]

You just have to count the number of step in your algorithm right ?

[raven cove]

no im supposed to find the theta notation of the overall algorithm

[kindred linden]

For example if there were n step then it would have a complexity of n

[raven cove]

Yea but doesnt the inner loop go to 9i ? In other words it stops when k = 9i - 1

Outer loop sums from 1 to N

[kindred linden]

Yes but what is the maximum value of k at the end of the algorithm?

[raven cove]

Uhhhh i have no idea

[kindred linden]

Well the algorithm just increase k (forget about x)

And stop at 9i

[raven cove]

Ok im following

[kindred linden]

But I goes up to n

So at the end k will be at 9n

[raven cove]

Right im following

[kindred linden]

So now that we got that

You have to understand that in order to calculate any complexity of an algorithm, you have to count the number of thing your algorithm do. For example here if does k =k + 1 and x=x^2

[raven cove]

Wait

So we ignore the outer summation since the inner loop runs to 9i?

So in a way they get tied together

[kindred linden]

At first tell me if you understand that

Because if you do then it will be way easier

[raven cove]

I think i get it

[kindred linden]

Okay good

Forget about wanting to sum thing up to get the complexity

It’s very effective sometimes

[raven cove]

Its the method ive been using to be honest

🤣

[kindred linden]

But here there is a more basic method

And informaticien are lazy people, so if a basic solution work, they will do the basic one not the hard one

[raven cove]

Okay tell me the basic method because I cant wrap my head around it without writing up summations

😭

[kindred linden]

Do you agree that the number of thing the algorithm do is equal to the value of k at the end of the algorithm?

(If we forget about the x=x^2)

[raven cove]

Right, forgetting the x

we are incrementing K

[kindred linden]

Yes

And we are not resetting it !

Very important condition

[raven cove]

Correct

[kindred linden]

Because if we were resetting it, we would have to sum the value of k every time we would do again the while loop

But we are not

So : complexity = number of thing the algorithm do = k at the end

Right?

[raven cove]

So basically; complexity: n = k ?

because the number of things the algorithm does is 9i

[kindred linden]

well at the end k=9n not n

[raven cove]

ohhhhh

[kindred linden]

But for a complexity multiplying by a constant doesn’t affect the complexity

[raven cove]

Yea true

I think i get it

[kindred linden]

So having a complexity of n or of 9n is the same

[raven cove]

Wait backtracking onto resetting K

so if K was inside the for loop

[kindred linden]

Yes

[raven cove]

then we would have to do a summation

[kindred linden]

Exactly

[raven cove]

Then it would be n^2 complexity

[kindred linden]

Yes

[raven cove]

Omg

i get it now

[kindred linden]

Because you are counting thing

But at each end of the loop you are saying “okay I did 9i thing, now I reset to 0 so here keep 9i for now on” and at the end you then have to sum all the 9i thing you did for i between 1 and n

[raven cove]

And this is for resetting K right

[kindred linden]

Yes

[raven cove]

I seee

so without resetting K, basically you stop at 9i things

[kindred linden]

Yes

[raven cove]

wowz

[kindred linden]

And then you do another step and stop at 9(i+1)

Etc.. up until 9n

[raven cove]

ahhhhh i see now

such a tricky question

i couldnt wrap my head around it

[kindred linden]

Absolutely

[raven cove]

but it makes sense now with your explanation

thank you so much 🙏🏻

[kindred linden]

You’re welcome

[raven cove]

.close

[topaz sinew]

Channel closed

Closed by @raven cove

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[upbeat minnow]

how do i find the deriviative of $y=2\cdot \cos x$

[thorny flame]

guy

[upbeat minnow]

i know the cos will turn into -sin x

so i know it'll be $2 * -\sin x$ but i'm not sure what to do with the 2

[thorny flame]

guy

[cursive mango]

That’s it lol

You got it

-2sinx

[upbeat minnow]

but what do i do with the -2?

like isnt there a rule where constants turn into 0?

[unborn kiln]

If u use product rule it'll just become -2sinx

$\frac{d}{dx} [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) \ y' = (0)(\cos x) + (2)(-\sin x)$

[thorny flame]

Akuma

[topaz sinew]

@upbeat minnow Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

Can someone please help me figure out what the 11th term of this geometric sequence is??

[inner dove]

just divide the second term with first

you will get -5x^3

which is d

now what is general formula for nth term

an=ar^(n-1)

a11=a(-5x^3)^10

what is a is first term

a11= -3x^2(-5x^3)^10

simplfy it and get your answer

[neon iron]

Oh wow

Wait I can figure this out

[inner dove]

good

[neon iron]

Thank you!!!!!

[topaz sinew]

@neon iron Has your question been resolved?

Channel closed

Closed by @agile breach

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pseudo sonnet]

for part b), I've been able to show that T*T and TT* have the same non-zero eigenvalues, but not that these have the same multiplicities

any suggestions on how I should do that?

[topaz sinew]

@pseudo sonnet Has your question been resolved?

[topaz sinew]

@pseudo sonnet Has your question been resolved?

[flat coyote]

If you have solved for the non-zero eigenvalues, then you should have already solved for the same multiplicities. If you want to share your proof that can make it a bit more clear.

[pseudo sonnet]

sure!

Let v be an eigenvector of T*T corresponding to eigenvalue λ =/= 0. Then T*Tv = λv => TT*T = λTv => TT*w = λw, where w = Tv

this shows that Spec(T*T) is a subset of Spec(TT*)

we can basically reverse this proof to show that Spec(TT*) is a subset of Spec(T*T)

thus the two are equal, and T*T has the same non-zero eigenvalues as TT*

...in retrospect, I should have said Spec(T*T) \ {0} or smth, but that's besides the point

[flat coyote]

If you are talking about the spectrums being equal, then that should give you the multiplicities for free.

Can you give me your class's definition of Spec?

[pseudo sonnet]

give me a second...

[flat coyote]

Np.

[pseudo sonnet]

it's just the set of eigenvalues

[flat coyote]

I guess that's fine, usually Spec is defined over the characteristic polynomial which gives you the multiplicity.

[flat coyote]

In that case, just do this argument but for any eigenvalue with multiplicity.

[pseudo sonnet]

what do you mean?

[flat coyote]

If there exist eigenvalue of T*T with some multiplicity, then you can repeat this argument with a different eigenvector but with the same eigenvalue.

[pseudo sonnet]

I see, that makes sense

well, in that case

there's nothing more to do ig

because the argument I presented earlier should work for any eigenvector corresponding to λ I think

is that right?

actually yeah it has to be I think

okay, sounds good to me

thanks for the help @flat coyote

btw, welcome to mathcord!

I hope you enjoy your stay here

[flat coyote]

Yep np!

[pseudo sonnet]

.close

[topaz sinew]

Channel closed

Closed by @pseudo sonnet

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lunar merlin]

hey can someone help me with these just do all of them

[lunar merlin]

i need a recap

so ill start with a

[fickle pelican]

okay what do u think is the answer of a

[lunar merlin]

hmm

move 2x^3

so

0 = -2x^3 16x

then fcatorise?

so

[mild wolf]

think of it as 2 x x x = 16 x

how can you simplify it

[fickle pelican]

u can do this

[lunar merlin]

ok that makes more sense

yeah then

[fickle pelican]

factorize it

[mild wolf]

you can get rid of a common x

[lunar merlin]

0 = -2x(x^2 - 8)

[fickle pelican]

good

now what possible solutions do u get

if km=0, either k=0 or m=0 or both are 0

so use that

to find possible solutions

[lunar merlin]

umm

not sure

well

i know either

[fickle pelican]

yes how

for either

[lunar merlin]

-2x = 0

or

x^2 - 8 = 0

[fickle pelican]

yes thats it

now solve for x

[lunar merlin]

but im not sure how to do the first one

[fickle pelican]

-2x = 0
x=0

[lunar merlin]

ah

then

[fickle pelican]

what multiplied by a number gives 0

[lunar merlin]

2sqrt2 for the other one

[lunar merlin]

i see

+-

[fickle pelican]

yes

those r the 3 solutions

[lunar merlin]

so x = 0 and x = +- 2sqrt2

[fickle pelican]

yes

[lunar merlin]

ah okay

got it

so for b. is it similar

[fickle pelican]

for b, u get (x-1)^3 = 16

[lunar merlin]

yeah

[fickle pelican]

then x-1 = cube root of 16

so x=cube root of 16+1

[lunar merlin]

3

[fickle pelican]

no

[lunar merlin]

huh

[fickle pelican]

cube root of 16 is not a rational number

[lunar merlin]

cube root of 16 is 2 right

[fickle pelican]

no

[lunar merlin]

ah

okay

[fickle pelican]

2 x 2 x 2 = 8

[lunar merlin]

yeah i juat realised

so what should i do

[fickle pelican]

express it in terms of cube root of 16

[lunar merlin]

ok

so

x - 1 = cbrt16

[fickle pelican]

yes

[lunar merlin]

so

x = cbrt16 + 1

?

[blissful sentinel]

yes

u can also plug in and check

[lunar merlin]

nice

thank u guys

.close

[topaz sinew]

Channel closed

Closed by @lunar merlin

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mossy holly]

Hello

[regal charm]

well try not to use AI on your math assignments lol

It's not reliable and doesn't help you in any shape/form

anyway

can u simplify that?

@mossy holly

[mossy holly]

Idk maybe

[regal charm]

multiply the -3 to every single element inside the matrix

[mossy holly]

Yes I've done

Is it like, -3 6
9 -3x

@regal charm

[regal charm]

good

now do that here as well

[mossy holly]

See, I've done that, but I guess I'm wrong

@regal charm

[regal charm]

?

[mossy holly]

@regal charm

[regal charm]

just answer this part i guess

so we can proceed at my pace

[mossy holly]

Umm I don't know

[regal charm]

?

[mossy holly]

What could it be possibly be -2y

[regal charm]

u just did the exact same thing for this:

so simplifying this should be trivial cuz u just did it

[mossy holly]

Huh?

[regal charm]

can u multiply 2 to every element?

write out the result

[mossy holly]

Ok

4 -2y
-2 4

[regal charm]

okay good

now can u add each element with its corresponding element?

[mossy holly]

Yes, but don't we have to multiply them

[regal charm]

there is no multiplication implied here or anywhere

your new matrix is also the same size

2x2

[mossy holly]

Oh ok ty

[regal charm]

so the first element would be the first element of the first matrix + first element of the second matrix

[mossy holly]

Yeah I know that

[regal charm]

first element of the first matrix = -3
second element... = 4

-3 + 4 = -1

okay then do it

[mossy holly]

Hmn ok

[regal charm]

so what's the result?

[mossy holly]

Let me send you

[regal charm]

what

6 + (-2y) is not 4y

[mossy holly]

Isn't 6+-2 = 4

[regal charm]

6 + -2y

not 6 + -2

if y was 100, you'd have 6 + -2(100) = 6 - 200 which is clearly not 4

[mossy holly]

Oh, so what would it be

[regal charm]

it's quite literally this lol

[mossy holly]

So it will be 6-2y

[regal charm]

6 - 2y

[mossy holly]

Ok

[regal charm]

fix this too

same mistake

[mossy holly]

Ok

-3x+4

[regal charm]

yes or 4 - 3x

so you have this

[mossy holly]

Huh

[regal charm]

i'm saying the addition leads to whatever is up there

[mossy holly]

Ok

[regal charm]

addition of orange gives green

[mossy holly]

But how does 6-2x becomes 2

[regal charm]

what

[mossy holly]

..

[regal charm]

i rewrote the left side as

the right side is quite literally this

[mossy holly]

Oh ok I'm dumv

[regal charm]

now equate each element with its corresponding element

since these matrix are equal -> every one of their elements have to be equal too

[mossy holly]

It's -2 not -2x

[mossy holly]

How would it be 😭

Is it like

[regal charm]

the blues match already cuz 1 = 1

the greens match also cuz 7 = 7

you want the yellowish orange stuffs to match

so you want 6 - 2y = 2

and you want the reds to match so you also want 4 - 3x = -2x

solve for the values of y and x that allow for the yellowish orange stuff and the red elements to match

[mossy holly]

OPPS ☠️

[regal charm]

yes u can make the changes yourself

[mossy holly]

Ok

[regal charm]

?????

u have literally not done what i told you to do tbh

solve for y

[mossy holly]

Ok so wouldn't we use Cramer's rule or inversion method 💀

[regal charm]

bruh

no

nothing is being multiplied here

[mossy holly]

Lol why are we studying that in book

[regal charm]

i think you're just too invested in all these formulas and stuff

that u can't see the big picture

[regal charm]

this is addition

[mossy holly]

Yea

[regal charm]

no multiplication here so you don't use either

[mossy holly]

Ok

I want to jump off the cliff

[regal charm]

u should fix your fundamentals tbh

[mossy holly]

How

[regal charm]

well learn the basic stuffs like adding and everything

idk how

but yeah

and also don't just start bashing formulas for every question u see

at least try to understand what the formula does (at the very least)

[mossy holly]

Ok

[regal charm]

anyway are we done? have u found the x and y value

[mossy holly]

Yes

[regal charm]

what is it?

[mossy holly]

2

[regal charm]

and is that how you'd write your answer?

anyway yeah it's correct

make explicit what u mean

[mossy holly]

Umm

Is it correct way to write? @regal charm

..

@regal charm

Mann

[regal charm]

x = y = 2 allows for the matrix to be equal

anyway yeah

[regal charm]

calm down

i just left for 2 mins 😭

[mossy holly]

Ok I'm sorry

Bro

2 more questions

And thanks for explaining me

@regal charm

[regal charm]

i'm sleepy

😭

u can ask anyway someone else will help

[mossy holly]

Huh

Noo you are good at explaining

Btw what time is it for you

For me its 1:03 PM

[regal charm]

it's early morning for me

like 5am

lol

[mossy holly]

Oh lol

Where do you live

[regal charm]

florida

btw just ask your question

[mossy holly]

Ok

Triangle question, find the value of x

[nimble garnet]

BD : DC = AB : AC
you know AB, AC, BD

[mossy holly]

Man sorry I was busy

[mossy holly]

Idk

@nimble garnet

[nimble garnet]

do you know the length of line AC?

[mossy holly]

Yeah it is 8

Bro

@nimble garnet

[nimble garnet]

mb i'm in other channels lol

and do you know AB? and BD?

[topaz sinew]

@mossy holly Has your question been resolved?

[mossy holly]

No

[topaz sinew]

@mossy holly Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crude pivot]

ha!

[crude pivot]

Too many words!

You may have the question

[neon iron]

nah it was hard for me to explain. nvm you may have the channel

[crude pivot]

The final line says those two ratios are the same

meaning that if you do it with ratio algebra instead, you get two fractions that cancel out m a little (assuming we sub in the actual values)

$\frac{x}{6}=\frac{8}{3}$

[thorny flame]

Book

[crude pivot]

since scaling those lengths all by the same value m just makes a similar triangle, m doesn't acually matter at all

solving that above means x is 16

If you didn't see how t oget that equation above, recall that that ratio we see can be equivalently written (before subbing) as: $\frac{\bar{DC}}{\bar{AB}}=\frac{\bar{AC}}{\bar{BD}}$

[thorny flame]

Book

[crude pivot]

Did this help?

[topaz sinew]

@crude pivot Has your question been resolved?

Channel closed

Closed by @crude pivot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hot trout]

LIttle lost on how he got a pi-2 - a = pi/4

[swift grove]

,tex $ 2(\frac{\pi}{2} - \alpha) = \frac{\pi}{2} $

$ \frac{\pi}{2} - \alpha = \frac{\pi}{4} $

$ \frac{\pi}{2} - \frac{\pi}{4} = \alpha $

$ \frac{2\pi}{4} - \frac{\pi}{4} = \alpha $

$ \alpha = \frac{\pi}{4} $

[thorny flame]

math X meth ✓

[hot trout]

I meant how he found r1 to be more specific

[swift grove]

can you translate to english?

from what i can make out, r1 = i1 because angle of incidence = angle of reflection

also observe the normal to the inclined mirror

since it is perpendicular by definition, $i_{1} + \alpha = \frac{\pi}{2}$

[thorny flame]

math X meth ✓

[hot trout]

Aaah yes didn't realize that

. close

.close

[topaz sinew]

Channel closed

Closed by @hot trout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[simple tartan]

Help with c please

[topaz sinew]

@simple tartan Has your question been resolved?

[topaz sinew]

@simple tartan Has your question been resolved?

[tranquil verge]

from the equation given
g(x) = integral of f(x)

so the first derivative g'(x) = f(x)

so, the fifth derivative will be g'''''(x) = f''''(x)

[simple tartan]

But wouldnt u get 0?

[outer laurel]

i think so

[simple tartan]

However, the answer sheet says 24

Which makes absolutely no sense

[tranquil verge]

i think it has to do with Taylor series since the rest of question is about it

or the graph shown, cuz it would be the integral of the fifth derivative of f

[simple tartan]

But if you took the integral and plugged 0

You would still get 0 no?

[tranquil verge]

if u integrate from 0

but if u integrate from -.5 to 0 that would be something

[simple tartan]

Why would you do it from -.5 when it's asking for g^5(0)?

[tranquil verge]

g^5(0), here zero is the end position of the integral

u still didnt specifiy the start

[simple tartan]

But g(x) = integral starting from 0

Of fx

[tranquil verge]

but then if u take the derivative, if we say integral of f(x) is F(x)
then g(x) = F(x) - F(0)

and F(0) is constant

[simple tartan]

Yah that makes sense

And then what do u do with the g(0)

[simple tartan]

???

[tranquil verge]

<@&286206848099549185>

[simple tartan]

I found it

Thank you

.close

[topaz sinew]

Channel closed

Closed by @simple tartan

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[quaint rain]

What would the derivative of f(x)^g(x) be?

[normal tapir]

you can rewrite it using an exp/log identity and then apply the derivative rules

[quaint rain]

would this be the answer?

[ebon flume]

lol blackpenredpen

[normal tapir]

yes that's fine

[ebon flume]

isnt that called logarithmic differentiation

[quaint rain]

maybe

.close

[topaz sinew]

Channel closed

Closed by @quaint rain

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[prime fog]

need help

[stray lava]

Please don't ping before 15m

[prime fog]

okay i didnt know

[topaz sinew]

@prime fog Has your question been resolved?

[prime fog]

need help

<@&286206848099549185>

[topaz sinew]

@prime fog Has your question been resolved?

[swift grove]

use the log base change formula

[prime fog]

My answer is 35

I just need confirmation

[swift grove]

its correct

[prime fog]

How do u know

[swift grove]

i jsut solved it

[prime fog]

Can i see ur work

do u know why (a+b)(a-b)=1

@swift grove

[swift grove]

so

i solved it in bit of a different way

ill send a pic

[prime fog]

okay

@swift grove

[swift grove]

had to write it in a legible way

[prime fog]

i see its similar to mine it was a draft so its bit messy

.close

[topaz sinew]

Channel closed

Closed by @prime fog

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hot dagger]

I just need to know how they got .6645

[topaz sinew]

@hot dagger Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hot dagger]

I just need to know how they got .6645

[radiant marlin]

you'd find the z-scores with 0.29 and 0.0203 of 0.25 and 0.3

then you subtract these 2

or just use a normal distribution calculator online and enter everything

[topaz sinew]

@hot dagger Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[oblique ivy]

is there an easy way to find the partial sums in b without writing out 100 terms

[pearl peak]

No calculator allowed?

[oblique ivy]

calculator allowed im pretty sure

[pearl peak]

Just use the sum option in a scientific calculator

That’ll save time

[oblique ivy]

Im not sure how to use that option

[dusk apex]

do you have something like a cas calculator

[oblique ivy]

I dont have any physical ones. Is there one online I can use?

[dusk apex]

maybe wolfram alpha

[oblique ivy]

I tried to use wolfram alpha and it didnt provide me a value, just another function

[dusk apex]

what is that function ?

[oblique ivy]

4\sum _{n=1}^{\infty }:\frac{\left(-1\right)^{n+1}}{2n-1}

oops

[dusk apex]

bruh

so it just spit it out back at you

[oblique ivy]

wolfram alpha gave me

that was for n=10

[dusk apex]

time to bring in the big guns

gg didnt get anything from the mathematica either

[oblique ivy]

yeah, I guess ill start writing then

maybe I could get some help with part c and d of the question?

[topaz sinew]

@oblique ivy Has your question been resolved?

[glacial adder]

do you remember what the alternating series truncation error says?

[oblique ivy]

I do not

[glacial adder]

it’s basically says that the error for the sum of the first n terms of the sequence is less than the absolute value of the next term

essentially $error<\abs{a_{n+1}}$

[thorny flame]

y0shi

[oblique ivy]

ok yeah

and then error is just R_n right?

[glacial adder]

yeah

that’s how they defined it

[oblique ivy]

so for problem c am I trying to find a value?

Because I know for d i am but the wording of c is what's throwing me off

[glacial adder]

honestly the wording is kinda weird

cuz i’m not sure if it wants a bound for what the error of partial sums in part b is or something else

[thorny flame]

y0shi

[oblique ivy]

that's what I was wondering. Does it just want me to state what a_n+1 is?

[glacial adder]

i think it just wants the definition of the error, like what i wrote up here

and maybe it wants you to plug n+1 into our sequence formula as well

[oblique ivy]

Is it asking me to prove that a_n+1 is < or equal to a_n?

and then get it ready for part d?

[thorny flame]

y0shi

[oblique ivy]

and then just use that for d?

[glacial adder]

yeah

basically setting the a_n+1 bit equal to 0.01

and solving for n

[oblique ivy]

and then a_n+1 is

right?

[glacial adder]

yeah

and just solve for n here

[oblique ivy]

does the 4 outside the summation play a role in this?

would I multiply the error by 4

[glacial adder]

yeah

[oblique ivy]

ok

imma try it

and would I set it equal to or less than

[glacial adder]

set it equal

[oblique ivy]

ok

I am struggling to solve for n

[glacial adder]

so essentially we can ignore that (-1)^n bit since the error is the absolute value

so we would just have to do $$\frac{1}{2n+1}=0.01$$

[thorny flame]

y0shi

[oblique ivy]

ok that makes things simpler

so I got 99/2

and now I solve for s_99/2?

[glacial adder]

well n has to be a positive integer

[oblique ivy]

so s_50

[glacial adder]

yeah

[oblique ivy]

ok

[glacial adder]

we always round up

because if we round down, the error would be bigger

[oblique ivy]

yes

and I have s_50 from part b

[glacial adder]

yeah use that

[oblique ivy]

and multiply by 4

[glacial adder]

well S_50 shouldve been multiplied by the 4 already

[oblique ivy]

yeah i just didnt do it yet on my paper. Didnt clarify thats my bad

[glacial adder]

oh wait our error is wrong then

cuz we need to include that 4

[thorny flame]

y0shi

[glacial adder]

should be this instead

[oblique ivy]

so 399/2 which is 200 rounded up

[glacial adder]

yep

[oblique ivy]

if s_200 is super long do I have to write the whole thing out?

or can I round after like 5 or 6

[glacial adder]

probably round it id say

[oblique ivy]

ok

I have another question about a different series

[glacial adder]

go ahead

[oblique ivy]

What is c asking me for

[glacial adder]

compare your partial sums for n=5, 10, and 20

to the actual digits of pi

and see how many decimal places it got right

[oblique ivy]

oh thats it?

[glacial adder]

yeah

[oblique ivy]

I thought it was harder than that

ok

And one more, what does this question mean in b when it says compare from a calculating utility

[glacial adder]

it just wants you to compare it to the value of pi on a calculator

[oblique ivy]

to see how many digits off it is?

[glacial adder]

yeah

[oblique ivy]

so the same thing as c in the last one?

[glacial adder]

yep basically

[oblique ivy]

and when it asks to add the first two terms does it mean to actually do addition?

[glacial adder]

yep

just add on two more terms

[oblique ivy]

ok

sounds good

thank you very much

[glacial adder]

yw!

[oblique ivy]

.close

[topaz sinew]

Channel closed

Closed by @oblique ivy

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[keen sorrel]

It’s something to do with like ratio thing

I get the triangle just not the pallalelagram

[topaz sinew]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[keen sorrel]

How do I find the missing length

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[prisma saddle]

Hi I’m very confused

[prisma saddle]

Directions are to write a quadratic equation

Number 40

[tulip sonnet]

Wdym

Nvm

[prisma saddle]

huh

[tulip sonnet]

Do you know the quadratic formula?

[prisma saddle]

Ye