help-36

[pseudo knot]

Beautiful solution

@bold needle Do you still want help

[terse siren]

mathematically?

[pseudo knot]

Yea

[terse siren]

show me

[pseudo knot]

Can't send full solution here right, I can dm you if you want, or I can just drop hints here for both of you

[terse siren]

okay

do the latter

[bold needle]

yes

[pseudo knot]

Ok so the main trick here is in values of an-1

[bold needle]

also if you can tell me how did he get this

[pseudo knot]

Yes

I got a range so i didn't need that exact sum

[bold needle]

ohh okayy

how

[pseudo knot]

So we know (an-1)² is a positive term bigger than 1

[bold needle]

yes

[pseudo knot]

Which means 1/(an-1)² will lie between 0 and 1

Now we square the formula of an both sides

We'll get
an² = an-1² + 16/an-1² + 8

[bold needle]

but we have 16/a_n-1) here

[pseudo knot]

Yes

[bold needle]

ohhhhh

[bold needle]

yes

then

[pseudo knot]

Multiply this range by 16

[bold needle]

yup i did this

[pseudo knot]

Now we can simply add (an-1² + 8) on both sides

Now we'll just pick one of the two

[bold needle]

so we'll get

a _ n-1 ^2 + 8 < a_n+1 ^2

yes

[pseudo knot]

So let's pick first 2 relation

Yea

So now we have an²-an-1² > 8

Just substitute n=2, 3,4,5.... And add all

You'll get an² > 8n+8

Plug in 100 in this you'll get your answer

[bold needle]

ohhh

can you get a lower bound too?

[pseudo knot]

Yeah by the other half

[bold needle]

also do you know why he did this

[pseudo knot]

Not sure lol

[bold needle]

ohh that makes sense

thanks!!!

[bold needle]

thanks anyways

[pseudo knot]

If you use this side of inequality you'll get the other bound

[bold needle]

yup got it

[bold needle]

ok i m finding it very bashy to plug in values
it there some trick here to get 8n+8 ?
sorry

oh wait its telescopic

lemme try

[pseudo knot]

You don't need to calculate them

[bold needle]

lower bounds gives of 24n +16

which is greater
or am i making a mistake

[pseudo knot]

a2² - a1² > 8
a3² - a2² > 8
.
.
.
.
.
a99² - a98² > 8
a100² - a99² > 8

Add all this

[bold needle]

yeah got it

[bold needle]

...

[bold needle]

but what about this

[pseudo knot]

Similarly the other bound would be

a100² - a1² ≤ 24n - 24

a100² ≤ 24n-24+16

so 24n-8

Should be correct

[bold needle]

doesnt it gives 8n+16 ?

[pseudo knot]

No

[bold needle]

where extra -8 from?

[pseudo knot]

we're adding 8 (n-1) times

We went from 2 to n

[bold needle]

oh n-1 terms

right

[pseudo knot]

Similarly we add 24, n-1 times

So 24(n-1) + the 16 from a1²

[bold needle]

aha!!

got it

thanks

hey! @pseudo knot
although thanks for the effort

but here's a problem
the bounds we took were not very crude

we get a_100 > 28.28

and

a_100 < 48.9

which doesnt help with options given as 28 , 29 , 30 , 31

[pseudo knot]

That's because the upper bound is too inaccurate with our method, we can get the greatest integer using lower bound to be 28

That'll be our answer

And here's the exact value 😅

[bold needle]

ok so I can plug in n = 104 in my lower bound
a_n ^2 > 8n +8

toh it will give
a_104 = 28.9

and we know that a_n is strictly increasing so

a_100 has to be less than 28.9
and greater than 28.28

hence floor is 28

yup that's the answer

[pseudo knot]

Yeah

[bold needle]

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[feral siren]

can someone help me with the last question please

[feral siren]

i dont get why the student does better in the first test

when it has a lower mean

[magic sparrow]

Is this a test?

[feral siren]

np

no

[mellow axle]

did you do part a and b

i assume you did, what did you get for them

[feral siren]

for a i got 0.3085

for b i got 0.3644

[royal gust]

A "point" in the first test is "worth more" than a point in the second test

[feral siren]

oh

i didnt read it properly

so

since he got higher than

in the first test

than most people

he did better in it?

[royal gust]

Basically yeah. He's "more ahead" in the first test.

In the second test, he's closer to the mean

Another way to put it, the probability of the first test result is low, so this student is an outlier (better scorer than expected)

[feral siren]

oh ok

that makes sense thank you for the help

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[worn linden]

I need help with this

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[worn linden]

the gods helped me

brightened my knowledge

now how do i close this

[near lily]

You do

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[worldly falcon]

How would you solve this vectors problem

Cuz our teacher haven’t taught us anything with adding vectors with actual numbers yet

[mellow axle]

are you familiar with the geometric representation of what's going on

[worldly falcon]

Yes

I know where the lines go but when the lines have numerical values I can’t anymore

[mellow axle]

do you know what kind of shape is happening with those vectors

[worldly falcon]

i'm picturing a triangle in my head

[mellow axle]

it's a parallelogram

x,y are two legs of it

x+y is the long diagonal

x-y is the short diagonal

[worldly falcon]

thank you, this makes all the sense

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[cedar iris]

hi

[cedar iris]

i need help here

to get a

[silver roost]

can you send your owrk

[whole pecan]

You have C and c and A

c/C = a/A

[cedar iris]

i have a last change for the problems# so

i wanna check if i’m doing it right and if the answer

is right

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[cedar iris]

<@&286206848099549185>

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[flint perch]

why was induction used in 28?

because can't you say that all ai = 0, so then Ker(T)= {0}

like the same as 29..

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[tranquil pine]

can somebody explain why we don't calculate this using curl

like this one

why are they different

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[tranquil pine]

<@&286206848099549185>

[formal trail]

in one of them they turned the line integral into a surface integral, and in the other one they turned a surface integral into a line integral

basically just doing whichever one is easier

[tranquil pine]

how do i know when to do what

[formal trail]

hard to say. see which one looks harder i guess

[tranquil pine]

bruh

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[tranquil pine]

consider complex numbers $Z_1, Z_2$ , then prove that $|{\frac{Z_1}{Z_2}}| = \frac{|Z_1|}{|Z_2|}$

[soft zealot]

Matchstick

[magic sparrow]

Shouldn't be too bad, what have you tried?

[tranquil pine]

i've let Z1 be a+ bi and Z2 be c + di

[magic sparrow]

Let's see if my sir wants to clear this instead of me @signal shell

[tranquil pine]

the RHS was $\sqrt{\frac{a^2 + b^2}{c^2 + d^2}}$

[signal shell]

Sir do you know of the polar form of a complex number?

[soft zealot]

Matchstick

[tranquil pine]

no, sorry havent learnt that yet

still kind of in the beginning, just been introduced to properties of modulus

[magic sparrow]

It's okay, you can prove it without that, it just would make it easier

What did you get for the LHS

[desert mantle]

have you seen this property for multiplication instead of division already?

[tranquil pine]

i multiplied top and bottom by conjugate

[tranquil pine]

|z1z2| = |z1||z2|?

this?

[signal shell]

Yes

[tranquil pine]

yes i've been through that one

[signal shell]

Ah then you just have to prove the simpler version of $|\frac1z| = \frac1{|z|}$

Do you see why?

[soft zealot]

Ultimate Chad

[tranquil pine]

no sorry

i dont see it

[magic sparrow]

Z1/Z2 = Z1 * 1/Z2

[signal shell]

^

Try using this property and using your knowledge of the above to conclude

[tranquil pine]

how do i prove this?

i got it

thank you so much!!

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[tranquil pine]

For the orthogonal, curvlinear coordinate systems $u$ and $v$ which have two vectors defined as
\e{align*}{
(A)u &= \vc*u_1A{u_1} + \vcu_2A_{u_2} + \vcu_3A_{u_3} \
(A)v &= \vc*v_1A{v_1} + \vcv_2A_{v_2} + \vcv_3A_{v_3}
}
I want to find a systematic method to do the following two things:
\e{enumerate}{
\ii Recover expressions of the magnitudes of the components of vector $(A)_v$ in terms of some algebraic combination of the magnitudes of vector $(A)_u$
\ii Recover expressions for the unit vectors of $v$ in terms of some algebraic combination of the unit vectors $u$, and vice versa
}

[tranquil pine]

so my friend told me this is really just change of basis, and what i should be doing is something like

convert the basis of v to be some combination of the standard basis, (x,y,z), then convert that Cartesian representation to a basis in u

As an example, lets assume we want to convert spherical coordinates to cylindrical coordinates. We can use the definition of spherical coordinates, which is:
[ (x, y, z) = (r \sin\theta \cos\varphi, r\sin\theta\cos\varphi, r\cos\theta)
]
We can take the partial derivative with respect to $r$, $\varphi$, and $\theta$ to recover the expression for the basis:
\e{align*}{ \hat r& = (\sin\theta\cos\varphi, \sin\theta\cos\varphi, \cos\theta) \
\hat\varphi & = (-\sin\varphi, \cos\varphi, 0) \
\hat\theta & = (\cos\theta\cos\varphi, \cos\theta\cos\varphi, -\sin\theta)
}

[tranquil pine]

but now im pretty stumped on what to do. This half-answers my second question i asked above, but i still dont know how to continue this process, and answer question 1

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[restive copper]

wondeting if correct

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[quartz arrow]

claiming 🙂

[marble agate]

dont need to write that, for the next time

[quartz arrow]

I tried to find the pdf of T a different way than the problem wanted me to and i got a rlly wonky answer. Im assuming its because I did somethign that im not allowed to with probability densities... anyways heres what i tried can someone tell me where i went wrong:

$f_t(x) = $ density for $X_1 = x$ AND $X_2 <= x$ + density for $X_2 = x$ AND $X_1 <= x$ then i subtract the probability density for $X_1 = x$ AND $X_2 = x$ b/c i overcounted.

Then cuz they are independent i assumed that the probability density for event A and event B is just the product of their corresponding densities

$f_t(x) = 2*(\lamba e^{-\lambda x} *F_X(x)) - (\lamba e^{-\lambda x})^2$

Which is completely different from the correct answer which is

$f_t(x) = 2\lambda e^{-2 \lambda x}$

[soft zealot]

elonmosqito96
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[quartz arrow]

ya ik its just annoying to add screenshots and copy paste my questions when someone claims b4 i finish typing

[marble agate]

ok, np didnt try to be rude

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@quartz arrow Has your question been resolved?

[quartz arrow]

@spring depot (p.s i know its much easier to do it the way the problem hinted but im curious why my approach doesnt work)

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[quartz arrow]

ok i give up...

.close

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[waxen sentinel]

Pls help with iii

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[waxen sentinel]

<@&286206848099549185>

[waxen sentinel]

<@&286206848099549185>

[hollow shard]

who is jmancurly

miggie i hit and run

[waxen sentinel]

@wind glen

[wind glen]

[zinc vector]

https://mathsolver.microsoft.com/en

use this

[wind glen]

No

That doesn't really help

💀

Gimme a moment ima switch to another device so I can type better

[waxen sentinel]

aight

thanks

[wind glen]

okay

u probably have to use i and ii to prove iii

[waxen sentinel]

Any luck?

[wind glen]

re-write the integral

with tan

[waxen sentinel]

then?

[wind glen]

wut equation u get

[waxen sentinel]

cos(5theta)tan(theta)?

[wind glen]

yes

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[wind glen]

Can you do it from there...

U can rewrite again

[waxen sentinel]

It’s 3am

.close

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[twin escarp]

hello, i cant perform the 1's complement subtraction

[true fulcrum]

1's complement of 10 (0010) is 1101. Add this to 1101 and we get 11010. Then we drop the leading 1 and add 1 to the result, resulting in 1011.

[twin escarp]

thank you so much

https://tenor.com/view/tate-drift-thumbs-up-gif-27534473

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[wintry kindle]

Why are these two statements equivalent:

[desert mantle]

check the vector space axioms

wait what do you mean with equivalent

there are clearly vector spaces over K which arent fields

[wintry kindle]

hm then I'd rather rephrase it to "why is a finite field F containing a subfield K (|K|=q) isomorph to some vector space over K"?

[desert mantle]

its not just isomorphic

it is a vector space

just check the axioms

[wintry kindle]

hm k

[desert mantle]

just like C is a vector space over R

[wintry kindle]

the part which still befuddles me is that we have a field containing a field on one side and a vector space over a field on the other

[desert mantle]

well its still also a field

[wintry kindle]

yeah but the vector field doesn't contain the field that it uses for scalar multiplication

[desert mantle]

why not

R is a vector space over itself

[coral prawn]

The scalar multiplication is the same as the multiplication of F

so basically

a vector space is a set of elements V and a set of scalars S and a scaling operation that behaves the way you'd expect it to and also V must form an abelian group

[coral prawn]

this is actually a very loose statement

yeah and the set of scalars must form a field

[coral prawn]

so what that's really saying is that if you take the multiplication of F as the scaling operation and F as the set of vectors and K as the set of scalars and make F an abelian group by inheriting the addition operation from the field structure and make K a field by inheriting the field structure then what you have is a vector space

and really the only thing you need to check is that the scaling behaves like you'd expect, and indeed it does

[wintry kindle]

ah

that's more explicit thx

[coral prawn]

no worries ^^

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[forest lodge]

In a certain Algebra 2 class of 21 students, 9 of them play basketball and 14 of them play baseball. There are 2 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

[forest lodge]

Can someone help me with this exercise

[coral prawn]

Maybe A can be the set of students who play basketball and B can be the set of students who play baseball

You're asked to find the size of the union of A and B

I recommend you draw a Venn diagram

You know |A| = 9 and |B| = 14

[forest lodge]

yeah

[coral prawn]

The size of the union is |A| + |B| - |their intersection|

[forest lodge]

how can I find the intersection?

[coral prawn]

you also know that the size of the complement of A union B is 2

So you can form an equation by stacking stuff up

|A| + |B| - |intersection| + 2 = 21

why? because
|union of A and B| + |the complement of the union| = 21

again, Venn diagrams are helpful

[forest lodge]

so 14 + 9 - x + 2 = 21?

[coral prawn]

Yup, you can denote the size of the intersection by x for example and then solve for x

and then you've pretty much got it

[forest lodge]

I got it wrong

I put the probability in decimals, but they wanted it in fractions without telling me 😭

i mean i got it right, but I had that error

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[fossil trout]

do i need to include the base of the cube where the cylindre is sitting on it?

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• 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.

[arctic fiber]

What is least area of line BP when area of triangle inside of trapezoid is less 32 and side lengths are 7 and 5 but the 2 points of triangles are on edge of trapezoid ABCD

[final saddle]

@arctic fiber Has your question been resolved?

[final saddle]

@arctic fiber Has your question been resolved?

[final saddle]

@arctic fiber Has your question been resolved?

[final saddle]

@arctic fiber Has your question been resolved?

[fringe zealot]

if you have a picture of this problem, can you send it to me?

[arctic fiber]

근데 넓이가 32cm²이하인데 식이 34 이하로 변형된 이유가 있나요?

[fringe zealot]

34로 잘못 본듯 합니다
답은 10이 되겠네요

[final saddle]

@arctic fiber Has your question been resolved?

[final saddle]

@arctic fiber Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

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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>.
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• Be polite and have a nice day!

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[fringe gate]

HELP MEEEEEEEEEE HELP how to solve for x In this 2>= In x

[ivory vessel]

are you familiar with logarithms

also didnt i !xy you

[fringe gate]

Yes kinda somewhat depends

[ivory vessel]

show your original problem

[fringe gate]

That is it

Just solve for x

[dense coral]

do you know the definition of ln(x)?

[fringe gate]

Yes

[dense coral]

right, so what does ln(x) do?

[fringe gate]

That’s a very broad question

[dense coral]

apologies then

[fringe gate]

Be specific

[dense coral]

what's the definition of ln(x)?

[fringe gate]

1/x

Natural log

[dense coral]

that's the derivative of ln(x)

[fringe gate]

Idk

[dense coral]

specifically, what is the relationship between ln(x) and e^x?

[fringe gate]

Idk tbh

[dense coral]

you're familiar with logarithms, is that correct?

log_2(x) means the logarithm with base 2

ln(x) means ...?

[fringe gate]

I just know In x is 1/x and e^x is just e^x

[dense coral]

ln(x) isn't 1/x

[fringe gate]

Ye ik logs

[dense coral]

the derivative of ln(x) is 1/x

[dense coral]

awesome

[fringe gate]

I meant derivatives

[dense coral]

ah

[fringe gate]

Ye

[dense coral]

you know this, correct?

[fringe gate]

That’s all ik

Yes

[dense coral]

alright

[fringe gate]

This is funny lol

[dense coral]

then ln(x) = log_e(x)

[dense coral]

[fringe gate]

Wdym

How

[dense coral]

that is the definition of ln(x)

it's the inverse function of e^x

[fringe gate]

I don’t get it

Can u explain it simply

[dense coral]

okay, which part is confusing?

you seem to know what log_b(x) means

[fringe gate]

When u said in x is log e x

[dense coral]

okay

log_b(x) means what?

[fringe gate]

a^b = c

loga(c) = b

[dense coral]

er, idk what a and c are here

maybe I'll be more precise

[fringe gate]

Just variables

Look

[dense coral]

log_a(c) = b would mean this yeah

[dense coral]

yeah that's what I have

alright cool

so what does log_e(x) = y mean?

[fringe gate]

e^y = x

[dense coral]

okay nice

[fringe gate]

^^

[dense coral]

so...

are you aware of the fact that log_b(b^x) = x?

and b^(log_b(x)) = x?

[fringe gate]

No

And idk how that’s relevant

[dense coral]

well uh, I should state outright

that ln(x) = log_e(x)

[fringe gate]

How

[dense coral]

that is the definition of ln(x)

[fringe gate]

Explain how

[dense coral]

I mean like

ln(x) is the number you'd raise e to in order to get x

[fringe gate]

How

[dense coral]

hm

that's like

the definition of ln(x)...

[fringe gate]

So I’m just supposed to memorize that

[dense coral]

you're familiar with the notion of an inverse function, yes?

f^-1(x)

[fringe gate]

No

[dense coral]

ah

that would explain the issue then

[fringe gate]

What is that

[dense coral]

well uh

[fringe gate]

Why do u keep typing like that

[dense coral]

the inverse function, which we denote by f^-1(x), is the function such that f^-1(f(x)) = x and f(f^-1(x)) = x

[fringe gate]

Ok I’ll just memorize that definition now how does that help answer this

[dense coral]

alright cool

the key point here is that e^x and ln(x) are inverses!

you want to undo the ln function on the right hand side to isolate for x, correct?

[fringe gate]

Why would u do that

How does that isolate x

[dense coral]

well, that's how we solve for x, is it not?

rn we have 2 >= ln(x)

we'd like (something) >= x

[fringe gate]

Idk that’s why I’m on discord asking random ppl for help

Yes

We want to isolate x

[dense coral]

okay, I've stated earlier that e^x is the inverse of ln(x)

this means that if we apply e^x on both sides of the inequality, we'll isolate x

[fringe gate]

Is that a rule

[dense coral]

yes, it's the definition of ln(x), in fact

[fringe gate]

I thought it was logex

[dense coral]

ln(x) is just a fancy way to write log_e(x)

[fringe gate]

Ok

How do we isolate x

[dense coral]

raise e to the power of both sides

[fringe gate]

Can I show u the answer key and ask u specific questions about it I feel that’s more productive

[dense coral]

sure

[fringe gate]

Why did they make it log

And how

[dense coral]

remember that ln(x) = log_e(x)

[fringe gate]

Oh yeah

[dense coral]

they're just rewriting it

[fringe gate]

Also how did they delete log completely

[dense coral]

see here

specifically here's what they did

[fringe gate]

Ok but how did they delete log

[dense coral]

log_e(p) < = 2
e^(log_e(p)) <= e^2
p <= e^2

[fringe gate]

I wish u could use the bot

[dense coral]

I'm sorry, I don't yet know how to use LaTeX

let me write in in MS Paint

[fringe gate]

Ok but how did e become to the power of 2 and how did log disappear

<@&286206848099549185>

[dense coral]

this is what I wrote earlier

[fringe gate]

I still don’t get how did the log disappear

[dense coral]

well, log_e(x) and e^x are inverses!

I said this earlier didn't I?

e^(log_e(x)) = x and log_e(e^x) = x

that's what it means for e^x and log_e(x) to be inverses of each other!

for a function f(x), the inverse function f^-1(x) has the property that f(f^-1(x)) = x and f^-1(f(x)) = x

essentially, f^-1(x) "undoes" the function f(x)

[fringe gate]

Is this what u mean

[dense coral]

correct

[dense coral]

does this make more sense now?

[fringe gate]

How does this apply in this context

[dense coral]

well, see the picture I posted

[dense coral]

this one

notice that in step 2, we have e^(log_e(p))

[dense coral]

by the property you wrote in this picture, that must be equal to p

that's how the e and log cancelled

[fringe gate]

OHHHHHHHHH

now it makes sense

[dense coral]

[fringe gate]

I’m still debating to unblock u or not

[dense coral]

it's your choice tbh

I stated that I don't mind being blocked by you

[fringe gate]

U sketchy

[dense coral]

and I'm not gonna hold a grudge against you for it

[fringe gate]

One day ur nice

The next

[dense coral]

I'm usually more like this haha

[fringe gate]

Ur weird

[dense coral]

I got a bit impatient two days ago

apologies for that

[fringe gate]

U hold evidence against me then used it when the time was right

[dense coral]

just because you blocked me doesn't make me consider not helping you

everyone deserves help you know

[dense coral]

I was trying to be witty for some reason

but I was also seriously concerned about your conduct at that moment

[fringe gate]

U remind me of hazye

[dense coral]

I don't think we're at all alike

[fringe gate]

Wdym conduct ?

U both have sketchy characters

[dense coral]

I didn't like how you shut the door in chebyshev's face and told them off

I'm not sure if you just had a really bad day or what

[fringe gate]

Wdym shut door

And told off

I was having a great day

[dense coral]

...I don't really want to rehash that moment by reposting the image ngl

[fringe gate]

It’s clear u have resentment

Post the image

[dense coral]

I'll just say that you weren't the nicest you could've been

[fringe gate]

Let us clear it

Post it

[dense coral]

okay, promise me you won't get angry at me for it?

[fringe gate]

Nope

I promise

[dense coral]

okay, give me a moment

[fringe gate]

So which part of this is shutting door and telling off

[dense coral]

so like, they were clearly trying to help you here

[dense coral]

"please do not talk in my channel if you won't help"

they were trying their best to, I promise

[fringe gate]

Yes because helping channels are for math help no ?

[dense coral]

correct

but they are a helper

[fringe gate]

Was she giving math help ?

[dense coral]

and a pretty good one at that

[fringe gate]

No

[dense coral]

they needed more context

[fringe gate]

I don’t like when ppl say nonsense things that aren’t related

Or helpful

[dense coral]

it's pretty hard to help someone if you don't know the full context behind their question

[fringe gate]

No they didn’t

The context was already given

Everything was

[dense coral]

okay, even if that's the case

[fringe gate]

Screeenshots of the whole problem

[dense coral]

why did you say that?

you could've just said your first message and left it at that

[fringe gate]

Because they were not saying things that were helpful to the math question

[dense coral]

if you didn't mean any bad intentions, you really came off as condescending there

[fringe gate]

Do u know the full context ? Of what happened

[dense coral]

I was in the help channel too you know

I flicker through many of them

[fringe gate]

I didn’t come off as anything u just interpreted it wrong

[dense coral]

how so?

I'm ready to admit fault here if you can tell me how

[fringe gate]

I said it without sugar coating or anything because I was looking for math help not things that aren’t related to math help. Just because I didn’t say it with roses and hearts doesn’t mean it’s condescending I’m just straightforward and I had to make 3 channels that day due to others being racist and trolling so I didn’t want any more bullshit and just math help simple

It’s not my problem u took it as condescending

[dense coral]

well, chebyshev and others didn't know about any of that

I trust that you had good intentions then

[fringe gate]

I even said please LOL

[dense coral]

even with good intentions then

I would really suggest not being so blunt

[fringe gate]

None of this is my problem tbh

[dense coral]

it gives off the wrong impression

[fringe gate]

It’s just ur issue

I don’t care about impressions I’m not here for that

I’m here for math help

[dense coral]

sure, but it was evidently many others' issues too

[fringe gate]

Again I don’t care about other ppl perceptions

I, not here to make friends

I’m here to get help

[dense coral]

believe me, people don't like to help if they feel like the person they're trying to talk to is being rude to them

[dense coral]

me neither!

it's not about how others perceive you

it's about the fact that many are much less willing to assist you if you come off the wrong way

that's a math help thing, not a perception thing

[fringe gate]

If they don’t want to help then that’s their choice I won’t change how I talk just to get help I can find that somewhere else then

[dense coral]

you can, but then you'll have to wait a lot longer

[fringe gate]

I don’t care

[dense coral]

then that's fine too

[fringe gate]

I don’t change for others

[dense coral]

I'm not gonna ask you to do whatever

I'm just informing you of the problem at hand

[fringe gate]

Good one

[dense coral]

I'm not trying to attack you here

[fringe gate]

Last time u were attacking me

And now u r informing me

Lol

[dense coral]

I was not in the best mental state yesterday ngl

lol

I also didn't have the context you just provided me

[fringe gate]

It’s whatever just don’t do that stuff again ur unblocked for now thanks for the help

[dense coral]

actually

let me formally apologize for yesterday

[fringe gate]

it’s not that serious

[dense coral]

that was probably a severe mistake on my part

[fringe gate]

I don’t hold hate

Or resentment

[dense coral]

I don't hold hate either

we're all good now?

[fringe gate]

yes

[dense coral]

then you can close this channel

[fringe gate]

Alt

.close

[final saddle]

Channel closed

Closed by @fringe gate

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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.

[copper knot]

Help

Stephen.

I see u.

Help me.

Please.

<@&286206848099549185>

<@&286206848099549185>

[zenith pollen]

here's the drawing, adding vectors is like putting them head to tail of each other

[copper knot]

Thanks

[zenith pollen]

so there's some triangle with side legnths 8,10,? and a length of 3 that splits up the 10 edge

[copper knot]

Right

But I need to find the numerical value

[zenith pollen]

yea I'd have to look up some median triangle theorem to find it

[copper knot]

Oh

Could u find an angle with cosine law or smthn?

[zenith pollen]

I think so yea, cosine law and another thing

apparently it has a weird name I've hardly seen before

[copper knot]

Aw he he he helll naw

This is Highschool calc how bad can it be

[zenith pollen]

this question is pretty evil lmao

[copper knot]

These are easier versions of my test questions

Apparently.

I’m cooked

TYSM tho!

[zenith pollen]

np np

[copper knot]

I’ll see if it works out

Byee

.close

[final saddle]

Channel closed

Closed by @copper knot

Use .reopen if this was a mistake.

[final saddle]

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.

[manic echo]

how do you find cos (arcsin sqrt x)

[formal trail]

you can draw a right triangle

[manic echo]

nvm i found a video

yeah

.close

[final saddle]

Channel closed

Closed by @manic echo

Use .reopen if this was a mistake.

[final saddle]

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.

Please don't occupy multiple help channels.

[long wraith]

Bro 💀 Your name...

[faint edge]

.close

[final saddle]

Channel closed

Closed by @faint edge

Use .reopen if this was a mistake.

[final saddle]

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

[coral horizon]

Help me

This question is of integration

[shrewd meadow]

what things have you learnt about antiderivatives?

techniques, formulas, all that

[coral horizon]

Integration by considering u

[shrewd meadow]

just substitution?

[coral horizon]

I am 10th passout

Not learnt much

[shrewd meadow]

🤔

[rancid flicker]

do you know about integration by parts?

[shrewd meadow]

can you transform sin(2x)?

...oh, nah
this question's answers clearly asked for integration by parts

[coral horizon]

Answer pls?!

[coral horizon]

Yea

I know

[rancid flicker]

so [\int u dv = uv - \int v du ]

[soft zealot]

dabeastmode_the_wannabe_nerd

[rancid flicker]

for functions of x, so u and v are functions of x

[shrewd meadow]

the problem now is to find which function to be u and which to be dv, so you can transform into the right-hand side

[rancid flicker]

what would be your guess for u?

[final saddle]

@coral horizon Has your question been resolved?

Channel closed

Closed by @coral horizon

Use .reopen if this was a mistake.

[coral horizon]

B

[final saddle]

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• Show your work, and if possible, explain where you are stuck.
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[midnight pasture]

Does anyone know how to represent a sum over $S_n$ as sums of $S_{n-1}$

[soft zealot]

ScarletPizza

[midnight pasture]

Ie $\sum_{k \in S_{n}}$

[soft zealot]

ScarletPizza

[midnight pasture]

Trying to generalize rather than a specific n

So I can use induction. As a straight proof doesn't seem to worj

[final saddle]

@midnight pasture Has your question been resolved?

[midnight pasture]

<@&286206848099549185>

[real sleet]

sums of $S{n-1}$ + $Sn$ ?

[soft zealot]

pubuyun

[real sleet]

or else you don't know what is Sn

[midnight pasture]

Sn is the set of permutations of n elements

[final saddle]

@midnight pasture Has your question been resolved?

[final saddle]

@midnight pasture Has your question been resolved?

[midnight pasture]

Anyone got ideas

[final saddle]

@midnight pasture Has your question been resolved?

[final saddle]

@midnight pasture Has your question been resolved?

[wintry kindle]

ys you can't restructure a sum over permutations using a sum of smaller permutations if the influence of the first component of the permutation is unknown

as we'd need to isolate it in order to split the sum

I mean you could create an additional sum for the first component and concatenate, if that helps

but it barely changes the initial structure

If we can help with the proof you're aiming for just post it :]

[final saddle]

@midnight pasture Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

Remember:
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• 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.

[final saddle]

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.

[real mesa]

where is b square in this equation of number complex

by using this method

[wind glen]

B is 4

$ax^2+bx+c=0$

[soft zealot]

w

[real mesa]

thanks

[wind glen]

Do .close if that's all

[real mesa]

how to close

.close

nvm mb

.close

didnt work

.close

[wind glen]

Idk

Lol

[real mesa]

bot went off lol

[final saddle]

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>.
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• Be polite and have a nice day!

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[gusty vapor]

hi

[gusty vapor]

$$y=x^2+2x+1$$
$$x+y+1=0$$

if (x1,y1) and (x2,y2) are the two solutions to the system of equations above, what is the value of y1+y2?

[soft zealot]

موثريستا

[candid mulch]

!status

[final saddle]

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

[gusty vapor]

7
what is y1+y2?

[candid mulch]

Have you tried anything before asking

[gusty vapor]

i tried all

[candid mulch]

Mind showing your work?

[gusty vapor]

i don't use a paper and pen

[candid mulch]

Screenshot then

[gusty vapor]

i will send you my mr's annotation

here

[candid mulch]

What do you usually do when you’re given two equations with two variables?

[gusty vapor]

what do we usually do?

[candid mulch]

e.g.
x+2y=3
4x+5y=6
How would you solve for x and y?

[gusty vapor]

you mean 4 tho right?

[gusty vapor]

ez

just put one in another

[candid mulch]

Only two: x and y

[gusty vapor]

na

x1 x2 y1 y2

(x1,y1) and (x2,y2)

[candid mulch]

Those are not variables

[gusty vapor]

https://tenor.com/view/cat-huh-cat-huh-etr-gif-15332443943609734737

[candid mulch]

Anyway you can actually solve the question in the same way: putting on in another

[gusty vapor]

Oh alr

what we gna do

[candid mulch]

By putting one equation in another
We can eliminate one of variable

[gusty vapor]

na

we got 4 2 eliminate

[candid mulch]

y=x^2+2x+1
y=-x-1

We can eliminate y here

[gusty vapor]

NO

[candid mulch]

?

[gusty vapor]

I AM NOT SOLVING IT AS PER YOUR THAT

I TRIED

AND FAILED

AND I CANTDO IT ANYMORE

I AM BURNED OUT

[candid mulch]

You can definitely solve that
-x-1 = x^2+2x+1
→ x^2+3x+2 = 0
…

Which gives you two values of x and their corresponding y aka y1 and y2

[gusty vapor]

so that's it?

ty ily

🙏🏻

.close

[final saddle]

Channel closed

Closed by @gusty vapor

Use .reopen if this was a mistake.

[obtuse flame]

that is not it, but i would encourage you to try to solve from there

[gusty vapor]

oh okay

what's next 🥰

[obtuse flame]

the next step would be to factorize the quadratic equation x^2+3x+2 = 0 as mentioned by Afi

are you able to do that?

[gusty vapor]

okay

yes!

(x+2)(x+1)

we get +1 and -2

which is gut-wrenching

[obtuse flame]

your factorization is correct

but one of the solutions you acquired is wrong

x + 2 = 0
x = -2

x + 1 = 0
x = -1

[gusty vapor]

ya

which are both false

I JUST CAN'T DO THIS ANYMORE

[obtuse flame]

what do you mean by both false?

[obtuse flame]

calm down, it's nearly finished

can you explain what you mean when you say both are false?

[gusty vapor]

okay

so

-1 and -2 are both in the choices

is this a curse from God?

[obtuse flame]

ah, i see, you are talking about the multiple choices given in the question

but those choices are referring to the value of y1 + y2

[gusty vapor]

yes

-3

[obtuse flame]

we have not found those values

[gusty vapor]

yes

[obtuse flame]

we should continue solving in order to reach that stage

[gusty vapor]

yes

[soft zealot]

misha

[gusty vapor]

yea

[soft zealot]

misha

[gusty vapor]

YEA!

@obtuse flame ty

[obtuse flame]

and the answer is therefore 1

[gusty vapor]

yippe

[obtuse flame]

@gusty vapor you're welcome, but i feel like you might not have a good foundation or understanding of the concepts that are being applied here

it would be a good idea to revise or relearn now while you have the chance

if you go to the next year with an unstable foundation in such topics, you'll have a horrible time

just some advice

[gusty vapor]

i have a good foundation and understanding of the concepts being applied right

but thank you for your concerns

🙏🏻❤️

.close

[final saddle]

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[orchid surge]

help pls

[granite bay]

yes?

Alright, now what does it mean?

[orchid surge]

i have to make all the other thing equal g

[tough basin]

t!help

[granite bay]

Akira stop man.

[orchid surge]

this one is getting used icl

[granite bay]

Alright.

[tough basin]

Mb

[orchid surge]

you good

[granite bay]

You first start by removing the fraction. Do you know how that is done?

[orchid surge]

timesing it by the denominator

[granite bay]

try it, and show me!

[orchid surge]

2 x g + h

[granite bay]

no no, like from the equation.

[orchid surge]

ohh

[granite bay]

Can you show me how you remove the fraction?

Or do I need to explain it?

[orchid surge]

a = 2 x g + h

i think

[granite bay]

Not quite 🙂

[orchid surge]

if not please explain

a = g + h x 2

?

[granite bay]

For example.

You have ,tex a = L/2

and then.

You want to remove the fraction (in this case, remove the 2)

You multiply on both sides by 2, and then you have isolated L. Meaning you have made L the subject.

[orchid surge]

oh so its 2a = g + h

[granite bay]

Yes!

and now we want the h gone.

In other words; moved to the other side.

[orchid surge]

so h + 2a = g

[granite bay]

Haha no.

To move the h to the other side.

[orchid surge]

is it take away

instead

[granite bay]

You do the opposite of what is happening.

It's like.

[orchid surge]

so h - 2a = g

[granite bay]

Remember, it's -h, not -2a

You haven't subtracted 2a from anywhere.

[orchid surge]

ohhh

-h +2a = g

[granite bay]

Yeah! you can definitely say that

Or 2a - h = g

It's the same.

[orchid surge]

thanks again ill be back soon

.close

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Channel closed

Closed by @orchid surge

Use .reopen if this was a mistake.

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Remember:
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[urban lagoon]

hi

[frail girder]

tf am u doing wrong

[urban lagoon]

.close

[final saddle]

Channel closed

Closed by @urban lagoon

Use .reopen if this was a mistake.

[frail girder]

oops

sorry

[vast raft]

what problem

[frail girder]

do u kno trig

there is supposed to be a 4Cos2x at the end

not 2Cos2x

.close

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[flint perch]

for finding inverse T, do you have to use standard basis?

[desert mantle]

no

[flint perch]

im confused because for 21, T in ex 3 is this,

this was the sol

[desert mantle]

and?

[flint perch]

sry im trying to send a picture

wifi is being weird

but T from c<-b is not the change of basis they used

and then I check to see if T is invertible..etc

which Im confused about..

@desert mantle

[desert mantle]

what exactly is your question

you didnt follow the problem statement

so you get different stuff

[flint perch]

ohh yea

I see

w respect to standard basis

that makes sense,Im so sorry

ok

[final saddle]

@flint perch Has your question been resolved?

[flint perch]

I swear I know how to do some of these questions

i know the process

but my calculations are so messed

messed up

😭😭try reading this

i’m getting confused

i don’t know if I should retry the question or just move on😭😭😭

ok i’ll redo

last time

[tulip coyote]

(what's the question there? derivative operator on the space spanned by { e^{-2x}, e^{2x} }?)

[flint perch]

yup

also your answer shouldn’t change with different span right?

so even if its spanned by { e^{2x}, e^{-2x} } the answer will still be the same?

It should be

[tulip coyote]

Just noticed that this is from another set of questions

[tulip coyote]

Well the inverse operator should give you the same function (though matrices etc may be a bit different)

[flint perch]

ok

i’m good

i do know what I’m doing

[tulip coyote]

[flint perch]

do you know what this notatiion is called?

1 linear norm?

[tulip coyote]

Forget the name but remember what it represents I just call them L^p spaces

[flint perch]

ok

i dont know why they are splitting it into two

it should be solvable if you just have 0 to 1

[tulip coyote]

The picture: at some points, sin(pi * x) <= 2x (so sin(pi * x) - 2x <= 0) and at others, you have the reverse, sin(pi * x) >= 2x, so sin(pi * x) - 2x >= 0

Remember how the absolute value is defined...

[flint perch]

sin(2x)?

pi right?

[flint perch]

what do you mean by that, as in how its defined when evaluating integrals?

[tulip coyote]

in general, with one being that
[
\abs{y} =
\begin{cases}
y & y \geq 0 \
-y & y \leq 0
\end{cases}
]

[soft zealot]

@tulip coyote

[flint perch]

yea

oh so hence why you have to split into two

[flint perch]

but why sin(2x)?

[tulip coyote]

Because integrating this is hard

[tulip coyote]

Oh, misread, thought it was a 2 sorryyyyyy

[flint perch]

oh okok nw!