help-17

[warped osprey]

what are improper integrals is that the same as definite integrals

[lilac pebble]

it means you can make the integral bigger than any given number

it's unbounded

[stark berry]

improper integrals either have infinities as their bounds

or some sort of discontinuity within the bounds

or at them

[warped osprey]

oh

this might be a dumb question

but why doesnt the graph look like this then

sorry bad drawing

[lilac pebble]

it's the area that gets big

not necessarily the function itself

[warped osprey]

wait so as you increase N, the area 'converges' to 1?

[lilac pebble]

what integral are we talking about?

[warped osprey]

part a

[lilac pebble]

you can make the area as close to 1 as you want by making N bigger

[warped osprey]

so the answer is this right but as N gets bigger, why does that mean the area is close to 1??

[stark berry]

yes

[warped osprey]

sorry im trying to make sense of this. Why does restricting the function to x>=1 mean that the area under the graph is getting closer to 1

[lilac pebble]

um

it's the upper bound that you're moving

not 1

https://www.desmos.com/calculator/3ewtn6sehp

you can move the slider

[warped osprey]

Wait a minute

isnt this literally just the same as drawing this

without all the converging stuff

[lilac pebble]

huh?

[warped osprey]

like drawing this function from 1 to infinity

um i think it was overcomplicating this the whole time

that 'converging to 1' statement is making me lost

[civic otter]

Converging means "having a finite value of the limit", in other words

In that case the limit as N → +∞ gives you a result of 1

[lilac pebble]

the blue area doesn't get bigger than 1

[warped osprey]

oh so correct me if I'm wrong but I just draw the integral from 0 to infinity and whatever that is, the area never exceeds 1?

[lilac pebble]

why would you draw the area from 0?

when it says 1

[warped osprey]

oh wait sorry i mean 1

[lilac pebble]

oh ok

is this a question or is this from an answer key?

[warped osprey]

that's the question

[lilac pebble]

they didn't ask you to find the limit

[warped osprey]

huh

[lilac pebble]

they asked you to evaluate the definite integral

N is finite

[warped osprey]

yea??

[warped osprey]

it is?

i thought it was infinity

[lilac pebble]

Like I got that as N -> infinity, the integral -> 1
you said this, so it sounded like you evaluated the limit

[lilac pebble]

yeah N is finite

[warped osprey]

oh ye i did

oops

ye i see what you mean

i think i get this now

thank you for ur time

[lilac pebble]

oh

[warped osprey]

??

is there smth im missing

[lilac pebble]

it says "establish the result that follows"

[warped osprey]

so i do evaluate the limit?

[lilac pebble]

i guess that means you should evaluate the limit

yeah

[warped osprey]

ah ok thank you

.close

[vocal sleet]

Channel closed

Closed by @warped osprey

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.

[polar jungle]

Im learning how to differentiate implicity to find y' in terms of x. I need help on number 11. I'm not sure I set it up right and which steps to take next

[scenic ravine]

You're trying to differentiate $\ln(xy)=tan^{-1} (x)$?

[twin meteor]

ƒ(Why am. I here)=I don't Know

[polar jungle]

I'm trying to differentiate (x^3 y^4)^5 = x-y

[scenic ravine]

So you want someone to walk you though all the steps, yes?

[polar jungle]

Yes please

[scenic ravine]

okay

[polar jungle]

If u can ofc

[scenic ravine]

I can, yeah

$(x^3y^4)^5=x-y$

[twin meteor]

ƒ(Why am. I here)=I don't Know

[scenic ravine]

so when we differentiate this, we first set x^3y^4=u for convinience

that gives us $u^5=x-y$

yeah?

[twin meteor]

ƒ(Why am. I here)=I don't Know

[polar jungle]

Oke

[scenic ravine]

so what do you get on differentiating this

we are differentiating wrt x , keep that in mind

[polar jungle]

Oke

So first I would do $5(x^3 y^4)^4$

[twin meteor]

Royal_Penguin01

[polar jungle]

Then for the inside I did $(3x^2 4y^3y')$

[twin meteor]

Royal_Penguin01

[scenic ravine]

uh

that's wrong

[polar jungle]

Oop

[scenic ravine]

remember the product rule

[polar jungle]

Ooh yeah huh

Ma bad lol

So it would be $(3x^2(y^4) + x^3(4y^3y')$

[twin meteor]

Royal_Penguin01

[polar jungle]

Or no?

[scenic ravine]

so the left hand side would be $5(x^3y^4)^4(3x^2(y^4) + x^3(4y^3y'))$., yes?

[twin meteor]

ƒ(Why am. I here)=I don't Know

[polar jungle]

Yup

[scenic ravine]

Now what about the right hand side

[polar jungle]

The right hand side would be $1-y'$

[twin meteor]

Royal_Penguin01

[scenic ravine]

yup!

$$5(x^3y^4)^4(3x^2(y^4) + x^3(4y^3y'))= 1- y'$$

[twin meteor]

ƒ(Why am. I here)=I don't Know

[scenic ravine]

Now for the ugly part. Solve for y'

[polar jungle]

So I would move $5(x^3 y^4)^4$ to the right hand side first?

[twin meteor]

Royal_Penguin01

[scenic ravine]

I'd expand the left hand side first

[polar jungle]

Ooh oke I see

WAIT Hold up!

I would have to multiply (x^3 y^4) 4 times😭!?!

[scenic ravine]

no

You can use laws of indices

$(x^3y^4)^4=. x^{12}y^{16}$

oops

[twin meteor]

ƒ(Why am. I here)=I don't Know

[polar jungle]

Ooh yeah

Oop ma bad lol

So the left side would look like this?

[scenic ravine]

yes, you now expand it

[polar jungle]

So would it look like this?

For my final answer I got $y' = 1 - 15x^14 y^20 / 20x^15 y^19 + 1$

[twin meteor]

Royal_Penguin01

[polar jungle]

It's suppose to be 15x to the power of 14

Then 15y to the power of 20

[scenic ravine]

$y'= 1- \frac{15x^{14}y^{20}}{20x^{15}y^{19}+1}$?

[twin meteor]

ƒ(Why am. I here)=I don't Know

[polar jungle]

Yes that's what I got

[scenic ravine]

let me check

,w differentiate (x^3y^4)^5=x-y with respect to x

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[scenic ravine]

if this is what you got, it should be right

[polar jungle]

Yes it is

Thank u for ur help!

.close

[vocal sleet]

Channel closed

Closed by @polar jungle

Use .reopen if this was a mistake.

[vocal sleet]

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.

[untold arrow]

Damn

[hard atlas]

\sqrt[3]{x}

[silk osprey]

you need a space

[twin meteor]

Cryolite

[untold arrow]

Finally

[silk osprey]

just take sin of both sides

[untold arrow]

Damn I'm dumb tysm

[vocal sleet]

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.

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.

[weary gale]

I was wondering if my work was correct

[vocal sleet]

@weary gale Has your question been resolved?

[weary gale]

!close

/close

[solar cape]

It's
.close I think

[weary gale]

.close

[vocal sleet]

Channel closed

Closed by @weary gale

Use .reopen if this was a mistake.

[vocal sleet]

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.

[pliant latch]

a is 35.5 deg, AC is 46.5cm and BC is 29.2cm, i solved AB to be 49cm but i cant get AB'

[pliant latch]

.close

[vocal sleet]

Channel closed

Closed by @pliant latch

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.

[wintry thunder]

can someone help me with this one "y=−x2−x−2", and Rewrite in standard form and give the vertex.

[scenic ravine]

$y=x^2-x-2$?

[twin meteor]

ƒ(Why am. I here)=I don't Know

[rough patrol]

do you know what completing the square is?

here, i will do this problem on a different quadratic, and then you can try it on this one

let us take the quadratic $y=x^2+6x+15$.

[twin meteor]

Arnavutköy

[rough patrol]

I want to write this in the form $y=(x+c)^2+d$.

[twin meteor]

Arnavutköy

[rough patrol]

where c and d are some constants

let us expand this out

$y=(x+c)^2+d=x^2+2cx+(c^2+d)$

[twin meteor]

Arnavutköy

[rough patrol]

so notably, we see that $2c$ is the coefficient for the $x$.

[twin meteor]

Arnavutköy

[rough patrol]

so if we want to write this in standard form for $x^2+6x+15$.

[twin meteor]

Arnavutköy

[rough patrol]

We want $2c=6$ then.

[twin meteor]

Arnavutköy

[rough patrol]

This implies that $c=3$.

[twin meteor]

Arnavutköy

[rough patrol]

Therefore, we have that $x^2+6x+15=(x+3)^2+d$.

[twin meteor]

Arnavutköy

[rough patrol]

Now, we can expand $(x+3)^2$ and solev for $d$.

[twin meteor]

Arnavutköy

[rough patrol]

We get that $d=6$.

[twin meteor]

Arnavutköy

[rough patrol]

Therefore, we can now write that $x^2+6x+15=(x+3)^2+6$.

[twin meteor]

Arnavutköy

[rough patrol]

Thus, $(x+3)^2+6$ is the standard form for $x^2+6x+15$.

[twin meteor]

Arnavutköy

[rough patrol]

Takeaway: assuming the quadratic is monic, the thing squared will be $x+\frac{b}{2}$, where $b$ is the coefficient of $x$.

[twin meteor]

Arnavutköy

[vocal sleet]

@wintry thunder Has your question been resolved?

[wintry thunder]

@rough patrol waitss,.. let me try and absorb everything that u just said for a couple of mins

@rough patrol so the key into solving the equation that i sent you, is completing the square. but then, since the coefficient of the x is 1, would that make it (x - 1/2x)^2 - 2?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[wintry thunder]

.reopen

[vocal sleet]

✅

[rough patrol]

you still need to change the constant term

and also it is just (x-1/2)

not (x-1/2x)

we look at the coefficient of the x term

[wintry thunder]

how was the x removed??

[rough patrol]

because we look at the coefficient of the x term and divide by 2

[wintry thunder]

i mean, in what process was made to remove the x

when you said that the new equation is (x - 1/2)^2 - 2?

mb if im too slow btwss

[rough patrol]

when we square this

it will be x^2+2(-1/2)x+(-1/2)^2

we can deal with the constant term later by adding a constant

but the important thing, is that 2(-1/2)x=-x

the idea is, when writing it in standard form, we want to get rid of that coefficient

[wintry thunder]

which is x, no?

[rough patrol]

yeah?

[wintry thunder]

so after figuring this out, what should be the next move then?

[bronze osprey]

if you have $y = a(x - h)^2 + k$, the vertex is just $(h, k)$

[twin meteor]

south

[bronze osprey]

so here a = 1

(that's the vertical stretch factor btw)

[vocal sleet]

@wintry thunder Has your question been resolved?

Channel closed

Closed by @wintry thunder

Use .reopen if this was a mistake.

[wintry thunder]

@rough patrol and @bronze osprey Thanksss

[vocal sleet]

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.

[untold arrow]

If r=m, then the equ has a solution. Why?

[untold arrow]

Why is it only when r=m

[hard atlas]

if r=m then the system is guaranteed to have a solution

if r<m then you dont know

if r=m then the columns of A span R^m, so some linear combination of them will equal beta

[untold arrow]

Mmm

What if r=n

[hard atlas]

then n<= m

and then its the same as before

rank <= min(n,m) always

so the only way for it to equal n is that n<=m

intuitively, n doesnt do much in the system. if you repeat one of the columns of A a few times then n changes but nothing about the solvability changes

[vocal sleet]

@untold arrow Has your question been resolved?

Channel closed

Closed by @untold arrow

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.

[vocal sleet]

Please don't occupy multiple help channels.

[thorn spindle]

for the second deriv part

i thought its only concave down when the second deriv is less than or equal to x

so why do they also say x>=1

shouldnt it be x<=1

going to sleep but if someone could answer this ill read it when i wake up
thanks

[lyric relic]

are you the real faker ?

[high kettle]

What do you think?

💀

[vocal sleet]

@thorn spindle Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[stone badge]

How to do this one?

[bronze osprey]

$(\cos^4 x + 3 \sin^2 x)(\cos^2 x) = 1 - \sin^6 x$

$(u^2 + 3(1 - u))u = 1 - (1 - u)^3$

[twin meteor]

south

[bronze osprey]

ah this is a show that question, not an equation

yes this is an identity

[stone badge]

I tried with the other side

[stone badge]

Yeah

I am trying to prove it

[high kettle]

\begin{align*}
1+3\tan^2 x \sec^2 x &= 1 + 3\tan^2 x\left(\tan^2 x + 1\right)\
&= 1+3\tan^2 x + 3\tan^4 x\
&= 1+3\tan^2 x + 3\tan^4 x + \tan^6 x - \tan^6 x\
&= \left(1+\tan^2 x\right)^{3}-\tan^{6}x\
&= \left(\sec^{2}x\right)^{3}-\tan^{6}x\
&= \sec^{6}x - \tan^{6}x_{\blacksquare}
\end{align*}

[twin meteor]

如月あやみ　Kisaragi Ayami

[bronze osprey]

first try to decipher my working

essentially do not write 1 as cos^2 and sin^2
and make both denominators cos^6

[bronze osprey]

elegant

[stone badge]

How did you get tan square x +1?

[bronze osprey]

$\sec^2 x = \tan^2 x + 1$

[twin meteor]

south

[stone badge]

Sec square

Is it a formula?

[bronze osprey]

yes!

[high kettle]

yes

[bronze osprey]

try multiplying both sides by cos^2 x

see what you get

[stone badge]

Oh my god I didn’t notice

Thank you

[stone badge]

If I do it like this do I get the same?

[bronze osprey]

yes and if you want another one, divide $1 = \sin^2 + \cos^2$ by $\sin^2$ on both sides

[twin meteor]

south

[bronze osprey]

possibly, yeah $a^2 + ab + b^2 = \frac{a^3 - b^3}{a - b}$

[twin meteor]

south

[bronze osprey]

ah so you get $\frac{\sec^6 x - \tan^6 x}{\sec^2 x - \tan^2 x}$, nice

[twin meteor]

south

[bronze osprey]

but like it's circular

[stone badge]

Is this a formula too? I don’t think I learned that

[bronze osprey]

yeah you've assumed what you wanted to prove

[bronze osprey]

yes

difference of two cubes

[stone badge]

Where did you get tan^6x-tan^6x at the end?

Of step 3

[high kettle]

the purpose is to make turn the first 3 terms into a (1+something)^3 format

so i added tan^6 x and then subtracted tan^6 x again

[stone badge]

I didn’t know this was possible

[high kettle]

you're just adding 0 so it's definitely allowed

[stone badge]

Thank you

[vocal sleet]

@stone badge Has your question been resolved?

Channel closed

Closed by @stone badge

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.

[past vessel]

Why is there an asymptote for y = 1

For theta = 0.5, r=1/0.5 = 2??

[past vessel]

???

[past vessel]

yes why y=1

If theta is 0.5, would r=1/0.5 = 2

[silk hare]

oh wait

there is x=1 but i don't know for x sorry 😅

[past vessel]

what??

[silk hare]

there is an asymptote for x = 1

but i don't know about the y axis

[past vessel]

No

[past vessel]

The asymptote is y=1

😭

Not x=1

[silk hare]

oops

[past vessel]

😭

[silk hare]

let's cry together

[past vessel]

.close

[vocal sleet]

Channel closed

Closed by @past vessel

Use .reopen if this was a mistake.

[vocal sleet]

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.

[unborn roost]

I need help with math problem

[stark berry]

[unborn roost]

how can i solve this ?

[unborn sundial]

solve what?

[unborn roost]

this ?

up there?

[candid magnet]

whats s

[unborn sundial]

do not see anything to solve, just the sum

[unborn roost]

yeah

tht 3 dots

and u need s i think

[outer warren]

don't troll

[unborn roost]

i am not trolling

i am just asking

if no thats ok i will ask someone else

[stark berry]

its been unsolved

it is unsolved

[unborn sundial]

so what exactly should be found in that picture?

[stark berry]

the non trivial zeros of the sum

[unborn sundial]

it's not an equation, or something to be solved

[unborn sundial]

I know that, just wanted the author to respond

[vast shale]

Its just a function. theres nothing to be solved

[unborn sundial]

that guy failed even in trolling^)

[unborn roost]

bro i am not trolling

i will ask someone elses

bye

[vast shale]

…

theres nothing to solve

[unborn sundial]

bye^)

[unborn roost]

ik da answer

bye

.close

[vocal sleet]

Channel closed

Closed by @unborn roost

Use .reopen if this was a mistake.

[steady plover]

bro knows the answer

[vast shale]

Bro is missing out on 1mil usd

[steady plover]

hes very humble

[flat whale]

<@&268886789983436800>

[versed bane]

don’t troll in the help channels.

[vocal sleet]

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.

[outer arrow]

Can anyone help prove the statement on top

[lilac pebble]

the implication only works if a != b and c != b

[outer arrow]

Yes , i didnt fit that in my screenshot

Also b and d arent 0

[lilac pebble]

there's a d?

[outer arrow]

Im not sure how to use the given aasumption

Damn , is my handwriting that bad

[lilac pebble]

does it say ad=bc?

[outer arrow]

Yea

Its a-b on left and c-d right

[lilac pebble]

all right

rather than expand,

try multiplying by (a-b)^3 and (c-d)^3

then combine (a+b) with one of the (c-d) and likewise on the other side

then you can divide by the common factor ac-bd

[outer arrow]

Yeah, its too messy to take a pic, but im currently trying that, i managemed to reduce

Hmm wait

[outer arrow]

I did get that common facor

[outer arrow]

Oh u calculated it too, i thought you saw something immediately that i didnt

Yeah im im there atm and im multiplying single c-d with a squared b squared to see where it goes

[lilac pebble]

i saw that combining those would yield ad and bc terms

better to do this

[outer arrow]

Yeah?

What?

[outer arrow]

Okax

Same on rhs i assume

[lilac pebble]

these all cancel

[outer arrow]

Aah i cant believe i didnt see it

Ty raph uve Always been my fav turtle

[lilac pebble]

😊

[outer arrow]

Solved

.solved

[vocal sleet]

Channel closed

Closed by @outer arrow

Use .reopen if this was a mistake.

[vocal sleet]

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.

[mild trench]

[biology question]

[mild trench]

how does the change in amino acid sequence change primary secondary and tertiary structure

is it something to do with the angles the bond form?

[flat whale]

#old-network message

bio server linked

[grand linden]

We’re cooking up the structures of proteins using food metaphors

The primary structure is the exact order of amino acids in the chain. Think of this like a recipe for a sandwich – the specific ingredients in the exact order. If you swap out an ingredient, like using peanut butter instead of cheese, the recipe changes. Similarly, changing an amino acid changes the sequence, which directly impacts what the protein can eventually "taste" like (function).

@mild trench ok so far?

[flat whale]

[mild trench]

😭

[mild trench]

ty

[flat whale]

!done

[vocal sleet]

If you are done with this channel, please mark your problem as solved by typing .close

[hushed pewter]

The rare bio helper. I don't know exactly if we allow this, but if you're being helpful, I ain't gonna say "boo"

[mild trench]

.close

[vocal sleet]

Channel closed

Closed by @mild trench

Use .reopen if this was a mistake.

[vast shale]

boblox

[vocal sleet]

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.

[long kraken]

Task 1

[long kraken]

A quadratic polynomial is determined by the prescription

Where c is a number.
It is stated that f has roots x₁ = 1 and x2 = -3

(a) Determine the value of the number c

(b) Determine the coordinates of the vertex of the graph of f

shouldn't we isolate/solve the equation?

or how will you do it?

[gilded marsh]

Try factoring first. like factoring 2x^2 +4x is 2(x- ?)(x+?)

for part a

[hushed pewter]

The calculation is very simple since they gave you both roots. I feel bad giving you this much info, but the problem leaves me no choice

Ah, david basically shared it

[gilded marsh]

if you know the roots.

[cold hedge]

(vieta formula best)

[vocal sleet]

@long kraken Has your question been resolved?

[long kraken]

I actually have to calculate the equation?

Just that, and get its coordinates

can I use the 2-point formula?

[long kraken]

.

[gilded marsh]

you need to calculate f(x) to find your C. its not necessary to use 2 point just solve 2(x-1)(x+3) for c

for the coordinates, you don't even need the c as you find -b/2a

[long kraken]

When I calculate 2(x+1)*(x-3) I get:

2x^2 -4x-6

ups

-1,3

Correct?

[gilded marsh]

yeah so c = -6

now to find vertex substitute what -b/2a gets you into the quadratic equation: and you fidn your coords

[long kraken]

what -6?

You mean -1,3?

[gilded marsh]

no. -1 and 3 were the roots to find C.

[long kraken]

So the answer to problem a is -1.3, which is our value c.

Or am I wrong?

[long kraken]

You have to explain how it gives -6?

[gilded marsh]

hmm? because a is from the first 2x^2 so a is 2
b is from 4x so 4, c is -6, the constant

[long kraken]

Yes, but once you solve the equation and get -1.3, what do you do next?

[gilded marsh]

oh that's the x coordinate, but you should be getting -1 i believe.

then you plug that into 2x^2 +4x -6

[long kraken]

I get two x values. x1 = -1 and x2 = 0

Sooo @gilded marsh

[gilded marsh]

two values?

it shoukd be one

when u plug in -b/2a

[long kraken]

huh

[long kraken]

Show what you get. I'm confused.

[gilded marsh]

sorry its sideways but here

[wraith python]

,rotate cw

[wraith python]

Have you learned about the Remainder Theorem by any chance?

[long kraken]

what

[long kraken]

It's not at all the same as this: 2(x-1)(x+3)

Beacuse I get 2 values

[wraith python]

Would you like to learn about the Remainder Theorem?

[long kraken]

I dont know whats it is...

[wraith python]

Would you like to learn about it?

It makes this problem really easy to solve.

[long kraken]

hmm let me check that out

Isn't there another way to solve it?

I like David's way.

This 2(x-1)(x+3) give me -1,3

and what should I use it for?

@gilded marsh

[wraith python]

Expand the result you found and compare it the to the expression 2x^2 + 4x +c. What does c equal?

[vocal sleet]

@long kraken Has your question been resolved?

[long kraken]

Expand, you say. How do you expand the pressure? Give a start and I'll pick up on that later. 🙂

[wraith python]

2(x-1)(x+3), expand that expression.

[long kraken]

Well, how do you expand? To make the expression longer? And why do we expand an expression?

[spiral mortar]

to simplify it

sometimes like terms cancel each other out

[vocal sleet]

@long kraken Has your question been resolved?

[vocal sleet]

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.

[ionic thistle]

Can anyone explain to me how to convert standard form into slope intercept form

[ionic thistle]

i been trying to figure it out for the past 30min since i have a test tmr

[flat whale]

[ionic thistle]

yo

[flat whale]

ax + by + c = 0 to y = mx + b ?

[ionic thistle]

you dont even have to do any work?

only rearrange it?

[flat whale]

rearranging could count as work

[ionic thistle]

💀

aint no way

alright

lemme see if it works

[flat whale]

do some problems to get fast

[ionic thistle]

can i ping you if i need help?

[flat whale]

just open a new channel or post your question in here

[ionic thistle]

oh

[flat whale]

any helper paying attention should be able to answer if they're interested enough

[ionic thistle]

does it matter if y is negative

like -y

[flat whale]

that just makes b a negative number

[ionic thistle]

???

lol its confusing

i'm trying to figure ot 1/2x-y=3

but when i rearrange it it turns into -y=1/2x+3

did i do something wrong?

[flat whale]

you rearranged incorrectly

[ionic thistle]

so it would be y=1/2x-3 right

since the negative + negative is positive

[flat whale]

this is incoherent

[ionic thistle]

bruh

[ionic thistle]

is this correct at least

@flat whale

[flat whale]

yes it is

[ionic thistle]

W

i'm too good

alright ty for your time

.close

[vocal sleet]

Channel closed

Closed by @ionic thistle

Use .reopen if this was a mistake.

[vocal sleet]

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 mulch]

Hey, how can i show that $X=L^2 | x_k > 0, \forall k$ has int(X) = 0? I was thinking about creating some open ball $Br(x_k)$, and then showing that there's no y in $Br(x_k)$ such that d(x,y) < r, but i can't develop this idea, can someone help me?

[twin meteor]

mrherbert7195

[limber falcon]

if I'm understanding correctly can't you grab a positive function x in X and then make an arbitrarily L^2-small perturbation such that this x is no longer positive?

what I would do is calculate the L^2 norm of this https://www.desmos.com/calculator/9bvqxoknsj and then substract it to the function, with parameters h and w such that the function is made non-positive and the support of the perturbation is small enough

[keen mulch]

This is a homework problem, we just saw some definitions of topologies and metric spaces, I'm trying to show this just using these concepts of metric and closed and open subsets

[limber falcon]

okay, but surely you've seen that in the metric space $L^2(X,\bR)$ the metric is given by[d(f,g)=|f-g|_{L^2}\coloneqq \sqrt{ \int |f(x)-g(x)|^2 , \dd x }]
my suggestion is to simply let $g=f-\varphi$, where $\varphi$ is the small perturbation above depending on $w$ and $h$

[twin meteor]

derivada.schwarziana

[limber falcon]

well not exactly the above function, but a translation of that

[limber falcon]

so d(f,g) will be just the L^2 norm of this

[keen mulch]

I just thought that if I take $x_k \in X$, it will exist an open ball $B_r(x_k) := d(x_,y_k) < r$ where $y \in Br(x_k)$ and r>0, then whit the standard metric defined on $L^2$, this would wield $(\sum_k^n|x_k - yk|^2)^{1/2} < r$

[twin meteor]

mrherbert7195

[limber falcon]

yes, the definition of open ball is the usual one, just taking the specific metric you're working with

I'm a bit confused about this -- by $L^2$ do you mean the space of square-summable sequences $\ell^2$ then?

[twin meteor]

derivada.schwarziana

[limber falcon]

I was assuming you meant square-integrable functions

[keen mulch]

yep, i'm sorry, it's $l^2$ indeed

[twin meteor]

mrherbert7195

[limber falcon]

okay. So in this case for sequences ${\bf x}, {\bf y}\in \ell^2$ the metric is given by [d({\bf x}, {\bf y})=\sqrt{ \sum_{k=1}^\infty |x_k-y_k|^2 }.]
Here you can try defining ${\bf y}=(y_k)_{k\geq 0}$ by something like
[
y_k = \begin{cases} 0, &\text{if $k< K$,} \ x_k+\tfrac 1n, &\text{if $k\geq K$} \end{cases}
]
for some large enough $K$ and then check that the distance $d({\bf x}, {\bf y})$ can be made smaller than any arbitrary $r$ for large enough $K$ using properties of convergent series.

[twin meteor]

derivada.schwarziana

[limber falcon]

so the key idea here is that you want the sum in that distance d(x,y) to be the tail of a convergent series

any convergent series should work, but the series of 1/n^2 (which should appear here) is known to converge

( @rain jasper )

oops wrong herbert sorry @keen mulch

typo, k should be \geq 1 here but the starting index doesn't really matter

[keen mulch]

but if the distance d(x,y) can be made smaller than any arbitrary r, this would mean that there's an $Br(x_k) \in X$ such that $Br(x_k)$ is an open set, such that the interior of X $\neq \varnothing$, right?

[twin meteor]

mrherbert7195

[limber falcon]

nope -- if you want to see that the interior of $X$ is empty, this means that for all $r>0$ and all $x\in X$ you have $B_r(x)\cap X^c\neq \varnothing$

[twin meteor]

derivada.schwarziana

[limber falcon]

so no matter how small r is, you can find an element y close enough to x such that y is not in X

the choice of element y, will depend on r

[keen mulch]

so showing that the distance of, $x_k$ to some $y \in Br(x_k) | y \rightarrow 0$, is going to 0 would mean that $x_k$ is converging to 0, wich is not part of X, a contradiction, so the interior of this subset of X has to be empty, right?

[twin meteor]

mrherbert7195

[limber falcon]

I'm not talking about convergence of the x_k's to y a priori, but you do want to find something close enough in the given metric

[limber falcon]

essentially what I said here, I guess my "x_k" is named "x" here

since you don't need the index at all

you just need to show that no x in X is an interior point

and for that it suffices to find, for any r>0, some y in l^2 such that d(x,y)<r but y not in X

y will certainly depend on r

[limber falcon]

and a way to explicitly construct this y starting from x is here

[keen mulch]

Oh! I think that I got it, so y is not on X cause for small values of K y = 0, but the distance of x to y for a large K is smaller than any arbitrary r, so that's a contradiction, but x is arbitrary so it can't have open balls for any x in X.

[limber falcon]

right

actually I think I made a small mistake

[limber falcon]

for k<K you should have y_k=x_k

basically you want some y that almost coincides with x

except for coordinates that are very high up

[keen mulch]

Thx for the help!!!!!

[vocal sleet]

@keen mulch Has your question been resolved?

[vocal sleet]

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.

[junior birch]

$$\lim_{n\to\infty}L_{n}=0$$
$$nL{n+1}+nL{n}-2=0$$

[junior birch]

$$\lim{n\to\infty}L{n}=0$$
$$nL_{n+1}+nL_{n}-2=0$$

$$\lim_{n\to\infty}L_{n}=0$$
$$nL_{n+1}+nL_{n}-2=0$$

I want to solve for the Generating function of $L_{n}$

[twin meteor]

LemonDeity

[junior birch]

$$\lim_{n\to\infty}L(n)=0$$
$$nL(n+1)+nL(n)-2=0$$

[twin meteor]

LemonDeity

[vocal sleet]

@junior birch Has your question been resolved?

[vocal sleet]

@junior birch Has your question been resolved?

[vocal sleet]

@junior birch Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[stone galleon]

Wondering what the catch is here

[dawn kestrel]

factor out x^2024 on the denominator and then use u-sub

[stone galleon]

U subbing what exactly?

[stone galleon]

Forgot to ping with reply

[tidal dock]

u = 1+(1/x^2023)

[stone galleon]

Alright seems like I'm on the right track

And then du is -2023/x^2024

dx

[tidal dock]

yes

[stone galleon]

Now do I just isolate x^2024 in the u sub?

Alright I got

1/2023 * lnu

+C

[vocal sleet]

@stone galleon Has your question been resolved?

[vocal sleet]

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.

[hasty badger]

Can I get help on understanding this?

[hasty badger]

Optimization problems

[vocal sleet]

@hasty badger Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[hasty badger]

.reopen

[vocal sleet]

✅

[unborn sundial]

It's not an optimization problem, just the ordinary differential equation. Do you know, how to solve one?

[vocal sleet]

@hasty badger Has your question been resolved?

[vocal sleet]

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.

[loud fable]

How am i suppose to evaluate this ?

[loud fable]

Pls help :(

[flat whale]

That's the laplacian

https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/04%3A_Line_and_Surface_Integrals/4.06%3A_Gradient_Divergence_Curl_and_Laplacian

[loud fable]

😭 I was on this same page some minutes ago but only read till curl cuz i thought i only needed to study till there
Thanks for the help

.close

[vocal sleet]

Channel closed

Closed by @loud fable

Use .reopen if this was a mistake.

[loud fable]

.reopen

[vocal sleet]

✅

[loud fable]

AHh i closed too soon
Dont i have a vector on the left and a scaler on right now?

[maiden iron]

no

curl is a vector

grad is also a vector

the problem here is that laplacian of a vector return a matrix

🤔

[desert hornet]

how

[maiden iron]

wzit no

mah bad

[loud fable]

?

[maiden iron]

grad is a vector tho

$\nabla = \begin{pmatrix} \frac{\partial}{\partial x} \ \frac{\partial}{\partial y} \ \frac{\partial}{\partial z} \end{pmatrix}$

[twin meteor]

Herels

[desert hornet]

I think Delta^2 just means the grad of the grad

[loud fable]

oh yeah , mb , i got confused

[maiden iron]

it is

[desert hornet]

but that's not what the laplacian is

I thought the laplacian was a scalar

[desert hornet]

that's what this says too

[maiden iron]

Laplacian can take a scalar as an input and it returns a scalar yes
but laplacian with a vector isnt

[desert hornet]

ahh okay

[loud fable]

ok i think i got it after reading a bit more , thanks for the help

.close

[vocal sleet]

Channel closed

Closed by @loud fable

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.

[quartz beacon]

Any way to find a diff approximation for the yellow circle

Because for the definition you want it to also be valid for p=0

And with this approach u can’t rlly do that

also ur making p and n be dependent on eachother which also is something you’d want to avoid

[lyric relic]

for p=0 it is clearly valid for every n

[quartz beacon]

no because u want to put n separately

U want to find an n

But by trying to put n separately ur taking the ln of 0

Which isn’t defined

And even if we let it work for p>=1 it still doesn’t remove the fact that n and p are dependent on eachother in this case

[vocal sleet]

@quartz beacon Has your question been resolved?

[vocal sleet]

@quartz beacon Has your question been resolved?

[vocal sleet]

@quartz beacon Has your question been resolved?

[hasty badger]

My teacher calls them optimization? I understand this one, which I assume is the continuous rate function, but I cannot grasp how to get rt

[vocal sleet]

@quartz beacon Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[mellow timber]

can someone help me with graphics kinetics plss high school lvl or higher

[vocal sleet]

Please don't occupy multiple help channels.

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

@mellow timber Has your question been resolved?

[vocal sleet]

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.

[torpid silo]

im a bit lost on the partial fraction decomp for the following 2 integrals; what would I split each fraction into?

[heavy yoke]

there is a table included here: https://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx

[torpid silo]

so for the first one I think I got it (below) and then solving for the constants the actual integral seems to be (-2/x) + lnx + 2ln(x-1) + C

but still a bit confused on the second one

[heavy yoke]

for the second one you have the same degree on the numerator and denominator (for partial fractions the denominator must have higher degree)

so you have to first perform polynomial division

[vocal sleet]

@torpid silo Has your question been resolved?

Channel closed

Closed by @torpid silo

Use .reopen if this was a mistake.

[torpid silo]

thanks!

[vocal sleet]

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.

[rain shadow]

hi, I'm trying to figure out this triangle but don't know where to use tan

[rain shadow]

like i don't know how to use tan for this triangle

[vocal sleet]

@rain shadow Has your question been resolved?

[rain shadow]

<@&286206848099549185>

[vocal sleet]

@rain shadow Has your question been resolved?

[rain shadow]

.close

[vocal sleet]

Channel closed

Closed by @rain shadow

Use .reopen if this was a mistake.

[vocal sleet]

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 jasper]

lim as x appraoches infinity for 3sinx

[distant shoal]

the limit does not exist

[vocal sleet]

@mossy jasper Has your question been resolved?

[vocal sleet]

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.

[quiet river]

whats the difference from number 16 and 17?

[quiet river]

i know how to solve 16 but not 17

[tawny nacelle]

the speed is the absolute value of the velocity

[quiet river]

but how does this change my steps of solving for velocity

12(t^2-3+2)>0
(x-1)(x-2)>0

[quiet river]

sorry 4 ping but i need additional help

i dont get why its from 0<t<1 and not just t<1

for number 17

[brittle reef]

speed is a scalar quantity

while velocity is a vector quantity

so in scalar quantities, there is magnitude but no direction

in vector quantities, there is both magnitude and direction

-100 m/s may have the same magnitude as 100 m/s, but they are in opposite directions

speed like higher says is just the absolute value of velocity

[quiet river]

ok but why does the speed question include 0

[brittle reef]

there's no negative speed

because if you differentiate the polynomial you get a x^3

specifically 4x^3 for the first term

and so negative outputs exist for the derivative of the position function

[quiet river]

ohhh right

[brittle reef]

but there is no real interpretation for a negative speed

yess

absolute value of something can never be something negative

so absolute value of velocity (speed) can never be negative

[quiet river]

ok i get it now

thanks 👍

[brittle reef]

ure welcome!!

[quiet river]

.close

[vocal sleet]

Channel closed

Closed by @quiet river

Use .reopen if this was a mistake.

[vocal sleet]

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.

[potent stirrup]

How do I solve this?

[hidden gyro]

y''=y

first solve the first part

you get

the soln is

ae^-x+be^x

and then do the same for the second part

[potent stirrup]

I did the same,

I got ce^{3x} + de^{-3x}for the second part

[hidden gyro]

yes

now you just have to plug in values which work

you have

ae^0+be^0 = 0

amd

[potent stirrup]

[1,2]

Are you trying to solve the IVP for first diff equation

If so, you get 1/2 e^x + -1/2 e^-x

ie a = -1/2, b = 1/2

[hidden gyro]

yes

and then solve the value and differential at x = 1

and p;lug it into the second eqn

[potent stirrup]

Isn’t this what you saying ?

If so, I’m stuck at a specific step here

[hidden gyro]

which step

[potent stirrup]

The last step is the final solution right?

The final answer

If so, phi(0) must be 0, can you try phi(0) at last step

@hidden gyro

Do you see what I mean

<@&286206848099549185>

[potent stirrup]

Here is the original question

[vocal sleet]

@potent stirrup Has your question been resolved?

[vocal sleet]

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.

[ember drift]

Hi im a bit confused with my algebra rn

[ember drift]

my inequality is -4(3x-1) < 2(-4x+3)

I have no trouble find the asnwer witch is -1/2

although the asnwer is -1/2 < x

[devout kindle]

alr, show you work

[ember drift]

Nah I know how to do the work

[devout kindle]

yes just show me, i will point out

[hidden topaz]

Probably because you divide by negative numbers, but not alternating the inequality sign

Check it carefully

[ember drift]

I know the asnwer but why is the final inequality set up like -1/2 < x

why -1/2 les than x

how do we know that

[lilac pebble]

you have to maintain the correct inequality throughout your solution

so that when you get to the end it will be correct

[ember drift]

I dont know how to do that

sorry

[lilac pebble]

you can do many of the same things that you do with an equality

but if you multiply or divide by a negative value, you have to flip the inequality

[ember drift]

oh is that really it

[vast shale]

If you are confused, you can begin by expanding the brackets and moving the x terms to one side and the non-x terms to the other side

do keep in mind what @lilac pebble said when you are doing that

[hidden topaz]

-12x + 4 < -8x + 6
-4x < 2
x > -1/2

[ember drift]

Thats not my problem I know how to solve it to get the other side of x

[devout kindle]

or when you take logs both side and if in log a (a < 1)

[ember drift]

so if you do this at all throughout the equation its flipped

[hidden topaz]

So what is your question?

[lilac pebble]

yes but be careful if you multiply or divide by x

i don't think that will be necessary for this problem though

[ember drift]

How do you set up the ineuqality answer once you found the other side of x

[lilac pebble]

and if you do it twice, it flips back

[ember drift]

in this case the asnwer was -1/2 but my question was what do you do with that once you get it

[hidden topaz]

To solve an inequality, the answer should be in the form x>2 or x<2 or something

[ember drift]

in this case where did I multiply or divide specifacally that made it flipped

[hidden topaz]

you can't say that -1/2 is the answer

and i think -1/2<x and x>-1/2 is both acceptable

But x>-1/2 is definitely better

[lilac pebble]

yes those are equivalent

[ember drift]

Oh I see

I have a test tommorow

[lilac pebble]

that's not what i mean by flipping the inequality

[hidden topaz]

just like you solve an linear equation, and you write 3=x as the answer

it is correct, but x=3 is more formal and recommended.

[hidden topaz]

Good luck

[vocal sleet]

@ember drift Has your question been resolved?

Channel closed

Closed by @ember drift

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.

[vast shale]

Far vision glasses are thin diffusing lenses. It helps to see things clearly. Which of the following pictures correctly represents this?

idk the answer please help 😭

[brittle reef]

hint: note where the focal point is located in each image and compare

[vast shale]

idk 😭

my prof sent this image and i cant get in contact with him

he hasnt responded in like 2 days

and the due date is tmr

[ember drift]

im in middle school are u doing physics?

[vast shale]

yeah

[ember drift]

oh

[vast shale]

were redoing a few simple stuff BUT I FORGOT ALL OF THEMM

HELP MEEEEEE

im so desperate i went to a discord server full of math people 😭

[brittle reef]

all incoming parallel rays from an object no matter its height will always cross the focal point

[vast shale]

sooo |||?

3 i mean

[brittle reef]

2

[vast shale]

TYSM

ILY

[vocal sleet]

@vast shale Has your question been resolved?

Channel closed

Closed by @verbal bobcat

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.

[full hatch]

You can bound it above by 1/e^x

[untold arrow]

At infty i think it's converged

But I'm not sure about the x=0

[wraith venture]

You can bound it above by 1/sqrt(x)

[untold arrow]

Ooh so it's converged either?

[wraith venture]

If you can show this converges and that that implies convergence of your integral
Both of which are easy

[untold arrow]

Yah thx, btw I wanna ask this one

Similarly, I have trouble with dealing it at the origin

[wraith venture]

Do you think it converges?

[untold arrow]

Idk

I think it's convergent at least at infty

But at the origin....Idk

[wraith venture]

Well at the origin sqrt(1+x^2) ~ 1 so that doesn't matter and it will behave like 1/x

[untold arrow]

Ooh

So it's 1/x^2

Divergent

[young plank]

Will you help me with a small doubt?

[untold arrow]

Am i correct

[young plank]

There are actually two, sorry for interrupting you!! My bad

[wraith venture]

Where did you get that square

[wraith venture]

#❓how-to-get-help open your own channel

[young plank]

I did that the other day however no one responded!!

[untold arrow]

According to this, sqrt stuff will behave 1/x, isn't? And then there's another 1/x

[wraith venture]

Happens
Try again

[young plank]

If you're free anytime after clearing this doubt, just drop me a text over here
I'll drop that question!

[young plank]

Sure as you say man!!

[wraith venture]

I literally said it behaves like 1
I'd be curious to see you argue how sqrt(1+x^2) behaves like x or 1/x near 0

[untold arrow]

Ooh shoot misread

[untold arrow]

Ok it's 1/x, still div tho

[wraith venture]

Yeah
So how do you argue that rigorously now

[untold arrow]

I understand now but need to reorganize to make it clear later, thanks!

[vocal sleet]

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.

[vocal sleet]

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.

[boreal remnant]

how do you derive the moments of the normal distribution

[tawny hollow]

You can use the moment generating function (mgf), and get the kth moment by differentiating k times and plugging in t = 0, where t is the argument of the mgf

[vocal sleet]

@boreal remnant Has your question been resolved?

[boreal remnant]

yeah but how do you derive the mgf

lol?

[tawny hollow]

Do you know its definition?

[boreal remnant]

not really, this came up in an unrelated problem where i need teh 3rd moment

[hybrid flicker]

E[e^(tX)]

[tawny hollow]

^

[hybrid flicker]

function of t

[tawny hollow]

It should then just be a calculation, unwinding the definition of the expectation

[boreal remnant]

ok so t is the desired moment here

so i need

[tawny hollow]

No?

[boreal remnant]

huh?

[tawny hollow]

Read this

[hybrid flicker]

we already told you what the moments are

[boreal remnant]

i need E[X^3] what does that have to do with e^

[hybrid flicker]

E(e^(tX))

differentiate once

E(Xe^(tX))

twice

[tawny hollow]

Differentiate and plug in 0 and see for yourself

[hybrid flicker]

three times

[boreal remnant]

oh i see

ok thanks i think i got it

.close

[vocal sleet]

Channel closed

Closed by @boreal remnant

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.

[tawdry mason]

can someone help with this

[vast shale]

there is a formula for this

[tawdry mason]

i dont know it

[civic otter]

You didn't do them in class?

[hushed pewter]

look up "trig product-to-sum formula"

I forget it off my head, but that should be the name you want of the thing you are looking for

[civic otter]

In my country they are called Werner formulas iirc

[tawdry mason]

oh okay that helps

hold up

im seeing different versions of the formula

like complete different versions

[civic otter]

Wdym?

Send them

[tawdry mason]

i got

cos(3x)-cos(5x)

[vocal sleet]

@tawdry mason Has your question been resolved?

[vocal sleet]

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.

[viral token]

Please help

[viral token]

This is hard for no reason

<@&286206848099549185>

[dusk trail]

hi i think u just have to add the outer ones

[hidden gyro]

no

[viral token]

No way it’s like that, each place shows their total permitter

Adding them would be weird?

That’s like adding all the sides to each place total

[hidden gyro]

first add all outer perimeters, than subtract the perimeter you counted which you didnt need to

[viral token]

So what would the answer be here? Exactly - sorry I’m not English

[golden herald]

So, to do this, it is best if you have two colours for you to trace this. First things foremost, you have to figure out the length of the blue, is that clear?

[viral token]

Yeah

[golden herald]

So, let's start from the left

imagine you added 120

you want to substract off the bits in the purple

[viral token]

Yup

[golden herald]

to do this, you can substract off 30 and 70 (they are the regions that share a border with 120)

[viral token]

But that would subtract the whole area and not just a corner? Or am I wrong

[golden herald]

But now, you have to ADD back in the red, because those regions were oversubstracted

[golden herald]

you are right

[viral token]

Yes so it wouldnt be that accurate?

[viral token]

Ohh

[golden herald]

we aren't done yet dw, i am just trying to explain the methadology

[viral token]

Okay

[golden herald]

Basically, you current sum is 120 - 70 - 30 + ??? with ??? to be the rest of the stuff that remains to be found

is that clear?

[viral token]

Yes

[golden herald]

so

[golden herald]

lets leave this as is for now, while keeping in mind that the red are the lengths we need to add back in alright?

So go to the far right with the 90

do the same thing, and add 90

purple is the length we need to substract off

[viral token]

Alrightt

[golden herald]

so what would happen if you substract off 100 now? try to draw the red lines you would need to add back in

[viral token]

I kinda got lost there with adding stuff back in

[golden herald]

remember: purple are things we need to substract off, red are the things we need to add back in

[golden herald]

we added 90, and the purple we need to substract, so we substract 100

but substracting 100 creates lines that we need to add back in

[golden herald]

try to remember how i did this, for example

@viral token are you still around?

[vocal sleet]

@viral token Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[grand linden]

Hi

[grand linden]

Consider the endomorphism ( f: \mathbb{R}^3 \to \mathbb{R}^3 ) such that:

[
f(v) = A v
]

with ( v \in \mathbb{R}^3 ) and ( A = \begin{pmatrix} 1 & 0 & 0 \ -1 & 2 & 0 \ -1 & 0 & 2 \end{pmatrix} \in M_3(\mathbb{R}) ).

[twin meteor]

jandro0103

jandro0103

[grand linden]

I don't understand what I should do, any advice?

[lyric relic]

you should find what "matrix associated with the endomorphism" means in your book

[vocal sleet]

@grand linden Has your question been resolved?

[grand linden]

i mean the first part "After completing..."

[grand linden]

A matrix associated with an endomorphism refers to the matrix representation of a linear map (or endomorphism) with respect to a chosen basis of a vector space.

[lyric relic]

oh ok.. you just need to add another vector to the two that have been already given to you...so that they form a basis for R^3

[grand linden]

literally any?

[lyric relic]

yes, as you are not given a specific way of completing the system in this case

e1 or e3 should be fine

[grand linden]

Is there any choice that makes everything easier for me?

[lyric relic]

.

[grand linden]

oh okay

thx