help-26

[snow vine]

Hmm, I mean you could use the general identities

[neon iron]

use this relation

[snow vine]

And the second part is to use the common facts

[finite grail]

how, I not only have two sin, but I have three multiplied + two

[snow vine]

sin(0)=0 sin(pi)=0 sin(2pi)=0 sin(pi/2)=1 sin(3/2pi)=-1

[finite grail]

the equation became too big

[neon iron]

that's the goal, to change product into addition so that terms start to get cancelled

[snow vine]

If I were in your position I would just plug and play with the general results

[finite grail]

i try again

[snow vine]

But maybe some simplification can be done

[neon iron]

I won't play this late at night though

[finite grail]

if I don't make simplifications for my teacher the homework is wrong

[snow vine]

At first I would cancel out the $sin(2x)$

[thorny flame]

Der Kitzler

[snow vine]

Since it is on both sides

So I have $sin(4x)sin(6x)+cos(9x)=0$

[thorny flame]

Der Kitzler

[finite grail]

nooo sorry

the equation was: there are no brackets; it's only: 2sinx'sin4x'sin6x+sin2x'cos9x=0

really sorry

I tried to use Wermer

[snow vine]

Hey, how about you start by writing this equation in an actual readable form

[finite grail]

now is correct

sorry

[snow vine]

Set brackets

[finite grail]

2(sinx)(sin4x)(sin6x)+(sin2x)(cos9x)=0

[snow vine]

use the double angular formula

and write sinx as sin(x)

Please

[finite grail]

for every one??? or only for sin2x?

[snow vine]

For all of them that have an even number

[neon iron]

that will be very long, if u keep simplifying everything so that the argument is x in the end

instead just use the relation where u can change the products into sum

[finite grail]

yessssssss

but the problem is how

[finite grail]

I have to simplify or it will be wrong for my teacher

[snow vine]

This will simplify everything

You can cancel all the sins out by doing it

[finite grail]

I try one moment

now is 8sinxsin3xcos3x+cos9x=0

[finite grail]

and i can't do anything

[snow vine]

Ahh okay, that sucks

[finite grail]

yeah

[snow vine]

Is it possible that the equation only has a solution when both terms are zero?

[finite grail]

no, the solutions are: kpi; pi/10+ kpi/5; pi/6 + kpi/3

[neon iron]

just use the identity bro lol

turn the products into sum

then see if anything cancels out

also, u can't cancel sin2x from both side as it might also be 0 for some value of x

if u do so, u will reduce the solutions that u will get eventually

[snow vine]

Since there are still even terms in sine you will not cancel out solutions

[finite grail]

yes, but I don't understand how

[neon iron]

yes, but then cos doesn't have anything in product then which will cancel out the solutions

[snow vine]

But your identity might be useful now

[finite grail]

could you try to make it please?

[snow vine]

You were also referring to the wrongly stated problem

[neon iron]

isn't is sin2x?

what's the corrected equation

[finite grail]

2(sinx)(sin4x)(sin6x)+(sin2x)(cos9x)=0

[neon iron]

are u sure it's this?

[finite grail]

yes

[neon iron]

alright, just open sin2x. Then cancel out sinx from both sides but while doing it, u must remember that one of the solutions is when x is a multiple of pi. Finally u will have 2 sin terms in product, and 2 cos terms in product which u can convert into sum of cos and sins using the identity

when simplifying two sin terms in product, use the second relation

put a+b/2 =4x or 6x depending on what simplifies earlier

[snow vine]

gives: 4(sin(4x)+cos(-2x))sin(3x)+cos(9x)=0

[neon iron]

u telling me?

[snow vine]

if you open sin2x you get an unsymmetrical expression

Hmm, but with the cos cos identity it might be possible

Where you got those even from, never seen those

[finite grail]

are prostaferesi formula

in italian

[snow vine]

I meant the expressions from @neon iron

They do not seem standard

[finite grail]

this?

[neon iron]

they are standard derived from sin(a+b) and sin(a-b) and cos for cos identity

[snow vine]

Never saw those in class

From which site you got them?

But yeah by combining the double angle formula with your identities it does seem possible

[finite grail]

I'm trying

[snow vine]

@finite grail does your teacher hate you or something 😦

[finite grail]

yes, probably our class

[snow vine]

Are you in university or high school

[finite grail]

high school

[snow vine]

Frick, then good luck, imma watching a movie now

[finite grail]

ok bye! thanks for the help

if I complete the equation I will send you it

[snow vine]

Okay pls do so and good luck

You have a VERY ambitious teacher

[topaz sinew]

@finite grail Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[short trail]

Sorry when I am back, but it seems like I am having issues with the amount dashes. I tried to solve it, but I did something wrong.
To clarify I don't fully understand what makes || so special aside from making the solution within that positive. I am a chemist not mathematician :c

[topaz sinew]

@short trail Has your question been resolved?

[short trail]

Unfortunately it has been 21 minutes, so I am obligated to simply ping T-T <@&286206848099549185>

[glacial saddle]

Hi

What is the question?

[short trail]

Well it seems like I did something wrong during opening the brackets

My result was 80/3 which was not accurate

[glacial saddle]

You have to resolve the integral on the left?

[short trail]

Yup

[rose zealot]

I found the problem

No no im sorry

[glacial saddle]

Ok remember the definition of absolute value

|a| is equal to a when a>=0, while is equale to -a when a<0

[short trail]

Yeah

[glacial saddle]

You have |3x+4| which is equal to 3x+4 when x>=-4/3

But you are integrating from 0 to 2 so you know for sure that x>=-4/3

Hence you can "ignore" the absolute value

And simply do the integral of that function without the absolute value in the middle

[short trail]

Hm. So I simply just ignore the |3x+4| and just treat it as 3x+4?

[rose zealot]

Bc it's positive

[glacial saddle]

Yeah, but it's important that you understand why

If you want I can try to explain it a little bit better

[rose zealot]

Since x is between 0 and 2

[short trail]

Oh

Because I am integrating from 0 to 2, it means that my value is positive

Because I am in the positive area

So if I'd have -1 to 2, that means I'd be in the negative?

[glacial saddle]

No, wait a sec

It's all about the definition of absolute value as I said before

The number in the brackets | | must be greater or equal to 0 to "remove" these brackets

Now, your number is 3x+4, and we know that $3x + 4 \geq 0 \iff x \geq \frac{-4}{3}$

[thorny flame]

Milo

[glacial saddle]

But as you said, you're integrating from 0 to 2, so x>=0 >= -4/3

Hence you can remove the brackets

[short trail]

I just realised that was not my task x-x

But I still need it

Sorry 😭

[glacial saddle]

No problem ahaah

[short trail]

But I still need it for b)

Because my HA is b and c

Not a

[glacial saddle]

Ok this is almost the same case

[short trail]

Yeah

[glacial saddle]

Study the absolute values

[short trail]

Gifted kid curse TvT

I suppose so

So I should just study the absolute values?

[glacial saddle]

We could say it's the first step

[short trail]

Darn alright TvT

So shall I close this channel?

[short trail]

Ohhh

Honestly this is much easier

[topaz sinew]

@short trail Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[neon iron]

Is 1.ō1 essentially the limit as x--> 1 of x+

[neon iron]

or is 1.ō1 = 1

[sweet shard]

Wot

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[edgy light]

in this question, we are not given refinement details

so we can not say about b,c and a is surely incorrect way of writing

but we are sure for D for every fucntion

[barren lion]

yes

the strategy is to take a common refinement, call it R, containing all of the points of P and Q together

then you have $L(f,P) \leq L(f,R) \leq U(f,R) \leq U(f,Q)$

[thorny flame]

Tushar

[topaz sinew]

@edgy light Has your question been resolved?

[edgy light]

tq

.clsoe

.clsoe

.close

[topaz sinew]

Channel closed

Closed by @edgy light

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.

[topaz sinew]

@still wasp Has your question been resolved?

[topaz sinew]

@still wasp Has your question been resolved?

Channel closed

Closed by @still wasp

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.

[acoustic spear]

Got no clue on where to even start

[topaz sinew]

@acoustic spear Has your question been resolved?

[acoustic spear]

<@&286206848099549185>

[novel coral]

The area of parallelogram is 1/2 d1 * d2 sinx

The problem is we are getting only one equation

[acoustic spear]

So 1/2xy sin(150°) = 100?

[novel coral]

Yes

[acoustic spear]

And then what

Do I just choose whatever number for x

[novel coral]

We somehow need one more equation

[acoustic spear]

Well that’s the whole question so

[novel coral]

Ya

Do u know the trigo formula for area of parallelogram

I am trying to do with that

[acoustic spear]

Nope

[novel coral]

Bruh

[novel coral]

@acoustic spear do you know any relation between d1 d2

[acoustic spear]

No

The only formula we’ve been taught in this chapter is the area of a triangle = 1/2absinC

Idfk where parallelograms came from

[willow chasm]

see its not asking to calculate exact values of x and y, just possible value of x and corresponding value of y wrt x

so there will be a range of answer

[willow chasm]

.

[topaz sinew]

@acoustic spear Has your question been resolved?

[novel coral]

If I get the answer I will dm you

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[acoustic spear]

There’s no need, we’ll be discussing it at school tmr with our teacher anyway. Thanks though

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

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.

[versed pecan]

how can I prove b) i) and b) ii)

I solved a) i) and ii)

but I got no idea how them being affine independent helps me

<@&286206848099549185>

[shadow meadow]

hi

[versed pecan]

hello

[topaz sinew]

@versed pecan Has your question been resolved?

[versed pecan]

.close

[topaz sinew]

Channel closed

Closed by @versed pecan

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.

[vale talon]

Can someone illustrate In a circle with a center R .YQ is a tangent at point G, and YM is a secant intersecting the circle at points M and B. If angle YMQ is equal 40, find the measure of angle YRQ

[topaz sinew]

Please don't occupy multiple help channels.

@vale talon Has your question been resolved?

[vale talon]

.close

[topaz sinew]

Channel closed

Closed by @vale talon

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.

[winter magnet]

Could I have some help with q4

[topaz sinew]

@winter magnet Has your question been resolved?

[sweet shard]

Use sine sum formula

[winter magnet]

whats that again

oh dw i know

[winter magnet]

.close

[topaz sinew]

Channel closed

Closed by @winter magnet

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.

[ancient falcon]

Can I get some clarification on the Quotient Rule (Calculus I)?

d/dx (a/b) is a'b-ab' correct?

[rose sierra]

No

[loud oasis]

not quite. the entire thing should be divided by b²

[ancient falcon]

THAT'S what I'm missing.. ok, thank you

Real quick... the product rule is

d/dx(ab) = a'b+ab'

No need to do anything extra, like in the quotient rule?

[loud oasis]

yes

you can actually derive the quotient rule using the product rule

[ancient falcon]

I'll have to check that out, but thanks for your help!

.close

[topaz sinew]

Channel closed

Closed by @ancient falcon

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.

[clear osprey]

I need help

[clear osprey]

Yo

[neon iron]

it's not clear

[clear osprey]

Wym

[neon iron]

the image u sent

and what's the question. Be specific

[clear osprey]

Ohh

[rose sierra]

judging by looking at them you need to use the law of sines or law of cosines

[clear osprey]

Frl

[neon iron]

.

[clear osprey]

Idk how too do it

[neon iron]

or u can also use vector algebra

[clear osprey]

Answers pls

[clear osprey]

Word

So like does a bot answer this for me

[neon iron]

no, we will. I mean random people

[clear osprey]

Oh frl

[neon iron]

what do u want to know, all 4 questions?

[clear osprey]

That’s sick

[neon iron]

frl?

[clear osprey]

Ye ye I have a couple more tho

[neon iron]

wdym

[clear osprey]

U get paid

[neon iron]

umm, no

ig

[ancient falcon]

He means he wants someone else to do all his work for him

[clear osprey]

Exactly

I think

Ye

[neon iron]

ohh, I'm sorry but u can't get that in channels

[clear osprey]

Huh

[neon iron]

we can help, not work for u

[clear osprey]

Ok can u helo

Help

[neon iron]

I can help u by explaining or telling u the method to solve it, u will have to solve for yourself

[clear osprey]

Ai bet

[neon iron]

?

[clear osprey]

Gimme the methods master

[neon iron]

already given

[neon iron]

.

[neon iron]

.

[clear osprey]

Idk how to do that

[neon iron]

ask your bots

[clear osprey]

How

[neon iron]

lmao

[ancient falcon]

Did your teacher give you an equation that looks something like (sin A)/a = (sin B)/b?

[clear osprey]

Where the bots at

[clear osprey]

Ye I think

[neon iron]

there are no bots lol. I was trolling

[clear osprey]

O

Oh

[neon iron]

use these formulas

to obtain results

[clear osprey]

BRO

what is this

What grade u in

[neon iron]

A, B, C are angles and a, b, c are sides. a is the side opposite to angle A, and so on

[neon iron]

I am in college

[ancient falcon]

That's basic trig

[clear osprey]

Damn

[ancient falcon]

Most people see this in high school, whether they remember it or not is another question

[neon iron]

also, I don't think u really care about their derivation, so just stick those formulas

[clear osprey]

Frl

[neon iron]

but if u do, u can derive that using trignometry

[clear osprey]

IDK WHAT U SAYING

is there a server that does the work for you?

[neon iron]

another method, if you're familiar with vectors, use vector addition to solve

[neon iron]

no. You have to do it yourself, atleast here

[clear osprey]

But is there

[neon iron]

I literally gave u the formula, what's wrong?

[clear osprey]

Idk trig

[neon iron]

idk, do u want people to find that too now?

[clear osprey]

Sure

[rose sierra]

blud you have to learn how to do it yourself

[neon iron]

well, use calculator for that. where it says, sinA just plug in the value of A in calculator

[neon iron]

exactly

[clear osprey]

It’s to hard

[neon iron]

well then leave it, first learn the basics

[ancient falcon]

Walking is hard, until you learn how

[rose sierra]

You ain't getting anywhere in life with that attitude

[clear osprey]

frl

[neon iron]

wth is frl?

[clear osprey]

For real

[neon iron]

for real?

ahh, okay

[clear osprey]

Yes

Il venmo u if you do it for me

[rose sierra]

You don't even need to know trig really you just plug the trig computations into your calculator

[knotty ledge]

stop offering to pay people to do your work for you please

[neon iron]

umm, what?

[neon iron]

exactly

[clear osprey]

WAIT WHAT

So it’s easy?

[neon iron]

what's venmo now?

[rose sierra]

Doesn't mean the calculator will solve the problem for you though you still need to solve/write the equations

[neon iron]

it's easy for someone willing to learn

[ancient falcon]

Another version of PayPal

[neon iron]

ahh

[clear osprey]

Ye

[neon iron]

do me a favor. Study and work hard, life will pay back to u for that

and I am happy and satisfied with what I have, I don't need your money

buy yourself a maths book with it

[clear osprey]

THERES RULES?

[pseudo sonnet]

yes lol

[clear osprey]

Damn

[neon iron]

yeah, for people like u

[clear osprey]

Nah racist

[ancient falcon]

Even math has rules, bud... order of operations, etc.

[neon iron]

who forget that discipline is important everywhere

[ancient falcon]

And on that note

[clear osprey]

Frl

[drifting swift]

every server has rules

[neon iron]

anyways, go study. All the best! and if u don't know how to do it, leave it and study the fundamentals

[clear osprey]

Kk

Ty

[neon iron]

no problem. have a nice day

u can close

[clear osprey]

Huh

[neon iron]

type .close to close channels. Once a channel comes to a conclusion, u should close it

[clear osprey]

L

Kk

.close

[topaz sinew]

Channel closed

Closed by @clear osprey

Use .reopen if this was a mistake.

[clear osprey]

.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[tacit star]

how would i find the expressin

$[w = \frac{2mu}{m^2 + M^2}]$

[thorny flame]

senate

[tacit star]

this was what i got

but it isn't correct

<@&286206848099549185>

helpppp

[topaz sinew]

@tacit star Has your question been resolved?

[tacit star]

<@&286206848099549185>

[tacit star]

.close

[topaz sinew]

Channel closed

Closed by @tacit star

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.

[winter magnet]

How do I prove that a line bisects another line

[winter magnet]

Or show it

[icy sky]

a line cannot be bisected

and this isnt true anyway

[molten raven]

You can show a line bisects a segment

[icy sky]

!original

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[winter magnet]

I need to show this

I need to show that line l bisects AB which is the line between where it crosses the axis

[topaz sinew]

@winter magnet Has your question been resolved?

[topaz sinew]

@winter magnet Has your question been resolved?

[topaz sinew]

Channel closed

Closed by @winter magnet

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[copper storm]

So imagine you have a square. It has 4 coordinates on the corners. [(x1,y1)(x2,y2)(x3,y3)(x4,y4)] you also have a point inside this square.(px,py) and you project the 4 corner points to be the same as 4 corner points on a quad [(u1,v1)(u2,v2)(u3,v3)(u4,v4)] how would you find the new projected point?(px',py')

[copper storm]

someone gave me these webpages and I read them, but they still don't fully answer my question: https://blog.mbedded.ninja/mathematics/geometry/projective-transformations/

https://rethunk.medium.com/perspective-transform-from-quadrilateral-to-quadrilateral-in-swift-5a9adf2175c3

[topaz sinew]

@copper storm Has your question been resolved?

[copper storm]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[topaz sinew]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[copper storm]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[mellow kraken]

What is your question please?

[copper storm]

So imagine you have a square. It has 4 coordinates on the corners. [(x1,y1)(x2,y2)(x3,y3)(x4,y4)] you also have a point inside this square.(px,py) and you project the 4 corner points to be the same as 4 corner points on a quad [(u1,v1)(u2,v2)(u3,v3)(u4,v4)] how would you find the new projected point?(px',py')

[mellow kraken]

You project the 4 points into what?

[dull sonnet]

I don’t understand your statement here

[copper storm]

@dull sonnet @limber mica

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[shrewd horizon]

!15m

[topaz sinew]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[copper storm]

it has been over 2 hrs

[copper storm]

<@&286206848099549185>

[topaz sinew]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[copper storm]

bro what?

dude I genuinely need help right now

like what is this?

yeah and 2:30pm in others

soo?

and others are awake

its 7:30 pm rn where i am

many people are awake

I sent the first message in this channel at 4:52pm where i am

that was after messages in another channel hours earlier

getting the same non responsiveness

I got more input on redit than on here

and all i got were 2 links

it was helpfull but nowhere near close to what i need

thanks!

[grim sable]

I don't know

I cant do linear alg

[copper storm]

[outer delta]

That's geometry at most, you want a magnification of the square of sorts and want the points to be congruent?

[copper storm]

I need to project the square onto the quad and the points inside the square as well

[outer delta]

what is a quad?

[copper storm]

quadrilateral

diagram

[outer delta]

are the transformations of the square uniform or random?

[copper storm]

wdum?

[outer delta]

well it seems you are in some terms transforming the square into the quad and then wanting to know where the point ends up

[copper storm]

yes

[outer delta]

if you know what the transformations are you should be able to apply them to the point, if the point changes with the square, cause PxPy could just be equal to Px'Py'

[copper storm]

well yes, but also it could end up in a different position

see i am trying to create a grid of 16x16 points on a face using 4 corner points

[outer delta]

not necesarrily, if only the border is changing then the inside won't always move

[copper storm]

and i am trying to project these points onto the quad

this is what i want

but with a grid of points

[outer delta]

what is your current level of math?

[copper storm]

well, I am a junior in high school, in AP Precalculus, but I will do whatever is necessary

[outer delta]

This is a level of math that is above most people in this server, It requires the knowledge of Euclidean geometry, linear algebra, and possibly calculus

[copper storm]

oh...

[outer delta]

and in the line of mathematics classes, linear algebra is typically learned/taught after calc 2

[copper storm]

...

my first thought to solving the 16x16 grid in quad was using bilinear interpolation

but somebody on redit sugested this

[outer delta]

this server?

Khan academy has linear algebra btw

[copper storm]

quadrilateral-to-quadrilateral transformations

[copper storm]

haha...

they provided this: https://blog.mbedded.ninja/mathematics/geometry/projective-transformations/

https://rethunk.medium.com/perspective-transform-from-quadrilateral-to-quadrilateral-in-swift-5a9adf2175c3

[copper storm]

ill look at it tomorrow

[outer delta]

yeah projective transformations is what requires all the classes

[outer delta]

this is why I asked if the transformations were uniform or random, if they're uniform using the quad-quad transformations then you can possibly get the point but if they're not it is going to way more difficult (projective geometr)

[copper storm]

yeah they are random

[outer delta]

[copper storm]

all to make textures in a 2d music based side scrolling platformer...

[outer delta]

?

[copper storm]

Geometry Dash

[outer delta]

oh

[copper storm]

yeah

[copper storm]

soo...

am i alone on this?

[outer delta]

You are free to wait for a graduate or graduate+ person, since its geometry dash you can their forums or try a comp sci approach, but both of those I am unsure too

[copper storm]

all i need is the math, i can implement it myself

how do i get in contact witha graduate/graduate+ person

[outer delta]

unfortunately you will have to wait for one, since they will respond to the @ helpers ping, also repost your question below this, or you can open a new help channel after closing this one so they don't have to scroll 10miles

[copper storm]

ok well thanks for your input!

Question repost:

So imagine you have a square. It has 4 coordinates on the corners. [(x1,y1)(x2,y2)(x3,y3)(x4,y4)] you also have a point inside this square.(px,py) and you project the 4 corner points to be the same as 4 corner points on a quad [(u1,v1)(u2,v2)(u3,v3)(u4,v4)] how would you find the new projected point?(px',py')

images:

<@&286206848099549185> Specifically a grad/grad+

nvm ill just continue this tomorow

.close

[topaz sinew]

Channel closed

Closed by @copper storm

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[neon iron]

\ExplSyntaxOn

\fp_new:N \scalar
\fp_set:Nn \scalar { 1 }

\NewDocumentCommand{\lmao}{m}{
\ds \int\sb1^{\scalebox{\fp_eval:n {0.8/\scalar}}{$#1$}} \hs{-0.9 cm}2x \dd x
}

\NewDocumentCommand{\bruh}{m}{
\int_compare:nNnTF {#1} > {0}
{
\lmao{\bruh{#1-1}}
}{}
}
$\bruh{20}$

\ExplSyntaxOff

[neon iron]

i found this integral, how should you go about solving it

[shrewd lance]

we can assume that to be a constant

the whole thing

[neon iron]

Okay

[lucid junco]

what in earth

[shrewd lance]

so we can also subtitute the upper limit as the constant?

so c= ∫1^c (2x)dx

[neon iron]

i see what u r getting at

[shrewd lance]

solving this we can get a quadratic in c -> c^2-c-1=0

but i kind of feel it's now quit right way?

[neon iron]

[
c= \f{1\pm \s5}2
]

[neon iron]

oh wow its the golden ratio

isnt it

[ionic oar]

$y = \int_1^y 2x\dd{x}$

[thorny flame]

Norbert Baudin

[ionic oar]

lol

its one of those problems

[shrewd lance]

yes something like this too

[neon iron]

$\phi, , -\phi$

[shrewd lance]

i thought of putting upper limit that

[ionic oar]

the other root isnt -phi

[neon iron]

but this feels incompelte

[shrewd lance]

yea

[neon iron]

yeah this isnt correct i think

there is something else

we dont know if this converges

we cant just assume convergence like that

[shrewd lance]

i think you cant put the upper limit var.?

[shrewd lance]

that too

but i can't think of another way , other than to assume

[knotty ledge]

if it converges, it should converge to one of the things seen

but yeah the real issue is determining whether it converges at all

[ionic oar]

cant be negative though right

[knotty ledge]

probably not

[ionic oar]

converges by virtue of cool result

[neon iron]

i think the issue is that

what we got assumes somehow that the integral is converging to both phi and -phi

which is uh kind of impossible

[ionic oar]

how did you get -phi again

[neon iron]

its a quadratic

c^2-c -1 = 0

[ionic oar]

the other root is not -phi

[neon iron]

yeah

its not

i just notated it like that

lets call it like

[knotty ledge]

well hang on how are we even evaluating the first n steps of this process

[neon iron]

$\phi, , \overline \phi$

[ionic oar]

ah

[ionic oar]

right i did think of that

cuz what would you have as the upper limit of the nth integral

[knotty ledge]

it doesnt seem like there is a sequence of numbers here to even talk about convergence

[neon iron]

do we build a recursive formula or something

[knotty ledge]

you wrote it down you have to decide what it means

[neon iron]

i think its like

a bunch of functions nested in itself

like

uh

[ionic oar]

$$f(n) = \int_1^n 2t\dd{t}$$
$$\lim_{n \to \infty} f^n(x)$$

[neon iron]

[
\m It = \int_1^t 2x \dd x = t^2 -1 \
\m I{\m It} = \int_1^{\int_1^t 2x \dd x}2x \dd x = \int_1^{t^2-1} 2x \dd x
]

[thorny flame]

Norbert Baudin

[ionic oar]

hm

[neon iron]

infinite nesting or something

[knotty ledge]

okay that is more tangible

[neon iron]

[
\m{a_1}t = \m It = \int_1^t 2x \dd x = t^2 -1 \
\m{a_2}t = \m I{\m It} = \int_1^{\int_1^t 2x \dd x}2x \dd x = \int_1^{t^2-1} 2x \dd x \
\m{a_n}t = {???}
]

[neon iron]

big boy question is what is a_n(t)

this is some weird ass recursion

[knotty ledge]

think you just square the last upper limit and take away 1

god knows if there a closed form for that

[neon iron]

[
\m{a_n}t = \int_1^{a_{n-1}(t)} 2x \dd x =\p{a_{n-1}(t)}^2 -1
]

woops

[knotty ledge]

-1

[neon iron]

yeah i think this is legit

[knotty ledge]

that doesnt seem that bad

you could probs gen func it

[ionic oar]

can't you just apply a limit to infinity on both sides

[knotty ledge]

i mean yeah we're just gonna get phi phibar again

[ionic oar]

yes

[knotty ledge]

but we dont know if a_n(t) converges

[ionic oar]

ah

[neon iron]

i guess we are stuck

how do you solve [
a_n(t) =\p{a_{n-1}(t)}^2 -1
]
i havent done recursion in ages

[neon iron]

[knotty ledge]

get good

[neon iron]

[odd pagoda]

this is very close to an identity for chebychev polynomials

$T_{2n}(t) = 2T_n^2 (t)-1$

[thorny flame]

Denascite

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

i feel like

regardless

this thing gotta converge to either phi or conj phi

for some interval

i think the problem is finding that interval of convergence rigourously

[topaz sinew]

@neon iron Has your question been resolved?

[whole geode]

A different, easier way to reason about the behavior of this sequence is to analyze the path of specific seed values to see which converge.

Let $b_{1,x} = x$ and $b_{n+1,x} = \int_1^{b_{n,x}} 2x \dd x$. Then consider the behavior of the function $b_{\infty}(x) = \lim_{n \rightarrow \infty} b_{n,x}$.

We can look specifically at the behavior of the values of x near phi and phi conj, above and below to see if they get nearer or farther away.

[thorny flame]

OmnipotentEntity

[neon iron]

Thank you for your response! i will look into this further but i have more urgent questions to ask about so i will close this now

.close

[topaz sinew]

Channel closed

Closed by @dim talon

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.

[next plover]

How do I find the S^2 ?

[topaz sinew]

@next plover Has your question been resolved?

[next plover]

<@&286206848099549185>

[topaz sinew]

@next plover Has your question been resolved?

[pine oxide]

he;;o

[next plover]

Yes

[topaz sinew]

@next plover Has your question been resolved?

[next plover]

.close

[topaz sinew]

Channel closed

Closed by @next plover

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.

[flint marsh]

Calculate the distance from point P to the midpoints of the circles.```

Could someone help me understand how to solve this?

[sharp wyvern]

consider origin at some points

and then you can just use simple chordinate geometry

[flint marsh]

I know the answers but I need to prove the answers through equations

[dark cargo]

i did it intuitively with similar triangles

triangle PQR is similar to triangle PST where Q and S are the upper points of tangency and R and T are the midpoints of the smaller and larger circle respectively

PQR and PST are both right triangle because the radii and the tangent line make a 90 degree angle

[flint marsh]

And based from that how can I find out what the length between P and R is?

[dark cargo]

from here u can figure out an equation to find that yes

[flint marsh]

Do you by any chance know what that equation is, cause that's kinda where I am stuck. What I am suppose to take with what to get my answer

[dark cargo]

so since the triangles are similar their angles will be the same and the ratios of their sides will be the same as well

we don’t know any angles here but we have some lengths

QR = 3 and ST = 7

[flint marsh]

RT = 10

[dark cargo]

there may be a better way to solve this but what i would do it set PR to x+3

and PT would be x+3+RT so x+13

since the two triangles’ side length ratios are the same, QR/PR = ST/PT

do u know how to create an equation from there?

[flint marsh]

Nah man, I'm completely lost tbh. Been at this for 3 hours.

[dark cargo]

all good. remember from before we found the values for QR and ST

[flint marsh]

Yep

[dark cargo]

lets plug those in

[flint marsh]

Like this?

[dark cargo]

yes almost there

maybe rethink PT

[flint marsh]

Wait no

[dark cargo]

yes this one is correct

[flint marsh]

So how do I continue from here?

[dark cargo]

do u know how to cross multiply?

[flint marsh]

Yep

[dark cargo]

alright go ahead with that

[flint marsh]

Like so?

[dark cargo]

yep

now u can solve for x

[flint marsh]

Legend👑

[dark cargo]

👏

[flint marsh]

Thank you so much

Actually appreciate it!

[dark cargo]

no problem!

[flint marsh]

.close

[topaz sinew]

Channel closed

Closed by @flint marsh

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.

[amber belfry]

i need to figure out if the squence An = arctan(n^2) converges or diverges

[amber belfry]

as I write out the terms I can see that its converging to a number

but how would i show it

[topaz sinew]

@amber belfry Has your question been resolved?

[amber belfry]

<@&286206848099549185>

[obtuse pelican]

Ye

[amber belfry]

how would i show that the sequence arctan(n^2) converges

[obtuse pelican]

evaluate the limit of the sequence at n → ∞ n\to\infty n→∞

[sweet shard]

what definition of convergence do you use

[amber belfry]

wdym

[sweet shard]

explain convergence to me

[amber belfry]

each new term in the sequence will be approaching a single value

[sweet shard]

just plug in larger and larger values for n then?

,calc atan(100)

[thorny flame]

Result:

1.5607966601082

[sweet shard]

what number does that converge to?

,calc atan(10000)

[thorny flame]

Result:

1.5706963267952

[obtuse pelican]

This number?

[sweet shard]

it's the same as asking, what value x does tan(x) ~ 100, tan(x) ~ 10000

[amber belfry]

ye

[amber belfry]

the reason im trippin tho is that isnt arctan bounded between -pi/2 and pi/2? so ~1.57 wouldnt make sense as an answer

[sweet shard]

what is pi/2 in decimal form

the first part what you said is correct

[amber belfry]

o wait lmao pi/2 is 1.57 rad lmao im dumb

tysm

.close

[topaz sinew]

Channel closed

Closed by @amber belfry

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.

[sleek rampart]

prove the following reduction formula

[dense rain]

If you look at the reduction formula, the term x ln(x)^n is a big hint that you should set u = (ln(x))^n and dv = 1.

[sleek rampart]

okay i will try that thanks!!

.close

[topaz sinew]

Channel closed

Closed by @sleek rampart

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.

[topaz tulip]

how do i draw a picture of tan^-1 to know if i should add or subract pi

[topaz tulip]

and why do i need to get pi involved

[topaz sinew]

@topaz tulip Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[neon iron]

Find the exact value of the remaining five trigonometric functions when $\tan(\theta)=\frac{-2}{3}$, for $\frac{3\pi}{2}<\theta<2\pi$

[thorny flame]

Matt

[neon iron]

How would I go about solving this? & Why is the inequality on the right included in the question?

My initial thought was to find cos, and since tan(theta)=sin/cos, I thought I could just say cos(theta)=3 but im pretty sure thats wrong lmao

.close

[topaz sinew]

Channel closed

Closed by @warped oracle

Use .reopen if this was a mistake.

[neon iron]

nvm i can use identities

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[pine anchor]

Can anyone help me fill the values for the last column? I'm kinda confused on how it works

[pine anchor]

this is the whole boolean function as well

[topaz sinew]

@pine anchor Has your question been resolved?

[livid ocean]

you have to take function OR of last three columns

[pine anchor]

so for the first value it would be: 0 OR 0 OR 1?

I missed the first lectures so i'm kinda lost 😭

[livid ocean]

yes, but did you mess your first column of last three?

[pine anchor]

I'm checking again right now

[livid ocean]

it should be x, not not(x)

[pine anchor]

Nooo

You're right

I'm been trying to learn this whole class in one day so i'm getting dizzy atp

Think the first column of the last three should now be
0
0
0
0
0
1
1
1
If I'm not mistaken again

[pine anchor]

To be sure, it returns 1 if at least one of the three values is 1 right? Otherwise it's 0

[livid ocean]

right

[pine anchor]

Then i'm not sure i'm following this teacher's slide correctly

for example on the first row all of them are 0s but at the end the value it's 1?

[livid ocean]

hmm, it has to be typo i think

because they got 0 and 1 for 1 and 2nd rows what is kind of strange

[pine anchor]

Yeh couldn't really figure that one either but you probably right

She probably mentioned it in her lecture but this what I get for skipping them 💀

That's probably it, thank you

.close

[topaz sinew]

Channel closed

Closed by @pine anchor

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[twin pollen]

A horse is pulling a cart, accelerating both the cart and the horse. Is the force of the cart exerted on the horse equal and opposite to the force exerted by the horse on the cart?.

[twin pollen]

This is physics but can someone help? I cant get an answer

[terse pier]

If you're taking this in a class, your course materials should have a statement giving you pretty much the answer word for word (but using words like "objects" or "bodies" rather than "horse" and "cart")

Can you review your course notes for that statement?

[topaz sinew]

@twin pollen Has your question been resolved?

[ancient falcon]

Evening @twin pollen

So... a horse is accelerating a cart, and the question asks if the forces exterted by the horse and the cart are equal and opposite?

Without more context, the simple answer is no... they are not equal and opposite - if they were, the horse wouldn't be able to move the cart

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[loud oasis]

that's not true

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[leaden marlin]

Can you show your integration?

[lapis urchin]

Sure

$\frac{\pi}{4}\int\sec^2x-2\sec{x}\tan{x}+\tan^2x$,dx

[thorny flame]

Ñøïr

[leaden marlin]

Can you show the work

[lapis urchin]

No, sorry, I'm in the bus

It's just what I did

[leaden marlin]

tan^2x can be rewritten as sec^2x - 1

and the integration is relatively simple

[lapis urchin]

$\frac{\pi}{4}[2\tan{x}-2\sec{x}-x]$

That's what I had found

[leaden marlin]

It should be - x

[lapis urchin]

Right

[thorny flame]

Ñøïr

[lapis urchin]

it makes 2√3-4-π/3 for π/3 inside the bracket

For -π/3 it just doubles right?

[leaden marlin]

Evaluate from pi/3 and - pi/3

[lapis urchin]

Oughtn't I evalueate from smaller to greater?

[leaden marlin]

evaluate pi/3 then -pi/3

so it’d be the pi/16(F(pi/3)-F(-pi/3))

[lapis urchin]

Why 16

Anyhow, I think inside the backets makes

2√3-4-π/3-(-2√3+4+π/3)

=4√3-8-2π/3

[topaz sinew]

@lapis urchin Has your question been resolved?

[leaden marlin]

Sorry it’s not 16, still 4

first part would be pi/4(sqrt3*2-4-pi/3)

[lapis urchin]

Yes

[lapis urchin]

I found this in total

[leaden marlin]

second part is - pi/4(-2sqrt3+pi/3-4)

you have a +4 instead of -4

So pi/4(4sqrt3-2pi/3)

around 3.79

[lapis urchin]

That comes from sec

-2sec(-π/3)

That's +4 yes?

[leaden marlin]

It’s -2sec(-pi/3) and and it is -4

[lapis urchin]

I see

I been thinking of 120 degree for -π/3

[leaden marlin]

sec(-pi/3) is 2 bc cos(-x)=cos(x)

and on unit circle you go reverse so it’d be 300 degrees

[lapis urchin]

I was considering it being in 2nd quadrant hence negative

I understand

It's something like

$\pi\sqrt{3}-\frac{\pi^{2}}{6}$

[thorny flame]

Ñøïr

[lapis urchin]

Ew

Anyways, thank you for the help

.close

[topaz sinew]

Channel closed

Closed by @lapis urchin

Use .reopen if this was a mistake.

[leaden marlin]

no problem

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[tough bough]

i need help with bii

<@&286206848099549185>

[finite ember]

ez

[sweet shard]

!15m

[topaz sinew]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[tough bough]

problem solved nvm

.close

[topaz sinew]

Channel closed

Closed by @tough bough

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.

[topaz sinew]

Please don't occupy multiple help channels.

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.

[real blaze]

In this question my answer is B. But i am a little confused at the definition of position should I count it as 0 or not because if i take f(x)=x^2 then it will be positive by f" and if i take any quadratic without 0 then it will be positive due to f)x)

[burnt badger]

Here's an example of a quadratic that is always positive:

x^2 + 1

The way this question is worded you can just try this example

And see what happens

[real blaze]

Nope. My doubt is should we have to add constant term with it or not?

[burnt badger]

To be "always positive" then yes

Positive definitely is non zero

[real blaze]

We can't take f(x)=x^2

As positive

[burnt badger]

0 is not positive

[real blaze]

Right. So when we can include zero

Non negative?

[burnt badger]

Yes

Zero is neither negative nor positive

So non-negative or non-positive both include 0

[real blaze]

Thanks

.close

[topaz sinew]

Channel closed

Closed by @real blaze

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.

[wanton island]

I'm having a hard time believing the solution to this problem. (When I say believe, I don't mean that I think there's an error. I'm sure it's right. I mean that it doesn't feel logical, but more like magic, which is just me misunderstanding.)

When solving a system of equations with just two unknowns, it makes sense to me.

The whole point of algebra is "balancing," and it feels wrong to temporarily "forget" about one of the equations. We end up messing with the 2nd and 3rd equation, find z for those two, but what guarantee do we have that the 1st equation is also satisfied by that z?

We end up multiplying the 2nd equation by 3 so that we can cancel the x when we add together the 1st and 2nd equations, but we don't multiply the 3rd equation. So, whatever answer we get from these manipulations seems like we have no guarantee that it will be true for the 3rd equation.

Why are we allowed to do multiplication to two equations (not the 3rd) and find an x, y, or z that satisfies those two, then act as if it must satisfy the 3rd one?

[wanton island]

Sorry if that's a bit cryptic and hard to understand. But boiling it down, it feels like we're manipulating 2 equations at a time, temporarily ignoring the 3rd, and never multiplying it by the same scalar, nor dividing it by that number. Then we just say that the x, y, or z still satisfies the one we left out.

And lastly, is this actually how one solves a system of equations with 3 unknowns? Something just generally feels wrong about it. It feels so brute force.

[burnt badger]

There's a suite of better techniques using objects called Matrices

Which you will learn about in a Linear Algebra class

You'll be able to solve linear equations with any number of variables

[wanton island]

Another thing, is it uncommon to use 3 equations in high school math? Every other resource I find, I can only see two equations being used. For example, the following picture:

This always makes sense to me. Everything that we do to one, the other receives the same treatment.

But when it comes to 3 equations, I can't understand the reasoning behind working with 2 at a time, getting an answer for one of the variable, and then just assuming it works for the last one.

[burnt badger]

It's not uncommon but you don't spend a long time on it in U.S. high school math education

[wanton island]

I feel like I have no guarantee that the variable will satisfy the 3rd equation.

[burnt badger]

Well sometimes you will get inconsistent systems that have no solution

That can happen with just 2 variables and 2 equations

[drifting swift]

the solution of a system of equation is not a single number but a tuple of numbers (a pair for 2 variables, a trio for 3). x, y (and z) are merely components of it

so like

if you have a system of three equations, (i), (ii) and (iii)

and you take equations (i) and (ii) and manipulate them in some way to make a new equation (iv)

and you glean some info about the solution from (iv)

your doubt basically becomes "Why would this info apply to equation (iii)?"

to which the best answer is "why would it not?"

[wanton island]

Take a simple example:

(i) 2a + b + c = 5
(ii) a + 3b + 8c = 32
(iii) 6a - 9b + 7c = 12

I'm indifferent to there actually being a solution here.

Okay, we want to eliminate a first. So, let's work with the first two equations.

2a + b + c = 5
a + 3b + 8c = 32

We can multiple the second equation by -2 in order to eliminate a

2a + b + c = 5
(a + 3b + 8c = 32) -2

2a + b + c = 5
-2a + -6b - 16c = -64

b - 6b + c - 16c = -59

...

Regardless of how it turns out, whatever that variable turns out to be, it has been manipulated by a scalar of -2.

Since we've at no point multiplied (iii) by -2, I don't understand how it tells us anything about (iii). Unless at some point we also multiply or divide it by -2.

Again, I'm sure this is just missing a very obvious logical understanding.

But my brain has been turned off mathematically for 10 years. So, rewiring takes a minute.

.close

[topaz sinew]

Channel closed

Closed by @wanton island

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.

[hardy meteor]

anyone give me a hint on what to drive this equation?

i suppose chain rule $\dv{w}{z}=\dv{w}{x}\dv{x}{z}$? then what's the second derivative? im stuck on this drivation

[thorny flame]

yehuihe

[topaz sinew]

@hardy meteor Has your question been resolved?

[jaunty leaf]

So your question is what is d^2 w / dz^2 equal to?

Use Leibniz rule

[hardy meteor]

it's very messy. could you give a initial derivation?

but am i right i suppose to use chain rule here?

[jaunty leaf]

You can use the chain rule, yes

I'm assuming you're trying to derive the bottom equation using the substitutions from (2), right?

[hardy meteor]

yes

if there is a different way please do tell

i suppose it's going to be extremely messy no matter what

[jaunty leaf]

I'd just find dw as $(-\alpha x^{-\alpha-1} y + x^{-\alpha} y')dx$, dz as $\beta k x^{\beta-1} dx$ and therefore find $\dv{w}{z}$.
After that I'd find $d \dv{w}{z} = (...)dx$ and divide by dz

[thorny flame]

EQUENOS

[jaunty leaf]

But this is essentially just the chain rule

[hardy meteor]

oh you are right.

i forgot differential. too much

[jaunty leaf]

Your approach does the same if you differentiate 1 step furter: $\dv{w}{z} = \dv{w}{x} \dv{x}{z}$, therefore $\frac{d^2 w}{dz^2} = \frac{d^2 w}{dx^2} \left( \dv{x}{z} \right)^2 + \dv{w}{x} \frac{d^2 x}{dz^2}$

[thorny flame]

EQUENOS

[jaunty leaf]

Although d^2 x / dz^2 will require some additional work

[hardy meteor]

nice

[hardy meteor]

this is better

thank you so much. i'll do the rest

[jaunty leaf]

alright

you're welcome

[hardy meteor]

.close

[topaz sinew]

Channel closed

Closed by @hardy meteor

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.

[ivory sorrel]

what does the notation $C^n$ mean in continuity?

[thorny flame]

Why am. I here

[ivory sorrel]

for instance I've been told f(x) E C(a,b)

what does that mean?

[drifting swift]

1. if you cannot type ∈ then you should replace it with in not E.
2. C^n(a,b) means the set of all real valued functions on (a,b) which are n times differentiable and whose n'th derivative is continuous.
3. as special cases, C is synonymous with C^0 and just means continuous functions, and C^infty means infinitely differentiable.

[ivory sorrel]

OK. Thanks !

.close

[topaz sinew]

Channel closed

Closed by @ivory sorrel

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.

[desert furnace]

i need help with no. 43

[desert furnace]

aren’t the diagonals of squares already perpendicular by definition?

how must i prove this?

[ruby mural]

Generally a square is defined as a rectangle with adjacent sides equal

Using this definition try to prove it

[topaz sinew]

@desert furnace Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[fathom sinew]

How to integrate a number with a variable as the power.

[fathom sinew]

I use substitution, u = 4-7^x

[drifting swift]

what integral do you get after this substitution?

[fathom sinew]

dont know how to differentiate 7^x

ill just check what it would be

[drifting swift]

do you know how to differentiate e^x

[ivory sorrel]

The differential of $a^x$= $a^x ln(a)$

[thorny flame]

Why am. I here

[ivory sorrel]

where a is a constant

use that

[fathom sinew]

yh

ok

[drifting swift]

the = should not be outside dollars

also derivative* (but don't ask)

also \ln

[fathom sinew]

what would the integral of ${-1}/{\ln(7)}$ be

[thorny flame]

(っ◔◡◔)っ 🤍 cosygod 🤍

[restive inlet]

-1/ln(7) is a constant

[fathom sinew]

what do you mean

[torpid sparrow]

You take that outside

[restive inlet]

ln(7) is just a number

the reciprocal is also just a number

as is its negative

you should know how to integrate constants

[fathom sinew]

integration of constanst just becomes the variable

idk how to type in those dollar signs, but -1/ln(7) be -ln^-1(7) and integration of that is -ln^0(7)/0

which is error

[drifting swift]

no

ln(7) is just a number

it is not a variable

it is just a number

[fathom sinew]

oh

so

so like, it becomes ln(7)^x

idk.

[torpid sparrow]

Maybe checking the basics again it is a good opportunity for you to refresh all I’m sure you already know

[fathom sinew]

which one

integration of ln

oh

xln(x) -x

[torpid sparrow]

I would say all the basics integrations

[fathom sinew]

no

im good on that

[torpid sparrow]

Doesn’t look like

[fathom sinew]

yh

[drifting swift]

no

what would be the integral of 8?

[fathom sinew]

8x

in terms of x

[drifting swift]

and that of 1.94591?

[fathom sinew]

1.94591x

so yh integral of 5 dx is 5x

• c

[drifting swift]

ok and finally