help-28

[plush eagle]

in question 1

[hollow geode]

Note, polynomials with real coefficients obey Complex Conjugate Root Theorem

[fleet zodiac]

doesn't the zero's mean those are the x-values when y =0?

unless im wrong

[plush eagle]

yeah, thats something like when i-1 is a root, so is i+1, right?

[hollow geode]

yep

so since i is a root, you require -i to be a root

so you need a poly with x=1,2,i,-i as roots

[plush eagle]

okay so the factoring would be (x-1)(x-2)(x(-i))?

[hollow geode]

no

cause you know you have 4 roots

and (x(-i)) is nonsense for being a factor

if x=1 is a root, then x-1 is a factor is correct

apply that for the rest.

[fleet zodiac]

$x \pm i$

[glossy valve]

Vladilena Milizé

[fleet zodiac]

ayy it worked

[hollow geode]

#latex-testing

[fleet zodiac]

well it also works for the question

[plush eagle]

okay so would the factors be -1,-2, -i(isn't -i = 1?), and i? I thought that factors were the opposite of roots?

[hollow geode]

.....

[tulip marlin]

-i = 1?

i = -1?

i^2 = -1 so (-1)^2 = -1? hope not.

[fleet zodiac]

$i = \sqrt{-1}$

[glossy valve]

Vladilena Milizé

[hollow geode]

so 1) You seemed to ignore what I said, about x=1 means x-1 is a factor
2) No

[fleet zodiac]

your math teachers lied to you for past few years that it right 😄

[plush eagle]

okay, i'm genuinely confused. could you maybe walk through this one with me, and maybe I can try the next one on my own? the factoring part is really confusing me

[hollow geode]

what is the factor associated with x=2?

[fleet zodiac]

what mosh said is what you need to do

"You seemed to ignore what I said, about x=1 means x-1 is a factor"

apply what you did for x=1 to the other 3 roots

then expand

[hollow geode]

I don't need an echo btw

[plush eagle]

(x-2) right

[hollow geode]

yes

and for x=i?

[plush eagle]

(x-i)

[hollow geode]

and the last root?

[plush eagle]

(x+i)

[hollow geode]

yes

so a factorized form of the polynomial is $$p(x)=(x-1)(x-2)(x-i)(x+i)$$

[glossy valve]

Mosh

[plush eagle]

okay, i see. so then, do i distribute?

[hollow geode]

and by CCRT, this is guaranteed to have real coefficients

yes

[fleet zodiac]

do last 2 first

[hollow geode]

you expand that to write it in standard form

[fleet zodiac]

makes everything easier

[plush eagle]

so i would do x * x, x*-2, -1*x, -1 * -2 then repeat for the x and i on the other side or distribute through the whole thing?

[fleet zodiac]

huh

[hollow geode]

you expand the entire thing.

[fleet zodiac]

first one

after you do it for both do the same thing for the 2 new polynomials you just made

[plush eagle]

so it would be

x^2-2x-1x+2+x^2+xi-ix+i^2 ?

$x^2-2x-1x+2+x^2+xi-ix+i^2$

[glossy valve]

kaii

[hollow geode]

wrong

given you have a degree 4 polynomial

and you wrote a quadratic

[fleet zodiac]

you have the right variables you need to multiple the 2 instead of add

$(x^2-2x-x+2)(x^2+ix-ix+i^2)$

[glossy valve]

Vladilena Milizé

[fleet zodiac]

then simplify and expand again

[torn jolt]

Uh how much about imaginary numbers do you already know?

[plush eagle]

i dont think im doing something right..? x^2 * x^2 gives x^4,, x^2 * ix gives ix^2 and reverse for -ix and after that im stuck

[plush eagle]

i took alg II during 10 grade, or i was, but covid hit and the class stopped midway

and i never got to finish it

[torn jolt]

I see

[plush eagle]

the school system tried doing class over video call, but they just called it quits so my knowledge really isnt all that good. so now im struggling in precalc / math analysis

[torn jolt]

Uh I don't think just doing one problem will help you learn anything

Imaginary numbers is not something

U can learn on plain text

Are you familar with imaginary plane?

How multiplying by i rotates by 90 degress?

[plush eagle]

yeah we did some imaginary numbers, i remember that vaguely

[torn jolt]

Ok ig u dont know about this that when u a point a+bi multiply c+di a+bi rotates by the angle of c+di and streches by its magnetude

From where u were stuck u were stuck

U were using plain algebra to compute that

But it has a geometric meaning

without that it's not complete

[torn jolt]

Are you familar with this?

I don't think so

[plush eagle]

i barely learned about it before the cut off, so not really. everything you're saying seems kinda new to me

[torn jolt]

Yes u have to expand them but if u just understand the arethmetic it will never be clear

U can look into 3b1bs lockdown math series

There is a 1hr video about imaginary numbers

[plush eagle]

ok, imma do that asap. thanks for that

[fleet zodiac]

ignore the right side of pic

but you should know this

or at least first 3

[plush eagle]

yeah ive seen that before, thats why i said i=1; although i was incorrect its i^2=-1

https://youtu.be/5PcpBw5Hbwo is this the video @torn jolt

[fleet zodiac]

$i = \sqrt{-1}$

[torn jolt]

Yes

[glossy valve]

Vladilena Milizé

[torn jolt]

Watch it and understand that imaginary isn't only algebra

It's much better than that

[fleet zodiac]

simplify each polynomial first

and turn the $i^2$ into a number

[glossy valve]

Vladilena Milizé

[fleet zodiac]

then expand

[torn jolt]

Wait

If u don't understand

(a+bi) (c+di)

And just solve it

Using algebra

Then it's not enough

Understand what it does completely

Which he dosent first af all

[plush eagle]

i think i might just watch a few lectures, and come back because I'm missing a huge chunk. as if something isn't clicking for me at all. im trying to apply it, and it's not working + I don't want to waste your time when someone else could use it better. thank you though, seriously for pointing me in the right direction.

[torn jolt]

You are missing a huge chunk

Multiplying by imaginary numbers isn't that just expanding and giving out the answer to get marks ☠️ it has to do with geometry

[plush eagle]

..well thanks anyway

.close

[full forum]

Channel closed

Closed by @plush eagle

Use .reopen if this was a mistake.

[full forum]

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.

[kindred cliff]

how do i solve this

[meager dew]

you chose the correct sub, but you didn't use that sub?

[kindred cliff]

wdym

[full forum]

@kindred cliff Has your question been resolved?

[kindred cliff]

i did

[full forum]

@kindred cliff Has your question been resolved?

[full forum]

Channel closed

Closed by @kindred cliff

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.

[cosmic hound]

how to simplify this expression?

[cosmic hound]

arccos(\sqrt((((1+cosx))/(2))))

???

.close

[full forum]

Channel closed

Closed by @cosmic hound

Use .reopen if this was a mistake.

[full forum]

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.

[torn trout]

If it asks find a general solution to y' = e^x, is this first order differential equation?
or does there to be y on the right hand side like solve y' = 1-y^2?

[kind cypress]

As long as the highest-order derivative is a first derivative, it is a first order differential equation

In the same way that x→ax+b is a linear function as long as a≠0, even if b=0

[torn trout]

ok thx

.close

[full forum]

Channel closed

Closed by @torn trout

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.

[vapid barn]

i don't get it

there can't be a global maximum

the function is unbounded

holy fucking shit

that's such a bad way to write that

0<=x,y<=1

is apparently supposed to mean two different compound inequalities tf

this apparently means

0<=x<=1

AND

0<=y<=1

i thought that this meant 0<=x, y<=1

bullshit

[twilit cypress]

Hry

I need help

[full forum]

@vapid barn Has your question been resolved?

[full forum]

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.

[whole parrot]

How do you test that 2 lines are perpendicular in 3d ?

[whole parrot]

Vectors not lines sorry

.close

[full forum]

Channel closed

Closed by @whole parrot

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.

[timid girder]

I don’t even know if I’m close

I also got 1/3 at one point

[full forum]

@timid girder Has your question been resolved?

[ivory cairn]

that third photo looks right

[timid girder]

Really?

Wow

I’m surprised if that’s the answer because it’s super out of my league in terms of difficulty

This problem is extra credit in my alg 2 class

[ivory cairn]

apparently it wasn't 🤷 good job

[timid girder]

What is your level in math

I just wanna be more confident I can take your word for it

[ivory cairn]

You shouldn't take my word for it. That math should stand for itself. How did you get that solution?

[timid girder]

I kind of just composed a bunch of probability equations

[ivory cairn]

Good

There's three cases one rolls and she stops, rolls a single 4 and rolls again, rolls no 4's and rolls again.
You have those three

the rolls and stops needs a 4,4 which is only 1/36 chances

The rolls one 4 and rolls again means she either got x,4 or 4,x. So there's a 10/36 probability, and a 1/6 for a 4 on the third roll

multiply those, that's your second term.

And so on for the third case

[timid girder]

Can you do the third case

[ivory cairn]

you tell me. It's the same reasoning as the second

[timid girder]

The third case that she rolls one x and one x. There is a 25/36 probability and a 1/36 on the 3rd roll

So 25/1296

[ivory cairn]

yep, because there's only 5 choices for each x (since neither can be 4)

[timid girder]

Yeah

But what’s the next step?

First case: 1/36
Second case: 10/216
Third case: 25/1296

[ivory cairn]

When you have mutually exclusive events (like you created here) to find the probability of any of those events happening, you just add the probabilities together

[timid girder]

Thanks

That helps me understand our probability unit a lot better

[timid girder]

.close

[full forum]

Channel closed

Closed by @timid girder

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.

[wheat talon]

Hi I am having hard time setting up eq for this poisson distribution

[wheat talon]

The question is that there is a goose attack happening at the rate of 5 attacks per week. A week is goose-free if no attack occurs that week.
and i want to determine the probability of goose free week

If X is the number of goose free weeks given an interval, then $X \sim Poisson(5)$ so $\frac{e^{-5} \cdot (\frac{5}{1})^1}{1!}$, is this correct?

[glossy valve]

meguuuuu

[full forum]

@wheat talon Has your question been resolved?

[wheat talon]

<@&286206848099549185>

[full forum]

@wheat talon Has your question been resolved?

[wheat talon]

<@&286206848099549185>

[wheat talon]

<@&286206848099549185>

[full forum]

@wheat talon Has your question been resolved?

[wheat talon]

anyone?

[gritty rose]

Fucking geese

You want P(X=0), not 1

[wheat talon]

Oh

Wait so when I have a question like this

What is a probability that in an interval of 16 weeks, there is at least 2 goose free day

What is X going to be?

because right now i have X defined as number of goose free weeks given an interval

Oh wait, is it going to be like this

Suppose that X is the number of goose attacks in an interval

Then P(X=14) is the total number of goose attacks in an interval of 16 weeks and 1 - P(x=14) is the total number of goose free weeks? @gritty rose

[wheat talon]

<@&286206848099549185>

anyone

[gritty rose]

What is X here? The same?

[wheat talon]

X is the number of goose attacks in an interval

[gritty rose]

You used X here to denote something else

Don't use the same variable for different things

[wheat talon]

I dont know which one to use thats why sorry

Why does P(X=0) make sense for when X is number of goose free weeks though

doesnt this mean 0 number of goose free attacks

[gritty rose]

Omg I'm so sorry

[gritty rose]

This was right all along

[gritty rose]

What is the exact question here

[wheat talon]

let me show you the question

[gritty rose]

Yea that's best

[wheat talon]

I am stuck on c) and d) mostly

[gritty rose]

Double nevermind. This was right all along

[gritty rose]

Is this an exam? Why does it have points?

[wheat talon]

assignmnet

my exams in on april

[gritty rose]

Use binomial distribution for c

[full forum]

@wheat talon Has your question been resolved?

[full forum]

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.

[grizzled lance]

Not sure how to begin showing this

[slow prairie]

<@&286206848099549185>

[slow prairie]

How do you solve this question?

[grizzled lance]

um idk that's why i posted the question

and why are u pinging helpers for my question

[steel dome]

Lmaooo

[lyric hemlock]

haha

[full forum]

@grizzled lance Has your question been resolved?

[grizzled lance]

Thoughts: So starting with showing that if P' lies on the circle, then P lies on the circle. $\frac{a}{b^*} = \frac{ab}{b_x^2+b_y^2}$. where $b=b_x+b_yi$ and likewise for the other complex numbers

[glossy valve]

azeem321

[hollow herald]

Do you know how to write a family of circle

[grizzled lance]

Not sure how both $\frac{a}{b^*}$ and $ab$ can lie on the circle unless $b_x^2 + b_y^2 = 1$

[glossy valve]

azeem321

[hollow herald]

tangent at a given point on a line?

[grizzled lance]

family of circle?

For the circle equation, I have $(x-c_x)^2+(y-c_y)^2=|a-c|^2$

[glossy valve]

azeem321

[hollow herald]

?

[hollow herald]

y/no (family of circles sharing a common tangent line at a specific given point)

if not, look it up

you can directly conclude

[grizzled lance]

ok, i will check it out

.close

[full forum]

Channel closed

Closed by @grizzled lance

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

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

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

[nocturne creek]

Can anyone please help me understand why the right side of the equation slope was taken -1

[full forum]

@nocturne creek Has your question been resolved?

[fathom saddle]

Slope of what?

I suspect we're missing context.

[nocturne creek]

We're studying parabolas, and this was a method of identifying how to check if an equation is a parabola or not. I think what we did here has some pre requisties from pair of straight lines but i didnt do that course, what i know is that slope of a line is -A/B so i can see how the left side of the equation slope is 1, but then the teacher said the right side of the equation slope is -1 without explaining, i can see how -(4+2c)/-2c is the slope, but i dont understand where the -1 comes from

[full forum]

@nocturne creek Has your question been resolved?

Channel closed

Closed by @nocturne creek

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 forum]

@torn jolt Has your question been resolved?

[neat bay]

Bruh what

[wise wyvern]

Ask a question first.

@torn jolt

[tulip marlin]

The answer is 2

[wise wyvern]

No, I got -2

[neat bay]

15

[wise wyvern]

0?

[tulip marlin]

alright close this channel

[neat bay]

Lol

[wise wyvern]

I did.

It's correct.

[tulip marlin]

• Discord TOS disallows users under 13

Are you under 13?

[wise wyvern]

Xd

[tulip marlin]

if not, you are trolling, so close this channel and stop

[neat bay]

Bruh

[wise wyvern]

ITS ZERO

I happen to be very good at maths, it's zero? I used calculator too.

Anyway, goodluck if you don't trust me. I'll exit.

[tulip marlin]

<@&268886789983436800> ^

[honest glen]

.close

[full forum]

Channel closed

Closed by @honest glen

Use .reopen if this was a mistake.

[full forum]

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.

[gritty bear]

Been really confused on this problem, can someone please help me.

[cold tangle]

Ummm....

[gritty bear]

😔 yes

What even was the point of this lol?

[fading steeple]

<@&268886789983436800> we have a troll posting this in various channels

[slender onyx]

ty

[cold tangle]

@gritty bear in which direction is it rotated

Clockwise?

[gritty bear]

It says it's rotated about x=2

[cold tangle]

By about it means with it?

[gritty bear]

Yes

That's my assumption

[cold tangle]

So its now y = 2

[gritty bear]

I'm still confused 😅

.close

[full forum]

Channel closed

Closed by @gritty bear

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.

[lucid void]

How do I find the side lengths

[full forum]

@lucid void Has your question been resolved?

[lucid void]

<@&286206848099549185>

[full forum]

@lucid void Has your question been resolved?

[shadow parcel]

@lucid void area is proportional to length^2

meaning area = b*length^2

notice that length can be anything

it could be the perimeter of the shape, or the side length, whatever

there is some constant b that makes the equation true

let s be the scale factor, then s*length_1 = length_2

That is the length of the second shape is scaled by a factor of s

what information is given?

$$area_1 = blength_1^2 = 4$$ $$area_2 = blength_2^2 = 25$$

[glossy valve]

DETOX

[shadow parcel]

this is all the information you need to solve for s

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

(echelon method)

2x + 7y = -8
-2x + 3y = -12

[fathom saddle]

See rules on helper pings

[torn jolt]

Oh

[proven nacelle]

Do you need to follow this method

Or..?

[torn jolt]

Yeah it say's "Use"

[leaden aspen]

First I believe you would want to check if this system has multiple solutions

If it only has one unique solution then use the echelon method

[tender rain]

why is that?

[leaden aspen]

Wouldn't you want the system to have only one unique solution?

Otherwise there would be many solutions

[tender rain]

Yes, there would. But remember what the echelon form for a linear system with infinitely many equations would look like.

[torn jolt]

It has two equations

[tender rain]

That could still mean there could be infinitely many solutions, or none.

[leaden aspen]

 2  7 | -8
-2  3 | -12
R1 + R2
2  7  |  -8
0  10 | -20

So 10y = -20
y = -2
Then sub in the first equation

[leaden aspen]

Ohhh

[torn jolt]

I thought y was 1??

[leaden aspen]

Is this what you call echelon method?

[torn jolt]

Yeah

[tender rain]

Weird

[leaden aspen]

Also this is a different question

[torn jolt]

I guess i don't really know I missed like 2 days of school

[leaden aspen]

This is what you wanted right?

[torn jolt]

Yeah thanks

[tender rain]

Did you ever learn how to represent this as a matrix?

[torn jolt]

I don't even know what a matrix is

[tender rain]

#whentheteachersaysechelonmethodbutthestudentsprobablyhavenocluewhyorhow

[tender rain]

Basically, what we understand under echelon form is this

That you get a "reverse staircase"

[leaden aspen]

You would want to form an inverted pyramid thing basically

Oh that's better lol

[torn jolt]

This is what happens when you miss days

[torn jolt]

Can I ask you a question?

[tender rain]

That's what we are here for

[torn jolt]

Alright so If we're going to college why do we need so much of this useless math

[leaden aspen]

The only day you're absent and something cool happens in the school 😢

[tender rain]

Because it's useful

[leaden aspen]

I wouldn't say this is useless

[torn jolt]

Literally pointless math that im never going to ever need nor remember

[tender rain]

Linear systems are used everywhere

[leaden aspen]

This is some of the basics

[tender rain]

at least as far as STEM goes

[torn jolt]

I'm just saying in general

[tender rain]

Do you like computer programming?

[leaden aspen]

You'll have to cope

[torn jolt]

Yeah

[leaden aspen]

Until you have an option to not choose maths

[torn jolt]

That's what i do

[tender rain]

Then Linear algebra will be useful to you

[torn jolt]

How'd you know that-

[leaden aspen]

Some parts of maths are used a lot in maths

[leaden aspen]

Graphics

[tender rain]

^

[leaden aspen]

I meant computer science lol

[torn jolt]

Nah that I program-

But thank you guys - 🥲

If you need anything dealin with computers hmu tho

[leaden aspen]

Just confirm with your teacher whether this is what he/she wanted with the echelon method

[tender rain]

Well, again, if you choose anything related to STEM, you'll need mathematics.

CS has a lot of interesting discrete mathematics going on e.g.

[torn jolt]

Thanks Again

[full forum]

@torn jolt Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

urgent

<@&286206848099549185>

<@&286206848099549185>

pls, I beg you

[dawn fossil]

why urgent

[torn jolt]

because i dont have time

[dawn fossil]

??

[torn jolt]

private stuff

[dawn fossil]

is this an ongoing test or what

[torn jolt]

no but i have due date

so many helpers and not 1 is available

[dawn fossil]

they have their own lives too

what tools can you use for this problem?

can you use code?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

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.

[karmic sluice]

hello, i'm not sure where to start with this question. we haven't learnt integration yet and i'm not very well versed with the characteristics of inverse trig functions. i'm aware that c is the y-intercept and that the derivative of arcsin is 1/(1-x^2).

[eager violet]

If f(x) = Aarcsin(Bx) + C, what's f'(x)?

[fossil stump]

^^

[karmic sluice]

AB/ \sqrt 1-(Bx)^2 ?

[nova basin]

"derivative of arcsin is 1/(1-x^2)" you forgot the sqrt, though it was probably a typo, but still

[karmic sluice]

oh yea mb

[eager violet]

Yeah, you need the √. Also, you forgot a parenthesis and the chain rule

[fossil stump]

Don't forget chain rule

[karmic sluice]

there's product rule too right

[eager violet]

There's no product

[karmic sluice]

oh a's a constant forgot

[eager violet]

You're not done tho. It's not Bx²

[karmic sluice]

AB/ \sqrt 1-(Bx)^2 ?

was i forgetting the parenthesis?

yea i don't really get how the 16 and 9 are in the square root

[eager violet]

You need the integrand to be of the form 1 - cx² in order to set things equal to each other. Perhaps you could factor something from 16 - 9x²? You won't be left with a whole number as a coefficient, but oh well

[karmic sluice]

sorry i don't really understand what you're saying

do you mean like 9(16/9-x^2)?

but i dont see how that would help

[eager violet]

Not quite. We want it to be 1 - cx², not c - x²

Where c is a number

[karmic sluice]

16(1-9/16x^2) yeh?

[eager violet]

Yeah

But remember that's in a square root

[karmic sluice]

4 (1-9/16^2)

wait no

4 \sqrt (1-9/16x^2)

[eager violet]

You can simplify the while expression. Remember that's on the denominator

[karmic sluice]

ahh i dont really feel like im simplifying it but

i got

AB \sqrt(1-9/16 x^2) / 4(1-9/16 x^2)

[eager violet]

•_•

[karmic sluice]

yea..

[eager violet]

I just want you to simplify -4/[4sqrt(1 - (9/16)x²)]

I don't know know why you have AB here

[karmic sluice]

ohh

that's just

-1/sqrt(1-(9/16)x^2)

so b is just 9/16?

but idk why the entire expression is negative

[eager violet]

Not 9/16

(Bx)² = B²x²

So B² = 9/16

[karmic sluice]

right

3/4

+-

[eager violet]

Arcsin is odd, so we can absorb the sign into A anyways

So we can just stick to +3/4

[karmic sluice]

alright makes sense

so a would be +- 1?

[eager violet]

No

Look at the numerator of both expressions

One of them is AB

The other is -1

[karmic sluice]

since b is 3/4, 3/4 A = -1

A is -4/3?

[eager violet]

Yep

[karmic sluice]

ohh

then i can just solve

alright

thank you for accepting my stupidness

you've beena great help

.close

[full forum]

Channel closed

Closed by @karmic sluice

Use .reopen if this was a mistake.

[full forum]

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.

[lost copper]

how do you prove that the monotone class generated by a ring is actually a ring?

[undone yew]

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

[full forum]

@lost copper Has your question been resolved?

[lost copper]

I see it's a corollary

But I don't understand how to pass from the case when G is an algebra to that when G is a ring

I know and algebra is a ring containing omega

[full forum]

@lost copper Has your question been resolved?

Channel closed

Closed by @lost copper

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

hello i need some help on some multiple topics i need to review on but cant remember how todo

[fossil stump]

[torn jolt]

mainly Simplifying expressions, factoring and systems of equations

[fossil stump]

You can just start by asking 1 question

[torn jolt]

okay so

how would i solve 20-(32x-3)-(4x-10) i know i need to get rid of the parenthesis then solve for simpify x down as low as i can i just got no clue where to start

[fossil stump]

You can't solve that. You can simplify it

To simplify:

1. Distribute all negatives (and in the process remove parentheses as appropriate)

2. Combine like terms

[torn jolt]

so take the one and distribute it to the 4x and -10 so that would become 4x+10?

.close

[full forum]

Channel closed

Closed by @echo arrow

Use .reopen if this was a mistake.

[full forum]

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.

[regal lynx]

How would I solve D=2S ∞ - 781.4?

[hollow geode]

what is 2S inf suppose to be?

[regal lynx]

I’m not sure it’s the formula my teacher gave me

[hollow geode]

post the question/formula accurately

ie picture or TeX it

[hollow geode]

so the infinite series

[regal lynx]

Yes

[hollow geode]

you compute S, then.. evaluate

[regal lynx]

This is my first time doing this unit, how would I do that

[hollow geode]

S_n is a geometric series

use the formula for S

$\sum_{n=0}^\infty ar^n=\frac{a}{1-r}, |r|<1$

[glossy valve]

Mosh

[regal lynx]

What would my n value be

Just 0?

[hollow geode]

No

your n value is infinity.

[regal lynx]

Now would I evaluate a/1-r?

[hollow geode]

a/(1-r)

but yes

given you know |0.7|<1 which guarantees convergence

[regal lynx]

Yep

My answer resulted in 7814/3

Thanks

.close

[full forum]

Channel closed

Closed by @regal lynx

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.

[void citrus]

How should I graph f^-1(x)=2x-4

[fossil stump]

Graphing 2x - 4: You have your y-intercept and your slope

Are you able to create a graph from this information?

[void citrus]

I know how to graph 2x-4, I am just confused on how to graph it when it says f^-1(x)=2x-4

f^-1(x) is especially confusing to me

[meager dew]

are you trying to graph the inverse of y=2x-4 or is y=2x-4 your inverse

[void citrus]

uh well the origibal equation was f(x)=1/2 x-5

then I inversed it to 2x-4

am I suppose to just graph it like y=2x-4?

[meager dew]

that's not what the inverse of that function is

[void citrus]

oh

I thought you were supposed to switch y and x, then write y in terms of x

[meager dew]

you are

seems you messed up somewhere

[void citrus]

oh

[meager dew]

(and to answer this, yes, you'd just graph what you get as the inverse)

however that specific inverse is not correct, so don't graph that

[void citrus]

I checked my working but I couldn't find a mistake

[meager dew]

can i see?

[void citrus]

question 10

[meager dew]

seems you wrote -5 as 2 lol

[void citrus]

oh lol

so it would be 2x-10

and I would just graph it?

[meager dew]

close

you have a sign error

[void citrus]

wait +

[meager dew]

yeah

and yes, you'd just graph that

[void citrus]

ok

tysm!

.close

[full forum]

Channel closed

Closed by @void citrus

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 aurora Has your question been resolved?

Channel closed

Closed by @winter aurora

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.

[tepid basin]

is this telling me to find the sin A?

i dont understand the fraction of sin A/2

i know that b = 16 after doing the math

oh wait thats the formula for half angle identity

[slow canopy]

so do you have any questions or did you solve it?

[tepid basin]

i'm still confused

entirely

[slow canopy]

about?

[tepid basin]

the whole problem

[slow canopy]

why?

[tepid basin]

on finding the sin A/2

[slow canopy]

first did you label all the sides and then find b (noting its a right triangle)

[tepid basin]

I understand the sin2A part

[slate thunder]

I think it can be solved using

Double angle formula

[tepid basin]

b = 16

wait let me try something

[slate thunder]

Have u solved $sin(\frac {A}{2})$

[glossy valve]

idk7

[slow canopy]

$\cos(2x) = 1 - 2\sin^2(x)$ then replace 2x with u, and you get: $\cos(u) = 1 - 2\sin^2\qty(\frac{u}{2})$

and then you can plug in ur values and solve for sin(u/2)

[glossy valve]

Brontochad (Shuri for honorable)

[slate thunder]

I think they have asked $sin$ not cosine

[glossy valve]

idk7

[slow canopy]

i know thats why i said solve for sin

[slate thunder]

I see

[tepid basin]

for sin2A it would be 2(12/16) * 16/20?

that i would solve for?

[slow canopy]

not 12/16

hypotenuse is 20

not 16

[slate thunder]

Uh wait

[tepid basin]

oh wait yes

,mb

12/20

[slow canopy]

then yes

[slate thunder]

Ya

[slow canopy]

2 * (12/20) * (16/20)

[slate thunder]

$sin(2x) = 2 cos(x) sin(x)$

[glossy valve]

idk7

[tepid basin]

which is 416/400 or 26/25?

[slow canopy]

,w 2 * (12/20) * (16/20)

[glossy valve]

Results provided by WolframAlpha

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

Requested by Brontochad#6969

[slow canopy]

24/25

because we know that -1 <= sin(x) <= 1, so the value should ALWAYS be in between those values

thats how you can check if your answer is right or wrong

[tepid basin]

got it

so for the formula of half angle identity

sinA/2

i got plus minus sqrt(4/40)

how would i know if its a positive or a negative?

@slow canopy

[slow canopy]

alright well the angle is clearly less than 90 degrees so sin(2 * that angle) should also be greater than 0

so it should be positive....but if you are just in geometry you can assume all the trig angles would be positive (up until where you learn about the unit circle)

[full forum]

@tepid basin Has your question been resolved?

Channel closed

Closed by @tepid basin

Use .reopen if this was a mistake.

[full forum]

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.

[spring solar]

I missed around a week of precalculus and i am stuck on specific solutions with multiple trig functions, ex:

[spring solar]

Wait, i got help from the teacher

.close

[full forum]

Channel closed

Closed by @spring solar

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.

[tough marsh]

For a codegolf challenge, I need to devise an algorithm f, that takes the first n digits of a real number a, such that for large enough n f(a[:n])=1 if a is rational. And also for the inverse, if a is irrational then there is an infinite increasing sequence of k1, k2, ... such that f(a[:k])=0
My idea for such f is finding whether there is a suffix of that sequence that consists of 2 identical words, like 2929, 312312.
This obviously works for a rational number, because after the second repetition, the added digit must be the same as the first digit on the repetition, so we can shift the repetition.
But I don't know how to prove that this f also works for irrational number, in sense that there is an infinite increasing sequence k1, k2, k3, such that f(a[:k]) =0

[full forum]

@tough marsh Has your question been resolved?

[tough marsh]

<@&286206848099549185>

[full forum]

@tough marsh Has your question been resolved?

[tough marsh]

<@&286206848099549185>

[full forum]

@tough marsh Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[haughty brook]

Hi! I need help on this question. Does part a look right?

If so, can I get help on the other parts. Thanks!

[zenith kernel]

Wrong

12 not 24

For example Z/12Z, the cyclic group of order 12

c Z/2Z times Z/2Z times Z/3Z
Where times I mean direct product

[haughty brook]

Oh okay, that makes sense ill look at that thanks

How could I find a group with that size though?

[zenith kernel]

Abelian cases is standard

Abelian groups of order n: first Prime factorization of n

n=Πp_i^e_i

Then for each e_i choose positive integers f_ij ,f_i1<=f_i2<=… such that their sum is e_i

Then you have an abelian group of order n: direct product of Z/p_i^f_ijZ

For example n=12=2^2*3

So Z/4Z times Z/3Z
Or Z/2Z times Z/2Z times Z/3Z

Those are all different abelian groups of order n up to isomorphism

Non-abelian cases have to be considered individually, no short cut

[haughty brook]

Oh okay I see... would showing those be enough in this case

[zenith kernel]

You just have to show 2 of them

One for b) one for c)

(Those two happen to be your only choice if you want them all be abelian

Like for c) you can use dihedral group D_6 (or D_12 I always confuse the symbol) coming up with Z/2Z times Z/2Z times Z/3Z might be easier

[haughty brook]

Oh okay thank you!

[full forum]

@haughty brook Has your question been resolved?

Channel closed

Closed by @haughty brook

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.

[cold tangle]

Multiply side a by side b

[torn jolt]

I got it

(x+7+x)^2

Is that it

.close

[full forum]

Channel closed

Closed by @terse tide

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.

[cold tangle]

(2x+7)^2 but yea

[torn jolt]

Yeah

Can u do this one above

.close

[full forum]

Channel closed

Closed by @terse tide

Use .reopen if this was a mistake.

[full forum]

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.

[jade fulcrum]

i have a major test tomarrow can someone help me with stuff so i can get a good grade tomarrow

[jade fulcrum]

i have some questions

[meager dew]

are you uploading them orrr

[vapid barn]

Just ask

Lol

[tidal citrus]

he died.

[full forum]

@jade fulcrum Has your question been resolved?

[neat bay]

@jade fulcrum what

[full forum]

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.

[kindred nebula]

Help with 12

I dont really understand

[light sonnet]

,rotate

[short crest]

use the pythagoras theorem

[light sonnet]

Hint: WY is the diagonal of the rectangle, WZ is the side. The diagonal and side makes two sides of a triangle

[kindred nebula]

ah yes so interior angles equal the sum of

180

and you can apply

pythagorean theorum?

[light sonnet]

Pretty sure it was 30 60 90

[short crest]

WZY is a a triangle so you can use it

[thorn dragon]

oh oops

[light sonnet]

I literally said this

[kindred nebula]

so 9 squared plus 10 squared = ans?

[short crest]

true

[light sonnet]

No

[short crest]

no

[thorn dragon]

i dunno i was thinking 30 60 90 but the ratios dont match up right

[short crest]

WY is the diagonal

[light sonnet]

Do you know Pythagorean theorem?

[kindred nebula]

yes

a2+bc = c2

[light sonnet]

Wasn't asking you

[short crest]

wait what

[light sonnet]

That's wrong

[kindred nebula]

b2

[light sonnet]

Improperly formatted

[light sonnet]

Still wrong

[short crest]

ii think he meant ^2

but dont know how to say it

[kindred nebula]

dude its a square + b square = c square

[light sonnet]

Still not talking to you

[kindred nebula]

and you can change the formula

depending on what you looking for

if you looking for hypotenuse

then its that

if you looking for leg

then its c2 - a2 = b2 or c2-b2 = a2

[light sonnet]

Then you should have properly said this because a2 means a times 2

[kindred nebula]

im to lazy to type a^2

[light sonnet]

Don't care

Format it properly

[kindred nebula]

ok

a^2 + b^2 = c^2

[light sonnet]

If you wrote a2, your teacher would mark it wrong, wouldn't they?

[kindred nebula]

depends on paper its really easy to write

simply because its not formatted in ASCII

so you can write it in any way you want

[light sonnet]

^ is literally just one extra keystroke

[short crest]

or just type alt 0178

[kindred nebula]

ye but mathematically inefficient to do that

[light sonnet]

As I said a2 and a^2 aren't the same

[kindred nebula]

ok

a^2

[light sonnet]

This is what you have to do for your question

[kindred nebula]

ok

[full forum]

@kindred nebula Has your question been resolved?

[kindred nebula]

14 and 16

[full forum]

Channel closed

Closed by @kindred nebula

Use .reopen if this was a mistake.

[full forum]

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.

[kindred nebula]

.

[kindred nebula]

14 and 16

[onyx glen]

,rccw

[onyx glen]

would have been better if part of the trapezoid was not cut off

does the pencil-writing have anything to do with either q14 or q16?

[kindred nebula]

nope

[kindred nebula]

oh sorry

there arent any vals

for F and C

[onyx glen]

"vals"?

[kindred nebula]

values

[onyx glen]

those points are still part of your diagram...

would you like it if part of your hand was chopped off because it was deemed to have no value

in any case

what are you having trouble with for q14?

[kindred nebula]

oh ok sorry lmao

[kindred nebula]

the question itself

[onyx glen]

please do not reply-ping me so often.

[kindred nebula]

like do you add 5x and 3x

[kindred nebula]

very sorry my reply ping is not turned off default

[onyx glen]

do you understand the relationship between the angles?

forgetting their expressions in terms of x and looking only at the diagram, what can you tell me about the angles DCB and ABC

[kindred nebula]

you mean like opposite,alternate

[onyx glen]

i'm not testing you on terminology here.

[kindred nebula]

oh they are all supplementary angles?

[onyx glen]

are they equal? do they add up to something? maybe something else?

[kindred nebula]

they have a intersection point?

[onyx glen]

no, that's nonsense.

they're angles, they don't have intersection points.

[kindred nebula]

they are alternate to each other?

??

[onyx glen]

i don't know what "alternate" means in this context

i think you're overcomplicating it

they add up to 180°.

[kindred nebula]

ahh ok

5x+3x+20+10=180

[onyx glen]

sure, yes

[kindred nebula]

ah ok got the ans thx

[full forum]

@kindred nebula Has your question been resolved?

[full forum]

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.

[split crescent]

ello, i need help. is this the right graph for this function?

[torn jolt]

yes

[split crescent]

are the open and closed points okay?

did i plot and use the right points?

<@&286206848099549185>

[full forum]

@split crescent Has your question been resolved?

[full forum]

@split crescent Has your question been resolved?

[full forum]

Channel closed

Closed by @split crescent

Use .reopen if this was a mistake.

[full forum]

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.

[arctic iron]

is the interval (6,10) continuous

[full forum]

@arctic iron Has your question been resolved?

[arctic iron]

<@&286206848099549185>

[fossil stump]

@arctic iron What do you think? Yes or no, and why?

[arctic iron]

im pretty sure it is because the interval doesnt include 6

if it did i.e. [6,10) then it wouldnt be continuous right

aw wait im pretty sure it would still be continous

how about [0,6) is that also continuous

[fossil stump]

It is continuous on (6, 10)

[fossil stump]

This is one of those small details from Calc 1 that I don't exactly remember, unfortunately.

[fossil stump]

What do you think? Any ideas?

[arctic iron]

im pretty sure it si

is

since the interval doesnt include 6

6

[fossil stump]

I think so as well - I'm not positive tho (it's once of those tiny things where the concept is there but it's a really small detail)

@arctic iron https://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx

That link may help

Especially if you know limits. If you don't know limits, don't worry too much

I think the idea is the following:

A graph f(x) is continuous everywhere except when there's a discontinuity there.

[fossil stump]

Therefore I believe this reasoning is correct.

[arctic iron]

.close

[full forum]

Channel closed

Closed by @arctic iron

Use .reopen if this was a mistake.

[full forum]

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.

[smoky sand]

Quick question: I have been doing variation tables and it takes way too long to create by substituting values to determine concavity and inflection points. Is their an easier way to?

[full forum]

@smoky sand Has your question been resolved?

[full forum]

@smoky sand Has your question been resolved?

Channel closed

Closed by @smoky sand

Use .reopen if this was a mistake.

[grizzled lance]

@smoky sand I believe there is a third derivative test for inflection points

[smoky sand]

.reopen

[full forum]

✅

[smoky sand]

I thought that was second derivitive

[grizzled lance]

ye

but there is one

for third

[vapid barn]

Third derivative is just the rate of change of concavity. That doesn't have a specific meaning I'm pretty sure

[grizzled lance]

hold on let me find the proof

[grizzled lance]

what do you think?

[smoky sand]

looks like too much reading that I dont know

[vapid barn]

Yes this is accurate

You run into issues where the f''(a)=f'''(a)=0

[grizzled lance]

but other than that case, is it fine to use for inflection points?

[vapid barn]

This accounts for that case

So yeah

I'm pretty sure there are also issues when the f'(a) = f''(a) = 0

[grizzled lance]

good to know. i read about this a while ago but wasn't sure if it could be used. saves so much time instead creating tables and sutff

[smoky sand]

😱

[vapid barn]

Consider this as an example

[smoky sand]

How do I use this, anything to getme away from variation tables

[vapid barn]

Is a line concave up or concave down

[smoky sand]

neither?

[grizzled lance]

neither

[vapid barn]

Yes. A line has no concavity

[smoky sand]

can someone simplify the proof into a concrete example?

[vapid barn]

Here's a better idea.

You give me an example of a problem

That you struggled with

We can walk through it

[smoky sand]

like for this is there a way to not have to do the table

[vapid barn]

Are you allowed to use a graphing calculator

[grizzled lance]

well this function is clearly decreasing

max will be at x=0

[smoky sand]

yea

well on the test no but this is just a worksheet

[vapid barn]

Alright then

The issue is finding the concavity immediately surrounding the inflection point

And the simplest way to do that is to plug in a number slightly smaller and slightly larger than the inflection point into the 2nd derivative

[smoky sand]

wait thats the simplest I thought that was the hard way 😭

[grizzled lance]

lol

this particular example is a really famous function

[smoky sand]

so we cant use the proof to do it immediatly?

[grizzled lance]

the gaussian i think its called

or the normal distribution one

[vapid barn]

But you don't know in which direction it changes from

An inflection point can either be concave up to concave down or concave down to concave up

[smoky sand]

that is why you need to do it for y' and y''

[vapid barn]

The inflection point itself does not give you that information unfortunately

[smoky sand]

if this was the simple way what is the hard way...just curious

[vapid barn]

This is the way. You have to know the sign of the second derivative surrounding the point

My advice to you would be to just get quicker at doing so

[smoky sand]

I know for concavity it is down if y'' is - but is the same true for y'?

[vapid barn]

If y' is negative then y is decreasing

A little tip: e^(anything) is always a positive number

You just have to take the sign of each factor in the product

[smoky sand]

yes so does it have to be within the interval or just -. Cause I can just use the signs rule to determine that without havng to calculate the value to test wheather it is in the interval or not

[vapid barn]

For smooth functions (which is what you'll usually be working with), the concavity or direction can only change at the zeros. So you only need to choose one point between each zero and then points outside those zeros

[smoky sand]

for more complex functions that involve e and ln idk what to plug in that would be less than those values

[vapid barn]

Just choose integers that are between the zeros

Like for this example, I would use -1, 0, 1

[smoky sand]

-1/2, 1/2

[vapid barn]

Yeah.
-1 < -1/2 < 0 < 1/2 < 1
So choose -1,0,1 as test points

[smoky sand]

ah

When it asks me to find the asymptote how do I do that. It says lim y = 0 as x approaches -and + infinity, so that the asymptote y = 0but I dont know why they do that

[vapid barn]

A little tip: e^(anything) is always a positive number

And this function has e^(-2x^2)

And let me just say this

e^(-inf)=0

[smoky sand]

e^inf is also 0 so asymptote is y=0

[vapid barn]

No

e^(inf) is inf

But the power of e is always negative here

So as we go to plus or minus infinity, we get e^(-inf)

So yeah the asymptotic is 0 because the function gets arbitrarily close to 0 on both ends but never achieves it

[smoky sand]

.close

[full forum]

Channel closed

Closed by @smoky sand

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.

[median pulsar]

ok so i followed the formula and i did
x (smallest number) , x-2 , x+2
then i made it into an equation doing
x + x+2 + x-2
and im currently stuck at 3x =0

[sweet ingot]

Huh?

Sum of three consecitive integers

[median pulsar]

?

yea

isnt that negatives

[sweet ingot]

Where does what you wrote come from then

[median pulsar]

i used the formula what our teacher gave us

oh wait

._.

[sweet ingot]

Lets think logically instead

[median pulsar]

that for positives

[sweet ingot]

Shall we?

[median pulsar]

.

[median pulsar]

i used the wrong formula

[median pulsar]

sure

[sweet ingot]

There is no need for “any formula”

If x is an integer what is the next integer?

How can you write that in terms of x

[median pulsar]

uh

x , x-2?

u there

[grizzled lance]

if x is an integer, what number comes after x?

[median pulsar]

another integer?

[sweet ingot]

If x is say 1

What is the next integer?

[median pulsar]

2 ?

[sweet ingot]

Okay

So why are you doing x-2?

You saying 1-2 is equal to 2?

[median pulsar]

no

[grizzled lance]

So what comes after x?

[median pulsar]

x +1?

[grizzled lance]

good

[sweet ingot]

Yes

[grizzled lance]

and after x+1?

[sweet ingot]

Can you solve it now?

[median pulsar]

yea

is the 3rd x+2?

ay

thanks

.close

[full forum]

Channel closed

Closed by @median pulsar

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.

[median pulsar]

so far im at
E= 2 (2y) -3
basically im stuck at 4y-3