help-17

[lethal flower]

No

[hard atlas]

more context would help. e.g. an example

[vocal sleet]

@lethal flower Has your question been resolved?

[lethal flower]

Lets say we have the set of binary numbers in 4 bits: {0000 to 1111}

If I focus on the first and second bit, there are 4 possibilities: 00, 01, 10, 11.

For 00, there are four 4 bit numbers ( group 1). For 01, there are another four ( group 2). For 10, there are four ( group 3). And for 11, there are four ( group 4.)

By considering the four permutations of the part, and putting the groups together, I get the entire set of 4 bit numbers back.

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lethal flower]

.reopen

[vocal sleet]

✅

[lethal flower]

. reopen

Now can this be applied to a general situation?

My problem is this:

I have a set S that has all the possible results of 5 people in a class.

Every element in the set is the combined result of the 5, in the form:

person A -- pass/fail
person B -- pass/fail
person C -- pass/fail
...
person E -- pass/fail

now if I take four subsets:

subset A has all the results where person A has passed

subset B has all the results where person A has not passed

If I unite the two subsets, do I get the entire set S back?

[hard atlas]

yes

[lethal flower]

Can you elaborate?

[hard atlas]

either A passed or didnt

[lethal flower]

Why does the union of a part's permutations lead us to all the outcomes?

[hard atlas]

the results will be in one of the sets

[lethal flower]

but why does exhausting the possibilities of a small part give us the entire answer?

[hard atlas]

this is the same as doing bitstrings of length 5, yes?

so subset A is all numbers starting with 1

subset B is all numbers starting with 0

every number starts with one of those two

[lethal flower]

It is a property of every number, true

But if we take the two, why do we get every number?

Why is the reverse true?

[hard atlas]

tell me a number I dont get

[lethal flower]

Let's explore this generally

[lethal flower]

But this is experimentally looking at the thing

Which principle allows the two to give every number?

[paper depot]

the law of excluded middle

[hard atlas]

well every number belongs to one of the two sets. so combining the two sets gives every number

[vocal sleet]

@lethal flower Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vast shale]

.close

[vocal sleet]

Channel closed

Closed by @lone pecan

Use .reopen if this was a mistake.

[vast shale]

.reopen

[vocal sleet]

✅

[vast shale]

I dont understand this at all

I getting brainfucked

[cyan crest]

hmmm

what makes this question difficult to understand for you?

[vast shale]

I get thatx=a

And

Y=b

I just dont understand

Xa sand all that

How am i supposed to know if they cross

[cyan crest]

you know what I think?

I think all the answers are correct

[vast shale]

Why??.??.

[cyan crest]

because all they say is that a and b are just not 0

they don't say anything else

[autumn chasm]

???

[mint plover]

Rudy do drugs

it's good for maths

[vast shale]

Huhhh

[autumn chasm]

Do I even know you?

[cyan crest]

also they don't give you the exact coordinates of point P

[autumn chasm]

Are you being sarcastic?

[cyan crest]

no

[vast shale]

Wait so they all pass bc they cant be zero

[cyan crest]

that's right

well, they all pass because a and b can be whatever you want them to be

positive or negative

they don't specify (further) constraints

[autumn chasm]

Interesting

Agreed

But i think if you take what they want you to take it should be D

[vast shale]

Ur wrong

Yeah D

Was the answer

[cyan crest]

why D though?

[autumn chasm]

No no he's right they haven't said a and b are distinct

[mint plover]

what question are yall discussing

[vast shale]

Because point P is (a, b)

[autumn chasm]

Like assuming a and b are distinct

[cyan crest]

ohhh

now it makes sense

[vast shale]

And if u put in thode valued

[cyan crest]

you need to take P as coordinate (a,b)

yep now I'm on the same page as rudy

[mint plover]

this? It says a,b not equal to 0 and P has coordinates (a,0) just satisfy and check condition

[vast shale]

Wait

So what do i do first

[autumn chasm]

P is (a,b) correct?

[mint plover]

drugs

[vast shale]

Yeah

[mint plover]

no

[vast shale]

I will math is fucking w me

[vast shale]

What

[autumn chasm]

So put the coordinates of P in all thr given lines to check which one passes through P

Only D satisfies

Also the fact that they've mentioned the point P is in 4th quadrant HAS to mean that a is positive and b is negative

[vast shale]

Ohhh yesh i trief it worked

[autumn chasm]

Good

[vast shale]

Alr ty Rudy!!

.close

[vocal sleet]

Channel closed

Closed by @lone pecan

Use .reopen if this was a mistake.

[autumn chasm]

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[near finch]

Cold somebody help me according to the answer key I got this very wrong but I don’t know how to determine if a graph is son of cos

[safe wyvern]

if you remember the definition from the unit circle

then you can see that sin(theta) starts at 0 when theta=0 and then increases as theta increases (and decreases as it decreases) for theta near 0

Whereas, cos(theta) starts at 1 for theta=0 and initially decreases as theta increases or decreases

that should be enough to tell what is cos and sin in the picture you sent

[near finch]

The thing that is confusing me is why are the y intercepts not (0,0 ) or (1,0)

Oh wait nvm

[near finch]

How do you know when theta is 0 and theta is 1

[safe wyvern]

you can find the point on the theta axis where it is 0. then you can check what the graph is doing for theta values near 0

[near finch]

My teacher was not here yesterday so we had to do the work on our own so that’s why I’m confused

[near finch]

What’s a theta axis…

[safe wyvern]

the axis that has the values of theta (the horizontal axis in the pictures you sent)

[near finch]

Sorry I’m really confused because none of the graphs start at 0

And only one starts at 1

[safe wyvern]

the graphs don't start at 0 (i.e. not intercept) but there is y value when theta is equal to zero

[safe wyvern]

why does the 1 matter? I'm just trying to discuss how to distinguish between cos(theta) and sin(theta) using the shape of the graph

maybe we can do one as an example

[near finch]

I mean if the y intercept is (1,0) it is cosine and if the y intercept is (0,0) is is sin or tan

And then the intercepts for cosine is pi/2 and 3pi/2 and the intercepts for sin is 0,pi, and 2pi

[safe wyvern]

this is true (I think you mean (0,1) though instead of (1,0)).

Let me explain a bit better.

All your graphs are of the form a*cos(theta)+b or c*sin(theta)+d

I want to teach you a way to distinguish whether it is cos or sin without using intercepts

the way you can do this is to consider what the shape of the graph looks like near theta=0

nothing about intercepts

[near finch]

Oh yea

I meant 0,1

[safe wyvern]

just how the graph changes as one decreases or increases theta a little bit

[near finch]

How do we know if we are increasing theta?

Is it just increasing the angle

[safe wyvern]

yes, or moving to the right on horizontal axis

so like here

The graph is initially increasing as theta increases from 0 (I can see this because the graph starts at -3 (it doesn't matter where it starts) and it moves upwards as I look from theta=0 to theta=pi/2)

[near finch]

How would we be able to tell it is an increase and not a decrease?

[safe wyvern]

because the graph is moving upwards

as theta increases

[near finch]

Wdym sorry

Oh wait

I undestand now

[safe wyvern]

okay great!

so we just want to be able to tell if this graph is of the form

a) a*cos(theta)+b

or b) or c*sin(theta)+d

well sin(theta) is increasing as theta increases through 0
whereas cos(theta) has a maximum at theta=0

the graph clearly does not have a maximum at theta=0 so it must be c*sin(theta)+d

and then I think you know how to work out c and d

[near finch]

Wait how would we know if it’s sin or cosine

[safe wyvern]

because cos(theta) has a maximum at theta=0

so a*cos(theta)+b will also have a maximum (if a>0) or a minumum (if a<0) at theta=0

but the graph above *doesn't * have a maximum there so if it's either sin or cos it has to be sin

[near finch]

But a non translated cosine graph before this new homework has a max at 1 or more

[jovial patrol]

For theta=0 cosine shows max value

[safe wyvern]

cos(x) has a maximum value of 1 at the point x=0

[near finch]

So how would we know what a theta maximum is?

[safe wyvern]

I'm not talking about the value of the maximum, but rather at what point on the horizontal axis corresponds to it

[jovial patrol]

see the graph at (0,0), these is max value on y-axis

[near finch]

Ohhh

[safe wyvern]

a*cos(theta)+b does not change the location of the extreme points (i.e. maxima and minima but it does turn maxima into minima and the other way around if a<0. that doesn't matter though for the purposes of this question where a>0 always)

[near finch]

So a theta max/min is just the max/min at the y intercept?

[safe wyvern]

roughly speaking yes, but let me clarify:

a function can have multiple maxima or minima

there is a maximum value of the function a*cos(theta)+b at theta=0 (since a>0 for all your examples)

But that's all we need to worry about for the purposes of this question

like cos(theta) also has a maximum (value of 1) at theta=2pi

but we only really need to worry about whether there is a maximum or not at theta=0 for the purposes of this question

[near finch]

How would we know if we don’t know if it is sin or cosine? Since that would change if it is 0 or the corresponding point

[safe wyvern]

if it is sin then it doesn't have a maximum at theta=0
if it is cos then it does have a maximum/minimum at theta=0

So you can look at the graph, ask: okay is there is maximum\minumum at theta=0?

if yes, then it's a*cos(theta)+b

if no then it's c*sin(theta)+d

[near finch]

So graph 1 and graph 3 would be sin and graph 4 and graph 2 would be cosine?

[safe wyvern]

exactly

[near finch]

So once we know that we can just use the amp and midline to find the right equation

[safe wyvern]

yep!

[near finch]

Ty!

[vocal sleet]

@near finch Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[lean token]

Can anyone solve question no. 1 c that is asking for Quartile Deviation coefficient of Quartile Deviation please somebody can do it please

[lean token]

Can anyone solve question no. 1 c that is asking for Quartile Deviation coefficient of Quartile Deviation

[lean token]

Can anyone solve question no. 1 c that is asking for Quartile Deviation coefficient of Quartile Deviation can someone please solve this please 🥺

[vocal sleet]

@lean token Has your question been resolved?

Channel closed

Closed by @lean token

Use .reopen if this was a mistake.

[vocal sleet]

@lean token Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[strange void]

I want someone to explain the gradient matrix and the equivalent gradient matrix line by line for me A

[cunning yew]

@strange void stop spamming channels

[bronze osprey]

I've closed the newer one you made

stick to this one pls

also in the help channels you shouldn't ask for people to explain concepts, cause well there's a lot of textbooks and YT videos floating around on the internet

if you want to use us humans wisely, ask a question about an exercise you have

or like a part of a video that you didn't understand

[vocal sleet]

@strange void Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[frigid comet]

I have an order of operations question. Which option in the photo is best for solving an area of a circle?

When I have (4/2pi)^2, what are the steps needed to solve? Why are the solutions different between the two different steps I took to solve? Which one is right?

[meager shoal]

both should be right if u plug in the correct values

,calc (4/(2pi))^2

[twin meteor]

Result:

0.40528473456935

[meager shoal]

,calc (4^2)/((2pi)^2)

[twin meteor]

Result:

0.40528473456935

[flat whale]

however you're calculating this is a mistake

[meager shoal]

that value is just estimation of 2pi

,calc 2 * 3.1415

[twin meteor]

Result:

6.283

[flat whale]

k is right. please review order of operations
https://www.mathsisfun.com/algebra/operations-order-calculator.html

and https://www.mathsisfun.com/operation-order-pemdas.html

[frigid comet]

Thank you!

[frigid comet]

Yeah what I’m learning here is that I need to use more parentheses when plugging equations into my calculator (TI-84)

I’ve been playing around with the parentheses I use in the calculator, and I’m getting different answers depending on the parentheses I use

[flat whale]

.

[flat whale]

.

[frigid comet]

So is my equation wrong here at the top of my page bc I don’t have the parentheses around 2pi? Or is it just that equations have to be plugged into calculators more specifically?

[meager shoal]

equation is not wrong

but i think u plugged it in the calculator wrong

[heavy yoke]

the top equation is not wrong, but when you enter it into a calculator as 4/2π the calculator reads that as
4 / 2 * π = (4 / 2) π
so to enter it into the calculator correctly you need to either use
4 / (2π) or 4 / 2 / π
or use the fraction mode (alpha -> F1)

[frigid comet]

Awesome thank you!

.closed

.close

[vocal sleet]

Channel closed

Closed by @frigid comet

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[strange void]

no one help me

[misty pollen]

what do you need?

[strange void]

I want someone to explain the gradient matrix and the equivalent gradient matrix line by line for me A

[misty pollen]

ok i don't know

i just know that it's a matrix with all the partial derivatives

i guess

[vocal sleet]

@strange void Has your question been resolved?

[vocal sleet]

@strange void Has your question been resolved?

[vocal sleet]

@strange void Has your question been resolved?

[vocal sleet]

@strange void Has your question been resolved?

[white palm]

send example of your gradient problem, maybe a screenshot

[vocal sleet]

@strange void Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[wicked grotto]

How can i get the f(x)=

[autumn chasm]

Do you know what sinusoidal functions are?

[signal loom]

A sinusoidal function is a function using the sine function. The basic form of a sinusoidal function is y = A sin (B(x - C)) + D, where A is the amplitude or height of our function, B is the change in period defined by 2pi/B, C the horizontal shift, and D the vertical shift.

[wicked grotto]

No i sont think so, but im german so maybe i know the german word

[signal loom]

here

[coral barn]

hi, if you can hire me, I will sovle your every problems. thanks.

[autumn chasm]

Okay you know what sin x is right?

[wicked grotto]

Wym by that

[signal loom]

A = 1 , B = pi , C = 0 , D = 0 , y = sin(x-pi)

acutally y = sin(pi-x)

[wicked grotto]

For which one

[signal loom]

left

acutally y = sin(pi - 2x) for left

[wicked grotto]

Why -2x

Bcs its 2 times period?

What letter is pi?

[flat whale]

,calc pi

[twin meteor]

Result:

3.1415926535898

[flat whale]

π

[wicked grotto]

Nah i mean a b c d

In the f

[vocal sleet]

@wicked grotto Has your question been resolved?

[bronze osprey]

you're talking about y = A sin(Bx - C) + D then

,rotate

[bronze osprey]

it's also y = sin(2x)

so A = 1, B = 2, C = 0, D = 0

,rotate

[bronze osprey]

this other one is trickier, cause the phase shift is hard to figure out from the graph

[autumn chasm]

I don't think he knows what sine is

[wicked grotto]

So thats the right one?

[bronze osprey]

yes

[wicked grotto]

Why is d=0

Isnt the highpoit at y =1.5

[bronze osprey]

because d is (max + min)/2

d is the average value of the trig function

[bronze osprey]

oh I wasn't doing that question

[bronze osprey]

I was still on this one

[wicked grotto]

Oh mb

[bronze osprey]

okay, if you're moving on then

the maximum for the 2nd question is indeed y = 1.5

and the minimum is at y = -1.5

so which letter does that information relate to: a, b, c, or d?

[wicked grotto]

A =1.5 , b =1, c =-2/3pi, d=1.5?

[bronze osprey]

I don't think you understand what d is

[bronze osprey]

d = 0

but yes the period is 2pi, the exact same as sin(x), so b = 1

it helps if you use a few words to support your answer

[wicked grotto]

I did this for d

[bronze osprey]

so y = 1.5 sin(x - (-2pi/3)) yep

[wicked grotto]

Oh now i get d

Ty for help

.close

[vocal sleet]

Channel closed

Closed by @wicked grotto

Use .reopen if this was a mistake.

[bronze osprey]

np!

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[vapid sequoia]

i'm a bit confused about this - does it just want me to solve it algebraically?

[vapid sequoia]

its a bit easier than a lot of the other questions lol

nvm

.close

[vocal sleet]

Channel closed

Closed by @vapid sequoia

Use .reopen if this was a mistake.

[vapid sequoia]

oop sorry cloud

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[finite hatch]

Am I doing this right

[finite hatch]

Part b

Cause now I can’t cancel the sqrt(2)

[paper depot]

this will be difficult!

better to realize your polynomial has real coeffs

thus (z+sqrt(2)i) will also be a factor.

thus (z^2+2) will be a factor

[vocal sleet]

@finite hatch Has your question been resolved?

[finite hatch]

oh ok thank u

.close

[vocal sleet]

Channel closed

Closed by @finite hatch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vast shale]

Rocío goes to the bakery and buys for breakfast 3L/ 2 + 4 loaves of bread, knowing that

How many loaves of bread will she buy for lunch, if she buys three loaves less than at breakfast?
she buys three loaves less than for breakfast?

[vocal sleet]

@vast shale Has your question been resolved?

[bronze osprey]

$ab = \frac{6^{1/3} - 4^{1/3}}{4}$ right

[twin meteor]

south

[bronze osprey]

difference of two squares

then if you can find what (a + b)^2 - 2ab = a^2 + b^2 is

a^4 + b^4 = (a^2 + b^2)^2 - 2(ab)^2 and that's enough information to figure out what (a^2 + 3b^2)(b^2 + 3a^2) is, after you expand it

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

oh right

[vast shale]

(a + b)^2 - ab = a^2 + b^2

I don't understand how they are equal... (a + b)^2 - ab = a^2 + b^2 + ab

is it necessary to know this in ordet to solve it?

[vast shale]

I havent been taught that one btw

I could deduce it tho

is this correct?

• a instead of b in one

[vast shale]

maybe there is no need to replace it

like that

What should be my next step? and what am I doing wrong?

<@&286206848099549185>

[bronze osprey]

what I'm suggesting is yeah that exactly

so if you find ab, you know (ab)^2

[bronze osprey]

and this is how to find a^4 + b^4 with the information you have

[bronze osprey]

woops, typo

missed the 2

[vast shale]

a^4 + b^4 = (a^2 + b^2)^2 - 2(ab)^2
oh ok, so this is like an equivalence

[bronze osprey]

yep, this is an identity

[vast shale]

Is this okay so far?

I think it's 1/4 instead of 1/16

[bronze osprey]

in fact it should be 1/2, cause 1/16 * 4 (6 - 4)

weird, L should be equal to 2

[vast shale]

why (6 - 4), from where

[bronze osprey]

I can check using Desmos one sec

[bronze osprey]

,w (a-b)((a-b)^2+3(a+b)^2)

[twin meteor]

Results provided by WolframAlpha

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

Requested by sooouth.

[bronze osprey]

let p = 6^(1/3) and q = 4^(1/3) for convenience

then after expanding you should get 4(p^3 - q^3)

if your original expression is correct ofc

[vast shale]

idk

w8

[bronze osprey]

you should get $\frac{1}{8} (p^2 + 6pq + q^2) = a^4 + b^4$

[twin meteor]

south

[bronze osprey]

from $\frac{p + q}{2} = a^2 + b^2$

[twin meteor]

south

[vast shale]

mm I didn't get this

[vast shale]

this looks a little bit like the identity I didn't know

[vast shale]

But it's different

[vast shale]

sorry, I need to regain my math habilities (all precalculus), which I studied last year, I stop practicing many months ago (been moving to another country and learning languages) and I'm revising from the beginning

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic crater]

How do I solve this using the method with the positive and negative thingy (I tried but made some stupid stuff)

[solemn oyster]

Wdym the positive & negative thingy o.o

[mystic crater]

Method of opposite coefficients

Yes

I had to translate it

[solemn oyster]

(-5) times the first equation, (2) times the second equation. Then add them up

[mystic crater]

Thats what i did

bruh

Is there a stupid mistake im not seeing?

[vast shale]

Is x=21/6???

[mystic crater]

i have no idea

[vast shale]

You dont have solution??

Isnt this a topic of pair of lin eq in 2 var.???

[mystic crater]

dude i dont have the answer

[vast shale]

What book is this from

[mystic crater]

-60 + 20 = not -5

[mystic crater]

why

[vast shale]

Cuz i asked

[remote patrol]

Are the questions asked separately? I mean 2x+3y is question A and 5x+4y is question B. If so maybe I can help

[mystic crater]

i looked up exercises on youtube coz i have an exam tommorow from this

[mystic crater]

bruh this is the same question its just the work i did but its wrong

[remote patrol]

Wow. Wise move

[remote patrol]

Ouhh

[solemn oyster]

First equation, its 45 not -45

[mystic crater]

oh

ill get into that in a second

[solemn oyster]

-10x - 15y = 45
10x + 8y = -10

So -15y + 8y = 45 - 10, -7y = 35, y = -5

Plug back, 2x + 3*-5 = -9, 2x = -9 + 15 = 6, x = 3

@mystic crater

[mystic crater]

oh okay

i guess that solves it

[solemn oyster]

Could you understand each step

[mystic crater]

yes

thanks

.close

[vocal sleet]

Channel closed

Closed by @mystic crater

Use .reopen if this was a mistake.

[mystic crater]

wait

[solemn oyster]

Yes?

[mystic crater]

no nothing i tought the command didnt work

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[plucky quail]

Can someone explain part d

[plucky quail]

There steps and my idea was let u =sech^n(x)

Then substitute the mclaurin seried of sech^n(x) into the mclaurin series of E^x

Im not sure if that would work, would it? And what did they do?

Ping me when u respond

[bronze osprey]

can you take a picture of just the questions

the text is too small

[plucky quail]

Ah sorry

I wanred everything im 1 ss thars whg

@bronze osprey

<@&286206848099549185>

[bronze osprey]

that works!

so you just sub in your answer for part (c) into 1 + x + x^2 / 2 (the Taylor series of e^x to the first 3 terms)

[plucky quail]

What did they do?

[bronze osprey]

ah so they factored out an e^1 = e

[plucky quail]

I think they rewrote it as e¹ X e^n/2x²

And applied three mclaurin series

[bronze osprey]

then they used this with x = -n/2 x^2 + ...

[plucky quail]

Oh they didn't split it into three E^(f(x))

Or did they?

[bronze osprey]

no they just split it into 2

1 and the other part

[plucky quail]

1 and two parts

So three?

Including e^1

My answer wouldtbe different if i did my approach no?

Btw

[bronze osprey]

no, the other part is $-\frac{n}{2} x^2 + \frac{n(3n + 2)}{24} x^4$

[plucky quail]

Because i would have 1+ (.....)

[twin meteor]

south

[bronze osprey]

the person who wrote this solution is being really clever

that's an unreasonably short solution

[plucky quail]

Wouldn't my method be slightly quicker i thought

😂

[bronze osprey]

what's your approach again?

[plucky quail]

U=

So write e^u =mclaurin series

Then sub my expression of sech^n(x) into u

Of the mclaurin series

Tbf mabye I aint quicker bc of some expansion

Yh thanks, its some tough question lmao

[bronze osprey]

yeah, so if you try to sub in the entire thing, (1 - n/2 x^2 + ...) into 1 + x + x^2 / 2

it would be very painful

[plucky quail]

The question as. Whole was tough

[bronze osprey]

STEP is tough in general ngl

[plucky quail]

Its not step

😂😂

[bronze osprey]

ah it's Edexcel mb

[plucky quail]

Its not even that

Some tough paper made by a elite skl

[bronze osprey]

no wait not Edexcel, AQA or smth?

ohhhh

[plucky quail]

Its for edexcel spec

Just custom made

[bronze osprey]

interesting

[plucky quail]

Btw

I don't think it would be that bad actually

[plucky quail]

Because u won't actually expand the

U would pick and choose

Ifyk what i mean

[bronze osprey]

of course you would

[plucky quail]

Wana sre another tough question i struggled on?

[bronze osprey]

it's just the x^2 / 2 that becomes a bit more tricky, figuring out which terms to include

[bronze osprey]

no thanks

I mean you can still post it for others

[plucky quail]

Nqh Its kl

😂😂

[bronze osprey]

I'm just saying don't expect me to help you on it

[plucky quail]

Nah i dont need help

It was jsut for u to attempt it

Found it a cool question

Even this q was pretty tough it had me smiling abit even tho i couldn't do it

Close.

.close

[vocal sleet]

Channel closed

Closed by @plucky quail

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.

[alpine mantle]

little bit confused by part ii

[alpine mantle]

is it just asking me to sketch all the induced subgraphs of G that have 4 vertices?

or all the isomorphic graphs that are isomorphic to one induced subgraph of G?

[vocal sleet]

@alpine mantle Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[heavy palm]

How do I solve this improper integral?

[heavy palm]

Oops

Sorry

I have two channels

Mistake

[heavy yoke]

you already closed the other one

[heavy palm]

Yea but it’s still named me

[heavy yoke]

it just takes a bit for closed channels to be recycled, don't worry about it

[heavy yoke]

anyway for this question you can do a substitution

[heavy palm]

U = cos2t?

[heavy yoke]

i don't think that would help in this instance

[heavy palm]

I guess the 2t right

Since it would just be cosu

[heavy yoke]

that should work

[heavy palm]

Can’t I take the integral of cos2t

Isn’t it like sin(2t) over 2

Or something

[heavy yoke]

well if you know the antiderivative already then sure

if you didn't know the antiderivative then you could substitute to get one

[heavy palm]

What would I put in for like

My bound stuff like uhhh

1/2(sin2t) when t goes to negative infinity

What happens then

Is it just divergent because it oscillates

Between -1 to 1

[heavy yoke]

it doesn't approach any one number, that's true

[heavy palm]

So it diverges right because of that

[heavy yoke]

yes, if the limit doesn't exist then it diverges

[wanton bloom]

It clearly diverges.

I mean.

[heavy palm]

.close

[vocal sleet]

Channel closed

Closed by @heavy palm

Use .reopen if this was a mistake.

[heavy palm]

.reopen

[vocal sleet]

✅

[wanton bloom]

Nothing.

[heavy palm]

For problem 30

Would the correct approach be to start with integration by parts

u = lnx

dv = 1/x^2

[scenic ravine]

no

[quiet echo]

You can actually just u-sub this one

[scenic ravine]

substitution

[quiet echo]

u=ln(x) works fine, since x=e^u and you already have a 1/x term for the 1/xdx

[heavy palm]

How would u = lnx work wouldn’t I have a 1/x left over

[quiet echo]

If you want to, sure, but the faster method is definietely subsitution

[quiet echo]

Hence why I said x=e^u

[heavy palm]

Oh

[quiet echo]

Then it just becomes standard

[heavy palm]

Thx

.close

[vocal sleet]

Channel closed

Closed by @heavy palm

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.

[heavy palm]

Is my setup for problem 41 correct

[autumn chasm]

Yes

[heavy palm]

.close

[vocal sleet]

Channel closed

Closed by @heavy palm

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.

[thorn spindle]

wtf

i got r = 3

so i plugged in x = -3 and x = 3 into the series

so the 3^n cancelled

which left n -> inf of n

which is infinity

[quiet echo]

$\sum_{n=1}^{\infty}n$ is divergent

[twin meteor]

;(

[quiet echo]

As well as $\sum_{n=1}^{\infty}n(-1)^n$

[sly sierra]

in any case, how could the interval of convergence possibly be (infinity, infinity)

[twin meteor]

;(

[sly sierra]

as soon as you know R=3, you know the interval is either [-3,3] or (-3,3] or [-3,3) or (-3,3), those are the only possibilities

[quiet echo]

Did you just take the limit of the sequence without considering what the actual convergence is

[thorn spindle]

yeah

cause i saw in a video

they got R and plugged in -1 and 1

into the series

then took the absolute limit

[quiet echo]

Yeah you're supposed to actually consider convergence

[quiet echo]

^

[thorn spindle]

wait so u dont need to plug values back in?

[sly sierra]

you always need to check the endpoints

[quiet echo]

You need to, but don't do what you did

[sly sierra]

i.e. check the value x = R and x = -R

[quiet echo]

You need endpoint to see whether the series converges at the endpoints

[sly sierra]

because they may or may not be included in the interval of convergence

[thorn spindle]

wait so did i do the endpoint checking wrong?

[sly sierra]

did you find that the series converges or diverges when x = 3?

[thorn spindle]

diverge

[sly sierra]

correct

how about x = -3?

[thorn spindle]

diverge as well

[sly sierra]

yep

[thorn spindle]

they were both infinity

[sly sierra]

so what is the conclusion?

[thorn spindle]

oh so that means the endpoints arent included

[sly sierra]

right

[thorn spindle]

so if you were to get -3 and 3 back

from checking

then they are included?

[sly sierra]

well if you got a finite limit at all

[thorn spindle]

oh so it doesnt have to be 3 or -3

[sly sierra]

nope, convergence just means the series has a finite limit

[thorn spindle]

okay

so if it converges when checking then its finite

[sly sierra]

yep

[thorn spindle]

so you put the [] instead of ()

[sly sierra]

yea [] if both endpoints are included

() if excluded

[thorn spindle]

yeah

[sly sierra]

and mixed form if one is included and the other is not

[thorn spindle]

okay that makes sense

so the answer is (-3,3)

[sly sierra]

(all four possibilities can happen, depending on the series)

[thorn spindle]

got it thanks

.close

[vocal sleet]

Channel closed

Closed by @thorn spindle

Use .reopen if this was a mistake.

[sly sierra]

yw

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[zinc hornet]

does anyone know how to do this?

[sly sierra]

did you try anything yet?

[glass oak]

do you understand what the question is asking?

[zinc hornet]

idk how to graph it with the t=0 t=1

smth like this (if that makes sense)

[flat whale]

you can just plot y vs x using this

y = (x-1)^2 is the result of eliminating t

[zinc hornet]

sometimes if the equation is like y=x+8, why do u graph only parts of the graph like a ray instead of a line? im confused about that😭

like idk when to graph the equation as it is or just parts of it

[flat whale]

you need to find the analogous x range using this

0 <= t implies 0 + 1 <= t + 1

[zinc hornet]

t can be any real number for this question tho
that restriction is for the others

[flat whale]

<@&268886789983436800> spam

[flat whale]

what question are you talking about

[zinc hornet]

#8 parametrics

[flat whale]

oh i see

yes then you just plot arrows on your parabola

[zinc hornet]

how do I know which direction it’s going in tho

[zinc hornet]

idk what the t= (number) labeled on the graph is about 😭

[flat whale]

https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(LibreTexts)/09%3A_Solving_Quadratic_Equations_and_Graphing_Parabolas/9.05%3A_Graphing_Parabolas

when t is all real numbers, then x is ?

[zinc hornet]

this is what I did so far

[flat whale]

yes that looks right

[zinc hornet]

is that it?

cuz I thought I needed to graoh the direction it’s going in and t values. how do I know where t=0 begins

sorry I just dont really understand parametrics

[flat whale]

it doesn't matter where t=0 is

for x = t + 1, increasing x is the same as increasing t

[zinc hornet]

just watched an organic chem tutor vid, i think I understand now

is this correct

[zinc hornet]

im confused… wouldnt t=0 be at the point (0,1) cuz when u substitute t = 0 into both equations, x would be equal to 0 and y is 1

[flat whale]

yes, but again t=0 does not matter

should probably fix that arrow pointing up

all your other arrows look right

[zinc hornet]

alr thank you

.close

[vocal sleet]

Channel closed

Closed by @zinc hornet

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.

[heavy palm]

Can someone explain this to me

[heavy palm]

How does 1+y^2(y^2+2) equal (y^2+1)^2

?

[autumn chasm]

Expand the bracket

What is it equal to?

[heavy palm]

y^4 +2y^2 +1

[fallow kindle]

Yep

[autumn chasm]

And what does (y^2+1)^2 expansion look like

[heavy palm]

I see

How do you know that compresses into that though

Is there a formula

Cause I don’t remember

[tawny nacelle]

it's a "perfect square trinomial"

(a + b)^2 = a^2 + 2ab + b^2

[tawny nacelle]

if we set y^2 = a, and b = 1, then this reduces to a^2 + 2ab + b^2

so that's why

[heavy palm]

Ok thx

.close

[vocal sleet]

Channel closed

Closed by @heavy palm

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[reef marten]

Hey guys i have a question

[hollow pendant]

!da2a

[vocal sleet]

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

[reef marten]

i am trying to figure out how to solve this exercise it says i need to give the integral of the following areas and like how am i supposed to do that without being given a function?

[hollow pendant]

Notice how each of the definite integrals have bounds that perfectly conform to the endpoints of given regions.

[hollow pendant]

You don't need to know the exact function, because you are given the area of each region. And, by definition, a definite integral is simply the area under the curve.

[vocal sleet]

@reef marten Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[real monolith]

do i like ask here to get help

[ashen sky]

Hello there fellas,
Guys I’m searching for a group of students auditing the course of Introduction of Mathematical Thinking by Stanford and Coursera. How can i find such a community online? Thanks in advance

[real monolith]

ok well can someone help me w graphing piece wise functions, i’ve watched several videos and examples, i cannot understand it for the life of me

[silk osprey]

what’s confusing

[real monolith]

literally like all of it, i don’t see how i am supposed to graph this

[silk osprey]

do you have an example

[viral plover]

can you share an example

sniped

[silk osprey]

do you know how to graph -x - 7 and x - 5 normally

[real monolith]

like the y-int is -7, then i go down one and right one?

[silk osprey]

yea

so if it makes it easier you can think about drawing these pieces individually like you would normally but then "erasing" the bits that are outside of the region you’re asked to plot them in

so here you would for example draw -x - 7 but then erase everything that isn’t in the region
-6 <= x < -1

you’re taking a piece of the functions restricted to a particular region/domain

[real monolith]

i’m sorry i re read that like 4 times i am still so confused

[silk osprey]

graph -x - 7
erase everything except where -6 <= x < -1

then graph x - 5

and erase everything except where -1 < x < 4

[real monolith]

did i graph that correctly lmao

[silk osprey]

no

it’s an entire line

not just down one right one one time

[silk osprey]

yep

but now get rid of everhthing except for the portion where x is between -6 and -1

[real monolith]

i don’t really understand

[silk osprey]

you only want what’s between the blue lines i drew

[real monolith]

but why? i though i had to have a line going on for infinity

[silk osprey]

because it’s how our piecewise function is defined

for -6 <= x < -1, f(x) = -x - 7

[real monolith]

so like that

[silk osprey]

nice

but can you make it an open circle at -1?

-1 isn’t part of our interval

it’s only -6 <= x < -1

click the dot or whatever

or -1

[real monolith]

i’m about to cry i don’t know what im doing

[silk osprey]

this is good

[real monolith]

so is that like it for the second one

[real monolith]

or this

[silk osprey]

well the x - 5 but should only be for -1 < x < 4

[silk osprey]

not this

[real monolith]

yeah i give up there’s no way for me to understand this, thanks for ur help 💕

[vocal sleet]

@real monolith Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[weak dome]

with 24, where does the 5 come from?

[weak dome]

im confused over what value the problem is asking us to find

these are my teachers notes

[hollow pendant]

They multiplied the top and bottom by 7.

[hollow pendant]

As a result, the denominator became 7 - 2 = 5.

[weak dome]

okay i got it sorry, i hadnt looked at one of the formulas i was supposed to use 😅

thanks!

.close

[vocal sleet]

Channel closed

Closed by @weak dome

Use .reopen if this was a mistake.

[weak dome]

.reopen

[vocal sleet]

✅

[weak dome]

im back im still confused

where does this come from?

damn me theres another formula

okay bye again

.close

[vocal sleet]

Channel closed

Closed by @weak dome

Use .reopen if this was a mistake.

[hollow pendant]

That's S, and it generally refers to the sum of the series.

If there is a subscript below S, like S_15, it refers to the sum of the terms up until n = 15.

[weak dome]

okay

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[civic saddle]

yes

i tried'

[paper depot]

"WHAT have you tried?" was not a yes/no question

[civic saddle]

oh

should i show my work

[cyan crest]

yep

[flat whale]

yes

[flat whale]

looks right. do you know how to turn a unit vector into one with length 7

[civic saddle]

idk

thast wherr i stuck[

[flat whale]

would you be able to answer the question if your unit vector were just (1,0,0)

[civic saddle]

the questions says it has magnitude 7 but its 18

[civic saddle]

what ? its on x axis

[flat whale]

yes

[paper depot]

when you multiply a vector by a number like 5, what happens to its length?

[flat whale]

can you find a vector on the x axis with length 7

[civic saddle]

increase

[paper depot]

increase how

be specific

[civic saddle]

5(i+j+k)= 5i+5j+5k

[paper depot]

not what im asking

[civic saddle]

so

[civic saddle]

(7,0,0)

[paper depot]

the relationship between |5u| and |u| for any vector u is?

[civic saddle]

idk

[paper depot]

when you multiply a vector by a number, its length is also multiplied by that number (or its modulus, rather).

the vector 5u always has 5 times the length of u

etc

this is something you should know

[civic saddle]

i have math exam on 2 june 3 chapters left vector,3d geometry,linear programming i want to finish it quick

[paper depot]

ok but how is that relevant

this is something you were missing and have to know anyway

but of course we aren't forcing you

[civic saddle]

i started vectors today

[paper depot]

if you want to ignore this knowledge that's up to you but please in that case explicitly tell me "i want to throw this away"

[civic saddle]

no i want to undersatnd vectord

[paper depot]

ok right

then hold off on the whining about how many exams you have

when you multiply a vector by a number, its length is also multiplied by that number (or its modulus, rather).

symbolically, $|c\vec{v}| = |c|\cdot |\vec{v}|$

[twin meteor]

Ann

[civic saddle]

?

[paper depot]

v is a vector, c is a number by which im multiplying it

[civic saddle]

ok

[paper depot]

|these| denote length of a vector and also modulus of a number

do you understand now what i am saying

yes or no

[civic saddle]

ok v is a vector (i+j+k form )

@paper depot

[paper depot]

i don't know how to respond to that. was that a question? a declaration? or what

[civic saddle]

What

[paper depot]

ok v is a vector (i+j+k form )

i do not know how to respond to this

[civic saddle]

Why

[paper depot]

bc you confused me

and you also didn't give me a clear yes or a clear no

so i will have to leave now

💀

[civic saddle]

Why don't leave

.close

[vocal sleet]

Channel closed

Closed by @civic saddle

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[boreal remnant]

take the derivative

[gentle nimbus]

yeah then uhhh find the zeros of the derivative

that should give you the time taken and you can reinput to get your value 🤔

[atomic pulsar]

thats the thing i dont know how

what equation or formula is this again

[bronze osprey]

oh have you studied derivatives?

you don't need them here actually: t = -b/(2a) works too

[atomic pulsar]

which one's a and which one is b

[bronze osprey]

ah so it's for y = at^2 + bt + c

[atomic pulsar]

i've nver learned that

[bronze osprey]

y = ax^2 + bx + c?

oh but you haven't learned the x = -b/(2a) part for the vertex right

well it comes from completing the square of y = ax^2 + bx + c

[vocal sleet]

@atomic pulsar Has your question been resolved?

[atomic pulsar]

no but i havent learned "at^2 + bt + c"

[bronze osprey]

it's the exact same as ax^2 + bx + c

it's just that instead of x you have t everywhere

[atomic pulsar]

oh

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vast shale]

i think im over thinking it

[vast shale]

I understand everything minues the logic that determined the value of N

[sly sierra]

what is N supposed to represent?

[vast shale]

I believe its the point where the sequence has the correct order

to be squeezed

[sly sierra]

so is it the smallest n that makes the inequality true?

[vast shale]

i believe so

[sly sierra]

the inequality is true for all n >= 1, right?

therefore N = 1

[vast shale]

im sure i understood that

not*

.close

[vocal sleet]

Channel closed

Closed by @desert kindle

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[proper nimbus]

i need help with (i)

idk where to get started

i tried (|a| - 1) - (5-a^2) >/= 10

[proper nimbus]

(if a is not an integer)

and (|a| - 1) - (5-a^2) >/= 8

if a is an integer

[vocal sleet]

@proper nimbus Has your question been resolved?

[vocal sleet]

@proper nimbus Has your question been resolved?

[vocal sleet]

@proper nimbus Has your question been resolved?

[spiral turtle]

@proper nimbus I'm not sure what is being asked because I am unfamiliar with this short form of set notation

What does A = [5-a^2 , |a| - 1] mean?

I assume it is related to set builder notation, but there is something implicit going on here that I need explicitly explained in order to convert between the two

[grim escarp]

dude in the channel w a mod?

<@&268886789983436800> @spiral turtle

yeesh

[autumn chasm]

Closed interval

A range i think

[spiral turtle]

Huh! I guess that would make a lot of sense.

Sorry, I was imagining stuff like set builder notation rather than a simple range.

That's quite silly of me

[autumn chasm]

[spiral turtle]

@proper nimbus What I would start with is recognizing that if your interval starts and ends with an integer then it contains end-start+1 integers in total.

So the range [3, 7] contains 7-3+1 = 5 integers in total, they are (3, 4, 5, 6, 7)

So you actually need (|a|-1) - (5 - a^2) + 1 >= 10

[vocal sleet]

@proper nimbus Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[vast shale]

hai

[vast shale]

i come with this sol from the book just more elaborated with an exxample

my question is how to prove that for every boolean function f there is always fA s.t f=fA?

this is the proof in the book but only construction of A (what I did) appears

how to prove the last part (checking that indeed f=fA)

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[cunning kettle]

isnt this supposed to be the other way around (less than or equal to)

[edgy gulch]

no?

[rugged orchid]

well the line is where they are equal

[cunning kettle]

since 0 is not bigger or equal to 3

[rugged orchid]

everything above the line will have the y value be bigger than the right side of the equation

hence ≥

[sleek saddle]

Pick a point and check

[rugged orchid]

that's why it's not shaded

[cunning kettle]

yes 0,0 didnt satisfy

[paper depot]

@cunning kettle they check the point (0,0) and find that it violates the inequality therefore the entire region it's in is not what we want

[sleek saddle]

Which region are you describing though

[rugged orchid]

so it's not shaded

so shade the other half

which is what they did

[sleek saddle]

If you are describing blue, pick a point from blue

[rugged orchid]

you dont need to do that

it's either above the line or below the line, pick any point and see if it's in the shaded region

if it's not then you shade the other half

[cunning kettle]

Yeah ik they didn’t shade it, we are trying to determine the inequality

[cunning kettle]

I’m confused why they did > and - sign in after y in the first line

[paper depot]

you should type >= if ≥ is unavailable

[cunning kettle]

Alr thanks

.close

[vocal sleet]

Channel closed

Closed by @cunning kettle

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[autumn chasm]

What's your doubt

[split flint]

How do you answer this?

OOPS

WRONG

[autumn chasm]

Also look at #help-30

Same question

[split flint]

Ben, Nico, Shaw, and five other classmates are sitting in a row. How many different way(s) is/are
there if no two of Ben, Nico, and Shaw sits next to each other?

[vocal sleet]

Channel closed

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

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[turbid moon]

The Mirror Room Problem (2D)
Imagine a rectangular room with dimensions M×N, where M and N are positive integers. This room is placed on a 2D coordinate system. We are interested in specific points within this room:

Points of Interest: These are points that lie on the vertices or edges of the rectangle.
Integer Coordinates: These points must also have non-negative integer coordinates (e.g., (0,0), (1,0), (0,1), etc., up to (M,N)).
The walls of this rectangle act like mirrors. We can place laser emitters at any of these points of interest.

How the Lasers Work:
When a laser is fired, its beam travels in a straight line.
The path of the laser beam must always have a slope of either 1 or -1.
When a beam hits a mirrored wall (an edge of the rectangle), it reflects, continuing to travel with a slope of 1 or -1.

The Core Problem:
What's the formula to find the minimum number of lasers needed to hit all the points of interest in an M×N rectangular room?

The image below is the 4x3 example. For this example, 2 laser emitters are required.

[hard atlas]

instead of just having one rectangle, imagine the rectangles tile the plane

and then instead of the laser mirroring it goes into the next rectangle

that should probably help

[turbid moon]

I just rephrased the problem

I just realized that the answer was technically infinite before

I'm mostly looking for an alternative solution to the one I have already found.

Perhaps I should head to help forum instead?

[vocal sleet]

@turbid moon Has your question been resolved?

[vocal sleet]

@turbid moon Has your question been resolved?

Channel closed

Closed by @turbid moon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vocal timber]

I have solved this question till here using the definition concept of Newton's formula. now I am not able to understand what to do after this

[vocal timber]

To find the required value

[pearl wadi]

could u send the original problem

so we know what the required value is

[vocal timber]

I particularly want to do this question by Newton's formula

[paper depot]

in the last line you should have T everywhere you put P

[vocal timber]

Yup I noticed it

[paper depot]

$T_{n+3}-2T_{n+2} - T_n=0$

[twin meteor]

Ann

[paper depot]

now you want to say something about T_11 - T_8

we are free to put any n we want

in this recurrence relation for the T's

[vocal timber]

Let n=8

[paper depot]

ok

so $T_{11}-2T_{10}-T_8=0$

[twin meteor]

Ann

[paper depot]

do you see how to continue now?

[vocal timber]

Is the answer 2?

[paper depot]

i don't know, is it?

show your work for how you got 2.

[vocal timber]

Option b

Transposition of terms

[pearl wadi]

yea should be 2

[paper depot]

work not shown, but the answer is indeed correct.

[vocal sleet]

@vocal timber Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[sullen condor]

.close

[vocal sleet]

Channel closed

Closed by @sullen condor

Use .reopen if this was a mistake.

[vocal timber]

T11-2T10 - T8 = 0
T11- T8/T10 = 2

[paper depot]

you could have (and should have) said "sorry, i'll be back soon/later/idk when"

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[vocal timber]

How to proceed after this using Newton's formula

[vocal timber]

How to approach

[plush condor]

Are you aware of the identity $a^n - b^n = (a - b)\left(\sum_{i = 0}^{n - 1} a^{i}\cdot b^{n - 1 - i} \right)$?