help-0

[regal surge]

.close

[lone heart]

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[nimble fern]

I am curious about what "x.vector b" means.

[alpine sable]

I need to find lambda somehow

[nimble fern]

hmmm

so, x is a scalar?

[alpine sable]

idk

its just given

[nimble fern]

or let's say, a constant?

[alpine sable]

idk

it just says the one line

this only

nothing else is specified

[nimble fern]

i see

that's so weird

[alpine sable]

eee

please answer according to that

💀

[nimble fern]

i bet it means this.
B is a point on a 2-D plane with coordinates (6,-8). lambda is a real number.
Let b be the positision vector of B, with |lambda•b|=30. Find lambda.

[alpine sable]

so what do I use here

like dot product is equal to cos theta

or what

[nimble fern]

i bet thats scalar product

[alpine sable]

hmm

dot product and scalar product are same things

?

[nimble fern]

nope

[alpine sable]

😭

[nimble fern]

e.g. $\vec{a}=x\vec{i}+y\vec{j}$ and $c\in\mathbb{R}$. Then $c\cdot\vec{a}=cx\vec{i}+cy\vec{j}$

[ocean seal]

Biscuity

[nimble fern]

that's for scalar product

[alpine sable]

yeah

alright

I need a method to find that answer

and after that I will learn vectors from basic level

any like suggestions?

[nimble fern]

so, what is lambda•c

[alpine sable]

idk 😭

[nimble fern]

in terms of i and j

[alpine sable]

I am 15 year old

what do you think what can be it

[nimble fern]

i gave you this example

[alpine sable]

yea I understood that

so you telling me

[nimble fern]

yea, it looks decent for 15 yo math

[alpine sable]

that lambda.b is x6i and -x8j

[nimble fern]

yep

[alpine sable]

what next

[nimble fern]

apple the |a| thing

[alpine sable]

what is apple?

[nimble fern]

like $\vec{a}=x\vec{i}+y\vec{j}$. Then $|\vec{a}|=\sqrt{x²+y²}$

[ocean seal]

Biscuity

[alpine sable]

yea I know that

I use that in physics 2d motion

oh oh

so

[nimble fern]

(x.b)^2=root( (6x)^2 + (-8x)^2) )

[alpine sable]

oh oh

it makes sense now

hold on

[nimble fern]

yes

[alpine sable]

owowowowoowo

[nimble fern]

correct

sorry, I don't really read books, I'd suggest Khan Academy

you can .close the channel when you're done!

[alpine sable]

sure

.close

[lone heart]

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[tribal furnace]

Using the letters from the word MANUSCRIPT, how many 4-letter arrangements (with
no repetition) consisting of 2 consonants and 2 vowels can be formed?

[tribal furnace]

For this question, I'm getting two different ways of doing it and don't understand which is right

So for my first way, I just did
3c2 * 7c2 *4!

Cuz you pick 2 vowels out of 3, 2 consonants out of 3 and then arrange them in 4 spaces

[foggy copper]

that seems sensible

[tribal furnace]

The other way is the longer way

I picked out out all the different vowels

We get

Ai, au and ui

[foggy copper]

but u can also have ia

and ua

and iu

[tribal furnace]

Yeah I was gonna get to that xD

[foggy copper]

sorry

[tribal furnace]

So I treated ai as unit

So we get ai * 7 * 6

So we do 7 * 6 * 3 cuz ai can be in any 3 spaces

And then multiply that by 2 cuz it can be ia as well

And multiply that by 3 cuz it can be ua, and iu

So I got 7 * 6 * 3 * 2 * 2

[foggy copper]

what aboyt splitting the ia

up

[tribal furnace]

No worries

[foggy copper]

e.g. amni

[tribal furnace]

Yep accounted for that case after that

So I realized that we had to split them up as well.

So I said we could have

a * 7 * u * 6
U * 7 * a * 6
7 * a * 6 * u
7 * u * 6 * a

So we do 7 * 6 * 4 * 3

3 cuz could be ai, au or ui

[tribal furnace]

And if we add this to this we should have our answer

I got 1260 for this way and about 1500 something for the previous one.

So idk which one is right or what I did wrong

[foggy copper]

i mean this second thing is so muddled the error could be anywhere

[tribal furnace]

Fair enough

But is the first way right? I couldn't visualize that way properly

And as I don't have answers, I can't even check

[foggy copper]

i'd say the first way is right ye

[tribal furnace]

Ty

.close

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[thorn ginkgo]

help

[thorn ginkgo]

needs to be written as a ratio

[foggy copper]

well we know that there are 30-9=21 non-carp fish

and if ⅓ of those are sticklebacks then you can find the # of those woth simple division

[lone heart]

@thorn ginkgo Has your question been resolved?

[lone heart]

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[strange flicker]

how does this indicate order-ness? can someone explain this better than the textbook?

"the Polish mathematician Kazimierz Kuratowski (1896–1980) published the following definition, which has since become standard. It says that an ordered pair is a set of the form
{{a}, {a, b}}.
This set has elements, {a} and {a, b}. If a != b, then the two sets are distinct and a is in both sets whereas b is not. This allows us to distinguish between a and b and say that a is the first element of the ordered pair and b is the second element of the pair. "

[strange flicker]

{{a}, {a,b}}...so this is a set containing two elements. the first element is a set containing a, second is a set containing a and b..how does that tell us a is the first element ?

[real gazelle]

The point of this construction is that {{a},{a,b}} is NOT the same as {{b},{b,a}}

[ocean hawk]

maybe this will help: https://math.stackexchange.com/a/1767649/993372

[real gazelle]

whereas {a,b} is the same as {b,a}

[strange flicker]

mm , ill give this a read.

[strange flicker]

i see...so . {{1}, {1,2}} != {{2}, {2,1}} , so in addition to your example... if its {{a}, {b}}, it also wouldnt work because {{1}, {2}} === {{2}, {1}}? But i will read the article now. tyty

[ocean hawk]

yes, even though {1, 2} = {2, 1}

[lone heart]

@strange flicker Has your question been resolved?

[strange flicker]

ok i see. so.. a set notation simply shows the unique identity (elements) in a container (set) . Theres nothing in it that tells us order. But mathematician like Kuratowski/Felix Hausdorff shows us that we can put these variable in such a way it shows unique-ness with respect to x and y relative to each other. The article goes on to say, it doesn't really give us on how to choose which is first or second. whether we read from left to right or right to left is up to anyone...in the end these numbers are just plotted on the x,y axis, wether you line up x first or y first. - its the same point on the cartesian graph.

i think i get it

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[gentle panther]

need help with finding the range

[gentle panther]

i tried asking chatgpt for questions and answered it with wolfram

im confused asf

chatgpt gave me this question

Let p(x) = x^2 + 3x − 2

[vale wigeon]

NEVER USE CHATGPT FOR MATH.

[gentle panther]

oh damn fr?

[vale wigeon]

yes

[gentle panther]

what should i use then?

to practice

[vale wigeon]

textbooks? idk

there is not a one-stop-shop resource

[gentle panther]

also i knew that the domain for this is all real numbers

idk how to get the range

[lone heart]

@gentle panther Has your question been resolved?

[lone heart]

@gentle panther Has your question been resolved?

[lone heart]

@gentle panther Has your question been resolved?

[lone heart]

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[tardy arrow]

How to graph

[flint belfry]

is

x^2 +xy +x -y-2 factorisable?

[vale wigeon]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[vale wigeon]

!original

[lone heart]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[flint belfry]

whatwhat

mine sent first?

race condition maybe mb

[vale wigeon]

the other person's name got on the channel

split second difference

[tardy arrow]

Sin(ωt)

[flint belfry]

yh

[tardy arrow]

If f=60 hz

ω=2pif

So its sin(120pi(t))

How would you calculate the intervals?

Like (pi/2)/120pi?

Or differently

.close

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[alpine sable]

Can someone please check my graph for this?

[foggy stirrup]

the problem asked you to use 4 values and youve used 5 but other than that its good

[balmy night]

I mean it looks fine to me

[alpine sable]

What about this one?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

@balmy night @foggy stirrup I’m really sorry for the ping but i would really appreciate it if you could help me with this. It’s totally alright if you don’t want to. Sorry again for the bother.

[balmy night]

It’s ok to ping me I don’t mind

I’m really sorry to tell you this, but temperature is always on the y axis. Your volume is on the y axis

Wait what r u measuring first

Hold on.

[alpine sable]

Temperature I think

[balmy night]

I mean is this chart related to something or are they just telling you to graph the points

[alpine sable]

They just telling to graph points

[balmy night]

But yea, your x axis is independent and your y value is depending on what the x axis is.

[alpine sable]

They also had another graph in the question prior to this, that they asked questions about, which also didn’t mention anything but assumed that temperature was independent

[balmy night]

Oooh wait don’t listen to me

Ok yea I had to make sure

You’re good

It’s temperature and time

[alpine sable]

One more thing I wanted to ask

Do you think i should have have gone with 258 K instead of 258.15 K and such?

I mean would that be an issue as class interval is like 20 K

[balmy night]

I honestly don’t know

It depends on the teacher tbh. Saying 258.15 I don’t think will hurt your grade unless they’re asking you to round down or up

Especially since you drew the graph on paper and the dots are in between the right intervals

[alpine sable]

But if I change that to 258, would that be a better bet?

Or would she point out that it’s not precise enough

[balmy night]

That really depends on the teacher. I never had a teacher that punished me for being more precise unless it said to round up or down.

I would keep it the same

[alpine sable]

Okay can you please check one more?

I’ll post it here in case you can

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

I got it

Thank you so so much animelover

I really appreciate it

Have a good one mate

.close

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[neon vigil]

I am in AP Pre-Calculus and am struggling to answer this question. What I found was (-inf, -3),(0, 5). Can someone help me solve this and properly format my answer?

[neon vigil]

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[neon vigil]

my answer is correct, however deltamath will not accept my answer

.close

[lone heart]

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[lone heart]

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[mystic nebula]

How do I solve this without a calculator

[plucky sluice]

More context

What is the cubing function?

$x^3$?

[ocean seal]

Xenophon

[lone heart]

@mystic nebula Has your question been resolved?

[mystic nebula]

Thats all the context they give me to work with

[plucky sluice]

Ok, assuming that the function is x cubed, what do you think the answer is?

[mystic nebula]

no idea.

I know what it looks like on a graph but I dont know why

Ik the origin is 0,0

same goes for any other function

like x^2 or cube root

[lone heart]

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[mystic nebula]

.reopen

[lone heart]

✅

[mystic nebula]

<@&286206848099549185>

[plucky sluice]

Try graphing x^3 on Wolfram alpha

[mystic nebula]

Yes I'm not allowed to use a calculator for this section on a test

I understand how the graph looks

but how do I apply this to other functions?

[plucky sluice]

Are you learning calculus or algebra?

[mystic nebula]

Pre calc algebra

[plucky sluice]

Basically, concavity depends on the rate of change of the slope of the function

For a cubic, that changes at 0 because (-1)^3 is -1

It's an odd function

Not sure how much deeper I can go with just algebra

[mystic nebula]

guess ill just blame the curriculum

[plucky sluice]

I think you're just supposed to be familiar with the shape

[mystic nebula]

wish it went deeper with explaining problems :/

[plucky sluice]

All odd powered functions will be similar, but you really need calculus for this imo

[mystic nebula]

yea i can memorize the shapes but what if it wants me to apply something to it

[alpine sable]

there are end behaviors associated with polynomial functions

also roots tell you about the roots and turning points where u need to graph

but yes, accurate curve sketching requires calculus

[lone heart]

@mystic nebula Has your question been resolved?

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[lapis crow]

need help

[slate vortex]

I'm guessing the types are like
Linear, quadratic, exponential?

[lapis crow]

maybe

i didnt know what they meanrt

[slate vortex]

oh

[lapis crow]

how would ik if it is linear

[balmy night]

It’s linear if the equation isn’t raised to a power, rooted, log, etc. a constant line if you will

[lapis crow]

i see

so 4 is linear

[balmy night]

Line isn’t the best terminology since they’re all lines lol

Correct

This is a strange question because the definition of each graph for the answer IS the explanation

[lone heart]

@lapis crow Has your question been resolved?

[lone heart]

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[fringe lynx]

need a little help with the range on this one. Would it be just , -1, 2, and, 4? or something else. Also wondering if I did the domain part right

[delicate sand]

i dont think its a function

but

it would be written like {x,y,z}

[ocean hawk]

Why isn't it?

[delicate sand]

2 y value

[ocean hawk]

FYI you can combine intervals for the domain

[delicate sand]

ah ok

[ocean hawk]

Where?

[delicate sand]

2 x value i mean

At -2

[ocean hawk]

No

One is an open circle and the other isn't

[delicate sand]

im not sure what thise circle are

[ocean hawk]

Then don't answer the question...

[delicate sand]

mb

[fringe lynx]

lol

[magic cipher]

Cnan you guys help me real quick?

[fringe lynx]

wait for someone to go to your help channel

[magic cipher]

Alright ty

[fringe lynx]

@ocean hawk you there?

[ocean hawk]

Yes. Combine intervals for the domain

The range would be -1, 2, 4

[fringe lynx]

ok thanks thats what i was thinking

.close

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[wide elbow]

hey

[wide elbow]

so i need help with these and my teacher is refusing to help me for whatever reason

she doesnt help us when we ask and when we do alto of the time she just says "go watch the recording" and then doesnt post it

[maiden glen]

you just need to apply these rules

so for angle 1, lines l and m are parallel, so it has the same measure as the 22 degree angle above it

the rest are similar

for the second picture, use the rules to form equations in x and y, then just solve for x or y

[wide elbow]

wait so

its 22 because theyre parallel?

await no

lemme rephrasde

theyre the same distance away from eachother

22 degrees

and since its the same for the last one

it makes it 22

[maiden glen]

angle 1 is corresponding to the 22 degree angle

so they are equal

[wide elbow]

ok

so then angle 1,2,3 are 22?

therefor 22 being the answer?

the messaure is 22 and the relationship is parallel

[maiden glen]

use the names here

angle 1 corresponds to the 22 degree angle

[wide elbow]

so correspodinging?

[maiden glen]

angle 2 is alternate to angle 1

[wide elbow]

alright so should i put that as awnser

[maiden glen]

yes, that's what the question is asking for

[wide elbow]

alr ty ty

and what now for the 2nd one

[maiden glen]

the first set are interior angles so they add up to 180

form an equation then solve for x

similarly, the second pair of angles are alternate, so they are equal

again, form an equation then solve for y

[wide elbow]

im very lost

sorry

[maiden glen]

these are interior angles

they add up to 180

[wide elbow]

ok

[maiden glen]

try forming an equation with this information

[wide elbow]

(6x-32)(4x+2)

correct?

[maiden glen]

no

and an equation needs an equals sign in it

[wide elbow]

(6x-32) = (4x+2)

?

[maiden glen]

these angles add up to 180 degrees

so add them

[wide elbow]

yes

[maiden glen]

and set them equal to 180

[wide elbow]

the math is not mathing

how would it add them up

like

;-;

im missing something

[maiden glen]

you just add them:
(6x-32) + (4x+2) = 180

[wide elbow]

ok

what from there

[maiden glen]

solve the equation for x

[wide elbow]

21?

s the asnwer rifght?

[maiden glen]

yes

[wide elbow]

and N is

8.3

[fallen wigeon]

If my teacher gave me this I’d genuinely start tweaking.

You need to remember that if the degree is given, it’s usually = to the other side of the equation. I’m doing similar work, but for me it’s usually

x=y°

(Correct me if I’m wrong)

Hopefully that helps with the rest :)

[maiden glen]

show your working

[wide elbow]

yeah it doesnt heelp i have 16 more assignments and and a project i have to get done by TONIGHT

[maiden glen]

I'm guessing you added them together to get 180

[fallen wigeon]

Oh I just read the rules sorry lol

[wide elbow]

bngl i just said a random number

[maiden glen]

right

[wide elbow]

yes

[maiden glen]

they're alternate angles

so they are equal

they're not interior, so they don't add up to 180

you should be setting the angles equal for your equation

[wide elbow]

could you ecplain easier lol

if possible

[maiden glen]

these are alternate angles

as in this case

so they are equal

[wide elbow]

ok

so i just say theyre eqaul?

[maiden glen]

form an equation

[wide elbow]

10y+4)=(11y)

[maiden glen]

yes

[wide elbow]

or

[maiden glen]

now solve for y

[wide elbow]

oh

is it 4?

[maiden glen]

yes

[lone heart]

@wide elbow Has your question been resolved?

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[ocean seal]

Jeremy

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[waxen turtle]

Don't know where to start😭

[white crater]

try putting it into an equation

[waxen turtle]

How

[white crater]

percentage decrease formula

[waxen turtle]

Idk that

Oh

[white crater]

oh

wait

here

[waxen turtle]

Ty

.close

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[molten pivot]

Given a non-empty totally ordered set R with the four properties

R does not have a least nor a greatest element;
the order on R is dense (between any two distinct elements there is another);
the order on R is complete, in the sense that every non-empty bounded subset has a supremum and an infimum; and
every collection of mutually disjoint non-empty open intervals in R is countable (this is the countable chain condition for the order topology of R),

is R necessarily order-isomorphic to the real line R?

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[alpine sable]

How to do this question with using arithmetic sequences formulae?

[alpine sable]

How to do this question with using arithmetic sequences formulae?

Using this formula

[late agate]

figure out what you have

shuffle all the extra fluff from this question and find out the "first term" and such

[alpine sable]

first term is 1967

right?

[late agate]

yeh

wait no

first term is within the context of what they want you to figure out

[alpine sable]

200

km

?

[late agate]

yea

[alpine sable]

the common distance is 2

[late agate]

I don't like this question tbh, its written like an 14th century math question

[late agate]

yes

you got 2 of the 3 things you need

[alpine sable]

Okay

[late agate]

last one comon

[alpine sable]

but what is the general term

i think it is 2020

[late agate]

the general term is literally the equation

n is the time

or number of terms

[alpine sable]

is 2020?

[lone heart]

@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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[wild garden]

question is if a,b is on f(x) what would it become after these transformations (ignore the work on the paper). I think I'm doing the order wrong? first I did vertical and hor shift +reflect , then I did reciprocal, then I did another shift, then I did inverse. I tried inverse first and it didn't work either? (checked on desmos)

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[alpine sable]

im stupid i dont even know how to multiply

[alpine sable]

the right symbol is pi

btw

would be that
135 right?

no

how not?

two things

one, pi is irrational, meaning you cannot compute the expression and get a precise number as a result

So, you have to approximate pi in some way if you want to get something

3.14 for example

oh okay you are not at the level of this conversation, ill wait for somone else 🙂

probaly frownyfog know

[prime badge]

two, you don't want to multiply it, it's good enough

[alpine sable]

ohh okay but if i just put 135 is right anyways right

(the expression you sent above would be the only simplified version you can have, any approximations of pi would just be approximations and not a true equality)

if that-s the final ans for example

[prime badge]

you just stick pi with 3, so 3pi/4

[alpine sable]

pi is equivalent to 180

[alpine sable]

Why so dismissive? Are you here to troll or actually get help?

You've done this with other helpers in your previous channel

[alpine sable]

because im talking about radians

in radians pi is 180

not "3.14"

[void nymph]

jesus

mate

no

in radians pi is pi

in degrees pi is 180

[alpine sable]

pi is not equal to 180 and you are confusing yourself. Plus you have provided 0 context to allude this to begin related to trigonometry or angles

[alpine sable]

is in degree pi is 180?

aight

you right

[void nymph]

when you're doing angles yes.

otherwise pi is the ratio of the circumference to the diameter

and that's all it is

[serene flume]

3/4 x pi = 3pi/4 or 3/4 x 22/7 = 33/14

if u are working on degree to radian its

radian = degree x (pi/180)
degree = radian x (180/pi)

[pale kestrel]

<@&268886789983436800> this user has been pretty rude a few times from what I've seen so far.

[alpine sable]

haha what are you talking about

[alpine sable]

ohh

let me see again

[serene flume]

wait wha-

[pale kestrel]

#help-41 message
#help-41 message
#help-41 message

[serene flume]

EXPOSED

[alpine sable]

are you harassing me?

[pale kestrel]

I don't want to make a big deal out of this, but I don't think that hostile attitude towards people trying to help you is appreciated.

[serene flume]

btw if u wanna report im sure there will be a channel for that

[pale kestrel]

That's why I pinged moderators.

[serene flume]

it will be easier for moderator to read everything because there will be conversation in between here

ok so is it clear? @alpine sable the pi thing

[alpine sable]

there is a calculator bot or something here_

[serene flume]

what are u trying to ask actually

even im confused

[alpine sable]

You should start behaving better, if you're not going to help then it's better not to do anything, I haven't done anything to you, besides the pi boy was with the idea that pi was 3.14 and when he found out that pi was worth 180 he stopped writing

[alpine sable]

in my calculator

i put

arcocos 1/-sqrt(2)

[void nymph]

the usage of the word worth lmao

[alpine sable]

and the answer is 3/4 * pi

or 3 * pi / 4

XD

let me take a screenshot

[serene flume]

i have no idea what in tarnation are u talking about

[void nymph]

my man is confused as all

'tarnation'

[serene flume]

use tarnation instad of hell 👍

saves u lots of trouble

[void nymph]

good advice

[serene flume]

cuz those reporters dont understand it

[alpine sable]

sorry

well that's the answer in radians

[serene flume]

not talking about u

[alpine sable]

3 * pi / 4

[alpine sable]

never heard that word before

[void nymph]

yeah

[serene flume]

hell = tarnation

[serene flume]

so what is ur question

[void nymph]

,wolf arccos(-1/sqrt(2))

[serene flume]

what is the thing that u doesnt understand

[void nymph]

oh is wolfram not here or what

oh there we go

sigh

[ocean seal]

Results provided by WolframAlpha

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

Requested by percykel

[alpine sable]

well my answer was 135 and that was the answer i wrote, but then i saw you said the answer was 33/14 and its confused me a lot

[void nymph]

yeah it is 135

[alpine sable]

i dont know english sorry:(

probably that's why i dont get you sometimes

lol

well that's it percy, see you man, probably ill come back in 10 minutes

.close

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[cinder sundial]

Quantum dots are extremely tiny - just a few millionths of a millimetre across.

[cinder sundial]

What is few millionths of a millimetre

What if I want to express it using mathematical notations

[zealous lichen]

I think you mean scientific notation

[cinder sundial]

Yes

[next brook]

A millionth of a millimeter is a nanometer, or 10^-9 m.

[serene flume]

what is a millionth tho

1 000 000?

but in reverse

[next brook]

1 divided by 1000000.

[serene flume]

i see thanks

[next brook]

Like a "third" is 1 divided by 3.

[serene flume]

thanks

[vale wigeon]

more generally "an N'th" means 1/N, for N ≥ 3.

[cinder sundial]

That’s quite useful, thank you

I think the question is solved

.close

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[keen violet]

Hi

[keen violet]

[
\sum_{k=1}^n k^2 = \f{n(n+1)(2n+1)}6
]

[ocean seal]

ProPlayer

\[
\sum_{k=1}^n k^2 = \f{n(n+1)(2n+1)}6
\]
```Compilation error:```! Undefined control sequence.
l.58 \sum_{k=1}^n k^2 = \f
                          {n(n+1)(2n+1)}6
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]```

[pale kestrel]

So the usual proof is via induction

once uve fixed

[keen violet]

Can't I just split in 2 n's and put formula for each individual n

[vale wigeon]

\frac btw

[keen violet]

I tried it comes up with the same formula as the one in n³ rather than n²

[keen violet]

Ik mb mb

[keen violet]

For n(n+1)/2 individually for each n and multiply

[vale wigeon]

??

(a+b)^2 isn't the same as a^2 + b^2 tho.

[lone heart]

@keen violet Has your question been resolved?

[keen violet]

N² is n times n right

So individually put the formula and do? Or why not

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[past knot]

I dont know how to do point b

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[past knot]

<@&286206848099549185>

[past knot]

<@&286206848099549185>

<@&286206848099549185>

[past knot]

<@&286206848099549185>

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@past knot Has your question been resolved?

[past knot]

<@&286206848099549185>

[past knot]

@pallid scarab

<@&286206848099549185>

.close

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[alpine sable]

factorize

ab + ac = 0
a(b + c) = 0

1. a = 0

2. b + c = 0

?

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[sinful anvil]

guys does this mean i have to do completing the square

[nimble fern]

do you know what is "completing square"?

[nimble fern]

here's a site explaining what is completing square

https://www.mathsisfun.com/algebra/completing-square.html

[tardy stag]

yes, is the answer to your question

[sinful anvil]

thank you

!close

.close

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@mint patio Has your question been resolved?

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@mint patio Has your question been resolved?

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[alpine sable]

.close

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[short sedge]

You have two coins on your pocket. One of them is a fair coin. The other is a biased coin (30% chance of heads when tossed). 

The coins look and feel the same, and you can no longer tell which is which. If “tails” is the actual outcome of the toss, what is the probability that you tossed the fair coin?```

so this uses bayes. 

P(fair coin) = 1/2 = P(biased coin)
P(T) = 1/2 (this part im not sure about)

then by bayes, the P(fair coin | T) = 1/2. but this is wrong, cuz it should be 5/12

[vale wigeon]

nope, you don't know that P(T) = 1/2

you know P(T | fair) = 0.5

but P(T | biased) = 0.7

[short sedge]

oh i see

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[undone plover]

hello i was wondering if i was doing this right?

[tacit arch]

Yes

[undone plover]

cool thanks

.close

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[runic hull]

do you know how to find the equation of a straight line given two points on that line?

well dy/dx will be the slope where dy is the difference between the y values and dx is the difference between the x values

you have two points on a straight line in this question. you can use that to find the equation of that line

not sure where you got that from ...

What are the two points given in the question on the straight line you want to find the equation of?

oh I see you found the slope of line segment connecting (-5,6) to (-3,-2)

okay let's forget about the equations of the lines for now

do you see how to simplify ff(-3)?

you do have some information about f, though

for instance, what is f(-3)?

f(-3) will be a number which is the value of f when x=-3. you can find this by looking at the graph

yes

so can you simplify ff(-3) to be f(?)

I'm asking what ? should be here

ff means "f composed with f", so ff(x)=f(f(x))

i.e you take x, find out what f(x) is, and then plug f(x) back into f

yes

that is true, the last thing you wrote

Using the definition of ff(x):

ff(-3)=f(f(-3))=f(?)

which bit don't you see?

It's not a trick question: there's only one fact you can use at this stage and that's f(-3)=-2

no, unfortunately

okay, so if you have f(-3)=-2

that means you can replace f(-3) with -2

our goal right now is just to simplify the composition ff(-3) to be f(?)

you can plug whatever number you want into the function f, even a number you get by applying f to another number

yes!!

so now the problem is just to find f(-2)

no it's because f(-3)=-2 so we can replace f(-3) with -2

so f(f(-3))=f(-2) simply because f(-3) and -2 are the same number

it's okay; maths is like that. it's impossible until it's obvious

so the problem has been reduced to find f(-2). there are two line segments; which one is relevant in this case?

i.e which line segment should we look at when x=-2?

why that one?

that's not really relevant ... both line segments have x values in the negatives

the point is: the line segment from (-3,-2) to (7,18) is relevant when x takes a value between -3 and 7
the line segement from (-5,6) to (-3,-2) is relevant when x takes a value between -5 and -3

do you understand this by looking at the graph?

you can also think of it this way: if you were to draw a vertical line up from x=-2 which line segment will you hit?

yes, it's the one form (-3,-2) to (7,18) because -2 is in the range -3 to 7

so now all you need to do is find the equation of the line connecting those two points

it's easy to check that y=2x+4 is the correct equation for that line, but you should be able to find it just by using the two points

yes because f(x)=2x+4 for x in the range -3 to 7

so f(-2)=2*(-2)+4

no problem, hope the rest of the question goes well

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[alpine sable]

the only answer i can think of is x-2

[clear moth]

u have to divide x-2 into the polynomial

[alpine sable]

ik this equates to 0

[clear moth]

no no

don’t sub in 2. i meant using long division, divide x-2 into the polynomial

[alpine sable]

so this divided by all the answer choices

and see what gives me 0?

[clear moth]

uhh one sec

you know how x=2 give u zero?

[alpine sable]

yes

[clear moth]

and if u bring the 2 over u get x-2? and that’s why it’s a factor?

[alpine sable]

because x=2 so x-2=0

[clear moth]

try the same thing the opposite way for the other answers. i.e for x+4 try sub in x=-4

[clear moth]

yh

[alpine sable]

why neg

[clear moth]

(x+4) -> x+4=0 -> x=-4

[hollow lark]

or you could also try and think of a quadratic that you multiply (x-2) to get the cubic in the question and then factorise that

[alpine sable]

idk what that means

[alpine sable]

so should i just flip each sign

[clear moth]

yeh sub each in

[alpine sable]

okay im doing this now

[clear moth]

it’ll take a while but if u don’t know how to do what skelaboi said or are not able to long divide polynomials then you have to do this way

[alpine sable]

(x+4) gives me -48 so thats not it

[clear moth]

correct

[alpine sable]

(x-1) gave me 12

[clear moth]

ok

we need zero

[alpine sable]

(x+6) gave me -240

-3 gave me -6

next is 72

[clear moth]

ok

[alpine sable]

okay

(x-4) gave me 0

[clear moth]

nice

[alpine sable]

so did (x-2)

and (x+3)

[clear moth]

nice

[alpine sable]

okay

[clear moth]

there’s ur three answers

[alpine sable]

those are my ansswers

perfect

thank you so much

.close

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[dim kettle]

Hi

[dim kettle]

Why is it including the solutions with y=0

[clear moth]

tbh man idk bc it’s not in english

[dim kettle]

It just takes the 2nd line and says

If y=0 then x=

Or if x=1/2 then y=

[dim kettle]

But this shouldnt be

Y should be != 0

4 solutins

[runic hull]

if you're solving 2xy-y=0 then:

x=1/2 and y arbitratry

and

y=0 and x arbitrary

are both two sets of solutions

[dim kettle]

So the system has 2 set of solutions?

[runic hull]

the single equation 2xy-y=0 has two infinite sets of solutions

the system of equations will have less solutions

[dim kettle]

What are the system solitions

[runic hull]

well, consider the two cases:

Case 1, x=1/2:

you can plug this back into the first equation and solve for y

Case 2, y=0:

same thing

except solving for x

[dim kettle]

The solutions are diffeerent with the 2 cases

[runic hull]

what do you mean by that?

[dim kettle]

If I choose case1 i get different results than case2

No?

[runic hull]

you probably will yes

[dim kettle]

But usually in a system of 2 variables and 2 equations i cam get a real value of the 2 variables that doesnt change

Why in this case it changes

[runic hull]

It's not that it changes, it's just that there are multiple solutions

here's a silly example

y=x^2-5x
y=-6

if you solve this system you you will get two pairs of solutions (x,y)=(2,-6) and (x,y)=(3,-6)

you can see why if you draw the graphs y=-6 and y=x^2-5x. these intersect in two places

similarly, if you draw the graphs of the equations you have, you'll see they intersect in multiple places (i haven't solved it, I don't know how many)

in other words, there are multiple pairs (x,y) such that those equations are true. this is not such a weird thing, you just happen to mainly have experience with equations where there is a unique solution

[dim kettle]

How do I know the amount of pair solutions

[runic hull]

for my example?

[dim kettle]

Always

Hkw do I tell ok now I find the 2 pair of solutiond

[runic hull]

you just have to actually solve it and see how many pairs you get

[dim kettle]

What if I have 3 lines

[runic hull]

i.e

y=x^2-5x
y=-6

substitute second into the first

-6=x^2-5x
x^2-5x+6=0
(x-3)(x-2)=0

exactly two possibilities: x=3 and x=2

[dim kettle]

I can have a lot of options

[runic hull]

okay so straight lines you'll have 0, 1, or infinitely many solutions. try to visualise the number of ways a pair of straight lines can intersect: either they're the same line, they're parallel and don't intersect, or they intersect at exactly one point

[dim kettle]

Ok I understand this but here u solved normally

[runic hull]

we're solving "normally" in your case too

maybe this is the thing that is confusing:

if 2xy-y=0 then y(2x-1)=0

then either y=0 or x=1/2. But at least one of these has to be true

do you see why?

[dim kettle]

Both must be true?

Wait i write

[runic hull]

at least one

not both

[dim kettle]

If I just put

Y=0 in the first line

Can I be able to find all the solutions

[runic hull]

that won't be all of the solutions, but you will find some of them

[dim kettle]

So in any system with x variables

I have to take a variable and put it= something

And solve the rest

And do this for each variable over again

[runic hull]

well ... you need to use the information from one equation in another

in this case we happen to see that the second equation 2xy-y is solve for constants y=0 or x=1/2

but if this were x-y=0 instead, all we could do is subsitute y=x into the other equation

but the idea is mostly right: you want to eliminate variables one by one

[dim kettle]

But what if the lines are long and each time u do this u get with x=eddbes/ehej

How do u tell how many options u have

I dont understand

You just keep going until one line gives you multiple real solutions for 2 variables or more and use that different potential results?

[runic hull]

it's different for every system. there's no more exact set of rules to solve every non-linear system

[dim kettle]

This?

[runic hull]

you can keep going and hopefully you end up with one line that's just in terms of one variable and you can solve that

[dim kettle]

Ok

So if one line gives multiple options thats when I know

[lone heart]

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[iron gorge]

im totally stuck right now

can i somehow bound |s|?

[mortal trellis]

s is in the interval [0,t]

tho the |s| isnt the important part to get rid of here

[iron gorge]

yeah true, so i can bound the s by t, and then can i somehow bound the remaining integral by max s in [0,1] |f(s)-g(s)|?

or is the t in the upper bound of the integral causing problems

[mortal trellis]

no you can bound that by 1

[iron gorge]

s?

[mortal trellis]

the t

in the upper bound of the integral

you actually dont want to bound s. you will see why

[iron gorge]

oh okay, so if i bound the t by 1, then i can bound the whole thing by max s in [0,1] |sf(s)-sg(s)|

?

[mortal trellis]

yes but not exactly what you want

it was good factoring the s out

you want to get d(f,g) somewhere

[iron gorge]

max s in [0,1] |f(s)-g(s)| would give me the d(f,g), but i dont see what to do with the s

its max would give me 1, thus not a contraction

[mortal trellis]

d(f,g) is a number

so you can move it out of the integral

what are you left with

[iron gorge]

can i move |f(s)-g(s)| outside even tho we are integrating wrt s?

[mortal trellis]

well that is gone now

you bounded it by d(f,g)

[iron gorge]

ahh i see

so like this

and then i end up with 1/2d(f,g)

[mortal trellis]

yes

[iron gorge]

amazing, thanks!

[mortal trellis]

you're welcome

[lone heart]

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[lone heart]

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[native temple]

https://www.youtube.com/watch?v=4hG3yQBVFwg&t=546s This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1". Converts to a regular inequality and then does this } -1 + 7 < x -1 + 7 < 1 + 7 \text{ Next he does something vert very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$

[lone heart]

Please don't occupy multiple help channels.

[ocean seal]

Nerdy_Coder

https://www.youtube.com/watch?v=4hG3yQBVFwg&t=546s This video is proving this limit  $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1". Converts to a regular inequality and then does this } -1 + 7 < x -1 + 7 < 1 + 7 \text{ Next he does something vert very confusing. } \newline 6 < x + 6 < 8 \text{ now }  \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
```Compilation error:```! Misplaced alignment tab character &.
l.57 https://www.youtube.com/watch?v=4hG3yQBVFwg&
                                                 t=546s This video is provin...
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.```

[spare fern]

Hey guys could someone help me out with this?

[native temple]

Lex you don't need help like your fridman just practice gitting good again

You got a phd

[spare fern]

Alright :/

$$x^{2}\le36+y^{2}$$

[ocean seal]

Lex1729

[spare fern]

this is my question anyway

[native temple]

so this is okay what are you finding?

[spare fern]

I'm just not sure if my answer is correct

I'm supposed to graph the conic section

[native temple]

x^2 - y^2

[wild umbra]

lex this channel is already occupied, and also nerdy coder there is no need to open another chaneel if you already have one #help-39

[native temple]

wait i'm confused

I had one

oh let me get outta here

.close

[lone heart]

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[wild umbra]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[native temple]

.close

.lose

.close

.close

.close

/close

[wild umbra]

chill bro

its already closeed

[wild umbra]

[lone heart]

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[vapid steppe]

why is the answer not T3 for part b

[wary stream]

Why would it?

[vapid steppe]

since its vertical

[wary stream]

The mass is hanging from T3

And T1 is holding it up

[alpine sable]

It does have an upward foce component

[vapid steppe]

isnt T3 holding it up

[alpine sable]

Equal and opposite forces

[wary stream]

If T1 wasn't there, then it falls

[vapid steppe]

so its always the one connected to teh roof

[alpine sable]

if T3 wasn't there then it falls as well

[wary stream]

The mass hanging off of T3

The FBD is drawn at the point where all the tensions meet

[lone heart]

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[alpine sable]

can someone help me with this one

please?

n is natural

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[light bridge]

in a set notation, does ':' mean the same as s.t.?

[light bridge]

if so why isnt b) equivalent to the definition

Here are the answers

[lone heart]

@light bridge Has your question been resolved?

[harsh swallow]

No i don't think so

: or | means a condition

for example in (f)

it's saying

A is the set of all numbers y/y+1 where the condition is that y is in N

While if you were to write (f) using s.t.

it would be different

[light bridge]

lol

[harsh swallow]

wrong choice of words

they should've said

"where"

Such that implies something

Choose numbers such that condition applies

just saying

these numbers

and then such that

doesn't make much sense at least not to me

as in

1, 2, 3 such that condition

[light bridge]

can you elaborate i still dont understand

[harsh swallow]

'such that' is less clear to me than if they had used 'where'

for example

(f)

A is the set of all numbers y/y+1 where y is in N

this is what f is with the : or |

but with such that

A is the set of all numbers y/y+1 such that y is in N

but y is in N is not dependent on y/y+1

it's a condition you apply to y/y+1

[light bridge]

but i dont see how the sets are different with b) and the definition

because in both case the values in the set would be the same

no matter if they are a condiftion or related

[light bridge]

oh is it because in b), it is y that where looking for

and in the original definition, x is what were looking for

[lone heart]

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[azure mesa]

Could I get some help with this? I'm really stuck :/
The question is :

Use the comparison theorem to determine whether the integral is convergent or divergent

[azure mesa]

I'm stuck in where to go after the initial integration by parts

<@&286206848099549185>

[lone heart]

@azure mesa Has your question been resolved?

[azure mesa]

<@&286206848099549185>

[azure mesa]

Please? 😭

[azure mesa]

<@&286206848099549185> one more try, I'd really appreciate help

[lone heart]

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[lone heart]

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[safe tartan]

For a set of parametric equations like x=3t and y=t^2-3 and -4<=t<=4, can the domain for the graph be subbed into the domain for t?

[safe tartan]

For example -12<=3t<=12

[lone heart]

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[lone heart]

@safe tartan Has your question been resolved?

[lone heart]

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[trim dome]

need help finding (d)

What does "Use function notation to write g in terms of f." mean

[foggy current]

Example: the parent function of g(x)=(x-1)^3 is f(x)=x^3, and using function notation to write g in terms of f we have g(x)=f(x-1)

[trim dome]

how would that apply to this problem

would it be g(x) = f(x-2)

@foggy current

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[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

no

<@&286206848099549185>

.close

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[proven tendon]

Is my solution for showing convergence for this series using comparison test valid?

[tacit arch]

what's in the numerator of the original series

[proven tendon]

2n + 3