help-0

[hoary sigil]

Heyy, 2 problems here

1. Is completing the square the right way to find coordinates of a min / max points on a cubic graph?
2. if so, please help me to complete the square, im stuck : /
   tysm in advance

[flint pecan]

first of all you did not complete the square properly

[hoary sigil]

thats why im here :0

[flint pecan]

why did you subtract 5?

that doesn't make the constant equal to 5

[hoary sigil]

from what i understand i need to divide 3 by 2, and put it in brackets, and make everything equal to -5?

[wet temple]

hey can u pls help me with this question. For the following weighted undirected graph, briefly trace the steps taken by the following algorithms in determining the minimum spanning tree: (a) Prim's Algorithm (b) Kruskal's Algorithm

[mystic parrot]

though im studying in the second grade in high school, idk that at all, sorry

[crystal tiger]

Read what the algorithm does, it’s really easy

And stop posting this in random channels

[wet temple]

pls send me the steps it would be great help

[lone heart]

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[native flicker]

Need help with part c) of this question from Lebl intro to real analysis 2.

[native flicker]

I have chosen a derivative of [2,2,4,-4] and this gives me $\frac{\sqrt{(2h_1^4+12h_1^2h_2^2+2h_2^4)}}{\sqrt{h_1^2+h_2^2}}$ but im not sure how to show this approaches 0 or if it even really does, in which case I might have the wrong derivative. Is there a trick or something to this I am not seeing?

[ocean seal]

JxFriz

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[frigid zinc]

why ans is D

[marsh rapids]

do you have any information about the offset that is supposed to exist between the 2 ?
Otherwise I'm not sure how you could say whether it's B or D

[echo forum]

lol

u can trace it easily w online tool

also should be trivial imo

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[idle raven]

can I get an explanation

[idle raven]

am I just counting all the 70-74?

then if i get 4 I divided it by 100?

[tacit arch]

,tex .original

[ocean seal]

riemann

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[warm silo]

Stuck on this prob

My ans is coming out to be 2/5

But it is given 4/5

[vale wigeon]

how are you getting 2/5?

[warm silo]

I made cases

[vale wigeon]

show your work. maybe you miscounted

or maybe your case breakdown was faulty

we cannot tell

[pale vigil]

How do open a question chat?

[warm silo]

My bad

I got it now

I hàd to multiply 2 in each case

Since there is no replacement

.close

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[oak bridge]

Hi. Im studying binary operations. I need to find out if said operations is operation, if it is is commutative, associative, if it has neutral element, and find inverse element
Very simple example: on R

[oak bridge]

Okay, how would I go about finding if it is commutative.
x * y = x
and also
y * x = x
?

[alpine sable]

This is wrong

A binary operation is commutative if x o y = y o x

Clearly here we have a binary operation which discards the second element

So it cannot be commutative

Because y o x = y

[oak bridge]

but why y o x = y ? and not x ?

[mortal trellis]

the operation by definition just gives back the first element

the names of the elements dont matter

[oak bridge]

I understand

Do you know where I could exercise on similar examples like one above ? with explained answers ?

[alpine sable]

Any theoretical cs book or abstract algebra book

[idle raven]

@tacit archsorry for keeping it open i went afk my bad..

[oak bridge]

Thank you. Could weyou maybe finish my example ? for the assoc, neutral, and inverse ?

[mortal trellis]

we are not doing work for you

[oak bridge]

Okay

[peak bough]

Associative means (x * y) * z = x * (y * z) for all x, y, z ∈ R. Does your example satisfy this property?

[oak bridge]

no clue

[peak bough]

What do you get from evaluating (x * y) * z?

[oak bridge]

xyz

[peak bough]

What?

[peak bough]

Use the information given here in the picture

[oak bridge]

then x o z

[peak bough]

And what does that give you, when you evaluate that?

[oak bridge]

hmm, so from the picture I know it always returns the first value ? so it would be x ?

[peak bough]

Yes

[peak bough]

That is the left hand side of this you have now evaluated

Now we need to check the right hand side, to see if the property is met

[oak bridge]

So here x * (y * z) I need to first evaluate (y * z).
Do I do get y here ? because it returns first element ?

[peak bough]

Yes, exactly

[oak bridge]

and x * y is again x

[peak bough]

Yep

[oak bridge]

I understand, thank you.

[peak bough]

So it is associative

Now to see if there is a neutral element. An element (often denoted "e") is a neutral element on * over R if for all x ∈ R, x * e = x = e * x

A way to think of this, is that e is a neutral element if it "does nothing" to x no matter which side you "apply" it on

(As a side-note, you can also talk about a one-sided neutral element, that only has to either hold the property x * e = x or e * x = x, but when we just talk about a neutral element in general, we usually mean both a right-side and left-side neutral element)

[lone heart]

@oak bridge Has your question been resolved?

[oak bridge]

In example likex°y = x+y-5
if I want to find neutral element,
I would replace y for e, like so: x+e-5 = x ?
But in case ( x ° y = x )
I only have x. How can I incomporate e ?

[oak bridge]

so its like x ° e = x but we know we always get just x so e can be any number

so if it can be any number, we cant define e ?

and thus, cant confirm existence of inverse elements ?

[peak bough]

This is correct yes. Another property of a neutral element is that it's unique. So this property (that x * e = x for any chosen e) is a way og disproving that a neutral element exists

[peak bough]

And yes, you can not define an inverse element if there isn't a neutral element, since an inverse element (-x) to x has to satisfy that x * (-x) = e = (-x) * x. But if a neutral element isn't present under this operation, then it can never satisfy this property.

[oak bridge]

If I modified my operation to x°y = 2x How would I look for neutral element here ? (in real numbers)
We know it has to satisfy x ° e = x
Our operations again ignores second variable. It returns first variable times two.
x ° e = 2x
So again, we cant define neutral element ?

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[tall stone]

a^2*b^2+a^2+b^2+4>=6ab prove it

[ivory pivot]

$a^2b^2+a^2+b^2+4\ge 6ab$

what is \geq?

[ocean seal]

everg

[ivory pivot]

it also work \ge

$a^2+b^2\ge 2ab\implies a^2b^2+a^2+b^2+4\ge a^2b^2+2ab+4$

[ocean seal]

everg

[ivory pivot]

so it s tronger to prove:

$ a^2b^2+2ab+4\ge 6ab \implies a^2b^2-4ab+4\ge 0 $

now lets call $x=ab$

[ocean seal]

everg

[ivory pivot]

so you have to prove that $x^2-4x+4\ge 0$

[ocean seal]

everg

[ivory pivot]

its true because it is $(x-2)^2$

[ocean seal]

everg

[tall stone]

why did u change 6ab as a^2*b^2+4+2ab

[ivory pivot]

where?

[tall stone]

here

[ivory pivot]

no i don t touch 6ab... i only note that $ a^2b^2+a^2+b^2+4\ge a^2b^2+2ab+4$.. so instead of proving that the LHS>6ab i prove th stronger result RHS>6ab

[tall stone]

why do we need that proof

[tall stone]

i mean this

[ivory pivot]

because its uncomfortable to work with ab and a+b ..so i search a way to have only ab or only a+b

[tall stone]

did u prove that a^2+2ab+4 is less then a^2*b^2+a^2+b^2+4 and than proved for lower eq > 6ab?

[tall stone]

?

[ivory pivot]

yes exxxactly

[tall stone]

ok i got u

thk

[ivory pivot]

its like x^2+2>=0 but i can prove that by simply prove that x^2>=0

because i use that x^2+2>=x^2

[tall stone]

it's tricky

[ivory pivot]

very

good luck for the future

[tall stone]

I will remember this

.close

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[odd owl]

Someone can explain and give me a picture that how works roots? (Cube root, squade root etc).

[tall stone]

a^2=b √b = a ? like that?

[odd owl]

2 √4096

like this

[tall stone]

4096 it 2^x

i guess 11

2^12

so 2^(12/2) =

2^6 = 64

[tall stone]

https://www.youtube.com/watch?v=hlB8o1kgq6M&ab_channel=MySecretMathTutor

[odd owl]

thanks man

i will watch it

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.close

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[lone sapphire]

What's the terminology or structure of functions that can not be represented in graphs?

[alpine sable]

What

[lone sapphire]

My homework it's to tell functions that can not be represented In graphs

but I'm struggling at this

[simple spire]

Which graphs

[alpine sable]

Ah

How about the function which is 1 at all rational numbers and 0 at all irrational numbers

[lone sapphire]

chart

[simple spire]

ah

[umbral veldt]

Like dirichlet function?

[lone sapphire]

I don't think so, I searched and saw many charts of it

[worn fox]

your question is vague, what kind of functions? what do you specifically mean by representing as a graph?

[lone sapphire]

two dimensional graphs

[worn fox]

and what is your definition of graph?

[lone sapphire]

the relation between two values

in a graph, or "drawing"

[tacit arch]

still vague. show the original problem

[tacit arch]

screenshot or picture is best

[lone sapphire]

He said that once the definition of a function is a relation that can be graphically represented, meaning that every function must necessarily be represented by a graph. Thus, in order to prove that not every function can be represented using a graph, he asked us to research and find one that couldn't be. I don't have a photo, because I didn't take a photo of the board with the question, but I have wrote the following "Research about a function that cannot be represented in a graph".

[tacit arch]

"every function must necessarily be represented by a graph."
and
" prove that not every function can be represented using a graph, he asked us to research and find one that couldn't be"
be more specific in the second sentence that doesn't contradict the first sentence

every function has a graph yes. not every graph corresponds to a function

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[limpid turret]

!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

[limpid turret]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

@alpine sable Has your question been resolved?

[alpine sable]

Alright

[alpine sable]

1

[pseudo ice]

Do you know how displacement and velocity are related?

[alpine sable]

No

[pseudo ice]

you don't? Where is this question from, if I may ask?

[alpine sable]

IGCSE 2018 Jan p1r Maths B past papers

Hw

[pseudo ice]

Cool cool - well let me search the spec for that if I can find it

Are you familiar with differentiation, by any chance?

[alpine sable]

Like dy/dx things?

[pseudo ice]

yea

[alpine sable]

Oh right, I have to ask this too

How do you find gradient?

Unrelated to this question

[pseudo ice]

Erm, well, I don't think I have a nice tl;dr for that tbh

[alpine sable]

So here

This was the question

[pseudo ice]

Well that's pretty much it - the dy/dx is what you found? You mean to find the dy/dx or to find the points that have a given gradient?

For the part b, just solve that $9x^{2} - 30x = -25$ for $x$

[ocean seal]

@pseudo ice

[pseudo ice]

Anyways, reason I ask this is that velocity is the rate of change of displacement with respect to time, that is, the velocity for your s in the original question would be ds/dt

They ask you to find where the particle is at instantaneous rest, so where the velocity is zero, so solve ds/dt = 0 and all

[similarly, the acceleration is the rate of change of velocity with respect to time, or, equivalently, the second derivative of the displacement with respect to time]

[alpine sable]

Hm?

Ooh

Can you do stuff with 9x^2 and 30x when the power of x is not the same?

[alpine sable]

Also forget about this question. I can ask my teacher for that

But this I can’t cause she said it’s easy but I’m still not thee yet

But besides that, Idk how to do this

[pseudo ice]

What do you mean by "do stuff"?
[notice that you basically have a quadratic equation in x]

[pseudo ice]

Yea you might get a better explanation than I may be able to give, well, at least not without virtually developing a whole course or something

[pseudo ice]

But the tl;dr'ed version of what you'd need to do is there, in case you end up wanting to try it

[pseudo ice]

All three parts, or a part in particular?

[alpine sable]

Ohhh

You move the -25 to the left side

[alpine sable]

All 3 parts

[pseudo ice]

Yep, and from there I think you'll be fine with that

[pseudo ice]

Cool cool, fair enough

[pseudo ice]

So for the first part, notice how there are 350 550 people in total, made up of x adults and y kids

How many adults and kids are there in total?

[alpine sable]

350?

Also I think that’s 550

[alpine sable]

Cool. I got 5/3 which was the correct answer

[pseudo ice]

Yep, you're right, I can't read

[alpine sable]

How do you set up an equation with that information?

[ocean seal]

@pseudo ice

[alpine sable]

Uhh.. ratio?

[pseudo ice]

Erm, alright

If, say, I have two children and two adults that I want to send on a trip, how many people are going on that trip?

[alpine sable]

4

[pseudo ice]

Cool cool, how did you get that 4?

[alpine sable]

I added x and y

what

2 + 2

Oh I subconsciously guessed it right

[pseudo ice]

Yep you accidentally answered the question I wanted you to answer

[alpine sable]

So is it like x + y =550?

But then how would you still find x and y

[pseudo ice]

That's what's coming, all you need to do is give that as your answer to a

[alpine sable]

Ooh

Alright

[pseudo ice]

So now, there's part b

Remember, x adults and y children

How much did all the adults pay in total? How much did the children pay, bearing in mind that 50 of them have a discounted price?

[alpine sable]

Hmm uh

I don’t think I get it yet

[pseudo ice]

Let me rephrase the first question: if I have x adults, and each of them must pay £22, how much money must I get from those x adults in total?

[alpine sable]

22?

Ooh

Wait

My brain

I know there’s; like this thing

uhh

Okay I can’t htink about it

[pseudo ice]

...alright, let's go back - if we had 69 nice adults and the adult fee was £22 per person, how much would all those 69 adults have to pay?

[alpine sable]

1518

[pseudo ice]

...how did you get that?

[alpine sable]

22 multiply x?

[pseudo ice]

There we go, the answer to my question again

Now, let's do similar, keeping that 22x in mind: we have 50 children, and from that, there's a fee of £12 per child, but each of those 50 children get a discount of £5. How much do those 50 children need to pay me? 🤑

[alpine sable]

50 - 5 x multiply y?

[pseudo ice]

Not quite... note that here we won't need any x or y

[alpine sable]

Ooh

[pseudo ice]

The answer to this question will just be a number

[alpine sable]

Oh

I forgot about the 50 children

2250?

[pseudo ice]

not quite, how did you get that?

[alpine sable]

Oh

Gosh

Is it 150??

Oh cool

[pseudo ice]

Walk me through the way you want to get the answer...?

[alpine sable]

(12-5) x 50

[pseudo ice]

,calc (12 - 5) * 50

[ocean seal]

Result:

350

[pseudo ice]

The right way of course

So keep that in mind again: we have 22x, and we have 350, now...

From those y children, we lost 50 of them, but now the remaining ones must pay £12. How much money do I get from those remaining children?

[alpine sable]

Okay

y - 50 x 12

Is it like that?

[pseudo ice]

kind of

[alpine sable]

Hmm

[pseudo ice]

[check the react I gave - what do I want you to do?]

[alpine sable]

22x + 350 - 550 first?

[dapper bolt]

Can someone help me get the second one?

[pseudo ice]

!help

[lone heart]

Please read #❓how-to-get-help

[alpine sable]

I thought those were purple crab pinchers

[pseudo ice]

I wanted you to bracket that properly

[alpine sable]

Oohh

Lmaoo

[pseudo ice]

I can tell what you mean by that, buuttt that isn't how it reads

[alpine sable]

so (y - 50) x 12?

[dapper bolt]

dude it literally says to go here

🤷‍♀️

[alpine sable]

Nah it says to go to the available channels

These are occupied

[pseudo ice]

Not help-0 specifically

[dapper bolt]

ohh

ok💀

i got confused

[alpine sable]

It k

[pseudo ice]

No worries - just look in this section and bear in mind the numbers might be different

[alpine sable]

So what do I do with this now?

[pseudo ice]

https://tenor.com/view/lets-put-it-all-together-rosanna-pansino-mixing-mixture-blending-gif-19252902

[pseudo ice]

We have this...

[dapper bolt]

what do they mean

[pseudo ice]

...and this...

[alpine sable]

Oh wait is it like this?

[dapper bolt]

like do i go to one and put my question?

[pseudo ice]

...and this, and that forms our total

[alpine sable]

Yep

Just like you did here

[dapper bolt]

oh

[alpine sable]

But in thsoe channels

[dapper bolt]

ok

[pseudo ice]

Almost but not quite, that 550 should be something else...

[the 22x + 350 is fine]

[alpine sable]

8600?

[pseudo ice]

...that's what it should be equal to

[alpine sable]

right okay lemme think about it for a sec

22x + 350 - y = 8600?

[pseudo ice]

cloooseeeeeeee

[pseudo ice]

What do you think I wanted you to do with it?

[alpine sable]

Not sure

I think

[pseudo ice]

What did the 22x represent? What did the 350 represent? What does the 12(y - 50) represent?

[alpine sable]

22x is adults, 350 is the amount of money 50 children had to pay, and 12(y -50) is children without the discount

[pseudo ice]

And in total, what should all of that make up?

[alpine sable]

8600

[pseudo ice]

...well, yep! can you use that to make an equation then?

[alpine sable]

okay

So

22x + 350 + 12(y-50) = 8600

[pseudo ice]

...can you simplify that down for me?

[alpine sable]

22x + 350 + 12y - 600 = 8600?

[pseudo ice]

Some more please

[alpine sable]

22z + 12y - 250 = 8600

[pseudo ice]

Maybe again?
[also that should be an x, not a z, but minor]

[alpine sable]

oOh okie

Does 8600 stay the same?

https://tenor.com/view/drinking-beer-bird-parrot-drinking-beer-gif-12698533

[pseudo ice]

[well, I don't want it to, at least]

[alpine sable]

Ooh

So I have to change it

[pseudo ice]

[again, at least I want you to change it]

[alpine sable]

22x + 12y = 8850?

[pseudo ice]

So now we have that $22x + 12y = 8850$ (this is the answer to part b) and also that $x + y = 550$ (this is the answer we got from part a)

[ocean seal]

@pseudo ice

[pseudo ice]

So I leave it to you to solve(!)

[alpine sable]

hmm eh?

Okay wait

[pseudo ice]

[alpine sable]

X + y = 550

And

and 550 people had to pay 8850

So is it like a subbing situation?

Like you find for one first and then sub that answer in the next one

[pseudo ice]

You could, you have two linear equations
[
x + y = 550
]
[
22x + 12y = 8850
]

[alpine sable]

Um, probably not

I think

[ocean seal]

@pseudo ice

[alpine sable]

Oh

Now I see it

I think

[pseudo ice]

(or you could do elimination, whichever you would prefer)

[alpine sable]

what’s elimination?

[pseudo ice]

E.g. multiply the first equation by 22, you get it to be $22x + 22y = 12100$, then subtract the second equation $22x + 12y = 8850$ from that, you get that $10y = 3250$ and so on...

[ocean seal]

@pseudo ice

[alpine sable]

Oh

Alright

Also could you check if this one is correct?

[pseudo ice]

,w x - 8 < 4 + 5x, 4 + 5x <= 10 + 2x

[ocean seal]

Results provided by WolframAlpha

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Requested by chartbit#3171

[pseudo ice]

Should be $x - 8 < 4 + 5x$ you're considering

[ocean seal]

@pseudo ice

[alpine sable]

Ah okie

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[thick vigil]

Guyss What do we call if the one equation is the solution of the given point and the other one is not?

[remote heron]

"solution of the given point" what do you mean

[wary stream]

You mean extraneous?

[thick vigil]

Hmm the consistent and dependent?

[thick vigil]

The first example is consistent and independent?

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[thick vigil]

<@&286206848099549185>

Hi guys?

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[alpine sable]

hey

[alpine sable]

A rectangle has a perimeter of 20m

Find a function for the rectangles area based on the length of one of its sides

[young plover]

Have you tried to set up an equation

[alpine sable]

yes

[young plover]

Could you take a picture

[alpine sable]

im stuck in that part

i end up making an equation for the perimeter

[young plover]

So you set up 2w +2l =20

[alpine sable]

yes

[young plover]

Is there any other information given

[alpine sable]

A rectangle has a perimeter of 20 meters. Express the area of the rectangle based on the longitude of one of its sides

thats the textual question

[gusty gorge]

on the length of one of its sides?

[alpine sable]

@young plover i just end up with sometthing like f(l) = l+x = 20

which obviously doesnt work

[young plover]

If you did that l+x=10

You need all four sides

[alpine sable]

yes but it has to be in terms of the area

[young plover]

a=lw

10=l+w

[alpine sable]

Oh

Im getting it now

[young plover]

l=10-w

A=(10-w)w

A=10w-w^2

Is this what you’re looking for?

[alpine sable]

I dont know

Im confused

Oh

I completely misunderstood the question

its just calculate the area of a rectangle if its perimeter is 20 m

based on the length of one of its sides

So the length of its side would have to be less than 20 right?

@young plover

[young plover]

Yes

All the sides add up to 20

20=2l+2w

If you factor the two and divide you get what’s above

[alpine sable]

and how do i get the area from that

[lone heart]

@alpine sable Has your question been resolved?

[young plover]

You can’t

It’s insufficient material

You could only really find the maximum area enclosed my a perimeter of 20, but that’s using some calculus

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[stable grotto]

we have regular triangle ABC . Distance from A to a plane p is 51 , from B - 45 from C -27 . find the distance from the center of the triangle to the plane .

[lone heart]

@stable grotto Has your question been resolved?

[stable grotto]

<@&286206848099549185>

[brazen basin]

yes?

do you need help

[stable grotto]

yes

[brazen basin]

wait

can you give me the diagram or something?

[stable grotto]

it will look a little bit ugly but i will try my best

[vale wigeon]

is it known whether or not the triangle intersects the plane

[brazen basin]

k

[vale wigeon]

cause i think the answer might depend on that.

[brazen basin]

i agree

[stable grotto]

one sec

[brazen basin]

im waiting

[vale wigeon]

ah, so it does not intersect the plane.

then there is a cheaty somewhat-linear-algebraic argument you can pull.

[stable grotto]

i think not

ok i am listening

[vale wigeon]

imagine the plane goes through the origin. we can place it at O' if we want but it doesnt really matter

then the function from R^3 to R which sends every point P to the signed distance from P to your plane (positive if above, negative if below) is a linear function

and O = (A+B+C)/3

[stable grotto]

So OO' will be the mean of 51,45,27?

which is 41

[vale wigeon]

yes

[stable grotto]

can you give me some sort of intuitive idea why the formula you showed me is true ? Or/and how to search the theoren in google ?

Or if it's not too lengthy theorem can you prove it here?

@vale wigeon

@brazen basin

[vale wigeon]

augh

dont have the energy for that sorry

[stable grotto]

how to search ?

[vale wigeon]

dunno.

[stable grotto]

here O A B anc C are radius vectors ?

[vale wigeon]

i'm using the points to stand for their position vectors, yes.

[stable grotto]

ok

tnx

.close

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[main cedar]

can someone help me solve this

[gray isle]

what have you tried?

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[alpine sable]

can somone help me with this

[lone heart]

@alpine sable Has your question been resolved?

[rugged wind]

is p=3?

[alpine sable]

that was on the answer sheet yeah, may you tell me how you found it

[rugged wind]

just use the midpoint formula

$(-2+p)/2 =0.5$

[ocean seal]

Σ♡

[alpine sable]

ohhh okay thank u smm

[rugged wind]

and do u know how to do question b?

[alpine sable]

for b) to find a, do i do the vertex form?

[rugged wind]

no

u just need to multiply it

(x+2)(x-3)=0

then u get the answer

because of the x-line have intersect so x=2 and x=3

[alpine sable]

ohh i see

one sec

[alpine sable]

@rugged wind so can i replace the x with 0.5?

my H value

my answer is a=2

[alpine sable]

<@&286206848099549185>

wait nvm i solved it

.close

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[strange fractal]

Hi i need help with question c!

[strange fractal]

Idk what the question means

[latent shore]

In part a you need to calculate the area for the base of a rectangular box

You got all the dimensions

[strange fractal]

I need help with c

[alpine sable]

I think it means how many small jewelery boxes would fit in the bigger box

Area of the bigger box/ area of smaller

[strange fractal]

Ohh ok tysm

Let me checjk

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[orchid perch]

the lifetime of a battery in days, X, is geometrically distributed, batteries of factory A have an average lifetime of 10 days, of factory B 14 days, of C 16 days, 1/3 of the batteries in the storage are from A, 1/6 of B and 1/2 of C
given that a battery has worked for more than 12 days, what is the probability that its from factory C?

[orchid perch]

im not sure how to approach this?

is the average lifetime of a battery just the expected value of X?

[latent shore]

Use the cumulative distribution function

Then use Bayes' theorem to find the probability that a battery is from factory C

Knowing that that it has worked for more than 12 days

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@orchid perch Has your question been resolved?

[orchid perch]

.close

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[final hare]

help with 21

[final hare]

not sure how to start or what to do

[pseudo ice]

,rccw

[lone heart]

@final hare Has your question been resolved?

[final hare]

<@&286206848099549185>

[sand pawn]

@final hare which part on 21?

there are 3 parts therein apparently

[final hare]

part a

[sand pawn]

That is very easy,

[final hare]

how do i do it?

@sand pawn

[sand pawn]

Hmm, let me give you a visual

The triangle in question can be visualized as follows

[final hare]

how do. we know that?

is that what itmeans with dropping perpendicular to the x axis

[sand pawn]

the values of a1, a2, a3 can be arbitrarily chosen just as I did

I wish if I can visualize it to you through some video or shit

[final hare]

no its fine i understand

so just to get the rough. shape

is like that

[sand pawn]

yeah

[final hare]

what to do after that

to form the equation

[sand pawn]

Can I have a video chat with ya?

[final hare]

ok

[sand pawn]

Accept the request

[lone heart]

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[hard aspen]

help

[minor needle]

apply log laws on the RHS

then compare numbers inside the logs

[hard aspen]

ook lmme try that

i have no idea how to proceed i got till ( x +y)/3 = (xy)^1/2

[minor needle]

it's fine

now notice that x/y + y/x = (x^2 + y^2)/xy

[minor needle]

square both sides of this one and think about how to proceed

[tender dew]

aeems like identity for common denominator

[hard aspen]

ah

[tender dew]

aside them being 0

[minor needle]

(x+y)/3 = (xy)^(1/2)
(x+y)^2/9 = xy
(x^2 + 2xy + y^2)/9 = xy
(x^2 + y^2)/9 + 2xy/9 = xy
(x^2 + y^2)/9 = xy - 2xy/9 = 7xy/9
(x^2 + y^2) = 7xy

x/y + y/x = (x^2 + y^2)/xy = ...

[hard aspen]

got it

tysm

.close

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[shy silo]

is this even correct ? i always have a hard time where there are too many terms and i dont know which one to multiply and all in mathsolver microsoft they evaluated it to 4(3s^2 - 4)/(s^2 + 4)^3 how can i achieve that ?

[rocky grove]

$\dv{s} \frac{2}{s^2+4} = \dv{s} 2(s^2+4)^{-1} \
= -2(s^2+4)^{-2} \cdot 2s = \frac{-2\cdot 2s}{(s^2+4)^2}$

[ocean seal]

VulcanOne

[shy silo]

yeah and then again derivative wrt s

[rocky grove]

Okay

So like

$\dv{s} -4s(s^2+4)^{-2} = -4\left( (s^2 + 4)^{-2} -2s(s^2 +4)^{-3} \cdot 2s\right)$

[ocean seal]

VulcanOne

[near burrow]

hello

i dont know.

[rocky grove]

Uhh

You looking for help?

[near burrow]

ok

[ornate ginkgo]

Please open your help channel if you have a question to ask for.

[rocky grove]

What ok?

[near burrow]

i m french

[alpine sable]

me too

who can help me to understand mathematical derivative please

[rocky grove]

#❓how-to-get-help

@near burrow @alpine sable #❓how-to-get-help

[alpine sable]

oh sorry

[shy silo]

[rocky grove]

https://cdn.discordapp.com/attachments/490557019623915520/1081604052464455790/1000057838007226480.png

So like

[shy silo]

can you do it using the quotient rule again ? or does it become too complex ?

[rocky grove]

$-\frac{4}{(s^2+4)^2} + \frac{16s^2}{(s^2+4)^3}$

[ocean seal]

VulcanOne

[rocky grove]

You can use whatever approach you deem easy as long as you reach the final result properly

[shy silo]

actually your way seems easy ngl

[shy silo]

can you explain this a bit more ?

[rocky grove]

Okay

So I took the -4 outside the derivative operation because I can just multiply the result by it in the end

So I have 2 parts

2 functions being multiplied

s and (s^2 + 4)^{-2}

[shy silo]

and then you simply took the derivative of s and (s^2 + 4)^{-2} ?

[rocky grove]

Yep

And used product rule

[shy silo]

ahh yeah the product rule kk

so fx was s and gx was (s^2 + 4)^{-2} right for the product rule ?

[rocky grove]

Yep

[shy silo]

shouldn't it be s * -2(s^2 + 4)^-3 (2s) + (s^2 + 4)^-2* (1)

[rocky grove]

Yep

[shy silo]

then how is your -2s(s^2 + 4)^-3 . 2s etc ?

[rocky grove]

Hmm

[rocky grove]

Should be the same thing

You forgot the -4 from the outside

[shy silo]

yep but the terms should be in addition ?

how are your terms in substraction ?

[rocky grove]

They are

[shy silo]

ahh shit

[rocky grove]

Well same thing from the other side lol

[shy silo]

yeah yeah

lol

okay so how did you achieve the final answer in the end

[rocky grove]

I simplified and multiplied the -4 from the outside

[shy silo]

yep thank you

16s^2*

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[dusky kernel]

sb help

[dusky kernel]

This problem has been proved in general form ig

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@dusky kernel Has your question been resolved?

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[alpine sable]

i cant figure out how to do area of a shaded compound shape

[pseudo ice]

Is the shaded the area you want?

[alpine sable]

i need it for both shapes but yes we can do shaded

[harsh swallow]

There's a formula for the area of a trapezoid

[alpine sable]

it isn’t a trapezoid though

[jagged cobalt]

you cant see the trapezoid? inside the circle

[alpine sable]

that’s a rectangle

in a circle

[jagged cobalt]

that is not a rectangle

[jagged cobalt]

you sure youre looking at this

[alpine sable]

yes

[jagged cobalt]

why do you think thats a rectangle?

[alpine sable]

oh waitt

i see it now

i had to turn my computer the other way

the way i looked at it the lines were straight like a rectangle on the sides

[jagged cobalt]

anywho.. if you want the shaded area what do you think you need to do

[alpine sable]

find the area of the circle

?

[tawny crown]

You'd also want to subtract something from it

[alpine sable]

what would i subtract

[tawny crown]

What's not shaded?

[alpine sable]

so for the area of the

trapezoid

i got 112.5

[tawny crown]

That's correct

[alpine sable]

so for the shaded area

the diameter is

26

[tawny crown]

Yes

[alpine sable]

so that means radius is 13

so i would do 13 squared pi?

[tawny crown]

There you go, you just solved it on your own

[tawny crown]

Yes and then subtract the trapezoid

[alpine sable]

ok thank you

[lone heart]

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[modest zinc]

I had my professor helped me work this out but I want to know how he got that answer

I understand everything else but idk how she got her answer

[whole shell]

which part are you stuck on?

[modest zinc]

I’ve done the long division and everything. It’s just that integral that I don’t know what to do

This part specifically

[lone heart]

@modest zinc Has your question been resolved?

[whole shell]

ok so the first integral

youre fine with right?

[alpine sable]

It should be 2aTan(t/2) instead of 4aTan(t/2)

[whole shell]

a?

[modest zinc]

Wait, I think I know how they got that

[alpine sable]

Arc

ArcTan

same as Tan-1

[whole shell]

yes

but

[alpine sable]

i dont know how to type it

[modest zinc]

Isn’t it because of the constant?

[whole shell]

ive never seen someone just say a for arc

[modest zinc]

Isn’t that why the 4 is in front?

[whole shell]

yh

well acc

[alpine sable]

2aTan(t/2) sorry

[modest zinc]

Why 2?

Where did the 2 come from?

[whole shell]

it should be 2

yh

[alpine sable]

4/(t^2+4)
=>1/((t/2)^2+1)
=>2aTan(t/2)

[alpine sable]

when u take derivative of aTan(t/2) we get d(t/2)/t=1/2

we want to cancel this part

so we multiply it with 2

[modest zinc]

Is there a way you can write it out😅

I’m sorry

[alpine sable]

sure

[whole shell]

or you can do, integral of 1/(t^2 + 4). t = 2tan(u). dt = 2sec^2(u). 2sec^2(u)/(4tan^2(u) + 4) = 2sec^2u/4sec^2u = 1/2. integral of 1/2 du = 1/2 u. u = arctan(t/2)

so integral of 1/t^2 + 4 = 1/2 arctan(t/2)

since you have a 4 as a constant

it becomes 4 * 1/2 arctan(t/2) = 2 arctan(t/2)

[alpine sable]

You can do this as well

[whole shell]

basically the rule is. integral of 1/(t^2 + a^2) is 1/a arctan(t/a). best to just remember it

[alpine sable]

Yes

[modest zinc]

Okay thank you!!

.close

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[alpine sable]

what

[alpine sable]

what the i mean in infinit

.close

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[true stratus]

Does anyone mind checking this work for me, finding tangent, normal and binormal vectors.

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@true stratus Has your question been resolved?

[true stratus]

<@&286206848099549185>

[lone heart]

@true stratus Has your question been resolved?

[lone heart]

@true stratus Has your question been resolved?

[lone heart]

@true stratus Has your question been resolved?

[frail rivet]

all looks good I believe

I think it's usually easier to calculate t,n, b in unit vectors though

[true stratus]

wdym

[frail rivet]

well usually they are used as unit vectors with the curvature \kappa no?

[true stratus]

yeah but how would i have solved like that

[frail rivet]

wait nvm

your t, n and b are already unit vectors

with $\frac{\dot{\vec{r}}}{\abs{\dot{\vec{r}}}}$

[true stratus]

right

hey so since i have you here are you any good at creating vector functions given intersecting surfaces?

[ocean seal]

b3s4d

[frail rivet]

sorry my latex was fcked up

are you taking theoretical mechanics?

[true stratus]

no just vector calculus

[frail rivet]

hmm I'm not sure if I've done that sorry

[true stratus]

can i send you something and see if it makes any sense?

[frail rivet]

sure but I can't promise anything

someone else surely will know though

[true stratus]

essentially im given two functions: z=2x-4 and 5(x-2)^2 + (y+1)^2 = 5

and i want to find the vector function of where these two surfaces intersect

ends up looking like this

so im trying to find the function of where they intersect. So it looks like the function will be eliptical

I just need to know where to start in order to find the function

[frail rivet]

I think you have to substitute to get a single equation

[true stratus]

I agree, so would i rearrange into x= (z+4)/2 and then substitute that into the other equation?

[lyric vapor]

Yes

[frail rivet]

that looks like a good plan

[true stratus]

ok let me do that real quick

So now that ive done that what would be the next step

[frail rivet]

So we need a parameterized curve

like p(t) = (x, y, z) written with t I believe

So we can express x with z and y with z

so we can choose z as our free variable?

[true stratus]

make t=z?

[frail rivet]

basically

and then choose x and y accordingly and see if that makes any sense?

[true stratus]

ok let me try this rq

x=(t+4)/2

z=t

y is kind of a bitch to solve for. its really putting my algebra through its paces lmao

[frail rivet]

5(x-2)^2 + (y+1)^2 = 5

y = ±sqrt(5 - 5(x-2)^2) - 1?

[true stratus]

let me check

looks right to me

now i just plug in (t+4)/2 for x and that should be it?

[frail rivet]

No

or...

[true stratus]

since x=(z+4)/2

and z=t

[frail rivet]

ah yeah

you're right

[true stratus]

i can always check this vector function if it is the same as those intersecting surfaces i sent earlier

[frail rivet]

yes

it should be an ellipse as you said earlier

[true stratus]

yeah i dont think thats it sadly

[frail rivet]

Are you sure?

[true stratus]

unless my 3d grapher is trippin i dont think so

[frail rivet]

I've graphed it and it looks like an ellipse

[true stratus]

can you send a screenshot?

[frail rivet]

that is the +sqrt, and if you graph the -sqrt it completes the other half

[true stratus]

oh ok. I was missing the other half which is why i thought it looked wrong

alright last question and ill stop bothering you

when im writing this all into the r(t) would i would the + and - in the sqrt part of the y vector?

[frail rivet]

yea +-

[true stratus]

awesome, thank you. I really appreciate it

[frail rivet]

no worries it was a fun problem

[true stratus]

yeah definitely

[lone heart]

@true stratus Has your question been resolved?

[lone heart]

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[dire flume]

hi

[dire flume]

question is all inverse trig function use -1 in there sohcatao

Because my calc is saying error :"D

hype is 10 adj is 11 and opp is missing

so i input cos-1 (11/10)

[gray isle]

how is your hyp longer than your adj

[dire flume]

I have no clue

It was given to us and am lost

[gray isle]

do you have an image of te problem

[dire flume]

yess

[gray isle]

you didn't properly identify the positions

[dire flume]

h uh?

[gray isle]

the hyp is the side opposite the right angle

and will in this case be 11

and 10 is the side adjacent to your angle

[dire flume]

ohhh hype is 11 and 10 is adj

ohh okay ty

[lone heart]

@dire flume Has your question been resolved?

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[steady basin]

is the set of all imaginary numbers a real vector space?

[vale wigeon]

is it?

are you having trouble verifying any of the axioms? if so, which ones?

[plain flame]

complex or imaginary?

[steady basin]

imaginary

[vale wigeon]

the way it is phrased i am led to assume we are talking about {it : t in R}

i.e. pure-imaginary numbers

[steady basin]

ye

well i would think it isnt

since imaginary numbers arent real

[plain flame]

0 is real

but yes its a vector space

[steady basin]

is 0 an imaginary number tho

0i?

[plain flame]

fair point

{it : t in R} is a vector space

[steady basin]

so is the set of all imaginary numbers a real vector space?

im still not sure if it is or isnt

[plain flame]

{it : t in R \ {0} } isnt

[plain flame]

depends on how you define imaginary numbers

[vale wigeon]

what is causing you doubt?

[steady basin]

'all' imaginary numbers

[plain flame]

so include 0?

[steady basin]

ye

[vale wigeon]

did you write down the defn of your candidate space and go through the axioms?

yes or no

[steady basin]

yes

[marsh rapids]

iR = Span(i)

[vale wigeon]

did you have trouble verifying at least one of the axioms?

[steady basin]

i think it satisifes all the axioms

[vale wigeon]

you think or you know?

[steady basin]

its the word 'real' which is putting me off a bit

real vector space

[vale wigeon]

real vector space means a space over the field of real numbers,

[steady basin]

yh but imaginary numbers arent real numbers, thats whats throwing me off a bit

thats whats making me unsure

[vale wigeon]

but the question as to whether or not an object is a vector space comes down to the axioms of a vector space and nothing else.

[steady basin]

ok

well in that case

it is a real vector space

[lone heart]

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[fallow pagoda]

these solutions say the second derivative is this... but i dont get how? shouldnt the 20 be a 40 instead??

[fallow pagoda]

-20 times -2 is 40 so why is the second derivative that..

[whole shell]

@fallow pagoda yh it should be

They're wrong

[fallow pagoda]

ok thanks

.close

[lone heart]

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[sick warren]

Hi

[sick warren]

I have a question

I'm going to translate

We have to discover the values of m and n

Knowing that P(x) divided by x²+x+2

[ruby current]

consider the form of the divisor

[sick warren]

Is rest 0

[echo socket]

You could use the fact that if P(x) is divisible by x^2 + x + 2, then its other factor would be a linear polynomial

[ruby current]

well it must be degree 1

[echo socket]

Specifically, it would be 3x - 1

[ruby current]

and the constant term is determined

and so is the leading term

[echo socket]

So that the coefficients would make sense

[sick warren]

Ok

[ruby current]

-1*

[sick warren]

Could you explain how you do that

Because I have problems understanding English

With a lot of specific terms

How do you reach 3x-1?

[echo socket]

I "chose" 3x because 3x and x^2 will get multiplied into 3x^3

Which is the leading term in the P(x)

[lone heart]

@sick warren Has your question been resolved?

[sick warren]

Ok

And after that?

What do I do?

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[past knot]

is x^2 -xy +y^2>0 for all x,y real numbers?

[past knot]

<@&286206848099549185>

[strange meadow]

• After 15 minutes, feel free to ping <@&286206848099549185>.

well frick i pinged too

hypocritical anyyways

it doesn't hold i dont believe

oh wait it does

im stupid

wait no it doesn't

[pliant cedar]

$x^2-xy+y^2=\left(x-\frac{y}{2}\right)^2+\frac{3y^2}{4}$

[ocean seal]

𝕾ilver𝕾oldier

[soft breach]

X/4 - 2018=56
X=(56+2018)×4

[past knot]

so it is true?

[strange meadow]

oh wait it holds

[soft breach]

X/4 - 2018=56
X=(56+2018)×4

[tawny crown]

≥

[pliant cedar]

when x = y = 0 this is 0

otherwise it is not

it is positive

[pliant cedar]

? if u have a question, please read #❓how-to-get-help

[past knot]

ok thanks

[lone heart]

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[alpine sable]

Is this correct it's my first time integrating by substitution

[alpine sable]

The first question

[minor needle]

,w d/dx -3/2cos(x^2)

[ocean seal]

Results provided by WolframAlpha

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Requested by Modus#7591

[alpine sable]

@minor needle so am I correct?

i dont understand

[minor needle]

yeah that's true

[alpine sable]

okay

[minor needle]

this is the way you can check result of the integral

[alpine sable]

can you like be on for one more minute

Im trying the next problem