help-39

[sharp smelt]

I'm not sure then, sorry

[pearl pond]

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[real oyster]

Hello, so i see here they used a^2 but both a's aren't equal how can they just add them? it should have different values, if they used different letters then they cant solve anymore, wouldn't that make more sense?

[midnight haven]

Ah I think I might get your issue, because the video incorrectly used variables lol so you end up with 3 variations of "a"

1. "A", referring to the point A. This actually is not important beyond referring to the triangle, so whenever they use A in math they are referring to the 2nd variation
2. "A", referring to area. In this case the area A = Length * Width = a * a = a^2
3. "a", referring to the length of both lines AB and AD

Does that help any? If not where exactly do you still struggle?

[real oyster]

I see

[real oyster]

I understand, they never really explain this thank you

.close

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[shut dawn]

The left red circle is the circumcircle of PQR

and the right one is the left one reflected about PQ

I want to prove that the right one is a mixtilinear incircle of ABC

My question is, how do I know that the reflected circle is tangent to P and Q (instead of just intersecting)?

[pearl pond]

@shut dawn Has your question been resolved?

[shut dawn]

<@&286206848099549185>

wait

i can just first draw the mixtilinear incircle first and show that the two are symm abt PQ

.closeo

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[midnight haven]

visually the answer is 1/2 the parallelogram = 1/4

but i guess you’re not supposed to do that?

everything looks congruent to its other pair lol

[pearl pond]

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[acoustic path]

can you tell me what fraction PTRU is of PQRS?

[pearl pond]

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[lapis lynx]

Apparently, you were supposed to take the limit of S_n to infinity. Can someone explain how I was supposed to figure that out?

[sharp vigil]

the definition of the sum of a series is the limit of partial sums

[lapis lynx]

so when they say S by itself, it that just the sum of the entire series?

[sharp vigil]

from context it would appear that way

[lapis lynx]

alr thanks

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[stuck widget]

this is a physics question but I feel like it's easy enough that someone could help answer it, what would be the maximum height it reaches?

[stuck widget]

because I was able to find the time it reached the top but it so small it doesn't really effect the height (since I rounded to 3 significant figures)

wait nvm

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[uneven adder]

Hi, can someone please help me understand why c = r-s?

[next dove]

by triangle law of vector addition

vec(C) + vec(s) = vec(r)

[uneven adder]

Thank you! I’m unfamiliar with that law so I’ll read up on it. That is exactly what I was looking for to set me in the right direction though!

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[plucky nebula]

hello

[plucky nebula]

if a subspace has the same dimension as its vector space, does that mean that they are the same

bit of context

[wet osprey]

in finite dimensional cases yes

im not sure about the infinite dimensional cases

[plucky nebula]

would you be able to explain why this is true?

for the finite case

[pearl pond]

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[pearl pond]

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[grave parcel]

Hey

[grave parcel]

Can someone help me understand this

Where did they get the 6x+3y=51 from?

[pearl pond]

@grave parcel Has your question been resolved?

[grave parcel]

<@&286206848099549185>

[olive plinth]

2x+y=17 right?

[grave parcel]

Yes

[olive plinth]

multiply 3 each sides

[grave parcel]

OH GOSH IM DUMB

I realised

AHHHH

THAnk you for that. Can you help with this one

[olive plinth]

scalar multiply

[grave parcel]

Hm what’s that?

[olive plinth]

scalar multiply of two perpendicular vectors are 0

dont' you know?

[grave parcel]

Nope that’s not what we are learning

[olive plinth]

then what are you learning?

[grave parcel]

The topic on this one is perpendicular and parallel lines

Based on coordinate geometry

[olive plinth]

ca you get the distance of two points

[grave parcel]

Yes

[olive plinth]

between 3 points?

[grave parcel]

No

[olive plinth]

just use k

using k, you can get the distances

then use teh pidagoras

[grave parcel]

Ok thank you

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[grave parcel]

Hi

[grave parcel]

Dumb question but can someone teach real quick

I just don’t know where to start

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[short orchid]

guys pls help

[ripe moat]

maybe You can solve this through an ellipse

[light helm]

!status

[pearl pond]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[inland ivy]

not necessary, there's a much easier way of going about this

[wet swallow]

Differentiation?

[light helm]

no

easier

[ripe moat]

I think ellipse is also easy

[inland ivy]

no

[ripe moat]

just rewrite in standard form

[inland ivy]

much easier

[inland ivy]

not required.

please let OP answer

[wet swallow]

Oh

Lol

[wet swallow]

@short orchid

[inland ivy]

okay well this is not using the properties of an ellipse at all

[toxic dove]

._.

[pearl pond]

@short orchid Has your question been resolved?

[short orchid]

Wait whats the standard form

[ripe moat]

this is the standard form of an ellipse but check if you get the answer correct

[short orchid]

Uhhmm

Whats supposed to be the x, y, a, and b againn?

Sorry guys i just started 11th grade but i have to study 12th grade math

[ripe moat]

Put logp as x , logq as y

bring the 9 from rhs to denominators on lhs

[short orchid]

Okkk thankuuu

[wet swallow]

Have you learned ellipses

[short orchid]

Not yet

[ripe moat]

the maximum value of x in this eqn can be a
for y it can be b

[short orchid]

Okkk i’ll try

Thankuu sm

[ripe moat]

ye sure

[short orchid]

Holdon i have another qs

How do i do letter e and f

[ripe moat]

write 1 as log 2 to the base 2

and write 2 as log 16 to the base 4

[wet swallow]

For (e) 1 =$log_2(2)$

[jolly parrot]

David

[short orchid]

Ohh

How do you know the base

Ohhh i think ik it now

[wet swallow]

Property of log: $log_x(x)=1$

[jolly parrot]

David

[short orchid]

We want to make the bases of the logs the same rightt

[wet swallow]

Yes

[short orchid]

Okkkk thankuu smmm both of u

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[pearl pond]

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[plucky nebula]

hello

[plucky nebula]

im really confused on how to do b and c

<@&286206848099549185>

begging

shaking

and crying

[stone portal]

Do you know how to find the matirx representative of a linear transformation?

[plucky nebula]

yeah

you can sub the standard basis vectors

and T(vi) will form the columns of the matrix

[stone portal]

Then do exactly that in this case

[plucky nebula]

what would the standard basis vectors be for the basis {1,i} tho 🤔

i thought initially it would (1,0)^T and (0,1)^T respectively

[stone portal]

1 and i as elements of C are vectors and form a basis of C as a vector space over R

[stone portal]

It doesn't have to be standard- any two basies of the vector spaces

[stone portal]

(1,0)^T isn't in C

[plucky nebula]

wait i have the rotation matrix right. Wouldn't it need a 2 by 1 vector to find anything relevant

[stone portal]

The point is that C is treated as a vector space over R

Not all vectors are column vectors- say polynomials

[plucky nebula]

okay that makes sense

then how would we use the rotation matrix?

[plucky nebula]

also, by roation matrix im referring to this

<@&286206848099549185>

[stone portal]

The column vectors are the representations of the abstract vectors as coordinates are column vectors

Sorry had a phone call

[stone portal]

That's exactly the answer for b

It's the representation of f as a transformation from C to C with respect to the basis {1,i}

[plucky nebula]

omg i am so stupid i forgot a minus sign here

but yeah

that makes sense then

[stone portal]

Plug in 1 and i into f and convert the outcome into vectors with basis {1,i}

Which is close to what you did

[stone portal]

And you see how to solve c?

[plucky nebula]

hmm i still am getting a confused with c

i can't do the same thing i did the last time right

[stone portal]

Why not

[plucky nebula]

so could i then convert the basis vectors into (1,0) and (-1/2, sqrt(3)/2)

they are both linearly independent and have the correct dimension

so i assume it should work

[stone portal]

Not necessary

There's nothing special about the basis {1,i}

[plucky nebula]

so then how would i go about this

[stone portal]

Similar to what you said

Find f(1), see how it decomposes in terms of {1,ω}

Find f(ω), do the same thing

This gives you the columns of the matix

[plucky nebula]

okay this is the fundamental crux of my problem. I don't really understand how we can do f(1) and f(w)

i'm not really familiar with the rotation matrix so the only way i can think of doing this is to do rotation matrix * [x,y]

[stone portal]

Oh ok, this also works

[plucky nebula]

so what i ended up doing it is just thinking it about in terms of complex (as in multiplying the vector by cis(2pi/3))

[stone portal]

Easier than dealing with matrices

[plucky nebula]

and it is correct

man this was way easier than i initially conceptualized

maybe its cause its 5am

anyways

thanks for your help

really appreciate it

.close

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[stone portal]

Best hours to be awake at

[plucky nebula]

lmao

have a test tmr and at this point i hate myself to much to stop

so once again really appreciate all the help out of your time

[stone portal]

No problem

[pearl pond]

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[fallow aspen]

How can I help simplify this problem? I am doing this for self-study

Here is my math so far that I don't know if it is correct

(2x^2 times 2√'y)(2√'2 times 2√'x times 2√'y) Law 5

I am unsure how to simplify beyond this point

[elfin cloud]

Could you maybe write what you have using latex or write it down (nicely) and make a picture? Because it isnt really clear right now

[fallow aspen]

Yeah for sure, let me upload that. One sec

@elfin cloud

[elfin cloud]

How did u arrive at sqrt(2x^2) for the first term?

[fallow aspen]

I figured that 4√'8 would be 2√'2 because the square root of 3√'8 is 2, so 2√'2 would be one more of that

wait nvm, that isn't right at all

I got confused because 2^3 is 8

[elfin cloud]

But you did remove the 2 later on in the second 4th root

Soooo what ended up with is actually correct

[fallow aspen]

Really lol?

So the 4th one is correct, the former ones aren't?

[elfin cloud]

Lets start from the beginning to avoid some confusion

First of all

I would combine everything under the same root to make it easier right?

Because everything is under a 4th root

[fallow aspen]

That does sound easier

[elfin cloud]

Yes

So you would get

[fallow aspen]

4√'8x^6 times y^2 times 2x^2 times y^2?

[elfin cloud]

$\sqrt[4]{8x^6 y^2 2x^2 y^2}$

[fallow aspen]

yeah

[elfin cloud]

(Took me a while haha)

[fallow aspen]

no worries

[elfin cloud]

Yeah you agree this is rhe result?

[jolly parrot]

thijs2725

[fallow aspen]

Yeah, you are just putting everything under the square root 4

law 1

[elfin cloud]

Now what would be easiest to do?

[fallow aspen]

Would it be easiest to break up each term into what the squared into?

[elfin cloud]

Could be but in my opinion there is an easier way

We want rhe equation to get smaller first

What can we simplify

[fallow aspen]

Combine all the x and y terms?

[elfin cloud]

Yes

[fallow aspen]

maybe like 16x^8? and y^4?

[elfin cloud]

And how would we do that?

Yes exactly

[fallow aspen]

you times them together by multiplying their coefficent's and adding exponents

[elfin cloud]

$\sqrt[4]{16x^8 y^4}$

[jolly parrot]

thijs2725

[elfin cloud]

Now it is already really compact

Now we can more easily distribute the root over the individual terms

[fallow aspen]

Oh I see 4√'16 is 2

[elfin cloud]

Yes

And the 4th root of x^8?

[fallow aspen]

I see so once we simplify we get 2x^2 and y?

[elfin cloud]

Yup

$2x^2 y$

[jolly parrot]

thijs2725

[elfin cloud]

That is the solution

[fallow aspen]

Thank you, this was an awesome explanation. I finally understood the problem

.close

[pearl pond]

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[elfin cloud]

My tip to you would be to first see what terms can be combined before you start with the rest

[pearl pond]

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[terse kettle]

hello there

[terse kettle]

i have three questions

these three

for question 5, i dont even understand the question in first place

dont even know what they want exactly

[bright kindle]

in ques 14 just use tan(a-b)

[terse kettle]

mmm what forumla is that again?

[bright kindle]

(tana-tanb)/ 1+tana*tanb

[terse kettle]

yes what is the name of that formula?

[bright kindle]

for ques 12 just solve it and check when costheta is zero

[terse kettle]

ah ok

[bright kindle]

and 2sintheta+1 is zero

[terse kettle]

so simple calculations

[bright kindle]

lol why do u care

[bright kindle]

yes

[terse kettle]

cause.......i dont know if it come in the future

ooooh

i see

thank you

and the fifth question?

[bright kindle]

i think the ans is d for that

[terse kettle]

hmm

and why is that?

[bright kindle]

u just have to check when the ans will be negative

in what range

[terse kettle]

it is indeed correct

how so? im completely clueless

i dont even understand the question

[bright kindle]

the points where the function will be zero are

0
-b
a
and c

put them on the no line

[terse kettle]

let see

what do i plug and where?

[bright kindle]

i dont think they have taught you that yet seeing how clueless u are

like this

[terse kettle]

wait

thats interval notation ye?

[bright kindle]

what?

[terse kettle]

interval notation

[bright kindle]

yea

u can ping me if u need anymore help

[terse kettle]

sure

thanks

i appreciate all your help

[pearl pond]

@terse kettle Has your question been resolved?

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[terse kettle]

thank you

.close

[pearl pond]

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[sterile turtle]

help with a ii) State the Domain pls

i can

uh wait

say this is the graph for x

but then how do i find the pts?

do i have to diff to find max and min?

[pearl pond]

@sterile turtle Has your question been resolved?

[sterile turtle]

<@&286206848099549185>

[fervent crow]

hi?

[sterile turtle]

hi

[fervent crow]

im not a helper 😭

im the one need help

[sterile turtle]

??

[fervent crow]

opps i have roll helper

[pearl pond]

@sterile turtle Has your question been resolved?

[sterile turtle]

.close

[pearl pond]

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[copper grove]

Can someone explain deeper how the answer is correct? Like it's on my choices at my assignment but I wanna get it more how it got the answer

[cosmic raptor]

so f(x) = 4 + 5x^2

if we plug in say -1+t into f(x)

we get f(-1+t) = 4 + 5(-1+t)^2

plugging in something into a function directly replaces all instances of the original variable with what you plugged in

[copper grove]

I'm kinda stuck how it got 5x² and 10x and how the 9 is suddenly on the last, like did it changed positions

[cosmic raptor]

ah i see

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

and then you do foil

(-1)(-1) + (-1)(x) + (x)(-1) + (x)(x)

1 - x - x + x^2

x^2 - 2x + 1

and then we can replace the (-1+x)^2 from plugging in with this quadratic

4 + 5(x^2 - 2x + 1)

[copper grove]

Ohhh wait I'm tryna understand

[cosmic raptor]

do you know foil?

[copper grove]

Yeaah

Holdup im tryna solve

Im a lil slow

[cosmic raptor]

that's ok lmao

[copper grove]

This may sound stupid since I barely remember math from junior high school but is like x times x equals to x^2 or not

[cosmic raptor]

yes it does

[copper grove]

Ohhh

[copper grove]

I'm only a lil confused at this part

[cosmic raptor]

all i did was add up like terms

and then rearrange

so -x-x = -2x

which gives us 1 - 2x + x^2

and then i moved stuff around

to give us x^2 - 2x + 1

[copper grove]

Oh okok I'm slowly getting it

[cosmic raptor]

thats great!

-x - x = -2x

not 2x

[copper grove]

Oh

Ohhhh

Right

What do I do next again

[cosmic raptor]

now you can just swap (-1+x)^2 with what you got from foiling

and then distribute the 5 to all the terms

[copper grove]

Wait wdym swap

[cosmic raptor]

we know that (-1+x)^2 = x^2 - 2x + 1

that means that we can swap the 2 of them whenever we want and get the same answer

[copper grove]

Wait I'm still kinda slow sorry

[cosmic raptor]

ur good

[copper grove]

I still don't get this part

[cosmic raptor]

so if i have x + 5 = y
and x = 4
i can swap x with 4 in the first equation
and get 4 + 5 = 9 = y

[copper grove]

Ohhh I'm slowly getting it a bit

[cosmic raptor]

that's good!

keep pushing!

[copper grove]

So like how will I write the equation

Like the next step

[cosmic raptor]

4 + 5(x^2 - 2x + 1)

[copper grove]

Ohhhh

What do I do next after this

[cosmic raptor]

now simplify

distribute constants

then add like terms

[copper grove]

Wait I don't get it

[cosmic raptor]

so we can use the distributive property on 5(x^2 - 2x + 1)

to distribute the 5 among each of the terms

giving us 5 * x^2 - 5 * 2x + 5 * 1

or 5x^2 - 10x + 5

[copper grove]

I'm still confused at that part

[cosmic raptor]

the distributive property says that if you have something like 5(a+b)

you can distribute the number on the outside

by multiplying every number on the inside by it

so if we had 5(3+4)

we could do 5 * 3 + 5 * 4

which equals 15 + 20 = 35

[copper grove]

Ohh okok I'm getting it a tiny bit

[cosmic raptor]

we can verify this works by simplifying the inside of the parentheses first
5(3+4) = 5(7) = 35

[copper grove]

Ohhh

[cosmic raptor]

now we can't simplify the inside of our parenthese in our problem since its all variables

but we can use the distributive property

since we know it'll give us the right answer

[copper grove]

Ohhh

[copper grove]

Could you explain this moree

[cosmic raptor]

$5(x^{2}-2x+1) = (5\cdot x^{2}) + (5 \cdot -2x) + (5\cdot 1)$

[jolly parrot]

890s

[copper grove]

Okok wait

[copper grove]

So like 5 * x² is 5x²?

[cosmic raptor]

yes

[copper grove]

OH

OHHH

Okayy so after this what do I do next? Do i add 5 and 4 to get 9

[cosmic raptor]

yep

and then that's it

[copper grove]

Ohhh okay I got it noww

Thank you soo much I appreciate you for helping me!!

[cosmic raptor]

np!

!done

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

[copper grove]

.close

[pearl pond]

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[pearl pond]

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[uneven smelt]

what does it mean if something is homotopic to the constant map

[fringe robin]

is constant map just everything sent to one constant

[pearl pond]

@uneven smelt Has your question been resolved?

[uneven smelt]

is ot the same as being contractible?

.close

[pearl pond]

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[uneven smelt]

thanks

[marsh tangle]

I am not the most qualified person to be answering/questioning this but a topological space X is contractible if the identity map on X is null-homotopic right? so how are they same?

[uneven smelt]

.open

.reopen

[pearl pond]

✅

[uneven smelt]

sorry i meant

if every map from X is homotopic to the constant map, would the space X be contractible?

[marsh tangle]

I think you're right

[uneven smelt]

thank you

[marsh tangle]

I genuinely can't think of a proof but it feels right

[uneven smelt]

#alg-top-geo-top

.close

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[inland plank]

i tried to solve a linear system by elimination, both the x and y variable were eliminated. But the constant on the right is not zero. What does this mean?

[inland plank]

i also had a similar problem but the constant on the right became zero, what does this also mean?

[cosmic raptor]

no solution: the lines are parallel

[cosmic raptor]

infinite solutions: they are the same line

[inland plank]

if i leave it as 0=0 as the answer is that okay? i dont have to find y or x?

the instruction is solve each system by elimination

[simple jasper]

You can, you can also put like "infinitely many solutions"

Typically you will either put (x, y), no solution, infinitely many solutions

[inland plank]

alright thank y'all

.close

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[uneven smelt]

we get homology groups by taking the boundary maps between n skeletons and taking ker n/im n+1 right. and it kinda means n holes in a space?

cohomology is similar but instead we look at boundary maps between maps from a n skeleton to a graded ring? not sure what it means help please

[uneven smelt]

@versed mica hi

@midnight haven ambassador chan

[pearl pond]

Please do not ping individual helpers unprompted.

[midnight haven]

holy fuck

😭

[uneven smelt]

D:

[midnight haven]

erm what the sigma is topology

[uneven smelt]

u asked me to go back to topology :(

[midnight haven]

I feel harassed by that problem

[uneven smelt]

werent u the ambassador D:

[midnight haven]

ambassador to 4th grade problems yes

[uneven smelt]

oh

close enough

[midnight haven]

real

[uneven smelt]

howd u figure i did topology anyway

[midnight haven]

I am stalking you 😊

[uneven smelt]

aww 😊

[midnight haven]

😊

why is topology

[versed mica]

this what not a question maam/sir/it

[uneven smelt]

it issss

im asking for clarification on what homology and cohomology means

[versed mica]

refer to the textbook you stole this from

[uneven smelt]

..

[midnight haven]

did you just start topology or?🤔

nvm you're postgrad, orz

[midnight haven]

respect your elders

[uneven smelt]

kinda yea

[versed mica]

we can tell

[uneven smelt]

then helppppppppppppp

[midnight haven]

I think knief likes you

[versed mica]

beggars can’t be choosers

[uneven smelt]

so true

help please knief

[uneven smelt]

i think we all like me

[midnight haven]

real shit, I can relate to that

[versed mica]

no you cant

[midnight haven]

I like their pfp though

[uneven smelt]

me?

[versed mica]

!vol

[pearl pond]

Helpers are just people volunteering their time to help you. Be polite and patient.

[uneven smelt]

wowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

[uneven smelt]

u just said

[midnight haven]

I bet knief is blushing right now

[versed mica]

topology is far too remedial for me to partake in

perhaps you can refer to:

https://discord.com/channels/268882317391429632/326138737606262786

[uneven smelt]

u were doing quadratics earlier

[midnight haven]

"topology without tears" is what I am procastinating to do

[midnight haven]

that's my level 😭

mine*

[uneven smelt]

whats remedial

[versed mica]

😂😂😂

[midnight haven]

quadratic problems 😈
topology 😨

[versed mica]

are you kidding

[midnight haven]

nah they're blushing, just like you.

it's joeover

as the ambassador to the community

[uneven smelt]

[versed mica]

i don’t doubt it

[midnight haven]

damn it's 5:36

[versed mica]

cap

it’s 1137

[fossil jewel]

You e daters are all weird

[midnight haven]

American

[midnight haven]

nah bro it's just topology istg

[uneven smelt]

@fossil jewel help

[versed mica]

coak said edater

😂😂😂

[fossil jewel]

Am or pm?

[midnight haven]

coak thinks we're like him 😂

[versed mica]

pm

[fossil jewel]

Strange

[uneven smelt]

not like the other girls

[versed mica]

everyone needs a sense of community

[midnight haven]

foreal man

[versed mica]

indeed

[midnight haven]

so sigma

[midnight haven]

so you're a sigma girl?

W

[versed mica]

this isn’t rizz bro

[midnight haven]

how do I rizz up a topology girl anyway

[versed mica]

wild

maybe coak was right about you

[midnight haven]

impossible

[versed mica]

😹😹😹

[midnight haven]

nah coak is the edater

I am just trolling

[fossil jewel]

Hey babe I see your sets are closed

[versed mica]

pause

[fossil jewel]

Let me open them

[midnight haven]

high school ah math rizz😭

[uneven smelt]

u help them with topology

[versed mica]

steady state head conduction is a minor

[midnight haven]

Our love is like the topology on A and B {{},{A,B},{A}}: it's not discrete, and everything else is trivial (down to homeomorphism).

[versed mica]

.close

[pearl pond]

Channel closed

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Use .reopen if this was a mistake.

[midnight haven]

real

[uneven smelt]

:(

[versed mica]

!nogpt

[pearl pond]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[midnight haven]

it's not gpt

bruh

[pearl pond]

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[craggy yew]

can someone double check this for me?

[deft jacinth]

so small

[versed mica]

blurry ahh

[vital estuary]

looks fine to me

both picture wise and solution wise

[craggy yew]

thanks

alr im done here

.close

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[mint ridge]

is there anything wrong with this

[unborn abyss]

that seems right to me

[fleet sky]

looks correect

[midnight haven]

it is correct

you should talk to your teacher @mint ridge

or just let it go, shit happens in online assignments

[mint ridge]

LOL!!

i thought i was crazy thanks guys

.close

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[frozen wharf]

pretty sure the answer is c

if i m not wrong its c right?

i mean b

20 ft

[next dove]

none of the b and c

[frozen wharf]

then?

is it d then?

[next dove]

yeah

[frozen wharf]

alr so i add in the value of the ground

gotcha

ty

.clsoe

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[iron gate]

Such an innocent looking inequality is giving me trouble

[iron gate]

Nvm I got it

.close

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[pearl sundial]

I’ve gotten to sin7theta =-1

And got the two solution -pi/2 and pi/3

It’s saying there’s two more in the mark scheme

How am I supposed to know how many distinct solutions it has?

[pearl pond]

@pearl sundial Has your question been resolved?

[pearl pond]

@pearl sundial Has your question been resolved?

[pearl pond]

@pearl sundial Has your question been resolved?

[snow seal]

What equations solution is this?

[pearl sundial]

Part b

I subbed all of the above for sin7theta

[snow seal]

I think you saying sin(-pi/2) ?

[pearl sundial]

Wdym

I got 7theta = -pi/2

Which is in the ms

[snow seal]

In part b there is polynomial and solution cannot be -pi/2

Because pi is transcedental

Its not very nice with polynomials

Maybe you find sin(-pi/2)=-1 is solution?

Its very interesting for me how you solve it because i think a litle and there are cosines. How you get rid of cosines?

[merry carbon]

(as in you found 7theta to be pi/3? How?)

[pearl sundial]

Wait my bad pi/3 isn’t it

3pi/2

[pearl sundial]

The actual one would be -pi/14 I think

Because that’s 7theta

It’s also go

-5pi/2

And 7pi/2

How do I know how many distinct solutions to look for?

[snow seal]

How you get this solutions? They are θ ?

[merry carbon]

Well, you'd have at most 7, as that's a polynomial of degree 7

[pearl sundial]

I see

But this is only 4

[merry carbon]

(whether you'd get up to 7 distinct ones, is another matter-)

[pearl sundial]

Sin^-1(-1)

[pearl sundial]

I also don’t know what this means

[pearl sundial]

How do I know how many to look for?

[merry carbon]

Anyways, from those, you can always check whether sin(theta) gets you distinct ones, though of course remember that all solutions you find would be restricted to the range [-1, 1]

[pearl sundial]

I don’t follow sorry

[snow seal]

Actually its easy just set sin7θ =0

[pearl sundial]

Wdym

Is that to find how many solutions there are?

[snow seal]

If you set that value you get polynomial with variable sin θ

[merry carbon]

As in, if you're considering real solutions, the way you're going about it, setting x = sin(theta) will get you solutions between -1 and 1 inclusive, as that's the range of sin for real inputs

[pearl sundial]

Ahh I see

Of and here

The range is -7 and 7

Before we change to theta?

From 7theta

Ah ok

[snow seal]

to find possible solutions

[pearl sundial]

Hmm

But like 7pi/2> 1

[merry carbon]

Maybe so, but remember that you're effectively making the substitution x = sin(theta) to turn this into 1 + sin(7theta) = 0

[pearl sundial]

Ye

Sorry I’m still not quite getting it

[merry carbon]

That substitution, x = sin(theta), while theta needn't be restricted in itself, you will have sin(theta), and so x, between -1 and 1 for as long as theta is real

[pearl sundial]

Ok I see

And if I keep adding 2pi eventually it’s over?

[pearl sundial]

How do I use this

To determin home many

[merry carbon]

The values you found [or will end up finding] for theta, -pi/14, 3pi/14, -5pi/14 and pi/2, each give you a distinct choice of x, of course

[pearl sundial]

Ohh so with each of them

[merry carbon]

There are at least two more I think you can find too

[pearl sundial]

X is different

There’s only 4 on the solution sheet

So whilst 7theta is the same

X itself is different?

[merry carbon]

Well, you can find 7theta, then theta, then x from x = sin(theta), at least that's what I think they want you to do?

[merry carbon]

(actually, I say that, but haven't verified any of them, so there's that )

[pearl sundial]

Ok I think I get it now

Thank you

-rep

.close

[pearl pond]

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[merry carbon]

.reopen

[pearl pond]

✅

[fallen acorn]

chartbit goated as always

[merry carbon]

I thought you were gonna correct me or point out something I'd missed

[nimble osprey]

TRUE

[merry carbon]

.close

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[merry carbon]

[pearl pond]

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[restive wedge]

i have a quick question

[restive wedge]

i just did this and like i just realize i mightve forgotten something

or i jsut done need it

right

so

previously i converted cos7x into this

right

by using

this formula

now

the red underlined one

is that i have up top

i completely forgot about the yellow underlined one

does that matter

or not?

[pearl pond]

@restive wedge Has your question been resolved?

[pearl pond]

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[true narwhal]

is a percent discount a linear increase?

[true narwhal]

I was doing an sat practice question and it said there was a discount on an item and i picked linear decrease and I got it wrong

why is it an increase even though the discount is causing the price to go down

[strong jackal]

Can u send the full question ?

[true narwhal]

i dont actually have it. I did the question a while ago but I remembered it rn.

I do remember what the question was about though

it was talking about like a pair of jeans and there was a discount and the options were either linear increase or decrease or exponential growth or decay

[elfin cloud]

It is not linear

A percentage is exponential

[true narwhal]

so if the price of the jeans get discounted by 50 percent

thats exponential?

[elfin cloud]

You have to look at it in a broader sense

If i have a pair of jeans worth 10 bucks

I discount then by 50%

It becomes 5 bucks

Now I discount them again by 50%

[true narwhal]

nah theres no second discount though

[elfin cloud]

Now it is 2.5 bucks

[true narwhal]

its one and done

[elfin cloud]

A one and done thing cant be linear or exponential to my knowledge because there isnt a pattern

I would think your question was asking about the percentage fact

And percentages are exponential

[true narwhal]

dang

[elfin cloud]

It would be exponential decrease in price by 1 time unit

[true narwhal]

i can't remember the whole question so thats mb

[elfin cloud]

Original price * 0.5 ^ t

Where t is the amount of times the discount is added

[true narwhal]

if a discount increases is that a linear increase?

so if the discount was -10 and it became -12

is that a linear increase or decrease?

[elfin cloud]

It would only be linear if the discount is a constant

So a 10 bucks discount would be linear

And id the price goes down yes thats a decrease

So from -10 to -12 would be a -2 decrease

[true narwhal]

yeah i hjad a question like that but i got it wrong after i pout decrease

my tutor just said its actually an increase

bc the discount is increasing

which confused me like crAZY

[elfin cloud]

Would be impossible for me to tell you right now without having the question

But yes it could have been they were asking about rhe discount apecifically which is indeed frustrating

But impossible for me to say right now

Only thing I can tell you right now is carefully read what they are asking about

If they ask about the discount and not about the price of the jeans it could make a difference in the answer

[true narwhal]

Ok thanks

.close

[pearl pond]

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[midnight haven]

yo

can someone help me

[pearl pond]

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[wintry wave]

This is a question on my homework from discrete structures.

How am I supposed to match the arrow diagrams if no function or relation definition is given?

[eternal tulip]

a function is a relation from X to Y such that every x in X corresponds exactly one y in Y

[merry carbon]

(exactly one )

[wintry wave]

Oh so all the numbers with one arrow then?

Going to different ones of course

[eternal tulip]

yes. I was getting confused with surjectivity. I mean to say that not ALL ys in Y need to have a corresponding x

[merry carbon]

It's easy to end up mixing the words up, I always end up doing that

[eternal tulip]

every x must have only one arrow coming out of it

if it has multiple, its not a function

[wintry wave]

More simple than I thought, thank you guys

[eternal tulip]

for example you see why (c) is not a function

(look at 4 in the X set)

[pearl pond]

@wintry wave Has your question been resolved?

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[tough narwhal]

Help me

[tough narwhal]

I am alright?

[merry carbon]

You can't pull the e^x out of the integral, because it depends on u

furthermore, why'd you rewrite the e^x to u - 1

[tough narwhal]

I cant?

Because e^x = u-1

[merry carbon]

You can't pull anything that isn't constant with respect to what you're integrating with respect to out of the integral, no
and, take a look at what you've basically written, if you didn't rewrite it [e^x as u - 1], what would you have?

[tough narwhal]

1/ex

But i font understand i can see that method

I dont*

For example

[light vale]

how do u solve the d bit of this

[tough narwhal]

.

[pearl pond]

@tough narwhal Has your question been resolved?

[pearl pond]

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[merry carbon]

.in this one, you don’t need to remove any terms in the integral, but in the one you were doing, you (should!) have noticed that the substitution also gets rid of the e^x you had there

[west bluff]

I and III are pretty much trivial, but I need some help with 2

[west bluff]

I know what we're doing is moving the point of inflection to x=0, but I don't get how that geometrically leads to the quadratic term vanishing

[cursive wraith]

the point of inflection is where you have Y'' = 0

what does the quadratic term represent in terms of Y?

[west bluff]

Yup

[west bluff]

I don't get the question

Wait, do you mean it defines the x coordinate of the point of inflection?

[cursive wraith]

say that after substitution you get Y = x^3 + ax^2 + bx + c

what does a represent?

[west bluff]

The coefficient of the quadratic term?

[cursive wraith]

yes, and how can you find it using Y and its derivatives?

[west bluff]

And -3 times the x coordinate of the point of inflection of f

[west bluff]

Well, it'll need to vanish in the point of inflection

Wait

Would the fact that we're moving the graph so that a is specifically 0 be enough to solve this?

[cursive wraith]

we don't know that a is 0 yet

we know that we moved to "0 is the point of inflection"

what does this mean about Y

[west bluff]

That -A/3 must be 0

?

[cursive wraith]

huh?

no

not -A/3

[west bluff]

Well, and that it changes concavity at the intersection with the x axis

[cursive wraith]

-a/3, i would say yes

[west bluff]

Hm, alright

So all I needed to notice was that I was moving the graph so the x coordinate of the point of inflection was 0

[cursive wraith]

you get it right? since for any cubic X^3 + AX^2 + BX + C the inflection point is at -A/3

and when we do the substitution X = x - A/3, we have two pieces of knowledge:

• Y = x^3 + ax^2 + bx + c is the form of the new cubic
• the inflection point is moved to x = 0

so the inflection point is simultaneously at -a/3 and 0

-a/3 = 0

a = 0

[west bluff]

Alright, now I got it

Thank you

.close

[pearl pond]

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[jaunty jacinth]

How do we tell if a limit increases or decreases without bound

[jaunty jacinth]

Wait my bad wrong Pic

[spare lark]

Wdym by "limit increases or decreases" ?

[jaunty jacinth]

well the answer is does not exist right, the answer requires you to explain why (it says the answer is decreases without bound as x approaches -3 from the left) but idk how to tell that without graphing

[spare lark]

It does exist, since sqrt(x^2-9) goes to 0+, at x = -3 coming from the left, it decreased without bound, the limit is -inf

[jaunty jacinth]

oh, so how do you tell if it is increasing or decreasing tho

[feral sedge]

Whether it's negative or positive

[spare lark]

The function ?

[feral sedge]

It can't go to infinity if it's negative

[spare lark]

?

-inf ?

[hot aspen]

Sorry thought x is approaching 0, it is -infinity

[feral sedge]

If the function is negative when x<-3 it won't be going to +infinity

[hot aspen]

"-3/0+"

[jaunty jacinth]

ok ty

[spare lark]

Ok i get what you said

[feral sedge]

np

[jaunty jacinth]

.close

[pearl pond]

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[pearl pond]

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[candid solar]

This problem is asking me to: "write an expression in factored form for the area of the shaded portion in the figure."

How do I go on solving this?

[green dew]

js calcumate the area of that big blue rectangle at the middle

then the two small vertical rectangles

at the sides

[candid solar]

what do i do with the x's?

@green dew

[green dew]

ur gonna keep them

theyre js there

ur not gonna solve for them

[candid solar]

cuz like they want me to create an expression instead of solving it

and have it come into factored form

[green dew]

yeah

cause theres an x

they ask for a factored form

there is no reason to ask for a factored form

if u can find x

[candid solar]

oh ok

[green dew]

theres an easier way to do this

u can calculate this by thinking this is a rectangle

so u multipply 8 and 18

then subtract the four squares

that are on the edges

makes it easier for factoring too

[candid solar]

so it'll be (8*18)-(4(2))?

[green dew]

2?

[candid solar]

where would i find the expressions for the issing squares

missing*

[green dew]

u know the squares that im talking about on the image?

on the edge of this blue rectangle?

[candid solar]

yes

u mean the corner squares or the 2 rectangles?

[green dew]

do yk how to find their area?

[green dew]

corner squares

[candid solar]

ik the formula for it

[green dew]

ok

whats the lenght of these squares?

they all have the same length for their sides

[candid solar]

x

[green dew]

exactly

[candid solar]

?

[green dew]

so whats their area

[candid solar]

x2

[green dew]

each square has an area of x^2

what about all the 4?

[candid solar]

4x^2

?

[green dew]

yes

do yk how to find the area of that blue figure

if it were a rectangle?

[candid solar]

l*w

[green dew]

substitute values

[candid solar]

so would the expression be like (18*8) - (4(x^2))??

[green dew]

bravo

wait no

why 18*4?

[candid solar]

mistype

[green dew]

what was it meant to be then

oh ok

bravo

now factor it out

whats the GCF

between those two terms

[candid solar]

4

[green dew]

perfect

[candid solar]

so when simplified i'd get 4(36)(-x^2) as my result?

[green dew]

u add two useless parentheses that make this look wrong

added*

[candid solar]

oh sohot

[green dew]

do yk where ur at fault?

[candid solar]

yea

[green dew]

fix it then

[candid solar]

4(36)4(-x^2)

i think that's how it is for factored form

[green dew]

nooo

the factoring formula (or distributive relation) says that;

ab + ac = a(b+c)

[green dew]

this doesnt follow it

[candid solar]

ohh so
4(36-x^2)?

[green dew]

bravoo

[candid solar]

mb about that

[green dew]

now u can actually stop there

but

if u wanna flex ur muscles ig

u can still factor it out

ever heard of the difference of two squares?

[candid solar]

ye

[green dew]

isnt 36 and x^2 twoo squares?

[candid solar]

yes
(6)^2 - (x)^2
which would be
(6+x)(6-x)?

[green dew]

exactly

now plug that in

in the old expression

[candid solar]

so then all watered down 4(6+x)(6-x)

[green dew]

bravo

ur done now