help-27

[restive river]

So 2 and 14?

hmm

(x,y)

Why did you switch up

Cause you were wrong reading it i told you

No but

Sigh

That's (x=2,y=2) and (x=8,y=14)

Always has been

This fucking equation

Clearly says something else

Oh

OMG

Give me a second for my eyes to adjust

Lmao cause what’s happening

It's not a math problem it's a reading problem lol

look its 1 in the morning

and I have 6 math assignments Idk how to do due by midnight

im trying my hardest

Yeah

Well i hope you're good with the slope being 2 now

Huh?

Oh yes

I am

Bro

You don’t know how much you just helped me

With this 1 math assignment

5 more to go

Wait

Wait

It’s done some stupid shit again

godspeed

It just asked me

To find the table values

And decimals and some shit

I figured it out

How do I round this to the third decimal

Wait you don’t

Cause of the four

I need help with the last question about function notation

how do I figure out how to solve the function notatino

I have no idea what im looking for here

[devout snow]

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[keen copper]

how do I solve quadratic Equations

[shy fable]

you can use the formula

substitute your values

[keen copper]

alr

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[toxic reef]

Given the set of ordered pairs defined on the Cartesian product V = {0,1,2} x {0,1,2}. I define an addition and multiplication operations table. So I know V is a vector space.

[toxic reef]

My question is how to find a subspace of V with dimension = 1? And how to verify it is also a vector space ?

[wicked turtle]

in any vector space, you can choose any specific nonzero vector v, then the set of all scalar multiples of v is a 1-dimensional subspace

[toxic reef]

So something like {1} ?

[wicked turtle]

that's not even an element of V, is it?

[toxic reef]

To my understand V = {(0,1),(0,2),...}

[wicked turtle]

right

[toxic reef]

so select 1 vector is like {(0,1)} ?

[wicked turtle]

right

then take all scalar multiples of that vector

[toxic reef]

but I cannot prove it is closed under addition

[wicked turtle]

why not?

v + v = 2v

for example

which is a scalar multiple of v

more generally,

av + bv = (a+b)v

[toxic reef]

I got an addition and multiplication table

[wicked turtle]

sure, the usual arithmetic on Z3

[toxic reef]

How can prove it is a vector space ?

[wicked turtle]

i thought you already did that

[toxic reef]

I prove V as a vector space with 10 axioms, do I need to do the same with {(0,1)}?

[wicked turtle]

no it inherits the axioms from V, you just need to show that it's closed under addition and scalar multiplication

[toxic reef]

but (0,1) is a vector right? I remember something about subspace has a null vector, so need something like (0,0)?

[wicked turtle]

(0,1) is a vector

i am not saying that {(0,1)} is a subspace

i said you have to take the set of all scalar multiples of (0,1)

which is: {(0,0), (0,1), (0,2)}

show that this set is closed under addition and scalar multiplication

[toxic reef]

I got it now. Can I ask about dimension? dimension is about number of vectors in a space, {(0,0), (0,1), (0,2)} has dimension of 3?

[wicked turtle]

no

the dimension is the number of vectors in a basis of the space

you can show that {(0,1)} is a basis for {(0,0), (0,1), (0,2)}

btw, your entire space V only has dimension 2

a basis for V is {(1,0), (0,1)}

[toxic reef]

you talk about the V = {0,1,2} x {0,1,2} ?

[wicked turtle]

yes

[toxic reef]

I thought its dimension = 3? like (1,0,0),(0,1,0),(0,0,1) ?

[wicked turtle]

there are only two coordinates

the elements of V are vectors like (0,1) or (1,2)

not (1,0,0)

[toxic reef]

Oh got it now

Thank you so muchh

you are better than any materials to me 😂

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[dense monolith]

Hello, I am really stuck in these two problems and do not know from where to start

[dense monolith]

Does anyone know how to solve them?

<@&286206848099549185>

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[craggy shard]

2/ -3 answer in fractions

[craggy shard]

is it negative 2/3 or 2/-3 ?

[lone ravine]

• 2/3 = 2/(-3)

[craggy shard]

ok

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[tired dew]

$n! > n^m$ where $n >= (2m+1)$ i asked about the base case the other day and im struggling to prove the inductive step for n=k+1

[woven radish]

Samjamhawkeye

[tired dew]

The base case shows that $(2m+1)!>(2m+1)^m$

[woven radish]

Samjamhawkeye

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[tired dew]

$n! > n^m$ where $n >= (2m+1)$ i asked about the base case the other day and im struggling to prove the inductive step for n=k+1

[woven radish]

Samjamhawkeye

[tired dew]

i have got the base case just to put it out there :))

just not the inductive

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[tired dew]

<@&286206848099549185>

[restive river]

You want to prove (n+1)!>(n+1)^m knowing n! > n^m

(n+1)!=n!(n+1)> n^m * (n+1)

Then you want to prove n^m * (n+1)= n^(m+1)*n^m >n^(m+1)>(n+1)^m

So : n^(m+1)>(n+1)^m i don't know how to prove it, maybe with newton's binomial theorem

I don't even know if you need to prove it tbh

What grade are you in anyway?

[tired dew]

first year uni ://

literally the first week back and this is one of the questions

[restive river]

I would just admit n^(m+1)>(n+1)^m for m>=1

[tired dew]

yeah? i mean ive been able to prove the base case. me and my friends were able to get it but proving the inductive stage has been terrible ://

[tired dew]

<@&286206848099549185> Is there anyone that can do this?

[restive river]

Maybe in some early university channel

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[candid urchin]

help please

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@candid urchin Has your question been resolved?

[candid urchin]

<@&286206848099549185>

[stray lark]

|(2(cos[pi/6] + isin[pi/6]))^n|
= |2|^n * |(cos[pi/6] + isin[pi/6])^n|
= 2^n

therefor you need n such that 2^n > 100 (so n > 6) and you need (cos(pi/6)+isin(pi/6))^n to be real
applying de moivre's you can find (cos(pi/6)+isin(pi/6))^n to be cos(n*pi/6)+isin(n*pi/6)
so you need the imaginary component to be 0, sin(n*pi/6) = 0 means n*pi/6=0,pi,2pi,&c so n=0, 6, 12, &c
so your smallest case such that n>6 is 12

I think idk

[candid urchin]

oj

wait

sorry

oh i see

so i can test for on=6

i get 64

so no

12

4096

so ye

theres only 6 and 12, so im guessing answer is C

ah correct

thank you @stray lark

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[main tangle]

given z, what is z^16?, choose between A,B,C,D,E.. there seem to be alot of these kind of questions on my upcoming exam and i have no clue how to solve them

[hollow pollen]

eulers formula

for writing a complex number

[main tangle]

exponential form?

[hollow pollen]

$z = |z|e^{i*arg(z)}$

[woven radish]

Gijs

[hollow pollen]

yes

[main tangle]

this

yea

ok

[hollow pollen]

yeah same thing

[main tangle]

and then just do that form to the power of 16?

[hollow pollen]

yes

and then convert it back

[main tangle]

but what if r=/=1 lmao

[hollow pollen]

?

[main tangle]

1 i mean

having to calculate 2^16 f.eks seems not very nice

[hollow pollen]

$(re^{i\theta})^n = r^ne^{i\theta*n}$

[woven radish]

Gijs

[main tangle]

yes

[hollow pollen]

yeah well luckily r is 1 here

[main tangle]

so thats what im saying

yes it is

but what if im unlucky

is there another way

[hollow pollen]

then you write 2^16

[main tangle]

and just leave it?

[hollow pollen]

yeah

[main tangle]

fair enough haha

[hollow pollen]

my prof wouldnt kill me for that

besides you could just remember 2^10 = 1024

2^6 = 64

2^16 = 1024*64 = 65536

[main tangle]

💀

thank you tho, ill go continue studying

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[devout snow]

@deep vortex Has your question been resolved?

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[sullen arrow]

Can anyone help me about the question?

[devout snow]

@sullen arrow Has your question been resolved?

[devout snow]

@sullen arrow Has your question been resolved?

[restive river]

Which one ?

[sullen arrow]

To show that

$\lim\limits_{t\to\infty}y(t)=M$

[woven radish]

black_tea

[restive river]

I think

Oh no nvm

[sullen arrow]

It's only one question lol

[restive river]

Im french so the language doesnt help

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[sullen arrow]

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[fair pond]

I used squeeze theorem to find that lim of x2cos1/x = 0

Now i need f(b) to = 0 to prove that its continuous

What’s throwing me off is the cos1/x part

Cause cos1/0 gives infinity

And that makes me wonder whether continuity doesnt exist

[restive river]

1/0 is undefined

[fair pond]

So what value of b

Is defined

To prove continuity

[wooden wraith]

This is true

Now you want the function to be continuous at x=0

What is the definition of continuity at a point?

[fair pond]

F(a) = lim x->a f(x)

[wooden wraith]

Right, and if you define b=0, then that is true

[fair pond]

How can you prove cos1/x = 0 tho

If b is 0

That means cos1/x = 0

[wooden wraith]

Why does it mean that?

[fair pond]

Doesnt cos1/x mean its undefined

[wooden wraith]

Only if x=0

But that part of the piecewise function is specifically for where x=/=0

The function is defined as piecewise specifically to avoid that problem

Because the top part isn't defined at 0

But the overall function f is.

Hopefully that makes sense

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[slow glacier]

ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or a.all().

[slow glacier]

Keep getting this error, not sure what to do and I can give the context if needed

[long kettle]

Context would be helpful

[slow glacier]

Ok

whats that command to paste code in again?

buy = train.copy()
sell = train.copy()
buy[zscore_60_5>-1] = 0
sell[zscore_60_5<1] = 0
buy[60:].plot(color='g', linestyle='None', marker='^')
sell[60:].plot(color='r', linestyle='None', marker='^')
x1, x2, y1, y2 = plt.axis()
plt.axis((x1, x2, ratios.min(), ratios.max()))
plt.legend(['Ratio', 'Buy Signal', 'Sell Signal'])
plt.show()```

This is the block I have rn Im just trying to like graph something

plt.axis((x1, x2, ratios.min(), ratios.max()))```

just having problems with these two lines

oh wait shit this is the math server

idk if i can still ask here

[long kettle]

It's probably fine

[slow glacier]

Oh alright, yeah Im just having trouble with the plotting

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[muted sierra]

https://cdn.discordapp.com/attachments/486841085210132490/1026353228809502751/unknown.png

[muted sierra]

would this be the correct answer?

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[misty dirge]

Hi all. I'm just a bit stuck on how to find r in this case!? Thanks :D

[misty dirge]

I was thinking of using the quadratic formula or polynomial solver on a graphics calculator but I don't know what to do with the r^2 in the denominator

[main coyote]

I think you multiply both sides by r^2? since r != 0 anyways

[misty dirge]

Can i multiply the left side with r^2?

[main coyote]

0 * r^2 = 0 owell

[misty dirge]

I was thinking about that too, is it valid to do so?

[main coyote]

i think it is

[misty dirge]

So it would be 0 = -750 + 4pi r^3 right?

[main coyote]

yeah and from here it's pretty obv what to do

[misty dirge]

okey, thank u bro

[main coyote]

[misty dirge]

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[candid urchin]

m1a= T-m1gsin(theta)

m2a=m2g-T

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[candid urchin]

.reopen

[devout snow]

✅

[candid urchin]

.close

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[silk island]

hello is there anybody eho is good at math please? need help with f2=y + 3.|x+1|

[silk island]

<@&286206848099549185>

pls it is urgent my life depends on it

[plain prism]

ok

[silk island]

i need a graph

[plain prism]

do u have the original problen

problem

[silk island]

yes

[plain prism]

can i pls see

[silk island]

f2

please hurry

[plain prism]

i see

[restive river]

just use desmos

[silk island]

all i need is graph

[plain prism]

i dont understand the period

[silk island]

what is desmos

[plain prism]

does anyone know what it could mean?

it's a graphing utility

https://desmos.com

[silk island]

WHAT

[timid fractal]

how do you even graph that

isnt that a line?

[restive river]

no

[plain prism]

u can graph this

its just that i dont understand the period

[timid fractal]

oh its subscript

i have no idea what that means

[restive river]

you have to make 2 cases

x<-1 and x>-1

[plain prism]

I'll just assume it's a 3

[restive river]

which gives you
y = x^2 -3x -3 for x<-1

and y = x^2 + 3x + 3 for x>-1

[plain prism]

r u sure

[restive river]

Now complete the square to find the equation of the parabolas

[restive river]

what do you think is wrong

[plain prism]

nothing

[silk island]

thank you so much

[plain prism]

yw

[silk island]

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[plain prism]

have a nice day

[devout snow]

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[orchid lake]

can someone help me get the solution for this? (composition of functions)

[orchid lake]

if possible something like this

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[orchid lake]

<@&286206848099549185>

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@orchid lake Has your question been resolved?

[violet wind]

Where can you use kilometers

what equation could you put trip distance in

[orchid lake]

this is the original problem

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[gleaming socket]

Find f(x) and g(x) first

Wait it's already given

So find g(f(x)) since f(x) is independent and g(x) is dependent

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[restive river]

Is there something like similarity of 3D shapes?

[pseudo basin]

sure is

and volumes of similar shapes scale cubically

i.e. if the scaling factor between two shapes is k then their ratio of volumes is k^3

[restive river]

Thought so.

Does this problem have all the necessary information?

[restive river]

Can I assume like h1/h2 = B1/B2?

[pseudo basin]

no

[restive river]

B is the base area.

Okok

[pseudo basin]

yes it does

[restive river]

Let me try once more then. Let's see if knowing this would help me psychologically lol.

[restive river]

What about H1/H2 = h1/h2 where H is the height of the pyramid and h is the height of the triangle?

[pseudo basin]

uhhh

well you could do that

but it will not help you much

[restive river]

okok

[restive river]

I cannot seem to make any progress. May I get some hints?

Or an approach?

[pseudo basin]

volumes of similar shapes scale cubically
i.e. if the scaling factor between two shapes is k then their ratio of volumes is k^3

you know the ratio of volumes for the big pyramid and the small pyramid

find their scale factor

[restive river]

oh

GOT IT!

[restive river]

So, h = 12/cbrt(3)?

like

0.5 = 1/k^3

[pseudo basin]

yes, the height of the small pyramid is 12/cbrt(2)

i assume this was a typo on your part and you meant cbrt(2) and not cbrt(3)

[restive river]

AH yes.

Thank you so much !!

[restive river]

Crucial information that I overlooked.

.close

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[restive river]

hi

[restive river]

can someone help me

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[placid hedge]

hi

[tawdry wave]

how would I answer this using separable differential equations I used physics but not idea how to do it the calculus way

would it be dv/dt = g ?

[devout snow]

@tawdry wave Has your question been resolved?

[restive river]

nope

g is acceleration

[tawdry wave]

But isn't the derivate of velocity acceleration ?

<@&286206848099549185>

[hasty atlas]

Yes

[hasty atlas]

Nope

Here g is constant

Use Time of flight = 2u/g

[tawdry wave]

I was trying to find the answer using separable differentiable equation I use physics to find the answer the firs time

[hasty atlas]

Why are you using integration and differentiation here?

Here acceleration is constant right?

[tawdry wave]

im not really sure my its from my homework for that section

[hasty atlas]

Even if you use it , you'll get the same result

Oh

[tawdry wave]

alll the other questions it was obvious to use separable equations

this one was not so obvious for me

so was wondering how I go from the word problem to a separable differentiable equation

[devout snow]

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[tawdry wave]

<@&286206848099549185>

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[restive river]

i need help with this and where to start

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[tall marlin]

a

[tall marlin]

this is what i got so far

how would i find x and dx/dt

idk if im correct for x

[remote meteor]

1. let h be depth of fluid at time t, let r be radius of surface of liquid at time t

2. differentiate with respect to t

3. use dv/dt = 2, h=8

[tall marlin]

yeah but what is r when h = 8

and how would i find dx/dt

[remote meteor]

By similar triangles
r/h = 4/16

r = h/4

Then find volume

pi/3 • (h/4)^2 • h

[tall marlin]

what would i use the volume for

[remote meteor]

Differentiate implicitly

dV/dt = 3pi•h^2 / 48 • dh/dt

[tall marlin]

Like this?

.close

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[crimson knoll]

12 students from each of Engineering, Science, Humanities, and Social Science were nominated to represent their faculties. 9 of these 48 students will be randomly chosen to be on the student council. Find the probability that at least one of the four faculties will be unrepresented on the student council.

kinda stuck on the question, i think a straightforward solution is to just calculate 1 - probability when all groups are represented however I can't wrap my head around how i'd find that. the other solution I see is I make cases when a group is included or not and use the inclusion exclusion principle? any hints? thanks!

[devout snow]

@crimson knoll Has your question been resolved?

[crimson knoll]

<@&286206848099549185>

[solid spire]

Think of it like colored balls in a sack

12 green, red, blue and yellow

What's the probability you don't get any reds for example

Mb should be 9 difference

@crimson knoll

[crimson knoll]

i see

why do you do product?

shouldn't it be sum?

@solid spire

[solid spire]

Let me see

Yeah I think so

Mb

[crimson knoll]

what happens when its 12/48?

like

um, not sure if I understand properly still..

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[hollow onyx]

how did this happen?

[grim burrow]

distribute the a inside, and then subtract axy' on both sides

and then just factor y' out of the common terms and solve

[restive river]

Help

I have aids

[devout snow]

@hollow onyx Has your question been resolved?

[hollow onyx]

subtract axy' both sides?

[grim burrow]

yes

[hollow onyx]

how does that look like

[grim burrow]

uhh you just subtract both sides by axy'

put a -axy' on both sides of the equal sign

[hollow onyx]

yeh i get that but idk if i did it right

like uhh

wait

[grim burrow]

send me a screenshot

im too lazy rn to latex

[hollow onyx]

apologies for the hand writing

its morning and im dying

[grim burrow]

the first step is correct

but something escalated in the second one

[hollow onyx]

ic

[grim burrow]

by subtracting both sides by axy', this is what i meant

[hollow onyx]

oh just the axy'

[hollow onyx]

i dont see any other common factor other than y'

[grim burrow]

and....it came that i have to latex either way

your equation is wrong

it should be $\frac{1+y'}{2\sqrt{x+y}}-axy'=ay$

[woven radish]

waler

[hollow onyx]

ic

i still dont get how it became like this

[grim burrow]

but yes, the trick is to have a common factor of y'

[grim burrow]

we are getting there

[grim burrow]

can you continue with?

as in do common denominator for the lhs

[hollow onyx]

oh ok leme try

ah i forgot the 2 in the 2nd pictures denominator

actually ama fix my hand writing

did i do this right?

[grim burrow]

yes

now simplify everything and factor out y' if possible

[hollow onyx]

ok so

that i dunno how to do

;-;

[grim burrow]

that's just algebra...

[hollow onyx]

yeh i forgot tha

[grim burrow]

can you combine the fraction for me?

[grim burrow]

right, sorry, had to do sth

yes, everything looks good

so bascially what you have now is just $$\frac{1+y'-2axy'\sqrt{x+y}}{2\sqrt{x+y}}=ay$$ correct?

[woven radish]

waler

[hollow onyx]

OH

im so dumb

or maybe im sleepy

i cant sleep yet cause i have to do and understand many things ;;-;

[grim burrow]

right, i'll take that as a you know what to do now

[hollow onyx]

yes ty

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[echo lion]

why is 2pi/3 equal to 3

[jovial crane]

Is it?

[echo lion]

2pi/k

for period right?

why is it 3

im watching a tutorial and i dont understand

[potent nebula]

they probably want you to find k

[grim agate]

maybe its best if you post the actual thing like photo maybe

[potent nebula]

yeah

right

[echo lion]

ok

sry

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[nimble plinth]

is it

(-1)^n * something * (x+9)^(-1-n)

<@&286206848099549185>

[jovial crane]

Heyyy

[nimble plinth]

Hi

[jovial crane]

I don't get the question

[nimble plinth]

need general formula

to derive Derivative

<@&286206848099549185> pls help

[jovial crane]

I don't know how to do that sry

[nimble plinth]

its alr

thanks

anyway

[potent moon]

It should be something similar

[nimble plinth]

im not getting it

[potent moon]

I will have to calculate fully

[nimble plinth]

will appreciate if u do it

[potent moon]

This doesn't fit the second derivative

[nimble plinth]

Oh

[potent moon]

Can you show your work here?

I remember that you need to take multiple derivatives before you see a pattern that you generalize

[nimble plinth]

Im on pc

[nimble plinth]

yeah

but

here we need the general formula

[potent moon]

Yes, you can form that once you see the pattern of the initial derivatives

So find those first

[nimble plinth]

Okay

I tried that but couldn't generalise the Co efficient

its very late where i live, guess ill give it another shot tomorrow

thanks anyway

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[restive river]

Is r! * (r+1) = (r+1)! ?
If so, could someone explain how to get that?

[fossil chasm]

definition of factorial

n! = n * (n-1) * (n-2) * ... * 1

(n+1)! = (n+1) * (n+1 - 1) * (n+1 - 2) * ... * 1

[restive river]

Ohhh

So that statement is correct?

[restive river]

This one

@fossil chasm

[restive river]

yes

Alr thanks

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[tropic blaze]

Hello, can I just see the process of solving this partial fraction?

[tropic blaze]

The teacher gave some really simple examples in class and this was on the HW

I would just like to know how to get from that image to this image below

Ik you'd have to expand the denominator and then divide the polynomial

that gives me 1 + a remainder of (-2x^2 + 10x + 56) / the expanded of (x-1)(x+3)^2

idk how to really do the A B C method

[potent moon]

We do this by Partial Fractions

You can look it up and practise some simpler questions before coming back to this

[potent moon]

Equate this to A/(x-1) + B(x+3) + C(x+3)^2

Then take the LCM

[tropic blaze]

Yeah and then if I multiply them....

Ohhh

[potent moon]

After that, compare the coefficients

[tropic blaze]

the B isn't counted towards them

I was multiplying it like Left side = A*(x+3)^3

with the B denominator

you don't need to

that cleared up a lot of things

I was using complete the square to solve some of them

[devout snow]

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[restive river]

1/4 = 2/8

no bruh

i just said what 1/4 is equal to

that should be more than enough

yee

gang wrong channel

[devout snow]

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[uneven steppe]

need help with p-adics

[uneven steppe]

According to this, in a 3 adic system

|5| = 3 ^ (-1)

|6| = 3 ^ (-1)

|9| = 3 ^ (-2)

which is fine

as the number increase the p-adic evaluation becomes less

but |27/5| would be something like 3 ^ (-(3-1)) = 3 ^ (-2)

27/5 is 5.4

so |5| is 1/3

|6| is 1/3

but |5.4| is 1/9 ????

is that correct

seems very counter intuitive construction

<@&286206848099549185>

[devout snow]

@uneven steppe Has your question been resolved?

[uneven steppe]

no

[devout snow]

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@uneven steppe Has your question been resolved?

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[prime brook]

how would you find the table of values for y = square root 2 ?

[prime brook]

figured it out

.close

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[prime brook]

.reopen

[devout snow]

✅

[prime brook]

no wait i still dont get it sorry

i dont udnerstand how mathaway got those numbers for y

Okay wait NOW i understand it, what a silly question, my apologies

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[restive river]

Can someone please tell me if I did this correctly

[restive river]

For number 6

I got 1/6, 1 and -1 for my zeros

[devout snow]

@restive river Has your question been resolved?

[restive river]

I'm sorry my paper is a mess

But I divided these polynomials and got 2x²-4x+1 with a remainder of -10

Is that correct

Question number 4

<@&286206848099549185>

Pleas

Any1

[dim yoke]

i got the 2x^2-4x+1

[restive river]

Wit a remainder of -10?

[dim yoke]

no instead subtracted by 10/5x-3

its really hard to explain it to you here

let the <@&286206848099549185> do the explaining

[restive river]

Ok

Wym subtracted by 10/5x-3

Dont get that part

[dim yoke]

you want to divide the leading coefficients of the numerator 5x-13 and the divisor 5x-3

multiply 5x-3 by 1

and then subtract 5x-3 from 5x-13 to get new remainder

-10

which means the answer is 5x-13/5x-3 = 1+-10/5x-3

[fierce heath]

you have to put it on top of 5x-3 because of some reason i have no idea about

maybe bec if you multiply it by 5x-3 it will become 10

-10 ≠ -50x+30

[restive river]

Wait so

[restive river]

Dude wtf

I thought the answer was 2x²-4x+1

[restive river]

I'm getting two dif answers now

[fierce heath]

IDK

[restive river]

I'm sory

I'm confussd

And tired

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[rotund dawn]

Why is the answer to c) x = -2?

[rotund dawn]

Or is that not the answer and I'm reading it wrong? Would an undefined slope have no formula for a line passing through the point?

[foggy granite]

your slope is undefined when your line is vertical

[rotund dawn]

only when it's vertical?

[foggy granite]

the line x = -2 is the unique vertical line that goes thru (-2.4)

yes

[rotund dawn]

is there a reason that is?

[foggy granite]

how you gonna have slope when you dont budge in the x direction

change in y/change in x

but change in x is 0 so ur kinda dividing by 0

[rotund dawn]

oooh, like i can divide 0 by any value (except 0)

but i cant divide any value by 0

[foggy granite]

rule 1 of math, never try to divide by 0

[rotund dawn]

so no change in x = undefined cause you can't divide by 0

[foggy granite]

sort of the reason yes

[rotund dawn]

but y=0 and the slope is 0

[foggy granite]

yes

[rotund dawn]

so undefined slope, think of it as y/0

aka not possible

[wild creek]

think of it as "infinitely steep"

[rotund dawn]

ty for the clarification :0

[foggy granite]

to be slightly more rigorous, the reason you cant define a slope is because you need 2 different x points and take their difference

[rotund dawn]

:)*

[foggy granite]

but u got just one point where x is defined

[rotund dawn]

that makes sense

also a good way to think of it

[foggy granite]

both infinitely steep and negative infinitely steep

[wild creek]

yes

[rotund dawn]

so x is just infinitely whatever value the point originally is when the slope is undefined

gotcha

[foggy granite]

yes

in the y direction

with x unchanging

[rotund dawn]

oh wait

im still confused as to why the y isn't included still?

[wild creek]

because y doesnt matter

[foggy granite]

what do you mean by not included

[wild creek]

its litteraly the set of points (x,y) such that x=-2

[rotund dawn]

right

[wild creek]

and y can be whatever

[rotund dawn]

so when the line is horizontal the slope is 0?

and vertical it's undefined?

[foggy granite]

yes

[rotund dawn]

and the reason that is, is because the change in X when the line is vertical = 0, and to find slope it's simply y_1/x_1

and you can't divide by 0

that all sounds good?

ty 🙂

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[jade bobcat]

Hey I need help with Rational and Irrational number:(?

[devout snow]

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[restive river]

how do i integrate this

[grim agate]

split cos^3 as cos^2 * cos

[magic pine]

i prefer cos * cos^2

[grim agate]

how tf is it different

[magic pine]

it isn’t lol

[grim agate]

then use pythagorean identity on cos^2 to get 1-sin^2

and rest is just u sub

[restive river]

Hmm

[wild creek]

linearize using exp def of cos + binomial formula

[grim agate]

[restive river]

do i make u = sin

[grim agate]

[restive river]

i got

1x - ((sinx)^3)/3

i think thats wrong?

[grim agate]

show your work

[bright burrow]

Well you can try using cos3x formula and rearranging it

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@twin harbor Has your question been resolved?

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[dim leaf]

H

[dim leaf]

3x^2-3x-6 this is what i came up with just wanted to check if it's right

[restive river]

Evaluate that quadratic at x=2

[dim leaf]

wdym

[restive river]

Is 3×2^2-3×2-6 > 0?

[dim leaf]

no

[restive river]

Therefore x≠2 so we can simplify

[dim leaf]

wait

[dim leaf]

these are the value of x

x=(-∞,-1) x=(2,+∞)

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[umbral niche]

is this right answer?

<@&286206848099549185>

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@umbral niche Has your question been resolved?

[umbral niche]

.close

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[pearl abyss]

The teacher solved this gradient in class but I don't understand what he did

[pearl abyss]

He used spherical coord and got to this

I don't get how arccos of that is phi

Nvm he just changed his notation for Phi and that confused me lmao

.close

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[restive river]

Can anyone help me with 9

[restive river]

Im not sure how to start

I could start by finding the equation of the tangent

But idk which coordinates to hse

[supple knot]

there are two tangent lines

[restive river]

Ohh

[supple knot]

one at each of the two given points

[restive river]

so there are two equations?

[supple knot]

yes

s means two or more tangents

[restive river]

Oh yes

Sorry I didnt notice that

Wait I will do it

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[reef thicket]

fish with a population of 50 are causing serious problems in a pond. If the population increases by a factor of 5 each year, what will the population be in 8 years' time? Using y=ab^x

[strange arch]

rlly?

[reef thicket]

50(5)^8

is wrong apparently

[strange arch]

why would it be considered incorrect

[reef thicket]

thats why im here lol

[strange arch]

well that's the answer, I don't see any nasty trick statements

[reef thicket]

okay good beacuse i thought i was going insane

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[mild granite]

is this correct?

[umbral creek]

yea seems okay to me

[mild granite]

ok and one more question

[chilly barn]

Q:

[umbral creek]

okay so sin is positive

tan is negative

so which quadrant?

[mild granite]

2

[umbral creek]

yes

now you can draw a triangle

and find out tan

[mild granite]

sense tan= opp/adj

[umbral creek]

yes

but before that

let’s simplify

sinθ is $\frac{\sqrt{12}}{4}$ right

[woven radish]

duckiescute!

[mild granite]

yes

[umbral creek]

can we simplify that

[mild granite]

sqr3/2

[umbral creek]

yea

what is sine

opp/hyp rifhr

right*

so opposite is sqr3

hyp is 2

find adj

and you can get tanθ

just remember to add a negative

since tan is negative in second quadrant

[mild granite]

so would i use a^2+b^2=c^2

[umbral creek]

yes

[mild granite]

so is adj c

[umbral creek]

no

hyp is always c

so use $a^2=\sqrt{c^2 -b^2}$

[woven radish]

duckiescute!

[mild granite]

so a is sqr 3

[umbral creek]

why is a sqr3?

[mild granite]

because opp is a

[umbral creek]

no

here opp is b

a is what you want to find

so a is asm

adj

[mild granite]

so a^2+sqr3=2^2

[umbral creek]

sure

$a^2 +(\sqrt{3})^2 = 2^2$

[woven radish]

duckiescute!

[umbral creek]

solve for a

[mild granite]

so i solved for b and c

so do i subtract or add them together

[umbral creek]

you have this

to solve for a

you want only a on one side

everything else you move to the other side

so how to move the (sqrt3)^2 to the other side?

[mild granite]

you add

[umbral creek]

okay

look at the picture

is a and the sqrt 3 added or minus

[mild granite]

add

[umbral creek]

yes

when you move to other side

you do the opposite sign

what’s opposite of add

[mild granite]

subtract

[umbral creek]

yes

so subtract :)

[mild granite]

so c=1^2

[umbral creek]

yes c is sqrt1

which is

1

[mild granite]

yep

[umbral creek]

so adj is 1

now you can find tan

[mild granite]

so tan is 3

[umbral creek]

are you sure

what is opposite side

the length

[mild granite]

oh so i flip it

[umbral creek]

oh nono

[umbral creek]

^^

what’s the length

for opp

[mild granite]

1

[umbral creek]

that is for adj

[mild granite]

so it would be 3

[umbral creek]

no

[mild granite]

bc hyp is 2

[umbral creek]

remember they say $sinθ= \frac{\sqrt{3}}{2}$

[woven radish]

duckiescute!

[umbral creek]

what is sine

opp/hyp

[mild granite]

yes

[umbral creek]

opp is the top number

hyp is the bottom number

so bottom number 2 so hyp is 2

what is the top number

[umbral creek]

for here

[mild granite]

3