help-10

[onyx belfry]

I used this: https://en.wikipedia.org/wiki/Laplace_expansion

[covert mesa]

I need friends

[onyx belfry]

You should use the fact that if a product of 3 terms is 0, then at least one of the factor is 0, so you can put the factors to 0 and see what you get

[twin vine]

de la primer ecuacion no podes sacar los autovalores donde se anula?

[covert mesa]

Alot od friends needed

How do i find out the area of a house

Idfk how to

Ohh

I knew that

Nc replying

[warm shale]

gmdn

[covert mesa]

U look abf 200 btw

20*

[onyx belfry]

Yes

[twin vine]

-2

[onyx belfry]

Exactly @twin vine

Yes. So now we have to study the subspace $V_3$ and $V_{-3}$ that I wrote earlier

[warm shale]

cristorenzo99

[onyx belfry]

These here!

No problem! I'll give it a try too

We need to study $V_9$ not $V_3$ or $V_{-3}$

[warm shale]

cristorenzo99

gmdn

[onyx belfry]

Put $\alpha=-3$ for example and study what happens if $\lambda=9$

[warm shale]

cristorenzo99

[onyx belfry]

Then do the same with $\alpha=3$

[warm shale]

cristorenzo99

[onyx belfry]

Don't we have also $\alpha+3$ as $a_{2,3}$?

[warm shale]

cristorenzo99

[onyx belfry]

I think it does... because you get two different things to study

Exactly

Ok!

Remember don't study when $\lambda=-2$!

[warm shale]

cristorenzo99

[onyx belfry]

Because it's algebraic mult. is 1, so the geometric one is going to be 1 as well

Yes

I believe it's the opposite

But that property works because of this fact

I got that you can diagonalize the matrix only for $\alpha=-3$

[warm shale]

cristorenzo99

[onyx belfry]

Correct! Check for $\alpha=3$ too

[warm shale]

cristorenzo99

[onyx belfry]

But you don't know why!

[onyx belfry]

Because $1 \leq G.M. \leq A.M.$, if $A.M.=1$, you get:

$1 \leq G.M. \leq 1 \implies G.M. = 1$

[warm shale]

cristorenzo99

[proud sorrel]

Hi

How can I get help

Ah ok

[onyx belfry]

Here you get $\begin{cases} x = 0\ z = 0\end{cases}$ that is a subspace of dimension 1

[warm shale]

cristorenzo99

[onyx belfry]

Don't worry!

Yes

No problem! It's a pleasure!

[obtuse pebble]

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[bleak crest]

Hello, currently learning about Complex numbers and Quaternion from internet. there are some steps they calculate short and I want to confirm to understand better but when I calculate again the result does not match with them. can anyone point out where I calculated wrong?

[bleak crest]

Here is my calculation

[obtuse pebble]

@bleak crest Has your question been resolved?

[bleak crest]

<@&286206848099549185>

[swift grail]

What is the issue dog

dawg

[bleak crest]

I did the cal and the results do not match

idk whats wrong

[swift grail]

Let me check brother

[bleak crest]

ok brother, ty

[swift grail]

Give me 6mins

[bleak crest]

ok brother, take your time

[swift grail]

check your cross product step correctly bro

the last 2nd step

[bleak crest]

cross product, oops I thought I could break the brackets normally.

my brain dead :))

ty brother, now everything make sense

[swift grail]

you can call me daddy

[bleak crest]

love u :)))

anw have a good day

im gonna close this

.close

[obtuse pebble]

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[blazing mason]

rq can someone explain to me how to apply CAST rule

[blazing mason]

like ik the functions are positive in diff quadrants but y do u need to change a ratio to negative

Like y does this become - root 3

[civic zealot]

becase tan(x) = sin(x)/cos(x) and sin(x) is negative in that quadrant, while cos(x) is positive

(-)/(+) = (-)

[blazing mason]

do i slap a negative onto wherever thats negative?

like in q3 it would be negative aswell?

[civic zealot]

wherever what's negative?

[blazing mason]

like sin cos tan

[civic zealot]

in q3, tan(x) is positive.

I assume this is is the CAST rule you're talking about? It tells you which quadrant the main three functions are positive.

[blazing mason]

yea

so basically when I look at my related acute angle

i just find which quadrant it falls under and decide whether its positive or negative?

[civic zealot]

yes

[blazing mason]

what would happen if i convert say sin to cos?

[civic zealot]

in what way?

[civic zealot]

you'd need to check where the angle x is.

[blazing mason]

lets say q1

[civic zealot]

then cos(x) is positive, and x+pi/2 is in q2. so sin(x+pi/2) is positive.

[blazing mason]

cos in q2 is negative so im not following

[civic zealot]

you said x was in q1

[blazing mason]

doesnt it form something like this?

so the angle would be in q2

[civic zealot]

x+pi/2 would be in q2, yes.

[blazing mason]

what would happen for cos to sin

[civic zealot]

cos(x) is positive.
sin(x+pi/2) is also positive.

[blazing mason]

i mean like cos(x +pi/2) = +-sin(x)

[civic zealot]

x+pi/2 is in q2, so is cos(x+pi/2) positive or negative?
x is in q1, so is sin(x) positive or negative?

pick the + or - so that the signs are appropriate.

[blazing mason]

ok so it would be cos(x+ pi/2) = -sinx?

[civic zealot]

yes

[blazing mason]

ok got it

thanks

.close

[obtuse pebble]

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[spring moon]

i have no idea how to even start this

<@&286206848099549185>

[wintry token]

Hello

[spring moon]

hi

can you please help me

im very confused

[wintry token]

Ok

[gritty bolt]

Do you know how to find inverse of a function?

[spring moon]

ya u replace x with y right

[gritty bolt]

f(x) with y

[obtuse pebble]

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[edgy needle]

how would i do this

i think the sin graph is translated 30 degrees?

[ancient drift]

Draw the graph of sin x on the same axes

Then observe the transformations

[edgy needle]

uh

[ancient drift]

Are you sure about that

[edgy needle]

isnt that sinx..

[ancient drift]

The period of sin x is 360

[edgy needle]

um

so 360 divide 4

oh each of my things is 90

[ancient drift]

Yea

[edgy needle]

um

[ancient drift]

Just redraw that again

Yeps

Might also want to draw on the negative side

[edgy needle]

how does this help me

[ancient drift]

Alright now

Look again

[edgy needle]

yea

[ancient drift]

Are you sure the horizontal shift is 30deg?

[edgy needle]

idk..

how do i know

is it 10 degrees

[ancient drift]

Yea

[edgy needle]

oh

[ancient drift]

Then we can find the period of this wave

Which is 90 deg

[edgy needle]

wait why

which wave

oh

ur right

90

[ancient drift]

Yea

[edgy needle]

bc it moves one to right

okok

[ancient drift]

Therefore a is?

[edgy needle]

4

[ancient drift]

Mhm

[edgy needle]

what the heck the asnwer says b is 40

[ancient drift]

Yea

I'm getting to that

b is not necessarily the horizontal shift

[edgy needle]

what the flip

[ancient drift]

sin(a(x+c)) where c is the horizontal shift

Is the way we write the function

[edgy needle]

wow why do they deceive me

in the question

[edgy needle]

they couldve put this!

is it the same for

cos?

[ancient drift]

Well its the same for any wave

They didn't really deceive you at all

That's kinda on you

[edgy needle]

😢

for this is the asymptote

x = 3?

and y = 0

[ancient drift]

No vertical asymptotes here

Just the horizontal one

y=0

[obtuse pebble]

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[dry horizon]

.close

[obtuse pebble]

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[round bobcat]

I dont understand what verticle stretch/shrink is and what horizontal stretch/shrink is. im supposed to understand them and know how to identify them on a graph. the question are example questions that im trying to understand

[tepid yoke]

So you understand horizontal and vertical translations, just not stretch / shrink?

[round bobcat]

no i dont understand that either

[wary badger]

go to khan academy then, you won’t get an entire lecture on that here

we help with specific problems

[round bobcat]

what do i search up on khan academy for this

[wary badger]

transformations of functions

[round bobcat]

alright thanks

are horizontal and verticle translations shift functions?

[wary badger]

what

shift functions?

[round bobcat]

chatgpt said they were the same thing i just asked it lmao

[wary badger]

translation is synonymous with shift if that’s what you meant

[round bobcat]

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[robust hound]

whats the formula for knowing this
25.000 = 100
? = 1

[craggy tundra]

wat

[robust hound]

what

[craggy tundra]

what even is that lol

25.000 = 100?

[brazen gorge]

can you send a picture of the problem you are referring to?

[kind hawk]

you divided on the right by 100, so also divide on the left by 100

some type of proportionality thing probably

[craggy tundra]

☠️

dang how did you get that

[robust hound]

so 25.000 = 100
250 =1?

[frozen fractal]

Dawg we need context

[craggy tundra]

omg it actually is propotionality

[brazen gorge]

yep

but don't use "=" for that ahah

[robust hound]

what do we use

[brazen gorge]

maybe :

[craggy tundra]

-> or smth

[frozen fractal]

: or /

[brazen gorge]

25000 : 100
250 : 1

[craggy tundra]

= means equal

[robust hound]

lol

[craggy tundra]

25000 is not equal to 100

[frozen fractal]

I mean it could be unit conversion

Which is also proportion

[craggy tundra]

also you used . as a separator

i thought it was a decimal

[robust hound]

owh ok

[obtuse pebble]

@robust hound Has your question been resolved?

[obtuse pebble]

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[haughty coyote]

Taylor expansion with remainder formula

[heady turtle]

I know, but it's not alike

[haughty coyote]

then rewrite it to be alike, it's the same thing

[heady turtle]

hmm how to rewrite that...

[haughty coyote]

||f^(6)(xi) x^6 / 6!||

[heady turtle]

ooh wait

tysm got it now

[obtuse pebble]

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[haughty coyote]

that is one way to close a channel

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[surreal wadi]

Can someone tell me how to get cpd and dpb

[surreal wadi]

It feels easy yet I don't understand

[errant galleon]

Are u trying to figure out the angle of angle CPD and angle DPB?

[surreal wadi]

Yep

How to get it

[errant galleon]

does it not say 95°?

[surreal wadi]

I don't think that was the right answer

[errant galleon]

yea that does not look like 95°

is circle's angle is supposed to sum to 360

and a straight line* should sum to 180

[surreal wadi]

So how do you get it? I can't understand the yt videos

[errant galleon]

can you give me like the whole question or the homework? I cant jus look at a wrong diagram and figure out ur task

were u originally given angles? and like supposed to draw them?

@surreal wadi ?

[surreal wadi]

yeah I think we were supposed to figure out the minor arcs and major arcs

[errant galleon]

major arcs r the ones with an angle greater than 180°

if its smaller

its minor arc

[surreal wadi]

So both are major arcs

Do u add or subtract?

[errant galleon]

im still lost, your circle doesn't even sum to 360???

[surreal wadi]

https://tenor.com/view/crying-reaction-sad-table-slam-gif-22790012

I hate math man I DONT KNOW

[errant galleon]

yea in that case, its just 95° and 140° since they arent asking for any arcs, < that notation stands for angle

[hidden compass]

!original

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[errant galleon]

@surreal wadi Angle CPD is 95º and angle dpb is 140º according to your diagram

[errant galleon]

would be the best if u have this

idk what kind of circle that is bruh, since a circle is 360º

[surreal wadi]

I don't have the original problem my teacher makes stuff up from his mind

[surreal wadi]

Hold on

Yeah no I think you're right

It doesn't 360

[errant galleon]

yea

so u dont have the original questions, and where are you pulling these numbers from

[surreal wadi]

From thus

[surreal wadi]

.

[errant galleon]

@surreal wadi where did you get your diagram from

[surreal wadi]

Teacher

Board

[errant galleon]

did ur teacher draw a circle and write all those numbers

[surreal wadi]

Yes

[errant galleon]

did you guys learn like acute angles and obtuse angles?

[surreal wadi]

Yeah in elem

[errant galleon]

or its just that he didnt have the effort to make it into a 360

[surreal wadi]

I think that's it

[errant galleon]

under your circumstances, thats the solution

you can blame the rest on your teacher

since that doesnt add up to 360

your principal would agree with me

[surreal wadi]

Can you tell me how you got those?

[errant galleon]

so the notation <

that stands for angles

right

[surreal wadi]

Okay

[errant galleon]

and CPD

means C and D are 2 ends of the angle

as if they are like lines

and P

is their intersect

where they meet

and you know if 2 lines arent parallel

they meet

and intersect

and their intersection would have an angle

so <CPD is just an angle

not any arcs

u following?

@surreal wadi

[surreal wadi]

Yeah but my teacher calls them major arcs though

[errant galleon]

that cant be...

u use 3 letters, with a curve

above

@surreal wadi and you had this symbol/notation

[surreal wadi]

Thank you

[errant galleon]

did you figure it out?

so what was wrong

ur teacher?

[surreal wadi]

Nah

[errant galleon]

whats confusing u except the fact that the circle doesnt add up to 360

[surreal wadi]

I honestly don't know

[surreal wadi]

How to get cpd and dpb

[errant galleon]

example

[surreal wadi]

Do u need to like subtract or add?

[errant galleon]

u dont subtract or add

u take that number

and write it down

57º is still 57º

lets take this for example, what is <ABD @surreal wadi

[surreal wadi]

35

Degrees

[errant galleon]

yea

and your paper said 95

i forgot the other one

do u get it now?

[surreal wadi]

Wow I'm so dumb

Thank you so much

[errant galleon]

would u mind saying thank you CISUN CHEN

like state my name, its for school

[surreal wadi]

Thank you CISUN CHEN

Can I ask one last question

[errant galleon]

tysm have a nice day lol

[errant galleon]

yea

[surreal wadi]

How do you get DO from this

150 is the answer but I forgot how I got it

[errant galleon]

do is a minor arc

[surreal wadi]

Yeah

[errant galleon]

do you see how it has a curve?

[surreal wadi]

Yep

[errant galleon]

and it has only 2 letters?

2 letters plus a curve is minor arc

and 3 letters plus a curve is major arc

[surreal wadi]

Okay

[errant galleon]

u see how <DPC is 95º? and <CPO is 65º? what does DPO become?

like <DPO

you add right?

95+65

since u r combining arc DC and arc CO

[surreal wadi]

Not across DB AND ST OR OS?

Hwo do you know which path to go to

[errant galleon]

can u post the image again?

scrolling up is a lil hard

nvm i got it

[surreal wadi]

Did I get the wrong answer or something

[errant galleon]

in that case thats MAJOR ARC and major arc are 3 letters

what u meant is Major Arc DTO

[surreal wadi]

Oh thank you

[errant galleon]

in this instance its just DO

so its minor

[surreal wadi]

Thank you CISUN CHEN again

[errant galleon]

ur welcome

have a nice day

[surreal wadi]

I'll pass this test thanks to you bro 🙏 😊

You too

.close

[obtuse pebble]

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[jovial helm]

A rectangle ABCD has measure (3x+2) cm by (2x+4) cm.

A second rectangle PQRD is removed from rectangle ABCD, just like diagram
shown above. Perimeter of the shape ABCDPQR is greater than 27 cm but
less than 52 cm.

Find the range of possible values for x. 🙏

[grand yoke]

note that the perimeter of the shape is the same as perimeter of rect. ABCD

[jovial helm]

how'd you know that

[grand yoke]

RQ = DP, QP = RD

cos RDPQ is rect.

@jovial helm is this okay so far

[jovial helm]

I think so

what do I do next

[grand yoke]

alr

so we can find perimeter of ABCD in terms of X

as we know AB and BC

[jovial helm]

yeah

[grand yoke]

alr

can you show me the perimeter of ABCD in terms of X

cos from there its easy to solve

[jovial helm]

2[(2x+4) + (3x+2 ) ]

[jovial helm]

right

?

[grand yoke]

yes

so $27<10x+12<52$

[warm shale]

Death.cv

[grand yoke]

$15<10x<40$

[warm shale]

Death.cv

[jovial helm]

I see it now but one thing why is this

im a bit slow on shapes

[grand yoke]

oh

RQ = DP, QP = RD
cos RDPQ is rect.

or imagine popping the corner in and out

[jovial helm]

thats crazy how its still the same

I can see it a bit now

[grand yoke]

yea same reaction when i first learnt that

[jovial helm]

Thanks

[grand yoke]

no probs

if you're done you can do .close

[jovial helm]

.close

[obtuse pebble]

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[gloomy pelican]

I was working on some limit problem and to finish it off I have to calculate this as n -> $\infty$, How do I do it?
$n^{2}\left(\frac{2n}{\sqrt{n^{2}+n}+\sqrt{n^{2}-n}}-1\right)$

[warm shale]

ω

[gloomy pelican]

Stolz's theorem?

[inland sleet]

Hmmm I think about get rid of this sqrt my multiplication and then u get 2n sqrt(something)/n⁴ and some stuff and then this equal to 0 - 1 = -1

[gloomy pelican]

this limit is equal to 1/8

not -1

[gloomy pelican]

where /n^4

[inland sleet]

U sure? I also check it from graph it's -1

[gloomy pelican]

its multiplied

by n^2

$n^{2}\left(\frac{2n}{\sqrt{n^{2}+n}+\sqrt{n^{2}-n}}-1\right)$

[warm shale]

ω

[inland sleet]

Multiple 2x(sqrt(x²+x)-sqrt(x²-x)/((sqrt(x²+x)+sqrt(x²-x))(sqrt(x²+x)-sqrt(x²-x)))

And then u get 2n as big term above and n⁴ below and then calculate this limit and them don't forget the - 1

[inland sleet]

Oh my bad didn't saw the n²

[inland sleet]

Hmm wait wait I think I'm wrong

Sorry

[errant gulch]

The degree in the numerator is > the degree in denominator......how is this 1/8 ??

[gloomy pelican]

no worries

[errant gulch]

Should be infinity no?

[gloomy pelican]

its 0 * infinity

so

it can be convergent

no

[gloomy pelican]

thats true for polynomials

[errant gulch]

The heck

Wolfram also says infinity

[gloomy pelican]

it doesnt

what

[gloomy pelican]

look here

wolfram can be wrong but not in this case ;p

[errant gulch]

We are solving this right?

[gloomy pelican]

no

ah wait

yes

thats it

[errant gulch]

Checked on two different sites, the answer comes out to be infinity

[gloomy pelican]

it doesnt

maybe your n^2 is out of the limit thats why

[errant gulch]

Can't help sorry, i am still puzzled as to how can this thing be defined 😵‍💫

If someone explains, please ping

[gloomy pelican]

my prof said this is very common for analysis

like something is 0*inf

so we multiply by n^2

sometimes by n or logn and some interesting stuff happen

im trying to apply Stolz's theorem its ugly but maybe it works

[errant gulch]

If there was no n^2, then answer would be 1

[gloomy pelican]

it would be 0

[errant gulch]

Yea mb

[inland sleet]

U should get this
g(x)=x^(2) (sqrt(x^(2)+x)-sqrt(x^(2)-x))-x^(2)

And then get rid of the x from inside the sqrt and then u will get the result

[errant gulch]

You mean, I can't put in the limits?

[inland sleet]

Sorry Nothing lol my bad

[gloomy pelican]

wheres the denominator

[inland sleet]

But why I get 1/8

[errant gulch]

You are getting 1/8 without n^2 term?

[inland sleet]

h(x)=((2 x^(3) (sqrt(x^(2)+x)-sqrt(x^(2)-x)))/((sqrt(x^(2)+x)+sqrt(x^(2)-x)) (sqrt(x^(2)+x)-sqrt(x^(2)-x))))-x^(2)

U have This when u simplify it u get the one above

[inland sleet]

Yee

[errant gulch]

Uhhhhhh
Can you send what you did?

[gloomy pelican]

is this waht you mean? $h(x) = \frac{2x^3 \left( \sqrt{x^2 + x} - \sqrt{x^2 - x} \right)}{\left( \sqrt{x^2 + x} + \sqrt{x^2 - x} \right)\left( \sqrt{x^2 + x} - \sqrt{x^2 - x} \right)} - x^2$

[warm shale]

ω

[inland sleet]

Wait imma write it and send it

[inland sleet]

Yes and then simplify it

[gloomy pelican]

$g(x) = x^2 \left( \sqrt{x^2 + x} - \sqrt{x^2 - x} \right) - x^2$ and this

[warm shale]

ω

[inland sleet]

Yes this last one and then get the X outside the sqrt(...

[gloomy pelican]

$g(x) = x^3 \left( \sqrt{1 + \frac{1}{x}} - \sqrt{1 - \frac{1}{x}\right) - x^2$ and this

[warm shale]

ω
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[gloomy pelican]

and how does that work?

[errant gulch]

Wait what if we take the n^2 and then send it to the denominator like (1/n^2)
Gives us a 0/0 form and then we can apply L-Hosp

[gloomy pelican]

its still 0*infinity

I cant apply L'hosp

thats the thing

[gloomy pelican]

but I can apply Stolz's theorem by doing exactly what you said and its a discrete L'Hopital so that should do it

idk if it works its very ugly

[errant gulch]

I have no idea on how to apply it, you could try with that.
I tried using l hosp and it's just gettin lengthy

[obtuse pebble]

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[wary hemlock]

So

Idk if you guys help with this stuff

[deft magnet]

Velocity = frequency * wavelength

And then you should be able to observe wavelength from the graph

[obtuse pebble]

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[stray timber]

i dont understand what the second like is asking me to do?

[stray timber]

do i replace s with s-9?

[rotund sundial]

shush pls

[stray timber]

?

wht did i do

[unreal musk]

What’s the context of this, Laplace transforms?

[stray timber]

yes

.close

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[soft fable]

how do i solve by completing the square

[gleaming saffron]

post what u have done

[tepid yoke]

Do you have a specific problem?

[gleaming saffron]

we will guide you

[soft fable]

this is what i have tried

oops

[gleaming saffron]

a lot happening

[soft fable]

YEAAAA

Idek what i’m doing

[gleaming saffron]

ok slow down the steps

you have the right idea i have no clue what happened midway thru

you can just start by putting the x^2 + 8x bit into brackets

so youd get (x+4)^2 which is right

but if u expand (x+4)^2 you would get x^2 + 8x + 16, and you started with x^2 + 8x

so you need to -16 from both sides not add

[soft fable]

What the heck!!!!

My math teacher was like

Always do plus

[gleaming saffron]

always do minus

other way around

[soft fable]

What the

With any equation?

[gleaming saffron]

well

say if it was (x-4)^2

the last term would still be +16

so you would still need to -16

always minus

does that make sense

[soft fable]

Yea kind of

Like you mean when you foil it out

It would be +16

[gleaming saffron]

yeah so you always minus

[soft fable]

Okay

[gleaming saffron]

i also dont know what happened

u went from x+4 to x+3

[soft fable]

OH SHOOT

Oh it’s bc

i was looking at my examples LOL

Hold on

[gleaming saffron]

lol

try the question again

try write a bit neater please too itd help us all

[soft fable]

Wait so

• the 16 from both sides??

[gleaming saffron]

yeah

you have to do the same thing to both sides

wait no

NOT both sides lol

[soft fable]

Wait it should be both sides

[gleaming saffron]

no

[soft fable]

Oh

[gleaming saffron]

i had a lil brain fart sorry

youre trying to get (x+4)^2 to expand to x^2 + 8x
but (x+4)^2 expands to x^2 + 8x + 16
so youd need to just take away -16 from (x+4)^2

left side only sorry

regardless have a go and lmk if anything happens

[soft fable]

Okay thank you

[gleaming saffron]

hows it going

[obtuse pebble]

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[edgy sierra]

Can yu help me understand where I went wrong here? The steps I took are as follows:

1. Brought the product rule up. f(x) * g'(x) + g(x) * f'(x)
2. Worked ut the derivative of f(x) and g(x):

f(x) = (x^2 + 10)
f'(x) = (2x)
g(x) = (x-3)
g'(x) = 1

3. Wrote out the equation and plugged in for product rule:

(x^2 + 10) * 1 + (x - 3) * (2x)

4. Solved:

x^2 + 10 + 2x^2 - 6x

5. Simplified:

3x^2 - 6x + 10

6. Plugged in 0 for f'(x)
   3(0^2) - 6(0) + 10 = 10

7. Then worked on m = y-y_1 = m(x - x_1)
   y - (-30) = 10 (x - 1)

y + 30 = 10x - 10
y = 10x + 20

[hexed agate]

Something wrong in your fourth step

Oh you fixed it next step

[edgy sierra]

my bad missed the x, I wrote it on my notebook paper

but yeah I think at LEAST up to 5 is correct

but past that I dont really know where I got it wrong at

[hexed agate]

Can you explain step 6

[edgy sierra]

So, because it says at the point (0, -30)

I took the formula 3x^2 - 6x + 10

and plugged in 0 for x

so 3(0^2) - 6(0) + 10 = 10

[hexed agate]

Why equal to 10

[edgy sierra]

wait

yeah

I think that's right

there's a +10 and everything else would be 0

[hexed agate]

The idea is wrong

[edgy sierra]

0^2 is 0, so 3(0) is 0, and 6(0) is 0

[hexed agate]

You first find the equation of tangent line

And then plug in 0 and -30

[edgy sierra]

Desn't the derivative automatically give us the equation of the tangent line?

f'(x) should = 3x^2 - 6x + 10, due to the product rule right?

f(x) = (x^2+10)(x-3)
f'(x) = 3x^2 - 6x + 10

at least..

I know the derivative gives the slope of the tangent line to the curve at any point of the original function

Oh I see

I messed up at step 7

It's 10(x-0)

y-(-30) = 10(x-0)

which gets you y = 10x-30

[hexed agate]

Oh yeah

[edgy sierra]

.close

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[scenic lake]

Is there a list of helpers that offer Calculus 2 tutoring (I would pay) ? I need lots of help, and would have to ask questions back to back to back in this server to learn and get through my course since I haven't taken a math class in around 5 years.

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[sturdy tiger]

heyyy i might be kinda dumb (i’m in algebra 1 i might be pretty young) but i’ve been struggling with this for a bit and i need help!!!

[prime swallow]

The slope of the perpendicular line is the negative reciprocal of ur current slope

So if u had a slope of 2

The perpendicular slope is -1/2

[sturdy tiger]

ohh

lemme see

[prime swallow]

And first solve everything as

Y=

Isolate y

That’s what slope intercept form is

[sturdy tiger]

here’s the part i struggle at most

it’s probably because i get decimals i have to check my work

i got like 65.333 when i multiplied 7/3 by 28

[prime swallow]

u can keep them all as fractions

no need to simplify to decimals

[sturdy tiger]

wait wdym?

i don’t need to distribute?

[thorny idol]

you can keep the fractions as fractions, without converting to numbers like 63.333

[sturdy tiger]

ahh i see

[thorny idol]

don't do the division

[sturdy tiger]

so it would just be
y+7=7/3x?

[prime swallow]

its asking for slope intercept thats y=mx+b

i think ur tryna put it in point slope

[sturdy tiger]

i am

OHH

i got it

i missed a step

so it’s talking about perpendicular lines, once i turn the equation “5x-3y=4” into slope intercept form i need to change the slope to the perpendicular version

from that it wouldn’t change into a decimal

[prime swallow]

nice yes

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[wooden coyote]

Hi. I want to self-study math.
I need to learn all middle school and high school math in 1,5-2 years. Could you write a list of books to self-study school math, please.
L: English or Russian.

[sacred pulsar]

why do you want to study math? whats your goal?

[empty cypress]

use Khan academy

it covers pretty much all of middle and high school math

[sacred pulsar]

i agree but it could be hard knowing what and in what order to study in

[empty cypress]

it pretty much goes in order

[wooden coyote]

1. I like math (now) and i want to gain more knowledge about it. 2. Finish school.

[obtuse pebble]

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[timid silo]

Need some help with this question, when I sub in the axis of symmetry to find the y coordinate for the vertex, answer shows up as 9.375, when it’s really meant to be -4.875. Have I done a silly mistake or something else?

[timid silo]

,rotate

,close

.close

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[obtuse pebble]

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[jagged yacht]

"The angle between CE and the base ABC is 33.89"

Simple question. I just want to know where the angle 56.81 and 33.89 is located on the diagram and how to identify and understand where it is referring to for future questions.

[obtuse pebble]

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[obtuse pebble]

@jagged yacht Has your question been resolved?

[onyx belfry]

I believe that's the angle between the triangles AEB and ABC

[jagged yacht]

would you be so kind as to help draw where it is because im still not getting it

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[unreal jewel]

Спростити булеві вирази, використовуючи закони та тотожності алгебри
логіки, згідно варіанту у таблиці 1.2.

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@unreal jewel Has your question been resolved?

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[timid silo]

не понимаю

english pls

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[urban glen]

I have to prove f to he a bijection here right?

But how do I prove that it's an injection or surjection, doesn't look too obvious

[restive gorge]

What are the definitions

[urban glen]

Wdym

For a mapping to be an Injection, no 2 different numbers can map to the same element

(∀x in the domain of f, f(x)=f(y) => x=y)

E.g if a mapping f:ℝ->ℝ has f(x)=x²
Then it isn't injective

Because f(2)=4=f(-2) so 2 numbers both map to 4

is a counterexample

For a mapping f to be a subsection the image of f has to cover the entire codomain

E.g if f:ℝ→ℤ, f is surjective if im(f)=ℤ

[restive gorge]

Ok good you know what you are talking about, you answered your own question

I have to add on here, do you wanna prove that it is bijective, or do you have to?

As far as I am concerned, you can assume that it is bijective, meaning assuming that f^-1 exists. They just want you to show that it's identical to f

[urban glen]

I think I have to, f has to be bijective for f^-1 to be defined no?

[urban glen]

Ohhh

I don't think I can assume f to be a bijection

[restive gorge]

Yes but why would I want you to show something, when it might or might not be true in the first place?

[urban glen]

Cuz if it isn't, f can't be equal to f^-1

[restive gorge]

nope

if it isn't then the question is flawed

[urban glen]

I know it has to be

[restive gorge]

cause there wouldn't exist an f^-1 at all

[urban glen]

But I want to show it

[urban glen]

Yeah ikik

[restive gorge]

Then go ahead.

The difficult part I only see here is the injectivity

[urban glen]

Yea

Thats what im stuck on

[warm shale]

bacc (unhelpful)

[urban glen]

Yup

How do I show that that implies x=y directly

Ohhh wait

okay nvm

[restive gorge]

Another way could be to show it is strictly monotonous

then that implies injectivity too

[urban glen]

I can multiply each side by (x+1)/(x+1) and (y+1)/(y+1) respectively

maybe

Would that help anything

Nah

[urban glen]

I haven't covered that yet

[restive gorge]

,, (x+a)(y-1) = (y+a)(x-1)

[warm shale]

bacc (unhelpful)

[urban glen]

Yup

Ahh I see

[restive gorge]

I think it's a mtter of expanding the terms now and hoping for they cancel out

which seems to be the case eg. xy will cancel

[urban glen]

Thats what im doing rn

On my whiteboard

That I can't hang on my wall at uni lmao

I'm sat on my grubby ass floor

ay-x = ax-y

Cool, injectivity proven

[restive gorge]

Now you're happy like a happy meal

But see, looking up definitions

That's basically the core of doing math

[urban glen]

Fair

Idm doing that ig

@restive gorge

Need a smidge more help pls

[restive gorge]

sounds weird

[urban glen]

Lol

I'm proving f to be a surjection rn

I said let α,β∈S

Then f is subjective if there exists a β such that f(β)=α

surjective*

But

[restive gorge]

for every y value in the codomain there exists at least one x

[urban glen]

I'm getting f(β) to be a(1+α)/(a+1)

Which is not α lol

I let β=(α+a)/(α-1)

[restive gorge]

But I dont know why you wanna prove that

f maps by definition to im(f)

so it is surjective by definition

[urban glen]

Wdym by definition

Just because f:S->S ?

[restive gorge]

yes

A surjective function is a function whose image is its codomain

[urban glen]

Oh shit ya lol

Yh

When I've proven that f is a bijection, how do I show f=f^-1 ?

wait hm

[restive gorge]

one question

[urban glen]

Yup

[restive gorge]

you proved injectivity

[urban glen]

Sorry if I'm being dumb

[restive gorge]

you proved this is equal

if x = y

[urban glen]

Yh

oh

[restive gorge]

sorry i meant that this implies x = y

[urban glen]

Yh yh

Ik what u mean

[restive gorge]

ironically

x = (y+a)/(y-1) is the inverse just need to solve for y

[urban glen]

Is that the "proper" method for finding inverse mappings?

[restive gorge]

yes

[urban glen]

Feels a bit like.... not a fully justified method

Actually

it's a reflection in line f(x)=x so ig it makes sense

[restive gorge]

well

the domain of f(x) is the range of f^-(x)

so that's why we flip x with y

[urban glen]

Yh

It seems less proper for some reason

Ooh wait

Could just say that f○f^-1(x)=x

so f(f^-1)=x

then that justifies swapping x and y

No? @restive gorge

[restive gorge]

yea

[urban glen]

Cool

Ty

[obtuse pebble]

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[heavy zealot]

Is this question put wrongly?
"I'm moving at 100km/h to the north (with respect to the ground), a train is moving in my opposite direction and its relative speed with respect to me is 10km/h, what's the speed of the train relative to the ground, and in which direction?"

[heavy zealot]

Just a random thought I had lol

[timid silo]

You shouldn't define the direction of the train if you are asking for it in the question itself

[heavy zealot]

But thats the part im doubtful about

Is it wrong?

I mean I am specifying which direction it is going but the answer is that it actually goes my same direction

[timid silo]

That's the problem

[heavy zealot]

I had an existential crisis because it made no sense and this question randomly popped in my mind

Just wanted to make sure lol

[timid silo]

"I'm moving at 100km/h to the north (with respect to the ground), a train is moving with a relative speed of 10 kmph with respect to me. What's the speed of the train relative to the ground, and in which direction?"

There

[drifting wraith]

i think it's unambiguous enough

[heavy zealot]

Yeah I mean that makes sense, it's just a random question I thought of while exercising mentally (dont ask me why)

But it was hilarious because it took me a few minutes to realise what was going on

[drifting wraith]

cuz 10 km/h means it's either going 90 or 110

[timid silo]

Oh yeah

[drifting wraith]

and only 90 makes it appear to move towards you, so it's not like there is more than 1 good answer

it could be worse

[heavy zealot]

But 90 in the direction im going, right?

[drifting wraith]

yes

[heavy zealot]

But the question says it goes the opposite direction

I mean it makes sense that theres only that correct answer logically

[timid silo]

I will leave

[drifting wraith]

yes, i'm saying it could be worse

[heavy zealot]

Alright nothing important just needed to confirm im not having brain damages

Thanks yall

?close

.close

[obtuse pebble]

Channel closed

Closed by @heavy zealot

Use .reopen if this was a mistake.

[drifting wraith]

but it's bad

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[willow rivet]

Is this channel avaliable?

[obtuse pebble]

Please don't occupy multiple help channels.

[gleaming saffron]

yes

[willow rivet]

How would I start to solve this problem

[thorny idol]

,rotate

[willow rivet]

What should I do first

[willow rivet]

Now what

Could I do 180-68?

[thorny idol]

those are 90°, not 180°

[willow rivet]

So 90-68?

90-30?

Angle 3=92?

[thorny idol]

why?

[willow rivet]

What should I do next?

[thorny idol]

the angles of a triangle should always add up to 180°

[willow rivet]

22+60+ <3=180?

98?

Ty

Would X=100

[thorny idol]

,rotate

[thorny idol]

yeah

[willow rivet]

How would I find y

[willow rivet]

Would I do 180-75?

[thorny idol]

no, its not a 180 angle

this is about parallel lines cut by a transversal

[willow rivet]

How would i find out how many degrees is it

Is it 90 degrees?

Can you tell me how to find y please

[civic zealot]

are those lines parallel?

[willow rivet]

Yes

If you scroll up a little you can see the original picture if that helps

Can you help me find y please

[obtuse pebble]

@willow rivet Has your question been resolved?

[willow rivet]

No

[leaden ginkgo]

!status

[obtuse pebble]

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

[willow rivet]

I'm solving for y now

I found out that x was 100

Do you know how to figure out y?

7

@leaden ginkgo

[obtuse pebble]

@willow rivet Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

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

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

[tired bough]

can someone do these 2 equations?

[nova vale]

hi

[tired bough]

hi!

[nova vale]

Do u know l hospital

[tired bough]

hahaha no 😦

[nova vale]

oh

[tired bough]

i'm really bad at maths

well maybe i do, english isnt my first language so we maybe call it a different way

[shut lagoon]

You should just be able to divide both the numerator and denominator by sqrt(n) in the first one.

L’Hopitals rule would probably work, but it would also involve derivatives of roots and they aren’t particularly fun to work with.

[tired bough]

thats probably something we didnt even learn lol

[nova vale]

do yk derivatives

[tired bough]

so i can ignore the roots until i "clean up" the equations, no?

[tired bough]

...no

[shut lagoon]

Not really. When you have those forms where the powers of n maths in the numerator and denominator, you can essentially always divide through by the highest power of n

In the first one, the highest power is sqrt(n)

[tired bough]

so for example sqrt(n^2+n)

i divide wioth n^2

[shut lagoon]

No, n

[tired bough]

oh

im so cooked

[shut lagoon]

I find it hard to explain what I mean by highest power

But the idea is that even if n is under a root, just take the biggest power in it, and apply the root to it

So for sqrt(n^2 + n) the biggest power inside is n^2 which becomes n after taking the root

[tired bough]

ohhhhh

[shut lagoon]

You can check that the biggest power in the numerator of your first limit is sqrt(n)

[tired bough]

so sqrt(n^2+n)= sqrt(n^2(1+1/n)

then i remove the sqrt with the power

and its n(1+1/n)?

[shut lagoon]

You’ll still have 1+1/n under a root

[tired bough]

yea

i forgot that

yea yea i get the concept now

[shut lagoon]

But the idea is that if the powers match in the numerator and denominator, once you’ve taken the highest power out they cancel

[tired bough]

and what if i have a quadratic equation under the root with lim

for example4

[shut lagoon]

And then all the 1/n terms go to 0

[tired bough]

lim(n-sqrt(n^2-2n+3))

how do i apply the quadratic formula there

[tired bough]

yup i got it

ty bro

i was referring to this example earlier

[shut lagoon]

I would do conjugate with this one

[tired bough]

hmm

not sure what that is lol

just googled it, i do

mb

[shut lagoon]

That’s fine!

[tired bough]

but still not sure how i would apply it to this example

sorry for being slow bro i just have a test tomrrow

[shut lagoon]

It’s ok dw about it

The conjugate itself is just n + (big sqrt)

You want to multiply by conjugate/conjugate

This will make the numerator a difference of squares (which you can remove the sqrt with)

[shut lagoon]

And then you’ll be left with a limit similar to the one you had in your first examples here