help-36

[trail mango]

z -> i^z is clearly not injective

as was shown by the first two lines

this is like saying 1^2 = (-1)^2 so 1 = -1

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[paper cobalt]

I dont know how to simplify this..

[fluid sky]

Well u seem to have forgotten that there's a square root sign over x+h

[paper cobalt]

oh

well

regardless it's wrong..

I wonder what I did wrong

[fluid sky]

Yeah but the square root sign is supposed to appear somewhere else too

What is $\frac{1}{\sqrt{x+h}}+\frac{1}{\sqrt{x}}$

[soft zealot]

SilverSoldier

[paper cobalt]

hm

wdym it's supposed to appear somewhere else too?

[fluid sky]

Can you simplify this?

Oh wait

Right I see what you did wrong

[paper cobalt]

hm?

[fluid sky]

You messed up the signs

And there's no square root of h

[paper cobalt]

wdym

explain please

or show where

i'm a visual learner 😅

[fluid sky]

There is no $\sqrt{h}$

[soft zealot]

SilverSoldier

[fluid sky]

There's only just h

[paper cobalt]

wdym

[fluid sky]

In your answer u put h also under the square root sign

[paper cobalt]

numerator or denom?

[fluid sky]

Denominator

[paper cobalt]

so then it should be $h\sqrt(x)(x+h)$

oops

[soft zealot]

xNiden

[fluid sky]

\sqrt{put whatever inside here}

But yes the denominator shud be that

And then in ur numerator you messed up the signs

There's a minus in front of the first term, but there's a plus in front of the second one

You have factored out a -15, but do you get the given result when you multiply through by that ?

According to how you have written your answer?

[paper cobalt]

No I'm confused

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[opaque dock]

I'm not sure how to do this problem, not even where to start

[iron mist]

Do you know what vertical asymptotes are?

[opaque dock]

yes

but what do they mean by factors of the denominator

[iron mist]

When do vertical asymptotes happen in rational functions?

[opaque dock]

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[cold basin]

why is this wrong?

[scarlet sequoia]

How do you get from 7y-2z = 27 to z = ?

[tardy timber]

Coefficient of x¹¹ in (2x²+x-3)^6

[cold basin]

just added 2 on both sides and divided both sides by 7

ahh i see i messed up y a little later should by 3y = -39 y = 13 but

ik thats still wrong

y came out to be like 5

actually ig it should be 13/2 but that still gets me no where

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[round heath]

A group of 180 people watched movies on Netflix, of which 95 watched Dabangg, 100 watched Avatar, and 100 watched RRR. 50 people watched Dabangg and Avatar, 40 watched Avatar and RRR, and 55 watched Dabangg and RRR. Find the number of people who watched only RRR and Avatar.

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[wraith vine]

hi!

[wraith vine]

guess who’s back!

WAIT NVM

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[tacit sorrel]

Hello I need help. I don't understand what is expected in the statement.

[fair rain]

A is 800

[tacit sorrel]

"Complete the following expressions" (we cannot use the calculator)

[fair rain]

B is 4

[tacit sorrel]

did you use calculator for this ?

[fair rain]

Yes

But you can do

[tacit sorrel]

omg thanks !!

[tacit sorrel]

how did you do for this

[tranquil pine]

🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱

🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱

🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱🇮🇱

[tacit sorrel]

need help for the b pls

[tacit pilot]

You need to do a trinomial

Think of 2 numbers that add up to -4 and multiply to 3

Or just use the (-b±sqrt(b²-4ac))/2a

[tacit sorrel]

Thks I did like this and I found 3 and 1

[tacit pilot]

1 and 3 add up to 4 not to -4

-1 and -3 would work

[tacit sorrel]

oki wait please

I do it again

@tacit pilot ??

[tacit pilot]

ok wait so if you got a case like this:
au²+bu+c=0
You can plug it into the formula I sent before
In your case a = 1 b = -4 and c = 3

I will send an image of it so you understand it better wait

[tacit sorrel]

Oh okk I see

[tacit sorrel]

and what are the 2 numbers here plezse

[tacit pilot]

-3 and -1

That would be the solution in both ways

[tacit sorrel]

Thank you 🙏🏽

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[severe pivot]

Apparently this answer is wrong, anyone see what I did wrong here?

[severe pivot]

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[tranquil pine]

Pls help me find acceleration for 8-

[tranquil pine]

8a

[vital crag]

,rotate

[tranquil pine]

I don’t get what formula I need to use here. I know that they both need to be converted to meters I believe

This is her answer

[vivid walrus]

sph3u is a physics question

[tranquil pine]

All this is related to math tho she told us

[vivid walrus]

this is kinematic

are you familiar with this

just apply it and then solve for a

[tranquil pine]

So what formula do I use

Cause I was looking at the acceleration formulas, they all use time

But time isn’t given here

I did 306250000 as an answer

Idk if that’s the same as 3.1x10^8

[vivid walrus]

rounding

$v^2=v_o^2+2 a \Delta x$

[soft zealot]

Akira 🍉

[vivid walrus]

this is the formula you need apply to it

to find the a

[tranquil pine]

So it would rearrange to

[charred chasm]

is this supposed to be the answer?

[tranquil pine]

And I replace vf and vi with V?

[tranquil pine]

Yh

[charred chasm]

That's... odd. The speed of causality is just a bit shy of 3 x10^8 m/s

[tranquil pine]

Im wondering. Is the whole V 3500m/s or is Vi 3500m/s

[tranquil pine]

It’s sig figs

[vivid walrus]

just V

[charred chasm]

Doesn't matter. That satellite would be moving faster than light 😅

[tranquil pine]

lol

[tranquil pine]

Ight so I replace it with that

Instead of vf2 - vi2 it’s only v2?

[vivid walrus]

mhm

[tranquil pine]

Tysm

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[mental basin]

hi!

[mental basin]

i need help with prefix

like

write in base power form with the unit gram

a) 15mg

b) 412 ul

c) 0.8dl

[versed crater]

What does mg stand for?

[mental basin]

miligram

[versed crater]

Double l but yes

[mental basin]

soz

[versed crater]

Milli means 10^-3

[mental basin]

yea

but how much is gram

?

[versed crater]

A gram is 1 gram

1g = 1 gram

[mental basin]

so

[mental basin]

answer: 0.15

[versed crater]

0.1g is 100 mg

[mental basin]

0.015 g

[versed crater]

Where are your units

0.015 what

[mental basin]

?

[versed crater]

Right

15mg = 0.015g

[versed crater]

Do we need it in scientific notation?

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@mental basin Has your question been resolved?

[mental basin]

so then

0. 000 180 mg

-close

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[real juniper]

How do i simplify this

[real juniper]

I know there is away to only get it of sin and cos

[royal gust]

The x² polynomial doesn't mix with the trig very well

[real juniper]

i want to use l'hospital rule

so i get it to cos/sin only i can do it

[royal gust]

Oh this is a limit. To 0?

[real juniper]

yes

0^+

[royal gust]

Can add the fractions together

[real juniper]

can i assume 1/x^2 = 0 ?

i cant right

[royal gust]

[sin²(x) - x²cos²(x)] / x²sin²(x)

That's still very ugly, but could be L'h'd.

[real juniper]

do i have to times it by the conjugate or what

how do i get the term away

@royal gust

do i just do it like a normal fraction

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[jolly cradle]

Does anyone know what these parenthases mean?

[static blade]

Should be the floor function https://en.m.wikipedia.org/wiki/Floor_and_ceiling_functions

[jolly cradle]

why did my teacher give me this then lol we never learned it

alr thx im going to watch a vid on it now

[static blade]

👍

[jolly cradle]

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[spiral furnace]

If you have an arbitrary matrix A, is (A^-1) * (A^2) = A?

[grizzled tusk]

yes, as long as A^-1 is defined, it's true

because (A^-1) * (A^2) = (A^-1 A) * A = I * A = A

by definition of inverse

[spiral furnace]

Thanks!

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[slow halo]

what formula/concept do i need to use to get started on this?

[dreamy shadow]

i would asume you need to use the dot product to be able to solve this, if memory serves me correct

[slow halo]

i tried that but i got stuck

i ended up with -4+3p = 7|b|cos4/21

[dreamy shadow]

• taken form wiki

but so like we can rewrite the dot product to solve for the angle and since we know the angle we should be able to get something from this

but it was awhile since i last did vector geometrics

[slow halo]

wait no ignore this

and the angle would be approx 79

i just dont know how to put it all together

wait i think im getting cosine and theta mixed up

either way i dont know how to progress

wait i think i got it

thanks for your help

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[ancient thistle]

Hello

[ancient thistle]

Can someone help me

@torn elm

Sorry, I had to leave

But yes, I still do need help

[lethal totem]

what is ln(a)-ln(b)

[ancient thistle]

ln(a/b)

[lethal totem]

ok

then use continuity of the logarithm

[ancient thistle]

wdym by continuity of a log

[lethal totem]

so this becomes:
ln (lim (3x+1)/(5x+1))

you can bring limits INSIDE OF continuous functions

[ancient thistle]

Ohhh

Okay

[ancient thistle]

Then would the answer just be ln(3/5)?

Hmm

It's correct

Thanks

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[sacred egret]

Hello

[warm ether]

greetings

[sacred egret]

So like i just got a question is it always going to be to the base of 5

[grim badger]

No because it depends on the number

[sacred egret]

How will I determine what number to use

I got this formula but don’t know what to do or what it means

[grim badger]

Like $8^{\frac{4}{3}} = \left(2^3\right)^{\frac{4}{3}} = 2^4$

[soft zealot]

dldh06

[sacred egret]

Um

Still don’t understand

[sleek token]

can you identify n and m in this? $\sqrt[4]{x^{7}}$

[soft zealot]

saad

[sleek token]

using this

[sacred egret]

4 is N and 7 is M?

[sleek token]

correct

how would you convert that to exponential form?

[sacred egret]

Ummmm

I have no idea 🙁

[sleek token]

how would you go from the last form to the first form?

[sacred egret]

Multiplication

[sleek token]

well, you're not wrong, you can do it like that

but it would be easier to just use the exponent rule

[sleek token]

so this just becomes $x^{\frac74}$

[soft zealot]

saad

[sacred egret]

Alright

So uhhh

Like $125^{\frac{4}{3}} $

Like $125^{\frac{4}{3}}$

[soft zealot]

Junior

[sacred egret]

Figuring out how to type out

$\sqrt[3]{125^{4}}$

[soft zealot]

Junior

[sacred egret]

@sleek token probably wrong

Is it supposed to be

4 on left

3 on right

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@mild cove Has your question been resolved?

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[ashen beacon]

hiu

[final saddle]

Please don't occupy multiple help channels.

[ashen beacon]

I desparately need help gentlemen!

[blissful meadow]

Your parabola will have an equation of the form $$ax^2 + bx + c$$

[soft zealot]

Azyrashacorki

[blissful meadow]

When does a function intersect the y-axis?

[ashen beacon]

ok

what do I do with these points?

[ashen beacon]

when x is 0

[blissful meadow]

Ok. Plug x=0 in the general form of the equation.

[ashen beacon]

okokok

[blissful meadow]

This will give you the value of c

Then you should plug both points in the resulting equation, and solve for the system

[scarlet atlas]

The function intersects the y-axis at c. This is true for all functions.

[scarlet atlas]

⬆️

[ashen beacon]

yeah so

-5 will be C

[scarlet atlas]

Yes

@ashen beacon (0,-5)

[scarlet atlas]

This is the y-intercept

[ashen beacon]

yes

[ashen beacon]

what do I do now???

[scarlet atlas]

Not sure

[ashen beacon]

oh

[ashen beacon]

hi

[blissful meadow]

Yeah so you have c=-5

[ashen beacon]

yess

and these other points

[blissful meadow]

Now you use the points and plug them in

[ashen beacon]

into where though?

[scarlet atlas]

Plug them into what tho

Ye

Shiz I'ma learn something too tonight

[ashen beacon]

haha

I can do these ones but usually with a vertex right

[blissful meadow]

The equation

[scarlet atlas]

What class is this btw

[ashen beacon]

pre cal 12

[blissful meadow]

You get an equation with 2 unknowkns

[ashen beacon]

or math 100 in college

[blissful meadow]

actually 2 equations

[scarlet atlas]

👍

[ashen beacon]

oh ok what do I plug in for

[blissful meadow]

a(-1)^2 + b(-1) - 5 = -9

And the other one

You now have a system of 2 linear equations

[scarlet atlas]

This is a parabolic function, not linear though...will this still work?

[blissful meadow]

Once you plug in the points it's linear in a and b

There is no x^2 you just plugged in 1 and -1 ...

[ashen beacon]

holdup

[ashen beacon]

u plug in x two times righht

bc there is a x squared and just x right??

this is my main concern

[blissful meadow]

No

You plug your points

In the equation ax^2 + bx - 5 = f(x)

You have two points to plug

f(-1)

f(1)

[ashen beacon]

im lost

[ashen beacon]

U see tgeres two x values right

So if u take the points -1,-9

U plug y for -9 and the x points for -1?

[blissful meadow]

Yes.

[ashen beacon]

Ok that was my question

And then u do that for the other one righr?

[blissful meadow]

Yes

[ashen beacon]

Then solve for both a and b? Values

[blissful meadow]

Yes

[ashen beacon]

thank you!

[final saddle]

@ashen beacon Has your question been resolved?

[ashen beacon]

shit bro

I tried it but the variables just cancel each other our

out

[blissful meadow]

Right I have more time now so I'll go over it with you

[ashen beacon]

here Ill show u

okok thanks soo much

[blissful meadow]

(-1,-9) yields the equation a(-1)^2 + b(-1) -5 = -9, or a - b = -4.

(1,-3) yields the equation a(1)^2 + b(1) -5 = -3, or a+b = 2

Let's just add both equations together. This is valid, because we're adding equal values on both sides.

So :

a - b + (a + b) = -4 + (2)

So we have 2a = -2

Or a = -1

Then we plug a = -1 in one of the equations we had to find b : a+ b = 2, so -1 + b = 2, so b = 3

[ashen beacon]

yes I got that too

[blissful meadow]

Ok

[ashen beacon]

no wait

[blissful meadow]

That's it

[ashen beacon]

I got a-b=2

maybe I did that wrong

[blissful meadow]

Most likely yes.

[ashen beacon]

how?

shouldnt it be the same

a(-1)^2 -b(-1)

a-b

oh fuck

i put the wrong x value

jhaahah

I got it!

y= -1x^2 +3x-5

lets gooo

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[ashen beacon]

hi

[final saddle]

Please don't occupy multiple help channels.

[blissful meadow]

Can you compute g(0)?

[ashen beacon]

yes

1/2

[blissful meadow]

good

[ashen beacon]

then f(1/2) should be the first functoin right?

[blissful meadow]

Indeed

[ashen beacon]

I choose that one because x is gonna be bigger than 0

okok good!

[long charm]

hii

[ashen beacon]

then I plug in 1/2 for x^2

hi

and the answer I got is 9/4

i hope that is right

[ashen beacon]

how would I do the next question

[blissful meadow]

Let's just write something to help us a little. Let's say f(x) = z.

Then you have g(z) = 1/2

What value of z would make that true?

Provided you know g(z) = 1/(z^2+2)

Hint : you've sort of seen this in the last problem.

[final saddle]

@ashen beacon Has your question been resolved?

[ashen beacon]

1/2

right

what is this subject called?

decomposing functions?

I want to watch a video on it

@blissful meadow

.close

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[quasi plinth]

https://media.discordapp.net/attachments/409596215697866773/1158838095525982238/image0.jpg?ex=651e5c54&is=651d0ad4&hm=713418bace936a9d05017870d7e6b4bfa21a408cd7d8fd4f0871b6db2ff488db&

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@quasi plinth Has your question been resolved?

[blissful meadow]

So you want L3 to be perpendicular to the plane. In particular, it must be parallel to a vector orthogonal to both vectors generating the lines. You can find such a vector using a cross procuct.

[quasi plinth]

Cross product between which vectors

[final saddle]

@quasi plinth Has your question been resolved?

[blissful meadow]

The vectors that make up the lines. (1,1,0) and (0,-1,-2)

[quasi plinth]

Alright this is for point 1 what about 2 and 3?

[blissful meadow]

Then this line will have the form t*V + P where V is the normal vector you found, t is a free variable and P is a point you have yet to find.

So we are looking for P here.

If L3 crosses the L1, then there is some lambda (abbrv L) such that in the L1 equation, L*(1,1,0) + (0,0,2) = tV + P

Similarly, if L3 crosses L2, you must have some other value, say M such that M*(0,-1,-2) + (1,-2,-4) = tV+P

So then it's just a matter of solving a system of linear equations

Actually, thinking back at it, since L3 is perpendicular to the plane spanned by L1 and L2, the only way it can intersect both lines is at the intersection of L1 and L2. So the missing point is this intersection of L1 and L2.

[quasi plinth]

Something like this?

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[gray merlin]

hello! can i ask? Why is there an N after (cos mx)

[final saddle]

Please don't occupy multiple help channels.

[scarlet sequoia]

Chain rule of derivation

[gray merlin]

how

[scarlet sequoia]

I think it's supposed to be an m

[gray merlin]

is it product rule and chain rule

[scarlet sequoia]

Replace the final "n" by "m" to have a correct formula

Might help to write it as $y' = \sin(mx)(-\sin(nx)\cdot n) + \cos(nx)(\cos(mx)\cdot m)$

[soft zealot]

rafilou2003

[gray merlin]

so the x is gone

[scarlet sequoia]

What's the derivative of mx?

[gray merlin]

m

oh got it

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[eternal wharf]

Can anyone help me with this?

[tired walrus]

you pick which of the four numbers is the sole element of A and B, and then for the other 3 numbers you have 3 options each: belong to A, belong to B, or belong to neither

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[tranquil pine]

why is the first one undefined but the second one isnt?

[tiny gorge]

wdym "defined"

[tranquil pine]

i corrected it

[tiny gorge]

they both blow up at x=0

[tranquil pine]

but x^2 goes to infinity

[tiny gorge]

,w plot (2x+1)/x^2

[tranquil pine]

that other one isnt defined

[soft zealot]

Results provided by WolframAlpha

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

Requested by bungo.the.original

[tiny gorge]

,w plot (2x+1)/x

[soft zealot]

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

Requested by bungo.the.original

[tiny gorge]

first one blows up to +infinity as x->0 from either side

second one blows up to +infinity as x->0 from the right, and blows up to -infinity as x->0 from the left

[tranquil pine]

but one is undefined

2x+1/x is undefined

[tiny gorge]

who is telling you that

why is it undefined

[tranquil pine]

maple

[tiny gorge]

and what do you mean by undefined

neither one has a limit as x->0

[tranquil pine]

this is what i mean

[tiny gorge]

ah i see

yes it's because of the graph i showed above

[jagged cosmos]

Maybe they are referring to one having a limit tending to infinity and one having no limit as one side tends to - infinity and the other end tends to +infinity

[tiny gorge]

the second one goes to +infinity if you approach x=0 from the right, and it goes to -infinity if you approach x=0 from the left

[tranquil pine]

it is because one diverges or?

[tiny gorge]

they both diverge, but the first one diverges to +infinity from either direction

maple is making a distinction between the two situations

[tranquil pine]

if one where to answer 2x+1/x the answer would be undefined

whereas 2x+1/x^2 would be inft

[tiny gorge]

or "does not exist"

[tiny gorge]

that's what i would write personally yes

[tranquil pine]

yes, does not exist

[tiny gorge]

the reason people make the distinction is that there's more information being conveyed in saying that the limit equals +infinity

and in some contexts (like the extended real number system), a limit that goes to +infinity actually converges

[tranquil pine]

that wasnt clear to me

what am i missing

in the first one as x-0 since the denominator is way larger, it will go to infinity right

sine c/0.0000000000001= inft

[tiny gorge]

referring to the two plots i showed earlier, do you agree that there is a difference in behavior at x=0 between the two functions

for both functions, as x gets small, the function goes off to infinity, the only difference is that for the one with x^2 in the denominator, it goes to +infinity on both sides, whereas for the one with x in the denominator, it goes to -infinity on one side and +infinity on the other side

in some contexts it's useful to distinguish between these types of behavior

in elementary calculus it's usually not useful to distinguish, and you say that both "do not exist"

but maple has no idea what context you're in

so it's giving the most info that it can

[final saddle]

@tranquil pine Has your question been resolved?

[tranquil pine]

ok

so when a function approaches some both sides

it sort of cancles out?

whereas if you approach from 0^+ is 0.00000000000000001 instead of -0.0000000000001

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[unborn basalt]

.close

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[tranquil pine]

I don’t understand the part encircled in blue

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[tranquil pine]

d

y(t)=3.sin(πt/4)

Establish the equation of a harmonic movement of double amplitude, of the same period, and delayed by a quarter of a period.

pls help me

i cant find the delay

[hidden kernel]

+pi/4?

[gritty solar]

what's the period?

[tranquil pine]

period is 8

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[shut bough]

can someone help me with my pre calc test

[tranquil pine]

what

[hidden kernel]

#❓how-to-get-help

[tranquil pine]

oh thanks

[grim badger]

No

[hidden kernel]

O_O

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[pallid forge]

I will use this right now

[pallid forge]

My Further Maths teacher gave us a question: "Find a Matrix M which Projects all points to the line y=mx, such that the Projection (on y=mx) is the least distance to the original point" (So say we have point P, and it's Projection on the line y=mx "Q", QP is perpendicular to OQ). My question here is this: Could someone check my answer please?

Here it is (2x2 Matrix) :

(where M is the matrix written such that (a , b | c , d) is a 2x2 matrix with top row: ( a b) and bottom row: (c d)

[1/((m^2) +1)] * (1 , m | m , m^2 )

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[normal hill]

Firstly we can divide both sides by 2 cant we?

[tawny ferry]

.close

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[tranquil pine]

I need to figure out what positive integer >=0 and <= N - 1, which should replace X1 to make the congruence true. I thought it'd be 1, but apparently it's not?

[robust mulch]

!show

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

[tranquil pine]

My mistake, here's what I did:

• Calculated the modulo of 65%67, which is 65
• Calculated the modulo of -937 by using the division algorithm, which was negative 66

That lead me to the conclusion that adding 1 to -937 would result in the modulo 65 instead of 66, right? The program is telling me 1 is incorrect, so I'm kind of stumped on where to go from here...

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[tranquil pine]

<@&286206848099549185>

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[waxen prawn]

Let $f:B(0,1) \rightarrow B(0,1)$ be a holomorphic function such that $f(\frac{1}{2})=\frac{1}{4}$. Determine the set of possible values for $f'(\frac{1}{2})$.

[soft zealot]

Casiel368

[waxen prawn]

B(0,1) is the open unitary ball centered at 0 on the complex plane

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[waxen prawn]

<@&286206848099549185>

[bleak skiff]

Hey

[waxen prawn]

Yes?

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[waxen prawn]

<@&286206848099549185>

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[civic ether]

Could someone help me with this

or at least with understanding this cuz i don't see where GK can be a perp to AF

i guess they're using this model

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@civic ether Has your question been resolved?

[final saddle]

@civic ether Has your question been resolved?

[fast salmon]

just do pythag on this and solve for x

@civic ether

[civic ether]

how do you know they're all x though?

[fast salmon]

Because you divided equally from the same midpoint to corners of the square

[civic ether]

oh bruh

nobody pointed that out

[civic ether]

can u explain this too?

[fast salmon]

I literally can't follow with the wrong variables

But I think the method I just showed is way easier

[final saddle]

@civic ether Has your question been resolved?

[civic ether]

your method is nice

except i don't see how u can just label it as x's

like okay

but not convincing

those are equal yes ofc (yellow) cuz midpoint separates into half

but i don't follow for the x's tbh

[fast salmon]

There is a way to prove my statement

With congruency

@civic ether

@civic ether

<@&268886789983436800>

Spam above

Now I'm wondering why I went to prove ACB and CED was equal I could have just used RHS

As AC = B[and Midpoint of CE]

Which is same as CD

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[hoary turret]

I'm trying to understand (2). I'm struggling to understand the necessity of the subcases.

He says that we "must" prove that when a >= 0 and b <= that a + b >= 0 is <= a - b. And then also says the we "must" prove the second subcase that when a + b <= 0-a - b <= a - b.

I see that it is, but I'm failing to understand the selection of proofs. Why, for example, do we need to prove that -a - b is <= a - b when a + b <= 0? Why, for example, do we not need to prove that when a + b <= 0 that -a - b <= a - b?

I'm not understanding why we've chosen these specific inequalities as proof and why they're necessary and why they're in the order that they're in.

[tired walrus]

!msgdel

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[tired walrus]

why not

show what

[desert mantle]

tex is something to write down mathematical stuff. it doesnt check whether they are true

do you mean the command to ask wolframalpha?

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[obtuse pagoda]

I don't understand

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[obtuse pagoda]

<@&286206848099549185>

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@obtuse pagoda Has your question been resolved?

[tranquil pine]

its just shifted by ten

@obtuse pagoda

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[cursive marlin]

What is the function definition of this? like y=?

[desert mantle]

this is not a function

it doesnt pass the vertical line test

[cursive marlin]

wdym? vertical line test?

[desert mantle]

there are two y values for a single x value

[gritty solar]

The equation to the curve would be $y^2 = 4ax$ if that's what you're looking for

[soft zealot]

NEON

[lyric breach]

$y^2 = x$

[soft zealot]

KAVA

[lyric breach]

but that is not a function

[cursive marlin]

How do you guys know it by just looking at it?

[gritty solar]

Well $y^2 = 4ax$ is the general equation of a parabola with axis along the positive x axis

[soft zealot]

NEON

[gritty solar]

The exact equation would be hard to tell

[lyric breach]

It is good to memorize end behavior and shape of graphs for certain equations

[cursive marlin]

okay

[lyric breach]

So part of it is just experience

[gritty solar]

Or if you know how the graph of $y = \sqrt x$ looks like you can maybe work from there

[soft zealot]

NEON

[echo needle]

y^2=2x looks good

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[thorny iris]

i know this is pretty basic stuff but i'm not sure how to do this problem

[thorny iris]

i know i'm supposed to start by taking the derivative of both sides but i'm not sure how to get the derivative of xy

[gritty solar]

Product rule

Remember that y is a function of x

[thorny iris]

gotcha

gimme one minute im trying to work through the whole thing

would it just be 0 for the xy part?

[gritty solar]

It wouldn't

[thorny iris]

🥲

[soft zealot]

NEON

[thorny iris]

i think so

actually wait do i 💀

[gritty solar]

What would it be?

hmm

[soft zealot]

NEON

[gritty solar]

Does this look familiar?

[thorny iris]

product rule

[gritty solar]

yes

[thorny iris]

idk why in my head i was telling myself x' was 0 💀

ok so im gonna redo that but correctly this time

ok so i'm ending up with -2x+2y now (with the deriv. of 4xy being 4x +4y)

i know i have to be doing this wrong 🥲

[scarlet sequoia]

how is the derivative of 4xy : 4x + 4y ?

[thorny iris]

i have no idea what im doing here 😭

[scarlet sequoia]

what's the derivative of y? with respect to x

[thorny iris]

that's where i'm stuck

[gritty solar]

well

[thorny iris]

im kinda stuck on the basic concept of derivatives with respect to something

[gritty solar]

Can you work out $\dv{x}(xf(x))$

[soft zealot]

NEON

[thorny iris]

that would be the chain rule right?

[gritty solar]

still product rule

[thorny iris]

oh 😭

yeah i should be able to

it would be (x')(f(x)) + (f'(x))(x) right?

[gritty solar]

Perfect

And what is x'

[thorny iris]

1?

[gritty solar]

so all in all we have f(x) + xf'(x)

$\dv{x}(xf(x)) = f(x) + xf'(x)$

[soft zealot]

NEON

[gritty solar]

Can you differentiate both sides of $y = f(x)$ for me?

[soft zealot]

NEON

[thorny iris]

on the left side am i getting the derivative of xf(x) or d/dx (xf(x))?

[tranquil pine]

What you trying to doing here

[gritty solar]

What?

[thorny iris]

sorry for making this so confusing 💀

OH i was looking at the last image

shit 💀

[gritty solar]

Don't worry this bit is confusing to most beginners

It becomes second nature later on

[thorny iris]

y' = f'(x)

[tranquil pine]

Are you facing problem in the differentiaon of two multiplied function?

[thorny iris]

i thought you were asking me to differentiate both sides of this 😭

[tranquil pine]

Dude. Lol. It's the same

[gritty solar]

$\dv{y}{x} = f'(x)$

[soft zealot]

NEON

[gritty solar]

Simply replace f(x) with y and f'(x) with dy/dx

[gritty solar]

Here

[gritty solar]

Wait why did you change it to 1

y' was right

[thorny iris]

oh 😵

changed it back

OH

[gritty solar]

Do you understand what I mean

[thorny iris]

i think it's clicking

[next iris]

https://discord.com/channels/268882317391429632/1159940087237333012

[thorny iris]

ok so going back to the original problem now i have
$\dv{y}{x} x^2-4xy+y^2 = \dv{x} 4$

[soft zealot]

loganthebrewer

[thorny iris]

hoping i did that notation right

[gritty solar]

You can't differentiate select elements

[thorny iris]

ok i totally fucked up the notation on the bot

[gritty solar]

You need to differentiate the whole thing

And uh we aren't done

[thorny iris]

my bad 🥲

[gritty solar]

$$\dv{x}(xf(x)) = f(x) + xf'(x)$$
$$y = f(x) \implies \dv{y}{x} = f'(x)$$
$$\dv{x}(xy) = y + x\dv{y}{x}$$

[soft zealot]

NEON

[gritty solar]

Does this make sense?

Its a summary of what we've done

[thorny iris]

got it

[gritty solar]

Now we can move on to your implicit differentiation problem

$\dv{x} x^2 -\dv{x} (4xy) + \dv{x} y^2 = \dv{x} (4)$

[soft zealot]

NEON

[gritty solar]

Do you think you can handle it now?

Was it only the d(xy)/dx part that was bothering you?

[thorny iris]

i think so

[gritty solar]

Alright then I'll leave you to it

[thorny iris]

i'm gonna leave this room open while i try this just to confirm my answer

just realized that i messed up the basic algebra :|

what am i doing wrong here?

<@&286206848099549185>

[thorny iris]

original problem for reference

[tranquil pine]

in the first line, y² will differentiate into 2y.y'

[thorny iris]

could i get an explanation for why it gets differentiated like that?

that sounds right but i'm not really sure how it works

[tranquil pine]

we're differentiating y with respect to x, i.e. dy/dx, that's why x² will become 2x.1 but y² will become 2y.y'

if we differentiate x with respect to y, i.e dx/dy, x² would become 2x.x'

[thorny iris]

ohh ok

ty

not sure what to do now that i have two terms with y' 😭

[tranquil pine]

take y' common for those two terms, shift everything else to RHS so you only remain with y' on LHS

[thorny iris]

i've gotten it to this point

[tranquil pine]

take y' common on the right, shift the remaining to LHS

[final saddle]

@thorny iris Has your question been resolved?

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[winged python]

I need help with this, I tried 8cos(t)i+8sin(t)j but nope, says wrong answer

[winged python]

☝️ Calculus III question

asked for circle with radius 8, my mind went straight to unit circle, the 8 infront would give it that radius, and at t=0 the point is (8,0) so I don't get what's wrong

(╯°□°)╯︵ ┻━┻

(if anyone replies plz ping me so I get a notification, I'll be working on other problems in mean time)

[warm ether]

as t increases it should fill out clockwise

yours does so anticlockwise

@winged python

(just put a - in front of the t's)

[winged python]

Oh, so a negative t

I'll try that

That's what I was missing! And it makes sense to have the t negative to flip the orientation, tysm for the help @warm ether !

[warm ether]

no worries

[winged python]

.close

[final saddle]

Channel closed

Closed by @winged python

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[tawny frigate]

How do I approach this problem?

[desert mantle]

multiply out the left side and compare

[tawny frigate]

Let me try

[tawny frigate]

left multiply?

(x
y
z) *(1 -1 1
-1 1 -1
1 -1 1)?

[eternal lichen]

No, multiply the left side. It will be a matrix

[tawny frigate]

hmm

left side of the equation you mean?

[eternal lichen]

Yes, ofc

$a*a^T$

[soft zealot]

Xenophon

[tawny frigate]

oh okay

[final saddle]

@tawny frigate Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

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.

[frosty swift]

I don't even know where to begin

[void valley]

you know a formula for the general term?

of arithmetic progression

[tranquil pine]

the sum of an arithmetic progression is (1st term+last term)*number of terms/2

try subbing the values in

[frosty swift]

oh, yeah

un=u1+(n-1)d

[frosty swift]

okay so

n/2 (12-78)

what next tho?

oh wait can I do

s = n/2 (12-78)

s = n/2 (-66)

-363 = n/2 (-66)

-363 x 2 = n (-66)

-726 = n (-66)

-726/66 = n

n = -11?

okay and then for common diff

un=u1+(n-1)d

=12+(-11-1)d

=12-12d

-78-12 = -12d

-90 = -12d

d = 7.5?

<@&286206848099549185>

[urban sky]

-726/-66=n

why will the number of terms be negative

[frosty swift]

wait so
-726 = n (-66)
is
-726/-66=n?

I thought the -66 becomes 66 no?

[urban sky]

you divided by -66

so -726/-66

[urban sky]

yes

[urban sky]

why?

you are dividing not adding

[frosty swift]

eee my bad

okay so it becomes
-726/-66 = n
11 = n

[urban sky]

yes

[frosty swift]

un=u1+(n-1)d

-78=12+(11-1)d

-78 = 12 + 10d

[sterile swallow]

Yes

[frosty swift]

-66 = 10d

d = -6.6

[sterile swallow]

No

[frosty swift]

now?

[sterile swallow]

No

[frosty swift]

i- wait what

OH

[urban sky]

-90 = 10d

[frosty swift]

OMG

yes

d = -9

[sterile swallow]

Yes

[frosty swift]

god ty

[sterile swallow]

Good

[frosty swift]

<@&286206848099549185>

for a, -256/512 is -0.5

so common ratio is -1/2 right?

[sudden matrix]

yep

[frosty swift]

okay for b

un=u1 x (r) ^ n-1

so

un = 512 x (-0.5) ^ 12-1

un = 512 x (-0.5) ^ 11

what

where did I go wrong

is it
un = 512 x -0.00048828125???

so un = -0.25?

[urban sky]

yes

[frosty swift]

i doubt myself too much

okay now I have no clue how to find sum of infinite series

i dont know how to find sum of geometric series honestly

only formula for sum ik is n/2 (u1-un)

[urban sky]

that is for Arithmetic progression

there is a different formula for geometric

[frosty swift]

iii dont knw it

is geometric formula same as infinite formula?

[urban sky]

this is for finite number of terms

and Sn= a/1-r for infinite series

a is the first term

[frosty swift]

oo okok

so

wait

is it

Sn = a / 1-r
sn = 512 / 1-(-0.5)

or

Sn = a / 1-r
sn = 512 / 1-0.5?

[urban sky]

r is -0.5

[frosty swift]

i- wait so which one

[urban sky]

this one

[frosty swift]

HUH

wait but prev when inputting

sn = n/2 (u1-un)
becomes
sn = n/2 (12-78)

when 12 is the first number and -78 is the last one

shouldn't it become
sn = n/2 (12-(-78))?

[urban sky]

its n/2(u1+un)

[frosty swift]

im so stupid awoiejm

okok ty

okay so

Sn = a / 1-r
sn = 512 / 1-(-0.5)

sn = 512 / 1.5

sn = 341.33

[urban sky]

also i forgot to tell you sum of geometric series only exists if |r|<1

[frosty swift]

wait what

what if it's 2?

1, 2, 4, 8, 16

can we not use sum formula then???

[urban sky]

for infinite

[frosty swift]

O

someone smack me

[frosty swift]

this is correct tho yes?

[urban sky]

its fine for finite series

[frosty swift]

noted

[urban sky]

for infinite |r|<1

[urban sky]

yes

[frosty swift]

u mad smart fr