help-27

[robust dust]

addition can be viewed as a function that takes a vector and returns a scalar (the sum of its components)

so you can compose it with another function that takes a scalar argument

it's just super weird looking because + is written infix

[supple knot]

yea i'm mostly guessing at what alex wants

[restive river]

It's basically what desync said

[supple knot]

@restive river can you clarify what you mean

[restive river]

Just wanted to verify this. But I think it makes sense noe

But what would be better notation

[robust dust]

define a new function g:R^n->R

by (x1,x2,...xn) -> x1+x2+...+xn

so you can consistently write everything in function notation

[placid rover]

mindreaders the lot of u

[supple knot]

u jelly

[robust dust]

you can also kind of mix fold notation in and write +/(x1,x2,...xn)

but this is uncommon

[placid rover]

[restive river]

Second question

Firstly

This is a proper definition for what a matrix is right:

$M : \Z_{[1, m]} \by \Z_{[1, n]} \to \R$ where
[
M(i, j) = M_{ij}
]

[supple knot]

no

[placid rover]

lex get some better notation

theres also no such thing as 'proper'

Z_[a, b] is absolutely cursed

[robust dust]

if you wish to view a matrix as a function I guess that works? but your Z restriction is cursed

[restive river]

Hmmmmmm

[wicked turtle]

i've seen worse, but it isn't great..
the only somewhat standardish and compact notation i've seen for the first n positive integers is [n]

[placid rover]

compact is not the only issue

[n] is rather overloaded

[wicked turtle]

well if it's not, then just write {1,2,...,m} x {1,2,...,n}

[placid rover]

I would not say it is standard

[wicked turtle]

of course

[placid rover]

{1, ..., m}

[wicked turtle]

that's why i said standardish, haha, at least i've seen it from multiple authors

[placid rover]

I would need quite a bit of context to clock what you meant

if u write me f : [m] x [n] -> R

i dont think most ppl would be able to tell

[wicked turtle]

agree, anyone using that should say, "where [m] means..." when they first introduce it, otherwise it's gonna be cryptic

[robust dust]

where [m] means {m,m+1,m+2,...}

[placid rover]

rather than think about this though, it is better to first define R^n

[placid rover]

tbh if ur going down this route u might as well take the set defn of numbers

0 = {}
n = {0, 1, ..., n-1}

then we have M : m x n -> R

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[opaque terrace]

just learned discontinutiy stuff and i'm struggling

i think it's 1,5 and 7

[wicked turtle]

can you describe how you would remove the discontinuity at 5?

[opaque terrace]

Honestly I don't know

[placid rover]

a removable discontinuity is an x value where you redefine the function

so that the new function is continuous at that point

f(5) = 3.5 right now for example.

You could redefine it to be f(5) = 10 say. But you have to choose something to make the new function continuous at 5

[opaque terrace]

Oh ok

So thinking that, it woiuld just be 1 and 7 then I think

[placid rover]

yes.

[wicked turtle]

the discontinuity at x=5 is called a "step discontinuity" or "jump discontinuity", and those are never removable

just fyi

[devout snow]

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[solemn ginkgo]

alr my math teacher ain't answering so lemme copy my email and send it

"Alright, for the homework thing I found on google classroom. I need to solve 8 divided by 8/9. I used a calculator and it was 9, but I am still super confused on how this works.. What I think is 8/1 divided by 8/9. 8 divided by 8 is 1, 1 divided by 9 is 1/9.. How do I turn 1/1/9 into 9??
Also..
-4/5 + 1/2 = -3/10. How? Thought it'd be -5/7."

[solemn ginkgo]

idk how to work the bot still

someone teach me how to work that equation bot and ill like make the equations easier to understand

,help

[woven radish]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[robust dust]

dividing by a fraction is the same as multiplying by its reciprocal (the fraction "turned upside down")

so 1/(1/9) = 1 * (9/1) = 9

[solemn ginkgo]

ohh yeah

[robust dust]

also brackets

(1/1)/9 is not the same as 1/(1/9)

for future reference

[solemn ginkgo]

so then 1/8 ÷ 8/9 that makes life easier lmao

what abt the second one?

[solemn ginkgo]

(ty)

[robust dust]

you can't add fractions like that

[solemn ginkgo]

(it's been all summer I'm so confused LMAO)

[robust dust]

you've just added the numerator and denominator

if you do that to 1/2 + 1/2 you would get 2/4

which is 1/2, and is clearly wrong

you need to have the same denominator on both fractions

[solemn ginkgo]

ah yea now I remember

[robust dust]

when you see 4/5, it's 4 * one fifth, and 1/2 is 1 * one half

they're not the same thing, so you can't add them directly

[solemn ginkgo]

so the lcd is 10

i think

-8/10 + 5/10

ohhh

now i see

thank u! sorry I'm dumb 😭💀

tyty :]

.close

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[robust dust]

no worries -- nothing to be sorry for, we're all learning here 🙂

[devout snow]

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[iron pond]

Well I was watching a video about equations with radicals because like everything in maths I find them hard to do and saw the guy do this equation which is fine but I don't really understand the last part, 0= x(x-4) and then puts as a result x = 0 and x=4 without so much as an explanation, it blew my mind, could anyone explain why he did that?

[jaunty mantle]

If I tell you a*b = 0

What can you tell me about a and/or b

[iron pond]

What...?

Sorry, I don't really understand what you're trying to ask

What a? What b?

[jaunty mantle]

Some arbitrary a and b

But I tell you

When I multiply them I get 0

What can you tell me about this a and b I picked

[devout snow]

@iron pond Has your question been resolved?

[iron pond]

I don't know

Am I supposed to tell you what number they are?

[jaunty mantle]

Yes

0 is very special

If I have a number a

[iron pond]

Well one of them has to be 0

[jaunty mantle]

Exactly

So if x(x-4) = 0

Then one of them has to be 0

So either x is 0 itself

Or x is 4 which gives 4(4-4) = 4*0 = 0

[iron pond]

Oh!

Now I get it

You had me extremely confused there for a second

Thanks, though

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[west tinsel]

hi

[west tinsel]

z^2 = i

using this formula, but my result is 1 and i?

which is not correct

1 * e^i(0+p * pi)

[devout snow]

@west tinsel Has your question been resolved?

[wicked turtle]

what did you use for |w| and arg(w)?

[west tinsel]

for |w| = sqrt(a^2+b^2)

for arg(w) = a/|w|

[wicked turtle]

what specifc numbers

[west tinsel]

a = 0, |w| = 1

[wicked turtle]

why is arg(w) = a/|w|, that doesn't sound right

arg(w) is the angle, and the angle of i is pi/2, not 0

[west tinsel]

really?

[wicked turtle]

a/|w| would be the cosine of the arg

[west tinsel]

ya i figured it out now

[devout snow]

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[west tinsel]

i needed to take cos(v) = 0

which is pi/2

[devout snow]

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[worn python]

Can someone help me with grade 8 math?

[worn python]

I really can't understand this 😭

[timid whale]

do you know

the properties

of a transversal

[worn python]

No 😓

[strange arch]

but you are familiar with properties for angles

e.g. the angles G & E form a "semicircle" or rather, their sum must be 180°

[worn python]

I don't know the basics at all 😭

[strange arch]

hm I currently can't visualize stuff as I'm travelling, but you do know that a full circle has 360° degrees right

[worn python]

Yes

[strange arch]

if you split the circle into two equally sized semicircles using a diagonal that cuts through the circle, the two angles on both sides must have 180° each

[worn python]

Oh

[strange arch]

since you just split the 360° in 2

now if you look at the first task, G & E & F & H together form a circle if you draw the angles into the image

meaning their sum must be 360°

if that becomes clear to you, all further steps become easier too

[worn python]

I'm starting to understand 😅

[strange arch]

applying the same principle as I mentioned above, we now "cut" the circle of GEFH into two with a diagonal, where on the upper side are GE and on the lower side HF

since each side must have 180°, G+E = 180° and H+F = 180°

I know there are two diagonals cutting them in the image, just consider the one going up from left to right for now

which is the one that cuts GEFH into GE & FH

[worn python]

Ok 😅

[strange arch]

that was the important step

because now you know G+E = 180°

and you're already given G = 72° in Task 1.

therefore E = 180°-72° = 108°

[worn python]

Oh 😭

Tysm

[strange arch]

you'd say G and E are supplementary

because of the above explanation

[worn python]

Oh

[strange arch]

now, try continuing with 2. and so on and mention whenever you're stuck

[worn python]

So H is also 72°?

[strange arch]

nop

look at only G & H for instance

both of them together form another semicircle on a diagonal

meaning their sum is 180°

[worn python]

Ohh

[strange arch]

likewise H&F together form a semicircle

E&F do as well

[devout snow]

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[mint cove]

Is the current through each resistor the same as the current through the battery, I’m new to this stuff so I’m just a little confused

[red turret]

In a series connection, the current stays same while in a parallel connection, potential difference (voltage) remains same.

[mint cove]

so voltage is the same but current is different at each of the points?

[red turret]

this is a series connection

[mint cove]

idk what the means

[red turret]

https://www.khanacademy.org/science/physics/circuits-topic/circuits-resistance/v/circuits-part-2

[mint cove]

I think I get it now, since it has to go through each of the resistors it slows it down for the entire series and as such the current is constant throughout, right?

[red turret]

well, there is only one path for the current, so it cant change.

[mint cove]

alright, thank you

.close

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[restive river]

Good evening, I need help understanding this evaluation of function

[static oracle]

basically you just substitute the given value into the place of x

[restive river]

No no

I was confuse of like

The x is value

[static oracle]

what

[restive river]

Like X = 2x+4

[static oracle]

yea that's given right

[restive river]

Ye

I was confuse on how

To solve it that way

[static oracle]

just think of it as a number

substitute it and continue solving

you should end up at the ans then

[restive river]

So if there's like X^2

It should be (2x+4) (2x+4)

[static oracle]

yes

doubled

[restive river]

So it's like 2+2

Wait x

2x2 is 4
While 2x4 is 8

(2x^2+8x+8x+16)

[static oracle]

you solving this?

[restive river]

I'm solving it on paper

Ignoring the pic atm

[devout snow]

@restive river Has your question been resolved?

[restive river]

No.

[restive river]

So in the 2ns image

2nd*

The X is X+6

The one I got confuse is

How I can solve it

[devout snow]

@restive river Has your question been resolved?

[long pasture]

although i dont like such notations, i think it's just finding
f(x+6)

which you replace all the x's in the original f(x) into (x+6)

and simplify

[devout snow]

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[cunning perch]

hi I just had a question

[cunning perch]

when drawing a box and whisker plot, do u need to add the outliers as well

when I searched it online, it said yes, but it didn't show the outliers within the lines so i was confused

the max and min lines I mean

[devout snow]

@cunning perch Has your question been resolved?

[cunning perch]

.close

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[heavy tinsel]

I'm trying to understand the relationship between expected wait time and probability. For example, let's say that person A is taking turns rolling a d6, and person B is taking turns rolling a d4. Players want to wager a fair amount for who will roll a 1 first. We know that person A's expected wait time is 6 turns, and person B's expected wait time is 4 turns. But I'm not sure how to get from that to determine what is the probability that person B sees a 1 before person A does

[paper latch]

what happens if they both roll a 1

[heavy tinsel]

Then they would continue rolling until one has a 1 and the other doesn't

[winter torrent]

in that case it's simple enough, there are 24 possibilities; in how many of them does A win? in how many of them does B win?

[heavy tinsel]

The actual problem I'm trying to solve is this: Player A is flipping coins until he gets sequence TTH, and B is flipping until he gets TTT. I've calculated that A's wait time is 4 flips, and B's wait time is 6 flips. I'm not sure if this would be the same answer as the above question (I thought it would be simpler to ask that one)

[heavy tinsel]

but there are an infinite number of possibilities. A and B could roll 3s for a thousand turns, for example

[winter torrent]

yep, and they'll be right back where they started

the only possibilities that matter are the ones where either A or B win

[paper latch]

the original question is easier; consider playing until TT occurs

before TT occurs, no one could have won

[winter torrent]

are they the same coin or different coins

[paper latch]

o wait yeah sorry

important distinction

[heavy tinsel]

they each have their own coin

[paper latch]

ignore what i said then

[heavy tinsel]

That does make sense. I think I understand for the dice question.

[winter torrent]

ooh TTH has a strong advantage here i think

[heavy tinsel]

yes, TTH has a big advantage

[paper latch]

Solution to the dice problem

[heavy tinsel]

(sorry in meeting looking at this in a min)

[paper latch]

basically even if u dont use that exact thing, i would just recommend drawing a tree diagram

which may be recursive

[heavy tinsel]

right

[winter torrent]

the diagram for the coins is much more involved

[heavy tinsel]

yeah I'm a bit stuck haha

for wait time it wasn't too bad

[winter torrent]

actually ttt has one advantage which is that they're more likely to win ties

this is like a Markov chain problem or something, there are so many states (13 or so)

[heavy tinsel]

this is harder than I thought it was going to be

I was trying to come up with a good brainteaser for a smart friend

[devout snow]

@heavy tinsel Has your question been resolved?

[devout snow]

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[devout snow]

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[steel sage]

Given two square matrices of the same size D and N, D is diagonal and N is nilpotent. Do we have det(D+N)=det(D)?

[steel sage]

Someone gave me a counterexample

So not true

.close

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[vernal lotus]

need help with a few problems

[devout snow]

@vernal lotus Has your question been resolved?

[vernal lotus]

<@&286206848099549185>

[restive river]

what

???

[vernal lotus]

can yu help me

[restive river]

ye

lemme see

[vernal lotus]

.close

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[restive river]

idk

im too stoopid

[devout snow]

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[low walrus]

$\int_{2}^{5/2}(\sqrt{4x-x^2}+2)\sqrt{(\frac{4-2x}{\sqrt{4x-x^2}})^2 + 1}dx$

I'm thinking there has to be a faster way to solve this monstrosity of an integral but I can't seem to find it. I honestly don't even know how to approach this so help would be appreciated lol

[woven radish]

NepDep

[rapid merlin]

I think what comes to mind first is to take
$$u = \sqrt{4x - x^{2}}$$

[woven radish]

Sherif Player

[rapid merlin]

But I have no idea if it would help

[low walrus]

yeah, where would du go

maybe expanding the square might lead to a solution

but nothing stuck out to me when i did that

ill just do it a second time and see whats there

[rapid merlin]

$$du = \frac{4-2x}{2 \sqrt{ 4x - x^{2}}} dx$$

[low walrus]

yeah i found nothing when i expanded the square

maybe i set up the integral wrong to begin with?

[woven radish]

Sherif Player

[rapid merlin]

Doesn't work very well

[low walrus]

This is the original problem, i need to find the surface area of the solid of revolution

im thinking if i set up the integral wrong this might be an easier question in disguise

i shouldve used y rather than x

[prisma snow]

lemme try

[rapid merlin]

So you say we should have takin the integration with respect to y not x?

[low walrus]

well not really

i was taking integration with respect to y but i wrote it as x because im dumb

[rapid merlin]

As it is around y-axis

$$Y^{2} - 4Y + 4 = 4 - X^{2}$$
$$X^{2} = 4Y - Y^{2}$$
$$X = \sqrt{4Y - Y^{2}}$$
So we want to take the integration of that one

[woven radish]

Sherif Player

[prisma snow]

ok i got it

[low walrus]

oh

oh my god im an idiot lol

i was integrating the wrong function

[prisma snow]

do you want working

[low walrus]

i was just taking the one i saw and thought it was in terms of y for some reason

[prisma snow]

here it is if you are interested:

[low walrus]

so the derivative of that would be 4-2y(4y-y^2)^-1/2

[prisma snow]

oops wait

[low walrus]

wow youre fast

but the answer key said the answer was 2pi

[prisma snow]

yeah i forgot to square too

[low walrus]

this is so helpful

thx

[prisma snow]

nws

[low walrus]

.close

[devout snow]

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[devout snow]

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[pastel pasture]

$\int e^{\cos x} \left ( \frac{x\sin^3 x + \cos x}{\sin^3 x} \right ) , \dd x$

[woven radish]

NEON

[stark shuttle]

That looks ugly

[pastel pasture]

Oh boy it sure does

The worst part is I don't even know where to begin

There's no clue in this structure

[stark shuttle]

My guess is to simplify and IBP?

"I think"

[pastel pasture]

perhaps but what does simplify entail

[stark shuttle]

Maybe changing the sin^3?

What does Wolfram say?

[pastel pasture]

the one on top or bottom

,w integrate (e^(cos x))(xsin^3 x + cos x)/(sin^3 x)

[woven radish]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by neonperseus

[pastel pasture]

💀

[sinful gust]

,w integrate (e^(cos x))(xsin^3 x + cos x)/(sin^3 x) dx

rip

oh wait

this isnt that bad

nvm

it is

[sinful gust]

where did you get this integral from

part of a solution to a DE?

[hybrid snow]

,w integrate (e^(cos x))(xsin(x)^3+ cos x)/(sin(x)^3)

[woven radish]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by umbraleviathan

[hybrid snow]

Bro

[red turret]

ayoo

where you got this from?

btw not sure, but the denominator is sin^2x lol

crosscheck if possible

and this question will use this (if it really is sin^2(x))

[pastel pasture]

Bro why is everyone so interested in the origin of the question lmao

In any case, it is the cube of sine

[woven radish]

Dyssrupt

[sinful gust]

that tells whether it might even be solvable in many cases

[red turret]

oh

[red turret]

this is why

[pastel pasture]

We have more robotic integration

[pastel pasture]

Oh wow

No mine definitely says cube

[red turret]

hmm

[pastel pasture]

meh I'll figure something out

.close

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[restive river]

For c I'm guessing you can't have both can you?

[stark shuttle]

Uhhh

[pseudo basin]

why can't you have both

a person may hold a passport and a VRC at once, can they not?

they need only present one at the checkpoint, but they can give either one...

[young crane]

What country?

Never entered a country w a voter’s card

[restive river]

you can enter your own country with a voter's card

[young crane]

If I leave the country won’t I return w a passport?

[winter patrol]

noones saying you don't unless you lost it for some reason

[restive river]

But you don't need both of them do you?

[winter patrol]

in the scenario its just saying that you don't technically need one

[restive river]

I think the word "need" is what's making me hesitant

[robust dust]

you don't need both, is not the same as you can't have both

[restive river]

its inclusive or

[robust dust]

which is what you've said

[wicked turtle]

you need to have at least one of them

they're not saying you must have only one of them

contrast with the "soup or salad" example

[robust dust]

exclusive or would be them telling you that you can't enter if you do have both

[winter patrol]

or an item costs
1 euro or
2 usd

can't hurt to have more money

[young crane]

Losing a passport serious issue!!

[winter patrol]

noones saying it isn't

[wicked turtle]

i bet you'll spend some time in an interview room being grilled if you try to enter even your own country without a passport

they'll want to know where you've been, at least

(unless you're in a passport-free zone like the EU)

(d) seems like possibly a trick question, your institution wants you to publish and they may or may not care if you also perish as long as you publish 😁

[pseudo basin]

you don't need both but you aren't forbidden from entry with both

[winter patrol]

(there are potential issues if they aren't your own though)

[young crane]

Not where I live

[winter torrent]

Jorji is that you

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[fervent patio]

I wanted to find the best u such that
log_2(x+1) is best aproximated by x+u(range 0-1).
I calculated the integral of the difference and set it equal to 0 to minimize the difference (https://www.wolframalpha.com/input?i2d=true&i=Integrate[Divide[ln\(40)x%2B1\(41)%2Cln\(40)2\(41)]-\(40)x%2Bm\(41)%2C{x%2C0%2C1}]%3D0) and the answer came out to be around u≈0.057305.

A different source said that it was 0.043.
Where did I go wrong?

[stone stump]

difference? absolute difference? absolute difference squared?

there are quite a few different options of what "approximates best" means

[fervent patio]

Uh

[fervent patio]

It was to minimize the |average difference |

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[restive river]

"We will have a future, provided that people believe in science"

[restive river]

In if...then form then this is just "if people believe in science then we will have a future", correct?

[fallen saffron]

yeah seems correct

[restive river]

Ok ty

. close

. Close

. close

. close

. close

Bruh

.close

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[pseudo basin]

quintuple coose

[devout snow]

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[dusty valley]

I need help understanding angle addition identities. I'm working on sin(A+B) = cos(A)sin(B) + sin(A)cos(B). I'm not sure how to draw the 2 triangles on the unit circle. This is what I have tried in Whiteboard:
https://wbd.ms/share/v2/aHR0cHM6Ly93aGl0ZWJvYXJkLm1pY3Jvc29mdC5jb20vYXBpL3YxLjAvd2hpdGVib2FyZHMvcmVkZWVtLzAxYWMwODI1YWVhMDQ4ZTk4OWU2NmUyN2Y2NzJkZDY1X0JCQTcxNzYyLTEyRTAtNDJFMS1CMzI0LTVCMTMxRjQyNEUzRF81Y2IzYWI3Mi03YTBiLTRiNTQtODFiMS00MTMwMmE5YzA4OTQ=

[dusty valley]

Will I draw the 2 triangles as overlapping or as literally next to each other, not overlapping?

This is a ghost town....I'm frightened....

Hello, Hello, Hello?

[pseudo basin]

it has been ten minutes.

[pseudo basin]

after getting through microsoft's login bullshit, i can say: this is somewhat of a poor diagram.

[dusty valley]

I know, I'm learning

[pseudo basin]

i can show you a better diagram if you're okay with that.

[dusty valley]

Yes, of course, thank you.

[pseudo basin]

it has the drawback of only really working with angles between 0 and 90°

but it is very visual

[dusty valley]

Well, I guess it's a first step. I'm just going through the Khan Academy and this is on the menu.

[pseudo basin]

tell me if you need me to label stuff on the diagram.

[dusty valley]

Ah, so the first thing I see is that my assumptions of the angle having to be drawn always horizontal/vertical are wrong. It can be drawn literally at any angle.

[pseudo basin]

of course.

an angle's still an angle no matter how you spin it.

anyway i copied this from a tutoring session whiteboard so just tell me and i will put point names on it.

[dusty valley]

Okay, that helps tremendously so far. I need to remember that the triangle spins

[pseudo basin]

most anything in geometry spins

[dusty valley]

Okay but can this be drawn and visualized on the unit circle also. I just noticed this is a free standing triangle. I only see 1 point that is in bold and I'm not sure it's on the perimter of any circle.

[pseudo basin]

visualizing this on the unit circle requires some vector shit.

if you're ok with that, i can try making one.

[dusty valley]

Well, it's worth a shot. I'm a beginner but I'll look at it. Thank You.

[pseudo basin]

be warned i'm going to take some time with this

[dusty valley]

No problem, I'm here for a few years, so please take your time. I'm not going anywhere.

[devout snow]

@dusty valley Has your question been resolved?

[pseudo basin]

here

i said it was vector bullshit and it is vector bullshit, mostly some mildly annoying vector algebra.

also i forgot to color-code them in steps III and IV, oops.

@dusty valley

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[floral blaze]

all these are vectors:
AF=AB+AC; CE=2AB; BD=1/3BC
There are two questions. no1 is answered, and am stuck in no2 :
express AE as a function of AB and AC
I Answered till here:
AE=AC+CE
=2AB+AC
Is it finished or do i have to calculate it

[floral blaze]

$AF→=AB→+AC→; CE→=2AB→; BD→=1/3BC→
Express AE→ as a function of AB→ and AC→$

[woven radish]

Minds&Moves

[floral blaze]

Someone told me that it's solved

but we're looking for AB+AC not 2AB+AC

[supple knot]

did you draw a picture

[floral blaze]

no

so is it solved orrr?

[devout snow]

@floral blaze Has your question been resolved?

[floral blaze]

<@&286206848099549185>

<@&286206848099549185>

[ancient ravine]

!15min

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[floral blaze]

Its passed 15 minutes!!

[floral blaze]

!!

[ancient ravine]

You ping the helpers two times in one minute

[floral blaze]

oh.. cuz they said feel free to ping helpers

[ancient ravine]

Read it

[floral blaze]

ok

so? helps?

[floral blaze]

<@&286206848099549185>

[devout snow]

@floral blaze Has your question been resolved?

[devout snow]

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[forest lily]

is

(450)/(4* pi *r^2) = dr/dt

correct

.close

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[weak cape]

Simplify. Rationalize all denominators. Assume that all the variables are positive.

[weak cape]

I tried to solve this question but I got -(90-42sqrt3)/269.. how to solve it?

[sonic smelt]

Doesn't seem right, could you show your work?

[sacred spade]

Yeah not what I'm getting either

[sand dove]

In those cases, always multiply by the conjugate, I assume it's what you've done but there might be a miscalculation somewhere

[devout snow]

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[autumn osprey]

Hi, I'm trying to learn Basic Calculus and I have a quiz by next week. I am having a hard time following the "Introduction to Limits" since I have skipped the majority of algebra itself. I am having a hard time understanding it.

I cannot explain it in a concise manner but I have this image, I do not have any work because I am just studying it and have no idea what the solution is because of my lack of knowledge in Algebra.

This is just the first image, there are a ton more that get progressively difficult. This is not homework, this came from a presentation sent by our teacher to study at home.

I have tried to search videos like Khan's Academy's explanation but they use f(x) without the "lim" and it's driving me crazy on what's right.

[autumn osprey]

<@&286206848099549185>

[sacred spade]

Gotcha

So do you want it just explained or?

[autumn osprey]

I want to know how to solve it including its actual solution, I have a hard time understanding its whole concept because of my lack of Algebra knowledge. My teacher said that algebra is going to play a huge part in this and that this topic is required and mandatory to learn to be able to understand and progress our calculus course.

I have a lot more images coming up with longer equations, I've tried searching for videos about it but they are confusing.

[sacred spade]

Mmm

Alrighty

[autumn osprey]

I do not even know how and when I should consider a limit a constant.

[sacred spade]

So, what it's saying is, as x approaches some number C

what does f(x) approach?

Or, view f(x) as y

[autumn osprey]

L?

[sacred spade]

Correct

As y approaches some number, being the limit L

[autumn osprey]

It's also confusing because the equations differ.

[autumn osprey]

Yes, L would be the answer right?

So how do I solve it? Is there any formula procedure to follow?

[sacred spade]

So, for any y= a constant value

Like, 1, 0, e, or 1835

What would y equal if x = 0?

[autumn osprey]

If 0 is constant, will the answer be 0 as well?

[sacred spade]

Well okay lets say we are given the equation y=0

What would y equal if x=0?

[autumn osprey]

Sorry, I am having a hard time solving this, I do not know but is it still 0? I am sorry for being this difficult.

[sacred spade]

We're basically moving away from the limits for now

I'm asking what would y equal when x=0 for the equation y=0 (a horizontal line)

[autumn osprey]

Sorry, I still don't get it. Can you teach me while I take notes?

[sacred spade]

Gotcha

[autumn osprey]

I just don't have any knowledge of mathematics, I skipped a lot of math courses and I regret doing it resulting in me not knowing anything from graphs to probability even fractions. This feel like a Level 100 boss in a game in easy mode.

[sacred spade]

Ooooh

okay

Lets start with the most basic equation then

y=x.

[autumn osprey]

I basically have the intellect of an elementary student in math, only in math.

[autumn osprey]

Yes?

I wrote it down.

[sacred spade]

so, what does x equal if y = 1?

(plug in 1 for y)

[autumn osprey]

Should I pull up a graph?

[sacred spade]

Sure.

[sacred spade]

Actually, pull up desmos.com

it's a graphing feature that would help us quite a bit

[sacred spade]

Now, put in y=x

[sacred spade]

Now, on this graph

We have the x axis (the darker horizontal line)

and the y axis (the darker, vertical line)

[autumn osprey]

Yes, I'm listening and taking notes.

[sacred spade]

Basically, we want to find where on the x axis it equals 1

and, where on the red line that x=1

For this specific line, we can see that x =1 at where y=1

and vice versa

okay that was really badly explained

If you need a better one lemme know before continuing

[sacred spade]

Okay okay lets back track

Basically, on the graph, the line examines exactly where the y value is equal to the x value

For example, when we trace where y is equal to 1, then the x value is equal to 1.

[autumn osprey]

Yes.

[sacred spade]

So, by tracing the line, what is the value of y when x equals 2?

[sacred spade]

Okay so I'm going to have you make that line, and now put y=x on top of it.

Where these two lines cross, that is the solution for y.

[autumn osprey]

Is this right?

[sacred spade]

Not quite.

This is what you should have.

[autumn osprey]

Oh, sorry I didn't know Desmos could do that.

[sacred spade]

No problem.

Basically, this means that, when x is equal to 2, then y is equal to 2

[autumn osprey]

Sorry for being difficult, I didn't know I was this bad in Algebra. I'm going to try and understand this one in my time. Will this be essential in Limits?

[sacred spade]

for the equation, y=x

[sacred spade]

Well... calculus requires the knowledge of everything before it

And it will be quite needed

[autumn osprey]

Holy damn... I am hopeless.

[sacred spade]

not quite.

now word problems, you probably don't need to go over

But as long as you learn all of the different equations, as well as most of trig you should be fine

Now, that's a hell of a task

quite literally condensing all of grade school math into a small timeframe

But, I believe it is possible to do

Understanding the graph and the linear equation is one part of it.

[autumn osprey]

The problem is I do not have a simple guideline as to where to start. Like.

1. Learn Addition
2. Learn Subtraction
3. Learn Multiplication
4. Learn Division

I'm trying to be on the right track, chronological order may be the right term? Like in movies, it gets progressive as it goes on like it gets harder as it goes on.

Like movies, you will not know the plot of what you're watching if you are watching part 4 before part 3.

Is there a proper way on what I should learn to prepare me for basic calculus?

I may be able to study everything before tomorrow.

[sacred spade]

1. Learn the coordinate plane
2. Learn linear equations (What is slope? what are the different forms of the linear equation? what is m? what is b?)
3. Learn quadratic equations (What is a vertex? how do you know if it is a max/min? what are roots/solutions/zeros? how do you factor? Quadratic Equation? How do you find domain/range?)
4. learn higher order polynomial equations (what are even/odd polynomials? What is synthetic division? How do you use p/q to factor? What is domain restriction?)
5. Learn Rational functions, root functions, logarithmic, and e (What are they, how do they shift? What is e used for?)
6. Learn Trig (what is soh cah toa? sin, cos, trig, and their opposites? How do you shift them? What is csc, sec, and cot? what is the inverses?)
7. bring it all together in calculus.

Here's a basic guide for equations

These go through the different levels of algebra, like the basics in pre-alg, then alg 1 with linear equations and quadratic equations, then geometry with triangles and trig, then alg 2 with higher order polynomials as well as rational functions, roots, and logarithms. and finally, the rest of trig.

I'm going to be honest, I don't believe someone can do this in a day

But, it's possible.

And I have high hopes for you

I can vc to help you learn

[autumn osprey]

I'll study these things first personally then maybe ask for help again here. I am going to dig up some notes I may have written in the past grades and see if it may help in this current situation.

[sacred spade]

but the real goats are khan academy

[autumn osprey]

Yes, it's been recommended by many.

[sacred spade]

not starting at calc

[autumn osprey]

I'm going to try it again.

[sacred spade]

but definitely starting at lower grade levels

[autumn osprey]

I'll study these before I reach college, or else I may need to change my engineer course to something more timid like architecture.

[sacred spade]

architecture requires a vast knowledge of physics, of which is calc based.

unless you are the designer, which requires less of it

but it does require less calc than engineering, that is true

I do believe that you can perservere, and I'm here for it

[autumn osprey]

Thank you, I have taken notes for the steps you've recommended. I will be closing this channel now. Not everyone had the patience to withstand my illiteracy in Mathematics. Thank you for setting me on the right track again, at least this time I know where to actually start. Thank you again.

.close

[devout snow]

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[timber kite]

how do i solve this and whats the answer?

[lapis flint]

!show

[devout snow]

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

[timber kite]

i dont now how to start it

do i take the inverse tangent of -12/5 and subtract it with the inverse cosine of 3/5?

[winter patrol]

you shouldn't be using any inverse functions for this question

it's also supposed to be a non-calculator question

draw reference triangles, apply pythag and based on the location of the angles
determine
sin(A), cos(A), sin(B)

[timber kite]

like thatv

i have this

is 33/65 right?

[devout snow]

@timber kite Has your question been resolved?

[devout snow]

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[restive river]

why is this not good now?

in notebook says -1/3 not -2

[wooden veldt]

Can you provide the question

[restive river]

why is this not good?

I looked in the notebook and I have two different results

does not match -2

x/3 is x here 1?

[wooden veldt]

Just a picture of the statement of the question from where ever you're reading it from

[restive river]

or regular x

[wooden veldt]

Because we do not know what you're doing without the question

[restive river]

is the solution I pictured good?

last example

3*e

[wooden veldt]

Without knowing what the question is how could I possibly answer that

[restive river]

hyh

Derivative

[wooden veldt]

Of? This is alot easier if you just send a picture of the question

[restive river]

I already have a solution, but I'm styding

[wooden veldt]

So you never took the derivative of -5/3

[restive river]

i guess no

[wooden veldt]

And the derivative of -5/3 is?

[restive river]

0?

but why is the derivative of (-1/3-5/3)

huh

someone else

how to the dervative of e pow(x+2)?

<@&286206848099549185>

brb have to eat

[robust dust]

just do chain rule on e^x and x+2

[devout snow]

@restive river Has your question been resolved?

[sacred spade]

To better answer this, you multiply the derivative of e^(x+2) times the derivative of x+2, which is the chain rule

[devout snow]

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[tender wind]

e^-x where x is = 0

[tender wind]

gives what

E^-0 is still 1 right

[quaint citrus]

$e^{-0} = \frac {1}{e^0} = \frac 11 = 1$

[woven radish]

Stephen

[quaint citrus]

Or just

$e^{-0} = e^0 = 1$

[woven radish]

Stephen

[strange arch]

Use l'hop.

[tender wind]

alr

ty

sin (1) is 0 right

nvm

[quaint citrus]

Other way around

[tender wind]

huh

[quaint citrus]

Sin(0) = 0

[tender wind]

Ohh

yes

sorry

.close

[devout snow]

Channel closed

Closed by @tender wind

Use .reopen if this was a mistake.

[tender wind]

.reopen

[devout snow]

✅

[tender wind]

when i differentiate e^-x

it gives e^-x still right

with *-1

[quaint citrus]

Right

[tender wind]

e^-x and this stays the same

it doesnt go back to e^x

[quaint citrus]

So e^-x * -1

[tender wind]

got it

[quaint citrus]

No

It doesn’t go back

Maybe I shoulda said “yes”

But u get it

[tender wind]

kk

so

1+1 over 1

2

[strange arch]

:o what a neat number

[tender wind]

[strange arch]

if you get 0, 1, 2, π or e then the answer must clearly be correct

[tender wind]

wait really

[strange arch]

:D

no

[quaint citrus]

Lol it’s a joke

[tender wind]

ah

i thought it was a trick

[strange arch]

it was meant as a joke like the ones who make questions are lazy

[quaint citrus]

Unless ur a uni teacher and wanna trick ur kids

[tender wind]

hahaha

[quaint citrus]

A dastardly action indeed

[prisma snow]

reminds me of a time where we had to simplify a tan equation and the result was 1 + 1 💀

[quaint citrus]

Lol

[tender wind]

in this lim should i transform it into -tan x over cos x

[main gull]

No

[tender wind]

how do i evaluate this

-sin x / cos^2 (x)

[main gull]

My bad, I might have gotten confused when I said this

[main gull]

This works

[strange arch]

Plug in

@tender wind

[devout snow]

@tender wind Has your question been resolved?

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[robust dust]

!status

[devout snow]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[plush light]

3

So basically I thought in order to solve this problem you would have to take the derivatives of both of x(t) and y(t) and see what value of t both of the derivatives result in 0

[robust dust]

so what did you get

[plush light]

the derivative of x(t) is 3t^2 - 6t

the derivative of y(t) = 12 - 6t

so t has to be 0 or 2

but it has to be 2 because it has to satisfy y(t) too

[green kelp]

Yea

[robust dust]

all good so far

[plush light]

so now we just plug 2 back into x(t) and y(t)

[ripe mason]

could not agree more

[green kelp]

Bro solved it by himself

[restive river]

lmao

[plush light]

what

no

i got it wrong though

[restive river]

what did u get

[plush light]

x(2) = 8 - 12

-4

[restive river]

ye

[plush light]

12

[restive river]

ye

so A?

[green kelp]

[plush light]

oh

[restive river]

lmao

[plush light]

bruh

thanks guys

[restive river]

no problem

[plush light]

.close

[devout snow]

Channel closed

Closed by @plush light

Use .reopen if this was a mistake.

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.

[tawny summit]

HELLO

[tawny summit]

?!

ANYONE HERE

<@&286206848099549185>

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[tawny summit]

i need help with algebratic equations

PLEASE

I SAW U DUDE

YES

[lyric hornet]

Be patient, post your question, and if you're respectful someone will help

[tawny summit]

sorry

its my first time

can u help me

pleas

E

[quaint citrus]

Post ur question homes

[tawny summit]

is that me

okay

i dont have like a paper

but i was wondering

wait wait

Do u know what algebraitic equations is

because im not sure on how to do it

[quaint citrus]

Hmm

I think I know what ur referring to

But send a problem so I can see what ur having trouble with

[quaint citrus]

Alright

[tawny summit]

how do i do it

[quaint citrus]

So what’s troubling u with this

[tawny summit]

the formula

what do i do first

how do i solve it

[quaint citrus]

There’s no actual formula to these

But essentially, u wanna get all the terms with an x on one side, and all the terms without an x to the other side

[tawny summit]

the only one with an x is 2x

[quaint citrus]

Good

But there’s also a term without an x on the left side

How would u move it to the right

[tawny summit]

i have no idea

but are u talking about the 7

-7

hello

uh

SORRY IF IM DUMB

[quaint citrus]

No, the -3

[tawny summit]

oh thats easy

-3 turns into +3

since uhm

You are basically doing the equation backwards

so its 2x + 3

[quaint citrus]

Wdym by turns into

[tawny summit]

what about the 7

[quaint citrus]

No

[tawny summit]

?

[tawny summit]

Is it right

[quaint citrus]

No

[tawny summit]

oh

[quaint citrus]

Maybe it would be more helpful if u watched a video on this concept first, maybe this one could help: https://youtu.be/q3g68vcMXxM?feature=shared

[tawny summit]

subsitutes

[quaint citrus]

To at least get a foundation

[tawny summit]

kay

This guy boring

Boom

easy dub

i found out

okay

MY BAD

so

negative 3 becomes positive 3

[quaint citrus]

Don’t say becomes

[tawny summit]

lets pretend there is a mirror line

[quaint citrus]

It doesn’t make sense

[tawny summit]

so it happens on both sides

what shall i say

Substitute

?

[quaint citrus]

The opposite operation

So currently it’s minus 3 on the left

So we add 3 to both sides

[tawny summit]

yeah

OH

that makes sense

okay

PRETEND THERE IS A MIRROR LINE OKAY

[quaint citrus]

Ok

[tawny summit]

so now its like 2x+10

so now

we need to find out what x is

so x X 2 = ?

5

5 X 2 = 10

X= 5

ez dub

come on

dab me up

[quaint citrus]

No

[tawny summit]

WHAT

its not right ?

[quaint citrus]

What’s -7 + 3

[tawny summit]

uh

-10

Where u come from

this dude helped me out

and i did it

nO

HOW

I WATCHED THE VIDEO

Is it 10

7

My bad

haha

SOEELING MISTKWE

4

my bad bro

my keyboard

HENSN,SHSHHAIO

WHY IM I SO DUMB

STUPID MATHS

im in the dark

okay

wait

Where did the other dude go

THAT WAS MY GUY

[quaint citrus]

-7 + 3

[tawny summit]

my GuY

[quaint citrus]

Same as 3-7

[tawny summit]

EZ

-4

ahem

I CANT DELETE IT

WHAT

uh

helllo

i NEED HELP MY GUY

please bro

u a smart dude

[quaint citrus]

Homey

Why u use calculator

What’s the point

[tawny summit]

i didnt

i worked it out before

The other guys help

helped me work it out

just wrote it down to check

[quaint citrus]

Ok so now what do we have now

[tawny summit]

lets see

-5

X=-5

[quaint citrus]

Show how u got that

[tawny summit]

okay

so

is it right

OKAY

[quaint citrus]

No

[tawny summit]

MIRROR LINE

HEHM,AKJ

HOW

STUPID MATHS

[quaint citrus]

What happened after u added -7 + 3

What did u so from there

[tawny summit]

i did 3+-7

then it becomes positive

10

2 x x = 5

[quaint citrus]

What is 3 + -7

[tawny summit]

hold up

im gonna use everything i have

[quaint citrus]

How do u keep getting 10 lol

[tawny summit]

10

look at this my dude

i do 3+7

[quaint citrus]

That’s not what we’re doing tho

[tawny summit]

since a positive and a negative converts into a positive

[quaint citrus]

It’s 3 + -7