help-23

[upbeat swan]

Ohhh wait no

Ok so i think

That

A mixture of 50% oil and 50% is poured to fill up the entire container

After a few days

The bottom part will only be occpupied by the water

And the entire oil will be in the top part

The line through the middle is basically imaginary

[quaint pier]

What's the question actually?

[upbeat swan]

An imaginary line seprating the 2 liquids after a few days

Just for reference

[upbeat swan]

Which of the pictures describes the process the best

[quaint pier]

Ohh

[slate ingot]

FINALLY

[upbeat swan]

But im not sure if the oil graph only describes the oil from the top container

Can i also see the oil in the bottom container on that picture?

[slate ingot]

Kinda yes

Youll see an emulsion

With a%oil and b% wat3r

[upbeat swan]

OMG

Wait

Wait wait

Nah i thought i had something but i didnt

😂😂😂😂😂

[upbeat swan]

Ok so is this correct?

[slate ingot]

Yes

[upbeat swan]

Okok

Lwts look at the starting image

Why are there 2 vertical lines

In the bottom left and top right

[safe radish]

@upbeat swan Has your question been resolved?

[safe radish]

@upbeat swan Has your question been resolved?

[upbeat swan]

ok i will just leave it at that

thanks for the help

.close

[safe radish]

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[analog tinsel]

.

[safe radish]

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[gaunt raptor]

why cant we say log 2 to the base infinity tends to 0?

[summer coral]

you cant really have infinity as a base

you can say the limit as b approaches infinity of log_b (2) is zero

[warm warren]

on a more serious note, stop using infinity as if it were like any other normal number. it is not.

infinity is a symbol, not a numbe

[open wedge]

idk if the sign matters here, but really, it's just $\lim_{b \to +\infty} \log_b 2 = 0$

[flat frigate]

1 divided by 0 equals Infinity

[warm warren]

you can't say log base infinity. It's like saying log base some symbol. That purely doesn't make sense, does it?

so we have to take limits.

[gaunt raptor]

yes i meant it tends to infinity mb

[gaunt raptor]

ty

.close

[safe radish]

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[safe radish]

Available help channel!

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Remember:
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[half berry]

Uh i need help immediately , for the first paper for b4 2<x<3 how come when finding the probability i can use the formula f(b^- )-f(a) so like 3 val i think is 1 but the closest val before is 5/6 and f(a) 2 is 5/6? thats where the little points/dots are at so it ends up being 5/6-5/6 but for the second paper the second graph we have 0<x<5 we do f(b)-(a) 1-.75=.25 what defines if we use the val just before or not is it if like each point is a jump like the first paper at x= 1,2,3 it goes up but the second paper it continues on 5,6,7,8,9 idk if im explaining my confusion correctly but could anyone explain the difference of how i find each probabilities 🥹 sorry if i sound confusing

[half berry]

This is just some practice problems btw nothing graded but my exam on this stuff is soon and im just confused on this part

[safe radish]

@half berry Has your question been resolved?

[half berry]

Help🥹

[fathom jewel]

I have a difficult time decoding your doubt, but what's always done is, you compute the area of F'_x in the interval [a,b] when P(a=<X=<b)

[half berry]

Hmm uh let me try and reexplain so for the first paper for question b4 they have 2<x<3 and to find the probability they do the value before f(3) minus the value of f(2) but for the second paper when we have 0<x<5 they do the value of f(5)-f(0) what defines if we do the value before or the exact is that a better explanation of my confusion 🧍‍♀️

[fathom jewel]

Ok I see

[half berry]

So because the first page all the numbers have like an end point and a starting to the next jump we calculate the probabilities differently?

So when we have 2<x<3 we take f(3) before the jump which is 5/6

But since 0<x<5 5 doesnt lie on some like jump its just on that line we take 1- the (0)

?

[fathom jewel]

The point is, if the jump is not on the endpoints, then in continuous distributions you can "ignore" them

IF they lie on the endpoints like in 2<x<3 <- the 3 here, then you don't bother entering, you are just enough interested into what happens really really close to 3 rather

the thing is < 3 means you never reach 3

so you can actually get to the jump

[half berry]

Oh

That does make sense

That’s why its the value just before

Okay thank you

My exam is in like 10min😸

[fathom jewel]

Good luck!

[fathom jewel]

.solved

[safe radish]

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[fathom jewel]

<@&268886789983436800>

[safe radish]

Available help channel!

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Remember:
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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.

[nocturne lance]

hello

[safe radish]

@nocturne lance Has your question been resolved?

[nocturne lance]

<@&286206848099549185> PDE/ODE question. this should be within my abilities I'm just having a hard time for some reaosn

[granite jewel]

idk maybe like 4 or something

[nocturne lance]

pardon?

[nocturne lance]

sorry im not sure what you mean

[granite jewel]

no im just joking idk i cant really help on this sorry

mb for wasting ur time or anything

[safe radish]

@nocturne lance Has your question been resolved?

[safe radish]

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Remember:
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[modest turtle]

Hey

[clever tinsel]

please send your question if you have one.

[mighty mango]

@modest turtle is this your question?

[modest turtle]

Oh yeah

[clever tinsel]

assuming it is, what have you tried and what do you not get?

[modest turtle]

Wait let me try it again

[clever tinsel]

sure.

[modest turtle]

I keep getting like -4s to the power of -9/-5s to the 4 and it says it’s wrong

[clever tinsel]

well first of all, you have a negative exponent, and second of all you have not simplified the fraction.

also, the -4 is wrong.

by the way, use ^ to denote powers.

[modest turtle]

Do I start it off by like multiplying -3 and 3

[clever tinsel]

that part is not wrong. but don't forget that the -4 is there as well.

[modest turtle]

What now?

[clever tinsel]

don't forget the -4 is in the brackets as well.

[modest turtle]

Ohh

Like this

[clever tinsel]

the cube of 4 is not 125, I'm afraid.

[modest turtle]

Oh it’s to the power of

[winged flare]

did you just do 4 x 3 = 12

[modest turtle]

Or something

[clever tinsel]

I mean I presume you took (-5)^3. which is wrong.

oh wait that's an s, my bad.

so no, -12 is even worse, that's (-4)*3, not (-4)^3.

[modest turtle]

So 64?

[clever tinsel]

don't forget your sign.

the number is correct though.

[modest turtle]

I worked it out I got it right

Now next one

[clever tinsel]

do you want to try it yourself first?

[modest turtle]

Yeah

[clever tinsel]

sure, go ahead.

[modest turtle]

Do I have it right so far

[clever tinsel]

correct.

[modest turtle]

Am I done?

[clever tinsel]

no.

[modest turtle]

Don’t I do the quotient rule or something like Subtract the exponents

[clever tinsel]

yes.

[modest turtle]

Did I get it right?

[clever tinsel]

no.

[modest turtle]

What did I do wrong

[clever tinsel]

why is there still a t in the numerator?

[modest turtle]

So 3?

[clever tinsel]

rewrite your fraction.

[modest turtle]

Like that

[clever tinsel]

correct.

[modest turtle]

I don’t think I can start this one

[clever tinsel]

why not?

[modest turtle]

It doesn’t look like the other ones

[clever tinsel]

in what sense?

[modest turtle]

It’s bigger

[clever tinsel]

doesn't matter. the same strategy works.

[modest turtle]

Alright so do I start with the parentheses first

[clever tinsel]

well you should.

[modest turtle]

A negative times a positive is a negative right

[clever tinsel]

yes.

[modest turtle]

Alright what now

[clever tinsel]

do what you were doing earlier, letter by letter.

[modest turtle]

Do I subtract

[clever tinsel]

subtract what from what?

[modest turtle]

The exponents

[clever tinsel]

yes, if you mean applying the standard quotient rule of exponents.

[modest turtle]

Is this right

[clever tinsel]

no, for several reasons.

[modest turtle]

Dang

[clever tinsel]

your p and x are both unsimplified. why are two of each still present?

[modest turtle]

After I subtract the Exponents what happens

[clever tinsel]

nothing? what are you expecting to happen other than there being only one instance left of each letter, anyway?

you should have exactly one p and one x left after simplifying.

[modest turtle]

Oh um I don’t know

[clever tinsel]

show your work after your subtraction.

[clever tinsel]

correct, though could be a little neater.

[modest turtle]

I forget is it 4 times 4 or 4^4

[clever tinsel]

4^4. there's nothing indicating multiplication here.

[safe radish]

@modest turtle Has your question been resolved?

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cunning zinc]

Did I do this correctly

[mortal sandal]

we don't have enough information to determine what you were supposed to do

[cunning zinc]

Oh sorry

I forgot to send the question

[forest mountain]

not this being the same q as the channel above 😭😭

[cunning zinc]

Determine f’(-5) estimate to 1 decimal place

[mortal sandal]

reasonable approximation i guess

[cunning zinc]

Will it work?

[mortal sandal]

yeah

[junior smelt]

May as well forward it just in case

[cunning zinc]

Oh damn a clsssmate in here

[mortal sandal]

just haven't seen that method of approximation before

[cunning zinc]

Wait where did u get this

[mortal sandal]

but ig it's a better approximation then the normal limit version

[junior smelt]

The message links to the channel

[cunning zinc]

😭😭im lost

[cunning zinc]

Ok so should I continue it

[white gazelle]

is it -1/2

[mortal sandal]

this finding average ROC over [5-h, 5+h] thing

i haven't seen it used as a method before

but it seems like a sound method

[cunning zinc]

The teacher never taught us this 😭

[junior smelt]

(I'm guessing that you may be expected to draw a tangent line, and find the gradient of that?)

[cunning zinc]

How will this work

[junior smelt]

If you'll excuse the shit diagram, draw something like the purple line, and then find the gradient of that, which does appear to be about -1/2

[cunning zinc]

👍

Thank you

[junior smelt]

(that may not be the way they intend you to do it, but it is a way I have seen that questions like this are meant to be done )

[cunning zinc]

👍👍thank you

[white gazelle]

i feel like drawing tangents is weird

like u gotta be really accurate

[clever tinsel]

didn't someone already answer you in your own channel?

[junior smelt]

It can be, I'm not a fan of doing it that way, though at least from the experience I have, there's some leniency given for the answer you get, though take that with a pinch of salt and all

[cunning zinc]

Sorry @junior smelt but I had the same question as ram

For question 26

Josh said where it’s steepest slope but not maximum value I think

[junior smelt]

Yeah, steepest slope, "where are you increasing the most"

[cunning zinc]

Ohhh

Wait

Doesn’t it say maximum value

[zinc pawn]

maximum value of f'(x), not f(x)

[clever tinsel]

the value of the first derivative at a point is exactly the slope of the function at that point.

[junior smelt]

(Maximum value of f'(x), the derivative )

[clever tinsel]

so the maximum value of the first derivative of a function is exactly where the function is steepest.

[cunning zinc]

Yea I thought it would be highest at x =2

For f’(x)

[cunning zinc]

Yep wouldn’t it be at the end of the steep

[zinc pawn]

the derivative doesn't exist at x=2, though

you have a sharp point on the graph

[clever tinsel]

no.

[cunning zinc]

Ohh so cusp doesn’t count

[zinc pawn]

yes

[cunning zinc]

So x = 1?

[clever tinsel]

be very careful: just because a graph is continuous, doesn't mean it's differentiable (at a point).

[white gazelle]

yes

[junior smelt]

(you could say something about the one sided derivatives there, but you gotta be careful with how you state it)

[zinc pawn]

derivatives can fail to exist if
f is discontinuous at x=c
the slope of the tangent line from the left is not the same as the slop of the tangent line from the right of x=c (sharp point on graph)
or
the tangent line is vertical (infinite slope)
@cunning zinc

at least those are typical ways derivatives can fail to exist

[white gazelle]

that's lowk obv that it should be 1

i think

idk

cuz the slope is 1

[clever tinsel]

well if it was obvious for the helpee, we would not be here. let's not treat a fact as obvious first.

[white gazelle]

fr

<@&268886789983436800>

[clever tinsel]

<@&268886789983436800>

[junior smelt]

(to be fair, it seems like they're classmates )

[clever tinsel]

that's fair. this cat shall refrain from further commenting on their behaviour for now.

[cunning zinc]

@zinc pawn I’m wondering how u got x=3

[zinc pawn]

for which question?

@cunning zinc

[cunning zinc]

26

[zinc pawn]

I didn't say x=3

I said on [0,3] is where the function f(x) is increasing at the greatest rate

from x=0 to x=3

just by looking at the graph

@cunning zinc

[cunning zinc]

Oh

Not the maximum value then

So would it be around x = 2

[zinc pawn]

and actually, I misread it
it should be on [0,2] where f(x) is increasing at the greatest rate, not [0,3]

[zinc pawn]

the derivative does not exist at x=2, though

[cunning zinc]

Cusp

[zinc pawn]

yes cusp/sharp point

[cunning zinc]

Oh

Ok

[zinc pawn]

26. is simply asking the what the maximum value of the derivative is, not at what point that maximum occurs at

but yes, it would be infinitely close to x=2

but not at x=2
to answer your question @cunning zinc

[cunning zinc]

Oh

[cunning zinc]

Ok that makes thank you

[zinc pawn]

No problem :D

[safe radish]

@cunning zinc Has your question been resolved?

Channel closed

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Remember:
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• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
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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.

[terse fulcrum]

I need help understanding this with Trigonometry.

[timber karma]

you only need to remember the top right quarter because everything else is symmetric

[terse fulcrum]

Alright, but what does it actually do?

[minor goblet]

what do you mean

[terse fulcrum]

Well, I see it. But I have no idea what we actually use it for.

[minor goblet]

it’s just like a fact

[terse fulcrum]

Well...🥀

[minor goblet]

it tells you the coordinates of a point on a circle some degrees around

and you know points on a circle are of the form (cos theta, sin theta)

[terse fulcrum]

Yes,

[minor goblet]

so its just a few examples of pairs of theta <-> cos,sin

[buoyant shadow]

this is some values of sin and cos
it lets you avoid using calculator sometimes

[obsidian cobalt]

Hey kira can you help me with one?

[terse fulcrum]

About what??

[minor goblet]

why is bro trolling

[terse fulcrum]

IDK

[obsidian cobalt]

Oh I see now lol where is the math stuff at lol

[terse fulcrum]

In another help room.

[obsidian cobalt]

Which one

[terse fulcrum]

Any...

[obsidian cobalt]

This one

[terse fulcrum]

No... you are actually going to get reported by someone.

[obsidian cobalt]

Alright fine

[terse fulcrum]

<@&286206848099549185>

[spare thistle]

?

[terse fulcrum]

I am having trouble with this UNIT CIRCLE

[spare thistle]

!status

[safe radish]

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

[spare thistle]

No.?

[terse fulcrum]

1 to 2. I would say 1.5...🥀

[terse fulcrum]

I know what it is, I know how it works. But, I have never done anything with it yet.

[spare thistle]

Rounded up what is the closest 1 or 2 😭

[terse fulcrum]

1

[terse fulcrum]

Not really rounded up but closer to a one.

[spare thistle]

Letmetrytounderstandbrb

[terse fulcrum]

Close enough?

[spare thistle]

On the unit circle every point is written as cos θ, sin θ, which means the x-coordinate is the cosine of the angle and the y-coordinate is the sine of the angle.

Wait can I see the pic again?

[spare thistle]

Does this help

[terse fulcrum]

So... if we had cos(sqrt3/2) and sin(.6) how would we do that?

[spare thistle]

You said you knew what to do 🥹

[terse fulcrum]

I said I know what it looks like. I know what the lables are... not what to do. 😢

🥀🥀🥀

[spare thistle]

For cos(sqrt3/2) that's like asking what's the cosine of an angle that's sqrt3/2 radians? Back of the circle, I saw cos(30°) or cos(pi/6) = sqrt3/2, so answer is sqrt3/2. For sin(.6), need calculator, sin(.6) ≈ 0.56.

I just asked my friend that her name is iris thanks to her for telling me what to type 😛

I just put Everything that she said 1-1

[terse fulcrum]

Is she here currently?

[spare thistle]

Nope

He hates discord

she

Did that do 🥹

[terse fulcrum]

Ok, so when mapping it then we would make the first mark from where the Hypatanuse and Opposite converge at 30°?

[spare thistle]

It's midnight I don't wanna think I'm on a call with her I'll just ask her 😭

[terse fulcrum]

It is also midnight for me... so...😓💀

[spare thistle]

So you're plotting 30° start at the positive x-axis, move up 30° counterclockwise and mark the spot. That's (sqrt3/2, 1/2).

Why does she sound so weird talking to me 😭

[terse fulcrum]

Yeah, that is what I thought. Ok. So, what about Sin(.6)?

[spare thistle]

I don't wanna think let me ask her 🥹

[terse fulcrum]

🫡🥀GG we are cooked

Lol

[spare thistle]

The value of sin(0.6) is approximately 0.5646.

She texted me it 🥹

[terse fulcrum]

Yes. So, what do we do with .5646?

[spare thistle]

She said use a calculator to get the exact decimal

[terse fulcrum]

And then do what with the Unit Circle?

[spare thistle]

I feel like she's using ChatGPT...

Wait imma ask her to open her screen

SHES USING CHATGPT WHEN I WAS ASKING HER 😭😭

She has a 1.2 gpa 🥹

[terse fulcrum]

🫡🥀GG we are cooked.

[spare thistle]

I don't wanna think and she's using ai which is agaisnt the discord server...

ask someone else I wanna sleep 🥺

Find a mod or a helper

[terse fulcrum]

But. Who needs sleep these days?

[spare thistle]

ME I HAVENT SLEPT IN THREE DAYS.

[terse fulcrum]

It only is if someone knows about it. And, I didn't here anything

[terse fulcrum]

That makes four of us.

[spare thistle]

Four?

[terse fulcrum]

FOUR

[spare thistle]

Four?

[terse fulcrum]

FOUR

[spare thistle]

Four?

[clever tinsel]

okay wait, so what remains as the question?

[spare thistle]

YESSS

I can finally sleep 🥺

[terse fulcrum]

What do we do with .5646 as sin on a UNIT CIRCLE?

I understand what we do with Cos

But about Sin

🤔

[spare thistle]

Yet I asked me about cod 🥺?

[clever tinsel]

did that value come from somewhere else, like a calculation or something?

[terse fulcrum]

Yes, sin(.6)

[clever tinsel]

so you found out that sin(0.6 rad) = 0.5646. but in what context are you finding this value?

otherwise this appears to just be a random calculation.

[terse fulcrum]

Just simply sin(.6) cos(sqrt3/2)

[terse fulcrum]

I just assumed values for sin and cos to know what to do with them on the UNIT CIRCLE.

[clever tinsel]

so you want to find the final value of sin(0.6 rad) cos(sqrt{3} / 2 rad)?

[spare thistle]

You assumed?😭

[terse fulcrum]

Well, I want to know what we do with those values on the UNIT CIRCLE.

[clever tinsel]

or, what exactly is your original question?

[spare thistle]

Her status was 1

[terse fulcrum]

What do we do with sin and cos on a UNIT CIRCLE.

[clever tinsel]

nothing? it's a reference to the sine and cosine of those angles.

[terse fulcrum]

Basically WTF do we actually do with a UNIT CIRCLE and how.

[clever tinsel]

you use it to understand the signs and behaviour of the sine and cosine functions (and indirectly the other circular / trig functions as well).

[terse fulcrum]

Yes, how would I go about that?

[clever tinsel]

by using this concept and relating it to the circle with values you gave.

[terse fulcrum]

So... how would this work. "t" is the arc, yes?

[clever tinsel]

t is the angle between the positive x-axis and the given line.

this angle is always taken counterclockwise.

[terse fulcrum]

Yes, so ot is simple to see with a protractor and such devices.

[clever tinsel]

well most of the time the angle will be given or information is given for you to find it, so.

[terse fulcrum]

So, then how do we define the line on the picture other than positive x?

[clever tinsel]

unless the topic at hand is geometric constructions.

[clever tinsel]

the same way you do for positive x.

just rotate the radius a tad bit further.

[terse fulcrum]

How do we know what is 'just a tad but further'?

[clever tinsel]

if you wish to ask a question or ask for clarification, please use a message. a ❓is interpreted as something wrong with the statement.

[terse fulcrum]

Ok, I see

[clever tinsel]

you said other than positive x, so negative x, I suppose. then just rotate the radius until it's pointing to the left instead of to the right.

the unit circle works for all possible angles from 0 to 2pi radians (or 0 to 360 degrees).

and the coordinates of the point on the circle where the radius intersects are always (cos t, sin t).

[terse fulcrum]

Well, I am not talking about x. I am talking of the line that also spreads from the middle that is darker than the rest

[clever tinsel]

I don't see any line that is darker than the rest.

[clever tinsel]

so the radius.

[terse fulcrum]

Yes

[clever tinsel]

it's the same darkness as the rest of the circle, but I digress. also please don't spam reply pings.

ok, so what's wrong with the radius?

[terse fulcrum]

Like, do not press the respond button before sending a message responding to a statement you made?

I was just curious how we determine the radius and it's position.

[clever tinsel]

no, but rather turn pings off.

[clever tinsel]

I don't get what you mean by determining the radius and its position.

[terse fulcrum]

The radius is going to be the appotanuse of the triangle, yes?

[clever tinsel]

the hypotenuse of the right triangle in consideration, yes.

[terse fulcrum]

So, how do we decide where the hypotanuse is. Like, how do we know it goes there and not in any other billion other ways?

[clever tinsel]

by looking at the positions of the adjacent and opposite sides as well.

[terse fulcrum]

So that is what we use cosine and sine for here?

[clever tinsel]

it depends on what you mean by use.

if you mean for the coordinates, yes.

if you mean for some other purpose, then I don't know what you mean.

[terse fulcrum]

Well, if cos(sqrtx/3) and sin(.6) then what?

[clever tinsel]

again, context!

what are you even trying to do with those two values?

!xy

[safe radish]

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.

[clever tinsel]

I will not entertain two random values without any context whatsoever.

[terse fulcrum]

I am trying to figure out how we form a triangle on the unit circle. I am new to trig and told this is what I should work on first. So, all I know is that cos(sqrtx/3) and sin(.6) are values that will form a triangle within the unit circle.

I am struggling with the actual formation of the triangle itself.

[clever tinsel]

show the original question on paper or on the website or in whatever resource you are using.

[terse fulcrum]

I don't know how to form these triangles. I see them, but I do not know how to put them there or create them.

[clever tinsel]

once you've drawn the radius on the circle, draw the line from the radial point (henceforth, this term will be used to refer to the intersection point of the radius and the circle) to the x-axis. that's your opposite side.
then from the origin, draw a horizontal line to meet that opposite side. that's your adjacent side.

that is if I interpreted your question correctly. if not, then I don't know what you're asking.

[terse fulcrum]

Ok, I see.

[terse fulcrum]

Thank you, this is what I have been asking. I suppose I got bonus information. Thanks.😊

[clever tinsel]

please do not spam reply pinging.

you can reply ping from time to time, but don't reply ping on consecutive messages please.

[terse fulcrum]

Ok

If you don't mind me asking, why not?

[clever tinsel]

too many pings in a short period of time is annoying.

[terse fulcrum]

Ok

.close

[safe radish]

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[glass sparrow]

can anyone help me pls

[junior smelt]

For the part a), are you sure the range you stated for E is correct?
(Also, ignoring that for a second, can you take square roots of negative numbers?)

[safe radish]

@glass sparrow Has your question been resolved?

[safe radish]

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[glass sparrow]

oh yes that is right

[glass sparrow]

it alr in the equation of E(x)

[safe radish]

@glass sparrow Has your question been resolved?

[safe radish]

@glass sparrow Has your question been resolved?

[glass sparrow]

.close

[safe radish]

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[modest thistle]

considering I have $f(x) = {e^{x+2}+3}$ so i get smth for ... x value. but i sometimes learned that the +3 is some sort of constant and so.... what does each number mean here

[flat frigate]

PainAndLight

[normal moss]

f(x) is a function

It takes an input, here it's x, and returns an output

[modest thistle]

yeah i know, but like. but iirc there was like a reason there was the constant there

maybe i confuse something here

[normal moss]

Um

Well

It's just the expression of the function

[modest thistle]

but I think I could without evaluating the whole fnc that the func will look like ... postive or neg

[normal moss]

It could have been e^{x+2} + 49090

[modest thistle]

or smth like that

so a constant could mean liked fixed cost?

[normal moss]

That is something that basic exponential functions make pretty clear, yeah

[modest thistle]

or constant cost

[normal moss]

What do you mean, cost?

!xy

[safe radish]

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.

[modest thistle]

no its example in my head

[normal moss]

Oh

It simply means

[modest thistle]

like saying the function evalutes the cost each month... +3 would be like i get 3 dollars each month from my granny

[normal moss]

We take an x

Raise e to the power of x+2

So for example if we pick x = 2

We raise e to the power of 4

And then add 3 to that

e^4 + 3

[modest thistle]

yes

why e tho

[normal moss]

Uh, no

Because that's your function

$f(x) = e^{x+2} + 3$

[modest thistle]

ok, ill look up e again, i forgot its meaning

[modest thistle]

whyn ot

why not

[normal moss]

It's the Euler's number

Well let's say it did tell us some random cost each month

At month 0

The cost is f(0)

[modest thistle]

yes

[normal moss]

= e^2 + 3

e ≈ 2.72

So approx. 2.72^2 + 3

≈ 10.4

Not 3

[modest thistle]

i mean

[normal moss]

The + 3 actually increases the cost by 3

[modest thistle]

ok ok

[normal moss]

If you had -3

[modest thistle]

yes

[normal moss]

Then you could perhaps think about it like "grandma gives me 3$ each month"

[modest thistle]

ye

[normal moss]

So the cost is 3$ less each month

[modest thistle]

yes thats good

thats what i meant

[normal moss]

Ah I see

Then yes

[modest thistle]

i remember noe

now

[normal moss]

It's just s constant term

Not dependant on x

[modest thistle]

thats good

[normal moss]

You add 3 everytime, no matter what x is

[modest thistle]

yeah, now i can kinda assign the numbers to some realistic value

[normal moss]

What do you mean?

[modest thistle]

is it true that there are formulas that have no real real life occurence yet... like theyre completly theoretical

[modest thistle]

i mean like money growth

[normal moss]

Oh, yes

If my bank balance grew exponentially, I would be very happy

[normal moss]

Sure

[modest thistle]

:O

[normal moss]

I mean, many theories, formulas etc. were found without clear practical usefulness at the beginning

[modest thistle]

ill start a business that grows exponentially, in very tiny small steps

[modest thistle]

weird

[normal moss]

For example, imaginary numbers

At first there was a lot of skepticism around them

[modest thistle]

i would too

be skeptical

[normal moss]

But now they are used all the time in fields like electrical engineering, quantum physics, etc.

A lot of math is discovered a significant amount ahead of practical uses

[modest thistle]

thats weird.

but I think its costly more effiicient to raise a math genius than build smth and hope it works like imagined

[normal moss]

Well, not really if you think about it

Mathematicians are interested in the patterns that many different things have in common, they rarely care about how one thing works in a specific case

And in the end, mathematicians are simply curious

[modest thistle]

mhhh

math is weird. (everyone) can learn it . "simplest" math has good appliance. and it seems to have literally universal meaning

anyway

thx

ill close now

[normal moss]

Yes exactly

[modest thistle]

:)

[normal moss]

At one end it's extremely simple

Like adding numbers

[modest thistle]

yeah

[normal moss]

On the other end, it can get unfathomably deep

That's what's fascinating to me

[modest thistle]

yeah m2

[normal moss]

No problem! 🙂

Hope I've helped you

[modest thistle]

yes u did

.close

[normal moss]

[safe radish]

Channel closed

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[safe radish]

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[broken ether]

Hey there

[broken ether]

Sorry, i am INCREDIBLY bad at math and always have been and I’m studying for an exam where I’m really confused

[still stone]

just give the question

[broken ether]

The correct answer is B

How does drama club have 50% more participants than science club

Wouldn’t it need to be 40%

[still stone]

here's the thing

its not the percentage of the total

but the percentage of the particpants in the club itself

i think

also strangely they're both false statemets

i think this is a mistranslation

[broken ether]

are u German

this is in German

[still stone]

what's the original

[broken ether]

Solution

[still stone]

yeah okay so

uhh

let's just take a sample of 100 alright since its 100%

[broken ether]

okay

[still stone]

statement once says: that sports club has double the members of chess club

but 35 is not double of 15 which is 30

so do you understand?

[broken ether]

yes makes sense

just #2

Ohhhh i think i understand

50% of the science club is 10%

[still stone]

now for the second statement, it says that the theater club has 50% more than the other club

[broken ether]

so 20%+10% is that 30% then

[still stone]

yeah 50% of 20% is 10%

so do you get now?

its not the percentage of the whole 100%

but only the 20% of the science club

[broken ether]

yesss makes sense now

awesome 😁

thanks for the help

.close

[safe radish]

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[safe radish]

Please don't occupy multiple help channels.

Channel closed

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as this action is irreversible, and this channel may abruptly lock.

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[silk talon]

hey guys I was working on 6

and I had to use the solution bank, basically I get everything about the method of the quesiton

[visual linden]

Okay, part a?

[silk talon]

EXCEPT the beginning

because it says it's 2 angle in a triangle, but the solution I followed represents it as 2 different triangles

and that's got me confused

https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Factiveteach-prod.resource.pearson-intl.com%2Fr00%2Fr0069%2Fr006953%2Fr00695332%2Fcurrent%2Falevelsb_p2_ex7mix.pdf

this is the solution im doing

[visual linden]

Ig they did that for simplicity

[silk talon]

right but if you tried to put it on the same triangle

it wouldnt make sense right?

since one angle's opposite would be the other's adjacent

and they dont share

[visual linden]

No it would make sense, it'd just be a bit complicated

[silk talon]

could you show me cuz I cant imagine it

I tried to do it

so one angle I say the opposite is 3 and the adjacent is 4

when I go to the second angle it just falls apart

like no matter what I choose

[visual linden]

I mean how I think of them

Imagine a non-right angle triangle

Wait can you draw and send pics of it, just draw a random triangle ABC

(Not right angled)

[silk talon]

ok one sec

yeah i got it here

@visual linden

[visual linden]

Okay, now draw a perpendicular from B to AC

[silk talon]

ok

[visual linden]

Okay, now name the intersection D

[visual linden]

So BD/AD could be different from BD/CD

[silk talon]

yeah

makes sense

[visual linden]

But it's technically the same triangle, you're just focusing on parts of it

Eh TBF depends on how you want to say it, but yeah, I've shown you how to visualise it

[silk talon]

hmmmmm

the only thing is like

how can you say BD and DB could be different

that's exploding my mind rn basically

[visual linden]

Oh wait no no, I'm not saying that

It's like 5 and 5 are same

But 5/7 and 5/13 are not

[silk talon]

right

I think it's because they don't share the same opposite (numerator)

that's really irking me

[visual linden]

I mean if thinking of it as two different triangles helps you, then yeah go ahead

But it's not entirely two different triangles

[visual linden]

Think of it more like ABD and CBD

[silk talon]

ahh ok and they both share 12 as the adjacent

that way it could with BD as 12

since tanA is 9/12

do they even have to share it though?

[visual linden]

You could say that, BD = 12, AD = 9, CD = 5, and AC = 14

[visual linden]

Yes, because they've specified that they're two angles of the same triangle, i.e. ABC

[silk talon]

yeah they'd have to share one line i guess

but man this feels so

what you call it, arbitrary?

IDK im still not really clocking it

[visual linden]

Well when you're looking at a question, look at firstly finding the absolutes

Two angles A and B in triangle(ABC) are such that tanA = 3/4 and tanB = 5/12

So, they've said they're two angles in ABC, that means it's one triangle

Also, do you know about inverse Trigonometry?

[silk talon]

like arctan stuff?

[visual linden]

Yup, so arctan(3/4) is just 37 degrees

IIRC

[silk talon]

yeah

[visual linden]

And arctan(5/12) is, eh, roughly 23 degrees

So it's basically just a way of showing angles, if it helps you think like that

[silk talon]

Yeah thinking about it as just an obtuse triangle with those angles

that happen to have a tan ration of whatever

is a bit easier but

I think im fixated on opposite/adj

[visual linden]

Yes, almost all angles are like that, any scalene triangle, and if you draw a perpendicular from one point to the opposite line, the ratio basically matches the inverse Trigonometry ratio you get from the angle you already know

[silk talon]

but yeah the triangle is obtuse so thinking in terms of opposite/adj is probably the wrong way to go about it

[visual linden]

Yup, I mean you still can, you just have to draw a perpendicular from one point to the opposite line and then work with that as two right-angled triangles

[silk talon]

It's better to think of it like that with invisible perpendicular inersections ig

[visual linden]

Yup, it's always easier to draw and then think about it until you're proficient

[silk talon]

I think I get you but even in the above explanation tho

[silk talon]

like here

[visual linden]

Yes?

[silk talon]

This lets them share BD as the adjacent 12

but now we're not even looking at tanA and tanB

We're looking at tan ABD ect

Which is really tan(180-(A+90)) ect

like it's just not really clicking into place

wait a minute thats just tanA

wtf

[visual linden]

Oh wait yeah, that's just tan(A)

[silk talon]

Ok I think imma leave it here and hope my brain computes this in its own time

cuz rn im not getting it haha

[visual linden]

Yeah I mean just think of it in terms of inverse Trigonometry, that helps

[silk talon]

I'll try and learn about that

.close

[safe radish]

Channel closed

Closed by @silk talon

Use .reopen if this was a mistake.

[visual linden]

Alright then, also you could wait for a better helper

[silk talon]

ahh it should be fine u did great

[safe radish]

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[calm stream]

In page 81, question 39 of Stewart's Calculus the problem states:

$
f(x) = \begin{cases}
0 \text{ } \text{if $x$ is rational} \newline
1 \text{ if $x$ is irrational}
\end{cases}
$

Prove that $\lim_{x\to 0}f(x)$ does not exist if $\lim_{x\to 0}f(x) = L$.

[flat frigate]

Toaster

[fathom jewel]

\\ not \newline gng

[calm stream]

In page 81, question 39 of Stewart's Calculus the problem states:

$
f(x) = \begin{cases}
0 \text{ } \text{if $x$ is rational} \
1 \text{ if $x$ is irrational}
\end{cases}
$

Prove that $\lim{x\to 0}f(x)$ does not exist if $\lim{x\to 0}f(x) = L$.

[flat frigate]

Toaster

[plucky elk]

use sequential definition of limit

[fathom jewel]

What have you tried

[calm stream]

Honestly I've been just staring at a blank page for 60+ minutes and everything I've done just ended up nowhere

[lavish magnet]

This is so me

[calm stream]

What is the sequential definition of a limit?

[fathom jewel]

[calm stream]

Interesting, the book's never told me yet

[main matrix]

a sequence ${a_n}$ converges to a value $a$ if, for every $\epsilon > 0$, there exists some positive integer $N \in \bZ^+$ for which $|a_n - a| < \epsilon$ for every $n \ge N$

[main matrix]

basically, if a sequence gets arbitrarily close to a value eventually, the sequence converges to that value

[calm stream]

So it works for my piecewise function?

[main matrix]

A function $f: \bR \to \bR$ has $\lim_{x \to 0} f(x) = L$ iff, for every sequence ${x_n} \to 0$ (with $x_n \ne 0$), we have $f(x_n) \to L$

[main matrix]

so what you should do is find two sequences that converge to zero, but when applying $f$ pointwise to those sequences, they converge to diff values

[main matrix]

i.e., find two sequences ${x_n} \to 0$ that give two different limits for $f(x_n)$

[main matrix]

@calm stream is this covered in your book?

i just realized this might not be an analysis question

[calm stream]

I'm in the epsilon-delta section in the first cchapter of stewart's (idk why it's here), for refrece i had to google what $f: \bR \to \bR$ is

[flat frigate]

Toaster

[main matrix]

f: R -> R just means an ordinary real-valued function

[main matrix]

did he discuss sequences and how they converge at all?

if not then you should do this with epsilon-delta

[plucky elk]

then what definition of limit did you learn

[calm stream]

Yeah, I was thinking of doing it with epsilon-delta because sequences are in chapter 11 of the book

[main matrix]

are you familiar with this definition?

For every $\epsilon > 0$, if there exists $\delta > 0$ such that if $0 < |x - c| < \delta$, then $|f(x) - L| < \epsilon$, then $\lim_{x \to c} f(x) = L$.

[calm stream]

Yeah, that's the formal $\epsilon, \delta$ definition right? Where the $|x-c|$ part is the distance in the x axis from c and the $|f(x)-L|$ is the distance in the y-axis from L right?

[flat frigate]

Toaster

[main matrix]

yes

[main matrix]

wait this is stewart?

[calm stream]

Yeah

[main matrix]

well i'm not sure how formal your proof is meant to be then

are you familiar with the density of the rationals/irrationals in the reals?

[calm stream]

wait, what's that?

[main matrix]

if you have any interval in the reals, you can always find a rational/irrational number in it

for example, if $a, b \in \bR$, then the open interval $(a, b)$ must contain infinitely many rational and irrational numbers

[calm stream]

Oh yeah

[main matrix]

did your book/class/wtvr teach you that?

[calm stream]

No, I'm self-studying through the book

[main matrix]

did your book teach you this property of the reals though

from my understanding stewart isnt really a rigorous calc book

[calm stream]

It's in the appendix

[main matrix]

okay

well if you know that

[main matrix]

then you can force a contradiction here

assume $\textstyle \lim_{x \to 0} f(x) = L$. then, for every $\epsilon > 0$, there exists a $\delta > 0$ such that $0 < |x| < \delta$ implies $|f(x) - L| < \epsilon$

[main matrix]

so $x \in (-\delta, \delta) \setminus {0}$ (x can take on any value in the open interval $(-\delta, \delta)$ except $0$)

[main matrix]

note that any open interval in the reals must have a rational and irrational number, then choose a value of epsilon to contradict this statement

i hope this makes sense

[calm stream]

Oh yeah, so all I have to do is to find a value of epsilon so that $|f(x)-L|$ isn't less than $\epsilon$?

[flat frigate]

Toaster

[main matrix]

what is the value of f(x) when x is rational? when x is irrational?

since you know $x \in (-\delta, \delta)$, $x \ne 0$, you know $x$ can be either rational or irrational. what does this mean for $|f(x) - L| < \epsilon$?

[calm stream]

for rationals $|-L|<\epsilon$ and for irrationals $|1-L|<\epsilon$

[flat frigate]

Toaster

[main matrix]

Yes that's very good

[main matrix]

Now show there's a value of epsilon where both of these statements cannot be true simultaneously

That is, find a specific value of epsilon

[calm stream]

Ohhh, $\epsilon \leq 1/2$?

[flat frigate]

Toaster

[main matrix]

,w solve |x| < 0.5, |1 - x| < 0.5

[flat frigate]

Results provided by WolframAlpha

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

Requested by altanis_

[main matrix]

Yep

So you have a contradiction

So lim x->0 f(x) is not L

Meaning no limit exists at 0

Hope that helped :)

[calm stream]

OH, ty so much

.close

[safe radish]

Channel closed

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[safe radish]

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[crude light]

Hi there im confused about how I labelled these forces

[crude light]

I dont know where to put Fr

[stoic torrent]

what do you mean "where"

in eqautions or in diagram

as in diagram you have put it correclty

[opaque fern]

Friction always acts parallel to thr contact surface

[stoic torrent]

Oh Fr is friction, not reaction force?

[crude light]

Yeah just in the diagram

Friction is Fr

[opaque fern]

Also what is H

[stoic torrent]

Oh well then

[crude light]

So wheres that sorry

[stoic torrent]

Thats what i was wodnering too

[crude light]

H is horizontal

V is vertical

[opaque fern]

Those are not forces

[stoic torrent]

Well just think using your real life scenarios

where do you think it would be

[crude light]

No i know that but in the mark scheme it says this

[stoic torrent]

do you mean the normal forces?

[crude light]

Meaning that H has to be vertical so on the wall

[crude light]

Yes, my teacher just says use V and H

for those type of questions

[stoic torrent]

That horizontal equation is correct but you have made it wrong

Horizontal means parallel to the earth right?

[crude light]

parallel to the earth?

Sorry i dont get that

[twin cairn]

horizontal means perpondicaler to g pooling of earth

[crude light]

https://tenor.com/view/ball-line-drawing-bounce-gif-15071310

Like thats horizontal ik

But in the mark scheme it says that H should be vertical

[stoic torrent]

Yeah and why have you mde it verticsl in diagram

[stoic torrent]

they just took a differnt angle

[crude light]

Because once i resolve up and down it says Tsintheta = H

Ohh

so my angles are wrong?

[stoic torrent]

-# hes not at taht level yet gng

[crude light]

For T

[stoic torrent]

no they are correct

[crude light]

she and yeah im not 😭

[stoic torrent]

You can take different angles

[crude light]

Ohhhh

And with Fr

is that right?

[stoic torrent]

for example you took angle of string with horizontal, your teach took one with vertical and string

[stoic torrent]

sorry abt that misgender

[crude light]

Okayyy so i just need to keep it consistent and i'll get the same answer?

[crude light]

Its ok

[stoic torrent]

Well Fr is always perpendicular to the surface of contact force

[crude light]

dw

[stoic torrent]

Yeah but Fr isnt right direction

[crude light]

so its meant to be like this?

[stoic torrent]

aka H in this case

[twin cairn]

so from my understunding the think is not moving so what suppose to happen is if you combine both the force of the string and the wall you should get a perfect vertical opposite to g

[stoic torrent]

Thats right and thats what we are doing no?

[crude light]

to g?

[twin cairn]

p

p = mg

[stoic torrent]

Hold on i think you rteacher took V as friction force

[stoic torrent]

whats p

[crude light]

I dont think so

isnt p the particle

wait so is this right then?

if Fr is perpendicular to V

[stoic torrent]

no

[crude light]

but H still needs to be there

Or are u saying H is Fr

[stoic torrent]

Fr should be in the direction of V

[stoic torrent]

😭

[crude light]

Same way??

[stoic torrent]

No no hold on a sec

[crude light]

Sorry im so lost

[twin cairn]

i study physics in a different language so sorry if i miss up the symbols continue with the guy it is better than get confused with me

[crude light]

Yeah its ok thank you for trying to help though 😺

Just maths here

Plus im in england so maybe thats why its different

[stoic torrent]

Right lets go back to direction of wall forces

[crude light]

💀 yea fr

[stoic torrent]

-# oh am indian😭

[crude light]

Ohhh niceee different ethnicities

[stoic torrent]

Right so well as your teach rightly said, there are two forces of wall acting

One vertical and one horizontal

[crude light]

Yeah

[stoic torrent]

Well what the teacher forgot to mention was that the vertcal force is taken as friction here

[crude light]

Oh wow

[stoic torrent]

Technically friction is a wall force right?

[crude light]

I mean its just an opposing force to the wall no?

I mean its perpendicular

[stoic torrent]

Well it does push the wall does it?

You can slide your hand down on a vertical wall

like irl rn

[crude light]

Ok

[stoic torrent]

and tell me does friction slow down your hand

or does it push you rhand away from the wal

[crude light]

yeah

it goes upwards right?

[stoic torrent]

YEAH!!

[crude light]

Ohh ur so smart

[stoic torrent]

So well now thats your fricton settled

[crude light]

Had to really think about that one 😭

[stoic torrent]

😭

[crude light]

Thank you so much

ok last question

With D

[stoic torrent]

Np but, qsn isnt done tho

[crude light]

Oh 😭

is there a force at D as well

[stoic torrent]

Yeah well where is friction or as your teach calls it "V"

[stoic torrent]

Correct the diagram

[crude light]

this is the whole question btw

[crude light]

Its down

[stoic torrent]

yeah i got that its asking tension

[stoic torrent]

well not exaclty, its actually up

[crude light]

Oh yeah sorry so when my hand was on the wall, friction acts in the same direction

[stoic torrent]

wait if you slide your hand down, its going to be up, if you slide it up, its going to be down

[crude light]

Yea

Opposite

[stoic torrent]

so well

[stoic torrent]

Yeah!!

[crude light]

So surely it should be going down no

because V is going up

[twin cairn]

as a general rule friction is always opposite to the direction of movement

[stoic torrent]

Its in defn of friction that its always going to oppose relative motion between any two

[crude light]

Ok thank you :)

[crude light]

let me try redraw it

[stoic torrent]

Sure

[crude light]

so Fr is V as well?

[stoic torrent]

Yeah!!

[crude light]

Yayyyy

You're so helpful thank you so much yajant 🥰

While im at it can i find another quick question just to see how to find angles

[crude light]

legit better than my teacher

[stoic torrent]

You wlcm!!

[crude light]

and thank you as well no

nox

[stoic torrent]

Sure

[stoic torrent]

-# thats kind of you to say but please do be respectful to ur teach😭😭

[crude light]

you're right mb 😭

[stoic torrent]

all good then!!

[crude light]

i mean idk what im doing but

how would i resolve P

[stoic torrent]

Hm one sec lemme read

[crude light]

okk and let me give the full question if u need it

[stoic torrent]

Yeah thast better generally

[crude light]

yeah true

like with these questions the hardest thing for me is labelling the diagram

ill try and could you please see if im correct

holdon

[stoic torrent]

Oh okay

sure

[twin cairn]

you are welcome, another problem you are a hard-working good for you!

[crude light]

thank you 😃

you too

[crude light]

so essentially, i dont know if the forces are right

and for P

Idk where to put theta

angle

[stoic torrent]

right heres a trick, for friction, even if you assume direction is wrong, you would just get negative value when you caclualte

[crude light]

Ooooo

So smart, love that

Okay so if its negative it just means it'll be in the opposite direction

[crude light]

So even with this question did it even matter lol

But u just had to know if it was up as opposed to right

[stoic torrent]

Yeah but its better to do it correctly right😅

[twin cairn]

I think he get's it right thought

[stoic torrent]

and also, your Qsn are elementary so far, which is why this will work mostly

[crude light]

true 🤣 but its good to know

[crude light]

elementary?

[twin cairn]

it should be at the right not left

[crude light]

for this question?

[twin cairn]

he meant not university level i guess

[crude light]

oh okay fair enough yeah

[twin cairn]

I did something similir in highschool physics (never in math)

[crude light]

oh its cuz in england we do mechanics for maths

in year 13

[low drift]

yea i did in maths too

[crude light]

basically last year of high school

[crude light]

yeah bane of my existence

[crude light]

anyways how will i label theta

for P

is there a trick for that?

i always get confused

[stoic torrent]

yeah but not uni also, even higher physicis in school (what i am doing currently) too

[crude light]

wow smart lad

[low drift]

mechs in maths will usually be different

[crude light]

yeah true

[low drift]

9.8 is used for gravity in the spec i did

[crude light]

yeah mine too

9.8 is g

[low drift]

yea

9.81 for physics though

[stoic torrent]

Well so have adam and NoX got it covered orr?

[crude light]

😭 such a small difference but makes sense

[twin cairn]

yeah pendulums

[crude light]

Which angle is labelled theta