this was not what i was asking about. i asked, "are they both withdrawing at the end of '10?"
#help-19
wooden python
dense topaz
yes
wooden python
right
ok
so why not figure out what happens with X's finances then
cause his stuff is known and can be calculated in full
(im still shaky if we want the principal + (post-tax interest) to be the same, or only the post-tax interest. but at this point i am afraid to ask)
you dont need formulas, you need some understanding of what is actually happening money-wise and to communicate it sensibly enough for someone else (me) to understand 😭
faint knot
whats happening? why are they both withdrawing?
sturdy cape
because of the financial crisis two years prior
Beautiful command of language there /s
wooden python
whats happening? why are they both withdrawing?
yeah ngl like
the math is less complicated than the communication
also like
the way im trying to solve it
it looks as if the 30% tax rate just ends up irrelevant to the problem
sturdy cape
(im still shaky if we want the _principal + (post-tax interest)_ to be the same,...
"We want the amount of money Y deposits, so that post-taxation Y ends up with the same amount of money that X does, assuming they both withdraw at the end of 2010"
wooden python
same post-tax interest == same pre-tax interest, or something
sturdy cape
Is probably how I would resolve the question
wooden python
(im still shaky if we want the _principal + (post-tax interest)_ to be the same,...
.
sturdy cape
!xy is in order, perhaps
odd edgeBOT
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.
sturdy cape
i.e. send a photo or a screenshot, ideally
wooden python
so let me try to dumb this down for myself and hopefully for anybody else reading
dense topaz
its not english
wooden python
what language is it
dense topaz
the photo
wooden python
if it's got euros it is most likely some european language
dense topaz
yea
sturdy cape
its not english
ahem
wooden python
ok what language
and post it anyway
not what we're asking for 😭
post the original French please
wooden python
or German or Spanish or Italian or whatever
sturdy cape
En quelle langue
-# in what language
wooden python
graaaaaaaaaaaaaaaaaaaaaaaaah
ok
anyway
i think i have managed to dumb it down for us stupid anglos
X has a bag of money with €8440 in it.
At the end of '06, he puts it into a deposit account @ 4% p.a.
At the end of '10, X withdraws the entire sum from his deposit account.
30% of the INTEREST goes to the tax man; the rest remains with X.
X ends up with some amount of money.
Y also has a bag of money with €???? in it.
At the end of '08, she puts it into a deposit account @ 2% p.a.
At the end of '10, she also withdraws the entire sum from her account.
30% of Y's INTEREST goes to the tax man, and the rest remains with Y.
Y ends up with the SAME AMOUNT OF MONEY AS X.
How much money did Y start with?
if you're so insistent on not giving us the original, untranslated problem text,
then you will have to read through this and tell us whether it is correct or not.
and you will have to make DAMN SURE that you understand everything in both languages and can certify correctness!
swear on your entire family's lives?
do you have something helpful to contribute?
yeah, anyway, you'll still want to begin by working out X's finances in full detail, i.e.
- how much does the total grow to?
- how much does he withdraw, and how much of that is interest?
- how much does he pay in interest?
- in the end, how much cash does X have in hand in '10?
are you going to contribute in any meaningful way to this conversation or are you just going to try to shut me up and nothing else
this is incorrect
30% interest tax does NOT mean simply multiplying the interest rate by 0.7
<@&268886789983436800> harassment/toxicity?
dense topaz
how do i proceed after this?'
wooden python
you're going to need to hold off on that calculator for a bit, that's for sure.
anyway, €9443.52 is Y's target for her investment operation.
she starts with an unknown principal. let's call it P.
she puts it in the bank at 2% p.a. for 2 years
can you give me an expression for the amount of money in there just before she withdraws it?
don't simplify anything yet.
are you telling me that Y will see the very same P at the end of '10
that would be grounds for her to call up the bank and stir up a shitstorm
cause her shitass bank didnt even fucking pay her any interest
don't you agree?
do you know how to calculate compound interest in general?
maybe at this point you could drop a formula.
but i will require you to tell me what each and every letter in it stands for.
ok let me try to make your formula-search a bit easier.
given a principal P, an interest rate r, and a duration t (in years), what will be the future value of a compound-interest deposit?
give me a formula for this.
only the formula for now, don't plug anything into it.
cool.
ok
now what we have here is that we know the interest rate (2%, so r=0.02) and duration (t=2 years),
but our principal right now is just P (unknown).
plug in the known bits, and keep the unknown bits as they are,
to give me an expression for the amount of money in Y's deposit account just before she withdraws it.
this is almost correct but you did one step that was unasked-for, unnecessary, and counterproductive.
i would have rather seen you say:
[FV = ] P * (1 + 0.02)^2
and it'll also be easier to combine that 1 + 0.02 into 1.02
so, in keeping with the spirit of narrating everything in full detail, we get this:
After 2 years, the sum in Y's deposit account grows to 1.02^2 * P.
Of this, we have P as principal and (1.02^2 - 1) * P as gross interest.
that make sense to you thus far?
aight wonderful.
can you get me an expression for the net interest (i.e. what remains of the interest after taking away 30% as tax)?
don't simplify any numbers.
you can begin your answer with NI =
@dense topaz
ok, shall we go into a reminder of how tax works at the most basic level
wooden python
30% interest tax does NOT mean simply multiplying the interest rate by 0.7
.
you definitely understand something wrong.
i have been trying to guide you through the correct thought process, but right now i feel like you're trying to throw it all to the ground and try to do your own thing.
this is both frustrating and upsetting for me.
are you willing to continue with what i'm guiding you through?
yes or no.
ok.
your current sticking point is that you don't know how to apply 30% tax on the interest, correct?
(not interest rate; the interest itself.)
you use something * 0.7, but that something isn't P.
also i am a bit unhappy that i didn't get a clear "yes" nor a clear "no" to my question.
ok, so your confusion is somewhere else?
to repeat something i said earlier:
After 2 years, the sum in Y's deposit account grows to 1.02^2 * P.
Of this, we have P as principal and (1.02^2 - 1) * P as gross interest.
i asked you whether you understood this, and you said yes.
what i now want you to do is to turn this gross interest into net interest by applying 30% tax to it.
Do you know how to do this?
A) "Yes; let me try."
B) "No; tell me how."
C) "Secret third option."
ok
do you know how to apply tax in general? or indeed how to apply any sort of percentage increase or decrease?
ok, how do you do it in general?
forget all this investment stuff and all of the problem data. tell me how to apply a tax (at a known rate) on a sum of money (also known)
that... is going backwards relative to what i'm asking.
the type of question i'm asking is more along these lines:
A fridge used to be sold for €600 but now it's discounted by 15%. How much is its price after the discount?
yes
would be better if you used * for multiplication rather than x
but yes 600 * 0.85 is correct for the new discounted price of the fridge
ok, so you understand that applying a 15% discount means multiplying the price by (1 - 0.15), which is 0.85
yes?
dense topaz
yes
wooden python
mathematically tax works the same way, only it's applied to incomes and the difference between pre-tax (gross) and post-tax (net) is what the tax man takes away
so,
to apply a 30% tax on the interest, by what should we multiply the gross interest?
no
that would be slapping a seriously hefty 70% tax. you want to tax at 30% not at 70%.
right
so you need to multiply the gross interest by 1-0.3, or just 0.7.
wooden python
After 2 years, the sum in Y's deposit account grows to **1.02^2 * P**.
Of this, ...
which means, to drag us all the way back here,
that Y ends up with P as principal and 0.7 * (1.02^2 - 1) * P as net interest.
her total cash-in-hand at the end of '10 is thus P + 0.7 * (1.02^2 - 1) * P,
which is equal to [1 + 0.7*(1.02^2 - 1)] * P.
does this make sense to you?
no
dense topaz
i cant still calculate it
wooden python
you're going to need to hold off on that calculator for a bit, that's for sure.
anyway, €9443.52 is Y's target for her investment operation.
she starts with an unknown principal. let's call it P.
P is Y's starting amount. it is her principal.
wooden python
i cant still calculate it
im not asking you to calculate anything yet.
im asking you to read the shit i say and tell me whether it makes sense to you 😭
when i want to get you calculating something, i tell you to go calculate it
ok, let's maybe recap the entire story.
i will even put it down on paper.
dense topaz
does this make sense to you?
i think so
wooden python
recap of all that we've discussed thus far.
please read all this carefully. do not run off to plug shit into any calculators -- i have more to say, but i need you to signal to me that you understand all of this.
when you're done reading, and are ready to continue, ping me.
dense topaz
when you're done reading, and are ready to continue, **ping me**.
yes i we can continue
wooden python
right
now the first part of this rather long conversation was to figure out what condition actually needs to happen between X and Y.
and we got that they have to end up with the same cash-in-hand at the end of all their financial machinations.
dense topaz
yes
wooden python
now, X ended up with €9443.52.
Y wants to end up with the same.
thus, we have: $$[1 + 0.7 \times (1.02^2-1)] \times P = 9443.52$$
clever fjordBOT
Ann
wooden python
capisce?
ok, we're one step away now
can you do it yourself
.... no
i think you need to reread my paper photo, tbh
cause we've already accounted for all interest and taxes.
there is zero need to try to apply tax a second time or interest a second time or some ex-recto service fee that we didn't know existed
dense topaz
okay
wooden python
yes, but show me what you are planning to calculate before actually pressing the = button.
"switch" is definitely a bad way to phrase it.
dense topaz
"switch" is definitely a bad way to phrase it.
multiply
sturdy cape
Not the right action
sturdy cape
**Ann**
You understood up to this point, right?
including how we arrived at it?
Is that to say (1+0.7*(1.02^2-1)) *9442.52?
dense topaz
ye
sturdy cape
Because... no?
wooden python
this is incorrect.
sturdy cape
You understood up to this point, right?
Firstly - just to clarify
wooden python
A) "Let me try again."
B) "So what should I do?"
C) "Secret third option."
dense topaz
B
sturdy cape
That bit in the square brackets is a mess, but it's a number, right?
So we have $[something] \times P = 9443.52$, right?
clever fjordBOT
Waes (Wires)
wooden python
let me strip it down to its barest essentials
forget about this equation for now and take a way simpler one with the same structure
$8 \times Z = 94$
clever fjordBOT
Ann
wooden python
how do you find Z in this? @dense topaz
mmm wrong notation.
i think you have the right idea, but try phrasing it better.
dense topaz
i divide both sides
wooden python
you divide both sides by what?
dense topaz
z=94/8?
wooden python
"I divide both sides by 8, and this gives z = 94/8."
yes thats correct
your equation looks like
[SCARYNUMBER] * P = 9443.52
do you see what to do now?
it does indeed!
sturdy cape
wdym how do you continue
wooden python
well,
in 8*Z = 94, you divided both sides by 8 because the Z was getting multiplied by 8.
now, in [scarynumber] * P = 9443.52, by the exact same logic, what should you do?
"everything written" is too imprecise.
what exactly are you dividing by?
mmmm okay that's gonna be a no.
what you did there is like
it's as if you saw 8 * Z = 94 and went off to calculate 94*8
try again
right, yes, correct.
so then P = ?
again show only the calculation
ie dont go putting anything into the calculator until i tell you to do it
first off, 9443.52
and second,
let's follow through on what you said,
and divide both sides by [scarynumber],
so you would have $$P = \frac{9443.52}{1 + 0.7(1.02^2-1)}$$
clever fjordBOT
Ann
wooden python
(i have filled the "scary number" in here)
do you understand this? @dense topaz
no calc yet
ok
now go put that in your calculator
,calc 9443.52/(1+0.7*(1.02^2-1))
clever fjordBOT
Result:
9183.8020772552
alright uhhh
some cents of difference there, i guess?
but ok, good enough i guess. round it off to 2dp (because money) and you are good to go.
can i say one final thing that i would like you to take away from this
math is not and should never be about blindly plucking formulas and putting numbers into them without knowing what you're doing.
every single problem has some logic behind it, and unless it's the sort of thing you could do in your sleep, you should always always always talk it out as fully as you can.
yeah rushing is very bad
odd edgeBOT
odd edgeBOT
Available help channel!
brazen ermine
odd edgeBOT
odd edgeBOT
brazen ermine
than2s
brazen ermine
windows on-screen keyboard?
yes
wooden python
consider getting an external usb keyboard if yours is this borked
nocturne mica
what in the world happened to your kb
brazen ermine
5t w6r2s r6er3y b4t s60e sett5ng 5s d5st4rbed
nocturne mica
does your kb use uiohjkbnm for a numpad
looks like the case, but either way get it checked yeah
brazen ermine
the 2eyb6ard 5s a 3at6 2eyb6ard
wooden python
wait i think i might know what this is
brazen ermine
there 5s n6 n40*ad
wooden python
does it have an fn key
maybe that thing's stuck and so it's reading your press of the o key as a numpad six etc
nocturne mica
was about to ask if you had numlock on
brazen ermine
okay
odd edgeBOT
Available help channel!
jovial iris
odd edgeBOT
nocturne mica
that looks like the wrong orientation after reflecting just over the x-axis
jovial iris
I forgot to reset it
nocturne mica
what else would be the issue be?
jovial iris
I had to reset where it's position is
nocturne mica
okay, and what problems do you have with this question?
other than the whole resetting position thingy that you have fixed
jovial iris
okay, and what problems do you have with this question?
I keep getting it wrong, but I'm confused about translating 3 units to the right
nocturne mica
can you do the reflection first?
jovial iris
It's do difficult
nocturne mica
sure, do you have an idea where to start then, with the reflection?
you're right in that the triangle would end up on the other side of the x-axis for obvious reasons
but do you at least know how the triangle would be oriented?
if not, you can just reflect each point across the x-axis separately
you will still get the same result as if you considered the triangle as a whole
jovial iris
nocturne mica
that's the y-axis
but you've gotten the right idea about reflection
now try doing the same, but reflecting across the x-axis instead
jovial iris
nocturne mica
there we go
now from here, a translation 3 units to the right isn't too terribly complicated, i hope?
jovial iris
nocturne mica
looks about right
jovial iris
3 units right
jovial iris
I got it correct, thanks for helping me:)
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
jovial iris
!done
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
jovial iris
.close
odd edgeBOT
jovial iris
.reopen
odd edgeBOT
✅
brave sundial
yo
nocturne mica
anything else?
brave sundial
nocturne mica
!occupied unfortunately
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
ivory grove
yo
hi, welcome to the mathcord! check #❓how-to-get-help and open your own channel 
ivory grove
you can either calculate it or do it visually
for calculating, you can set D as the origin and then multiply all the coordinates by 2
to do it visually, do smth like this with the line you have and make sure the base is two times the original base
jovial iris
I don't usually know how scale factor of 2 looks like
odd edgeBOT
@jovial iris Has your question been resolved?
odd edgeBOT
@jovial iris Has your question been resolved?
elder wasp
With permission, @amber veldt
odd edgeBOT
With permission, <@205675981845954560>
elder wasp
Excersises on induction would be much appreciated ❤️
amber veldt
Sure
from Knuth
Define the Fibonacci sequence as follows:
$$F_0 = 0$$
$$F_1 = 1$$
$$F_n = F_{n-1} + F_{n-2} \text{ for } n \ge 2$$
clever fjordBOT
gfauxpas
clever fjordBOT
gfauxpas
clever fjordBOT
gfauxpas
amber veldt
We will prove $F_n \le \phi^{n-1}$, and then as an exercise you will prove that $F_n \ge \phi^{n-2}$
clever fjordBOT
gfauxpas
amber veldt
Call the property "$F_n \le \phi^{n-1}$" $P(n)$
clever fjordBOT
gfauxpas
elder wasp
Oh, did not know that you can do that!
amber veldt
forgot to see we're proving it for all $n \ge 1$
clever fjordBOT
gfauxpas
amber veldt
If $n=1$, then $F_1 = 1 = \phi^0 = \phi^{n-1}$, so $P(1)$ holds.
clever fjordBOT
gfauxpas
elder wasp
so not n >= 2 okay
elder wasp
one is weak, the other is strong
amber veldt
lol
elder wasp
uhhh, does it have to do with boundaries?
amber veldt
strong induction is, instead of assuming it's true for some k, you assume it's true for all numbers up to k
it sounds stronger than induction, but you prove it by induction
that it works
elder wasp
okay, so different starting assumptions but same technique
clever fjordBOT
gfauxpas
amber veldt
so P(1) and P(2) are both true
this is quite common, needing two base cases
okay so induction hypothesis:
assume P(1), P(2), P(3), ..., P(k) for some k
note that we're assuming then that
$$F_{n-1} \le \phi^{n-2}$$
$$F_{n} \le \phi^{n-1}$$
clever fjordBOT
gfauxpas
amber veldt
adding these together we get
$$F_{n-1} + F_n = F_{n+1} \le \phi^{n-2}+\phi^{n-1} = \phi^{n-2}(1+\phi)$$
clever fjordBOT
gfauxpas
amber veldt
$$=\phi^{n-2}\phi^2 = \phi^n$$
clever fjordBOT
gfauxpas
amber veldt
we showed that $F_{n+1} \le \phi^{n+1-1}$ and the result follows by induction
clever fjordBOT
gfauxpas
amber veldt
questions?
elder wasp
What is the name of the book and do you have the page number/excerise number?
amber veldt
The Art of Computer Programming Volume 1 by Donald Knuth
elder wasp
I'm taking screenshots and printing it out so I have something to do on the train
amber veldt
this was from section 1.2.1
Exercise 1.2.1.4 is:
Prove that the Fibonacci numbers satisfy $F_n \ge \phi^{n-2}$
elder wasp
Guess I'll loan the book from the library tomorrow then!
clever fjordBOT
gfauxpas
elder wasp
I'm actually excited to attempt this in the morning
Is it okay if I ping you tomorrow to share my proof if I can't find the book/my proof differs from the books?
amber veldt
sure
elder wasp
Thank you once again Gfauxpas
I really, really am thankful ❤️
Screenshots printed, time to head to bed
Goodnight, Gfauxpas ❤️
.close
odd edgeBOT
odd edgeBOT
Available help channel!
tawny coral
odd edgeBOT
tawny coral
can someone help pls
vernal yacht
,rotate 180
clever fjordBOT
odd edgeBOT
@tawny coral Has your question been resolved?
tawny coral
<@&286206848099549185>
ivory grove
what have you tried?
ivory grove
tawny coral
what have you tried?
i don’t even understand what the question is asking tbh
ivory grove
i don’t even understand what the question is asking tbh
you're trying to cover the triangle in the diagram with a bunch of hexagons that are cut into equilateral triangles
tawny coral
ohhh
ivory grove
it gives you the length of the diagonal of the hexagon (which means you know the side length of the small triangles), and also the side length of the surface
can you take it from here?
ivory grove
one triangle base 0.1 m
6 triangle bases 0.6m
no, the hexagon's diagonal is 20 cm
"the shortest distance between opposite vertices"
= diagonal
the 0.6 cm refers to the surface that's in the diagram
odd edgeBOT
@tawny coral Has your question been resolved?
opaque dagger
How do I calculate the surface area of these figures
honest turtle
,rotate
clever fjordBOT
nimble blaze
addition and subtraction of areas of common figures
for the fist one consider drawing a rectangle around the triangle
nimble blaze
there are some tricks you could apply for the second and third one:
move a piece somewhere else and you'll get simpler shapes to work with
nimble blaze
what did you do after that?
nimble blaze
there is a way to use the lengths you've determined to get the area using herons formula,
but that's quite tedious and not the method I was hinting towards
Pythagoras isn't needed here
did you do what I recommend and draw a rectangle around that triangle?
opaque dagger
yup
nimble blaze
now the sum of the areas of the
shaded and the 3 newly formed white triangles will give the area of that rectangle
opaque dagger
i got a
calculated the entire rectangle
then the 3 new triangles
and did the entire rectangle area - the 3 triangles area
i got 5,5 cm2
nimble blaze
yep
opaque dagger
i meant that whoops
wrote it down withthe 2 tho
c is hard tho
i got 7,55 cm2
is that correct?
nimble blaze
can you show your work?
and don't round
nimble blaze
don't use decimal approximation for pi
leave pi as pi
and don't use a calculator for this, it's not needed
opaque dagger
my head calculating is not that good so i used calculator
oh this couldve been way easier
nimble blaze
the numbers are small enough that is more than reasonable to do on paper
and leaving pi as pi, you don't have to do anything with long decimals
opaque dagger
move 1 piece of the circle to bottom right, then calculate half the circle and the rectangle
0,5 x pi x 1^2 = 1,57
1,57 + 6 = 7,57
opaque dagger
the numbers are small enough that is more than reasonable to do on paper
and lea...
but how do you calculate out of your head with pi
nimble blaze
leave pi as pi
e.g 5pi would be 5pi and leave it as that
in your case leave 0.5pi as 0.5pi
or write that as pi/2
so you'd leave the final result as
pi/2 + 6
opaque dagger
that makes sense
thank you
but what if r was more than 1
how would that work
dont know that from the top of my head
opaque dagger
so if i write down 9pi on a test as an answer it should be correct
nimble blaze
yes, unless told to round
opaque dagger
okay, thank you very much
odd edgeBOT
Available help channel!
earnest zenith
I know for a) the meaning of g(4) is if the insulation depth is 4 inches, the estimated annual heating/cooling cost is $2750
How would I explain b and c?
earnest zenith
For b) I know that g(9) is 1500
nocturne mica
well, look at what g outputs and what f is taking. does it make sense to use the output of g as the input to f?
(for b)
for c, do the same thing but with the input of g and the output of f
odd edgeBOT
@earnest zenith Has your question been resolved?
earnest zenith
Thanks
dreamy totem
Is the thing in the yellow right? I double checked using lhopitals but I used the trig Identity and I got 0.. but like I I have 0/0 since sin also approaches 0 so idk if it counts as being done
forest sky
i don't really see how you just conclude that the limit is 0 in the second line
safe vapor
Is the thing in the yellow right? I double checked using lhopitals but I used th...
Do you even need a trig identity here? You can just seperate to $\lim_{t\to\0} \frac{1}{sin(8t} - \frac{cos(8t)}{sin(8t}$
fucking hell
$(\lim_{t\to 0}\left(\frac{1}{\sin(8t)}-\frac{\cos(8t)}{\sin(8t)}\right))$
clever fjordBOT
Stitches
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
odd edgeBOT
@dreamy totem Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
languid orbit
hi im doing a chapter on the homomorphisms and the isomorphism theorems in group theory and was wondering if i could have a hint for this question
languid orbit
ive figured out that $ \mathbb Q /\mathbb Z$ comprises of cosets in the form $q \mathbb Z$ where $q \in \mathbb Q \cap [0,1)$
clever fjordBOT
lifelong dumbass
wooden python
hi im doing a chapter on the homomorphisms and the isomorphism theorems in group...
disproving isomorphism of groups is way easier
by finding eg an element in one with some property that cannot ever possibly be satisfied in the other
rough birch
a really easy property you can always check is orders of elements
clever fjordBOT
lifelong dumbass
languid orbit
which has order 4
with exception to the identity, every element in $\mathbb Q $ has infinite order
so you can't produce an isomorphism
sorry is that wrong
or
rough birch
no thats totally right
odd edgeBOT
odd edgeBOT
Available help channel!
shrewd trellis
with this, why did he write f’(x)>0, shoudnt he have written f’(2)>0
shrewd trellis
safe vapor
,rccw
clever fjordBOT
shell haven
I mean I guess you aren't wrong
nocturne mica
looks like he wants you to first say that f'(x) > 0, then can you conclude it is increasing
shell haven
Yea
safe vapor
with this, why did he write f’(x)>0, shoudnt he have written f’(2)>0
Yeah you're not wrong, he was just trying to explain that if f'(x) > 0 at your point of itnerest (x = 2), function is increasing
shell haven
You could also do f'(2)=56>0
safe vapor
Saying f'(2) > 0 would probably suffice, but you did neither
graceful viper
even f'(x)>0 is bad imo, u shouldve justified that f'(2)>0 though
shell haven
You could also do f'(2)=56>0
My teachers accept that kind of presentation
Ion if yours would though
shrewd trellis
So next time I just write f’(2) >0 - increasing
shell haven
So next time I just write f’(2) >0 - increasing
Ye
odd edgeBOT
Available help channel!
jaunty minnow
I need some help on this
odd edgeBOT
I need some help on this
jaunty minnow
I'm so confused where to start
I feel like I should plug in 39 m/s in for t, but its not a time
But I'm also given two time intervals for each question
But how do I find the distance?
Divide the time intervals by the velocity?
to get position?
*multiply
shell haven
I need some help on this
Have you learnt integral mean value theorem
cyan cape
Have you learnt integral mean value theorem
isnt this derivitives?
jaunty minnow
isnt this derivitives?
^^
jaunty minnow
Ye
shell haven
Average velocity is displacement/time
jaunty minnow
Divide the time intervals by the velocity?
from physics I feel like I should do this
shell haven
So I guess you just integrate to find the displacement
jaunty minnow
Ye thats what I thought
shell haven
Divide the time intervals by the velocity?
That would give average acceleration
shell haven
or change of time x velocity
Well in this case it's a bit more complicated than that actually
Have you learnt integration yet
warped glacier
Have you learnt integration yet
they don't need to know this for now
cyan cape
So I guess you just integrate to find the displacement
isnt this just avg rate of change not integral mean value theorem
acc
warped glacier
I need some help on this
the average velocity is just (change in distance) / (change in time)
shell haven
Oh nvm
warped glacier
the same formula
very different
warped glacier
so $\frac{h(t_2) - h(t_1)}{t_2 - t_1}$
clever fjordBOT
south
shell haven
Welp alright ye
jaunty minnow
isnt this just avg rate of change not integral mean value theorem
y2 - y1 / x2 - x1
cyan cape
vavg = (h(b)-h(a)) / b-a
shell haven
Not the displacement function
Sorry bro I was holding my breath a few minutes before this fr
jaunty minnow
ah fuck its that formula
cyan cape
same thing i said
jaunty minnow
where do I start tho 💀
cyan cape
where do I start tho 💀
use the formula for the given points
then round
i think thats
literally it
shell haven
I can't read I'm a deltarune fan
jaunty minnow
but how do I find f(x+h) ?
cyan cape
I'm supposed to give exact answers
oh yeah mb
jaunty minnow
thats what I'm lost about
cyan cape
just write until 4 dec places
cyan cape
oh makes sense
graceful viper
just do (h(8) - h(7)) / (8-7)
for avg rate of change
jaunty minnow
damn bruh
warped glacier
h is your change
no, h is the height function
that's not the same as the h for 'small change'
warped glacier
that's not the same as the h for 'small change'
we're not using this kind of h cause we already have two different points
so we just sub in the numbers
cyan cape
vavg = h(b) - h(a) / a - b
vavg = h(7) - h(8) / 7 - 8
vavg = 232.33 - 258.88 / -1
vavg = -26.55/-1
vavg = 26.55
shell haven
I need some help on this
And the instructions also do say to round to 4 d.p
cyan cape
holy shit im cracked
shell haven
And the instructions also do say to round to 4 d.p
So do round
jaunty minnow
mb
cyan cape
how the hell you get 7
graceful viper
h(7)
graceful viper
denominator should be 8-7 first off
warped glacier
,calc 39 * 7 - 0.83 * 7^2
clever fjordBOT
Result:
232.33
pretty sure he forgot the 8
jaunty minnow
vavg = h(b) - h(a) / a - b
vavg = h(7) - h(8) / 7 - 8
vavg = 232.33 - 258.88 /...
Is see
why is h changing tho?
cyan cape
why is h changing tho?
h is your function
warped glacier
why is h changing tho?
the function isn't changing
cyan cape
im inputting 7 and 8
warped glacier
you put in two different time values ^
cyan cape
and then it gives me 232.33 and 258.88
jaunty minnow
Ok let me try something
shell haven
would you guys be surprised to know that
No
graceful viper
the intuition behind AROC is that it is the gradient of the secant line connecting the two points (a, f(a)) and (b, f(b)).
you are getting a rough approximation of the overall change during the interval b-a
cyan cape
ur essentially just going back to grade 9 math and using advanced formulas to do them
cyan cape
Ok let me try something
ay man you done
jaunty minnow
same thing
cyan cape
it is
graceful viper
that is another formulation but u dont need that here
cyan cape
theres no use for +h
shell haven
f(x+h) - f(x) / h
The process here is just this with smaller and smaller values of h for x=7
jaunty minnow
the intuition behind AROC is that it is the gradient of the secant line connecti...
Right, thats the average.
cyan cape
arent we just using the given intervals but theyre already precalculated
jaunty minnow
I thought they were asking for the derivative
cyan cape
so we dont need to add or subtract h
jaunty minnow
which I was confused about
cyan cape
I thought they were asking for the derivative
they are
graceful viper
they are not
jaunty minnow
Ye they aren't
graceful viper
the derivative is a local approximation
cyan cape
im a lil lost
graceful viper
they are asking for AROC
cyan cape
dont they solve for
jaunty minnow
not instantanous slope
cyan cape
the exact same
oh wait
they dont
yeah
cant you calculate the slope at a point using derivitives
graceful viper
yes u can
the essence of this exercise is that as h->0 (the increment in the x values), the local approximation for change gets better
cyan cape
gotchu gotchu
graceful viper
great
cyan cape
I'm ahead of my class ish 😉
"ahead of my class" and its power rule
graceful viper
jaunty minnow
"ahead of my class" and its power rule
Its somewhere
graceful viper
derivative visualization
jaunty minnow
haku just a hater
jaunty minnow
https://tenor.com/view/secant-line-converging-to-tangent-line-animation-gif-1871...
Yes I see
cyan cape
haku just a hater
yeah because being ahead of your class would be doing calc 1 in grade 9
which is what i did
shell haven
yeah because being ahead of your class would be doing calc 1 in grade 9
Cool
Good for you
cyan cape
You're so sigma haku
😔 🥀 🥀
jaunty minnow
yeah because being ahead of your class would be doing calc 1 in grade 9
I was employed
shell haven
Surely this man is the genius of our generation
jaunty minnow
I couldn't
cyan cape
Surely this man is the genius of our generation
hey look all im saying is
cyan cape
you arent really ahead if power rule is quite literally the next lesson
jaunty minnow
I do know chain rule, quotient rule and some integral shit too
I just messed around with some stuff
shell haven
you arent really ahead if power rule is quite literally the next lesson
Let a man have his victories 💔
jaunty minnow
Let a man have his victories 💔
Yes please
cyan cape
I do know chain rule, quotient rule and some integral shit too
oh nice
wait is this
highschool calc or
uni calc
jaunty minnow
college
jaunty minnow
ye?
cyan cape
ah gotchu
wait
dont you learn all of this stuff in gr12
chain rule quotient rule all of that stuff
shell haven
dont you learn all of this stuff in gr12
People have different paths in education
cyan cape
People have different paths in education
makes sense
idk jst a lil lost i dont live in america
jaunty minnow
just calc 1
I look at calc 2 and was like
uhhh
taylor series 👍
anyway @graceful viper @cyan cape @shell haven thank you for the help!
really helped a lot
I got one more question tho
if thats fine
Is there no limit?
I'm a lil lost
graceful viper
as x->10, what happens to 8?
shell haven
Are horizontal lines
jaunty minnow
as x->10, what happens to 8?
doesn't change???
because its not a coefficent of x
so it it just 8
shell haven
Ye
warped glacier
yeah, '8' is a sneaky way of saying y = 8
and when you think about what y = 8 means, that means that y is always 8, no matter what x could be
warped glacier
yeah, '8' is a sneaky way of saying y = 8
cause the limit is always of some function
that function can be thought of as f(x) sure, so f(x) = 8
or it can be thought of as y, so y = 8
jaunty minnow
no worries!
I got one more
I can't figure this out
I thought is was 1
but its not
then I thought there was no limit and its not that either
OMG ITS -5 FUCK
one sec
warped glacier
yeah take your time to factor it
jaunty minnow
got it
dumb mistake
@warped glacier
Or this is something I forgot
it equals 0/0
I do a^2 - b^2 right?
or is that something else
warped glacier
I do a^2 - b^2 right?
yep!
jaunty minnow
Whats my b and a tho?
warped glacier
Whats my b and a tho?
well, you can compare $25 - x = a^2 - b^2$
clever fjordBOT
south
warped glacier
no
jaunty minnow
hm?
warped glacier
I'll give you another minute
warped glacier
so 25^2 - x^2
clearly that's not 25 - x
so a = 25 and b = x doesn't work
jaunty minnow
so
(25-x)^2 - (5- root x)^2
?
$(25-x)^2 - (5- root x)^2
Why doesn't it do the thing
@warped glacier
warped glacier
$(25-x)^2 - (5- root x)^2
$(25 - x)^2 - (5 - \sqrt{x})^2$
clever fjordBOT
south
warped glacier
you're overcomplicating it
jaunty minnow
that what I said
jaunty minnow
(25-x)^2 - (5- root x)^2
clever fjordBOT
south
jaunty minnow
$south likes billies$
clever fjordBOT
Adrift
jaunty minnow
w
hold on im working on it
@warped glacier is there no limit?
the bottom is zero
warped glacier
no
warped glacier
it's the same trick, factor something out so that you can cancel on top and bottom
warped glacier
you're still on this problem right
jaunty minnow
yes
can I factor 5?
but I don't understand because
wouldn't x need to be involved?
is it -5 @warped glacier ?
jaunty minnow
oh wait
warped glacier
so yes, a = 5 works
jaunty minnow
I have to multiply by the reciprocal right?
warped glacier
I have to multiply by the reciprocal right?
no
it's a difference of 2 squares like you said earlier
jaunty minnow
right?
jaunty minnow
so yes, a = 5 works
i said -5
warped glacier
**south**
so what's b here then?
after that you can just sub into (a + b)(a - b) directly
warped glacier
I did multiplied by the reciprocal and it worked
oh you meant the conjugate
so 5 + sqrt(x)
yeah that works
odd edgeBOT
Available help channel!
restive lodge
Limit evaluation, eliminating radicals in expression with conjugates, is this correct? Offer feedback
restive lodge
$$ \lim_{h \to 0} $$
clever fjordBOT
Kolo
restive lodge
in 1st pic
dawn scarab
Appears fine yeah
restive lodge
Appears fine yeah
Thanks, do you have any feedback?
dawn scarab
Not really, your workings are clear, this is typically how you deal with limits that have square roots in them. Good job 
restive lodge
.solved
odd edgeBOT
odd edgeBOT
Available help channel!
odd edgeBOT
solar peak
to the nearest integer
mystic nova
$4\log_2(3^-1)$ ?
clever fjordBOT
Alexis_Fx
mystic nova
or
mystic nova
$\left(4\log_2(3)\right)^{-1}$
clever fjordBOT
Alexis_Fx
mystic nova
bruhh
signal yacht
amazing
mystic nova
$4\log_2(3) - 1$
clever fjordBOT
Alexis_Fx
solar peak
yes
signal yacht
to the nearest int?
solar peak
yes
late dust
Throw away the -1, put it back at the end
solar peak
and the log 3 base 2
solar peak
how do i do that
late dust
Can you use a calculator?
solar peak
if i could would i have asked 💀
late dust
Fair enough
signal yacht
,calc 3^4
clever fjordBOT
Result:
81
Why didn't you start with that
signal yacht
so its like 6
solar peak
signal yacht
,wolf 4 log_2(3) - 1
clever fjordBOT
solar peak
so its like 6
they want [gif] in the original question so 5
signal yacht
yeah ok
signal yacht
they want [gif] in the original question so 5
yeah we can take one off in the end
solar peak
yeah
signal yacht
$c \log_a(b) = \log_a (b^c)$
clever fjordBOT
Percy
solar peak
yeah that part i got
signal yacht
haan toh
solar peak
how did they bring 6 and 7
solar peak
oh
signal yacht
(iitb cs pakka)
signal yacht
at least youre studying
solar peak
.close
odd edgeBOT
odd edgeBOT
Available help channel!
tall cairn
Is there a Bose integral like identity for when n is an even integer
tall cairn
In particular, I’m interested in solving an integral of the form t^2/(e^t - 1)
dawn scarab
Pretty sure you can do that using the geometric series
tidal matrix
Is there a Bose integral like identity for when n is an even integer
the best closed form for the bose integral that i know is $$I_n = \Gamma(n+1)\zeta(n+1) = n!\zeta(n+1).$$ So if $n$ is even, you are trying to find $\zeta$ of an odd integer, which i dont think has been done yet
clever fjordBOT
haseeb
tidal matrix
as for n=2, zeta(3) is known but we dont know a whole lot about it: we have some continued fractions, and whether it's transcendental is an open problem. so this method probably doesn't work :/
odd edgeBOT
@tall cairn Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
timber patio
guys i dont understand why they wanted to know the area between 2 and 3 first
timber patio
then why did they minus by 1/2 at the end?
orchid torrent
then why did they minus by 1/2 at the end?
$$\int^{3}{m} f(x) \dd{x}=\int^{3}{2} f(x) \dd{x}-\int^{m}{2} f(x) \dd{x}$$ and $\int^{m}{2} f(x) \dd{x}=\frac{1}{2}$ by definition.
clever fjordBOT
Civil Service Pigeon
orchid torrent
@timber patio Hello?
timber patio
<@1129308909681778788> Hello?
yes
timber patio
**Civil Service Pigeon**
ohhhh
odd edgeBOT
ohhhh
If you are done with this channel, please mark your problem as solved by typing .close
wide pollen
hey i would like to know if my steps are legit :
odd edgeBOT
hey i would like to know if my steps are legit :
wooden python
what's p
wooden python
uh ok first off am i meant to read this left to right or right to left
wide pollen
uh ok first off am i meant to read this left to right or right to left
left to right lol
wooden python
anyway uhh
feral halo
<@183668144404037632>
kinda random but
why's there a random floating infinity in the 3rd line 😭
wooden python
a lot of these inequalities are quite dodgy, including the pink ones
...due to those very same floating infinities
wide pollen
kinda random but
why's there a random floating infinity in the 3rd line 😭
lmao yeh my bad
wide pollen
...due to those very same floating infinities
ignore those floating infinities lol
😅
ima fix it
wide pollen
this one without them floating infinites lol
wide pollen
that is not kosher
ig theres a better sol
wooden python
yes there is
first since we have p(x) and p(1/x) in the picture, it doesn't hurt to figure out what these guys approach as x->+∞ -- and you've already done that, getting +∞ and -1 resp.
now looking at this motherfucker.
wide pollen
first since we have p(x) and p(1/x) in the picture, it doesn't hurt to figure ou...
yeh thats y i did those 1 and -1..
wooden python
- deg(p) = 4 and the leading coeff of p is 1
- so the 2p(x) term behaves like 2x^4
- and 2x^4 - p(x) behaves like 2x^4 - x^4 = x^4
- p(1/x) approaches -1 and so behaves as a constant
- p(x)/(1+p(x)) -- you've worked this guy out separately, it approaches 1 and so is also a constant
wooden python
yeh thats y i did those 1 and -1..
yeah i object to the breaking of the limit over the fraction bar tbh
you cant do that to ∞/∞ limits so brazenly
has your class taught you big-o or little-o notation?
it is going to make things very convenient and workable here.
wide pollen
has your class taught you big-o or little-o notation?
you mean bounds?
wide pollen
i mean shit like O(x^3)
not yet
wooden python
rip
ok then i guess you have to do something like
figure out ex recto that both num and denom behave as cx^4 plus some small bullshit
then divide num and denom by x^4
figure out that this makes them both have finite limits
compute those
wide pollen
yeah i object to the breaking of the limit over the fraction bar tbh
also if ik each blue limit exists?
wooden python
and win
wooden python
also if ik each blue limit exists?
the two left ones are infty.
wide pollen
the two left ones are infty.
youre right sry
wide pollen
figure out *ex recto* that both num and denom behave as cx^4 plus some small bul...
ex recto ?