Oh
#help-13
runic garnet
$\frac 34 a^{\frac 43} - 6a^{\frac 23} + 2 = 0$
wraith daggerBOT
sinful harbor
Ohhhh ok
wraith daggerBOT
runic garnet
3z^2 - 24z + 8 = 0
sinful harbor
runic garnet
is there another way u can solve this
sinful harbor
I used my calculator but u can use the quadratic equation
runic garnet
yea i mean if u plugged it in correctly that should be right
sinful harbor
Oh
runic garnet
and now we have
sinful harbor
Um that doesn’t make sense tho
runic garnet
z = a^(2/3)
sinful harbor
Ohhh yeah I forgot abt that
runic garnet
,w solve 3x^2 - 24x + 8 = 0
wraith daggerBOT
runic garnet
now what did u get
sinful harbor
Some numbers which it can’t be
Cuz they’re both less than 8 which I said was my minimum value
So I think ive done it wrong
runic garnet
ok show me how u got that
runic garnet
which answer makes sense to you
sinful harbor
21.164
runic garnet
there you go
sinful harbor
Should I plug it in to check?
wraith daggerBOT
sinful harbor
Oh yeah
YAY OMG
thank you sSO MUCH like I mean SO much I’ve been staring at that question for nearly 3hrs
runic garnet
yea np
runic garnet
have a good one
sinful harbor
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cedar kilnBOT
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steep depot
hi, can anyone help me understand this
cedar kilnBOT
hi, can anyone help me understand this
steep depot
the naswer is 2 sqrt 5 but i dont know why
cedar kilnBOT
@steep depot Has your question been resolved?
steep depot
<@&286206848099549185>
paper roost
What have you tried so far?
steep depot
i square rooted root 80 into 4root5, then i rationalised the dewnominator by timsing the 7/root5 into 28/4root5 by * them by 4
then i added to get 40/4root5
it didnt work so i tried to times 7/root5 into root 80 my timsing by 16 then adding
but i got 126?/4root5
but the answer was 2root 5 i dont know why
@paper roost u there?
paper roost
Yeah, a bit
An easier way would be to noticee that once you get $12\over4\sqrt5$, you can simplify this into $3\over\sqrt5$
wraith daggerBOT
Zayden
steep depot
oh right but i thoiught becouse 4 was attached to root5 coulkdnt do muhc w it
paper roost
You might find it useful to revise some basic stuff then
4root 5 means 4 * root 5
And since multiplying the numerator and denominator by the same constant does not change the value of the fraction
You can multiply them by 1/4
steep depot
ohh, i go tconfused wiht something else
like with factorising and cancleling the fractions
nvm continue
paper roost
$$\frac{12}{4\sqrt5}=\frac{4\times3}{4\times\sqrt5}=\frac{\frac14\times4\times3}{\frac14\times4\times\sqrt5}=\frac3{\sqrt5}$$
wraith daggerBOT
Zayden
steep depot
its alr i get it 🤣
after that do i just get...
hold on lemme try and finish it form there
i got stuck again 🤣🤣🤣🤣🤣
i got 10/root5
lemme let you explain it all the way throuhg my bad @paper roost
paper roost
i got 10/root5
You can rationalize now
steep depot
it already is : 7/root5 add 3/root5
steep depot
rihgt true
okay i get it now
2 root 5 by getting 10root5/5 then 2root5
thank you
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north crater
can anyone help me with this question?
cedar kilnBOT
can anyone help me with this question?
north crater
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fervent moon
help
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@fervent moon Has your question been resolved?
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@fervent moon Has your question been resolved?
teal frost
cedar kilnBOT
teal frost
Translated it with AI
So any questions about weird language ask me
This is what I tried to do, I might have gotten it wrong or just don´t know how to proceed
cedar kilnBOT
@teal frost Has your question been resolved?
teal frost
Here´s the start
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@teal frost Has your question been resolved?
harsh pond
This is what I tried to do, I might have gotten it wrong or just don´t know how ...
why did you write it as (x+1)^-1?
stiff parcel
I’m stuck with interpreting this question
cedar kilnBOT
I’m stuck with interpreting this question
@stiff parcel Has your question been resolved?
grave haven
is this correct
cedar kilnBOT
is this correct
stiff parcel
<@1310849628287008803> Has your question been resolved?
.reopen
vivid tundra
is this correct
it's right
but that 3rd line should be n²-n, not -1
north tinsel
I need to sum the following radicals not simplify but when i use Google calculator it simplifies
cedar kilnBOT
wheat jewel
I need to sum the following radicals not simplify but when i use Google calculat...
yes you need to learn your surd rules
weary flame
I need to sum the following radicals not simplify but when i use Google calculat...
you mean simplifying the radicals?
wheat jewel
split the part inside the square root into the multiplication of two numbers, where one of them is a square number
north tinsel
Yes but the homework reads sum the radicals bot simplify
wheat jewel
for example the first one, can be split into 9 * 6
north tinsel
But when i use Google it simplifies
wheat jewel
ok cool
and then you have to recognise that sqrt(9 * 6) can be split into sqrt(9) * sqrt(6)
and then you simplify sqrt(9)
north tinsel
Yep i know this one
wheat jewel
do the same for the other two surds
wheat jewel
Yep i know this one
ok then do it
ohhh
you want the number as a decimal?
like the answer as one number with a decimal
yeh just put it into the calculator
north tinsel
I need an answer of the type 54+28+12sqrt(y)
wheat jewel
I need an answer of the type 54+28+12sqrt(y)
it is not possible to put the answer in this form.
not much to understand really
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willow knot
cedar kilnBOT
willow knot
I don't understand why we are not investing into xc at the start
Only then we can get the benefit on the third year right ?
willow knot
I don't understand .. ?
willow knot
B is maybe strictly better
?
fair geyser
also this is weird, it looks like you can't invest into ABC later
willow knot
you would invest a,b,c in the first year since they yield in year 2 or 3
but investing into xc in y1 would not yield in year 3 it's not useful investment
willow knot
the problem only asks of retaining max cash in y3
fair geyser
so C is actually 2 year
there's no meaning in how they phrased it
literally a troll
oh the meaning is that you can't use C at the beginning
willow knot
yeah a and c you wouldn't
a can be used since it yields 0.1 every year
fair geyser
C is a 2 year thing that doesn't exist at the beginning
it appears a year later as an option
and that explains why B disappears
it just does
willow knot
Yeah
I still don't get why 0.1xa is not added in y2
Since it yields every year.
NVM I get my mistake
Does the problem tell us to invest only once into xa, xb, xc during all the years ?
@fair geyser Thank you
I understood everything I needed.
.close
cedar kilnBOT
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crimson sedge
If cos(t) = 0.6, evaluate what cos(-t) is
cedar kilnBOT
If cos(t) = 0.6, evaluate what cos(-t) is
bleak viper
cos(-x) = cos(x)
crimson sedge
Oh
Wait
Does that mean that
At point cos(t) and cos(-t) the values are the same cus they’re like symmetrical or sumn
cerulean sail
for even functions f(-x) = f(x)
Even functions are those where this is true
crimson sedge
Even functions are those where this is true
Yeah but how do i know when it’s true and not
😭
Ok wait
cerulean sail
"experience" I guess 
bleak viper
you can also just prove it
cos(x) = sin(90 - x)
replace x with -x
then use sin(A+B) formula
crimson sedge
Use a graphical method to determine the number of roots of the following equations “cos(x)-x=0” and “sin(x) - root (1-x)=0
Idk how to determine number of roots isnt it if u sub in certain values and it ends up as >0 and <0 then there’s a root between whatever 2 u subbed in?
cerulean sail
Graphical is telling you to plot y = cos(x) - x and y = sin(x) - sqrt{1 - x}, and "count how many times each cross the x axis [which is the line y = 0]"
crimson sedge
Graphical is telling you to plot y = cos(x) - x and y = sin(x) - sqrt{1 - x}, an...
Bru
How th do i even graph cos(x)-x
Do i solve for x
cerulean sail
Assumedly they want you to use a graphing calculator?
crimson sedge
It is without calculator
cerulean sail
Very strange of them to ask you to do it graphically then, quite painful 
crimson sedge
Ok nvm then not doing it
Last question
A window ledge 4 mins above the ground can just be reached by a 10 metre ladder. The foot of the ladder makes an angle (theta) with the ground (assumed horizontal)
A) write down the value of sin(theta)
B) calculate exactly how far up the ladder a person of height 1.8m needs to climb in order for the top of the person’s head to be level with the window ledge.
Im stuck on part B
Part A is 0.4, it was correct. Part B’s correct answer is 5.5 but idk how they got that
bleak viper
Very strange of them to ask you to do it graphically then, quite painful <:monke...
how
its simple graph
well, the first one atleast
crimson sedge
well, the first one atleast
Its ok i dont think it will be on the exam so we can skip it…. 😃
cerulean sail
its simple graph
y = cos(x) - x? I mean, it's not something I'd want to do "manually" (though it isn't "impossible")
Actually no wait-
crimson sedge
Oh
cerulean sail
Rearrange and plot separately 
bleak viper
yeah
crimson sedge
Graph cos(x) and y=x is what u mean?
crimson sedge
Okie thats easy
crimson sedge
A window ledge 4 mins above the ground can just be reached by a 10 metre ladder....
What about this
Im stuck on B
bleak viper
Im stuck on B
window is 4m above ground
the man's height is 1.8m
so he has to be 2.2 meteres above ground so that his head reaches the ledge of the window
but its asking how far he has to climb on ladder
so 2.2 is your perpendicular
hypotenuse part is the length of ladder he has to climb
you have sine of the angle the ladder is making with the ground
sin is P/H
plug the values
crimson sedge
Ah i see, ty
Much appreciated
I will close this so others can use it
Thanks man
.close
cedar kilnBOT
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half zenith
Where should I go with this question? I did p = 3 by hand and saw it had no real roots, but I don't really have any ideas for how to prove this
One idea I had is that if the graph goes below the y-axis by more than 1 unit, then of course adding one to that polynomial still ensures it has real roots, but I'm not sure how to incorporate that into a proof, or how to mathematically determine it
past wave
cedar kilnBOT
@half zenith Has your question been resolved?
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@half zenith Has your question been resolved?
cold timber
It cross x coordinate for p-1 time if don’t consider the +1, it is an even function, and it critical point is decreasing as p grow. Notice at p=7 there’s 6 root, then by above, at all p>=7, there’s p-1 root
cedar kilnBOT
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half zenith
It cross x coordinate for p-1 time if don’t consider the +1, it is an even funct...
Is this formal enough to be a full proof?
cedar kilnBOT
@half zenith Has your question been resolved?
cedar kilnBOT
@half zenith Has your question been resolved?
half zenith
Where should I go with this question? I did p = 3 by hand and saw it had no real...
<@&286206848099549185>
cedar kilnBOT
@half zenith Has your question been resolved?
potent fractal
Where should I go with this question? I did p = 3 by hand and saw it had no real...
Denote $g_p(x)=f_p(x)-1=(x-1)(x-2)\dots (x-p+1)$. Clearly $g_p(x)$ has $p-1$ roots, and it's negative on intervals $(1,2)$, $(3,4)$, ..., $(p-2,p-1)$. Denote $m_k=\min_{x\in (2k-1,2k)}g_p(x)$. For example $m_1$ is the minimum value of $g_p(x)$ on $(1,2)$, etc.
Note that if for some $p$ we manage to prove that $m_k < - 1$ for all $k$, then $f_p(x)=g_p(x)+1$ will have $p-1$ roots.
First, note that $m_k < g_p(2k-1/2) = (2k-3/2)(2k-5/2)\dots(2k-(2p-1)/2)$. If we manage to show that the last expression is less than $-1$ for large enough $p$ we will almost solve the question.
wraith daggerBOT
EQUENOS
potent fractal
If $p \ge 7$, then the last expression from above contains at least $6$ brackets, $2$ of which are equal to $\frac{1}{2}$ and $-\frac{1}{2}$, and some other $2$ have absolute value greater than $\frac{5}{2}$. Since $g_p(2k-1/2)$ must be negative, the entire expression is less than $-\frac{1}{4}\cdot\left(\frac{5}{2}\right)^2 < -\frac{25}{16} < -1$.
wraith daggerBOT
EQUENOS
potent fractal
Hence for p>=7 we proved that f_p(x) has p-1 real roots
Cases p=3, 5 can be done manually
f_3(x) has 0 real roots, f_5(x) has 2 real roots
cedar kilnBOT
@half zenith Has your question been resolved?
potent fractal
The question is not resolved, yet you didn't ask any questions regarding the suggested solution
half zenith
Sorry I just wasn’t sure about 1 small thing but I was busy yesterday
half zenith
Denote $g_p(x)=f_p(x)-1=(x-1)(x-2)\dots (x-p+1)$. Clearly $g_p(x)$ has $p-1$ roo...
I'm kinda new to stuff like this so excuse me if it's a bad question, but what made you take the step $m_k < g_p(2k-1/2)$?
wraith daggerBOT
Fear na bPónairí
half zenith
I can't make logical sense of where you got that from
And I find a similar thing happens in many solutions that I read
They make seemingly arbitrary decisions that seem to work out by the end
potent fractal
I'm kinda new to stuff like this so excuse me if it's a bad question, but what m...
m_k is the minimal value on [2k-1, 2k], while g_p(2k-1/2) is just some value at a given point from [2k-1, 2k], so m_k <= g_p(2k-1/2)
We could take any point x_0 from [2k-1, 2k], and still have m_k <= g_p(x_0)
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grim lantern
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grim lantern
<@&286206848099549185>
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tawdry pelican
Yes
tawdry pelican
Yes, and your method is correct
grim lantern
oh ok thanks for the confirmation
tawdry pelican
Actually, the ten possible solutions are easy to find: 4 orderings of (1,3,3,3) and 6 orderings of (2,2,3,3)
grim lantern
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wraith daggerBOT
! AzizKitten
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primal vigil
**! AzizKitten**
.
lyric narwhal
open a new channel, and don't delete your original message
primal vigil
ok
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crimson sedge
Hey guys, I'm a high-school student and I regret bunking my mathematics classes, that's why my mathematics is too weak that I could hardly pass my final exam of class 10th but as I want to go into the computer science field I decided to start mathematics from basic fundamentals to machine learning level, so I want to start with the book 'Everything you need to ace math in one big fat notebook', but the problem is my parents are upset from results and not allowing me to continue my studies so I want to get a PDF of this book, I request everyone please help, giving me a link of the PDF of that book or give me PDF directly. (I know after some weeks they'll get cool and let me buy the book, but that is too far and I want to start right now cuz, at current my eagerness to learn math is at its peak). Thanks in advance!
knotty harness
Dm me
knotty harness
I will be of help for you
crimson sedge
I will be of help for you
Thank you brother
crimson sedge
https://archive.org/details/everything-you-need-to-ace-math-in-one-big-fat-noteb...
Its not that book, have a look bro.
crimson sedge
why only that book
A great person suggested me that book.
crimson sedge
You can find different courses online (free) by MIT
Thanks bro I'll try
steep badge
I don't think finding a pdf of that book is possible rn
crimson sedge
But I don't want to take video courses, I belive more in paper pen.
crimson sedge
I don't think finding a pdf of that book is possible rn
Yea I tried so many ways but always failed.
crimson sedge
https://github.com/ossu/math
Is this really nice to try? And start from fund. to adv. ?
steep badge
It lists sources to learn from
problem solving - I don't really know
you can also go to #book-recommendations to ask for good books
crimson sedge
I'll check the whole the readme bro, thanks for providing the ossu!
steep badge
np
crimson sedge
you can also go to <#716264872018706443> to ask for good books
Damn, that looks too awesome, I didn't notice, thank you so much bro now I can get better books with real reviews instead of paid promotions.
cedar kilnBOT
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mighty drift
Hey guys, I'm a high-school student and I regret bunking my mathematics classes,...
just study become a math major until you get a good math BsC, and then you'll be close to having enough knowledge to tackle ML theory comfortably
crimson sedge
just study become a math major until you get a good math BsC, and then you'll be...
But the reality is I'm having problems in getting a good starting point for strong fundamentals.
mighty drift
Hey guys, I'm a high-school student and I regret bunking my mathematics classes,...
I regret bunking my math classes
That means you had the ability to, you just chose not to
then choose to
You have lecture notes, that should suffice
Reading math books is much more time consuming and hard than just following a class
You also learn much more, but it means it's especially hard to do for struggling students
crimson sedge
> I regret bunking my math classes
That means you had the ability to, you just c...
Yeah, it's actually true.
But about lecture notes...........I was a bad student, I've no old notes.
cedar kilnBOT
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cedar kilnBOT
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frail plover
help
wheat moss
don't spam channels please, just ask your question
peak prism
Hey all, how are you? 🙂
let $f: [0,1] \to \mathbb R$ bounded such that $\bar{\int_0^1} = 1, ~ \underline{\int_0^1}=0$
true or false -
a. for all $\epsilon > 0$ there is a partition P of $[0,1]$ such that: $1 \leq U(f,P) - L(f,P) < 1 + \epsilon$
b. there is a partition P of $[0,1]$ such that $U(f,P) - L(f,P) = 1$
I was thinking about using the Dirichlet function.
$f(x) = \begin{cases} 1 & x \in \mathbb Q \cap [0,1] \ 0 & else \end{cases}$
for any partition, I'll get that in any dx we have rational point so the supermum is 1. so the total of the upper bound is 1 and the infimum is 0 so the lower bound is 0.
so using that I get both a+b to be true in 1 example.
I feel like I'm missing something, cuz probably 1 of those is wrong. any help?
wraith daggerBOT
mtr123
cedar kilnBOT
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worn talon
cedar kilnBOT
worn talon
hi.. i dont have A.B to find the angle between A and B vectors
so i cant really use dot product
any ideas on how to find it
.close
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crimson sedge
help
crimson sedge
pls
unique nest
for a), might I suggest going from end to start, so to speak, by distributing the - (minus) in -(x^2-x-12) to each term. By rearranging the terms, you should get the initial form you have in your exercise
unique nest
it isn't, because if you open the brackets, you have -x^2 - 3x -4x+12
1 of the signs is wrong
crimson sedge
they are possible answers
unique nest
i got (-x-3)(x-4)
which method did you use to solve it
maybe I can see where the mistake happen
crimson sedge
unique nest
Ohh, I see, I was mistaken.
You are correct. let me see what's going on then with the options
unique nest
ok so, you are right. one way to solve it is by putting the - in the first bracket
so (-x-3)(x-4) is correct
but you can also put the - in the 2nd bracket
crimson sedge
yes i know but that’s not in the possible answers
crimson sedge
ok thank you
unique nest
and the 2nd ( ) becomes (4-x)
cedar kilnBOT
@crimson sedge Has your question been resolved?
hollow raptor
hello
hollow raptor
i have a doubt in a calculus q
this is the q
and this is my answer
i have substituted x for tan theta and then differentiated w.r.t theta in both functions to eventually find what the q is asking
But, the solution says its 1/4 (the ans)
Ahh i think i got it
Is my mistake that i differentiated wrt theta in the 1st function
but in the next one i differentiated wrt x?
cedar kilnBOT
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fierce bay
how can I prove this without sin and cos
cedar kilnBOT
how can I prove this without sin and cos
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).
dire geode
Is (u, v) the scalar product? And det the determinant? And tan = tangent function?
cedar kilnBOT
@fierce bay Has your question been resolved?
fierce bay
Is (u, v) the scalar product? And det the determinant? And tan = tangent functio...
yeah
dire geode
What does the determinant of a number mean
tulip steeple
Help?
cursive wing
Does anyone have an explanation for why the laplace inverse of this function does not exist
oh i can help you with that
tulip steeple
Like what is it even asking me
i tried to solve it like a regular linear inhomogenous
cursive wing
youre taking differential equations?
tulip steeple
yes
tulip steeple
no
cursive wing
okay
then first
we start with a substitution
can you give me a minute while i do the problem on a piece of paper?
cursive wing
wait
thats wrong i forgot a step lel
now i have to solve for A
thats your y(t)
now plug in 0 for it
cedar kilnBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
cursive wing
oh soryy
cursive wing
but i was doing it using annihilators
i think if you that problem
you have to guess
like x=e^{rx}
take derivateves of x
tulip steeple
they sat that y(t) -->0 as t--> inf
so i was thinking maybe it has something to do with that
cursive wing
did any of my answers work ?
i believe y(0) is just 0
and then when you take the derivative
its still 0
tulip steeple
did any of my answers work ?
the constants arent defined in the question so no
tulip steeple
i believe y(0) is just 0
and also no dice
tulip steeple
this professor makes us all feel that way
cursive wing
LMAO
cursive wing
the first one
try -3sinx
or -3sin(t)
lmk if it worked
i wanna see if my guess is correct lol
tulip steeple
nah
tulip steeple
nayyy
cursive wing
fuck me
oooh
are those one periods ?
wait no
the first one is half a period
this is 1.5 of a period
tulip steeple
yeah
cursive wing
hmmm
tulip steeple
I know the 3rd one
is iether some multiple of sin(4t) or cos(4t) from the particular soln
oh wait i have the DE of 3
not 2
cursive wing
the 3rd one?
tulip steeple
yes
cursive wing
that one most definitely has to be cos
since the way it starts at the top
but hold on
try cos(4t)
on my momma
tulip steeple
i guess i close now
cursive wing
okay but do you know why those are the answers>
tulip steeple
but change your pronouns to just him
tulip steeple
okay but do you know why those are the answers>
Not at all
cursive wing
sshiiddd
tulip steeple
like with the DE i can tell like what multiple is in the functio
like sin(4t) or whatever
cursive wing
you have to just think about what multiplying does to your function
tulip steeple
and i can kinda tell between the two which one itll be between sine and cosine
cursive wing
it dialates them
tulip steeple
oh
cursive wing
but honestly your homework is lowk stupid (maybe because idk what is going on) but looking at the graph it is so difficult to tell what is going on
i just eyeballed teh fuck out of those graphs
tulip steeple
but honestly your homework is lowk stupid (maybe because idk what is going on) b...
like istg
if the graph had numbers its no diff
cursive wing
yeah frfr
tulip steeple
i still have 3 other questions if u wanna help me xd
cedar kilnBOT
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wary widget
is this right and i don’t really understand what they want me to so on question 3
vivid wadi
is this right and i don’t really understand what they want me to so on question ...
in a function y = mx + b, what does m and b represent?
wary widget
m is the slope and b means the y-intercept
vivid wadi
what is the value of m in the equation you found?
cedar kilnBOT
cedar kilnBOT
Available help channel!
random kelp
cedar kilnBOT
pseudo lily
random kelp
Im not exactly sure how to parameterize the surface here, and how to do the dot product between the flux and the surface to get the amount of flux going through the surface
glad peak
Im not exactly sure how to parameterize the surface here, and how to do the dot ...
For parametrisation: r(u,v) = (u, v, f(u,v))
random kelp
okay but how do I get from the cartesian form to the u,v dimension
glad peak
As for the flux: normal dot flux
random kelp
i mean i only have flux in one dimension though?
like x,y & z are in the exponent
so its not like I can have F(x)i + F(x)j + F(x)k
random kelp
oh, so if the surface is closed I should use divergence?
What about if I had a sphere?
Should I apply the divergence theorem then since its also a closed surface?
glad peak
Ah it’s not flux since it’s a scalar field, not a vector field
random kelp
? So what do I do
glad peak
Integrate over the volume with the scalar field as the integrand
glad peak
Should I apply the divergence theorem then since its also a closed surface?
But to answer this question, yes.
For flux integrals that is
Not for this situation
random kelp
are flux integrals only for vector fields?
glad peak
Yes
glad peak
Correct
random kelp
Integrate over the volume with the scalar field as the integrand
hmm but I dont know what this means
glad peak
Well the question asks for the total mass
So immediately, you are thinking of the object as a whole, not just the surface
Since the inside will contribute to the mass, right?
random kelp
sure, yeah
pseudo lily
random kelp
did you mean doing something like this?
glad peak
You are also given the mass distribution of the object. This tells you how much each portion of the object weighs
Yes
But the bounds are not correct
random kelp
why is the base any easier to integrate over
glad peak
Then extrude that to up in the +z direction up till the slanted plane
random kelp
its the same thing on each side
glad peak
It’s just the way I see it best. There are a lot of ways to setup the bounds
Do whatever is most comfortable for you
random kelp
Then extrude that to up in the +z direction up till the slanted plane
hmm how would I create an equation to model that though
glad peak
hmm how would I create an equation to model that though
You need the equation of the plane first
random kelp
the equation of the plane is x+y+z=2
glad peak
Now you want to be able to return a z value on the plane given an x and y value
So rearrange for z
random kelp
could I not also just get y in terms of x & z
glad peak
You can
glad peak
No because you will integrate over y, then z and be left with an expression of xs
I think you should try it to see what I mean
pseudo lily
So I need to add in dx because dx is my variable?
glad peak
You need to integrate over x yes
glad peak
Dx dy has to fill the base triangle, right
random kelp
yes
glad peak
So what would the bounds be for that double integral?
glad peak
Write the integral out in full
pseudo lily
glad peak
Yes this would be dy dx
But the bounds are correct
Now you wan to extend the triangle upwards, but only until the plane x+y+z=2
Since you extend up, you will integrate over dz
glad peak
Yes
random kelp
glad peak
Now notice that z depends on both x and y
random kelp
oh i made a mistake here
glad peak
So you want to integrate that first
random kelp
glad peak
You will want to do dz dy dx
glad peak
^
random kelp
WOOOHOO
I got it
thank you so so much
but just one last question
would sigma here count as a scalar field?
so its the same steps
glad peak
You tell me, does it return a scalar or a vector?
random kelp
well if i input x y and z
it returns a scalar
so I guess a scalar field 😛
also, the bounds look a little unclear to me
glad peak
How so
random kelp
for x for example, would the bounds just be 7,0
since x cant be negative but must be less than or equal to 7
glad peak
Well | | is modulus, which is defined how
random kelp
the modulus is the absolute value
glad peak
Yeah but how is it defined
random kelp
sqrt(x^2)?
random kelp
true
random kelp
x=7,-7
glad peak
Yes
random kelp
i figured
glad peak
So for |x| <= 7 the bounds of x would be?
random kelp
-7,7?
glad peak
Yeah
glad peak
No problem
random kelp
have a good day
glad peak
!done
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
@random kelp Has your question been resolved?
limber marsh
.close
reef dome
can some1 plz help me with 8b 😞
cedar kilnBOT
can some1 plz help me with 8b 😞
crimson sedge
Hint - use your answer from Part A to help find this purple angle as marked
Then you can find the third angle in Triangle BCD and use it to solve for CD.
wise phoenix
i just want to make sure im right on these as they are all decimals and rounding.
astral leaf
check ur work with a calculator
native heath
yes
astral leaf
at least show ur working if ur asking for help
instead of asking ppl to use calc for u
native heath
we're typically shit at square rooting in our heads anyway
wise phoenix
I did it on a calculator then asked gpt and it said some were wrong and i dont see how
astral leaf
gpt is ass sometimes
native heath
!nogpt tbh
cedar kilnBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
wise phoenix
ok
cedar kilnBOT
@wise phoenix Has your question been resolved?
pseudo hedge
cedar kilnBOT
pseudo hedge
I need help doing this problem. I have been following organic chemistry tutors video on how to do these problems, but this particular one is different. Instead of exponentially increasing its decreasing, causing the formula he used to map out the area for the graph reversed. I’ll link a video with this as well. Can anyone help me out with this or point me to a video out there that has more information about this?
dusk goblet
well let’s start by identifying the intervals and interval widths
dusk goblet
https://youtu.be/YTKQswb60Pw?si=c1vn9TojFQvFD7zC
yo i think we know how to do riemann sums
but thanks
lol
pseudo hedge
Just sending the video in case anyone was confused with what I was referring too
dusk goblet
nope
and the whether or not the function is increasing or decreasing is irrelevant here
we’re doing an approximation
dusk goblet
and the whether or not the function is increasing or decreasing is irrelevant he...
this is only important if you wanted to know if it’s an over or underestimate
pseudo hedge
well dont you have to find both over and under estimates and find the average of those to get the final answer
dusk goblet
bruh
pseudo hedge
one sec let me do the math
pseudo hedge
ok I got 754. the intervals I used were 0-4 and I plugged x into the formula given to find the y variables.
I then used the change of x formula and got 1.
I feel like that number is way too big though.
dusk goblet
you used what as your intervals?
pseudo hedge
(-infinity, 196), (196, infinity)
pseudo hedge
why do you need to know the intervals though? Dont you start off the problem by graphing the equation and then figuring out the change of x?
dusk goblet
i’m not sure you understand what a riemann sum is
pseudo hedge
I guess I dont
dusk goblet
why do you need to know the intervals though? Dont you start off the problem by ...
who said anything about graphing
pseudo hedge
look at the video I sent
dusk goblet
we are dividing the interval [6,14] into 6 equal sub intervals
pseudo hedge
this is what I have been following
dusk goblet
hence we need interval lengths of (14-6)/6
or 4/3
so we start at the left endpoint
and add 4/3
that will be the right endpoint
and continue on until we get to 14
then we will have our 6 sub intervals
after that we will do our approximation by taking the height of the rectangle to be the value of the function evaluated at the right endpoint of each of those sub intervals and multiply it by the base length of the interval which we have just determined to be 4/3 in this instance
pseudo hedge
where does 4/3 come from? I feel like I would be able to grasp this a lot better if you sent a video related to this explaining it in-depth. I just don't quite understand everything your saying.
dusk goblet
where does 4/3 come from? I feel like I would be able to grasp this a lot better...
$\frac{14-6}{6} = \frac{8}{6} = \frac{4}{3}$
wraith daggerBOT
knief
dusk goblet
where does 4/3 come from? I feel like I would be able to grasp this a lot better...
go to khan academy or some shit
dusk goblet
🤔
dusk goblet
after that we will do our approximation by taking the height of the rectangle to...
what was inadequate here
pseudo hedge
I am unfamiliar with sub intervals or intervals relating to these types of problems. If you cant be patient with people then why even try helping them in the first place.
get off your high horse being a math discord helper doesnt make you special
dusk goblet
I am unfamiliar with sub intervals or intervals relating to these types of probl...
huh
pseudo hedge
.close
cedar kilnBOT
dusk goblet
i literally asked you what was confusing
polar goblet
i literally asked you what was confusing
He’s speaking the truth
polar goblet
Your service is ass
dusk goblet
Your service is ass
you’re getting help for free
polar goblet
Customer service could be better
worldly chasm
!vols
cedar kilnBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
dusk goblet
@pseudo hedge i gave you a thorough explanation
you’re just upset you can’t figure out what (14-6)/6 is
pseudo hedge
thats the change of x formula. you plugged in b for 14 a for 6 and n for 6 as well
you just need to learn patience with people who dont understand a topic you do
dusk goblet
brother
dusk goblet
where does 4/3 come from? I feel like I would be able to grasp this a lot better...
"where does 4/3 come from"
dusk goblet
you just need to learn patience with people who dont understand a topic you do
this is ironic
pseudo hedge
discord fedora hat moderator in the chat
dusk goblet
not a moderator
pseudo hedge
ima go actually get a life and a job so i dont have to get butthurt being called out for being an ass in a dc server
later
dusk goblet
ima go actually get a life and a job so i dont have to get butthurt being called...
who’s butthurt?
dusk goblet
ima go actually get a life and a job so i dont have to get butthurt being called...
how original
pseudo hedge
wHo'S bUtThUrT 🤡 🤡 🤡
worldly chasm
<@&268886789983436800> sorry to ping, but this seems to be getting out of hand
prisma laurel
discord fedora hat moderator in the chat
indeed, no reason why you should be flaming people offering to help you so come back tomorrow
polar goblet
discord fedora hat moderator in the chat
For real
quiet plover
went from 🧐 to 🤪
cedar kilnBOT
Available help channel!
solid tusk
Hey, I'm trying to figure out the following question:
cedar kilnBOT
Hey, I'm trying to figure out the following question:
solid tusk
According to photomath, the answer is 22 over 5, but i'm confused as to where the 22 comes from
pastel vault
According to photomath, the answer is 22 over 5, but i'm confused as to where th...
can you send the Photomath working?
which step in there exactly is confusing you
solid tusk
wicked mantle
pastel vault
wow that was quick
wicked mantle
fr
solid tusk
So I multiply the 4 by 5 and the v by 5. Does the original 5v just cancel out? which is why its just 22 over 5?
(side note super fast tysm)
wicked mantle
So I multiply the 4 by 5 and the v by 5. Does the original 5v just cancel out? w...
Wdym by original 5v?
pastel vault
So I multiply the 4 by 5 and the v by 5. Does the original 5v just cancel out? w...
nothing cancels
$\frac{2}{5v} + \frac{20}{5v} = \frac{22}{5v}$
wraith daggerBOT
southlander!
pastel vault
what is cancelling with v in the numerator?
solid tusk
I'm just wondering why it wouldn't be 10v
I'm in a foundations of algebra course so this is new to me
pastel vault
why do you think it's 10v?
solid tusk
Wouldn't you combine like terms? 5v + 5v
I'm trying to figure out what I'm doing wrong if that makes sense
pastel vault
**southlander!**
we are combining like terms here
because both fractions on the left hand side have the same denominator
you wouldn't do $\frac{3}{5} + \frac{6}{5} = \frac{9}{10}$ right
wraith daggerBOT
southlander!
pastel vault
it's just 9/5
pastel vault
no worries!
solid tusk
@pastel vault @wicked mantle yall are saints
pastel vault
I mean hardly, most people know more maths than this level
I guess we explained well
I mean a lot of people can also explain this well
solid tusk
i havent done math in years so im having to learn the basics again
muted timber
then you need to make sure you pay attention to the definitions said basics, so they dont bite you in the ass later
formal nest
cedar kilnBOT
formal nest
Where does the blue equations come from ?
I see that they follow the derivative chain rule, but from which initial equation?
half salmon
Isn't it just the first equation at the top differentiated?
pastel vault
yeah lol
half salmon
But instead of y''(x)-xy'-y=0 its y''(x)=xy'+y
formal nest
Oh yhea
half salmon
thought i was missing something for a sec
brave pike
Ok quick probability question I don't understand
Suppose you have a 30 sided die and there are two players, a and b
Each player gets to pick a number, player a going first and b going after
The die is then rolled, and the player who picked the number closer to the roll wins the ammount shown on the die
Which player should you be to optimize your earnings?
chrome quail
Interesting question
brave pike
I have the solution I just don’t understand it
But here is my thinking
So in any given situation player 1 has to pick 15
Otherwise he risks giving up a large portion of the board and lowering his chances winning (ie if he picks 30 player b will pick 29 leaving him with only a 1/30 chance)
chrome quail
It's probably a balancing game, where the second player would have to choose between x1+1 or x1-1, with this decision being dependent on whether the added $ from x1+1 is worth the lower chance of winning (if player 1 picks over 15).
brave pike
With this however player b has to pick 14 or 16
chrome quail
So in any given situation player 1 has to pick 15
Not necessarily
brave pike
Yeah exactly
Why not
Any divination from 15 will lower your chances winning of winning by 1/30
chrome quail
Cause P1 has a higher potential return if he picks a number higher than 15. The If P1 picks 15, P2 would obviously pick 16 (symmetry). P1s EV is then ([1+15]/2)*(15/30) = 4.
brave pike
Ok I agree
The question is which player should you be
Wait also no
Heading back
Let’s say you picked 20
Then p2 would just pick 19
And ur chances of winning goes down drastically
Ur ev is now 1/3 * 25
Hmm actually that may stilll be greater
chrome quail
Then p2 would just pick 19
But in this case, P2 has a higher EV if he picks 21
Up until some point P2 should pick x+1. After this value, they should pick x-1.
so P2 picking 21 here reduces P1s ev even more
brave pike
Ok I see your point
But yes
With everything said and done I think 15 is still the most optimal for p1
As any positive ev will be undone by p2s pick
chrome quail
The EV of this game is 15.5 in total
I doubt the best P1 can do is 4 of this 15.5
Lets choose 20 for P1, which P2 reacts with 21. what does that give for each player's EV?
chrome quail
30+1/2
chrome quail
yeah i did the same mistake earlier
chrome quail
21 for p2 is 1/3*([21+30]/2)
brave pike
Ok so let’s say p2 choose 19
That’s 19/30 times 10
Ok so 6.3
Yeah it’s better to pick 21
Ok either way
We are in agreement that it’s better to be p2?
chrome quail
No
Here's my argument
if this was a continuous game, equilibrium would be obtained right?
Ie. there would be a value between 1 and 30 such that both players would have an ev of 15.5/2
chrome quail
And this value would be the "flipping point" for P2. Ie. the point where P2 should "flip" from x+1 to x-1
brave pike
Ok wait actually going back to point 1
Considering that p2 will always pick 1 away from p1
chrome quail
yes
brave pike
Where would this value actually be?
Is it possible to get close or is there a clear winner between p1 and p2
chrome quail
I think the only way one would "win" is because of the discretization of the sample space
like you can't pick 21.4
If we can find the flipping point for p2, that value should be the optimal pick for 1
brave pike
Ok so 15.5/2 is 7.25
Meaning it’s a really discrete value and there is an optimal pick that player 1 could take
Reguardless of what player 2 does p1 would be optimal
chrome quail
yeah, i think
we can calculate one sec
For a given P1 pick x1, the expected payoff for x+1 is greater than the expected payoff for x-1 if
1/30 series from x1+1 to 30 of n > 1/30 series from 1 to x1-1 of n
brave pike
I mean considering that the number is higher than 7.5
Can’t we just
Multiply it by 2
Subtract 1
And call that one of the optimal pics
chrome quail
wdym
chrome quail
more than 7.25
brave pike
Ok, but both get close right
Let’s take 8 for example
Then for ev to be 8 the player has to pick 15
chrome quail
Then for ev to be 8 the player has to pick 15
why?
brave pike
Only really big numbers with small probability will give 8 ev
Or a lot of the smaller numbers
Considering we get to pick and all the lower numbers automatically go to us
We won’t pick 1-8
chrome quail
Only really big numbers with small probability will give 8 ev
no, because the small probability reduces the ev
the only way you get a really high ev is if your opponent plays suboptimally
brave pike
Yeah so only way to get 8 is big numbers with low chance
Or small numbers with high chance
I’m new to probability btw but
What I’m trying to say is
chrome quail
How do you know its even possible to get an EV of 8 at all?
if the opponent plays optimally
brave pike
I don’t, I’m talking about player 1 and trying to find the equilibrium
chrome quail
go ahead
brave pike
Like there should only be one way to get 7.25 right
chrome quail
not necessarily, there might not be any way to get 7.25, or they might be multiple if P2 plays suboptimally
brave pike
Hmm ok
chrome quail
we're talking about a discrete set of rolls 1,2,3,4 etc
if it was continuous, any value between 1 and 30, then it would be possible to optimzie 7.25-7.25
chrome quail
where did 13.5 come from