we now pick any even number greater than K, say n_k=100000002
#help-10
timid silo
we now pick any even number greater than K, say n_k=100000002
ooh okayy I got it know
Thank you so muchh!!
For 2:
We pick epsilon =1
K= 1002 so we get x{1002}=2
Now we pick odd number greater than K say
K= 1003 we get x_{1003}=0
So |0-2|=2>1?
timid silo
Ah okay
For 2:
We pick epsilon =1
We can always choose an odd number greater than K
Then x{n_k}=0 for this odd number n_k
So |0-2|=2>1?
novel knoll
yes
timid silo
Thank you so muchhh! I really appreciate it!
novel knoll
Np
timid silo
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tepid idol
lean trail
.close
dusk fable
help
dusk fable
tepid idol
<@644864474905313292> Has your question been resolved?
No
dusk fable
I did long division for the integrand my answer is in the red circle but in wolframalpha its the one in blue circle how did it come up with that result?
kind hawk
.close
dont close a channel of someone else like that
wolfram alpha skipped a step
they already did partial fractions
dusk fable
they already did partial fractions
Oh ok, so I have to do partial fractions for this?
kind hawk
as the next step in the integration process, yes
dusk fable
as the next step in the integration process, yes
Ok thank you
lean trail
dont close a channel of someone else like that
Dark was occupying multiple channels
I thought they didn't know how to close it
#help-7 is still occupied by them for the same question
You can check
kind hawk
well then say that but still dont just close a channel
obtuse pebbleBOT
@dusk fable Has your question been resolved?
silk niche
for part b, the solutions say 3/8 x 5/8 x 10
obtuse pebbleBOT
for part b, the solutions say 3/8 x 5/8 x 10
silk niche
how did they get there>
obtuse pebbleBOT
@silk niche Has your question been resolved?
silk niche
<@&286206848099549185>
desert sinew
Variance of binomial variable is $np(1 - p)$. You can derive it by definition or simply check your notes on that 🙂
warm shaleBOT
jimmy1234
obtuse pebbleBOT
@silk niche Has your question been resolved?
icy osprey
obtuse pebbleBOT
timid silo
use quadratic formula
stable rain
ye
timid silo
or complete the square maybe
keen nebula
Number 2 ra pls😭
indian ah?
timid silo
does not look like it
obtuse pebbleBOT
@icy osprey Has your question been resolved?
icy osprey
Yes cuz i solve it😡🥲🥲
obtuse pebbleBOT
@icy osprey Has your question been resolved?
regal latch
Is it correct that this is 1?
obtuse pebbleBOT
Is it correct that this is 1?
timid silo
,w x^2+2=2x
warm shaleBOT
timid silo
Need Help is correct
warm shaleBOT
rugged pond
I've always had an extremally hard time with problems like this and is wondering what steps I need to take to solve this.
If a venue has 1500 visitors during a day and sells tickets for $167,500. How many tickets were sold.
Adults: $140 Per person
Youth: $90 Per person
I need 2 answers one for how many adults bought tickets and the other one for how many youths bought tickets.
obtuse pebbleBOT
I've always had an extremally hard time with problems like this and is wondering...
high lily
introduce variables representing number of adults
and number of youths
set up an equation for total visitors
set up another from the info about total sales
solve the system using substitution or elimination
rugged pond
Can you maybe explain how to do all that?
or maybe find a video explaining?
high lily
well there's to parts to this,
one part is representing the problem with equations
the other is actually solving
there are plenty of vids on the actual solving,
the first part is mainly comprehension
introduce variables representing number of adults
and number of youths
you can choose whatever variables you want, though picking ones that somewhat resemble what they're representing will reduce confusion at the end
e.g. A for number of adults, and Y for number of youths
does that first step make sense
rugged pond
Kinda, although i think ill try to find some video explaining these kinds of problems
high lily
system of equations word problems might get you what you want
the very first step is just introduce variables to make writing your equations a lot simpler
so that you don't have to keep writing number of adults and number of youths in your equations
rugged pond
Yeah i know, its just these kinds of problems i cant wrap my head around
mainly since i havent done enough of them
high lily
the next step is to use those variables and set up equations
If a venue has 1500 visitors during a day
If a venue has 1500 visitors during a day
would you be able to set up an equation with that piece of info
using A fornumber of adults and
Y for number of youths
rugged pond
that equation is the most problematic for me, but ive found a video explaining a similar problem so im gonna try to solve my problem with help from the video. So im gonna close this channel
thanks for the help.
.close
ivory willow
for an integral of a delta function (x^2-4) from -infinity to infinity
obtuse pebbleBOT
for an integral of a delta function (x^2-4) from -infinity to infinity
ivory willow
why is the area a half?
obtuse pebbleBOT
@ivory willow Has your question been resolved?
ivory cargo
obtuse pebbleBOT
hasty ferry
just plug things in
hasty ferry
replace x with rh and y with h
in f(x,y)
ignore what r is for now
just plug it in as r
and then use the restriction on r later
hasty ferry
yes but you plug in x=rh and y=h first
ivory cargo
wait dont i have a h too much
hasty ferry
perhaps some factorisation
ivory cargo
wrong lmao
hasty ferry
factorise the h^2
ivory cargo
hasty ferry
Ok you can surely take it from here
hasty ferry
at the top u have things multiplied under a square root
u can split it
so just square root the h^2
then it becomes h
it cancels with the denominator
then you have sqrt(6r-3) left
and then thats ur answer
hasty ferry
why is there a 2 😭
hasty ferry
yes because you have no h left
hasty ferry
there is nothing to do with r
thats it
the answer is sqrt(6r-3)
they say r>=1/2
just so that 6r-3>=0
so that you dont have square a negative
hasty ferry
i guess if u want to show it works for r>=1/2
hasty ferry
Yep
ivory cargo
you cant help more then?
hasty ferry
ok
hasty ferry
T_n is nth order taylor polynomial?
hasty ferry
i only learnt taylors theorem last wk lmao and im braindead
but gimme 5 mins
i will try think
hasty ferry
are you doing real analysis right now
ivory cargo
no im doing an introcourse
its very wide, we started with complex numbers, and then continuiety, differentiability integrals and now this
hasty ferry
@ivory cargo
Are you sure ur on the right track
I think
all you need to do is show that the derivative is bounded above by 1
for x>1
ivory cargo
you think so?
the problem is the exact same as in the link
and he solved it that way
ivory cargo
yeah
hasty ferry
they basically give you the answer
hasty ferry
there is nothing to plug in
if x>1
why is that equation above always less than n!
i will leave you to think about that one
XD
ivory cargo
aaahhhhhhhhhhh
ivory cargo
thanks bro
hasty ferry
$f^{(n+1)}(x)=(-1)^nn!x^{-(n+1)}=\frac{(-1)^nn!}{x^{(n+1)}}$
agreed?
Ok now if x > 1
then why is that less than n!
ivory cargo
how did you get that expression
ivory cargo
ah okay
warm shaleBOT
Marikyuun
ivory cargo
okay sleep well
warm shaleBOT
Marikyuun
obtuse pebbleBOT
@ivory cargo Has your question been resolved?
dry flint
hi
dry flint
i was thinking smthg like red robin but he said "However, it is not necessarily the case that every student shakes 1 hand in (b). We are assuming that there are N handshakes, but they are completely random -- it might in fact be, because it is random -- that the same two students shake hands with each other N times."
For part a) is it asking how many groups of 2 are possible to form of the students
is this relevant
short skiff
I think that part A and the questions you've linked to ask different things:
The question you've linked to asks "You have 2n students. How many ways are to divide these students into n pairs (groups of 2)?"
The question you're asked asks "You have n students. How many (distinct) pairs (group of 2) are there from these n students?"
As to what the one who responded to you said:
Having N handshakes at random means that at each of the N times, you choose one pair at random, and that pair shakes hands with each other. The pairs are chosen completely independently from each other. Meaning, as they said, it could be that the same pair is chosen multiple times.
Section B asks: "What is the probability that, assuming there were N handshakes, that each pair of students (there are N such pairs, using the notation from A) was chosen to shake hands with each other exactly once?"
obtuse pebbleBOT
@dry flint Has your question been resolved?
dry flint
so a is just 2^n?
short skiff
No, unfortunately. Are you familiar with the $\binom{n}{k}$ formula?
warm shaleBOT
RoiKadmon
dry flint
combinations?
short skiff
Correct. More specifically, this is the amount of ways to choose sets of (size) k from a group of n items.
In this specific example, you are looking for the amount of ways to choose pairs (sets of size 2) from a group of n students.
dry flint
So it would nC2
short skiff
Correct. This would be the solution to section A.
In section B, you are asked: Assuming you are choosing N pairs (from the N possible pairs in section A), what is the probability that you have chosen each pair exactly once?
dry flint
Doesnt nC2 not account for repeats tho
short skiff
Do you mean whether (student 1, student 2) and (student 2, student 1) would count as pairs or not?
Since these are combinations, then they are counted as the same pair. If you were counting permutations, though, then they would count as different pairs. There are different formulas for that.
Perhaps this table may help organize it.
Or, rather, did you mean whether pairs like (student 1, student 1) would count?
In this case, they're not.
dry flint
Oh so we use permutations since i think its different
short skiff
Normally, when talking about groups of objects (or people), the order of choice doesn't matter, so this would be a combination - not a permutation.
Imagine, for the sake of argument, that you are choosing a pair by choosing the first student, and then choosing the second student from the remaining students.
In this case, it doesn't matter whether you chose student 1 or student 2 first, because it would be the same group in the end.
dry flint
Oh ur right it says different pairs
obtuse pebbleBOT
@dry flint Has your question been resolved?
short skiff
Sorry for responding late.
Is there something you'd like me to explain?
timid silo
How many pairs are there when there are 4 people?
short skiff
That would be $\begin{pmatrix} 4 \ 2 \end{pmatrix}$, since you are finding how many combinations (groups) of size 2 (pairs) there are from a group of 4 items. (people)
warm shaleBOT
RoiKadmon
short skiff
Or, did you mean to ask Infectia?
warm shaleBOT
Result:
6
short skiff
These are 6 pairs, so I believe you've listed all of them.
Keep in mind that their order isn't important, so having {blue, red} wouldn't be a separate pair from {red, blue}, for example.
timid silo
i can list more so can you
short skiff
Wait, keep in mind you have 5 colors here.
warm shaleBOT
Result:
10
so i should get 10
which i did
okayy now it makes more sense
can we go back to 3 people?
short skiff
Do you mean: How many pairs we'd have if there were 3 people?
short skiff
Correct, which corresponds to $\begin{pmatrix} 3 \ 2 \end{pmatrix} = 3$.
warm shaleBOT
RoiKadmon
timid silo
Now i want to transform those pairs into numbers
1
2
3
Every number has the same probability
so now i am going to draw a tree diagram
we have 3 times a path for 3 times the same number
18 paths for 2 times the same number
and 6 paths for every time a different number
so the probability that exact n people b) is
,calc 6/27
warm shaleBOT
Result:
0.22222222222222
If there are 3 People
pls help me to find out for 4 people .etc
n people
is this already the formular?
2n/n^n
2*3/3^3 = 6/27
because for 2 people it also works
,calc 2*2/2^2
warm shaleBOT
Result:
1
And it makes sense that the probabilty always gets lower the more people we have
so for 4 people
,calc 2*4/4^4
warm shaleBOT
Result:
0.03125
short skiff
Keep in mind that you are choosing pairs, not people.
This means, in the case of 4 people, for example, that you are choosing one of the 6 pairs each time.
In that case, the "paths" in the tree that you've shown above (where each node would be a pair, not a person) would be N to the power of N, since you are choosing one of N pairs N times.
And now, you have to ask: Among these N^N paths, how many of them lead to an outcome where each pair has shaken hands once?
That would be the amount of ways to order N handshakes, which is N! ways.
timid silo
yes i can follow almost to the last senctence
That would be the amount of ways to order N handshakes, which is N! ways.
short skiff
May I explain that?
warm shaleBOT
Result:
6
each combo has the same probability
short skiff
Correct. We're assuming that we're picking the pairs at random.
timid silo
n = number of people?
short skiff
Yes, and N is the number of pairs, which is N = nC2.
timid silo
ah okay
now i want to see how many paths there are
is it 6^4, 6^6, 4^6 or 4^4 ?
has to be 6 first
,calc 6^6
warm shaleBOT
Result:
46656
because at the example with 3 it was 3^3
short skiff
The amount of paths in total?
That would be 6^6, because you are choosing N = 6 times, and each time, you are choosing one of the N = 6 pairs at random.
This tree is going to be too large to draw.
timid silo
Now we come to the for me interesting part:
And now, you have to ask: Among these N^N paths, how many of them lead to an outcome where each pair has shaken hands once?
quick look on b) again
short skiff
To reiterate what I meant:
We are looking for paths in which each of the N pairs was chosen exactly once.
timid silo
timid silo
And now, you have to ask: Among these N^N paths, how many of them lead to an out...
that would be the answer for b)
so we have to divide the paths / N^N
at 3 it was 6 paths
so is it just 3 * 2?
6*2 = 12
we could draw that
btw thanks so much for answering very cleary, i apreciate that
short skiff
so is it just 3 * 2?
Not precisely.
Think of it this way: Each path represents a different "order" of handshakes. How many different "orders" are there to all of the N possible handshakes?
dry flint
sorry i just got out of class
timid silo
welcome back
timid silo
`so is it just 3 * 2?`
Not precisely.
Think of it this way: Each path represents...
so now the order matters?
we can change the colors order here so we get 6
short skiff
For example, in the case of 3 people with three pairs, the different "orders" of people would be:
(student 1 -- student 2), (student 1 -- student 3), (student 2 -- student 3)
(student 1 -- student 2), (student 2 -- student 3), (student 1 -- student 3)
(student 1 -- student 3), (student 1 -- student 2), (student 2 -- student 3)
(student 1 -- student 3), (student 2 -- student 3), (student 1 -- student 2)
(student 2 -- student 3), (student 1 -- student 2), (student 1 -- student 3)
(student 2 -- student 3), (student 1 -- student 3), (student 1 -- student 2)
Not exactly: The order of the people within the pair doesn't matter.
We are still going to have nC2 pairs, not nP2 pairs.
However, since we are counting the amount of "paths" in a tree, and each path shows a different "order" in which each of the N handshakes were chosen, then we are giving importance to order.
short skiff
I'll explain what I mean by "order":
Suppose each "node" in the tree represents a pair.
We are interested in a path in a tree where all the pairs represent different pairs.
The question is: How many different paths are there where all of the N pairs are chosen?
timid silo
ok slowly i get there i guess
short skiff
May I try to draw how the tree will look like?
timid silo
we are just looking at this path
timid silo
May I try to draw how the tree will look like?
for 6^6???
short skiff
No, I mean for the n = 3 (and N = 3) case, just to explain what I mean by "nodes" that are pairs.
timid silo
we are just looking at this path
and now the question is how many order are there for this path
when we have 3 colors
wait
let me put this in a row
i have it
the question is how many permutations are there
which is 3!
,calc 3!
warm shaleBOT
Result:
6
Result:
720
then the formular is
N!/N^N
correct? 😅
yeeesssss ^^
thanks for walking me through 🙏
short skiff
By the way, this is what I meant by having the "nodes" being pairs.
Each time (as we step down the tree), we pick one of the N pairs, and we are looking for the amount of paths in which all the N different pairs appear. Different paths would have the N pairs appearing in a different order (for example, we can have the black-red, black-blue and red-blue path, and black-red, red-blue and black-blue path, which would show the same handshakes, but in a different order), and there are N! such paths.
timid silo
.close
dry flint
just finished reading all of this i understand!
dry flint
.close
btw for the previous problem, when we multiply by 7 and 21 u multiply the denominator right
dry flint
like the bottom of a fractioin
warm shaleBOT
Requested by /\#3608
timid silo
But 7 is 7/1
timid silo
$7=\frac{7}{1}$
warm shaleBOT
/\
timid silo
,calc 1/7!0.25^60.75*7
warm shaleBOT
Result:
2.5431315104167e-7
this was the right order and then one paper in wrong direction
1/7! • 0.25^6 • 0.75^1 • 7
and then we can put the 7 in front also
7/7! • 0.25^6 • 0.75^1
dry flint
7/7! • 0.25^6 • 0.75^1
what abt 3/4 probability its wrong orientation
warm shaleBOT
Result:
0.75
yes
pulsar cypress
obtuse pebbleBOT
pulsar cypress
Please help
arctic panther
i don't even know what to suggest without spoiling the answer
pulsar cypress
i don't even know what to suggest without spoiling the answer
just show me pleas
arctic panther
Kathleen paid 6.20
1 notebook for 1.40
and some pencils
so how much did she pay just for pencils
obtuse pebbleBOT
@pulsar cypress Has your question been resolved?
hoary rain
obtuse pebbleBOT
sharp flume
Mind if I give it a try?
hoary rain
sure
sharp flume
I'd probably try rearrange the equation first
something like:
y = (1-144x)/83
this can be plotted on a graph...
but 83 is a prime number
hoary rain
something like:
**y = (1-144x)/83**
should be 1-144x
sharp flume
yes my bad
hoary rain
and yeah the graphing doesn't really do anything cuz every point on the line is an answer but you ahve to find all possible integer answer
for example earlier question that i had
sharp flume
I was trying to rearrange the equation by treating it like a simultaneous one but that didnt work
hoary rain
the answer would be this one
since x = 9 and y = -31 works, but any combination of adding/substracting 104 and 359 also works
and i'm currently stuck on this one
hoary rain
I was trying to rearrange the equation by treating it like a simultaneous one bu...
yeah
i tried it with the very first question and realized that'snot how you solve it
shadow lava
obtuse pebbleBOT
shadow lava
I get the impression you need to see factored and unfactored form to truly understand the behavior of a polynomial such as this one
while the factored form is ideal, it shows a lot, it does not show the y-intercept with factored form
Or would there be a way to see that the y-intercept is indeed (0, -36) just by looking at the factored form? (just by having the red version and ignoring the blue version altogether)
obtuse pebbleBOT
@shadow lava Has your question been resolved?
delicate lion
obtuse pebbleBOT
delicate lion
Hello, $d_m$ is a set of samples $d_m = {(d_m^x(1), d_m^y(1)), \dots, (d_m^x(m), d_m^y(m))}$ of size $m$.
Why its space dimension is $\mathcal{D}_m = (\mathcal{X} \times \mathcal{Y})^m$, instead of $m$? thank you.
warm shaleBOT
Kin
delicate lion
.close
timid silo
Prove that each expression can have only positive values.
a^2 + b^2 − 2ab + 1
im struggling with this. normally id just complete the square but that wont work here
obtuse pebbleBOT
Prove that each expression can have only positive values.
a^2 + b^2 − 2ab + 1
...
wooden cipher
you do complete the square, you just have an extra 1
in other words it factors as (b-a)^2 +1
wooden cipher
no
timid silo
nice
wooden cipher
you refer to the trivial inequality and youre all good
high lily
you already have a perfect square
technically you could complete it by explicitly adding and subtracting 0
glad cobalt
obtuse pebbleBOT
glad cobalt
confused on the y-intercept
looks like it crosses the y axis at 1.3
1.3 as an fraction is 13/10
and idk what the point would be either
the slope is correct
viral blade
ye
there u go
but
i don't think you're supposed to guess the function by looking at the graph
i think you're supposed to use the points given
u found the slope that way correctly
viral blade
but there's only 1 point on the y-axis that's on the line between the points as well
glad cobalt
yea y-y1=m(x-x1)
viral blade
yea y-y1=m(x-x1)
ye use that
viral blade
i don't think 14/10 is 1.3
i don't have a calculator on me right now
but if i had to guess its' probably 1.4
,w 14/10
glad cobalt
ye use that
i got 6/11
warm shaleBOT
viral blade
yea wolfram seems to agree
misty jetty
i don't think 14/10 is 1.3
no i meant thata the y int is 14/10 not 13/10
so 1.4
y--4=(6/11)(x--5)?
glad cobalt
still says its wrong.
misty jetty
check my math tho
viral blade
positive still?
glad cobalt
misty jetty
-14/11
glad cobalt
-14/11 is the y intercept so what would the point be?
zenith epoch
guys is this true or false? i need the concept or theory
obtuse pebbleBOT
guys is this true or false? i need the concept or theory
high lily
can you think of a counter example?
chrome mesa
think holes
obtuse pebbleBOT
@zenith epoch Has your question been resolved?
vocal matrix
obtuse pebbleBOT
vocal matrix
need to simplify
do I divide first or take the factors of 2 out first
or do I add the numerator first
unique kettle
simplify the first or second image?
unique kettle
I would divide it by the two first
high lily
factor out 2 or divide terms individually
either works
vocal matrix
factor out 2 or divide terms individually
either works
ok so factor out 2 so then it would just be +- sqrt(6)
high lily
no
unique kettle
yes
vocal matrix
holy
unique kettle
oh wait nvm, 1+-....
high lily
its more or less stuff you should already be familiar with
general simplification practices
vocal matrix
ok
unreal pelican
Though, and I'm assuming you're solving for x, another way to solve it is to square root the (x+1)^2 and the 6 to get x+1 = +-sqrt(6)
vocal matrix
oh yea
unreal pelican
Then subtract 1 and get -1 +- sqrt(6)
vocal matrix
thats way easier
unreal pelican
No messy division with the quadratic formula
unreal pelican
thats way easier
In general, the quadratic formula, to me, is really a last resort
When nothing can be factored out, simplified, etc.
vocal matrix
When nothing can be factored out, simplified, etc.
yup
or
x = +- 4 sqrt(2) / 2
@unreal pelican
unreal pelican
I don't believe so, let me run through the math real quick to confirm
random depot
its wrong ecksdee
unreal pelican
So you would start with x = (8 +- sqrt(64-32))/16
Simplifying, you should get (8 +- sqrt(32))/16
nocturne minnow
So you would start with x = (8 +- sqrt(64-32))/16
Don't do the work for people
unreal pelican
Ah, I'm really doing this for myself, but I'm sorry
nocturne minnow
How did you get this?
vocal matrix
Simplifying, you should get (8 +- sqrt(32))/16
Yes I got that
I looked up the answer on wolfram alpha
And it looked like that
unreal pelican
Yes I got that
Oh, do you not know how to simplify from there?
nocturne minnow
Do you know how to simplify radicals?
vocal matrix
Oh, do you not know how to simplify from there?
Well I then got
nocturne minnow
But the final answer was 1/2 +- 1/ 2sqrt(2)
$\frac{1}{2} \pm \frac{1}{2 \sqrt{2}}$?
warm shaleBOT
dldh06
vocal matrix
8 +- 4sqrt(2) / 16
vocal matrix
$\frac{1}{2} \pm \frac{1}{2 \sqrt{2}}$?
Yes
nocturne minnow
8 +- 4sqrt(2) / 16
$8 \pm \frac{4 \sqrt{2}}{16}$?
unreal pelican
What do you do next?
warm shaleBOT
dldh06
vocal matrix
$8 \pm \frac{4 \sqrt{2}}{16}$?
8 is divided by 16 as well
nocturne minnow
And that's why parentheses are needed
unreal pelican
**dldh06**
The 8 should be divided by the 16
nocturne minnow
The 8 should be divided by the 16
I know, I was proving a point that parentheses are needed
unreal pelican
Oh, got'cha
unreal pelican
Is there a manual
I think the bot uses the same rules as LaTeX, so if you search up a guide on how to use LaTeX, you should be able to use it
vocal matrix
So the answer is not (+- 4 sqrt(2) / 2) ?
unreal pelican
So the answer is not (+- 4 sqrt(2) / 2) ?
Definitely not
nocturne minnow
So the answer is not (+- 4 sqrt(2) / 2) ?
How do you get this from $\frac{8 \pm 4 \sqrt{2}}{16}$?
warm shaleBOT
dldh06
unreal pelican
$\frac{8}{16} \pm \frac{4 \sqrt{2}}{16}$
warm shaleBOT
Zylo
vocal matrix
Is 8/16 not 1/2?
unreal pelican
AYY, finally!
unreal pelican
Is 8/16 not 1/2?
It is
unreal pelican
So then, what should be the answer?
stable rain
ITS A WEEB LES GOO
vocal matrix
So that’s the answer then
nocturne minnow
4/16 = 1/4
unreal pelican
Mhm
unreal pelican
4/16 = 1/4
I got that
vocal matrix
Then why does wolfram put the radical in the denominator
I thought you weren’t supposed to do that
stable rain
Then why does wolfram put the radical in the denominator
lol i meann
nocturne minnow
It's not common practice
stable rain
idt its really strict
unreal pelican
Well, it's really more of a formality than an actual rule
nocturne minnow
It's an answer
stable rain
ye
vocal matrix
Ok
unreal pelican
ITS A WEEB LES GOO
Yes, I am!
stable rain
so u can pick n compare
stable rain
Yes, I am!
YEEEEEEE
unreal pelican
This is truly a weeb moment
nocturne minnow
ITS A WEEB LES GOO
You honestly gotta stop going off topic in help channels. Seen you do this a lot, help channels are for helping not off topic conversations
nocturne minnow
But you clutter the channel with pointless talk
nocturne minnow
Plug in the values you got, and see if that results in 0
vocal matrix
neither of them are right
vocal matrix
just checked
stable rain
so uve to plug it in accordingly
notice the powers
and also if the a is 0 u cant use quadratic formula
nocturne minnow
Technically if a = 0, then it's not even a quadratic
vocal matrix
(+- sqrt(42) / 7)
is what im at right now
that the answer I need I think but how do I get to the exact form of sqrt(6/7)
from there
vocal matrix
unreal pelican
Oh, you can do that
vocal matrix
yea
unreal pelican
Well, just take the $\sqrt{\frac{6}{7}}$ and write is as $\frac {\sqrt{6}}{\sqrt{7}}$
warm shaleBOT
Zylo
unreal pelican
Oh, one more thing, don't forget the $\pm$
warm shaleBOT
Zylo
unreal pelican
When you take the radical of an even power, you must always include a $\pm$
warm shaleBOT
Zylo
unreal pelican
Though the quadratic equation is really unnecessary here, but if you're forced to use it, then I guess you have to
vocal matrix
I’m talking about getting sqrt(6/7)
From my answer
How do you turn sqrt(42) into sqrt(6) without also including the sqrt(7)
unreal pelican
Ahhh, got'cha
I don't think that $\pm\frac{\sqrt{42}}{7}$ is correct, though, could you quickly go through how you got to it?
warm shaleBOT
Zylo
vocal matrix
I’m not home but that’s what I got by using the quadratic formula
vocal matrix
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
vocal matrix
@unreal pelican
obtuse pebbleBOT
@vocal matrix Has your question been resolved?
vocal matrix
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
cedar lichen
!15m
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
timid silo
<@&286206848099549185>
neat valley
what have you tried/any ideas
obtuse pebbleBOT
@timid silo Has your question been resolved?
spark sail
dark mango
2pi * the integral from 1 to 2 of (x)(x^3)(dx)?
obtuse pebbleBOT
@dark mango Has your question been resolved?
dark mango
<@&286206848099549185>
obtuse pebbleBOT
@dark mango Has your question been resolved?
ancient wedge
I am quite stuck, How do you find the length of x?
obtuse pebbleBOT
I am quite stuck, How do you find the length of x?
ancient wedge
<@&286206848099549185>
obtuse pebbleBOT
@ancient wedge Has your question been resolved?
obtuse pebbleBOT
@ancient wedge Has your question been resolved?
brisk matrix
you can plot this as $f(x) = \sqrt{r^2-x^2}$, then let $f(x_0)=8$ and $f(x_0+4) = 4$
warm shaleBOT
maximo
brisk matrix
you should be able to find r from that alone, and finding x^2 should come along
ancient wedge
How?
brisk matrix
you have $r^2 - x_0^2 = 64$ and $r^2 - (x_0 + 4)^2 = 16$
warm shaleBOT
maximo
brisk matrix
you should be able to find the value of x_0 by solving for r^2 on both sides
and from there the value of r should come by plugging that x_0 back into the equations
after that you just need to compute f(x_0 + 2) and double it (since we're doing only half the circle with this function)
and that'll be your x
then just square it
ancient wedge
What is r and x in this equation?
brisk matrix
r is the radius of the circle
x is arbitrary
f(x) = sqrt(r^2 - x^2) plots the top half of a circle with radius r
do you happen to have the answer?
brisk matrix
f(x) = sqrt(r^2 - x^2) plots the top half of a circle with radius r
note that this is just a visualization, but you can also think of f(x) as half the height of a chord going from top to bottom of the circle with radius r
ancient wedge
do you happen to have the answer?
Not really.
brisk matrix
i got a whole number so im pretty certain this is a way to go about it
ancient wedge
Hmmm okay.
I wonder how the problem looks visually.
Is it three parallel lines in a circle?
brisk matrix
this is what my solution is doing
that's why we need to double the length we find at the end
ancient wedge
How do you find r with the equations?
brisk matrix
r^2 - x^2 = 64 and r^2 - (x+4)^2 = 16 -> 16 + (x+4)^2 = 64 + x^2 and you get a value of x
then just plug the x back into the original equation
oh
i did 8^2 accidentally
it should be 6^2
ancient wedge
X = 4?
brisk matrix
that's with the wrong equations
your equations should actually be r^2 - x^2 = 36 and r^2 - (x+4)^2 = 16
ancient wedge
What would x be?
ancient wedge
Hmmm?
ancient wedge
The answer is supposed to be an integer, my friend said.
brisk matrix
yes it is
x = .5 is not the answer
oh i see the confusion
the x we're talking about is different from that of the question
the point of finding x = .5 is that now we know r^2 - .5^2 = 36
so we have a value for r
then from there we can just take f(.5 + 2) = sqrt(r^2 - 2.5^2) = the x in the question over 2
then double it, square it, and you have the answer
ancient wedge
The radius is 6.02...
brisk matrix
specifically sqrt(36.25)
ancient wedge
Yeh, Then sub?
brisk matrix
then just take f(.5 + 2) = sqrt(36.25 - 2.5^2)
and that's half the length of the chord
ancient wedge
Oh, Its 120.
brisk matrix
yes
ancient wedge
What topic is this? I am going to study more about it.
brisk matrix
not sure. i'd say it's just geometry
ancient wedge
In here, is x the purple?
brisk matrix
no
that's just a representation of f(x)
x in the diagram is the location along the x axis
and f(x) is the height of the semicircle at x
ancient wedge
Hmmm, I thought it can be solved using construction, Didn't expect there to be functions.
one last qs, Why is it sqrt of the radius - x²?
brisk matrix
if we take the circle y^2 + x^2 = r^2 -> y = sqrt(r^2 - x^2)
brisk matrix
Hmmm, I thought it can be solved using construction, Didn't expect there to be f...
it may be, i just went to this because it's what im most comfortable with
ancient wedge
Oh damn, I have a lot of things going in my mind, How did the length of the chords (8 and 12) and the distance (4) used in solving?
brisk matrix
we used the lengths and distance to find the radius
if a is the location of the first chord, then we used f(a) = 36, f(a+4) = 16
from there we get the value of a
and from the value of a and the length we find r
ancient wedge
Oh we used 8.
brisk matrix
(8/2)^2 = 16 and (12/2)^2 = 36
jagged lance
So I have to prove $$\overline{\lambda \cdot \mu} = \overline{\lambda} \cdot \overline{\mu}$$What I got right now is $$\overline{(a+bi)(c+di)} = \overline{(ac-bd) + i(bc+ad)} = (ac-bd) - i(ad + bc)$$ $$= ac - bd - i(bc) - i(ad) = (a - ib)c - (b -ia)d$$ But I can't get to the right answer, anyone who could help me on my way? Thanks!
obtuse pebbleBOT
So I have to prove $$\overline{\lambda \cdot \mu} = \overline{\lambda} \cdot \ov...
warm shaleBOT
cedric_
fossil crag
Calculate the Right hand side as well
brisk matrix
your last step is wrong
jagged lance
your last step is wrong
The whole second line?
fossil crag
Yep
obtuse pebbleBOT
jagged lance
thanks
fossil crag
Np
warped flume
proven zephyr
give example
warped flume
<#488120190538743810>
maybe read this first
proven zephyr
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
small peak
How does one divide a polynomial by a letter like x?
obtuse pebbleBOT
How does one divide a polynomial by a letter like x?
kind hawk
I assume you mean you want to divide a polynomial by another polynomial?
in the special case of the polynomial g(x)=x ?
there is an algorithm for that, called polynomial long division, which works very similar to the long division algorithm you know from dividing numbers
obtuse pebbleBOT
@small peak Has your question been resolved?
small peak
I assume you mean you want to divide a polynomial by another polynomial?
Idk this is my problem and I’m trying to get rid of the x’s inf the beginning of the problems
At the top don’t mind the bottom parts
kind hawk
f+g is just shorthand for f(x)+g(x)
small peak
Yes but how do I solve the polynomials at the top?
kind hawk
yes
timid silo
can someone please explain how he found the turning point with differentiated AB^2 and not AB or didn't atleast square root it at the end?
obtuse pebbleBOT
Available help channel!
timid silo
hi
warm shaleBOT
timid silo
when it adds an extra power on from 6.6x10^3 to ^4
why does it go to 0.66 and not 66
I thought it only gets smaller when the power is a minus
ping when responding please
warm shaleBOT
Result:
6600
,calc .66*10^4
warm shaleBOT
Result:
6600
hi
timid silo
but that's wrong though
high lily
shift 1 dp back for the 6.6 → 0.66
shift 1 dp forward for the 10^3 → 10^4
to compensate thus maintaining the same value you started with
stable rain
idk i think always thinking of the base case is the best way to visualise
both ways work see what helps u most
timid silo
ok so what would I do for (4x10^-4) + (6x10^-5)
high lily
depends on personal preference which one you want to manipulate
high lily
multiply by 1/10 * 10
high lily
yes
shrewd pendant
I don't understand the construction they use to define a mapping from x to y. What does it mean to map a set of x to a single y?
obtuse pebbleBOT
I don't understand the construction they use to define a mapping from x to y. Wh...
stable rain
where does it say that
shrewd pendant
the line where they define p(y) and consider any set of x's that map onto a single y. below solution. Is where I am lost.
I can see how such a set can exist, but beneath the summation how they define x:y=(x) is what confuses me a little, what does this mean?
unique nebula
I can see how such a set can exist, but beneath the summation how they define x:...
Isn't it just the set of all x such that y=g(x)
shrewd pendant
that makes sense to me tbh
nice comment
so, then for let's say, Y = 2^X we would get a one-to-one function?
azure finch
small thicket
zenith epoch
what is this qustion means?
obtuse pebbleBOT
what is this qustion means?
final thunder