so going back to our formula
#help-36
static plinth
we know x bar
we know sigma
and the z score
you can solve for the mean now
well x bar should just be the 250 we’re given
that looks good
that seems right
yep
mmm i mean you can definitely approximate it using the empirical rule
it’s like approximately one standard deviation away from the mean
but the one that we got is much more accurate than that
yeah
68-95-99.7 rule
so basically 68 percent of all values lie between 1 standard deviation from the mean
yeah
that’s basically it
so we want to see how many standard deviations away we would need to go
such that the probability of the left hand side is equal to 80%
okay so we don’t know the mean
but we know that approximately one standard deviation away from the mean to the right, it should be 250
since that’s what we’re given
so using that, we can approximate that our mean should be 248
which is quite close to what we got using the normal distribution table
it’s called inverse normal
but i’m quite sure it requires the mean
yeah it’s that
but it requires the mean, standard deviation, and the probability of the area of interest
it’ll give you what x bar we would need to get that probability
but we know x bar and don’t know mu
mm im not really familiar with that
i mostly just use desmos
i see
yeah
i’m just more used to desmos
a lot of people use geogebra
it’s just that i’ve never really bothered to check it out
yw!!
final saddleBOT
final saddleBOT
Available help channel!
south kernel
It has nothing to do with mathematics but I'm desperate because I have a programming test tomorrow and I have to study
all these keys stop working at the same time, anyone know what it can be
final saddleBOT
It has nothing to do with mathematics but I'm desperate because I have a program...
vital surge
i applaud this question
final saddleBOT
@south kernel Has your question been resolved?
frail vigil
It has nothing to do with mathematics but I'm desperate because I have a program...
lucky the brackets still work lmao
my guess is that the row is connected to one „stream“ (idk how to say it) of cables and that one stopped working
final saddleBOT
@south kernel Has your question been resolved?
solid cobalt
Yes
versed crater
strong radish
its not wrong as long as n is not 0
formal trail
you can always multiply something by 1 (and anything divided by itself is 1)
you can multiply by sqrt(n/n), since sqrt(1) = 1
formal trail
this is wrong if n/(n+3) <0 because its in sqrt
you would get undefined = undefined anyway, so it doesn't really make a difference
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
tranquil pine
dis right?
regal hamlet
A set of integers ( (a_1, a_2, \ldots, a_n) ) forms a complete system of residues modulo (n) if and only if no two integers in the set are congruent modulo (n).
final saddleBOT
A set of integers \( (a_1, a_2, \ldots, a_n) \) forms a complete system of resid...
soft zealotBOT
Halex
regal hamlet
"$\Rightarrow$" Suppose that ( (a_1, a_2, \ldots, a_n) ) forms a complete system of residues modulo ( n ); for the sake of contradiction, let ( y \in \mathbb{Z} ) such that ( n \mid y - a_k ) and ( n \mid y - a_m ) for some ( k \neq m ), where ( k = 1, 2, \ldots, n ) and ( m = 1, 2, \ldots, n ). There exists (\theta, \beta \in \mathbb{Z} ) s.t $$ y-a_k = n \theta$$ $$y-a_m = n \beta$$
So we have $a_k + n \theta = a_m + n \beta$ which implies $a_k - a_m = n(\beta - \theta)$ and thus, $a_k \equiv a_m \pmod{n}$, which is a contradiction.
soft zealotBOT
Halex
regal hamlet
Having issues with the backward implication
Basically I need is to show that given any integer, it is congruent to at least one of the elements in the set modulo n
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
@regal hamlet Has your question been resolved?
plush crow
perhaps try contradiction. assume there are two integers in the set are congruent modulo n, then find a contradiction
final saddleBOT
@regal hamlet Has your question been resolved?
regal hamlet
perhaps try contradiction. assume there are two integers in the set are congruen...
that is what I did for the first implication
plush crow
maybe contra positive will work out
final saddleBOT
@regal hamlet Has your question been resolved?
cosmic bolt
**Halex**
it's a kind of pigeonhole situation, right? you have n numbers, you know none of them are congruent to one another; if there was some residue mod n which was not assumed in this set of integers, then you'd have n numbers distributed to at most (n-1) possible residues
so apply the pigeonhole principle & check what happens to numbers that have the same residue
lunar grove
final saddleBOT
proven solstice
hmmm, what have your tried with the equations
lunar grove
hmmm, what have your tried with the equations
solve it
i got x=4,x=11
the answer is x=4,y=7
lunar grove
i got x=4,x=11
why is 11 rejected?
proven solstice
you can get someone to fact check this if theres a better way, but if you sub x in to the perimeter, it wont equal 20
x=11 then P=11+11+5+y
y will be a negative value
and what do you do to negative values when theyre a length?
proven solstice
👍
lunar grove
For this whats the 2nd equation?
1st equation should be 18x+6y=126 right?
2nd equation should be the area
proven solstice
fheck your first equation again
lunar grove
5x+5x+3y+3y+8x=126
proven solstice
theyre added a bit incorrectly but yea thats right
lunar grove
then how would you find the area
(8x)(3y) the triangle on top idk
lunar grove
i would use pythagoras
howww u dont have the height of the triangle
proven solstice
do you know pythagoras?
lunar grove
yep
lunar grove
then you can use that to find the height
but i only have one number
pythagoras needs two at least?
a^2+b^2=c^2
proven solstice
the triangle is isosceles right?
lunar grove
i only got c^2 rn
proven solstice
so then the height bisects the base
lunar grove
8x divided by 2?
proven solstice
yep
proven solstice
remember, the height is 4x, you want to find the area of the top triangle
lunar grove
remember, the height is 4x, you want to find the area of the top triangle
nono i meant the height i found was actually 4/6
and then i did it till 4x+24xy=1020
proven solstice
?
proven solstice
this yes
x2 for the top triagn
triangle
these are one of the set pythag triangles that have integer numbers.
the ? shouldnt be 4/6x
lunar grove
the ? shouldnt be 4/6x
25x^2/4x^2 isnt it
then x^2 can be taken away since both has it
right?
proven solstice
write the first line of pythgagoras theorem again with the substitutions
it souldnt be divided
lunar grove
write the first line of pythgagoras theorem again with the substitutions
(4x)^2+(?)^2=(5x)^2
lunar grove
(5x)^2/(4x)^2=?
proven solstice
nope you should be minusing there
lunar grove
ye
proven solstice
then whats your equation for the area now?
lunar grove
12x^2+24xy=1024?
lunar grove
how do i solve it then.
proven solstice
so recall your first equation
lunar grove
18x+6y=126
proven solstice
and then do exactly what you did for the first question you showed
lunar grove
and then do exactly what you did for the first question you showed
idk why but i cant get to the answer
its different
proven solstice
can I see your working out?
lunar grove
proven solstice
the area should be 1020
proven solstice
👍
lunar grove
.close
final saddleBOT
final saddleBOT
Available help channel!
lunar grove
final saddleBOT
lunar grove
What does this question mean?
dense crystal
find values of x and y that satisfy those two equations
fast arrow
Solve the system
young bridge
rounding in pure maths? 💀
barren hound
you have the right idea just need to look over it for errors
final saddleBOT
dire thicket
can i get some help on this one pleasee
final saddleBOT
can i get some help on this one pleasee
dire thicket
final saddleBOT
@dire thicket Has your question been resolved?
dire thicket
.close
final saddleBOT
warm python
final saddleBOT
warm python
what do they mean by determine $\theta _n$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
signal vector
Find theta_n, for which an=cos(theta_n)
lethal estuary
you just need to show for what value of theta_n its cosine equals a_n
cold gorge
}
soft zealotBOT
ƒ(Why am. I here)=I don't Know
signal vector
Yeah, so theta_1 should be π/6
cold gorge
||2cos^2(x) - 1 = cos(2x)|| is a good place to start.
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
Which looks like teh half angle formula
signal vector
|| induct on n to prove a_n is the cosine of some angle ||
warm python
wait, what
oh
I was thinking of sin
IMO
hmm
so $\theta_2= \frac{\pi}{12}$
right
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
so then $\theta_3 =\frac{\pi}{24}$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
and so on
I have to prove this somehow
I actually don't know how to formally do induction
is there any other way
I mean I usually say that this pattern seems to hold good for any n
and thus its true
signal vector
Induction is just assuming that a statement is true for some n and proving that it is true for n+1. Here the statement is:
a(n) = cos(theta_n) for some theta_n. You assume this true, and compute a(n+1)
warm python
hmm
signal vector
Which is sort of what you did when you computed theta_2 and theta_3 and proved that they are cos(π/12) and cos(π/24). Just do it with an n instead
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
uh
soft zealotBOT
quickdoom
warm python
$a_{\xi+1}=\sqrt{\frac{\left(1+a_{\xi}\right)}{2}}$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
but we've defined $a_{\xi}$ as a trig function
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
which is
$a_{\xi+1}=\sqrt{\frac{\left(1+\cos\left(\theta_{\xi}\right)\right)}{2}}$
which is
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
$a_{\xi+1}=\sqrt{\cos^2\left(\frac{\theta_{\xi}}{2}\right)}$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
something feels off
signal vector
Yeah, there should be an absolute value
warm python
not that, the fact that $\theta_{\xi}$ is halved
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
the question asks me to prove that is $cos(\theta_{\xi})$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
signal vector
No, it asks you to prove that
a{xi+1}=cos(theta(xi+1)) for some theta(xi+1)
And your theta(xi+1)=theta(xi)/2
warm python
ah
this still seems a bit fishy, should probably read a bit on induction
thanks a lot!
signal vector
👍
warm python
so now to find $\theta_{\xi}$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
any hints
signal vector
Well you know theta(xi+1)=theta(xi)/2
signal vector
Keep applying the recurrence
warm python
I know $\theta_0$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
soft zealotBOT
ƒ(Why am. I here)=I don't Know
signal vector
=theta(xi), on the rhs
soft zealotBOT
ƒ(Why am. I here)=I don't Know
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
Now I first find $\lim_{n\rightarrow\infty}a_n$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
that would be
$\lim_{n\rightarrow\infty}\cos\left(\ \frac{\pi}{3\left(2\right)^n}\right)$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
signal vector
You arent computing the limit they want you to compute
orchid crystal
nothing, you don't need the limit of a_n as n approaches infinity
signal vector
Its an infinity x 0 form, which is indeterminate
orchid crystal
otherwise 4^n too is infinite, that isn't how a limit of products works
soft zealotBOT
ƒ(Why am. I here)=I don't Know
warm python
now I take the log of both sides
to the base 4
$\ln_4\left(L\right)=n+\log_4\left(\left(1-a_n\right)\right)$
soft zealotBOT
ƒ(Why am. I here)=I don't Know
signal vector
||you only need lim x-->0 sin(x)/x = 1 ||
signal vector
$\lim_{n\rightarrow\infty}4^n\left(1-cos(\frac{\pi}{3(2^{n}}\right) = \lim_{n\rightarrow\infty}4^n\left(2sin^{2}(\frac{\pi}{3(2^{n+1})}\right)$
warm python
oh right, I forgot that formula existed
hmm
yeah so the sin part would just be 1, right?
or wait
yeah
warm python
||you only need lim x-->0 sin(x)/x = 1 ||
I don't follow
warm python
where did the 4^n go
signal vector
To the denominator
warm python
ah
ok
got it
thanks a lot!
Do you have any books suggestions? First time I'm ssing such a problem
I pressume TOMATO is the best I can get?
signal vector
Yeah, theres a problem similar to this in that
final saddleBOT
signal vector
Problem 153 page 234, in the back of the book @warm python is pretty similar to this one
warm python
Problem 153 page 234, in the back of the book <@796939110815629322> is pretty s...
thanks!
final saddleBOT
Available help channel!
manic helm
i keep getting omega^2 rather than omega^2/n nad idk what im doing wrong
manic helm
i said mean of epsilon = 1/n sum of epsilon_i from 1 to n
then said Cov(epsilon_i, mean of epsilon_i) = Cov(epsilon_i, 1/n (sum of epsilon_i)) = 1/n [Cov(epsilon_i, sum of epsilon_i)]
and as Cov(epsilon_i, sum of epsilon_i) = Cov(epsilon_i, epsilon_1) + Cov(epsilon_i, epsilon_2) ... + Cov(epsilon_i, epsilon_n) = Var(epsilon_i) + Var(epsilon_i) ... + Var(epsilon_i) = nVar(epsilon_i) since epsilon_i are iid for all i in {1, 2 ... n}
then Cov(epsilon_i, mean of epsilon) = 1/n (nVar(epsilon_i) = Var(epsilon_i) = omega^2 ?
floral nova
I'm not going to read most of that in detail unless you tex it, but at a glance are you assuming that cov(eps_1, eps_i) = var(eps_i)?
manic helm
I'm not going to read most of that in detail unless you tex it, but at a glance ...
ye.......................
i thought cz they're iid it's the same thing isnt it...
omg
wait im stupid
it's = 0
floral nova
I'm just going to assume you figured it out from here.
manic helm
ye i think i got it
manic helm
I'm not going to read most of that in detail unless you tex it, but at a glance ...
so iid means the covariance of two variables is 0
unless it's the same variable
then it's var(epsilon_i)
floral nova
Yes
final saddleBOT
final saddleBOT
Available help channel!
fiery ferry
in triangle GHI, the side gh = 3 cm, the side HI = 18 cm, and the side GI = 20.5 cm. find the size of angel HGI
final saddleBOT
in triangle GHI, the side gh = 3 cm, the side HI = 18 cm, and the side GI = 20.5...
final saddleBOT
@fiery ferry Has your question been resolved?
final saddleBOT
@fiery ferry Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
bold elk
Yo
bold elk
I cant do this with the regular way
How should i do this
I think it has a trick did anyone see it?
<@&286206848099549185>
final saddleBOT
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.
bold elk
...
short cloud
Use the product rule ....
lethal estuary
you can multiply it out or use the product rule several times
low violet
Use the product rule ....
He asking for some other approach
That's what he is saying. Without doing these many multiplication...
bold elk
you can multiply it out or use the product rule several times
I dont think cuz our teachers give us this exercise as bonus and when he does this he doesnt want us to do it with the regular way so i think there is a trick
lethal estuary
what is the "regular" way
short cloud
I dont think cuz our teachers give us this exercise as bonus and when he does th...
I'm having a deja vu
bold elk
what is the "regular" way
Multiplation
low violet
Multiplly differentiatee and put value
short cloud
Ig I saw this trick somewhere
bold elk
Ig I saw this trick somewhere
Can u help
short cloud
Can u help
Lemme try
low violet
Can u help
Have you done the long way? What answer r u getting?
bold elk
Have you done the long way? What answer r u getting?
He give us some exampls wait
We have 24 / 1 / 3 / 4 / 5
Its one of those
wintry egret
just off first glance (so may not work), would there be a trick if we sub something like u = x-3 then we can kill some multiplication by diff of squares?
bold elk
just off first glance (so may not work), would there be a trick if we sub someth...
Can u please write this in a sort of paper im kinda bad at english
I didn't understand some words
solar glade
Use subtitution
bold elk
If u can of course
bold elk
Use subtitution
And what is this ?
solar glade
just off first glance (so may not work), would there be a trick if we sub someth...
Yes this one should work
short cloud
@bold elk yup substitution would work
bold elk
<@1135153163423457392> yup substitution would work
Oh sry to ask can someone just explain to me suatitution cuz i dont study with english
solar glade
Use u=x-3
short cloud
Oh sry to ask can someone just explain to me suatitution cuz i dont study with e...
U need to assume type
U = x+3
solar glade
And rewrite the function in terms of u
low violet
5-36+93-94+36= 4 answy
solar glade
U need to assume type
U = x+3
x-3
bold elk
And rewrite the function in terms of u
Alr wait guys ill try this
solar glade
You will get f(u) = u (u-2)(u+2)(u-1)(u+1)
And here u can realize u have double difference of squares
The rest is trivial
low violet
Then
low violet
We can apply a²-b² identity but how does this help?
solar glade
It will help to simplify faster
short cloud
We can apply a²-b² identity but how does this help?
We'll get u⁵-5u³+4u
solar glade
You can expand faster 2 brackets than 4
short cloud
And then just differentiate
low violet
u(u-4)(u-1)
Now put u=x-3
(X-3)(x-7)(x-4)
lethal estuary
We'll get u⁵-5u³+4u
4u, not 4u^2
low violet
u(u-4)(u-1)
Now put u=x-3
(X-3)(x-7)(x-4)
Well it just helped reduce 2 multiplication
solar glade
None?
short cloud
Well it just helped reduce 2 multiplication
Atleast it's better than 5
@bold elk wat was the answer
solar glade
Tell me when u do the product
short cloud
No it's wrong last part
bold elk
No it's wrong last part
Only the last one
short cloud
(u+1)(u-1) = (u²-1²)
solar glade
No
short cloud
Exactly
solar glade
And same for -2
short cloud
And same for -2
I remember myself using product rule for this 😂
solar glade
It is good for practice product rule anyways
bold elk
short cloud
Yess
bold elk
So its this ?
solar glade
No
short cloud
So its this ?
Now differentiate
Either multiply and diff or use product rule
bold elk
Why?
bold elk
Oh u did not finished
I know that i didnt finish but i mean its good for now?
solar glade
Yes its good
short cloud
Why?
U only made the eqns simpler
But the question is asking u to differentiate
One more to go
solar glade
Just expand now
bold elk
Now i should go back to x or ?
solar glade
Expand before
bold elk
Alr
short cloud
Just expand now
I'm wondering if we can differentiate in terms of u and then later on put the value of u and later 1
bold elk
Guys i only study U.V form how can i use it here ??
short cloud
Guys i only study U.V form how can i use it here ??
Wait lemme type
bold elk
Should i start for the first two or what
bold elk
Right
What do u mean by right Cuz now we only study U.V for but in this multiplacation we have 3 function
What should i do
short cloud
What do u mean by right Cuz now we only study U.V for but in this multiplacation...
$\frac{d}{dx}[f_1(x)f_2(x)f_3(x)] = \frac{d(f(x_1)}{dx}[f_2(x) f_3(x)]+\frac{d(f(x_2)}{dx}[f_1(x) f_3(x)]+ \frac{d(f(x_3)}{dx}[f_1(x) f_2(x)]$
@bold elk ???
bold elk
Wait wait
short cloud
$\frac{d}{dx}[f(x)g(x)h(x)] = f'(x)g(x)h(x) + f(x)g'(x)h(x) + f(x)g(x)h'(x)$
bold elk
My brain isnt braining
soft zealotBOT
TᖇᗩᑎᔕᑭᗩᖇEᑎT ᔕᕼᗩᗪOᗯ
bold elk
Yeah this is easier
bold elk
Yeah yeah
short cloud
Okay GL
short cloud
,rotate
soft zealotBOT
short cloud
So should i get back to x or keep developing
After you have differentiated put change the u to x - 3
And then find f'(1)
bold elk
What differentiated mean ?
bold elk
So i only have to put change u to x-3 right?
short cloud
So i only have to put change u to x-3 right?
Yeah
And after tat find f'(1)
U should get 24 as answer
short cloud
Ok do one thing don't put x+3
Just keep it in u
since u need to find f'(1)
When x = 1
u = 1-3 = -2
bold elk
Right let me retry
short cloud
Right let me retry
Just keep it there and substitute u = -2
U will get 24
I'm gonna sleep now
short cloud
Good job 💫✨
bold elk
I really appreciate it man
final saddleBOT
@bold elk Has your question been resolved?
cedar glacier
Hello! So, i have to calculate where parabolic flocks meet the x-axix.. the problem is, ladies and gentlemen, that there are little to no numbers to calculate with, which confuses me a bit, as we even have to draw one of the equasions later on, caan anyone please help me? I would get the root of x here normally, still 0 but i can do it.. but theres this t, its quite annoying, and also blocking my path of completing homework
final saddleBOT
Hello! So, i have to calculate where parabolic flocks meet the x-axix.. the prob...
zenith pollen
Hello! So, i have to calculate where parabolic flocks meet the x-axix.. the prob...
are you asking for 0=-x^2+2x-7?
cedar glacier
the equasion i was given was pt(x)=-x²+2x-t
zenith pollen
okay, for these things I just pretend t is some weird number like 13 and work from there
like treat it as if it was a number
cedar glacier
mm, alright! Thank you ^^ I can handle the rest then, only the t posed a problem
.close
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
tranquil pine
Im confused rn
I think i did it right but my answer is wrong
For f(2)
It says its supposed to be 1 but when i plug it in it gives -3
feral ginkgo
It says its supposed to be 1 but when i plug it in it gives -3
it's $2x^2$ so $2(2^2)$, but you only did $2^2$
soft zealotBOT
lgkoo
feral ginkgo
when calculating f(2)
feral ginkgo
lol don't mind
normal linden
so.... the antiderivative of 2/sqrt x wouldnt be 2lnsqrtx?
final saddleBOT
so.... the antiderivative of 2/sqrt x wouldnt be 2lnsqrtx?
solid cobalt
Nope
normal linden
does the rule just not apply if the x is sqrt
solid cobalt
Of course not
normal linden
okay thanks
solid cobalt
Do the derivative, you'll see it does not work
final saddleBOT
final saddleBOT
Available help channel!
stark apex
final saddleBOT
stark apex
wat do i dO
tranquil pine
Apply midpt formula
Wait, U can use polygon formula for vector addition
Do this for two small quad and the big quad
Then u will get equations
final saddleBOT
final saddleBOT
Available help channel!
stark apex
final saddleBOT
alpine yacht
it means $\frac{AB}{DC}=\frac{AE}{EC} = \frac{BE}{ED} = \frac{2}{3}.$
soft zealotBOT
lpieleanu
alpine yacht
note that triangles $AEB$ and $CED$ are similar
soft zealotBOT
lpieleanu
alpine yacht
because their angles have equal measure
therefore, ratios between corresponding sides are equal
stark apex
ohhok
howd u know it was 2/3 tho?
I only know that ab is 2/3 of dc but how do u know the legnths of the diagonals inside
@alpine yacht
sorry for ping
alpine yacht
I only know that ab is 2/3 of dc but how do u know the legnths of the diagonals ...
we know ae/ec and be/ed because of similar triangles
aeb and ced are similar and the pairs of corresponding sides are (ab,dc), (ae,ec), (be,ed)
stark apex
aeb and ced are similar and the pairs of corresponding sides are (ab,dc), (ae,ec...
so whats the length of ac then ?
stark apex
ohh
stark apex
only ratios
so what ratio is ae of ac?
final saddleBOT
Available help channel!
earnest pulsar
is there a good/free lecture on algebraic number theory somewhere? i only found books but im super slow with them
final saddleBOT
is there a good/free lecture on algebraic number theory somewhere? i only found ...
@earnest pulsar Has your question been resolved?
final saddleBOT
@earnest pulsar Has your question been resolved?
final saddleBOT
@earnest pulsar Has your question been resolved?
final saddleBOT
@earnest pulsar Has your question been resolved?
rocky lark
final saddleBOT
rocky lark
uh question is unclear
I'm confused about the question too this is all it gave me
rocky lark
2x - 20 = x +10
How may I do that?
rocky lark
Ah
tranquil pine
How may I do that?
they want you to find the answer of x
rocky lark
they want you to find the answer of x
Can you perhaps help me create a solution for that?
I get what is being asked now
tranquil pine
I get what is being asked now
cool now you willhave to proceed to solve the equation at ez
i think this video will help if you dont understand how to do it
rocky lark
i think this video will help if you dont understand how to do it
Thanks, I certainly don't understand how to solve it haha
tranquil pine
Thanks, I certainly don't understand how to solve it haha
oh um basically its a concept called transposition
used to solve equations
rocky lark
oh um basically its a concept called transposition
Solve: 2x - 20 = x + 10
Solution:
Subtracting X from both sides.
2x - x - 20 = x - x + 10
x - 20 = 10
Add 20 to both sides:
x - 20 + 20 = 10 + 20
Simplify:
x = 30
Answer: x = 30
rocky lark
I'm confused about the question too this is all it gave me
Is this the answer to here
Or it doesn't make sense
Sorry I'm not very good at math 😔
Anyone?
plucky orbit
its correct
rocky lark
its correct
Just want to confirm is what I am doing here correct too?
What does it mean write number only
Nvm
Just read the instructions
So for 1 the answer is 4 right?
tranquil pine
So for 1 the answer is 4 right?
yes....
rocky lark
.close
final saddleBOT
final saddleBOT
Available help channel!
abstract mango
final saddleBOT
abstract mango
can you see why is it showing me complex solutions? (using Sage Math)
abstract mango
i'm trying to find those points x seems to intersect in this graph
roughly -0.89ish, 0.45ish
this is what wolfram gave, when I clicked on approximate forms , it gave me x≈-0.85464, x≈0.40303 x≈1.4516
i don't really get how they got them from those complex numbers
final saddleBOT
@abstract mango Has your question been resolved?
final saddleBOT
@abstract mango Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
undone whale
hi
undone whale
whats the difference between sample mean and true mean
in terms of calculation
<@&286206848099549185>
tough root
whats the difference between sample mean and true mean
Sampling and Population Means?????
young bridge
whats the difference between sample mean and true mean
sample mean is the mean of the sample. true mean is the mean of the population
sample mean is calculated by taking the average of values in the sample only
young bridge
this why i hate stats
undone whale
Lol
young bridge
you know the variance equation for a sample?
final saddleBOT
@undone whale Has your question been resolved?
final saddleBOT
@undone whale Has your question been resolved?
olive crane
stone wagon
.close
final saddleBOT
final saddleBOT
Available help channel!
jagged seal
I have the following recurrence relation $T(n) = T(\frac{n}{4}) + 1$ and I need to remove the recursion
$let n = 4^k, k\in N$
$T(4^k) = T(4^{k-1}) + 1$
$...= T(4^{k-2}) + 1 + 1 = k\cdot 1 + T(1) = \log_4{n} + 1 = O(log(n))$
but my lecturer said it should be nlog(n) and I'm not sure how
final saddleBOT
I have the following recurrence relation $T(n) = T(\frac{n}{4}) + 1$ and I need ...
soft zealotBOT
lewis_f04
final saddleBOT
@jagged seal Has your question been resolved?
final saddleBOT
@jagged seal Has your question been resolved?
feral tendon
How can i isolate X solving this matrix equation
final saddleBOT
How can i isolate X solving this matrix equation
feral tendon
I dont have that info
tough tiger
Multiply by MX
You could try that at first
feral tendon
ok i see
tough tiger
You would get XN and not X
You don’t have any info on M and N ?
Other than M is invertible
final saddleBOT
@feral tendon Has your question been resolved?
feral tendon
You don’t have any info on M and N ?
nope
they just ask to solve that and isolate X
regal hamlet
it's a kind of pigeonhole situation, right? you have n numbers, you know none of...
could you elaborate please?
final saddleBOT
could you elaborate please?
regal hamlet
first time I heard about the pingeonhole principle
shadow tinsel
first time I heard about the pingeonhole principle
If a items are put into b containers, and a > b, then at least one container must contain more than 1 item
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
@regal hamlet Has your question been resolved?
regal hamlet
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
Please help me with my calculus problems
final saddleBOT
Please help me with my calculus problems
warm python
post it and maybe someone will help you
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
<@456226577798135808> Has your question been resolved?
Yeah
worthy spade
Hello there! I wanted help with my project works
craggy plume
X1 + X2 = the number next to x, in I), 14
X1 * X2 = the number term at the end, in I), 40
Think of two numbers that satisfy them and substitute into zemitrix's
worthy spade
lmfao i dont get it
tawny halo
quadratic
worthy spade
idk what is quadratic by any means
worthy spade
oh like a= x, b = 2 and c = 1?
tawny halo
Ye
worthy spade
idk how do i solve tho
worthy spade
ohjk
i asked chat gpt but it gave me irrelevant answer
so i hope i understand this
tawny halo
no need to ask chat got
worthy spade
i dont get it lmao
tawny halo
maybe people should learn quadratic before vieta
worthy spade
i guess so
tawny halo
why can't we solve then factorize
magic rampart
factorizing lets you solve for x though
uncut marsh
because usually we factorize in order to find roots
magic rampart
yeah
uncut marsh
not the other way around
https://youtu.be/U6FndtdgpcA?si=55GaBRrn6qQpmQtQ i suggest following through a step by step on how to factorize, havent watched the video but the guy's consistently pretty good
tawny halo
factorizing lets you solve for x though
Vieta is literally finding roots
magic rampart
vieta is using -b/a and c/a im not using that at all
im literally saying just grouping in pairs
tawny halo
vieta is using -b/a and c/a im not using that at all
a=1
magic rampart
sorry wait im getting confused the steps are different no?
final saddleBOT
@worthy spade Has your question been resolved?
worthy spade
not rlly
worthy spade
ok lmfao
magic rampart
so the question directly asks you to factorise
worthy spade
uhuh?
worthy spade
idk lmao
magic rampart
what do you mean you don't know
worthy spade
what is quadratic or those words
magic rampart
ok so these are quadratics
worthy spade
curious..
magic rampart
they are in the from ax^2 + bx + c where a, b, and c are numbers
such as x^2 + 5x + 6
worthy spade
like respectively?
magic rampart
yes
worthy spade
mhmk
magic rampart
the a is always the coefficient of the x^2
so if you had 2x^2 + 5x + 6
a is always the 2
worthy spade
ohk
worthy spade
yeah.
magic rampart
no im asking
worthy spade
a = x, b = 14 and c = 40?
worthy spade
lmfao i forgor
worthy spade
yeps
magic rampart
yep so a = 1, b = 14, c = 40
now to factorise
find two numbers that add up to b and multiply to give c
so in this case
your two numbers have to add to give 14
multiply to give 40
worthy spade
find two numbers that add up to b and multiply to give c
like 8+8?
magic rampart
try again
worthy spade
lmao how should i do it then
tawny halo
I have no idea what the teacher taught us
.
tawny halo
how many ways of factorisation are there?
One ye
soft zealotBOT
faiyrose
worthy spade
constant means the numbers?
i meant is the number a constant?
oh nvm
please continue
x?
x?
x * x is x^2 right?
idk
tawny halo
a/a
soft zealotBOT
faiyrose
worthy spade
lmao im dumb
x^2?
40?
lmao im a dum dum
40
40 duh
lmfao
-40?
20
thats simple multiplications
the same thing but its negative
10 lmao
lmao like i said earlier
i thank you for helping me do some basic maths but i rlly am on a time crunch
so i cant be bothered
is 10 * 4 ok?
10 * 4 = 40
10+4 = 14
oh yea
yep
soft zealotBOT
faiyrose
soft zealotBOT
faiyrose
worthy spade
yeah that what i meant
the part after that is rlly confusing
like uh
$x^2(4x + 10x) + 40(4x + 10x)$
soft zealotBOT
Healthy Sarcasm
soft zealotBOT
Healthy Sarcasm
worthy spade
it just go staight to it?
soft zealotBOT
faiyrose
worthy spade
lmao i thought that wont be necessary
thas it?
oh
wdym by factor like taking commons?
tha would be
$x(x + 4)+10(x + 4)$
soft zealotBOT
Healthy Sarcasm
soft zealotBOT
Healthy Sarcasm
worthy spade
wow
never thought it would be that easy
lmao im just dumb
anyways
thanks alot
.close
final saddleBOT
final saddleBOT
Available help channel!
fluid swallow
Hey, can someone explain me why B-XIn = P^(-1)(A-XIn)P please?
final saddleBOT
Hey, can someone explain me why B-XIn = P^(-1)(A-XIn)P please?
fluid swallow
Where A and B are similar and P is an invertible matrix
desert mantle
just multiply out P^-1 (A-XI)P
fluid swallow
If I do that I have P^(-1)AP - P^(-1)XInP
desert mantle
yes
fluid swallow
so I got B-P^(-1)XInP
desert mantle
X is a variable. you can treat it the same as a number
final saddleBOT
final saddleBOT
Available help channel!
paper crane
final saddleBOT
lofty spade
final saddleBOT
@paper crane Has your question been resolved?
stone wagon
notice that this is suspiciously close to half of option C... 👀
stone wagon
did you solve for t here?
paper crane
