@chilly tinsel Has your question been resolved?
#help-17
silk storm
Real quick: For a function to be a probability density function all of its y values must be larger than 0, correct?
vocal sleetBOT
Real quick: For a function to be a probability density function all of its y val...
silk storm
So when I am asked to make this a probability density function is it even possible?
Is f(2) not -6a?
lone linden
Real quick: For a function to be a probability density function all of its y val...
Yes, the output of a probability density function is always non-negative.
lone linden
Is f(2) not -6a?
lone linden
does the condition only apply to the given interval?
We're restricting the domain of the probability density function f to 0__<x<__1 if that's what you're asking
silk storm
We're restricting the domain of the probability density function f to 0__<__x__<...
Right, thank you!
🫂
.close
vocal sleetBOT
lone linden
Right, thank you!
vocal sleetBOT
Available help channel!
lavish vortex
X^2 + 2x + what makes a perfect circle?
vocal sleetBOT
X^2 + 2x + what makes a perfect circle?
flat whale
,tex .cts
twin meteorBOT
riemann
lavish vortex
,tex \.cts
So then is the answer 1?
flat whale
if by perfect circle you mean perfect square then yes
lavish vortex
Thank you
flat whale
,w expand (x+1)^2
twin meteorBOT
lavish vortex
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
hushed atlas
,rotate
twin meteorBOT
hushed atlas
Correct to say Left = right?
sharp delta
$a\sqrt{\frac{y}{p_1}} = a\frac{\sqrt{y}}{\sqrt{p_1}}$
twin meteorBOT
.RODATA
sharp delta
this is correct
pallid zenith
assuming that a isnt involved in the root
hushed atlas
Ok thanksss
sharp delta
yeah i wrote it out in latex cuz i couldnt tell if a was the root or a scalar
vocal sleetBOT
oak magnet
I missed free 200$ since 5min with all this
vocal sleetBOT
Available help channel!
hazy olive
can anyone help? i cannot make it through, i'm in first year of uni and i'm really frustered in this shit from highschool
vocal sleetBOT
can anyone help? i cannot make it through, i'm in first year of uni and i'm real...
hazy olive
using thalams theorem's i found AC but i can't find any realtion between the numbers given and the triangle on the right, so i cannot find the hippothenuse meaning d or diameter
hazy olive
yes, there are perpendicular
hazy olive
nop i found AC, but else from this, i used thalam's theorem finding AC and now on i don't know any more releations else from the given in the exercise
hazy olive
thalam's theorem's states that if a rectangle triangle is circumscribed into a circle, the diameter of the circle is the hippothenuse of the opposite triangle from the rectangle triangle
so... to find AC you can use: AD, AB and AE
in theory
tranquil trellis
thalam's theorem's states that if a rectangle triangle is circumscribed into a c...
ah
So the main observation is that ABD ~ ACE ~ ECF ~ AEF
tranquil trellis
thalam's theorem's states that if a rectangle triangle is circumscribed into a c...
and ~ AEF comes from this theorem
hazy olive
yes
so i'm sure there are assumptions or variables that should be given or something, bc in this form this exercise is incomplete and can't be sovler
solved'
vocal sleetBOT
@hazy olive Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
pearl wadi
if they gave t it would be a point not a curve wouldnt it
ripe basin
pick different points of t to find your corresponding x and y points then plot those
novel ridge
Yep
pearl wadi
eliminate the parameter,
x-1 = cos (t)
y/2 = sin(t)
square and add
you get a standard vertical ellipse
novel ridge
x(0) = 1 +cos(0) = 2
pearl wadi
no dont put values of t that would take forever
they have given sin and cos because they want us to square and add
yes then add the 2 equations
cos^2t + sin^t = 1
so (x-1)^2 + (y/2)^2 = 1 is our equation
@vague vessel i hope yk about ellipses?
this one is a vertical ellipse since denominator of y greater than denominator of x with center as 1,0
will look like this
why
ok i will sleep now just dm me and ill answer tomorrow
it is y^2/4 so a =2. there is nothing added or subtracted to the y term so the y coordinate of the center will be 0
amber wasp
vocal sleetBOT
amber wasp
Why is the 3 the horizontal asymptote
silk osprey
lim x -> inf
amber wasp
Im not in calculus, only pre calc, can you explain it a bit further so i can explain it to my friend
silk osprey
this is how horizontal asymptotes are defined
you consider the "end behavior" of the function
as x -> inf the fraction goes to zero leaving you with just 3
same thing applies for x -> - inf
amber wasp
What about the 1 though?
night zodiac
What about the 1 though?
Add 3 to 1/(x+2)^2 first, then compare the degrees of both polynomials.
In terms of algebra, you identify horizontal asymptotes by comparing the degrees. No need for calculus here if you haven't reached that level.
amber wasp
My friend is in calculus and im tryna help them
So im trying to just understand the reasoning as to why 3 is the asymptote
Because from what I know
If the degree of the denominator is higher then the degree of the numerator
Then the horizontal asymptote is 0
1/x = , 2/x = 0 3/x = 0
Etc etc
amber wasp
You take the the value of the two numbers with the highest power
Like 8x / 8x you just do 8 over 8
night zodiac
That right, but that's not just a value. To be precise, it's a ratio.
night zodiac
Then you should have no problem identifying the asymptote after you simplify your original problem
night zodiac
Not true. You need to add three to that rational function on the right, but 3 doesn't have the same denominator, so what do you need to do first?
night zodiac
No, no need to solve for anything right now. You want to simplify the above expression. It's like trying to add 1 and 1/2—what do you have to do to 1 so that it is in the correct form to add to 1/2?
amber wasp
Common denominator?
amber wasp
U have to multiply the 3 by x-2^2?
night zodiac
Close, but not quite. Remember that you have to have the same denominator for both expressions. 1/(x+2)^2 has the denominator of (x+2)^2, not x-2^2.
amber wasp
Oh ya sorry
Thats what i meant
I mixed up the signs
Okay so my function looks like this
12 + 1 over (x+2)^2
night zodiac
Not sure how you got that. I'd recommend writing it all out on paper.
amber wasp
3 multiplied by (x+2)^2 is 12
Bc for common denominator dont u multiply numerator as well
night zodiac
Yes, you're on the right track, but you don't get 12. It's 3(x+2)(x+2), so you FOIL.
amber wasp
Foiling gives me 3x^2 + 12x + 12
amber wasp
Oh rly
Whats the constant?
I factored what i got further and i got 3(x+2)^2
Is that incorrect
night zodiac
The last term in a polynomial without a variable.
amber wasp
No ik what the constant is, what is it in this equation
I csnt figure it iut
Not sure where i went wrong
night zodiac
It is 3(x+2)^2, but I'm guessing you messed up in your algebra. I recommended writing it on paper. What did you get when you expanded (x+2)^2?
amber wasp
X^2 + 4x + 4
night zodiac
Yep, then 3(x^2+4x+4) + 1?
night zodiac
Yep, nice!
amber wasp
Okay, now whats the next strp
night zodiac
What does your entire function look like now?
You can expand the binomial in the denominator for ease if you'd like.
night zodiac
No, you compared the degrees, so you're on the right track, but what does the rule state?
amber wasp
The asymptote rule?
night zodiac
Yep
amber wasp
If the degrees are the same then you have to find the ratio of the numbers with the highest degree
night zodiac
If the degrees are the same then you have to find the ratio of the numbers with ...
Yes, the numbers in front of the variable with the highest degree. Which are what?
amber wasp
3 and 1
night zodiac
And the rule states that you take the ratio of the numerator's leading coefficient over the denominator. So what does that mean?
amber wasp
3 over 1 = 3
night zodiac
Yes..
amber wasp
Thank u so much
night zodiac
Nice!
night zodiac
Sure thing. Take your time.
night zodiac
Yep, that's right.
However, I'm a bit wary of your formatting if this is a grading assignment.
night zodiac
Then you're fine. Looks good to me!
amber wasp
Have a good nigjt, might be back if my friend needs more help lol
night zodiac
Sure, and come back if you need some help too! We'd be happy to help.
vocal sleetBOT
vocal sleetBOT
Available help channel!
shell moon
Good evening, I have a question on the application of the candidates test in a peices wise function, I double derived both parts of the equations and got -12t+24 and 9/4(t-1)-1/2 respectively which means my points to test would be -1 0 2 and 15, -1 isn’t in the equation but my question is how would I test out since 0 2 are apart of a different part from 15
vocal sleetBOT
Good evening, I have a question on the application of the candidates test in a p...
shell moon
Also from 6 to 8 how would I do anything with it because it’s linear it’s double derivative would just be zero
wraith python
Why would you test t = -1? It is outside of the interval 0 <= t <= 15.
shell moon
I wouldn’t I would just ignore it sorry for not specifying
wraith python
When checking intervals like this, you always need to verify the edge cases, meaning the endpoints of each interval.
shell moon
So 6 and 8 would also need to be in that set I test
wraith python
Yes.
shell moon
My big problem is what equation would I use to test these with
I’m sorry if it’s a little dumb but I haven’t reviewed much of candidates in a while
wraith python
Use the intervals given. They are not always inclusive of the endpoint.
0 <= t < 6. Note that 6 is not included on that interval.
shell moon
Oh ok, so for 0 and 2 I would use -6t^2+24t and than change it for when it crosses another interval
wraith python
Yes.
shell moon
Okay thank you so much and for this portion of it I would just need to do the 1/b-a integral of the anti derivatives for each portion added up correct
wraith python
Yes.
vocal sleetBOT
vocal sleetBOT
Available help channel!
balmy furnace
I am very much struggling with the application of these concepts. I believe I understand how negation, converse, inverse, and contrapositive work in theory but when it comes to the example problems I am struggling. Can someone please walk me through how we tackle a problem like this?
vocal sleetBOT
I am very much struggling with the application of these concepts. I believe I un...
balmy furnace
So for any x, anything you cube should remain the same sign (positive or negative) correct? So S is true.
The converse of S would be q->p so I would think it's "For any x, if x^3 > 0, then x >0" which is B and so if I have a positive number and cube it, it stays positive. If I have a negative number and cube it, it becomes positive when squared, and returns to negative when cubed, so that should be true.
The contrapositive is not q-> not p, so I think it's G, but I think I'm wrong here and on the negation as those I'm not sure of.
vocal sleetBOT
@balmy furnace Has your question been resolved?
elder summit
huh
elder summit
dont getr how this is just cos pi x^-1
twin meteorBOT
parabolicinsanity
gentle nimbus
but it gives me a minus
🤷just sub in anyway it doesn't matter
burnt grail
prove by induction that product n(n+1)(n+2)...(n+r-1) of any consecutive r numbers is divisible by r!
I'm lowkey lost, i don't understand how to get to the proof. I tried p(k+1, r) in the inductive step and got to (k+1)(k+2)(k+3)...(k+r).
it can be shown as
p(k+1,r) = (p(k,r)*(k+r))/k
now but how do I prove the divisibility by r!
vocal sleetBOT
prove by induction that product n(n+1)(n+2)...(n+r-1) of any consecutive r numbe...
burnt grail
prove by induction that product n(n+1)(n+2)...(n+r-1) of any consecutive r numbe...
Should it be just simply divisible by r! because p(k,r) is divisible by r!
burnt grail
Should it be just simply divisible by r! because p(k,r) is divisible by r!
By induction hypothesis
I tried looking for proofs that they seemed to be rather complex
haughty bone
Do you understand how induction works?
I know its tough, took me a while to understand
Ill just outline it here again just to make sure
We want to prove that if something works for n, then it works for n+1, note that we dont have to actually prove that it works for n, just IF it works for n then it works for n+1, the inductive hypothesis is essentially the assumption that it works for n
burnt grail
We want to prove that if something works for n, then it works for n+1, note that...
yeah
haughty bone
in your case we want to prove that if P(n,r) is divisible by r! then P(n,r+1) is divisible by (r+1)!
The inductive hypothesis is kinda like this phantom assumption that the former is true, i like to just word it like i just did, if this is true, then is that true?
Then once you are able to prove that you can say.. well it works for n=1, therefore it works for n=2 then it works for n=3..... etc
so in your case we have to prove the following: if P(n,r) is divisible by r! then P(n,r+1) is divisible by (r+1)!
burnt grail
I see
haughty bone
You can do this like any other proof but ill just do it now quickly
burnt grail
(p(k,r))*(k+r) should be divisible by (r+1)!
haughty bone
(p(k,r))*(k+r) should be divisible by (r+1)!
Right so since its true, given that p(k,r) is divisible by r! then you can just apply your base case
haughty bone
(p(k,r))*(k+r) should be divisible by (r+1)!
is this the step you need help with
burnt grail
is this the step you need help with
yeah
burnt grail
prove by induction that product n(n+1)(n+2)...(n+r-1) of any consecutive r numbe...
It looks like I did the inductive step wrong at the first place?
instead of
p(k,r+1) = k(k+1)(k+2)...(k+r-1)(k+r) where divisibility has to be proven by (r+1)!
I took
P(k+1,r) = (k+1)(k+2)...(k+r-1)(k+r) and proved the divisibility by r!
But the both seem to be giving me the same result on the rhs
haughty bone
Yes you should be proving the first statement
burnt grail
P(k,r+1) gives me (p(k,r))*(k+r)
burnt grail
P(k,r+1) gives me (p(k,r))*(k+r)
which is divisible by r!
What should be the next step after this to prove divisibility by (r+1)!
haughty bone
if its divisible by r! you just have to prove that it is also divisible by r+1
not factorial^
P(k,r+1) is divisible by (r+1)! if it divisible by r! and (r+1)
so you essentially just want to prove that k*(k+1)*...*(k+r) is divisible by r+1
burnt grail
so you essentially just want to prove that k\*(k+1)\*...*(k+r) is divisible by r...
how to do this now
I can't seem to factor out r+1 from anything
vocal sleetBOT
@burnt grail Has your question been resolved?
topaz eagle
how to do this now
hint: if you're blocked, think about which condition that you haven't applied
vocal sleetBOT
@burnt grail Has your question been resolved?
pearl wadi
vocal sleetBOT
pearl wadi
then?
terse cipher
u need to go threw binomial thingy
vocal sleetBOT
@pearl wadi Has your question been resolved?
rough hound
6?
pearl wadi
u need to go threw binomial thingy
oh so multiply and divide by 2018!?
calm pecan
pearl wadi
ive gotten 1/2018! x summation (2018 C r)(r-1)
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
calm pecan
there is an identity.
pearl wadi
there is an identity.
which
calm pecan
you should know sum of binomial combinations
calm pecan
,wolf expression for sum of binomial coefficients
twin meteorBOT
Requested by percykel
calm pecan
oh goddamnit
pearl wadi
are you talking about the 2^n?
calm pecan
aight
pearl wadi
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
hushed atlas
vocal sleetBOT
pearl wadi
what is the question
vocal sleetBOT
@hushed atlas Has your question been resolved?
supple glen
Help pls
viral reef
vocal sleetBOT
Help pls
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).
@hushed atlas Has your question been resolved?
paper depot
. @supple glen напиши сообщение сюда
supple glen
vocal sleetBOT
supple glen
Помогите пожалуйста с 129 до 131 задания
paper depot
тут так устроена система, что когда ты посылаешь сообщение в пустой канал, то на него ставится твое имя
supple glen
Ок спасибо большое
paper depot
и это называется „открыть канал“
supple glen
А вы русский?
paper depot
русская
supple glen
А ок
paper depot
так
paper depot
я правильно нопимаю, что у тебя проблема со считыванием чисел с диаграмм?
supple glen
Да
paper depot
по высоте она докуда доходит?
supple glen
2
supple glen
Окей дальше
paper depot
то есть нам дано, что a_2 = 8; a_4 = 12
выражение для n-того члена найти справишься?
supple glen
Я тему прогулял в школе
.
supple glen
Всякое бывает
paper depot
что такое арифметическая прогрессия хотя бы знаешь?
supple glen
Да
paper depot
хорошо. скажи мне тогда определение
supple glen
Х6?
paper depot
???
paper depot
@akame.ga.kill. ты там не перенапрягайся преждевременно, а?)
lmao ffs bro left
well, that's that i guess.
.close
rare cedar
how to do this question? (edexcel international a level math statistics 1)
vocal sleetBOT
@rare cedar Has your question been resolved?
vocal sleetBOT
@rare cedar Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
atomic jasper
<@&268886789983436800>
modern flare
vocal sleetBOT
modern flare
It's in a different lanaguage but I can translate
It's highschool analytic Geometry and I need help please
vocal sleetBOT
@modern flare Has your question been resolved?
onyx spade
vocal sleetBOT
potent beacon
It doesnt work then
And it means it is like a vertical line
So you just have to think about angles
vocal sleetBOT
@onyx spade Has your question been resolved?
distant perch
\textbf{9.} The roots of the equation ( x^2 - n x + m = 0 ) are the nonzero real numbers ( a ) and ( b ).
The roots of the equation ( x^2 - 2 n x + 2 m = 0 ) are ( a^2 ) and ( b^2 ).
The value of ( m + n ) is:
[
\begin{array}{ll}
\text{(A)} & 1 - \sqrt{5} \
\text{(B)} & 3 - \sqrt{5} \
\text{(C)} & 1 + \sqrt{5} \
\text{(D)} & 2 + \sqrt{5} \
\text{(E)} & 3 + \sqrt{5} \
\end{array}
]
vocal sleetBOT
\textbf{9.} The roots of the equation \( x^2 - n x + m = 0 \) are the nonzero re...
twin meteorBOT
samuel
distant perch
I haven't done anything yet, I don't understand the statement affirmation
pearl wadi
sum of roots product of roots
distant perch
sum of roots product of roots
Oh, I just saw that I will need to study some stuff that I haven't studied yet in order to solve this question, thank you
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
stable relic
im forgetting something really basic here i'm sure, how do i find the intersection of these algebraically
vocal sleetBOT
im forgetting something really basic here i'm sure, how do i find the intersecti...
stable relic
im sure its a quadratic method of some kind but the square root is throwing me off
nvm i got it
.close
vocal sleetBOT
worldly shuttle
O
vocal sleetBOT
Available help channel!
untold bramble
e
potent anchor
untold bramble
it wrong
modern flare
then I dunno
untold bramble
ok
sweet phoenix
it is indeed 10.5
unless the units stated needed to be changed
if not yeah i think this is just a scummy question
pearl wadi
it is indeed 10.5
no
if you look closesly one box = 4 sq km
answer should be 42 @untold bramble
vocal sleetBOT
@untold bramble Has your question been resolved?
mellow urchin
(describing the picture better)
i've got a prism where the base is an equilateral triangle with side length x and height H
k is the length of the diagonal of the side of the prisms and α is the angle between the 2 diagonals
the task is to express the volume of the prism in terms of k and α
now:
- through law of cosines i arrived at
x = √(2k^2 - 2k(cosα)) - through pythagorean theorem i arrived at
H = √(-k^2 + 2k(cosα))
found the height of the base to be√[2k^2 - 2k(cosα)] * √3 / 2
from there i got the area of the base to be equal([2k^2 - 2k(cosα)] * √3) / 4
and by that gotV = [([2k^2 - 2k(cosα)] * √3) / 4 ] * √(-k^2 + 2k(cosα))
thing is -- i'm not even close to sure if that's correct; any help finding anything wrong?
vocal sleetBOT
(describing the picture better)
i've got a prism where the base is an equilatera...
cobalt ocean
unfortunately i believe your first step is wrong
i think it should be 2k^2 cos(a), not 2k cos(a)
@mellow urchin
mellow urchin
oh, right, since its multiplied 😅
cobalt ocean
your final answer should be simpler given that
vocal sleetBOT
vocal sleetBOT
Available help channel!
tacit slate
so confused, what to do
vocal sleetBOT
so confused, what to do
limpid jungle
So domain is the x values that is covers
So the graph has to converse x values less than and equal to 3
Range is y vakues
So graph has to cover y values in between and including -4 and 2
The graph you have there should work, as long as you bring the point on the right less than x=3
Wait wtf
That’s weird, because it looks like the graph you show there satisfies all those requirements
Maybe the software doesnt like that it’s just on zero?
Idk
vocal sleetBOT
@tacit slate Has your question been resolved?
native wren
vocal sleetBOT
@tacit slate Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
buoyant sinew
hi
buoyant sinew
I have no idea how to approach it to be honest
Professor just jumped straight from the simple stuff to this
edgy kayak
okay do you know why they have given the formula that they gave?
this one
like do you know why this represents rate?
edgy kayak
no, i know why it represents rate, im asking if you do
edgy kayak
okay so basically rate is defined as change
this could be change in time intervals
like you move from one place to another, if you divide the distance you moved with the time, you get the rate
similarly, your function divided at two different time intervals gives rate
buoyant sinew
okay
buoyant sinew
well i started a week ago
but aside from that no
apart from like very very entry level stuff
edgy kayak
how would you solve for a here:
ab/c = d
buoyant sinew
are you talking making a the subject of the equation or
edgy kayak
yes
buoyant sinew
guessing you would first multiply both sides by c
ab = dc
then divide both sides by b
a = dc over b
edgy kayak
correct
edgy kayak
this one
now here, think of Q(t_1)/Q(t_2) as k
so you want
k = the RHS
now if you have a/a given a≠0, how would you simplify this?
buoyant sinew
im confused im ngl 😭
buoyant sinew
1
civic otter
now if you have a/a given a≠0, how would you simplify this?
So what's this?
buoyant sinew
well it has to be equal to 1 im guessing
civic otter
well it has to be equal to 1 im guessing
You shouldn't be guessing, though 😅
edgy kayak
first after cancelling we will get
e^(rt_1) / e^(rt_2)
correct?
edgy kayak
have you heard of the natural log ln?
edgy kayak
okay do u know how to express
ln(a/b) in a different form
edgy kayak
yes
edgy kayak
this one
lets take ln on both sides here so we get
ln(k) = ln(e^(rt_1) / e^(rt_2))
(Recall i denoted the LHS as k before)
buoyant sinew
ok
edgy kayak
okay now express the RHS using subtraction
vocal sleetBOT
@buoyant sinew Has your question been resolved?
vocal sleetBOT
@buoyant sinew Has your question been resolved?
vocal sleetBOT
@buoyant sinew Has your question been resolved?
rustic shale
If I have
3x³ - x² - 7x + 5
How am I supposed to group it (I don't know if grouping is the correct term)?
paper depot
- are you sure you did not make any typoes
- what are you asked to do with it
calm pecan
factorise it?
rustic shale
1. are you sure you did not make any typoes
2. what are you _asked to_ do with i...
- No typos in the equation, although it was
-3x³ + x² + 7x - 5
Originally, I was just taught to always have the first x be positive - It's an inequality, it's set to more than or equal to 0, but I was given exercises where you need to factorise it so as to not have the x³, because we can't solve those yet
rustic shale
*factorise it?*
Yes
calm pecan
1. No typos in the equation, although it was
-3x³ + x² + 7x - 5
Originally, I ...
you were taught wrong
rustic shale
you were taught wrong
Wdym-
calm pecan
1. No typos in the equation, although it was
-3x³ + x² + 7x - 5
Originally, I ...
you dont have an $x^3$ in your question
rustic shale
Well I always doubted my math teacher's capabilities but still 💀
twin meteorBOT
Percy
rustic shale
you dont have an $x^3$ in your question
I have 3x³ though?
calm pecan
I have 3x³ though?
no, you have a typo, as ann pointed out
calm pecan
so you wanna solve an inequality?
rustic shale
If I have
3x³ - x² - 7x + 5
How am I supposed to group it (I don't know if gr...
I only need to know how I can factorise it
I'll solve it on my own, because it's against the rules to ask for homework solved
calm pecan
,w graph 3x^3 -x^2 -7x +5
twin meteorBOT
calm pecan
hmmmmmmmm
rustic shale
And even then, my teacher has peculiar ways of solving these, my math tutor told me they don't usually solve them this way-
calm pecan
okay hold on.
rustic shale
That's not a parabola, which is to be expected but still-
calm pecan
yeah
this is why we need the original question
you're doing it wrong*
*kinda
!xy please
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
rustic shale
The original problem is:
-3x³ + x² + 7x - 5 =<= 0
(Sorry for using computer science operators but I don't have "less than or equal to" on my keyboard)
paper depot
well as far as i understood OP, the original question was to solve the inequality -3x^3 + x^2 + 7x - 5 ≥ 0.
oh
i got the sign wrong
paper depot
The original problem is:
-3x³ + x² + 7x - 5 =<= 0
(Sorry for using computer sc...
the usual approximation to ≤ if you can't type this symbol is <=, following programming language conventions.
rustic shale
well as far as i understood OP, the original question was to solve the inequalit...
I switched the sign to=>= when I changed x's sign
paper depot
also you didn't "change the sign of x" but rather multiplied both sides by -1
rustic shale
the usual approximation to ≤ if you can't type this symbol is `<=`, following pr...
I was taught C, and it works that way, at least in the compiler I use, it works like that-
calm pecan
we want the roots
rustic shale
also you didn't "change the sign of x" but rather multiplied both sides by -1
Yeah that
rustic shale
we want the roots
Wha
calm pecan
whoopsie diasy
rustic shale
we want the roots
Oh?
calm pecan
yeah?
rustic shale
I'm confused 😭
calm pecan
well critical points
calm pecan
I'm confused 😭
were you taught wavy-curve
rustic shale
The original problem is:
-3x³ + x² + 7x - 5 =<= 0
(Sorry for using computer sc...
What I did with this was multiple both parts by -1, that's it
rustic shale
were you taught wavy-curve
Nope
Which is why I said all these must be factorised to remove x³
calm pecan
can you solve $(x-a)(x-b)(x-c)\geq0$
twin meteorBOT
Percy
calm pecan
No, I don't think so-
what do you plan on doing after factorising then?
twin meteorBOT
Percy
rustic shale
Well, it should ideally result in 2 smaller inequalities inside parentheses, so I set each of them to =0 and solve them, then draw the parabola and that's it
calm pecan
okay i think it's the variables tripping you up
rustic shale
okay i think it's the variables tripping you up
No I understand a, b and c are numbers
calm pecan
okay then
calm pecan
Well, it should ideally result in 2 smaller inequalities inside parentheses, so...
so like
rustic shale
Well, it should ideally result in 2 smaller inequalities inside parentheses, so...
Our teacher does this weird thing where you turn the inequality into an equation and solve it with the quadratic formula, but my tutor told me it can be done without it?
calm pecan
if you have $(x-a)(x-b) \geq 0$, you can solve it, and you'd do it graphically?
twin meteorBOT
Percy
rustic shale
if you have $(x-a)(x-b) \geq 0$, you can solve it, and you'd do it graphically?
After I have both Xs, yes
calm pecan
my net sucks im osrry
rustic shale
But we don't make the parabolas precise, we just draw them and color in the parts that the original question is looking for
rustic shale
Like, if it says greater than 0, then all points outside of the parabola that are greater than 0 are colored
rustic shale
so you *do* know wavy curve just for parabolas
Just parabolas, but we only draw it casually, we don't make anything precise
calm pecan
let's say you got this as $(x-1)(x-2)\geq0$, I'm guessing you'd draw the parabola 'roughly' and just make this line that goes through $1$ and $2$ and crosses the x-axis twice, yeah?
rustic shale
This is the exercise I did earlier, which was correct
twin meteorBOT
Percy
rustic shale
let's say you got this as $(x-1)(x-2)\geq0$, I'm guessing you'd draw the parabol...
Ye
calm pecan
okay
rustic shale
But rn I just need to factorise the inequality I showed at the start of this
calm pecan
do you know why it works? outside from that 'it's a parabola so'
rustic shale
do you know why it works? *outside* from that 'it's a parabola so'
Not really, our teacher doesn't explain these things (he refused to explain the quadratic formula-)
calm pecan
But rn I just need to factorise the inequality I showed at the start of this
,w give all factors of (3x^3-x^2-7x+5)
twin meteorBOT
rustic shale
Not really, our teacher doesn't explain these things (he refused to explain the ...
I feel like he's the reason I don't like maths -
calm pecan
alrighty lol
just to ensure that this all didn't amount to 'use wolfram', the key thing there was to notice that the sum of coefficients is 0.
so x=1 is a root.
and from there you can do a polynomial long division to get a quadratic for the rest
rustic shale
I'll try to solve it now and see how it goes
calm pecan
i wonder
rustic shale
i wonder
?
Alright something went wrong
I got
1 <= x <= 5/3
It was supposed to be
X => -5/3
rustic shale
Js on ur lhs
?
rustic shale
And on ur rhs
Rhs?
true cliff
to show u where the error is
rustic shale
No the ones on the left
rustic shale
OHHH
true cliff
Should be x^2+1-2x
true cliff
Ofc
rustic shale
Still incorrect-
rustic shale
The part on the left is still equal to 0 right?
And the one on the right is X = -5/3
calm pecan
@rustic shale give me a status update
rustic shale
<@1318689159916818463> give me a status update
I got it wrong, Light found two mistakes but it's still not correct
calm pecan
I got it wrong, Light found two mistakes but it's still not correct
what did you do?
rustic shale
<@1318689159916818463> give me a status update
calm pecan
oh lord
rustic shale
What did I do 😭
calm pecan
so this is kinda insane
rustic shale
so this is kinda insane
Did I make a mistake or is the approach completely non sensical?
true cliff
(X-1)^2 >=0 will mean that x can be any real number???
rustic shale
(X-1)^2 >=0 will mean that x can be any real number???
What? Why-
true cliff
Isnt a square always greater than or equal to 0 for all real values of x?
rustic shale
how did you get this table
It's hard to explain-
calm pecan
Isnt a square always greater than or equal to 0 for all real values of x?
you said 1
rustic shale
Anyways I have to go, tutor's here so I'll see what I can do with her
calm pecan
aight
true cliff
Anyways I have to go, tutor's here so I'll see what I can do with her
Okay
Remember
X is all real numbers cus square of anything is always more than 0 or equal to it
Tata goodbye
rustic shale
X is all real numbers cus square of anything is always more than 0 or equal to i...
Which x? The one on the left or the one on the right?
calm pecan
you should just learn wavy-curve
true cliff
Which x? The one on the left or the one on the right?
the left
rustic shale
you should just learn wavy-curve
😭
rustic shale
Even if I did, my teacher won't let me solve it that way
true cliff
Its always gonna be more than or equal to 0
calm pecan
Even if I did, my teacher won't let me solve it that way
yeah no its literally how we solve em
true cliff
Im js tryna make it common sense yk
calm pecan
wavy curvy is common sense 😭
vocal sleetBOT
@rustic shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
pp
vast shale
is xtanx = tanx^2
outer warren
no
green crow
no
green crow
unless he means tan(x²)
grim escarp
yeah no it's not
vast shale
unless he means tan(x²)
yea
grim escarp
(tanx)^2 means tanx * tanx
tan x^2 means tan of x^2
x tanx means x multiplied by the tan of x
the order of application of the trigonometric function matters
calm pecan
,w x=tanx
twin meteorBOT
vocal sleetBOT
frigid frigate
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
lime sonnet
vocal sleetBOT
lime sonnet
I need some help with this equation above. Im kind of terrible with these kind of equations
vocal sleetBOT
@lime sonnet Has your question been resolved?
faint pumice
okay for the question for this
vocal sleetBOT
okay for the question for this
alpine kestrel
!noping
vocal sleetBOT
Please do not ping individual helpers unprompted.
faint pumice
bruh she was heling me earlier
river arch
it looks correct though
faint pumice
thats why i pinged her specifically
bronze osprey
sorry it is brainfart
bronze osprey
thats why i pinged her specifically
you can just ping all helpers, after 15 mins
river arch
sorry it is brainfart
it looks like they combined the 9^(2n) with the (-1)^n
and the stray 9 with the 5
didn't notice the edit
alpine kestrel
i dont wanna repost the entire question
why 
bronze osprey
let's have more lazy helpers, win-win
alpine kestrel
perhaps this was infinitely less efficient 🤩🤩🤩🤩🤩🤩🤩
faint pumice
it was more efficient
paper depot
though would have appreciated OP saying so explicitly
faint pumice
foolish fools
paper depot
even with the word "follow-up"
vocal sleetBOT
vocal sleetBOT
Available help channel!
split compass
can anyone proove me why the definite integral always gives the area under the curve between two points a and b
opaque herald
Examine whether the function is one-one, onto, or neither.
Given function:
( f: [-2,2] \to \mathbb{R} ) defined by ( f(x) = x^2 ).
twin meteorBOT
vaikartana
opaque herald
pls solve and send anyonee
odd helm
what happened to the bot here
vocal sleetBOT
what happened to the bot here
paper depot
i think the bot glitched out
@opaque herald @split compass you both will need to get a new channel, sorry. technical hiccup.
@opaque herald we don't do your questions for you.
odd helm
Anyways is it true that the direction $f:\mathbb{R}^3 \rightarrow \mathbb{R}$ increases the fastest at $\mathbf{v}$ just $\grad f$ at $\mathbf{v}$?
twin meteorBOT
Xetrov
paper depot
yes
hybrid flicker
you didn't do b the way it was intended
hybrid flicker
yes
vocal sleetBOT
@odd helm Has your question been resolved?
odd helm
vocal sleetBOT
@odd helm Has your question been resolved?
severe stone
So I want to use <u-v,u-v> = <u,u-v> + <-v,u-v> But i am not sure if this is allowed since it isnt specifically an axioma so can someone help me out?
vocal sleetBOT
So I want to use <u-v,u-v> = <u,u-v> + <-v,u-v> But i am not sure if this is all...
severe stone
paper depot
it is axiom 2 combined with axiom 1
severe stone
But I am using - right
and I am not sure if it is allowed then
I know it works for +
but my prof is really strict so I am not sure if it is allowed this way
alpine kestrel
it is, just add the negative and you prove a corollary with minus
pseudo whale
How could we solve this without sub method ?
vocal sleetBOT
How could we solve this without sub method ?
paper depot
why's sub method forbidden
wild delta
need help with prime factorization in Z[i]
vocal sleetBOT
need help with prime factorization in Z[i]
wild delta
struggling of understanding the process of doing it. Several problems: 6+9i and 6+3i
paper depot
do you know the characterization of primes in Z[i]
paper depot
paper depot
a gaussian integer z is prime if one of the following conditions is true:
- z = ±1 ± i
- it lies on either the real or imag axis and its magnitude is a real prime congruent to 3 mod 4
- it doesn't lie on either axis, and |z|^2 is prime
so as a first step you could try factoring out as much of a real-integer factor as you could from these
as if you were factoring them like polynomials in school
so 6+9i = 3(2+3i)
wild delta
yea, then I was supposed to find the norm?
paper depot
well you can do that for each factor separately
except really it's only 2+3i you need to do it for
3 is a real prime that's also a gaussian prime
so we're done w/ that
and |2+3i|^2 = 13, so..
split compass
hey is there anyone to help
paper depot
hey is there anyone to help
!occupied
vocal sleetBOT
hey is there anyone to help
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).
paper depot
so it splits
how do you reckon it splits tho
whatever two factors it splits into, their norms must be integers multiplying to 13
wild delta
hmm
paper depot
it is in fact a gaussian prime
wild delta
because its norm or maginitude is congruent to 1 mod 4?
paper depot
no because it's not real nor pure-imag and its norm is prime.
like think of it this way
let $z_1, z_2 \in \bZ[i]$ be such that $z_1z_2 = 2+3i$
twin meteorBOT
Ann
paper depot
then $N(z_1)N(z_2) = 13$, yes?
twin meteorBOT
Ann
wild delta
okay
wild delta
yea
paper depot
ok right
N(z_k) are integers. real integers. natural numbers even
so one of them has to be 1 and the other 13
so in fact 2+3i does not have any nontrivial factorizations
vocal sleetBOT
vocal sleetBOT
Available help channel!
buoyant panther
vocal sleetBOT
buoyant panther
I don't understand on how to find P(A1)
paper depot
look at F(n) mod 21 and filter out the ones that are 0, 3, 6, 9, 12, 15, 18, 7 or 14.
warped ember
I don't understand on how to find P(A1)
mod 3 and all 0 mod 8 are multiple of 3
raven stone
look at F(n) mod 21 and filter out the ones that are 0, 3, 6, 9, 12, 15, 18, 7 o...
you sister, i apologised, u accepted my apology?
warped ember
you sister, i apologised, u accepted my apology?
yes
raven stone
there was a less rude way to ask that but yes sure <@957552694451666995>
idk, i may sound like that
raven stone
didnt understand-
wassup?
vocal sleetBOT
@buoyant panther Has your question been resolved?
buoyant panther
ok so.. how do i find the common multiple of 3 and 7 in fibonacci series?
alpine kestrel
you can dot them individually or together
buoyant panther
you can dot them individually or together
wdym?
alpine kestrel
either take mod 3 and mod 7 and count 0s or take mod 21 and count {0, 3, 6, 7, 9, 12, 14, 15, 18}
buoyant panther
either take mod 3 and mod 7 and count 0s or take mod 21 and count {0, 3, 6, 7, 9...
sir.. i dont think its possible to count these many numbers
buoyant panther
it’s just 100
In fibonacci sequence
zinc hornet
how would I find all six solutions of x^6 = 1? this is what I did so far
faint pumice
how would I find all six solutions of x^6 = 1? this is what I did so far
what makes you think there are 6 solutions
manic flax
what makes you think there are 6 solutions
they prolly mean complex as well
zinc hornet
what makes you think there are 6 solutions
wait r there not since it’s to the 6th degree?
faint pumice
they prolly mean complex as well
oh true
faint pumice
wait r there not since it’s to the 6th degree?
normal roots there should only be 2
zinc hornet
oh yeah I meant complex well basically all the solutions
faint pumice
yeah mb
manic flax
us euler's form yeah
zinc hornet
us euler's form yeah
can I use cis cuz my teacher doesn’t let me use euler’s form
like in something like this (idk what the method is called)
manic flax
how would I find all six solutions of x^6 = 1? this is what I did so far
yeah basically compare them, cos6theta=cos2npi
then find the diff values of theta that satisfy bw 0 to 2pi
zinc hornet
yeah basically compare them, cos6theta=cos2npi
then find the diff values of thet...
why cos?
also can u explain how u got like the cos2npi pls
zinc hornet
oh srry, what is cis tho idk?
It’s like a notation for cos(theta) + i sin(theta)
zinc hornet
is it like an abreviation?
yea
manic flax
nvm its actually correct lmao
ok so basically you the number to be 1 ryt
that means imaginary part is 0
or sin6theta=0
this happens when cos6theta=1
now 1 can be written as cos 2npi
does that make sense @zinc hornet
zinc hornet
does that make sense <@840570263702994968>
no🥲
zinc hornet
uhh which part, like the entire thing? or some specific part?
the entire thing
manic flax
ok let me try again
manic flax
how would I find all six solutions of x^6 = 1? this is what I did so far
you have this expression right?
so |r|=1, now lets focus on the argument
cis6 θ=1
=>cos6 θ+isin 6θ=1=cos2npi(eg. cos 2pi=1)
6 θ=2npi
how about now
?
zinc hornet
cis6 θ=1
=>cos6 θ+isin 6θ=1=cos2npi(eg. cos 2pi=1)
can I do like sin(pi/2) = 1 too instead of cos (2pi) = 1?
manic flax
can I do like sin(pi/2) = 1 too instead of cos (2pi) = 1?
wait no sin is for imaginary
so you'd have to equate it to 0