yeah
#help-28
torn jolt
hollow moth
but the second fibonacci number is 1? right? Doesn't it go F0 = 0, F1 = 1, and F2 =1 again?
so it wouldn't hold true for n = 2, right?
and what's phi(n-2)? Does that mean that the value of phi changes?
like im so confused with just understanding the problem
torn jolt
,calc ((1+sqrt(5))/2)^(2-2)
glossy valveBOT
Result:
1
yeah, its a power
hollow moth
okay im going to go try the proof now. Thakn you!
torn jolt
np :)
atomic blade
okay im going to go try the proof now. Thakn you!
Thakns giving
hollow moth
Thakns giving
I love thakns giving, my favorite holiday
atomic blade
Ong
hollow moth
i need help with basic algebra
how is phi^n + phi^n-1 equivalent to phi*n+1
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chilly blade
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atomic blade
!15m
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chilly blade
k mb
chilly blade
No
chilly blade
k
zenith vine
at the end of esch branch we can put the percentage chance of it bejng that event
so, 1/4 of them are 4 so off of 4 u would have 25%
not 4 has 3 options, so 75%
you following?
chilly blade
Yes
zenith vine
ok now for the other branches, u dont rly need the not 4 part bc we aren’t interested in that
chilly blade
👌
zenith vine
for it to be more than 3 we would have 4 or 5, 2 options so 50%
chilly blade
The answer is 50%?
zenith vine
ah i shouldve showed u this w fractions
chilly blade
Ok
chilly blade
Alright
zenith vine
now bc we have 2 probilities of 2 seperate events, we need to find out the overall probability of both events happening together if that makes sense
chilly blade
Alright
zenith vine
in this case we follow the branches of what events we want to happen, here that would be 4 and then more than 3
to find out the probability of those two, we would multiply our fractions together to find the overall probability
so, in this case, 1/4 x 1/2
zenith vine
yeah!
zenith vine
yeah!
chilly blade
So 12.5% is the final answer
zenith vine
mhm! :)
chilly blade
yup thank you
zenith vine
yw! did it all make sense?
chilly blade
yup
zenith vine
awesome! :]
chilly blade
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lone cobalt
Can someone help me with this
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Can someone help me with this
lone cobalt
tulip beacon
Can someone help me with this
We know that when it hits the ground h=0, so just solve a quadratic basically
lone cobalt
This is my teachers solution but I don’t understand where she got some of these numbers
For example a(t
lone cobalt
So those are by default
tulip beacon
Acceleration is always 9.8 in projectile motion yes
lone cobalt
Why is it - tho
tulip beacon
It’s acting the other way to the direction of the ball
So when you throw a ball up it’s going upwards and gravity is acting downwards
However when the ball falls back down this reverses
normal tree
wha
lone cobalt
Would mine be + or - 9.8
Sorry I just learned this today so I need more a bit more time
tulip beacon
-9.8, but this is unnecessary to answer the question
normal tree
you don't actually need anything involving physics to solve this problem
tulip beacon
Yea
normal tree
they tell you what the trajectory is
tulip beacon
Just quadratic
normal tree
and I don't believe that today is the first day you've heard of a quadratic lol
tulip beacon
That question
lone cobalt
And trying to do practice problems
normal tree
this looks like a calculus class right?
lone cobalt
Yup
normal tree
surely you've covered solutions to quadratics in many classes before, yeah?
lone cobalt
That question
I know how to solve quadratics
normal tree
what is h(t) equal to if the projectile hits the ground at time t
tulip beacon
Sure
lone cobalt
Question
What would c be
Would it be 40
Bc that’s the only thing that would make sense
lone cobalt
But I was confused because you mentioned a 0
tulip beacon
And c is 0
lone cobalt
We just do the quadratic formula
tulip beacon
But I was confused because you mentioned a 0
T=0 is a solution to the question, but that’s just because the ball started on the ground
lone cobalt
Eh when you don’t have a c
Do you still want me to do the quadratic equation
Or is there another way when you don’t have c
tulip beacon
Do you still want me to do the quadratic equation
Used the quadratic equation coz ur used to it
No point teaching tricks at this time
lone cobalt
lone cobalt
Btw
My biggest confusion was what’s the purpose of 40
So would the answer just be 8.16
lone cobalt
Can someone help me with this
Velocity of 40
tulip beacon
ahhh
Well I’m theory you can do questiob 2 ways
You could’ve used v=u + at, re-arrange for t, and find out how long it took to reach the max hieght
Times it by 2 to get the overall time to complete its trajectory
You would get same asnwer
tulip beacon
Yea OFC
sour topaz
thsi is a trick question, maybe not so related to math but does anyone know the right answer? (mine was 13)
rustic karma
22?
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zinc wigeon
so
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devout pike
https://i.imgur.com/OHLaGoA.png How would this question be done? Isn't this just true by definition?
devout pike
Like I can't think of a way to prove this
Like I wrote down
A x ∅ = ∅
B x ∅ = ∅
Thus A = B
wait im so stupid (illiterate moment)
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hot mango
How is this wrong? this method worked for the last problem
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How is this wrong? this method worked for the last problem
hot mango
I got closer
but I cant get the last one, yes I tried reversing it
<@&286206848099549185>
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devout kraken
Hi, I need help integrating a matrix, and exponentiating it.
devout kraken
$B_1 \frac{\hbar}{2} \begin{bmatrix}
0 & e^{-i \omega t}\
e^{i \omega t} & 0
\end{bmatrix}$
glossy valveBOT
walczyk
devout kraken
$H_{int}(t)=B_1 \frac{\hbar}{2} \begin{bmatrix}
0 & e^{-i \omega t}\
e^{i \omega t} & 0
\end{bmatrix}$
glossy valveBOT
walczyk
devout kraken
$U(t)=T\exp[\int_{-\infty}^{t} H_{int}(t') ,dt']$
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walczyk
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normal tree
is it not a componentwise integral
devout kraken
is it not a componentwise integral
what do you mean?
normal tree
like integrating the matrix is just integrating each component
it's certainly true for scalar multiplication and addition, and since integration is just that but some infinite sum
as for exponentiation, does it have distinct eigenvalues?
my guess is yes, because they come in complex pairs, and this seems to have only complex eigenvalues
though I might be wrong on that one
devout kraken
though I might be wrong on that one
I think I have to expand the exponential into a series of nested integrals
normal tree
then you can just diagonalize and be good yeah?
devout kraken
i think because it has to be time ordered that it gets more complicated than that
devout kraken
sorry idk anything about physics LOL
lol no worries; i found some notes that are pretty relevant but not the same; they still don't explicitly find U, http://www.pas.rochester.edu/~passage/resources/prelim/Quantum/UCB Notes/14 spinmagf.pdf
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gaunt kernel
Hello
gilded lion
JUST ASK
gaunt kernel
JUST ASK
here's my teachers solution, my only issue is not understanding why did my teacher set the resulting force on y axis to 0
i just dont get that
hollow grove
onyx glen
@gaunt kernel you want the resultant force to be horizontal
that means its vertical component should be zero
do you understand that?
gaunt kernel
do you understand that?
No sorry i didnt really get it
i am just not sure if i understand it correctly
gaunt kernel
<@885495383428595754> you want the resultant force to be horizontal
i understand why they did that, but i dont understand why it is right to do that
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jaunty mirage
i understand why they did that, but i dont understand why it is right to do that
Because in the question they mentioned that the resultant force must be only in the horizontal direction
Acc to the question we don’t want any resultant vertical component of force we want the force to be present on in the horizontal direction
So whatever force we calculated in the vertical direction we assume it to be zero
Do you get it? @gaunt kernel
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gaunt kernel
Yes i do but my teacher sets the vertical force to 0 even in questions that doesn't require it to be so
onyx glen
yes it does
the resultant force consists of a vertical component and a horizontal component
if the resultant force is to be purely horizontal,
it means that there has to be no vertical component to it,
or rather that the vertical component has to be zero
and that is what is done
there really is no better way to explain it
gaunt kernel
Because in the question they mentioned that the resultant force must be only in ...
Yes i do but my teacher sets the vertical force to 0 even in questions that doesn't require it to be so
onyx glen
... so you claim there is ANOTHER question you've got, in which the teacher's solution sets the vertical component to 0, even though there is no reason to have it be so? is that it?
gaunt kernel
... so you claim there is ANOTHER question you've got, in which the teacher's so...
Exactly
onyx glen
can you show the question and your teacher's work
i want to see if your claim holds water or if you misunderstood something or maybe the teacher screwed up
gaunt kernel
Never mind you are right, i messed up
not the teacher
It doesnt say it in the book, but he had changed the question in his solution, he wrote that at the bottom and i am just now seeing it
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kind kraken
Can someone help me with this question?
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kind kraken
vast fossil
a^(n - 1) =/= 1
vast fossil
Right
kind kraken
I do not understand why it is written $\frac{a^n.a^n}{a^{n-1}}=1$
vast fossil
I do not understand why it is written $\frac{a^n.a^n}{a^{n-1}}=1$
{n-1}
glossy valveBOT
13wrc
vast fossil
$\frac{a^n\cdot a^n}{a^{n-1}} = a^{n+n-(n-1)}=a^{2n-n+1}=a^{n+1}$
glossy valveBOT
A Lonely Bean
kind kraken
yeah yeah got this so we proved $a^{n+1}$ is equal to 1
glossy valveBOT
13wrc
kind kraken
what am I missing here?
kind kraken
a^(n - 1) =/= 1
I did not understandf
@vast fossil yo
hey could you please tell me why $a^{n-1} \neq 1$
glossy valveBOT
13wrc
kind kraken
<@&286206848099549185>
@vast fossil hey could you please help?
I think $a^{n+1}=a^n.a$
glossy valveBOT
13wrc
kind kraken
and by induction hypothesis we know that $a^n=1$ thus $a^{n+1}$ is equal to $a$
glossy valveBOT
13wrc
kind kraken
so the claim that $a^n$=1 is false
glossy valveBOT
13wrc
last agate
f:R-> R
last agate
Has 2 derivatives
And f³(x)+f(x)=x
I need to find monotony, extremums, convex and turning point
last agate
I think just cubing it
I've created a new function with this relation
And found the second derivative
granite hound
i'm not sure how u check for monotony, but the others' x-coordinates can be found by setting 1st derivative to 0, right?
I should have tried the qn first before typing
last agate
For monotony I check by finding the first derivative then the roots and finally by making a table
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north warren
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onyx glen
hold up
north warren
D_1^Z being integer divisors of 1
onyx glen
,calc (1^2 - 3)/(1 - 2)
glossy valveBOT
Result:
2
,calc (3^2 - 3)/(3 - 2)
glossy valveBOT
Result:
6
what exactly is the problem here?
loud hull
,w derivative (7x^{3})(3)^-1 - 2x
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,w derivative (7x^{3})(3)^-1 - 2x
glossy valveBOT
loud hull
[\frac{3(7x^{3})-(21x^{2}(0))}{3^{2}}]
[\frac{21x^{3}}{9} - 2]
glossy valveBOT
dopediscorduser
trail prairie
Where is my mistake?
7/3 is just a constant, why are you trying to differentiating it?
atomic blade
You don't use quotient rule
I mean you can but it'll be useless
7/3, like what VG said, is a coefficient constant
7/3 x^3 + 2x
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pseudo ether
hi
pseudo ether
i need help
i’m having trouble finding out what the equation would be
for both problems
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gritty rose
<@629300363094392844>
that's the wrong ping
pseudo ether
<@&286206848099549185>
amber widget
namaste munna bhai
amber widget
chal kaam bhol
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Show your work, and if possible, explain where you are stuck.
pseudo ether
I’m stuck at how to get the equation
but ik how to solve it
so if you could just tell me how to find what the equation is
that would be great
grave elm
So joshua can do 1 table in 3 hours. Thomas can do it in 7 hours. So joshua can complete 1/3 table in a hour, and thomas 1/7 table in hour. Together they can complete 1/3+1/7 tables in a hour
So if they have to complete 1 table, then (1/3+1/7)*t=1.
grave elm
lemme just repost it so I can see it here...
Madison cleans 1 house in 5 hours. So she can clean 1/5 house in 1 hour
grave elm
So if they have to complete 1 table, then (1/3+1/7)*t=1.
Can you modify this equation to find the resulting equation?
t=3.5, because it takes them 3.5 hours
Instead of joshua, there is Madison who can do it in 1/5 hours and instead of thomas, there is a brother who can do it in 1/t
so (1/5+1/t)*3.5=1
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oblique jasper
I have a question regarding proof techniques. My experience with proofs is very limited.
Someone on a different Discord asked this question and now I'm curious.
It's a drag-and-drop question.
There are three statements. Which option would you choose to either prove or disprove the statement?
The options are Contraposition, Counterexample, Induction, Direct, Existence and Exhaustion.
The statements are as followed:
(1) Prove that all numbers in the set of numbers from 1 to 10 are less than 11.
(2) Prove that all numbers less than 5 are odd.
(3) Prove that if a graph has n vertices, it has n-1 edges.
I would use an exhaustion proof to prove (1) because it is a small and finite set so it's easy to just go through each element in the set and then show that for each element it is indeed less than 11.
For (2) and (3), I would honestly just use a counter-example for both but since it's drag-and-drop, you can't use it for both.
My reasoning using a counter-example for (2) would be the case of where 4 < 5 but 4 is even so (2) is not true.
For (3), there are multiple options for the counter-example. Null graphs, complete graphs.
I'm curious to see how y'all with more proof experience see it.
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I have a question regarding proof techniques. My experience with proofs is very ...
@oblique jasper Has your question been resolved?
fast peak
checks out, seems like someone messed up when asking the question and didnt think about it being drag and drop
or maybe they wanted to write tree, who knows
in which case induction
oblique jasper
Yeah, that's what I figured as well
fast peak
not sure what they mean by the proof technique "existence"
unless its a counterexample in which case you call it counterexample
oblique jasper
This has honestly been keeping me busy for a while. I've been trying to get better at proving things so I really wanted to help him out.
Good to know I'm not going crazy.
Figured to ask here to make sure so thanks for that ;)
fast peak
wait I'm stupid they just mean "there exist" statements
oblique jasper
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oblique jasper
Thanks for the help by the way :)
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faint valley
Help
wide sundial
faint valley
wtf
im bugging
tnx for pointing that out , but at this point there is something wrong with me for not seeing stuff like this
its like memetic hazard it just not possible to see but its in plain sight
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faint valley
help 2
faint valley
Hey guys Im in a bit if a sticky situation here , does anybody see a better route I could have gone this seems like a lot of brute force calculations, for example did I miss a big cancel somewhere In first step?
in short multiplying this would take the whole page (maybe even more)
wise gate
Hey guys Im in a bit if a sticky situation here , does anybody see a better rout...
There is a very useful identity which appears in many occasions in math and can help you in this case
$A^n - B^n = (A - B)(A^{n-1} + A^{n-2}B + A^{n-3}B^2 + \cdots + AB^{n-2} + B^{n-1})$
Use it with $n = 3$ in the last denominator
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d឵
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tulip beacon
moments
torn jolt
(there's a physics server in #old-network )
tulip beacon
Hm
is it a distance x from b or a
i cant read the rest
Ok
Your diagram
in theory couldnt the mass of the 48g be pass the knife?
Ahh
ok
Yea
The system is in equilibrium yes
Taking moments about N
coz we know clockwise = counter clockwise
Yea
perfect
so we know W = 0.95N and is 5 cm away from N
and we know T is Y cm away from N with a force of 0.048g
???
lol
I havent done moments in ages
all g
Im a physics major struggling with a moments question 💀
does the wieght not act in the centre?
this diagram shows weight acting in the centre
so i was too assume it does
Unless it doesnt
i mean i think its still possible if it doesnt
YEa if u wanna take moments around A u can
Sure
that'll be great
Yea
i got that
I explain?
LIke i can draw a quick diagram if u want me too
Im puttign everything in standard units
so i use meters instead of cm and kg instead of grams
Its stupid, but the weight of the meter rules
acts in the centre
aka 50 cm inwards
or 5 cm away from the knife edge
coz the knife edge is 45 cm from A
hollow mortar
tulip beacon
YEA
YOu could do about A
but it wouldnt really make sense since moments about A is hard when u dont know x
wym?
in my working
r u talking about my 2nd equation or my 2nd diagram
Thats around the knife edge
The knife edge is the triangle on the diagram
The reason why we took
at the knife edge
is because we knew both distances
all g
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charred shadow
Hello, looking for calculus help. just started taking calculus and its much harder than i thought...
Need to find derivative of this and i have a few more after
charred shadow
wait idk why it flipped is there a command for that?
devout valley
,rccw
glossy valveBOT
devout valley
,rotate [angle] will also allow you to rotate by any [angle] of your choice (in degrees) 
,rotate 420
glossy valveBOT
devout valley
Anyways, maybe rewrite this in terms of powers of r?
light sonnet
```,rotate [angle]``` will also allow you to rotate by any [angle] of your choic...
What if I wanted radians?
devout valley
What if I wanted radians?
I was gonna say "convert it" but now that's got me thinking whether you can give a value and the bot evaluates it 
brb gonna test that out [edit: seems not 
]
charred shadow
I think I got it!
devout valley
I think I got it!
Sign I think, for your derivative of $-\frac{2}{5} r^{-1/2}$?
glossy valveBOT
@devout valley
devout valley
You'd get that the negative from the exponent should cancel out with the one that's already there to make it positive
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dense edge
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dense edge
is this correct or did I mess up somewhere with Product Rule, Power Rule, and Chain Rule?
I'm not sure if I should be taking d/dx 3 times or 4 times
the place I'm not sure if I messed up in particular is with this part
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pulsar gale
@dense edgelooks fine
you do know derivative calculators exist right
you can just ask there instead of having someone go through your work
thick minnow
,w diff sqrt(x + sqrt(x^2 + 1))
glossy valveBOT
thick minnow
check @dense edge
dense edge
Thanks, I just don't see how my answer is the same
In radical format it looks so strange to me and I'm trying to figure out how it converts to exponentials
dense edge
you do know derivative calculators exist right
i have tried the calculators as well but they answer in radical form. would you know of one that can convert radical to exponential?
thick minnow
I usually remember that derivative of sqrt(x) is 1/2sqrt(x)
it should be easy to see then
using radicals makes it hard to understand what is going on
dense edge
I usually remember that derivative of sqrt(x) is 1/2sqrt(x)
like this?
thick minnow
yep
pulsar gale
i have tried the calculators as well but they answer in radical form. would you...
you can just use the compare function to see if the two expressions are the same, or graph them
pulsar gale
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torn jolt
Then I plugged in 2 for P', 20 for v, 1/8 for P
I got this as my answer. can any1 confirm?
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torn jolt
<@&286206848099549185>
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torn jolt
!status
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What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
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worthy flint
Help
worthy flint
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fathom cairn
I did not understand why the calculations for a) and b) are different in order to get q.
fathom cairn
Or rather, I haven't checked the calculation path. What is the formula behind this?
Once the larger is divided by the smaller: 5/3 and then the other way round suddenly 12/18.
gritty rose
I did not understand why the calculations for a) and b) are different in order t...
they're different equations for q
fathom cairn
they're different equations for q
F.e. when I'm writing a test, how should I calc this shit? I dont know the formula bro that makes me so mad
It looks so easy
Fe= for example
glossy valveBOT
riemann
gritty rose
in 2a), a = 5, b = 3 and in 2b), a = 12, b = 18
gritty rose
**riemann**
do you know how to simplify
$\frac{aq}{a}$ ?
glossy valveBOT
riemann
gritty rose
correct
gritty rose
Once the larger is divided by the smaller: 5/3 and then the other way round sudd...
so your main mistake is finding the bigger number then dividing by the smaller numbers
gritty rose
**riemann**
q doesn't care which one is bigger, a or b
fathom cairn
I know I just want to find a method
gritty rose
**riemann**
this is the method, not yours
fathom cairn
in 2a), a = 5, b = 3 and in 2b), a = 12, b = 18
Why its not 2b) a=18 and b= 12?
glossy valveBOT
riemann
gritty rose
I did not understand why the calculations for a) and b) are different in order t...
is it the same as 2b)?
fathom cairn
plug in your a and b into the equation
Okey. Now If I do a=18 and b = 12 then it would be 0. …
I wont understand it
why is a=5 and b=3 and a=12 and b=18
That what I havent got
gritty rose
Okey. Now If I do a=18 and b = 12 then it would be 0. …
write this on paper
i don't know what you're doing
gritty rose
is it the same as 2b)?
and answer this
fathom cairn
is it the same as 2b)?
They re different tasks
gritty rose
yes
gritty rose
Why its not 2b) a=18 and b= 12?
that's why it's not a=18 and b=12
fathom cairn
How do I know bro
gritty rose
**riemann**
you only apply this to the correct a and b when you substitute in the numbers
a is always the number multiplying q
gritty rose
Okey. Now If I do a=18 and b = 12 then it would be 0. …
18 isn't multiplying q
fathom cairn
18 isn't multiplying q
Hm would It be possible? Or you'll get the wrong anser
I would get the wrong q
Okey
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dapper nimbus
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dapper nimbus
Need help finding the zeros I'm pretty stuck on
gritty rose
find the zeros of cos(y), then set y=3x-1 and solve for x
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wise hazel
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wise hazel
Hey how do I do q 3 4 and 5
torn jolt
pretty sure that this is the wrong server but I assume you use a formula
wise hazel
pretty sure that this is the wrong server but I assume you use a formula
What do you mean wrong servers it's a maths server no? And also thank for assuming you use a formula😂😂
glacial pasture
$T=2\pi\cdot\sqrt{\frac{r^3}{GM}}$
glossy valveBOT
AℤØ
glacial pasture
because its a maths server, not a physics server
#old-network theres a physics server in that channel
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unborn elbow
Can I get help with finding the exact value of each trig function
unborn elbow
I am learning how to find the exact value of trig functions. Heres a couple examples I am struggling with; tan - 29pi/6, csc -840degrees, csc 3pi, tan -11pi/3
I am not understand the conversion I guess? For example, when csc is 1/y, -840 degrees can be converted to 240 degrees giving me (-1/2, -sprt3/2), then I have 1/-sqrt3/2. I am having trouble reducing that and I don't know why lol
sharp vine
period of csc(x) is 2pi (360 deg), hence
you can add (subtract) multiplicity of 360
-840 + 3 * 360 = 240
unborn elbow
-840 + 3 * 360 = 240
Yeah I understand that, its moving further to the exact value
sharp vine
furthermore it might be wirtten down as csc(240) = -csc(60)
and now it's obvious I guess
generally in questions like this think about 30/45/60 angles (or pi/6, pi/4, pi/3)
unborn elbow
On the answer key it says its - 2sqrt3/3
sharp vine
-csc(60) = -1/sin(60) = -1/(sqrt(3)/2)
after rationalizing the denominator you'll get that
unborn elbow
Yeah the steps it takes to get there is what I am confused about
I missed some lectures so I am completely absent of how to do so
Like I don't know how to go from - 1/sqrt3/2 to - 2sqrt3/3
glossy valveBOT
Modus
unborn elbow
Okay I think I kind of understand it now
Could u help me with another example so I know I got it down?
unborn elbow
tan - 29pi/6
I've tried them all, still run into the same issue
What I did here was added 36pi/6 to get 7pi/6 giving me (- sqrt2/2, - sqrt2/2)
Would it just equal 1?
<@&286206848099549185>
sharp vine
first of all, why you write it as point
(two coordinates)
tan( -29/6 pi) is a number
unborn elbow
is that not how im saying it lol
sharp vine
tan(-29/6 pi) = tan(7pi/6) that's true
period of tan is pi
hence, you could add +30/6 pi to get tan(pi/6)
easier I think
unborn elbow
Okay true, that does seem easier
unborn elbow
Well that was bc I was going with 7pi/6
But if we are going with pi/6, then we have (sqrt3/2, 1/2)
sharp vine
I understand you're using unit circle but
write only value of a function, without argument
they're numbers, not points
unborn elbow
Well the way he has set it up, tan0= y/x, and pi/6= (sqrt3/2, 1/2)
How am I supposed to write it?
sharp vine
point on the unit circle is (x,y) = (sqrt3/2, 1/2)
and tan( theta ? ) = y/x
find tan and that's it
unborn elbow
So then 1/2 / sqrt3/2 ?
sharp vine
yes
sharp vine
dividing by a fraction = multiplying by its reciprocal
unborn elbow
So 1/2 times 2/sqrt3 ?
unborn elbow
Then I get to 2/2sqrt3, does that not reduce to sqrt3?
sharp vine
it reduces to 1/sqrt3
unborn elbow
And where do I go from there?
sharp vine
you can only rationalize the denominator (multiply whole fraction by sqrt3/sqrt3)
unborn elbow
Do I always do that when I am given a whole number over a radical? Just multiple by the denominator?
Because the denominator cannot have a radical? It has to be a whole number at all times, correct?
sharp vine
generally it can, but in maths we often rationalize the denominator of a fraction, so I'd say yeah you should do that
unborn elbow
Okay cool. I think I understand it all now. I really needed to refresh on solving fractions I guess lmao
Thank you! @sharp vine
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untold olive
Hi Im doing some practice problems for a competition but I have no idea how to do this one
hollow sable
Note that 42-5x_4 has to be a multiple of 4
Hence x_4=2,6
the rest should be clear
untold olive
i think i kind of see what u mean
from then on it would just be to list the combination of 4x_1 + 4x_2 + 4x_3 = 32, 12?
is there an easier way to do it other than listing tho?
@hollow sable
hollow sable
from then on it would just be to list the combination of 4x_1 + 4x_2 + 4x_3 = 32...
Divide this by 4
untold olive
ahhh i see
and then its just solve for x_1 + x_2 + x_3 = 8,3
so like basic combations problem
hollow sable
Yea
untold olive
thanks sm
hollow sable
untold olive
are u busy rn? i have a few questions i still need help with
but if ur busy i dont want to take all oyur time
calm trail
Can someone help me generate irreducible polynomials in $Q_3$? I looked at Hensel lifting but am extremely confused.
glossy valveBOT
ohNoiAmHere
hollow sable
I don’t know what generating irreducible polynomials in Q_3 is but thus video that may clear your confusion on Hensel’s Lemma: https://youtu.be/n-re4ral9Aw
calm trail
im looking at this cause it relates to the padics
and like i get what its doing
but like as far as i see its just approximate p-adic factorization
so my question is how does this lead me to an irreducible polynomial
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@calm trail Has your question been resolved?
calm trail
<@&286206848099549185>
torn jolt
ya?
calm trail
how does that method help me generate irreducible polynomials in Q_p?
the paper claims that it does but i do not understand
cause it starts by saying f is a product of monomials
so whats happening?
pulsar gale
@calm trailask in the advanced channels
this stuff is way too complicated for the general chat
random pollen
I have made an error in my calculations, but where?
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I have made an error in my calculations, but where?
lavish patio
I have made an error in my calculations, but where?
yes
u made a mistake in the first step
random pollen
go on
lavish patio
x-2 cannot be directly taken to the other side
u have to first take common denomiator for the 2x as well
and then only we can take it to the other side
random pollen
OR i could move that first x up in numerator first, right?
lavish patio
??
random pollen
so it becomes $\frac{2*2x-1.57}{x-2}$
glossy valveBOT
Duirky
glossy valveBOT
Duirky
random pollen
thats alright
and from there i simplify like i did before
lavish patio
no
random pollen
lavish patio
random pollen
ur missing the 2x(x-2)
I'm so sorry but i still don't get it. Doesn't multiplying with the denominator just leave the numerator behind?
It does - i think you have something wrong. i see my mistake
when multiplying everything by 4 i multiplied 1.57 by 2
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random pollen
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random pollen
No, I am wrong. sorry. I am an idiot
random pollen
AAAH i get it, sorry
lavish patio
i just dont know how to explain it
random pollen
yeah i need to bring over the +2x before i multiply
yeah, sorry m8, it's 1am, the grey one's not at its peak
lavish patio
over??
random pollen
subtract on both sides
lavish patio
u mean to the other side??
lavish patio
subtract on both sides
YES
stable heart
you are right, this step is not right
lavish patio
exactly
random pollen
i am so sorry
stable heart
also you might benefit from making variables instead of using numbers, make it much cleaner to work with
for example use $a=1.57, b=15.2$ and then you have $$2\f{2x-a}{x-2}+2x=b$$
glossy valveBOT
Duh Hello
random pollen
also you might benefit from making variables instead of using numbers, make it m...
Yeah, but this is school so i need to show my work. Figured this is the easiest way to rob my teacher of any BS reason to not give me full marks
And it's all part of a calculation with two equations and two unknowns
So i think it's gonna get a bit messy
stable heart
no teacher would ever remove marks for using a creative way to make the problem more reasonable
in fact, i think i would be more inclined to remove points if you dont do it
unless it is explicitly mentioned that you are not supposed to do that
which would be incredibly weird
random pollen
It would, yeah
In the grand scheme of the thing, i don't think using a variable would help all too much, but i appreciate it (it might just be my tiredness talking). Thanks for the help!
lavish patio
the teacher shouldnt cut marks for this but just remember to write that u r using variables that is a=1.57 and b=15.2
random pollen
The entire formula is a sort of "variable". It substitutes the other unknown variable in the math problem (1y = blablabla x*2 whatever), so putting variables in the "variable" like that would just cause confusion, if not for the teacher then for me.
Once again, tysm!
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lavish patio
np, do whatever is comfortable for u
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tired rampart
How would I start this problem?
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How would I start this problem?
tired rampart
a clearer version of the problem
atomic blade
Recall that $\cos^2(x) = 1 - \sin^2(x)$
glossy valveBOT
Umbraleviathan
tired rampart
Yep so do I replace the cos^2 with 1-sin^2?
limpid moat
then multiply the equation for $2^{\sin^2(x)}$
glossy valveBOT
everg
tired rampart
So I should multiply that with 2^sin^2 x?
now i have this
<@&286206848099549185>
tired rampart
bro what
tired rampart
this channel is occupied use another one
calm viper
Change $50 into Rupees
ionic estuary
now i have this
Well, for this equation to be equal to seven, make sin²x=1 and 1-sin²x=0
tired rampart
ok alr
so what does it mean by the "set of all real solutions" and what would it be here
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@tired rampart Has your question been resolved?
spring shard
for which values of a does this equation only have one solution? https://gyazo.com/eab8497637e888cf558fb3766423d81c when a is restricted to R
vast fossil
Haven't we already discussed this?
vast fossil
Okay, let us redo it then
Firstly, you can factor the x out
Yielding x * (3cosx - a) = 0, right?
vast fossil
Okay, so you got that x = 0 is always a solution, right?
spring shard
yes
vast fossil
So, since we want this equation to have only one solution
We are gonna need a to have a value such that cosx = a/3 has no solutions
For this you need to recall that cosx is generally some number between -1 and 1
spring shard
yes
vast fossil
-1 <= cosx <= 1
So, if a/3 would not be between -1 and 1
Then cosx = a/3 would be impossible, right?
spring shard
indeed
spring shard
I see
vast fossil
In the interval notation this can be written as
[
a \in (-\infty; -3)\cup(3; +\infty)
]
Or
[
a\in\mathbb{R}\ [-3; 3]
]
spring shard
I see
glossy valveBOT
A Lonely Bean
spring shard
But you get the point
Although what angles does cosine need to have when it only has one answer
spring shard
But you get the point
yup
spring shard
Although what angles does cosine need to have when it only has one answer
180 and 0 right?
vast fossil
Although what angles does cosine need to have when it only has one answer
Well we make sure that x = 0 is the only solution, so cosx = 1 I guess
fathom cairn
an algae culture is multiplying by 13.2 % per week. When will it have reached double its size?
fathom cairn
How do I find it with the log?
I assume the start value is for example 1000g and it has to double to 2000g
simple totem
can you express the population as a function of time?
fathom cairn
$log_a (2000)$
glossy valveBOT
Lupin
fathom cairn
can you express the population as a function of time?
I have to find the time
fathom cairn
Actually not
simple totem
so as to find the time that makes the population double
fathom cairn
I would write it down like this:
f(x)= 1000 * 1.132^n = 2000
simple totem
$f(t) = P_0 \cdot 1.132^t$
glossy valveBOT
maximo
simple totem
where P_0 is the starting population
fathom cairn
1000
simple totem
are you told it’s 1000?
simple totem
we don’t need the 1000 either way
we can just solve for f(t) = 2P_0
so P_0 * (1.132)^t = 2P_0
can you solve for t from here
fathom cairn
so P_0 * (1.132)^t = 2P_0
just divide by P_0 and then you have to do something to solve the brace
fathom cairn
yes
simple totem
$1.132^t = 2$
glossy valveBOT
maximo
simple totem
what can you do from here?
fathom cairn
Log
simple totem
what base do you want to use?
fathom cairn
$log_{1.132} (2)$
glossy valveBOT
Lupin
fathom cairn
To find t
simple totem
yes
simple totem
no
because P_0 would be 1000
so you’d have 1000 * 1.132^t = 2000
the P_0 is on both sides
glossy valveBOT
maximo
fathom cairn
so you’d have 1000 * 1.132^t = 2000
If you divide by 1000 it will be 2 again
fathom cairn
hmm In my memories I did it different. I knew how to solve it but I forgot
simple totem
well we are solving for t, and i can guarantee you this is how it goes
fathom cairn
well we are solving for t, and i can guarantee you this is how it goes
Hmm
okey thanks
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prisma cloak
a tomato is 900 dollars, I have 350 dollars, if I get 1 dollar every 5 seconds how many seconds will it take for me to buy a tomato?
runic bloom
are you really an undergrad?
prisma cloak
its just a little riddle
torn jolt
a tomato is 900 dollars, I have 350 dollars, if I get 1 dollar every 5 seconds h...
its a simple linear function
you start with 350, so thats your y intercept
you get 1 dollar every 5 seconds, meaning every second u get u get 1/5 dollars
so you have 350 + 1/5 t = y, i think you can continue from here?
prisma cloak
sorry bro my brain is afk
torn jolt
sorry bro my brain is afk
you want to find when you have 900 dollars, meaning when y = 900
so 350 + 1/5 t = 900
Solve for t
prisma cloak
10 seconds = 2 dollars
60 seconds = 12 dollars
1 minute = 12 dollars
10 minutes = 120 dollars
100 minutes = 1200 dollars
75 minutes = 900 dollars
50 minutes = 600 dollars
so it will take around 45 minutes
simple totem
that is not the ideal way to solve this
short siren
prisma cloak
that is not the ideal way to solve this
I know but my brain is afk
earnest perch
I know but my brain is afk
look up how to solve first degree equations
prisma cloak
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blazing drum
okay I found this on the web
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hollow moth
could someone please help me prove gcd(ad,bd) = |d| gcd(a,b)
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could someone please help me prove gcd(ad,bd) = |d| gcd(a,b)
@hollow moth Has your question been resolved?
hollow moth
<@&286206848099549185>
nimble current
hint: ||let the gcd of a and b be c and a=mc, b=nc||
@hollow moth if u need another hint, let me know
hollow moth
hint: ||let the gcd of a and b be c and a=mc, b=nc||
why did you set a = mc and b = nc?
like what if a and b are both prime numbers?
nimble current
then, c=1 and a=m, b=n
hollow moth
oh okay
nimble current
you will also need to use the fact that ||gcd(m,n)=1 by the definition of gcd||