and how you can replace those to get what you want
#help-36
desert mantle
grim nebula
@trail mango its the fibonacci generating function
grim nebula
its possibly clearer if you do x instead of 1/10
thin jay
i kiiiiinda see that c is constant so summing it and multiplying it should be the same
grim nebula
,, S(x) = \sum_{n = 0}^\infty F_n x^n
soft zealotBOT
rugged merlin
i kiiiiinda see that c is constant so summing it and multiplying it should be th...
Yeah like denascite said its as if you are dealing with a regular sum
So like 1 + 2 + 3 -> 2(1 + 2 +3) = 2*1 + 2*2 + 2*3
rugged merlin
i get that!!!!
Yep
thin jay
but like
rugged merlin
So 2(1+2+3) is like the LHS here and 2*1 + 2*2 + 2*3 is like the RHS here
thin jay
i dont understand why the person who did the reddid thingy added 2 extra terms shifted by 10x of the same number
because like
shouldnt F (to the subscript n) be always the same for the same n?
and why do the n change later ???
rugged merlin
shouldnt `F` (to the subscript `n`) be always the same for the same `n`?
Oh no not reallt
thin jay
what
rugged merlin
,, \sum_{k=c}^n a_k = \sum_{k=c\0o{-m}}^{n\0o{-m}} a_{k\0b{+m}}
soft zealotBOT
rugged merlin
You can do this
rugged merlin
😅
grim nebula
,, \sum_{n = 0}^\infty F_{n + 2} = \sum_{n = 2}^\infty F_n
soft zealotBOT
thin jay
ohhhhh
i see
kinda
why does the upper bound (infinine or k) need to be subtracter by 2?
in this case
i see how i can move the +2 to the bottom
grim nebula
in your case it doesn't matter because the sum is infinite
,, \sum_{n = 0}^{100} F_{n + 2} = \sum_{n = 2}^{102} F_n
rugged merlin
Cuz if you dont you'd be adding more terms than originally, in the finite case
grim nebula
theyre both F_2 + F_3 + ... + F_102
soft zealotBOT
thin jay
its like if you opened a window and you just shifted it
grim nebula
,align S(x) & = \sum_{n = 0}^\infty F_n x^n \
\sum_{n = 0}^\infty F_{n + 2} x^n & = \sum_{n = 0}^\infty (F_{n + 1} + F_n) x^n \
& = \sum_{n = 0}^\infty F_{n + 1} x^n + \sum_{n = 0}^\infty F_n x^n \
\sum_{n = 0}^\infty \f {F_{n + 2} x^{n + 2}} {x^2} & = \sum_{n = 0}^\infty \f {F_{n + 1} x^{n + 1}} x + \sum_{n = 0}^\infty F_n x^n \
\sum_{n = 2}^\infty \f {F_n x^n} {x^2} & = \sum_{n = 1}^\infty \f {F_n x^n} x + \sum_{n = 0}^\infty F_n x^n \
\f {\ds\sum_{n = 0}^\infty F_n x^n - F_0 - F_1 x} {x^2} & = \f {\ds\sum_{n = 0}^\infty F_n x^n - F_0} x + \sum_{n = 0}^\infty F_n x^n \
\f {S(x) - 1 - x} {x^2} & = \f {S(x) - 1} x + S(x)
thin jay
,align S(x) & = \sum_{n = 0}^\infty F_n x^n \\
\sum_{n = 0}^\infty F_{n + 2} x^n...
in the second line, how do you sum 2 to the bottom n on F without modyfing the "starting" n?
grim nebula
wdym
the second line is just a true statement
F_n+2 = F_n+1 + F_n
so the LHS = the RHS
thin jay
i suppose thats only true for the fib sequence because its defined as F_n = F_n-1 + F_n-2 right?
soft zealotBOT
grim nebula
i suppose thats only true for the fib sequence because its defined as `F_n = F_n...
yes
grim nebula
sum (a+b) = sum a + sum b
rugged merlin
I think you just need to freshen up on your sum manipulation
thin jay
I think you just need to freshen up on your sum manipulation
i never had sum manupulation 😭
grim nebula
blud copied the google metadata
rugged merlin
Just read that
thin jay
ima read and understand the sum manipulation thing first, and if i still dont get it ill open another one :p
rugged merlin
ima read and understand the sum manipulation thing first, and if i still dont ge...
Oki
final saddleBOT
rugged merlin
Np
final saddleBOT
Available help channel!
grizzled socket
In the cartesian plan graduated in meters, we illustrated the view of the top of the possible landing zone of a space probe. The vertices of this zone trapezoidal area correspond to the intersection points of a circle with 10 m of diameter and of the curve associated with a absolute value functon in which the equation is y = 3|x| - 9. Determine the area of the possible landing zone
final saddleBOT
In the cartesian plan graduated in meters, we illustrated the view of the top of...
grizzled socket
Idk how to start this
halcyon ether
Maybe by making a rough sketch?
night raft
Try assume the circle is centred at (0,0) and make an equation out of it
then find the intersection points of the circle and the absolute value function
but yeah a rough sketch is a good start
grizzled socket
It's been 4months since i did this notion so i kinda forgot
night raft
the equation for a circle?
grizzled socket
The absolute value function
night raft
do you know the definition of the absolute value function at least?
night raft
Cant be negative
Alright, if you know the graph |x| then 3|x| - 9 is just applying translations to it
ivory quartz
Question 4
When you roll two 6-sided standard dice, which of the following is the most likely to occur?
A. The sum of the two rolled numbers is a multiple of 5.
B. The sum of the two rolled numbers is a multiple of 3.
C. The sum of the two rolled numbers is a prime number.
D. The sum of the two rolled numbers is a multiple of 4.
E. The sum of the two rolled numbers is greater than 8.
I drew a sample space diagram to find every P(A) and just picked the one with the biggest x/36 which is C..
But I think drawing an entire sample space diagram in a fast-paced competition is rather tedious... Just wanted to know if there's a quicker way of solving this
final saddleBOT
Question 4
When you roll two 6-sided standard dice, which of the following is t...
halcyon ether
Question 4
When you roll two 6-sided standard dice, which of the following is t...
Drew a sample space? Can you show us
onyx peak
Question 4
When you roll two 6-sided standard dice, which of the following is t...
Just by looking at it, the most probable ones are prolly B and C.
Prime number is when the sum is 2,3,5,7,11
Multiple of 3 is when the sum is 3,6,9,12
12 cancels with 2, 3 cancels with 3 and you're left with 5, 7, 11 vs 6, 9 and at this point its not very hard to see that 5, 7, 11 wins, but you can compute the probabilities explicitly
if you're allowed to do this kind of heuristics, it takes like 30 secs
it's also important to know that the most probable sum is 7 and then the probability decreases linearly as you move further from 7
ivory quartz
Drew a sample space? Can you show us
smth like dis
onyx peak
smth like dis
you're writing wayyy to much stuff
you dont really need to write all the 5,3 stuff
you only need the sums
and if you look at it, the sums are same at diagonals
halcyon ether
Okay ig I don't have to draw a clearer one then
halcyon ether
and if you look at it, the sums are same at diagonals
What he said is right 
onyx peak
smth like dis
all you need is just this, you dont even need to continue after the 3 dots - spot the pattern and move on, no need to write it all out
All you need is to know how frequent each sum is
2 -> 1
3 -> 2
4 -> 3
...
7 -> 6
8 -> 5
...
12 -> 1
done
if you're in a competition, dont waste time by writing down all the bits that you can easily complete in your head
if its a very mechanical, obvious and predictable thing, thats a good sign that you probably dont need to write it all out
trail mango
amen
onyx peak
awomen layla
trail mango
ivory quartz
all you need is just this, you dont even need to continue after the 3 dots - spo...
icic... so list sums only... reduce as many symbols as you can... and compute most of it in your head
thx!
.close
final saddleBOT
final saddleBOT
Available help channel!
warm stream
next thorn
i see
true hinge
did **you** write those numbers on the figure?
This user is another channel, by mistake. We have been mostly talking in #help-27
next thorn
and i also now see that you're supposed to count the squares
halcyon ether
one of you shoould close it since it's still open
halcyon ether
Then tell them
true hinge
and i also now see that you're supposed to count the squares
Yes
south dirge
Then tell them
no hurry is there
next thorn
.close
final saddleBOT
next thorn
halcyon ether
no hurry is there
Yeah sure
true hinge
Alright.
south dirge
-# wait helpful can close?
halcyon ether
Yes
south dirge
-# i had no idea
next thorn
lmao
halcyon ether
Lmao
south dirge
<@1143796624393502721>
ty
final saddleBOT
Available help channel!
stable dew
what is the domain of
f(x)=xsqr/(1-xsqr)
final saddleBOT
what is the domain of
f(x)=xsqr/(1-xsqr)
rugged merlin
What is the domain of xsqr
onyx peak
Whats xsqr btw
stable dew
x^2
onyx peak
x^2?
stable dew
yeah
oh yeah f:R-{-1,1}-->A
we needa find A
i took f(x)=y
made quadratic
and took D>=0
stable dew
hmm?
R-[1,0]
oh wait it cant be zero caus of our domain
wait a sec
bruh i acdentally wrote doamin instead of range
:p
onyx peak
Even as the domain it looks wrong
stable dew
Even as the domain it looks wrong
?
south dirge
x can be 2 also
onyx peak
Its not the range either
south dirge
for domain, the only restriciting factor you need to see is that denomitr becomes 0
stable dew
for domain, the only restriciting factor you need to see is that denomitr become...
its just the domain that was given in the queston
i didnt find it
i needed to find A
onyx peak
But it looks more like the range. One of your endpoints is wrong and you should also think about the brackets ([
stable dew
But it looks more like the range. One of your endpoints is wrong and you should ...
yeah
i got that part
south dirge
Its fine lets do using y
stable dew
it can be 0 for x=0
south dirge
can you send your working so we can check?
south dirge
Bhai tu jee ka hai🥀
south dirge
sun na all this is fine but tune end mein kya kiya
stable dew
yeah bruh
just started 12th🥀
south dirge
y(y+1)>=0 tak theek hai
south dirge
yeah bruh
just started 12th🥀
-# oo 11th here
south dirge
Tune jo likha wo exact opposite hai
stable dew
huh?
south dirge
the range ke liye tune jo +-+ number line wala banay
stable dew
yeah
south dirge
usse toh -1,0 ke beech mein nahinho skta na
stable dew
yeah
stable dew
that why i excluded (1,0)
south dirge
that why i excluded (1,0)
*-1,0
south dirge
bro i thought you meant R is 1,0
south dirge
i put wrong bracket tho....
yeah
stable dew
bro i thought you meant R is 1,0
nah nah
south dirge
Acha phir toh sahi hai
south dirge
range is -inf,-1) U (0,inf)
stable dew
caus from quadratic it cant be equal to 0
south dirge
thats what u mean to say na
stable dew
range is -inf,-1) U (0,inf)
closed on -1
look at orginal f(x) and check if it can equal out critical points
south dirge
haan sry i meant ]
stable dew
kk no prob
stable dew
yeah
south dirge
2015 model🥀
south dirge
haan sry i meant ]
i copied the sqr bracket from google😭
stable dew
bro's cooked
really had to type "square bracket" in google and copy
south dirge
sed times
stable dew
@drowsy epoch wassup
drowsy epoch
hi
drowsy epoch
good n u
stable dew
-# hes busy thinking abt stars
nah hes busy being him
bru im think i just write every step now
that prolly the only way ima save myself
well ima go do sum more mistakes
cya later
.close
final saddleBOT
final saddleBOT
Available help channel!
mortal island
Getting back into it this morning, help me get through this?
final saddleBOT
Getting back into it this morning, help me get through this?
night raft
do you know log laws?
mortal island
Sort of
night raft
which one can you apply here
night raft
yep
night raft
no keep them there
mortal island
Do I foil it or just combine as normal?
night raft
wdym?
like expand it after you applied product rule
then yeah you can do that, keep them all as one bracket though
night raft
like after you do $\log_5 (3x-1)(4x-5)$
mortal island
So foil it????
soft zealotBOT
MxRgD
severe canyon
$\log_5{[(3x-1)(4x-5)]}$
mortal island
don't know what foil is
Idk it’s an acronym
soft zealotBOT
Alberto Z.
mortal island
I don’t remember what it means
severe canyon
**Alberto Z.**
I guess this is better
mortal island
But that’s how my teachers have always referred to it
severe canyon
I don’t remember what it means
Firsts, Outsides, Insides, Lasts
night raft
so yeah once you've done that, you can then apply this rule $\log_{a}b = x$ is the same as $a^x = b$
soft zealotBOT
MxRgD
night raft
i keep forgetting my \ 
night raft
12x^2 - 15x - 4x + 5 = 5^0
mortal island
Wait…why is it 5^0?
severe canyon
Right so how do I apply that- here
$$0 = \log_5{(?)}$$
soft zealotBOT
Alberto Z.
severe canyon
Or simply do 5^ both sides
mortal island
Ok-
Subtract 5 on both sides to get rid of that-
Square root to get rid of the square…?
modest badge
don't know what foil is
First Outside Inside Last, it's to remember to do multiply all necessary the terms when multiplying binomials
mortal island
Can I square root a negative….
modest badge
logarithms get really funky when you have roots of negatives in them
mortal island
I gotta get rid of this square somehow
night raft
Can I square root a negative….
That's how you get imaginary numbers
but I don't think the solution contains it
oh
it says no solution in one the options
mortal island
Oh is it just no solution?
night raft
yeah you can pick that
modest badge
i think you're doing the quadratic equation wrong
mortal island
It’s not a quadratic equation-
mortal island
Oh
night raft
,w solve 12x^2 - 15x - 4x + 5 = 1
soft zealotBOT
night raft
yeah so you should be getting real solutions
night raft
could you show your working out?
mortal island
night raft
,rccw
soft zealotBOT
mortal island
Ignore my horrid handwriting
modest badge
in the second to last step, you should add 5 to both sides to cancel the -5
mortal island
But the 5 isn’t negative
modest badge
ur right
mortal island
So adding would only make the 5 10
solar glade
Milo
night raft
do you know how to factor a quadratic?
solar glade
That's not how you are supposed to do
night raft
12x^2 - 19x + 4 is factorable
solar glade
You have to let 0 in one side, not -4
mortal island
That's not how you are supposed to do
No shit Sherlock id have an answer by now if it was 😭😭😭😭
solar glade
eitherway you won't be able to factor properly
modest badge
actually
mortal island
But I still wouldn’t have 0
solar glade
You better respect people here
mortal island
Because I have 5^0
mortal island
You better respect people here
Mb it was a joke twin
solar glade
But I still wouldn’t have 0
you will, if you subtract 1 to both sides
mortal island
Ok…?
modest badge
so left side = 0
0
mortal island
12x^2 -19x +4
solar glade
now factor that
mortal island
You can’t
solar glade
over reals
mortal island
19 is a prime number
solar glade
you can
mortal island
You can’t pull anything out of 19 besides 1 and 19
mortal island
????
modest badge
you have to use the quadratic formula to find the solutions
mortal island
None of this is in the example problem….
modest badge
can you share that one?
solar glade
Write -19x as -3x -16x
mortal island
What?????
solar glade
you will be able to factor like that easily
mortal island
????????
solar glade
12x^2 -3x -16x + 4
mortal island
You’re just confusing me
mortal island
12x^2 -3x -16x + 4
You can’t even factor that 😭😭😭😭😭
You can’t factor 4 by 3 or 3 by 4
solar glade
yes i can
you mean "you" don't know how to
you have to pay attention
instead of saying you can't
mortal island
I am bro tf
solar glade
when we are telling you that you indeed can
night raft
If you don't know how to then I'd advise you learn it or listen to arkimond explaining it
mortal island
I’m trying to but bro is confusing me
modest badge
None of this is in the example problem….
we are in this step right now, they just skipped the procedure
mortal island
There’s not a single thing you can pull out of all 4 of those numbers
solar glade
i literally only said rewrite -19x as -3x -16x
i don't think it's impossible to follow this step
mortal island
Ykw…I’m gonna put in a bs answer for this one and we can start over on a new problem
modest badge
factoring in this case is a little more complicated than just splitting a number into its multiples
mortal island
i can't help whoever doesn't want help
No I want help
But I’m lost on the step we’re on
So I’m saying- let’s start over on a new problem
From the beginning
Also the answer wolfram alpha gave was wrong- just sayin
modest badge
it means splitting the equation into chunks that can be rewritten
modest badge
we start the same as last time, combine the logarithms using the product rule
mortal island
Ok
That got me log_5 (12x^2 + 21x + 8x +14) which I then condensed into log_5 (12x^2 + 29x +14)
modest badge
correct. once that is done, you can write 5^LHS = 5^RHS, this will cancel out the logarithm
modest badge
we agree
mortal island
Ok now what
modest badge
now you subtract 25 from both sides, you want an expression that is = 0
modest badge
if you have some intuition with factoring quadratic trinomials into a product of binomials, you can do that
modest badge
then the quadratic formula is the best way
modest badge
it's arbitrary, but just remember them once you choose which is which
or wait+
what values do you mean?
the a, b, c?
mortal island
For the quadratic formula…
modest badge
it does matter
mortal island
Oh ok
modest badge
in this case, a = 12, b = 29, c = -11
mortal island
That’s why I was gonna do anyways
Do I need to keep the x’s and such- or just the numeric value
modest badge
just the numeric value
modest badge
you got the values?
modest badge
ok, now you should simplify the expression
modest badge
yes
modest badge
all correct
honestly i don't think there's an issue with using a calculator for that root
mortal island
What do I do w the -29…and….that fraction is really ugly
modest badge
unless calculators are completely forbidden
mortal island
Root first or division first-
modest badge
root first
mortal island
I’m not sure but I also don’t think that’s how they were taught to do it
I missed this whole group of lessons completely
The calculators were allowed to use…I’m not sure they can do this-
modest badge
can your calculators take the square root is a number?
once you do that, the fraction becomes much easier
modest badge
yes, now you do the addition / subtraction first, then the division
you'll get two different numbers
modest badge
why not?
mortal island
My phone calculator won’t put it in fraction form
I’m like barely functioning rn I can’t…remember what it is
modest badge
then simplify them manually on paper
modest badge
ok, i can help you with that. you'll get -66/24 and 8/24
mortal island
Yes
modest badge
which, whn simplified, give -11/4 and 1/3
modest badge
which, whn simplified, give -11/4 and 1/3
-11/4*
modest badge
But it can only be positive right?
yes, the value inside a logarithm can only be a postive number
mortal island
So….only 1/3?
modest badge
not necessarily, you need to try both in the original expression
just for thoroughness' sake
mortal island
(I have 2 attempts I’m not rly gonna risk it if it’s wrong it’s wrong I pick no solution)
(As long as the assignment is done)
Alright new problem- slightly more complex
modest badge
my bad, i wrote too hastily
mortal island
Ur good
modest badge
use the quotient rule in that case
mortal island
So literally just….. log_2 (2x^2 +2 / 3x +1)
modest badge
yes
mortal island
Right…what’s the next step here?
modest badge
no, there's an easier way
multiply both sides my 3x+1 to cancel out the denominator of the LHS
you get 2x^2 + 2 = 3x + 1
mortal island
Wouldn’t you have to foil the bottom tho-
modest badge
(3x + 1) / (3x + 1) = 1
modest badge
yes
severe canyon
You definitely need to brush up the basics. This has nothing to do with log stuff.
Also you need to be very confident in solving second degree equations (aka quadratics)
modest badge
bro is tired, cut him some slack
mortal island
I was up until 4 am last night doing this homework that’s still not finished
modest badge
so, 2x^2 - 3x + 1 = 0
mortal island
Yes
modest badge
now, you can use the quadratic formula again, but this expression is smaller than last time, so i think we can try factoring it rn
mortal island
now, you can use the quadratic formula again, but this expression is smaller tha...
I’m open to trying
modest badge
so, we're looking for an expression of the form: (mx + p) * (nx + q) = ax^2 + bx + c
in this case, a = 2, b = -3, c = 1
severe canyon
<@&268886789983436800>
mortal island
<@&268886789983436800>
modest badge
<@&268886789983436800>
mortal island
Twin
modest badge
let's proceed
modest badge
now, if we do FOIL of RHS, we get (mn)x^2 + (mq + np)x + pq
modest badge
Where does (mx + p) * (nx + q) come from?
it's just a general expression for a multiplication of two binomials
modest badge
yes
mortal island
Ok
modest badge
now, we match the terms on the RHS and LHS according to the degree of x they mulitply
mortal island
So is it….. (2x [other part]) * (2x [other part])
severe canyon
Nope, otherwise you would get 4x²
modest badge
no, in this case we split it into 2 and 1
mortal island
Ohhhh
mortal island
(mn)x^2 + (mq + np)x + pq = 2x^2 - 3x + 1
English please 😭😭😭😭
severe canyon
It is quadratic equation basics 
you should be very familiar with that
mortal island
It’s a joke 🥲
modest badge
so, we're looking for an expression of the form: (mx + p) * (nx + q) = ax^2 + bx...
i'm rewriting this
we multiplied the LHS, and have the expression we're trying to factor on the RHS
now, the x^2 term has mn in the LHS and 2 in the RHS, so mn = 2
mortal island
Yes
modest badge
so, we write m in terms of n, m = 2/n
mortal island
….idk if I follow
mortal island
Right
mortal island
Right
modest badge
now, for the term with x, mq + np = -3
mortal island
So…should we break the -3 up into 2 terms?
modest badge
let's do something else first
mortal island
Ok ok
modest badge
let's focus first on mn = 2 and pq = 1
modest badge
yeah to be honest, in usually just stick to the quadratic formula
once you use it a lot you learn to love it like family
mortal island
Yeah it’s kinda muscle memory
modest badge
but you mentioned you don't think your class did it that way, so i'm explaining the other approach
mortal island
I like clean cut concise- can use it over and over again and nothing changes
mortal island
but you mentioned you don't think your class did it that way, so i'm explaining ...
Honestly I have no clue what they did
She might’ve let them break out the good calculators for it
I know they said they got to use them at some point-
modest badge
for now, we know that mn = 2
mortal island
Yes
modest badge
let us split the 2 into 1*2
and say that m = 1, n = 2
we're just making an educated guess and seeing if it gets us somewhere
modest badge
now, for the term with x, mq + np = -3
so, now this becomes q + 2p = -3
but we also know that pq = 1
so we'e looking for two numbers that multiplied give us 1, but when q + 2p = -3
modest badge
no
modest badge
exactly
(actually, you can get an infinity of values like 5 and 1/5, but in this case the answer IS -1 and -1)
mortal island
Ohhhh
modest badge
so, m = 1, n = 2, p = -1, q = -1
modest badge
(mn)x^2 + (mq + np)x + pq = 2x^2 - 3x + 1
ALL THIS TO SAY
2x^2 - 3x + 1 = (x - 1) * (2x - 1)
that is how you factorize it
modest badge
so, (x - 1) * (2x - 1) = 0
now, we did all this because, if you are multiplying 2 values and the result is 0
that means that either 1 or both is 0 too
mortal island
Right….
modest badge
so we get two possibilities, x - 1 = 0
and 2x - 1 = 0
so now we solve for x in each of the cases
mortal island
So x=1 and x= 1/2
mortal island
It took the answers 🙏
modest badge
now you put them into the logarithm and confirm the inside is positiv
but since rn you're just adding positive numbers, it works as is
modest badge
cheers
mortal island
Look good so far?
Wait is the 19 out in front of the quadratic positive or negative
Because it’s negative in the problem but if you make a negative…negative- it becomes positive
does it matter either way?
final saddleBOT
@mortal island Has your question been resolved?
mortal island
THESE ANSWERS CAN ONLY BE POSITIVE RIGHT???????
modest badge
sorry, i went to the restroom and forgot i was here
modest badge
Because it’s negative in the problem but if you make a negative…negative- it bec...
yes, the 19 in front becomes positive
mortal island
Ok ok ok
tender nacelle
Howd i get such a big ln thingy. It should be 5/12
final saddleBOT
Howd i get such a big ln thingy. It should be 5/12
@tender nacelle Has your question been resolved?
final saddleBOT
quick delta
o
final saddleBOT
Available help channel!
late gazelle
how do you go about graphing letters using functions ?
final saddleBOT
how do you go about graphing letters using functions ?
lofty goblet
what does this mean
whole halo
go to the desmos unofficial discord for Big Suggestions
lofty goblet
do you mean actual letters of the alphabet
late gazelle
do you mean actual letters of the alphabet
or shapes and stuff in general yea
whole halo
are you using desmos to graph these shapes?
late gazelle
yea
whole halo
go to the desmos unofficial discord for Big Suggestions
they can show you some basics to doing this I think
lofty goblet
you could probably do them with the most basic equations
like linears and quadratics and maybe circle for letter O
late gazelle
what about more interesting ones like the greek alphabet
because those are more irregular
would i import a picture of it in desmos, and then trial and error until i can "cover" it
whole halo
its just a differently shaped letter, you dont need to overlay a reference picture
you can just bring one up then refer to it
I imagine youre not going for anything hard or fancy, just lines and circles maybe
try making sure you can draw lines and circles that start/end where you want them
final saddleBOT
whole halo
np
final saddleBOT
Available help channel!
dim gyro
When doing Sinx = sqrt(1-cos^2x)
final saddleBOT
When doing Sinx = sqrt(1-cos^2x)
dim gyro
Do you always do a positive square root?
Since it’s meant to be plus or minus right, how do you decide?
sonic crystal
When doing Sinx = sqrt(1-cos^2x)
what r u trying to do here?
formal trail
square root is always positive
formal trail
a better way to phrase it imo would be to say |sin(x)| = sqrt(1-cos^2(x))
and then determine the sign based on quadrant
dim gyro
So it depends on the angle of x?
formal trail
yes
dim gyro
So it’s not always positive then?
formal trail
sin(x) can be either positive or negative depending on what x is, yes
the most intuitive way imo is to draw the angle on the unit circle and see if it ends up with a positive or negative y-coordinate
dim gyro
Oh you mean like -sinx = sqrt ect
So you multply both sides by -1
But the actual root is always taken to be positive
Depending on quadrant
formal trail
the notation of square root is always used to mean positive
you can do sin(x) = +sqrt(...) or sin(x) = -sqrt(...) as appropriate
dim gyro
So for example
If x was inbetween 90 and 180
Sin would equal the negative sqrt ect
Since sin is plus in that quadrant and cos is negative?
formal trail
you said that sin is positive, so why would you add a - sign?
dim gyro
Because cos is negative at that range no?
Or is it just dependent on sin?
So only 180 to 360
formal trail
we're saying sin(x) = ... so the thing on the right side had better match the sign of sin
formal trail
yes
final saddleBOT
final saddleBOT
Available help channel!
crystal lion
just wanted to make sure that i got this right:
As t tends to infinity:
arctan(t) tends to pi/2
arctan(-t) tends to -pi/2
arctan(t^-1) tends to 0
?
final saddleBOT
just wanted to make sure that i got this right:
As t tends to infinity:
arctan(t...
rugged merlin
just wanted to make sure that i got this right:
As t tends to infinity:
arctan(t...
yes
crystal lion
thanks and does arctan(t^2) tend to pi/2 as well?
rugged merlin
thanks and does arctan(t^2) tend to pi/2 as well?
it is similar to arctan(t), so yes
crystal lion
kk thanksss!
rugged merlin
any arctan(t^n), n > 0, t -> infinity will be like that
crystal lion
.close
nimble basin
9^x - 4 • 3^x + 3 = 0
final saddleBOT
9^x - 4 • 3^x + 3 = 0
mossy chasm
lol
drifting idol
9^x - 4 • 3^x + 3 = 0
let y = 3^x, then y^2 - 4y + 3 = 0
timber leaf
Overthinking
timber leaf
Then factorization?
Yea solve quadratic
quasi rapids
Overthinking
this is why we LaTeX
timber leaf
this is why we LaTeX
nimble basin
I always stuck at q like these
nimble basin
If 3^x = 2 roots, can you use logs?
No I am in grade 10 logs are not in syllabus they r in 11
nimble basin
Where can I find more q like these
timber leaf
Textbooks
final saddleBOT
final saddleBOT
Available help channel!
mossy chasm
again, no idea what to even do, but its probably cauchy schwarz
final saddleBOT
again, no idea what to even do, but its probably cauchy schwarz
uneven idol
night raft
It probably is cauchy schwarz
mossy chasm
nvm might have accidentally found the solution after tweaking around even more
i love titu
should be M>155 right?
lime crest
220 positive integers which sum to 400 are arranged in a circle. Prove that there exists a string of integers along the circle which sum to $200$
final saddleBOT
220 positive integers which sum to 400 are arranged in a circle. Prove that ther...
soft zealotBOT
Copter
lime crest
i have no idea how to think of this problem
coarse monolith
-# then why respond gng
🥀
coarse monolith
zero point in typing this
🥀
south dirge
220 positive integers which sum to 400 are arranged in a circle. Prove that ther...
The integers can be same ?
As in repeated?
lime crest
if they were distinct then the sum would be way more than 400
south dirge
if they were distinct then the sum would be way more than 400
oh wait shoot yeah what am i thinking😭
quasi rapids
**Copter**
oh this is pigeonhole no
sturdy flax
<@&268886789983436800>
south dirge
<@&268886789983436800>
lime crest
oh this is pigeonhole no
yeah but im not sure how
quasi rapids
yeah but im not sure how
suppose x1, x2, ... x220 is our sequence of integers
let S1 = x1
S2 = x1 + x2
S3 = x1 + x2 + x3 and so on
||since xn is a positive integer, the sequence of sums is strictly increasing 1 <= S1 < S2 < ... < S220 = 400||
find the number of two sums that differ by exactly 200
as such you can just pigeonhole it
lime crest
hm
im kinda stupid
i get what youre trying to do tho
im just not suee how pigeonhole would work
quasi rapids
no its ok, you should find that there are exactly ||200|| pairs and since you have 220 sums and each of these sums must belong to one of the ||200|| pairs we found, this guarantees one pair must contain two of our sums
let the two sums in the same pair be Sm and Sn, st Sm - Sn = 200, can you rewrite Sm in terms of Sn and a bunch of other numbers?
lime crest
i suck at combi aaaa
quasi rapids
i suck at combi aaaa
i hate combi grinding it out was a pain
lime crest
no its ok, you should find that there are exactly ||200|| pairs and since you ha...
pairs of what?
quasi rapids
if you can rewrite Sm in terms of Sn and a bunch of other numbers and the other numbers are integer then we find the difference is exactly 200 which completes the proof
quasi rapids
pairs of what?
pairs of sums
severe verge
you have 220 numbers in that sum sequence which means there are at least 2 numbers in that sequence with the same remainder when divided by 200
lime crest
oh right that makes more sense
severe verge
and so their difference is divisible by 200
lime crest
since theyre distinct it must be = 200 since its bounded by 400
severe verge
i think you can finish from here
lime crest
since theyre distinct it must be = 200 since its bounded by 400
Si - Sj < 400 so Si - Sj = 200 and so there exists some sequence such that their sum is 200
quasi rapids
if you can rewrite Sm in terms of Sn and a bunch of other numbers and the other ...
||(in which case, m > n, $S_m = S_n + x_{n+1} + x_{n+2} + \dots + x_m$ and we see that the string of integers by definition sum to 200, thus completing the proof||
soft zealotBOT
wjs
severe verge
lol
lime crest
||(in which case, m > n, $S_m = S_n + x_{n+1} + x_{n+2} + \dots + x_m$ and we se...
i get Sm - Sn
lime crest
pairs of sums
why are their 200 pairs tho
quasi rapids
<@&268886789983436800>
severe verge
these bots
quasi rapids
why are their 200 pairs tho
{1, 201}
{2, 202}
{3, 203}
...
{200, 400}
lime crest
ohh
quasi rapids
{1, 201}
{2, 202}
{3, 203}
...
{200, 400}
is all possible integers from 1 to 400 that diff to 200
final saddleBOT
final saddleBOT
Available help channel!
north bison
i have an exam for a scholarship tomorrow arguably my most important exam soo far and i suck at math like as u can see in this photo i dont know anything from these questions.
final saddleBOT
i have an exam for a scholarship tomorrow arguably my most important exam soo fa...
cyan sandal
can you translate the questions
tired remnant
i need help with operatory combined
north bison
but im really bad at math cuz i dont pay attention
cyan sandal
ok have you started, or are you stuck on any particular step
wintry pier
i need help with operatory combined
pls open your own help channel.
north bison
ok have you started, or are you stuck on any particular step
I mean 13 kind of haunts me cuz its an easy question
tired remnant
someone here speak spanish
north bison
but i got it wrong and i dont rrally understand it
cyan sandal
I mean 13 kind of haunts me cuz its an easy question
i meant on the first one
but 13 is also fine
north bison
but 13 is also fine
i mean idk what do even do in the first one
cyan sandal
you can easily divide the fractions and find the sum
north bison
so like -2,256÷22,56=-0.1
cyan sandal
yes
cyan sandal
ok so
the first fracion equates to -0.1
second one is 10
-0.1 + 10 = 9.9
1 / 0.5 is the same as 1 * (2/1)
so 2
9.9-2 is 7.9
north bison
hm
Okay i understand the 13th thanks that wasnt hard
what about the one above it
12th
how does that work idk even how to start
cyan sandal
so you want to find the shaded region, which is a quarter of a circle cut out of a triangle
can you see that?
north bison
can you see that?
Wym
cyan sandal
like do you know what imean
north bison
the letters?
cyan sandal
no , the diagram
cyan sandal
yes, can you see that its 1/4 of a circle, cut out of a triangle
north bison
yea
cyan sandal
alright, so to find the shaded region you can find the area of the triangle and subtract the area of the arc
north bison
alright, so to find the shaded region you can find the area of the triangle and ...
arc?
cyan sandal
the sector of the circle
cyan sandal
you can ignore the letters honestly
north bison
Ok
cyan sandal
the formula for the area of a triangle is 1/2 * b * h
where b is 12, because 6+6, and the height is 6 (given)
1/2 * 12 * 6 = 36
cyan sandal
yes i know thats not the final answer
north bison
pi=3
cyan sandal
thats the area of the triangle
the area of a circle is pi * r ^2
if given r is 6, r^2 is 36, times pi which is 3 (given)
108 is the area of the circle, but since we only have 1/4 of it, we can times it by 1/4
, which is 27
36 - 27 = 9
north bison
wow
proper dagger
might wanna at least have the helpee do some of the calculation and reasoning themselves next time
north bison
might wanna at least have the helpee do *some* of the calculation and reasoning ...
nah its alr
i will understand both ways
anyways
proper dagger
no, that's for the helper, not you.
north bison
yea ik
cyan sandal
so do you understand how i got the answer
north bison
so do you understand how i got the answer
Yes
cyan sandal
alright next question
north bison
14
cyan sandal
alright thats fine, its the average of a sequence
north bison
value
cyan sandal
so say i have a sequence with 1 and 3, the average would be 2
north bison
so say i have a sequence with 1 and 3, the average would be 2
yea i understand that part
cyan sandal
the formula is the sum of the terms in the sequence, divided by the number of terms there are
so in my example it would be 1+3 / 2, which is 2
we can apply that to this
cyan sandal
because there are 6 terms in the sequence
so x is a term, 3 is one, 17 is also one e.t.c
north bison
Ohh yes
cyan sandal
(x + 3 + 17 + 27 + 23 + 29)/6 = 19
so your goal with this equation is to isolate x do you know how to do that
north bison
89÷6
cyan sandal
not quite, so you want to get rid of the fraction first
do you see how you can do that
north bison
no
cyan sandal
so if you ahve a fraction and yiu want to get rid of it, you can times both sides of the equation by the denominator
it works because you're doing the same thing to either side, so no change occurs
north bison
for example?
cyan sandal
in this case you would get x + 3 + 17 + 23 + 27 + 29 = 19*6
because 1/x * x is 1 because x/x is 1
north bison
okay
cyan sandal
so try to add the numbers on the left side and multiply on the right
north bison
so try to add the numbers on the left side and multiply on the right
Im way to stupid for that
cyan sandal
ill teach you a trick with this one
north bison
ill teach you a trick with this one
bet
cyan sandal
yeah and add them up
north bison
89
north bison
114
cyan sandal
yes
cyan sandal
so the equaton is x + 99 = 114
north bison
Amazing
north bison
i understood this one too yay
cyan sandal
last one
north bison
i have a feeling 15 is embarrasingly easy
cyan sandal
so let the "number" be x
youre given x/2 + 2x/3 = 21
what would be your first approach
north bison
umm
cyan sandal
so your goal is to add the fractions
north bison
3x/5?
cyan sandal
no, with addition you need a common denominator
north bison
6
cyan sandal
yes, and to get x/2 to something/6, what would you do
north bison
Idk add up x and 2
cyan sandal
ok so to get that to 6, you can multiply the denominator by what
north bison
2?
cyan sandal
2 * what = 6
north bison
6*2?
cyan sandal
in other words what is 6 divided by 2
north bison
also just one more clarification
cyan sandal
yep