i watched it
#help-13
dire geode
So you should know this doesn't matter
Since x goes to 0, so does sin(x)
Their ratio goes to 1
random kelp
because of the squeeze theorem right
dire geode
Sure that's one way to prove it
random kelp
but you'd need to take the reciprocal for that
dire geode
It doesn't matter
random kelp
why
random kelp
so regardless of anything, x/sinx or sinx/x will always equal 1?
dire geode
so regardless of anything, x/sinx or sinx/x will always equal 1?
No
The limit part is important
dire geode
so regardless of anything, x/sinx or sinx/x will always equal 1?
So then don't leave it out
dire geode
sinx/x = 1
No
random kelp
when the limit is approaching 0
dire geode
What you're typing and what you're thinking are different things
random kelp
So then don't leave it out
what am I leaving out
random kelp
Their ratio goes to 1
i think ive understood what you've said
since they have the same resulting answer of 0
their ratio goes to 1 when x is approaching -3
but thats very strange because when you get to 0 they become 0/0
dire geode
but thats very strange because when you get to 0 they become 0/0
What's the limit as x goes to zero of x/x
random kelp
What's the limit as x goes to zero of x/x
1
dire geode
but thats very strange because when you get to 0 they become 0/0
Is this still weird to you
dire geode
but couldnt that apply to any trig function
No
random kelp
or x/tanx
dire geode
cos(0)=?
random kelp
1
dire geode
0/1=?
cedar kilnBOT
@random kelp Has your question been resolved?
crude scroll
cedar kilnBOT
crude scroll
I’m not sure if I set this bounds up correctly
The region is the circle centred at (0,1) and radius 1
nvm
the bound should be r=2sin theta
.close
crude lagoon
cedar kilnBOT
zenith igloo
how do i solve this?
stray vale
cedar kilnBOT
stray vale
Hi can anyone help me with sinsiodal functions
cedar kilnBOT
@stray vale Has your question been resolved?
dull oxide
Hi can anyone help me with sinsiodal functions
stray vale
<:JustAsk:371662163489718273>
one seconds please
I already have the solved but I have more questions
can you help me with the domain
@dull oxide Also if you can tell me what this is
equation of the sinusoidal axis
is it the middle line or is it the actual equation
cedar kilnBOT
@stray vale Has your question been resolved?
high kiln
can you help me with the domain
the domain would be the interval over which you're drawing this graph
so to be clear you're interested in the x values
high kiln
is it the middle line or is it the actual equation
I understand this as the equation of the line, but I could be misinterpreting it
stray vale
so to be clear you're interested in the x values
I know that but I dont exactly know what the values of x are
its a guessing game pretty much
high kiln
if this is the only picture you're given then it does seem a bit ambiguous yeah
they should have had a finer grid to make it clear
high kiln
I think anyways that the graph is starting halfway between 180 and 90 degrees, which would be what angle
stray vale
ya
high kiln
and then it looks like it's ending halfway between 180 and 270
stray vale
ok
high kiln
there's two ways of writing that so I'm not sure which you're more familiar with
stray vale
its all good i wrote them
high kiln
ok great
high kiln
I understand this as the equation of the line, but I could be misinterpreting it
what I thought earlier was this
high kiln
although you can also write the function of the graph itself with what's shown, so I'm not confident that's the right interpretation
stray vale
high kiln
ah I see they're definitely asking for the equation of the line then
stray vale
ok
high kiln
since these are horizontal lines they should be quite straightforward to find
stray vale
Ill tell you all the information I found for a
max=2 min=-2
there is one period that lasts 720 units
domain is 0,720
range -2,2
amplitude is 2
stray vale
since these are horizontal lines they should be quite straightforward to find
How do you find the equation
high kiln
How do you find the equation
what information do you need to write the equation of any line
high kiln
we only need the equation of the axis line, not the sinusoid itself
high kiln
yeah it's a little easier
stray vale
it says equation of the sinusoidal axis
thats why i though
we were looking for the equation
high kiln
given the context, they're asking for a lot of information you can just read off so I don't think it's the function itself (we would at least need the period first for example, but they ask you for it right after)
stray vale
ok
This is grade 11
so i dont think there are any trick questions
so i think everything is straight forward
high kiln
yep
high kiln
what information do you need to write the equation of any line
so ^, we're just interested in the normal equation for a line
high kiln
how do I get the equation of the line
it would help to start with a general form, and see what you can fill in
stray vale
ok
stray vale
it would help to start with a general form, and see what you can fill in
How can I start?
stray vale
ya
high kiln
m would be the slope, and c would be the y intercept
can you fill in values for these with what you see on the graph
stray vale
whats next
high kiln
yep
since the slope is always 0, you're left with
y = c
in general, so you can just read off the y intercepts
stray vale
ya
-1
- Sketch one cycle of a graph of a sinusoidal function that has the following key features, and identify the remaining key features.
a) maximum: 3,
b) period: $1080^\circ, range: -7 \leq y \leq 11$
Also what is the period
wraith daggerBOT
deviousglxy
high kiln
Also what is the period
as in what is the period? it's like the length in x after which the function repeats
high kiln
asin[k(x-c)]+d
for this question you're looking at using this you gave me earlier
stray vale
i think i wrote the period wrong
for 2a
i wrote
there is one period that lasts 720 units
stray vale
ok
high kiln
f(x)=sinx+2
that wouldn't be the right one
stray vale
no lol
high kiln
yeah brain fart :P
stray vale
It wont let me make an equation in desmos peacfully
high kiln
**deviousglxy**
it still isn't right for this
maximum in the range, got it
I guess they don't tell you enough information for a) tbh
high kiln
very annoying :/
I suppose how they're thinking of it is starting with a sin(x) and then transforming it as they specify
that's the only way I can see that being answerable
anyways
stray vale
only way
thats the problem with online school
there is always missing information
making it impossible to be accurate
high kiln
if what they mean is maximum and leave everything else, then sine normally gives outputs [-1, 1], but we want it to be from [ _, 3].
because it's a sine we can already say what that blank would be
stray vale
-3?
stray vale
ya
high kiln
I'd then also assume we have a period of 360 degrees
stray vale
Well I already solved a I gotta do b
high kiln
since sin(x) on its own does
high kiln
f(x)=sinx+2
you wouldn't get this for a)
high kiln
3a)
high kiln
it worked in desmos
oh yeah, you get a sine function from [1, 3] so I suppose that does meet the requirements actually
b) is well defined anyways
wraith daggerBOT
deviousglxy
stray vale
were gonna need restrictions
high kiln
here we have all the info we need
stray vale
we can make x start at 0 and end at 1080
yep
ill try to get a formula
nvm I got no clue how to get it
high kiln
asin[k(x-c)]+d
I usually approach these problems with a general formula like this first
since they explicitly say what you need to find
we've been given the period so we should be able to find k
stray vale
ok
high kiln
we've been given the range so d should also be quite straightforward
c doesn't really matter here since we're only interested in sketching one cycle, which could be at any x
and the only thing left to find then would be a
high kiln
yep
high kiln
yeah and solve that for k
wraith daggerBOT
deviousglxy
high kiln
I'd say the easiest way to sketch this would be with the period, but it also helps to be able to find the function to graph it directly
high kiln
yeah looks right
cedar kilnBOT
zenith stag
,calc 360-255
wraith daggerBOT
Result:
105
tropic oxide
are you asking for help on a subtraction problem? @midnight nova
also stick to one channel
ah, i see you refuse to communicate.
cedar kilnBOT
@midnight nova Has your question been resolved?
short blade
.close
cedar kilnBOT
hybrid wren
When an object is accelerating in one direction and then begins to deaccelerate the velocity is reversed or is moved in a negative force from its current direction. However, since this train initially has a negative velocity the "velocity would switch to positive" and with that also be moving in the "right" direction.
is this the correct thinking for this question?
lone ferry
why would the velocity swithc to positive?
have you learned velocity time graphs yet?
hybrid wren
doesnt it reverse with deaccelleration?
hybrid wren
have you learned velocity time graphs yet?
no
lone ferry
oh okay
lone ferry
doesnt it reverse with deaccelleration?
wait so waht do you think is teh direction of acceleration here
hybrid wren
its initial was negative
lone ferry
yes because the direction of the velocity was the same as teh acceleration (we can't actually know because the problem doesnt say if initially the train was moving at constant velocity, which if it were, the acceleration would be 0) but since the train is slowing down
hybrid wren
wait doesnt it say the train was moving with a negative velocity?
lone ferry
yes, but it doesnt say constant velocitty
so we can't really assume if there was acceleration initially or not
but since its decelerating, tehre's definitely acceleration
hybrid wren
so its positive right?
lone ferry
yes
fair geyser
yes, the acceleration is positive
what's the direction, and is it positive is the same question
looks like a catch, i had to check, apparently it's the same thing
hybrid wren
what's the direction, and is it positive is the same question
these all all kinda "catchy" lol
😦
hybrid wren
yes, the acceleration is positive
so is it because the original negative velocity?
fair geyser
yes because the train is moving to the left, you need to accelerate to the right to slow down
and they established that right is positive
hybrid wren
yeah thats kinda what i was thinking
so that means that my original statement was alright?
fair geyser
yeah sure
hybrid wren
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
fast mirage
Positive acceleration.
cedar kilnBOT
fast mirage
<@778942595963158579> Has your question been resolved?
I didn't have a question.
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
someone teach me inverse
slate lintel
$x = \frac{2y+3}{5y+4}$ solve for y
hint: start with cross multiplication or in some way clearing the denominator
wraith daggerBOT
Hayley
jovial ravine
https://www.desmos.com/calculator/yamksv0gd7?lang=de
Ive tried but im stuck, how to put together L l H h to create this line? 
I marked the values with paint.
austere hull
what's the question asking you?
jovial ravine
Im not great describingit, im gonna try
Im trying to make a function that contains L l H h
With
h=y at x=0
H=y at x=L*l
@austere hull Likely not well worded, do you roughly know what i mean :/?
austere hull
nope
jovial ravine
@austere hull How could i explain it better? :o
wraith daggerBOT
Akira
austere hull
jovial ravine
I dont xD its for a mod, not homework.
austere hull
wait do you mean like how to put the letters on the desmos or what
tropic oxide
well we'd still like to know what problem youre solving
like be it for a mod or otherwise
as is youve abstracted away too much of the detail
so we cant really get a grip on what it is you're doing yknow?
jovial ravine
wait do you mean like how to put the letters on the desmos or what
How to combine the letters to create this function.
Give me a moment to explain :o
jovial ravine
so we cant really get a grip on what it is you're doing yknow?
H = max speed
h = min speed
L = max stamina
L*l = point where stamina affects speed, so l=0.5 means at half the stamina bar
But i cant find a way to combine the values to create the function 
tropic oxide
ok hold on
so let me see if i've got this right
in this game you are modding, your player character (presumably) has a stamina bar.
jovial ravine
Yes
tropic oxide
you want to make it so that your character moves at different speeds depending on how high their stamina is.
jovial ravine
Yes, the values represent ingame settings i made.
tropic oxide
and the way you want to do that is this:
if the stamina is at or above some threshold percentage, the character moves at their max speed.
but if the stamina goes below the threshold, then the character's move speed decreases linearly, down to their min speed at zero stamina.
is that correct?
jovial ravine
Perfectly correct! 🥳
tropic oxide
right ok
makes perfect sense
double getMoveSpeed(double currentStamina, double maxStamina, double stamThresholdPercent, double minSpeed, double maxSpeed) {
// assume 0 <= stamina <= maxStamina and 0 < stamThresholdPercent < 1
double staminaThreshold = stamThresholdPercent * maxStamina; // stamina threshold
if (currentStamina >= staminaThreshold)
return maxSpeed; // stamina above threshold => move at max speed
// go from minSpeed at currentStamina = 0 to maxSpeed at currentStamina == staminaThreshold
double stamPctUnderThreshold = currentStamina/staminaThreshold ;
return minSpeed + (maxSpeed - minSpeed) * stamPctUnderThreshold;
}
something like this
bit wordy but i think this is in compliance with SOME style guides
jovial ravine
No i already have the code in place. 😅
I was just asking for the function.
tropic oxide
wait, you weren't trying to code this?
what is your goal exactly
are you documenting existing code or
confused at your goal here lmfao
jovial ravine
Just a short formula that does this. :o
jovial ravine
Yes
tropic oxide
right ok so you could've said that.
jovial ravine
https://www.desmos.com/calculator/yamksv0gd7?lang=de
Ive tried but im stuck, how...
<-
tropic oxide
youre gonna need to make a piecewise function here
with somewhat more descriptive names for things than you wrote
not ideal but i tried
jovial ravine
Just the one line would be enough :o
I have it as: if (x <= L*l) then
tropic oxide
Just the one line would be enough :o
no, it would not.
jovial ravine
> Just the one line would be enough :o
no, it would not.
Why? 🤔
tropic oxide
you have to explain what all of your variables mean if you want their meanings to be known to more than 1 person
you have not done that
i have
i wrote down the meanings of all the parameters i introduced
min speed, max speed, stamina cap, stamina threshold %, everything is labeled as expicitly as possible
jovial ravine
This (orange) also works, but it includes L*h which is something that i dont want for the green line.
tropic oxide
listen
do you really want to stick with this naming scheme you've got
or are you not even understanding what i'm getting at by getting all fired up about names
jovial ravine
do you _really_ want to stick with this naming scheme you've got
No i dont have to they can change.
if (stamina <= maxstamina*l) then {speed = (line function)} else {speed = maxspeed}
I just dont know the line function.
tropic oxide
if stamina <= maxstamina * thresholdPercent:
speed = minspeed + (maxspeed - minspeed) * stamina/(maxstamina * thresholdPercent)
else speed = maxspeed
but this is basically the code
which i sent earlier
and which you rejected
then you said you wanted to do this in desmos, so i did it in desmos for you
but you didn't like that either
i don't know what you want
jovial ravine
but you didn't like that either
It just looked extremly complicated and im used to simple line functions. Im sry i was just overwhelmed.
tropic oxide
this is what piecewise functions look like in desmos.
yours is most naturally given in exactly such a form
thin hedge
crimson sedge
(Opening again because i dont think i quite understood last time)
How many possible arrangements can you have of a ternary string of length ten where there are at least four 0's in any position, or 00 at the beginning
The following are examples of acceptable strings:
0021211211, 1211000011, 0000000000
tropic oxide
count the invalid ones and subtract from 3^10
crimson sedge
count the invalid ones and subtract from 3^10
right, so the invalid ones would be:
string with only one 0
string with only two 0's that are not in the first two positions
string with only three 0's that are not in the first two positions
so we can start with the first, if we assume one of the positions has the 0, we are left with 9 positions of which only 1 or 2 are possible
meaning 2^9 arrangements for the first
tropic oxide
i think you've missed some...
crimson sedge
oh you are right
tropic oxide
i think it is better to break it down like this:
- any of
11 12 21 22followed by one of:
-- no zeros
-- one zero
-- two zeros
-- three zeros - any of
01 10 02 20followed by one of:
-- no zeros
-- one zero
-- two zeros
crimson sedge
OH that's actually much smarter okay
hmmm wait do we multiply by 4 if we take, say, 11 for the first category?
to account for the three other numbers
Question, is this process less tedious than using inclusion-exclusion?
tropic oxide
Question, is this process less tedious than using inclusion-exclusion?
yes
crimson sedge
yes
Okay may I ask for what was wrong with my solution for this using inclusion-exclusion?
I did the following:
We can fix four positions of the 10 positions to have 6 remaining, to account for the at least 4 0's possibility, then we can use the product rule on the remaining 6 to get 3^6
We can do a similar process with the "00 at the beginning" to get 3^8
we can exclude 3^6
which leaves us with 3^8 + 3^6 -3^6 = 3^8
im guessing it is the first
i cannot just "fix" 4 random positions, can i
muted bear
How did you get the exclusion part?
tropic oxide
this feels slippery
muted bear
Very
tropic oxide
We can fix four positions of the 10 positions to have 6 remaining, to account for the at least 4 0's possibility, then we can use the product rule on the remaining 6 to get 3^6
that's if you have EXACTLY four zeros.
and 2^6 surely not 3^6...
muted bear
category A would be ?
category B would be?
tropic oxide
this is all slippery as fuck
muted bear
You have to be very careful when youre making assumptions in combinatorics
crimson sedge
category A would be ?
category B would be?
-no zeros:
we have '11' fixed, then 8 remaining positions which leaves us with 2^8 choices
one zero:
same process but we can fix 3 positions instead, 2^7
two zeros:
2^6
three zeros:
2^5
meaning ultimately:
4(2^8+2^7+2^6+2^5)
is this right?
for the first category
muted bear
Ohh at least four zeros
Oops
One sec
Why is 11 fixed though? Cant it be 22 or 12 or 21?
muted bear
Dont forget about the position of the zero as well
You have n remaining spaces
You have to choose k to be 0s
crimson sedge
ugh wait
i cant just fix a 0
because it can be any of them?
okay is 4*2^8 good to go for the no-zero case first of all?
crimson sedge
You have to choose k to be 0s
also, why choose k? dont we have to permute it?
like
the order does matter does it not
muted bear
okay is 4*2^8 good to go for the no-zero case first of all?
Yeah, its the same as 2^10, which is picking either 1 or 2
For all of them
You cannot fix the 0 when you start getting them
crimson sedge
okay understandable
crimson sedge
also, why choose k? dont we have to permute it?
hmm
i guess it doesn't matter because the 'ordering' of the positions themselves doesn't matter, you are just looking to see which takes what 0
okay so it would be $\binom 8 1$ ways
wraith daggerBOT
crimson sedge
but how do you connect that..
wait is it simply 4*(8 choose 1) for the second case
muted bear
No, you also have the other 7 nonzero slots
crimson sedge
No, you also have the other 7 nonzero slots
2^7 + 8 choose 1?
heh
no hmm
u would be multiplying it wouldnt you
muted bear
Yup
crimson sedge
i cant wrap my head around this totally
oh wait
its clicking
okay
okay
okay
hmmmmmmmmmmmmmmmmm
i seeeeeee
muted bear
So based on the way youre doing this, your two groups are mutually exclusive and dont need pie
muted bear
I actually think this might be kind of aime level bashing, but the pie solution is not much better
crimson sedge
[
3^{10} -\bracks{\vp{\int}4\parens{2^8 +2^7\binom 8 1 +2^6 \binom 8 2 + 2^5 \binom 8 3} + 4\parens{2^8 +2^7\binom 8 1 + 2^6 \binom 8 2}}
]
crimson sedge
I actually think this might be kind of aime level bashing, but the pie solution ...
aime level bashing,?
wraith daggerBOT
muted bear
aime combi questions are notorious for being really bashy and prone to mistakes
crimson sedge
thats understandabble
crimson sedge
is this fine you think?
muted bear
Yeah i think it looks fine
wraith daggerBOT
crimson sedge
oh yeah i guess there should be an extra factor in there
hmmmmmmmmmmmmm
fair enough
btw garlic, just for my own understanding, but if you were to explain the binomial theorem in an intuitive way, how would you put it?
muted bear
Iirc theres some weird gen func thing you can do, but im not experienced enough with gen funcs to remember
crimson sedge
i heard a lot of explanations but i am curious to heaar more 
untold torrent
is this the final answer u guys got
crimson sedge
yeah
untold torrent
what does it evaluate to?
untold torrent
well ig ill write it
crimson sedge
oh okay thank you 
untold torrent
,w 3^10 - (4 * (2^8 + 2^7 * 8 + 2^6 * (8 choose 2) + 2^5 * (8 choose 3)) + 4 * (2^8 + 2^7 * 8 + 2^6 * (8 choose 2)))
wraith daggerBOT
wraith daggerBOT
untold torrent
@muted bear so i've tried solving this for fun and I'm getting a different answer
would it be fine if you help me figure out where it's wrong
oh
i see what i did wrong
nevermind
just when I'm about to type it
muted bear
Oh aight
untold torrent
@crimson sedge for the binomial theorem, just try to write all of the parenthesis (a + b) multiplied next to each other
then, the question is, what coefficient do you get in front of the a^k term for example
to get a^k, you need to multiply exactly k a's together, and you have (n choose k) ways of choosing the parenthesis from which the a's will come from
each one of those possibilities contributes a coefficient of 1
then, the rest of the parenthesis (n-k of them) will have to contribute b's instead
crimson sedge
then, the question is, what coefficient do you get in front of the a^k term for ...
yeah sure
untold torrent
so u also get b^(n-k)
so in general its a^k * b^(n-k) * (n choose k)
and you do this for every possible power of a
crimson sedge
okay so like
for example
(a+b)^4 for now
let's say we want to know the coefficient of a^4
since we are multiplying all 4 a's together, then it is 4 choose 5
untold torrent
well there's only one way to get a^4, which is to choose a from each of the parenthesis
crimson sedge
4*
untold torrent
so its 1
muted bear
you have all ↙️
untold torrent
no
untold torrent
you have all ↙️
what
muted bear
Swining pendulum analogy
crimson sedge
well there's only one way to get a^4, which is to choose `a` from each of the pa...
okay sure, and to get a^3, you have to multiply 3 of the parantheses together
so i guess 4 choose 3
untold torrent
yes, but u also get some b's
u can't just ignore the one parenthesis leftover
if you don't to take an a from it, you have to take b
so (4 choose 3) * b is the coefficient of a^3
crimson sedge
u can't just ignore the one parenthesis leftover
hmm
untold torrent
its like FOIL
each combination of stuff in the parenthesis gives you a term in the sum
and we're asking how many ways are there to get a term of a^3
you'd have to choose 3 a, and 1 b
and there are (4 choose 3) ways of doing that
crimson sedge
0 b no?
crimson sedge
oh i see
untold torrent
anytime you multiply, you'll get that the number of a's and b's add up to n
thats important to understand
because u must multiply something from each parenthesis
so the total number of a's and b's that you multiply are n
muted bear
Lex ill make the binom video for you at some point
crimson sedge
anytime you multiply, you'll get that the number of `a`'s and `b`'s add up to n
okay thats actually what i am having hard time understanding. I get its simply FOIL, but why does this have to be the case?
untold torrent
hmm
crimson sedge
i guess i get the n choose k part of binom theorem
untold torrent
like
crimson sedge
but not the a^n b^n-k part
crimson sedge
Lex ill make the binom video for you at some point
oh thank you!
untold torrent
imagine you have
(a+b)(a+b)(a+b)(a+b)
and you only choose the 3 first a's
when you multiply those 3 a's, you're gonna get a term of a^3 in the first three parenthesis
(a^3 + ...)(a+b)
but u still have one more parenthesis leftover
its still being multiplied
so the a^3 is not yet a term in the final sum
untold torrent
think of it as expanding the first 2 parenthesis, and then multiplying that by another parenthesis, and so on
each time u do that u must be adding an a or b to each term
ok i gtg
crimson sedge
no worries
crimson sedge
each time u do that u must be adding an a or b to each term
oh wait
oh wait
so its like
for every multiplication you have to make a choice of which other paranthesis you are using?
okay wait
this actually kinda is making me understand
i will think more
thank you
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
fiery whale
$\text{Show that if a and b are real numbers and } a \neq 0 \text{, then there is a unique number r such that } ar + b = 0$
wraith daggerBOT
monkagoras
fiery whale
I have tried to transform this into a logical proposition
I got the following:
$\forall a \forall b (a \neq 0 \land \exists r (r \neq a \implies ar + b = 0)$
wraith daggerBOT
monkagoras
fiery whale
However when I tried to prove by using this expression as base I got something very weird
Is the expression I did equivalent to the original statement?
fiery whale
nothing in the original statement says that r is not a
It says that there is an unique r
crimson delta
thats a different statement
fiery whale
fiery whale
thats a different statement
How do I express this uniqueness in this case then?
crimson delta
one thing you could write is $\forall a \forall b (a\neq 0 \implies \exists ! r: ar+b=0)$
wraith daggerBOT
denascite
fiery whale
one thing you could write is $\forall a \forall b (a\neq 0 \implies \exists ! r:...
Yeah, but that doesn't help much when developing the expression to prove the statement
crimson delta
yeah it doesnt
not sure why you want to translate it into a logical expression in the first place
just solve the equation for r
fiery whale
not sure why you want to translate it into a logical expression in the first pla...
For practice
crimson delta
if you can solve for r then r has to be unique
lunar lynx
**monkagoras**
You can prove this using contradiction method, i guess.
fiery whale
Proving by case is not that good for practice
fiery whale
You can prove this using contradiction method, i guess.
I was proving by contradiction from the start using the expression I sent
however I cannot find a way to express that uniqueness correctly :despair:
crimson delta
nothing about this needs contradiction
you just need $ar_1 + b = a r_2 + b \implies r_1=r_2$
wraith daggerBOT
denascite
fiery whale
**denascite**
Oh, that's a good way to write it, that helps a lot, ty
lunar lynx
That's contradiction. Lol. That's what i was talking about.
You assume first that let's say there are two namely r1 and r2 and then you show that they have to be equal.
lunar lynx
**denascite**
This i mean.
crimson delta
thats not what contradiction is
fiery whale
That's contradiction. Lol. That's what i was talking about.
You assume first th...
I thought you were talking about negating the expression then showing that its equivalent to F
crimson delta
there is no contradiction in sight
lunar lynx
I thought you were talking about negating the expression then showing that its e...
No. I didn't mean that.
crimson delta
for contradiction you would first have to assume that r_1 and r_2 are different, then arrive at r_1=r_2 and there you have your contradiction
which is completely unnecessary
lunar lynx
there is no contradiction in sight
What about assuming the contradictory statement that there exist two such r namely r1 and r2 ?
lunar lynx
for contradiction you would first have to assume that r_1 and r_2 are different,...
If you assumed that they aren't different in your proof, what did you even prove then by writing ar1 +b = ar2 + b ?
crimson delta
I didnt make the assumption that they have to be different
I am just saying that r_1 and r_2 are both numbers satisfying this property. and then showing that they are equal
I am not assuming that I have two distinct numbers r_1 and r_2 satisfying this property
lunar lynx
Then you didn't prove anything.
You said that x = y
and ax +b = ay +b
Thus, x is unique. That doesn't make any sense.
crimson delta
I didnt say r_1=r_2 at the beginning
let r_1, r_2 be some numbers satisfying ar_1+b=ar_2+b
then r_1=r_2
lunar lynx
I am just saying that r_1 and r_2 are both numbers satisfying this property. and...
You said they are two different numbers. Right ?
according to law of trichotomy, they are either equal or unequal.
You said that they aren't not equal, what else is left then ?
crimson delta
no I am not saying they are different
I am not saying anything about the relationship of the two at the beginning of the proof
only at the end I conclude that they are equal
lunar lynx
no I am not saying they are different
You said that they are not different - which leaves the possibility that they are same. 😐
crimson delta
I didnt say at the beginning of the proof that they are not different
I didnt say anything about them at the beginning of the proof
leaving the possibility open for both to be the case
but then due to the proof I found out that the only possible case is that they are equal
feral juniper
I am given these 4 vectors and I am supposed to find the Coordinates of v in the Basis B=(b_1,b_2,b_3) I already know that B is a basis of R^3 some help would be appreciated
feral juniper
do I just put b_1,b_2,b_3 in a matrix B and calculate Bv?
feral juniper
so I can write it a matrix and do the gaussian alogrithm?
crimson delta
yes
spice kraken
you can also do B^-1 * v
crimson delta
for that you would have to calculate B^-1. which is harder than solving the system
feral juniper
why does that work, let v be the given vector and w be the vector that represents v in Basis b
feral juniper
you can also do B^-1 * v
^
crimson delta
if w are the coordinates then Bw=v
w=(a1, a2, a3) with the notation from earlier
so w = B^-1 v
hazy flicker
Hello! Could somebody maybe help walk me through this?.. I have a couple questions
hazy flicker
so like, if BOTH the bounds are infinite, how do you set it up?
crimson sedge
[
\int_{-\infty}^\infty \map f x \dd x = \int_{-\infty}^a \map f x \dd x + \int_{a}^\infty \map f x \dd x
]
wraith daggerBOT
crimson sedge
Hello! Could somebody maybe help walk me through this?.. I have a couple questio...
Also start by finding the antiderivative for that
cedar kilnBOT
@hazy flicker Has your question been resolved?
indigo magnet
@hazy flicker close this Channel if you finished
hazy flicker
@crimson sedge @indigo magnet okay so what about this example :
like since one of them are zero how does it work instead
I think it is continious on the bound?..
so I guess it's like a normal one hold up
feral juniper
Let U be a linear Subspace of R^n how do I find a Matrix A over R such that
U = Ker(A)
feral juniper
Also U is given by the span of 2 vectors
tropic oxide
what's n
tropic oxide
hm
i mean ok like
you could find as many vectors orthogonal to U as it would take to extend a basis of U to one of R^n
and then just package these orthogonal vectors as rows into a matrix
feral juniper
so let u_1 , u_2 be the span of U
then I want to find
?
this a matrix is A, when v1 and v2 are orthogonal
tropic oxide
yeah but your u_i don't go in it
feral juniper
you could find as many vectors orthogonal to U as it would take to extend a basi...
also I am not given a Inner product space
so I cant use that
tropic oxide
why would that work?
i mean the kernel of a m × n matrix lives in R^n so
why not
also I am not given a Inner product space
so I cant use that
can you show exactly what you ARE given then
tropic oxide
i don't see anything that explicitly forbids referring to dot products in some capacity.
feral juniper
we had not defined the inner product at that point
tropic oxide
ok so then you could have said "we don't have access to inner products at all"
ugh this is gonna be annoying as all hell to write out
feral juniper
as far as I remember this was just an annoying calculation
crimson delta
I mean you dont have to use the words dot product and orthogonal
but the calculation is the same anyway, no?
feral juniper
actually yeah ig
cedar kilnBOT
@feral juniper Has your question been resolved?
topaz sleet
cedar kilnBOT
topaz sleet
I dont understand how to calculate the length of the shadow
cedar kilnBOT
@topaz sleet Has your question been resolved?
halcyon adder
What does divergent mean
cedar kilnBOT
What does divergent mean
long arrow
area under the curve cotgx on the interval 0 <= x <= pi/2 isn't finite
aka improper integral does not converge
halcyon adder
area under the curve cotgx on the interval 0 <= x <= pi/2 isn't finite
Why is it not
Because power -inf is 0, no?
long arrow
because result of the integral isn't finite (result of the limit is inf)
you can imagine cot(x) graph
x = 0 is an asymptote
if x tends to 0 from the right side we have that cot(x) tends to +inf
halcyon adder
Gottcha
Read that wrong
So you mean to say that if an integral is not finite it is divergent
slim crown
I got the integral given at the bottom and when evaluating it I got 9/2, and im not sure why its incorrect
slim crown
I got 1/3(-2x/3 + 2)^3 + x^2(-2x/3 + 2) then integrated again with respect to x
dawn junco
,w integrate 1/3(-2x/3 + 2)^3 + x^2(-2x/3 + 2) between 0 and 3
wraith daggerBOT
serene bison
how do i get this wrong?
cedar kilnBOT
how do i get this wrong?
serene bison
I found the height of the triangle, i know that using pythagorean theorem, 4^2+x^2=10^2
height = 9.16515138991
(1/2) 32*9.16515138991
and then add the base which is 8^2
which i get 210.64~
cerulean star
I found the height of the triangle, i know that using pythagorean theorem, 4^2+x...
You used the wrong numbers
Finish this
top figure is the top-down view projected against the ground plane.
bottom figure is a right triangle which stands up from the ground plane. y is the height.
oh
but I don't think you need the height y here
let y be the height of the triangle face, not the pyramid
then
4^2 + y^2 = 100, as you said
serene bison
i re did it and it said my answer was correct
i just did the same thing but didnt add the base
cerulean star
cool
serene bison
because it talks about the top of the pyrmid
cerulean star
good job
serene bison
.close
cedar kilnBOT
serene bison
.reopen
cedar kilnBOT
✅
serene bison
well
i wanna calculate it first and see if its right
but i dont want to this to close
(its a different problem)
204.1?
i found the slant height which was 13
5^2+12^2=13^2
wraith daggerBOT
.disorganized
cerulean star
so what's the problem?
serene bison
i use pi R l
serene bison
**.disorganized**
i dont really know what this means
wraith daggerBOT
.disorganized
cerulean star
surface area
oh...
they are including the base.
get rid of interior r
then like you said
it's pi*r*l
serene bison
umm
cerulean star
SCOTLAND FOREVERRRR (sorry I couldn't resist)
who the hell even said that
cedar kilnBOT
cerulean star
i guess im done here
um, you're welcome, I guess?
violet night
it's a reference in exactly one movie
This clip is goated https://www.youtube.com/watch?v=AVKR_kQnUR8
edit
whatever
cedar kilnBOT
Available help channel!
rancid surge
this is my work below;
n(s)=(10C1)(9C8)(2C1)
n(e)=(9C1).1.1.1
P=n(e)/n(s)=1/20
cedar kilnBOT
@rancid surge Has your question been resolved?
rancid surge
.close
cedar kilnBOT
rancid surge
this is my work below;
n(s)=(10C1)(9C8)(2C1)
n(e)=(9C1).1.1.1
P=n(e)/n(s)=1/20
.close
cedar kilnBOT
Available help channel!
uncut steeple
cedar kilnBOT
uncut steeple
Does anyone know how I can solve this question?
nova geyser
Use Power of Point
uncut steeple
Use Power of Point
???
frail fern
can someone please help me to find the area of the shaded portion using integration?
ancient valley
can someone please help me to find the area of the shaded portion using integrat...
woven flare
???
The power of a point theoreom has three parts, but the one that's relevant right now states that:
TS x RS = VS x WS
uncut steeple
Oh ok thanks
nova geyser
can someone please help me to find the area of the shaded portion using integrat...
bro this section is taken
uncut steeple
The power of a point theoreom has three parts, but the one that's relevant right...
Quick question
VS and WS are equal right?
woven flare
yeah, should be
nova geyser
VS and WS are equal right?
since it perpendicular we can say VS=WS
uncut steeple
I got 6 can you check is it right
uncut steeple
since it perpendicular we can say VS=WS
Ok thanks for confirmation
uncut steeple
I got 6 can you check is it right
Correct?
woven flare
yes
woven flare
sure
woven flare
well
uncut steeple
I have no idea about this one
nova geyser
I have no idea about this one
u can use a phytagorean theorehm
uncut steeple
I think ik what you mean but how do I get the full radius from that
woven flare
draw a diagram
uncut steeple
I did
woven flare
ok
uncut steeple
nova geyser
picture it
nova geyser
,w \sqrt{12^2*2}
uncut steeple
+2?
uncut steeple
Why plus 2
nova geyser
$a\sqrt{b}$
wraith daggerBOT
.ivmcs
nova geyser
Why plus 2
typo sorry
uncut steeple
Shouldn’t it be 12^2+12^2
nova geyser
Shouldn’t it be 12^2+12^2
u were correct
wraith daggerBOT
uncut steeple
Oh shoot yea
nova geyser
,w \sqrt{12^2*12^2}
plus it
uncut steeple
Ohhh
nova geyser
,w \sqrt{12^2+12^2}
wraith daggerBOT
uncut steeple
Ok where do I go from here
nova geyser
$12\sqrt{2}$
wraith daggerBOT
.ivmcs
uncut steeple
Oh wait that is the radius
woven flare
yes
uncut steeple
Damn
uncut steeple
Ye
This is 110 right
Or 250?
Please let me k ow which one of either cause it’s one of them
nova geyser
This is 110 right
how much is 1 circle have
uncut steeple
360
uncut steeple
Yea
nova geyser
RTS=360-70
uncut steeple
290
uncut steeple
You are crazy….
Can you stay on here cause I might have a few more small questions like these I need help in
nova geyser
cuz i have dif usage of that in myyy country
nova geyser
Can you stay on here cause I might have a few more small questions like these I ...
sure
uncut steeple
Thanks
nova geyser
I’ve drawn this
good
nova geyser
So where do I go from here
I am not sure because we have dif type of usage of symbol at math
nova geyser
nvm i know
uncut steeple
Oh ok how?
uncut steeple
nvm i know
??
uncut steeple
Is this 68?
uncut steeple
i am not sure lol
It’s fine lol I will look at it later
nova geyser
You not sure about this one whether <@855021191295533067> ?
i am bad at arc lol
cuz i studied math olympiad not school math question sorry
uncut steeple
Ok all good
This?
This one I’m not sure about at all
Yes, no?
<@&286206848099549185>
lone ferry
try drawing diagram
uncut steeple
Thank you your always saving me
uncut steeple
try drawing diagram
For which one v
uncut steeple
I need help with this @lone ferry
uncut steeple
I’ve drawn this
This being the diagram
lone ferry
try to draw diagram for this
uncut steeple
Ok, but can you explain the question is just replied to?
lone ferry
I’ve drawn this
what arc corresponds to angle D
uncut steeple
It’s confusing me
lone ferry
I’ve drawn this
draw this again but erase AB and Bc
lone ferry
yes
uncut steeple
So 2x+15=5x
lone ferry
(5x)/2
uncut steeple
Oh cause it’s an inscribed angle?
lone ferry
yes
uncut steeple
Ok answer is 75 thanks so much
lone ferry
ofc
uncut steeple
try to draw diagram for this
Ok I’m going to draw this now
Ok I. Drew it
How do I find radius though I don’t know EF
???
lone ferry
u drew the diagram wrong
uncut steeple
I did?
lone ferry
line EF is tangent to the circle at point E
lone ferry
yes
lone ferry
✅✅✅
uncut steeple
Wait mb that was bad question
Like sr would be half of 105?
Or not is the answer 150?
Mb for so many question I only have two short ones after this
uncut steeple
Or not is the answer 150?
I think it is right?
@lone ferry ????
Or it’s 255 🤦♂️
Idk
lone ferry
send ur work
uncut steeple
I have no work