I have 1 more question as well
#help-43
quartz yoke
urban kindle
sure
boreal girderBOT
quartz yoke
Lemme do this question
11/50?
Wow this is so ez
Thank you so much at @urban kindle 😭
urban kindle
npnp
quartz yoke
Like how do i write in a proper way in exam
urban kindle
haha no idea either
compact pewterBOT
cursive harbor
Like how do i write in a proper way in exam
Are you not using Bayes here
Just name the events A and B and write out the formula
That should be enough
quartz yoke
Uh
urban kindle
i dont think theyve been introduced to priors/posteriors yet...
that kinda is what we're doing here but intuitively?
quartz yoke
i dont think theyve been introduced to priors/posteriors yet...
Yes and what is that
cursive harbor
i dont think theyve been introduced to priors/posteriors yet...
Neither have I apparently, what is that
(it's possibly smth I know but I've never heard the terms)
urban kindle
https://en.wikipedia.org/wiki/Posterior_probability have fun with the rabbit hole!
cursive harbor
Oh okay that I know, didn't know it had a name
quartz yoke
.reopen
compact pewterBOT
✅
boreal girderBOT
quartz yoke
2 please
kind viper
this is a bit ambiguous
urban kindle
i think we can assume uniform dist :c
kind viper
it's not clear what we are supposed to count: is any mix of aces and kings OK, or do we want specifically all aces or all kings but no mixture?
cursive harbor
I assume the latter
kind viper
ok then there are exactly 2 favorable outcomes.
cursive harbor
Idk why they had to specify the parentheses at all
kind viper
i mean maybe this is a trick question where they fool you into taking one interpretation and then go SIKE and say it was the other all along
cursive harbor
Which makes it a bad question imo
quartz yoke
So far, all i worked in rd sharma, never felt anything this hard, tbh not even integrals except for the way to solve it
cursive harbor
What book is this one
cursive harbor
RD Sharma is usually better with wording
quartz yoke
Its actually an exemplar
ornate knoll
Im surprised u can do Rd
cursive harbor
There's three possible readings of this:
- 4 cards are a mixture of kings and aces
- 4 cards are either all kings or all aces
- 4 cards are all aces (and the kings is just mentioned there for some wild reason)
quartz yoke
I did 2 x 4/52 x 3/51 x 2/50 x 1/49
quartz yoke
To think ann has stepped in, i see smth fishy
ornate knoll
Add
urban kindle
I did 2 x 4/52 x 3/51 x 2/50 x 1/49
this is option 2
ornate knoll
I did this last year
cursive harbor
So you mean the second one in my message, Lizzie?
quartz yoke
Im surprised u can do Rd
Except for probability ig
ornate knoll
There's three possible readings of this:
1. 4 cards are a mixture of kings and a...
I dont get what ur saying im sry
quartz yoke
Ye dw, in no time i can low-mid diff this
ornate knoll
Lmao
cursive harbor
Im surprised u can do Rd
What shade is this lmao
ornate knoll
What shade is this lmao
Meaning?
cursive harbor
Why are you surprised that he can do rd
ornate knoll
I mean
Usually ncert and exemplar
Takes a lot of time
That u dont have time for rd
quartz yoke
Im focusing on concept building with medium pace
ornate knoll
Hmm yea I did trigo with Rd in 11th
quartz yoke
For which rd is way better
quartz yoke
So how do i procced this
ornate knoll
Now in 12th its really easy to do integration and diff
ornate knoll
So how do i procced this
Find the prob of 1st ace
quartz yoke
It shud be like
ornate knoll
Then find prob of 2nd ace
ornate knoll
It shud be like
1/52
quartz yoke
But i already got the ans
ornate knoll
Yes
quartz yoke
1/270275
ornate knoll
Just multiply by 2
quartz yoke
Then if king again, it doubles
ornate knoll
Cause u have to add king one too
ornate knoll
Then if king again, it doubles
Yesss
quartz yoke
But ans stops here
ornate knoll
They said
All aces
Or all kings
So u add
Their prob
So its either all ace or all kings
U can get one of the two
Hence y add
quartz yoke
Yes exactly if it was "all aces or kings"
quartz yoke
But it's "all aces(or kings)" ig
boreal girderBOT
quartz yoke
Its so u dont think that its only one of them
But ans shud think the same ig
compact pewterBOT
ornate knoll
Np :))
compact pewterBOT
Available help channel!
compact pewterBOT
cosmic crypt
Can you stop spamming the same message everywhere?
urban kindle
go away @limpid python
compact olive
soft stone
It is not allowed, it is the definition of SPAM
cosmic crypt
This is very weird, especially since the OP was asking for help on such questions a few months ago:
random path
Even if it weren't spam wouldn't it be self-advertising
urban kindle
😭
random path
And paid services
urban kindle
they weren't asking, they were sending it w no context to random channels
@limpid python .close
they're offering $6 per hour????
@limpid python close the help channel
thorny urchin
.close
last pine
i need help with b)
i think we know that the path must be made of 4 units in one diagonal direction (right up or right down), 2 units in the other diagonal direction (right down or right up), and 1 unit that goes down or up
compact pewterBOT
i need help with b)
i think we know that the path must be made of 4 units in one...
signal willow
i need help with b)
i think we know that the path must be made of 4 units in one...
yeah that analysis looks like it
last pine
so im thinking maybe its 7C4 and something else
signal willow
there's a couple of strategies from this point
last pine
like im not sure what to do with 7C4
signal willow
maybe don't do 7C4
signal willow
you have your one vertical unit
casework on that obviously works, right?
maybe you'll find a better solution after doing the casework, but for now, there's only 9 vertical units, which is basically 4 different cases
signal willow
you can exploit symmetry
last pine
oh yes ok
signal willow
okay technically each of the cases also splits into 2 cases: whether you go up or down
signal willow
casework: which one is the vertical unit used, and which direction you traverse it
signal willow
not necessarily the same
last pine
cause before this i was thinking like 7C4 * 5 * 2 would work because theres 5 vertical slots the vertical lines can be in and 2 directions yk
signal willow
so you have to do each case, if you choose to do this casework
last pine
oh
signal willow
we do dynamic programming with an extra state
so there's basically 2 states to keep track of - whether you have taken the vertical path or not
probably much cleaner
last pine
is there a way to do it without programming i dont think we've covered that in the class hahah
maybe its not needed hoepfully
signal willow
dynamic programming works like this:
Define the following function:
ways(position, taken the vertical) = number of ways to get from A to the given position on the grid, depending on whether you have already taken the vertical move
so now you can compute all the values, and then your answer is just ways(P, true)
basically, it's 18 relatively easy values to compute
but if you still want to do casework on which vertical line to use, you can do that solution instead
last pine
i was just thinking is there a cleaner way without dynamic programming idk hahah usually the problems from this place have shorter solutions
signal willow
not sure, I can show you my dynamic programming solution after you are done with either approach
compact pewterBOT
@last pine Has your question been resolved?
kind glen
The order and degree of the differential equation of all tangent lines to parabola y=x^2 is?
compact pewterBOT
The order and degree of the differential equation of all tangent lines to parabo...
kind glen
how do I write the differential equation?
strange ermine
!original
compact pewterBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
kind glen
The order and degree of the differential equation of all tangent lines to parabo...
this is the exact question
strange ermine
Mmh I'm not sure that the tangent lines form a differential equation
kind glen
.close
compact pewterBOT
compact pewterBOT
Available help channel!
rugged parrot
when doing u sub for definite integrals, is it better to write the bounds in terms of u and evaluate the whole integral, or find the integral in terms of u, and then convert it back to x and evaluate?
compact pewterBOT
when doing u sub for definite integrals, is it better to write the bounds in ter...
viscid canopy
when doing u sub for definite integrals, is it better to write the bounds in ter...
it is often easier to write out the bounds in terms of u from my experience
especially with trig integrals
rugged parrot
thought so, thanks
how do i do that? i dont really get it tbh
like lets take the integral of tanx from 0 to 2pi
i let u = cosx, then what do i do with the bounds?
viscid canopy
you see how u=cos(x)
the bounds correspond to x=0 and x=2π
so the lower bound will be u=cos(0) and upper bound will be u=cos(2π)
compact pewterBOT
chilly basalt
i m uinely stumped
ye, claim a new channel
kind viper
get one that doesn't have a name on it
chilly basalt
Send your question to https://discord.com/channels/268882317391429632/903463354654404658
compact pewterBOT
Available help channel!
mossy tulip
What does it mean for an equivalence relation to be stronger than another equivalence relation
compact pewterBOT
What does it mean for an equivalence relation to be stronger than another equiva...
signal willow
What does it mean for an equivalence relation to be stronger than another equiva...
probably that A is stronger than B if
A(x, y) -> B(x, y)
cursive harbor
What does it mean for an equivalence relation to be stronger than another equiva...
You can write an equivalence relation as a subset of A x A
signal willow
but to check, you can give more context
cursive harbor
If a relationship is stronger, its corresponding set is smaller
mossy tulip
Right, so I suppose a stronger equivalence relation will break the universe down into smaller equivalence classes?
cursive harbor
Yes
safe oyster
you will also hear such terminology as coarser and finer
mossy tulip
Such that equivalence classes formed by weaker equivalence relations will contain union one or more of the equivalence classes made by stronger relation, and uhh
safe oyster
but to check, you can give more context
give more context please
mossy tulip
Context is isotopy vs isomorphism
Of Latin squares
Both are equivalence relations
Isotopy allows relabelling of elements on the Latin square
Isomorphism does not
safe oyster
so isomorphism will be stronger than isotopy
safe oyster
Such that equivalence classes formed by weaker equivalence relations will contai...
yes
mossy tulip
safe oyster
infact it will be exactly a union of equivalence classes of the stronger one
mossy tulip
"An alternate way to define isomorphic Latin squares is to say that a pair of isotopic Latin squares are isomorphic if the three bijections used to show that they are isotopic are, in fact, equal."
Not understanding this
What 3 bijections
safe oyster
i would have assumed the 3 bijections are permuting rows, permuting columns, and relabelling the elements
mossy tulip
Hmm
safe oyster
but then it doesnt make to say they are equal since the domain,codomains of them dont match
cursive harbor
Is it trying to say the bijections are equality
Actually idk what latin squares are so Idk how they're defined
mossy tulip
Actually idk what latin squares are so Idk how they're defined
They are basically square grids where each row and each column has each element exactly once
I don't even get how this works lmao
Isn't the domain S
Of function g
How is it being applied to the Latin square itself
Ah rifht
It's cus L(i, j) is an element of S
Hmm
compact pewterBOT
@mossy tulip Has your question been resolved?
compact pewterBOT
@mossy tulip Has your question been resolved?
compact pewterBOT
@mossy tulip Has your question been resolved?
slender delta
Hello. I was stuck on a problem for about half an hour from a calculus book, so I decided to check the answer, but I don't understand it.
I don't quite get why the derivative g'(1+) is calculated from the formula for derivative of g for x > 1 and contains only '2b', when it should also have in its terms the difference of g(x+h) - g(x), but g(1) is ax^3 - 3x
compact pewterBOT
Hello. I was stuck on a problem for about half an hour from a calculus book, so ...
eternal pulsar
Hello. I was stuck on a problem for about half an hour from a calculus book, so ...
$g_+’(1)=\lim_{x\to 1^+}g’(x)$
boreal girderBOT
;(
eternal pulsar
So we only need to consider the right hand side, since we’re taking the limit from inputs greater than 1
slender delta
I am not sure of the definition you used, I know 2 formulas for derivative, and I use this one most of the times (sorry for bad formatting):
lim(h -> 0+) of [ f(x+h) - f(x) ] / h
so for g'+(1) according to this definition we would have lim(h -> 0+) of [ g(1+h) - g(1)] / h
so g(1) is in the definition of the right hand derivative according to this definition
pine osprey
I think its just a notation rather than a definition
eternal pulsar
so for g'+(1) according to this definition we would have lim(h -> 0+) of [ g(...
This isn’t quite accurate either
We would have 1^+ rather than 1
pine osprey
Yeah, more like lim(x->a) of (g(x) - g(a))/(x-a)
eternal pulsar
I am not sure of the definition you used, I know 2 formulas for derivative, and ...
I’m pretty sure that’s what they meant with the notation as well
slender delta
Yeah, more like lim(x->a) of (g(x) - g(a))/(x-a)
yes, this is the other definition used in this book (it's Calculus Early Transcendentals by James Stewart)
slender delta
that's what I have in this book
from what I read, both definitions are valid, but the definition Nr5 requires factoring (x-a) in the numerator most of the times
so it's harder to find derivatives than the one in definition 4
slender delta
$g_+’(1)=\lim_{x\to 1^+}g’(x)$
where can I find a proof or example online for this property though?
somehow it doesn't seem right to me, or maybe there's something I miss entirely
because I haven't seen it anywhere in this book until now
slender delta
I guess if there is such a theorem, solution would work
it's interesting that until now it hasn't been used or showed in the book, and this is chapter 3.1
anyways, thank you for help
.close
south niche
26…. I can’t visualize it for shit
compact pewterBOT
26…. I can’t visualize it for shit
south niche
south niche
Yes, on the xy plane we’d see the unit circle
twin idol
Alright
south niche
So that narrows it down to I, IV, and VI.
I can’t be it because z’s range is (0, 1]
My only problem is between IV and VI
twin idol
It looks like VI also loops
south niche
I can’t visualize that Z parametric at all
twin idol
Hmm
south niche
I guess Z is constantly oscillating between 0 and 1, so if it’s looping it has to be VI right?
twin idol
If you graph y = 1/(1+x^2), you'll have a grasp over how the z axis will behave
south niche
Ohhh so it’s like
twin idol
It has to be some oscillation that uses an exponential argument
south niche
it only has 1 small exponential change
Which you can see at the top of VI
Ohhh I’m finally getting it
.close
compact pewterBOT
compact pewterBOT
Available help channel!
static kettle
how I do this
compact pewterBOT
how I do this
nimble basalt
how I do this
in this specific case i think you can just solve it by inspection
you have y''=-36y
can you think of any functions that, when differentiated twice, give some constant multiple of the negative of the function?
static kettle
can you think of any functions that, when differentiated twice, give some consta...
i dont think i've learned this. what is this topic called?
short lantern
the general solution isnt what youre looking for, you can test each answer since youre looking for a specific solution
static kettle
the general solution isnt what youre looking for, you can test each answer since...
plug in each of the answer into the differential equation?
short lantern
yes, see which one gives you 0
compact pewterBOT
tidal sphinx
Yes
compact pewterBOT
Available help channel!
strange pendant
safe oyster
Can you send the question in English please
strange pendant
safe oyster
So what is your question
strange pendant
So what is your question
stuck on i
safe oyster
You could not prove that it is an equivalence relation?
strange pendant
You could not prove that it is an equivalence relation?
there is
where i got stuck
safe oyster
If R is an equivalence relation, then what does R need to satisfy
safe oyster
So which one are you having trouble proving
strange pendant
xRx ∀x ∈ X
safe oyster
<@961947864941068321> <@961947864941068321> <@961947864941068321>
If you had told me that you had trouble proving symmetry when I asked you at the start, it wouldn't have taken so long
safe oyster
Seriously?
safe oyster
You can't prove that gRg for all g in F?
strange pendant
g R g <=> g o f = gof
strange pendant
ye
strange pendant
Is it true that g o f = g o f for all g?
we need to use the definition of equality of functions
safe oyster
Okay?
safe oyster
Is it true that g o f = g o f for all g?
You are agreeing with this
So how do you not agree that it's reflexive
strange pendant
yes bit we need to prove the equality holds
strange pendant
that is where I am stuck
safe oyster
g o f and g o f are the same thing (and they both exist)
They are equal
I don't know how else to say this
Sure you can use equality of functions (whatever that means) to prove they are equal
But none of that is needed
They are the same element of a set
So they are equal
strange pendant
compact pewterBOT
@strange pendant Has your question been resolved?
compact pewterBOT
compact pewterBOT
Available help channel!
wintry knot
i am trying to take union of two arrays, here's what i have done: ```#include <iostream>
#include <set>
using namespace std;
int main()
{
int n1, n2;
cout << "enter the number of elements in first array: ";
cin >> n1;
int a[n1];
cout << "enter elements of the array: ";
for (int i = 0; i < n1; i++)
{
cin >> a[i];
}
cout << "enter the number of elements in second array: ";
cin >> n2;
int b[n2];
cout << "enter elements of the array: ";
for (int i = 0; i < n2; i++)
{
cin >> b[i];
}
set <int> s;
for(int i = 0; i < n1 + n2; i++)
{
s.insert(a[i]);
s.insert(b[i]);
}
cout << "after union: ";
for (auto it = s.begin(); it != s.end(); it++)
{
cout << *it << endl;
}
}but, for my output, i am getting a couple garbage values:enter the number of elements in first array: 5
enter elements of the array: 1
2
3
4
5
enter the number of elements in second array: 4
enter elements of the array: 4
5
6
7
after union: 0
1
2
3
4
5
6
7
256
9191456i could be wrong but i think the problem is here:for(int i = 0; i < n1 + n2; i++)``` because it is also considering the values common in both of the arrays. how do i fix this?
compact pewterBOT
i am trying to take union of two arrays, here's what i have done: ```#include <i...
wintry knot
oh also, just noticed, why am i also getting 0 as an element in my output?
wintry knot
different loops?
hushed magnet
currently you are using a[i] and b[i] with values i which are > n1, n2
that is undefined behavior
wintry knot
okay, makes sense
wintry knot
oh also, just noticed, why am i also getting 0 as an element in my output?
what about this?
wintry knot
different loops?
ah, got it. when i did this, it works fine; i think one of the allocated memory locations was 0 and it got sorted
hushed magnet
I am actually surprised that s has so few elements after this
wintry knot
why?
wintry knot
union does not contain repeated elements, right?
no?
5 elements of a and 4 elements of b
hushed magnet
your loop runs 9 times. and in each loop you are inserting 2 elements
hushed magnet
yes
hushed magnet
second option: one loop, build in a check that i is not too big
wintry knot
do not get what you mean by that
hushed magnet
if i < n1: insert a(i)
if i < n2: insert b(i)
wintry knot
right
wintry knot
if i < n1: insert a(i)
if i < n2: insert b(i)
but would not the time complexity be lesser in this case?
than the first approach
hushed magnet
should be more
first has two loops with n1 and n2 steps each
this one has 2*max(n1, n2) steps
and two costly if conditions
but who knows what the compiler actually makes out of that
compact pewterBOT
hushed magnet
you could of course be cheeky
and immediately insert the elements into s when you input them
hushed magnet
.reopen
compact pewterBOT
✅
hushed magnet
well you could still insert them into a, b
but that would be just for show
hence, cheeky
it would miss the point of the exercise (which is to combine two arrays)
but it would give the correct result
hushed magnet
I dont know what the compiler does with code like this
it should be a very tiny difference
cause really you are just moving the same statement to a different point
wintry knot
but aren't we using less for loops
hushed magnet
sure, but each loop does more
in total we do the same amount of steps
I dont know how costly it is to "start" a for loop
in practice this difference would never matter
wintry knot
can you please link me to a good youtube video which teaches how to calculate time complexity, if you know of any? it gets a little confusing for me at times
hushed magnet
I dont know one
for basic things like this, you really just need to count how often each for loop runs and how many steps you do in each iteration
wintry knot
but wouldn't that be a lot of work if you have a code with hundreds of lines?
like i have seen people calculate time complexities of complex codes in seconds
i have watched a couple of lectures on it but
hushed magnet
depends on the code
for some code you only need to see things like "oh three nested for loops, each going from 1 to n and each with a constant amount of steps in it, so O(n^3)"
wintry knot
isn't the amount of steps always constant?
hushed magnet
well the lines in the loop could themselves call functions which take some amount of steps
wintry knot
but still, that would still be constant to some extent, right? because there has to be a base condition
hushed magnet
each function in its implementation could again have a for loop or something
that depends on n
or i
or some other thing
if that happens, then stuff gets more complicated
compact pewterBOT
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Available help channel!
spiral obsidian
I forgot, what part of this equation is the normalvector?
compact pewterBOT
I forgot, what part of this equation is the normalvector?
hushed magnet
the cross product of (1,0,2) and (-2,1,2)
spiral obsidian
Thank you
gilded lark
2nd and 3rd
compact pewterBOT
2nd and 3rd
gilded lark
Multiple correct
kind viper
,rccw
boreal girderBOT
paper anchor
That denominator is not 0
Yeah that should give one
gilded lark
Yeah it did but not in options
paper anchor
It's c right?
winged dock
The general method to solve such questions is to equate the fraction to y
gilded lark
Yeah that should give one
Tho I have the solution but.I want to solve it myself so the minimum might develop a bit of a problem solving
gilded lark
It's c right?
Mope
paper anchor
1 - 4k > 0
paper anchor
Or wait, it's not equal to 0
winged dock
@gilded lark what did you try
gilded lark
The general method to solve such questions is to equate the fraction to y
Yeah theres the same in solution
But idk how well
gilded lark
<@1184081012381204507> what did you try
But denominator not equal to 0
And nothing truly
gilded lark
<@1184081012381204507> what did you try
I'll get -2 marks in that question 😭
winged dock
That is a condition you can check for later
gilded lark
That is a condition you can check for later
But how shall I equate it into y
U mean to take it = y
And solve then
winged dock
Wait I have another question
How do we find the range of the expression x²+bx +c / x² + dx + e
gilded lark
The answer is B for sure and might be more
winged dock
Have you done questions like these
gilded lark
I have
gilded lark
How do we find the range of the expression x²+bx +c / x² + dx + e
By putting it y
winged dock
By putting it y
Yes so we do the exact same thing here
versed verge
Anyone knows how LSTM works and can help me to understand it?
compact pewterBOT
Anyone knows how LSTM works and can help me to understand it?
compact pewterBOT
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Available help channel!
true lava
compact pewterBOT
true lava
,rccw
boreal girderBOT
true lava
for the thing 8(x-5)^2(X+2)
its asking to solve the following inequalities
and write in interval notation
cursive harbor
Observe that 8(x-5)² is always positive
So it comes down to the signs of the rest
(other than for equality)
true lava
yeah
yeah the rest are negative using the method of the line thingy
but im not sure what
interval notation it is
cursive harbor
Essentially
You can rewrite it as two things
One is an equality and one is a strict inequality
Then in the strict inequality you can get rid of the stuff which is always positive
cursive harbor
Observe that 8(x-5)² is always positive
Aka this
true lava
ok?
lime juniper
interval notation it is
do you mean you dopnt know how it applies here, or you dont know what interval notation is?
true lava
do you mean you dopnt know how it applies here, or you dont know what interval n...
idk how to use this method that my teacher explained and the interval notation is based off the method
cursive harbor
What method did you teacher explain
true lava
that line method
where you pick a value inbetween and sub it in to find if its negative or positive
lime juniper
okay sure
call the polynomial p
p(x) = 8(x-5)^2 etc
what are the roots of p? meaning, when is p=0?
lime juniper
good
are those the ONLY places p=0?
or could it be there's a fourth x we haven't found
p(104)=0?
lime juniper
correct, there are only those 3 places
now
let's suppose p is positive on some interval and negative on the same interval
it has to be that p crosses the x-axis if that happens
true lava
well i figured that out
lime juniper
oh, so you're good without more help?
lime juniper
well
what intervals do we KNOW the polynomial can't change sign?
any interval that doesn't solve p(x)=0
true lava
cant change the sign?
lime juniper
can't be both positive and negative in the same interval
true lava
yeah
lime juniper
since p crosses zero any place where it changes sign, any interval where p(x)=0 has no solutions has a constant sign
lime juniper
which is not a solution
so from -2 to 3 it is a solution
any other intervals where it's a solution?
to the inequality?
lime juniper
then p is positive
true lava
no there is only that then
true lava
so its -2 to 3 only?
lime juniper
(-2,3), [-2,3], (-2,3] or [-2,3)
you've narrowed down the interval to those 4 choices
true lava
yeah
boreal girderBOT
gfauxpas
lime juniper
to be precise that the interval means what range of x values you can use
true lava
yeah
lime juniper
you think you can help me with some more stuff
it's encouraged to make a new chat for each question you have if it's not related. is it related?
true lava
its the same page with the same title
lime juniper
okay shoot
boreal girderBOT
lime juniper
all 3 parts?
true lava
the first one so i know how to do it
lime juniper
so an important rule
definition:
the image of a function is the values it can take
for example, the image of the function f(x) = -2 is just {-2}.
if g(x)=x^2, the image of g is [0,+infinity)
Theorem
true lava
yeah
lime juniper
the image of an odd degree polynomial is all reals
the image of an even degree polynomial is NOT all reals
so why is that relevant here?
true lava
im not sure
lime juniper
because if the limit at -infinity is infinity, and the limit at infinity is -infinity
it means the polynomial can be any real number
because it connects every point in between
true lava
yeah
lime juniper
which means you've narrowed down the 4 possible answers to 2, which are?
true lava
a and d
lime juniper
really you don't need this theorem, but I encourage students to use theorems that narrow down a multiple choice question to half the possible answers with 3 seconds of thinking
to find the limit at +infinity or -infinity of a polynomial, you just look at the biggest degree term because that's the most "important" for large x
true lava
to find the limit at +infinity or -infinity of a polynomial, you just look at th...
yeah
but would it be c
i looked at the limits
lime juniper
the second one, you don't want to have to use the binomial theorem on (x+2)^5, but you don't need to for a similar reason that for the inequality question you didn't need to consider the behavior of 8(x-5)^2 in the polynomial 8(x-5)^2(x+2)(x-3)
lime juniper
don't think "mimic" is the right word but i think i know what youre saying
lime juniper
try to say it in a different way so i understand waht youre thinking
true lava
well a negative makes the end behavior flip right and an odd end beahavoir is and sorta s like shape
@lime juniper
lime juniper
<@205675981845954560>
i was cooking something!
true lava
oh ok
lime juniper
s-shape is good way to think of it
keeping in mind a straight line also is an odd degree polynomial though
but the idea is that the behavior at one end +infinity and the other end is -infinity
if you multiply an s-shaped function by an even degree polynomial, those infinite limits at infinity wont change, I think thats what youre saying
lime juniper
so is c correct or not?
no because thats an even degree polynomial ;____;
lime juniper
hello
yes d
there's another way to do this that applies for the second group of questions
true lava
i got answers for those already
true lava
b and a
lime juniper
hmm gonna have to disagree with you on that
did you narrow it down to the biggest degree term?
true lava
did you narrow it down to the biggest degree term?
yes
lime juniper
what are they?
lime juniper
but you cant forget the coefficient
true lava
i didnt?
lime juniper
okay, so, first 2 are 8 with what coefficient? second 2 are 9 with what coefficient?
true lava
they all got 2 but a and c are negative
true lava
because the end behavoir doesnt allow it
lime juniper
right, so, it cant be "b and a" like yoiu said
true lava
no i meant the 2nd question was b and the third was a
lime juniper
sorry im busy now i cant help anymore until later
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wind grove
hello i need help solving part a
compact pewterBOT
hello i need help solving part a
kind viper
hello i need help solving part a
!status
compact pewterBOT
hello i need help solving part a
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
uneven birch
Hint : use the center of the circle to partition the área
kind viper
yeah im gonna second shakigras here
wind grove
Hint : use the center of the circle to partition the área
what
wind grove
ohh okay yeah
kind viper
connect G and O with a line segment; this will split your area into two pieces -- one of them is a triangle (EGO), the other a sector (FOG)
wind grove
can you please help me visualise
kind viper
kind viper
this will split your area into two pieces -- one of them is a triangle (EGO), the other a sector (FOG)
do you know in general how to find the area of each of those shapes?
midnight stream
that's one formula
wind grove
so whats the one we need to use for this
midnight stream
but since you're given θ you'll need a formula that involves that
kind viper
you will find it more convenient to use the formula A = 1/2 ab sin(C) [via sides and angle between them]
you'll need to do a little bit of angle-chasing on the diagram before that tho
wind grove
you will find it more convenient to use the formula A = 1/2 ab sin(C) [via sides...
ohhh okay
wind grove
you'll need to do a little bit of angle-chasing on the diagram before that tho
this stuff lowkey makes my brain hurt
wind grove
i mean a orb
a
midnight stream
this stuff lowkey makes my brain hurt
do you understand what you need to do
midnight stream
you need to find the area of the 2 shapes you created as function of thera
theta
since without theta as a variable, you're not given enough information
kind viper
for a start, can you find either of these two angles i've marked here
in terms of θ, obv
midnight stream
the triangle has 2 equal sides
EO AND OG
also Ann lmk if you think I'm interfering negatively
wind grove
yeah
kind viper
which angles?
midnight stream
not all angles
wind grove
not all angles
then?
midnight stream
the angles are also equal?
this would be the case if all sides were equal
which they aren't
2 sides are equal, therefore
?
kind viper
yknow what @midnight stream you can take this oveer
wind grove
therefore two angles are equal?
midnight stream
yknow what <@965659970601357383> you can take this oveer
I can't, I don't remember the formulas lmao
midnight stream
therefore two angles are equal?
which two
kind viper
I can't, I don't remember the formulas lmao
bwuuh
midnight stream
I'll ping you when you're needed again
midnight stream
GEF and EOG?
no
midnight stream
wind grove
yess
wind grove
pi - 2 theta?
midnight stream
correct
wind grove
ty
midnight stream
which would mean that the green is
midnight stream
EOF is pi, correct
wind grove
i think
midnight stream
correct
wind grove
EOF is pi, correct
yes
midnight stream
you will find it more convenient to use the formula A = 1/2 ab sin(C) [via sides...
okay now does the formula Ann brought up seem useful
midnight stream
you'll need the length of 2 sides, a,b in this case and the angle that connects the two sides
do you have that?
wind grove
you'll need the length of 2 sides, a,b in this case and the angle that connects ...
which ones are a and b tho
wind grove
do you have that?
i dont know..
wind grove
oh yes
midnight stream
and we just found the red angle which is the angle that connects those 2 sides
so what's the area of the triangle
wind grove
wait so like EG is the side we're looking for right
midnight stream
we're not looking for any sides
we have all the information needed to use the formula
wind grove
ohh
midnight stream
we have the sides EO and OG as well as the angle EOG
wind grove
so like 1/2(6 * 6) * sin(2 theta)?
wind grove
pi - 2 theta then?
midnight stream
yes
wind grove
red is pi-2 theta
right mb
midnight stream
Area of Triangle = 1/2 x EO x OG x sin(EOG)
and then add the numbers
do the math
wind grove
ohhh right right
midnight stream
and let me know what you end up with
wind grove
thank you smm
wind grove
and let me know what you end up with
ofc
midnight stream
you're not done yet
wind grove
wait what
midnight stream
you want the area of the whole region, you've only found the triangle and you still don't have what you need for the triangle which js 18*sin(2θ)
wind grove
ohhhhhhhhhhhhhhh right thats only the area of the triangle
midnight stream
Area of Triangle = 1/2 x EO x OG x sin(EOG)
what's the result of this
what'd you find
wind grove
you want the area of the whole region, you've only found the triangle and you st...
we dont have what we need for 18 sin 2 theta?
wind grove
what'd you find
one sec
wind grove
what'd you find
18sin(pi - 2 theta)
wind grove
you'll have something really similar
i see
wind grove
bro im supposed to be doing 10th grade maths why is this so complicated
midnight stream
so sin(π-θ)=sin(θ)
I'm not sure how you're taught to write this
wind grove
so sin(π-θ)=sin(θ)
huh
midnight stream
you've either been asked to memorize it or derive it
wind grove
I'm not sure how you're taught to write this
im sorry im not following
midnight stream
but there's like a lot of ways to derive it
sin(pi-theta)=sin(theta)
that's just true
wind grove
but there's like a lot of ways to derive it
theyre... equal?
midnight stream
yes
wind grove
that's just true
goddamn
wind grove
but I'm not sure if you have to prove it or you're asked to know it
ive actually never come across this
midnight stream
you've probably come across this
wind grove
yeah
midnight stream
do you know how to find its area
wind grove
pi * r^2 * theta/2pi
midnight stream
correct so the area is the area of the circle (pi*r^2) and all of that multiplied by the portion of the circle it takes up (theta/2pi)
does the formula make sense to you
wind grove
yes
wind grove
so the pi cancels out and so we're left with 36 theta
midnight stream
correct
wind grove
so we add this to the area of the triangle
wind grove
okay, do we have everything we need to find the area?
yesss
midnight stream
the shaded region is those 2 regions, the triangle's and the sector's added
and you have the solution you were looking for
wind grove
and you have the solution you were looking for
thank you so much man
lowkey a life saver
midnight stream
do you need help with b?
midnight stream
can you repost the question cause I don't wanna scroll all the way up
random mica
can you repost the question cause I don't wanna scroll all the way up
pinned message
midnight stream
ty
midnight stream
any idea how you'd go about this
midnight stream
okay so the derivative
wind grove
36
midnight stream
good
midnight stream
36 theta + 36cos 2 theta
so why add theta
midnight stream
the other one is correct
wind grove
that was a mistake i didnt mean to write theta
wind grove
can you figure out the rest
is it 2.7
midnight stream
can you double check with someone else cause no battery, good luck man
wind grove
can you double check with someone else cause no battery, good luck man
yeah sure bro dw
midnight stream
do .close to close the channel
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pseudo shale
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icy topaz
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quartz yoke
bruh I was getting excited then they had to ruin everything in the last sentence
icy topaz
Why?
quartz yoke
do you know trig?
icy topaz
Hi.
icy topaz
I have found AP, AM and MC to all be equal.