and that is cosx e^sinx
#help-10
short crescent
so we can verify if they are equal by taking the derivative of e^sinx
(the + C doesn't matter here since the derivative of any constant is zero)
oak solar
how is the derivative of e^sinx equal to cosx e^sinx
short crescent
we would have to use chain rule for this
oak solar
im almost 12 i have almost no processing power left in my brain
short crescent
u-substitution, but the derivative version of it
primal wadi
im almost 12 i have almost no processing power left in my brain
you are almost 12 or the times is almost 12 LOL
oak solar
you are almost 12 or the times is almost 12 LOL
see thats what i mean, its almost 12
short crescent
$\frac{\dd}{\dd x} (e^{\sin x}) = e^{\sin x} \cdot \frac{\dd}{\dd x} (\sin x)$
warm shaleBOT
Krish
short crescent
do you remember doing something like this?
short crescent
oh- i would watch a video on all the different methods of taking the derivative
primal wadi
**Krish**
would prob best to write $\frac{\dd e^{sinx}}{\dd \sin x}$ instead of just e^{sin(x)}
oak solar
i get what u mean
tender blaze
im almost 12 i have almost no processing power left in my brain
careful with the language here
oak solar
nevermind i remeber
warm shaleBOT
qwertytrewq
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
oak solar
careful with the language here
yikes thats right
short crescent
ah okay
oak solar
my bad
short crescent
would prob best to write $\frac{\dd e^{sinx}}{\dd \sin x}$ instead of just e^{si...
is this what you meant or are you still editing
primal wadi
is this what you meant or are you still editing
yeah
short crescent
i feel like that makes it more confusing
oak solar
we would have to use chain rule for this
just to confirm, with the chain rule we would have to d the e and then the sinx by themselves and * them
oak solar
would prob best to write $\frac{\dd e^{sinx}}{\dd \sin x}$ instead of just e^{si...
lowkey the other one made more sense
short crescent
u skipped a step to do de^sinx/dsinx here
its just simply stating the same that $\frac{\dd}{\dd x} e^x = e^x \cdot \frac{\dd}{\dd x} (x)$
warm shaleBOT
Krish
short crescent
just to confirm, with the chain rule we would have to d the e and then the sinx ...
yes
short crescent
**Krish**
this is the full derivative of e^x, we just don't write d/dx (x) because it evaluates to 1. however when its not just "x" we have to be careful and take care of that derivative
primal wadi
i feel like that makes it more confusing
welp ok ig, fair point. i just didn't want the OP to get the wrong impression that d/dx f(x)= f(u) d/dx(u)
short crescent
i see, but yeah for e^x it wouldnt matter. i assumed they know its different for other functions lol
oak solar
still thank you guys everything made much more sense now
short crescent
of course!
primal wadi
Law of u-substitution: big if simplifies 
obtuse pebbleBOT
oak solar
.reopen
obtuse pebbleBOT
✅ Original question: #help-10 message
oak solar
sorry but about this one
i got to the point where i u sub the x^2+3
this leaves me with x*sin(u) du/2x
i lowkey dont know where to continue from here
high lily
cancel the x
oak solar
wait how
ruby orchid
Multiply the xsinu into the fraction
high lily
$\int \frac{\red{x} \sin(u)}{2\red{x}} \dd{u}$
oak solar
ohh like that
warm shaleBOT
ραμOmeganato5
high lily
technically 1/2
wild glade
can i not just do 1/2
yes
oak solar
and then the final answer is 1/2*cosu+c
oak solar
wym check my signs
oak solar
wait i have to swap signs when i integrate?
wild glade
in this case yes
because cos differentiate to -sin
so -cos differentaite to sin
and integral of sin therefore will have negative
wild glade
ye
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
viscid venture
what is the best way to do Factoring Polynomials
obtuse pebbleBOT
what is the best way to do Factoring Polynomials
viscid venture
like is their a way to do it in ur calcuatlor
restive gorge
If you have a calculator, I guess, you can try to find the roots
obtuse pebbleBOT
@viscid venture Has your question been resolved?
high lily
what degree is your polynomial
solar stump
-# idk, it's got a Bachelor's; why is that relevant? /s
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
tender blaze
<@&268886789983436800>
shut lagoon
<@&268886789983436800>
obtuse pebbleBOT
coarse storm
obtuse pebbleBOT
Available help channel!
keen notch
obtuse pebbleBOT
keen notch
hiya just wondering if there’s anything potentially wrong with the logic of my steps ?
particularly the second and third to last where i applied the triangle inequality
unsure because i know the triangle inequality only applies if the dot product between u and v is positive
shut lagoon
,rccw
warm shaleBOT
shut lagoon
Well the inequality you're talking about seems to be Cauchy-Schwarz.
In any case, it says that $|\vb{u}\cdot \vb{v}| \le ||\vb{u}|| ||\vb{v}||$, and since $\vb{u} \cdot \vb{v} \le |\vb{u}\cdot \vb{v}|$, you necessarily get that $$\vb{u}\cdot\vb{v} \le ||\vb{u}||||\vb{v}||.$$
warm shaleBOT
Azyrashacorki
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
misty acorn
hey idk how does the help work but i got this exercises, tho its in spanish i'm sure u can understand what it says cuz math is an universal language, i hope u can hlep me with some exercises cuz i don't know anything about maths
obtuse pebbleBOT
hey idk how does the help work but i got this exercises, tho its in spanish i'm ...
tardy epoch
should do one problem at a time and translate one at a time
misty acorn
should do one problem at a time and translate one at a time
oh okay so we got this equality (=720) then find "x"
tardy epoch
count how many x's there are
misty acorn
5
misty acorn
hmm so 6x?
tardy epoch
pretend x=12 first. what's the last term in the sum on the left and how many terms are there?
not 6x. shouldn't be guessing
finding x requires a calculation
misty acorn
pretend x=12 first. what's the last term in the sum on the left and how many ter...
k if x=12 then there's 12, 16, 20, 24, the another one must be 28 because (x+16)
tardy epoch
yes. count how many there are on the left side
tardy epoch
pretend x=12 first. what's the last term in the sum on the left and how many ter...
and answer the other question here too
misty acorn
pretend x=12 first. what's the last term in the sum on the left and how many ter...
6 terms
misty acorn
60
tardy epoch
k if x=12 then there's 12, 16, 20, 24, the another one must be 28 because (x+16)
so 28 is not the last term.
tardy epoch
right you'll always get +1 some even term because you can think of x = x + 0. write 5x = x + 4x. now can you count how many terms there are?
misty acorn
i didnt get it
tardy epoch
so 13 terms
it isn't that different than what you did here to get 13
tardy epoch
oh okay so we got this equality (=720) then find "x"
count again with D) 15
misty acorn
15 19 23 27 31 35 39 43 47 51 55 59 64 68 71 75
tardy epoch
why did you stop at 59
misty acorn
cuz i can't 59 plus 4 to get 60
tardy epoch
what does 60 have to do with option D)
misty acorn
oh lol im dumb
tardy epoch
the last term is 5x so you stop there
misty acorn
16 terms
tardy epoch
right you'll always get +1 some even term because you can think of x = x + 0. wr...
right. like i said here, 15 + 4 * 15 = 15 + 60 = 75.
you counted by 4s started from 15 until you got to 4x
how many terms is that?
tardy epoch
15 19 23 27 31 35 39 43 47 51 55 59 64 68 71 75
another way to write this is
15 + 0, 15 + 4, 15 + 8, 15 + 12, ..., 15 + 4(15)
misty acorn
right. like i said here, 15 + 4 * 15 = 15 + 60 = 75.
k 4 is the reason here or whatever is called in english, "15 +" the first term and * 15 the lenght of temrs
misty acorn
you counted by 4s started from 15 until you got to 4x
wasnt it to 5x?
tardy epoch
right you'll always get +1 some even term because you can think of x = x + 0. wr...
read
tardy epoch
it isn't that different than what you did here to get 13
you did it correctly once here
misty acorn
idk what u want me to do
tardy epoch
right you'll always get +1 some even term because you can think of x = x + 0. wr...
.
Do one more if you need to
misty acorn
k i got 14
so 5*14 is 70
14 18 22 26 30 34 38 42 46 50 54 58 62 66 70
there's 15 terms
obtuse pebbleBOT
@misty acorn Has your question been resolved?
misty acorn
not yet
obtuse pebbleBOT
@misty acorn Has your question been resolved?
obtuse pebbleBOT
@misty acorn Has your question been resolved?
fallen oxide
hey idk how does the help work but i got this exercises, tho its in spanish i'm ...
For the first have you tried S = n/2 (a + l) where l = a + (n-1)d
We know a and l so substitute n in terms of them from the second formula
tardy epoch
14 18 22 26 30 34 38 42 46 50 54 58 62 66 70
there's 15 terms
yea so when x=12, there are 13 terms. x=14, there are 15 terms, x=15, there are 16 terms. guess a pattern for number of terms for any x
obtuse pebbleBOT
@misty acorn Has your question been resolved?
fallow onyx
Hello, I would like some help on what I mean to try. Generally, I currently have the argument that $dim(U_1) + ... + dim(U_k) = dim(V)$, this argument is one that I take for granted and argue with. And with it I try to prove that $u_i \in U_i; i = {1, ..., k}; \sum u_i = 0$
My current thoughts spin around using the dimensional formula but I question how to prove that $dim(U_1 \cap ... \cap U_k) = 0$ or if there is a better way
obtuse pebbleBOT
Hello, I would like some help on what I mean to try. Generally, I currently have...
warm shaleBOT
Ace ≡ Lux ≡ Felix
haughty stump
so
We want to show that if $u_1 + u_2 + \dots + u_k = 0$ (where each $u_i$ is in $U_i$), then the only possible solution is $u_1 = 0, u_2 = 0, \dots, u_k = 0$?
warm shaleBOT
thecrumbeler2
haughty stump
then this is just a direct sum: $V = U_1 \oplus U_2 \oplus \dots \oplus U_k$
warm shaleBOT
thecrumbeler2
haughty stump
you do have to prove $\dim(U_1 \cap \dots \cap U_k) = 0$ but its not sufficient for k>2
warm shaleBOT
thecrumbeler2
haughty stump
they are not a direct sum because their dimensions (1+1+1=3) exceed the dimension of the space (2)
first step is gonna be to choose the bases for each of the subspaces
fallow onyx
We want to show that if $u_1 + u_2 + \dots + u_k = 0$ (where each $u_i$ is in $U...
Well, what I actually need to show is that $dim(V) = dim(U_1) + ... + dim(U_k) => u_1 + ... + u_k = 0$
warm shaleBOT
Ace ≡ Lux ≡ Felix
haughty stump
well
to prove $\sum u_i = 0 \implies u_i = 0$ using dims lets define $\mathcal{B}1 = {v{1,1}, \dots, v_{1,d_1}}$ to be a basis for $U_1$
warm shaleBOT
thecrumbeler2
warm shaleBOT
thecrumbeler2
haughty stump
if you consider the set of all these v combined $\mathcal{B} = \mathcal{B}_1 \cup \mathcal{B}_2 \cup \dots \cup \mathcal{B}_k$
warm shaleBOT
thecrumbeler2
haughty stump
the total number of vectors in $\mathcal{B}$ is just gonna be $d_1 + d_2 + \dots + d_k$
warm shaleBOT
thecrumbeler2
haughty stump
and $\mathcal{B}$ is exactly $\dim(V)$. cause a given is $\sum \dim(U_i) = \dim(V)$
warm shaleBOT
thecrumbeler2
haughty stump
cause $V = U_1 + \dots + U_k$, every vector in V can be written as a sum of vectors from these subspaces
aka the set $\mathcal{B}$ spans V
warm shaleBOT
thecrumbeler2
haughty stump
if a set of n vectors spans a space of dimension n those vectors have to be linearly independent
so clearly $\mathcal{B}$ is a basis for V
warm shaleBOT
thecrumbeler2
haughty stump
so going back to $u_1 + u_2 + \dots + u_k = 0$
warm shaleBOT
thecrumbeler2
haughty stump
again, each $u_i$ can be written as a linear combination of its own basis $\mathcal{B}_i$. When we plug those in, we get a long linear combination of all vectors in $\mathcal{B}$ equal to zero
warm shaleBOT
thecrumbeler2
haughty stump
and cause $\mathcal{B}$ is linearly independentthe only way for that sum to be zero is if all coefficients are zero
warm shaleBOT
thecrumbeler2
haughty stump
and if all coefficients are zero, then each individual $u_i$ must be the zero vector
warm shaleBOT
thecrumbeler2
haughty stump
lotta talking but i hope that made sense
basically, $\sum \dim(U_i) = \dim(V)$ plus the fact that the subspaces span $V$ means the union of their bases forms a basis for $V$
warm shaleBOT
thecrumbeler2
haughty stump
in any basis, the only way to represent the zero vector is with zero coefficients
therefore, $u_1 + \dots + u_k = 0$ forces $u_1 = 0, \dots, u_k = 0$
warm shaleBOT
thecrumbeler2
obtuse pebbleBOT
@fallow onyx Has your question been resolved?
fallow onyx
I can understand the argumentation and actually I never had thought of it that way, I do think that this may have been a bit too much for me
obtuse pebbleBOT
Available help channel!
sick thicket
obtuse pebbleBOT
sick thicket
I didn’t get the answer in the middle for question g
vestal steppe
Hi! What's the period of tan(2theta)?
sick thicket
Huh
vestal steppe
Well,
You are solving for tan(2theta) = 3/4, right?
So surely you need to keep in mind what the period of tan(2theta), no?
After all, solutions always repeat every period :)
vale pelican
Hi! What's the period of tan(2theta)?
the question might be "what is period?"
hollow ocean
actually, what IS the original question?
perhaps it would help helpers understand what's going on a little better?
vestal steppe
the question might be "what is period?"
Well in my defence, "huh" tells me nothing 😭
@sick thicket Do you know what the period of a function is?
vestal steppe
actually, what IS the original question?
It's blocked out, but I'm pretty sure the question is to solve the equation:
"4sin(2theta) - 3cos(2theta) = 0"
vale pelican
no yeah, we can't see the original question, only the answer in the answer key
vestal steppe
It's blocked out, but I'm pretty sure the question is to solve the equation:
"4s...
In this case I can see why there's an error; it's just on the last step.
hollow ocean
ah, I apologize then.
sick thicket
<@1354133211499860008> Do you know what the period of a function is?
The times it moves in one
vestal steppe
The times it moves in one
Definitely could be worded better 😭
The period is basically how long before a function "repeats" itself. For example, you might know that the period of y = tan(x) is pi, because every pi units the tan graph repeats, right?
I.e, it "repeats" the shape after pi, agreed?
sick thicket
Yes
vestal steppe
Nice.
So,
What's the period of y = tan(2theta)?
Chat if you don't know how to find the period, you can tell me 😭
sick thicket
I don’t
vestal steppe
No worries, let's look at a different question then:
Have you done function transformations before?
I.e
What's the difference between f(x) and f(2x)?
sick thicket
Double
vestal steppe
Indeed, but do you know what the difference is in terms of transformations?
I.e what kind of transformation is f(x) to f(2x) supposed to be?
This is the graph of y = tan(x)
This is the graph of y = tan(2x)
What do you notice about the green graph compared to the red graph?
sick thicket
It’s closest to the y axis?
vestal steppe
It’s closest to the y axis?
Yeahhhh that's true
But like what happened
Like why is it closer to the y axis?
Hint: Use one of these words
vestal steppe
ehhhhh close but no; the graph didn't move right per se.
If the graph moved then it wouldn't pass through the origin
sick thicket
Aww
vestal steppe
Hint: Use one of these words
Again the hint is to use one of these words :)
One of these words will explain exactly how you can go from the red graph to the green graph
sick thicket
Idk
vestal steppe
Idk
On this desmos graph, there is a play button
I want you to click it
And tell me what happens
Preferrably describe what is happening :)
vestal steppe
Would you not agree that
The curve sort of squished?
Like
The green curve was being squished into the centre?
vestal steppe
The reason why your final solution is missing a number
Is because you didn't correctly state the period
vestal steppe
Here you state this
However;
180 is not the period of y = tan(2x)
So you don't get all answers by adding multiples of 180 (though to your credit, you will get some)
vestal steppe
wat
vestal steppe
Oh that
Yeah when you are solving equations yes
But this is also another indicator of the period!
That is, the period of tan(2x) is 180/2 = 90
obtuse pebbleBOT
@sick thicket Has your question been resolved?
toxic harbor
please @ me
obtuse pebbleBOT
please @ me
toxic harbor
yes
vale pelican
if it is, never use × for products of numbers
hollow ocean
not recommended to use an x to denote multiplication when you have a variable x.
toxic harbor
yeh that easier
hollow ocean
anyway, let's see.
toxic harbor
ok
high grotto
please @ me
We gotta check if it's right or what?
toxic harbor
yep
hollow ocean
assuming you didn't make a mistake on cos(40) the method is mostly right but I will push back on one bit of notation here.
toxic harbor
assuming you didn't make a mistake on cos(40) the method is mostly right but I w...
ok
thanks
ill use this from now in *
hollow ocean
normally when writing a polynomial in terms of a variable, we prefer putting the variable last in any term.
for instance, I would write this as $x^2 - (12 \cos(40^{\circ}))x + 11 = 0$.
warm shaleBOT
go maximax or go home (Chiaki)
drifting mulch
Do u use cosine for getting the base of a right triangle
toxic harbor
why is the x outside the bracket?
hollow ocean
because it's being multiplied by 12cos(40).
toxic harbor
right i get it
hollow ocean
and this makes it clear that this whole polynomial is in x and nothing else.
high grotto
please @ me
U used cosine law
toxic harbor
can i please just have @hollow ocean as my only helper thank u
toxic harbor
<:blobcry:971797574916907028>
its so it doesnt get confusing if i have too many helpers it gtes confusing
anyway would my answer be correct considering i used wrong notations?
@high grotto u cananswer that if u want
hollow ocean
I don't get your values, that much I can tell you.
but since you've called for the other helper, I will step back.
high grotto
can i please just have <@1494726786523729920> as my only helper thank u
But since u have called for other helper I will stepback.
toxic harbor
better?
toxic harbor
But since u have called for other helper I will stepback.
we serious?
ok ill wait
please @ me when anyone gets here, thanks
pallid willow
your answers are no different from the answers Chiaki told you she didn't get.
pallid willow
that's quite immediately a sign that you've not fixed some other underlying issue
toxic harbor
Whats the point of discussion when U have solved the problem
idk if its right or wrong
toxic harbor
that's quite immediately a sign that you've not fixed some other underlying issu...
fixed (9 sqr 2)/2
pallid willow
the final answers are no different.
toxic harbor
what does that mean
pallid willow
(also to Chiaki, if you're watching, you know you can step back in any time)
hollow ocean
we mean what we said. this was your original answer.
toxic harbor
we mean what we said. this was your original answer.
correct
hollow ocean
I told you that I didn't get your answer, and you reworked it to the exact same final answers.
toxic harbor
hmm intersting, are my steps correct tho?
hollow ocean
assuming you didn't make a mistake on cos(40) the method is mostly right but I w...
^
toxic harbor
thank u
i have 1 final question
is it possible to make this into 2 triangles, i believe yes
hollow ocean
just draw in one of the diagonals.
high grotto
i apolgise if chatting with me was frustrating
Nah
But bro tis ez ques, u can do it
So try harder
toxic harbor
But bro tis ez ques, u can do it
im pretty sure i can
i just entered trig today so im still learning
karmic bronze
is it possible to make this into 2 triangles, i believe yes
yes
hollow ocean
so do you have anything else?
uneven schooner
But bro tis ez ques, u can do it
Um please don't talk down helpees, they may be at different stages of their mathematical education. Even if your intention was not to talk them down, they may interpret it as so; so it is best to avoid remarks such that 'this is an easy question' for many people may take offense to it.
toxic harbor
let me check
hollow ocean
but if there is and another helper interrupts me I will step back.
toxic harbor
Um please don't talk down helpees, they may be at different stages of their math...
i took it as motivation
uneven schooner
but if there is and another helper interrupts me I will step back.
Chiaki, your help is always appreciated. You're always free to help, and you're a good helper, so you may always continue
toxic harbor
but if there is and another helper interrupts me I will step back.
aight i respect ur boundaries
toxic harbor
Chiaki, your help is always appreciated. You're always free to help, and you're ...
I agree
hollow ocean
Chiaki, your help is always appreciated. You're always free to help, and you're ...
I do not like having 1000 people interrupting my conversation with someone that I'm helping unless their helping methods match mine.
toxic harbor
I do ***not*** like having 1000 people interrupting my conversation with someone...
understandable
anyway thank u all for the help, and that was my final question for now
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
frail vigil
given $f(x)$ and $g(x)$, is there any straight foreword method to find $f^{-1}(f(g(x)))$
obtuse pebbleBOT
given $f(x)$ and $g(x)$, is there any straight foreword method to find $f^{-1}(f...
warm shaleBOT
-TimeLord-
hardy widget
given $f(x)$ and $g(x)$, is there any straight foreword method to find $f^{-1}(f...
Assuming that the left-hand side is well-defined, recall
$$f^{-1} \left(f(u) \right)=u.$$
(If it's not clear, take $u=g(x)$.)
hollow ocean
did you mean g^-1 instead, perhaps?
warm shaleBOT
Civil Service Pigeon
frail vigil
did you mean g^-1 instead, perhaps?
no i meant g(x)
versed stratus
$g(f(g(x)))$?
warm shaleBOT
what a wonderful world(wai)
hollow ocean
no, I mean $g^{-1}(f(g(x)))$?
warm shaleBOT
go maximax or go home (Chiaki)
versed stratus
then what civil service said
frail vigil
If $f^{-1}(f(g(x))) = g(x)$, then:
Let $f(x)=x^2$
Then, $f(-x)=f(x)$
Then, $f^{-1}(f(-x))=f^{-1}(f(x))$
The, $-x=x$
Which solves to x=0. Meaning that $f(-x)=f(x)$ only when x=0. Am I missing something or did I do soemthign stupid?
warm shaleBOT
-TimeLord-
frail vigil
But this shows that any even fucntion cannot exist
zenith raft
olive oxide
what
zenith raft
f^{-1} doesn’t make sense in the first place when f isn’t a bijection
so this doesn’t say anything
frail vigil
f^{-1} doesn’t make sense in the first place when f isn’t a bijection
so for non one-to-one functions f^-1 cant exist?
zenith raft
yes
hollow ocean
f^-1 is not even going to be a function with f's unrestricted domain to begin with.
in fact, I believe that all even functions do not have an inverse unless the domain is restricted.
versed stratus
in fact, I *believe* that **all even functions do not have an inverse unless the...
the inverse map is only defined when it is bijective
hollow ocean
and even functions aren't bijective, to my knowledge.
obtuse pebbleBOT
versed stratus
and even functions aren't bijective, to my knowledge.
yes
frail vigil
<@&268886789983436800>
obtuse pebbleBOT
Available help channel!
worthy blade
Guys I can't solve this question I have tried everything trying cases even trying one by one and pluging values
obtuse pebbleBOT
Guys I can't solve this question I have tried everything trying cases even tryin...
worthy blade
Someone please help
I have to close it oops i have to go and if someone answers when closed and i can't close i will get banned 😭
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
graceful dawn
I have to plot the point of a quadratic equation it is in vertex form the problem is 2/3(x-1)^2 +5/2
obtuse pebbleBOT
I have to plot the point of a quadratic equation it is in vertex form the proble...
graceful dawn
So far I have the point (1,2.5) i cant figure out the other one
short crescent
$y = \frac{2}{3}(x-1)^2 + \frac52$
is this correct or is the x-1 in the numerator
scenic zenith
Not a quadratic
short crescent
ah in vertex form
graceful dawn
No (x-1)^2 is separate
warm shaleBOT
Krish
graceful dawn
Yes
short crescent
well, to start (1, 2.5) is your vertex
if you need to graph it you can just choose x-values near 1 and plug them in
graceful dawn
I figured that out I need the other point
short crescent
which "other point"?
graceful dawn
Either
wind tapir
why i cant send photos here?
graceful dawn
Yes
short crescent
if you need to graph it you can just choose x-values near 1 and plug them in
^
plug in x=0 and x=2 and see what you get and you can graph from there or if you want to be more precise you can plug more in
graceful dawn
Ok
wind tapir
i got 2 out of 10 , am i dum?
short crescent
i got 2 out of 10 , am i dum?
!occupied
obtuse pebbleBOT
i got 2 out of 10 , am i dum?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
wind tapir
sorry
solar stump
-# how did you get 2 out of 10 on a 44-mark paper
graceful dawn
.close
obtuse pebbleBOT
stoic breach
-# how did you get 2 out of 10 on a 44-mark paper
-# Without having his name writtten on the exam too.
-# Glad he handed it in as an anonymous.
graceful dawn
were you able to understand it?
Yes
deep kraken
-# Glad he handed it in as an anonymous.
Nahhhh 💀
short crescent
-# Without having his name writtten on the exam too.
i'm sure its implied that he got 2/10 when plugging in x = 10 for question 4 and sent the other photo on accident
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
random plaza
obtuse pebbleBOT
random plaza
Idk what to do at all
olive oxide
do u remember bpt
stoic breach
Have you tried similar triangles or any theorems that could be helpful like Thales?
olive oxide
-# sniped
random plaza
do u remember bpt
What is that
olive oxide
What is that
Basic Proportionality Theorem
olive oxide
random plaza
do u remember similar triagles
Yeah
random plaza
I've gotten 3 = kFE and AC = kFC
random plaza
which 2 triangles from the figure do u find similar?
ABC and FEC
olive oxide
can you find FE in terms of CD now?
olive oxide
Might actually be blind
it happens to the best of us.
olive oxide
one min
okay so
from both the similar triangle conditions so far can we say that $\frac{CE}{CB}=\frac{CF}{CA}=\frac{EF}{AB}$ and $\frac{CD}{EF}=\frac{AC}{AF}=\frac{AD}{AE}$?
warm shaleBOT
mee wunce
random plaza
**mee wunce**
One sec
random plaza
**mee wunce**
Is this the thales theorem thing
random plaza
Yeah
olive oxide
we just got CE/CB=k
random plaza
Ohhh
olive oxide
but we know that CF/CA is also k
random plaza
Okay I understand now
olive oxide
Okay I understand now
yepp thats all there is to thales theorem
olive oxide
🔥
random plaza
.close
olive oxide
!done
obtuse pebbleBOT
If you are done with this channel, please mark your problem as solved by typing .close
obtuse pebbleBOT
Available help channel!
opal marsh
obtuse pebbleBOT
opal marsh
e
pallid willow
!status?
obtuse pebbleBOT
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
1
pallid willow
what are the conditions for an inverse function to exist?
and, another thing. is this for calculus or algebra?
opal marsh
and, another thing. is this for calculus or algebra?
idk
opal marsh
what are the conditions for an inverse function to exist?
and
it has to grow either positively or negatively constantly
pallid willow
you dk? where did you get this problem from?
pallid willow
what is dk in idk?
old lily
sonderpants 😭
pallid willow
have you learnt about derivatives?
opal marsh
yes
pallid willow
ok good, that makes things a lot easier
pallid willow
it has to grow either positively or negatively constantly
do you perhaps have a better way of framing the condition of the existence of an inverse?
opal marsh
do you perhaps have a better way of framing the condition of the existence of an...
nope
pallid willow
I mean it's kinda correct in a way but there's a more precise phrase we are looking for
or word
pallid willow
have you heard of one-to-one then
pallid willow
this is the precise term I'm looking for
if f is to have an inverse, it must be one-to-one
now, let's look at each side separately
for the first part x <= 0, what kind of graph is it?
opal marsh
quadratic function?
pallid willow
yeah, but what shape is the graph?
opal marsh
U
pallid willow
close enough
so if we want this to be one to one, what must not exist in this interval?
opal marsh
half of the U
pallid willow
okay yes, but more specifically, what point must not exist in this interval?
opal marsh
positive values
opal marsh
idk
pallid willow
the turning point must not be in this interval
opal marsh
yes
pallid willow
why do you reckon this point cannot be in the interval?
opal marsh
why do you reckon this point cannot be in the interval?
two y values for one x
pallid willow
close enough
opal marsh
h
pallid willow
so now, for f(x) = x^2 + ax, what is the x-coordinate of the turning point?
opal marsh
0
pallid willow
well... close enough I guess
it's the point where the U transitions from going down to going up or the other way round
informally speaking of course
pallid willow
right.
now, you are told that f(x) = x^2 + ax when x <= 0
and you know that you do not want the turning point to be in this interval
opal marsh
yes
pallid willow
so the turning point must be greater than 0
or equal to 0, but main point is >= 0
solve for a.
opal marsh
huh
pallid willow
you know that the x-coordinate of the turning point is -a/2
opal marsh
yes
pallid willow
you also know that this turning point cannot be in the same interval as the function
the function is defined this way for x <= 0
so the turning point must be at x >= 0
opal marsh
0 then
pallid willow
what 0?
opal marsh
a..
pallid willow
a ? 0
what's the sign in the "?"?
is it less than 0? greater than 0? or something else?
opal marsh
greater than 0
opal marsh
wasn't it <=
pallid willow
the function is defined for x <= 0. but you want the turning point to not be in this interval
pallid willow
yes, but you want the turning point to, again, not be in this interval
for it to not be in x <= 0 means that it must be in x > 0
x = 0 is okay as well for the turning point because it doesn't break anything
so we want the turning point to be at x >= 0 so that it is not in the interval where the function is
pallid willow
you're the OP. you should close
opal marsh
idk how
pallid willow
!done
obtuse pebbleBOT
If you are done with this channel, please mark your problem as solved by typing .close
opal marsh
.close
obtuse pebbleBOT
pallid willow
<@&268886789983436800> and here
obtuse pebbleBOT
Available help channel!
acoustic flare
hellow
acoustic flare
i am new
nimble nacelle
question?
acoustic flare
no i wanted to tell u about me
nimble nacelle
You open this channel means you have a math problem to ask right?
This channel is not for that tho
nimble nacelle
If you want others to get to know you, you can go to discussion channel or chill channel
round nova
no i wanted to tell u about me
-# this is a help channel for math for specfic questions help if u want to talk in general might i recommend #discussion or #math-discussion or #serious-discussionor #study-discussion?
round nova
wel i will come for activities
!done
obtuse pebbleBOT
wel i will come for activities
If you are done with this channel, please mark your problem as solved by typing .close
acoustic flare
yes
round nova
to close the channel you need to type .close!!
otherwiseee it will stay open and other ppl wont be able to use this to get help for math questions 
acoustic flare
hmm i gues
round nova
hey no! if u do please ask!!
acoustic flare
i didnt recieve holiday work
dense yoke
I will take that as a no
in that case, please move to the discussion channels to chat
.close (you can reopen before the channel is reclaimed if you do have a question, or just grab a new channel.)
fierce cape
obtuse pebbleBOT
proud delta
it seems like an open question
fierce cape
wdym
fierce cape
you can try approximate it as normal
i dont even know how to do the 1st step bro
proud delta
this is a frequency count table
fierce cape
ok
just show me how to do it
cuz idk what to do
and i dont wanna spend too much time on this 1 question
solar stump
it seems like an open question
This sort of question is deliberate - you're meant to interpolate (assuming the data points are evenly distributed in the class)
fierce cape
the final c.f. is 37 yea
proud delta
This sort of question is deliberate - you're meant to interpolate (assuming the ...
fitting technique is available, but need to choose order
fierce cape
can u like teach me or explain to me how this question is meant to be done
solar stump
fitting technique is available, but need to choose order
-# You see, this will be syllabus dependent - in the UK this is the approach taught at, and expected at, the school (pre-uni) level
proud delta
can u like teach me or explain to me how this question is meant to be done
you can try calculate percentage for 17-25, i.e., 21/37=56.757%
22.5 - 25.5 falls in 17-25, rounding off
fierce cape
ngl i just did it like this following rnadom steps
i dont get the percentage method
thats probably some university type thing
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
languid tinsel
Any suggestions on finding the connected components of $(\mathbb R \times \mathbb Q) \coprod S^1$?
obtuse pebbleBOT
Any suggestions on finding the connected components of $(\mathbb R \times \mathb...
warm shaleBOT
ILikeMathematics
languid tinsel
Is there a good way to visualize this?
shut lagoon
Can't you just see it as the two spaces separately?
You get S^1, and then RxQ can be seen as R^2 with horizontal lines removed at irrational heights.
Or is the square union meant to represent something other than the disjoint union
So then the connected components of the disjoint union would be connected components of either spaces.
What do you think connected components of RxQ would look like?
obtuse pebbleBOT
@languid tinsel Has your question been resolved?
languid tinsel
Or is the square union meant to represent something other than the disjoint unio...
Its the disjoint union yes
languid tinsel
So then the connected components of the disjoint union would be connected compon...
So then the connected components of the disjoint union would be connected components of either spaces.
Why?
Oh, right
We have a bunch of elements looking like (x, i)
where i is 1 or 2
And there can only be stuff in one component from the same i
shut lagoon
Yeah essentially
languid tinsel
So first, we will get all of S^1 as a component
shut lagoon
Yes
languid tinsel
Now for R x Q, we will get a bunch of horizontal lines
R x {z} for z in Q
And thats all, right?
shut lagoon
Yeah I mean you could argue why you get exactly one connected component for each z in Q
But that's the idea
languid tinsel
Yeah I mean you could argue why you get exactly one connected component for each...
As in, argue why R x Q doesnt have any more connected components?
shut lagoon
Well rather argue that those connected components Rx{z} are all indeed disjoint.
As in like
languid tinsel
Also, maybe the wording should be "maximal connected components"?
shut lagoon
Yeah
languid tinsel
Because of course we can take a subset of S^1 right
halcyon pewter
<@&268886789983436800> might be a ryan ahh ping but idk
quiet wadi
yeah no spam in the help channels
obtuse pebbleBOT
@languid tinsel Has your question been resolved?
near raptor
obtuse pebbleBOT
near raptor
i always get confused on these types of problems
fossil crag
which question? / quelle question?
near raptor
which question? / quelle question?
i did big one
as in 1) and 2)
tho im unsure of the result
and i did 1) a) too
fossil crag
so you're on 1b)
near raptor
yeah
wispy iris
Hada dima dima?
near raptor
Hada dima dima?
La national blanc
wispy iris
Chmn soal
near raptor
2)a)
woeful edge
yeah
tu as q>p et p=3
tu peux utiliser le resultat de I- 2) et puis le theoreme de Gausse
near raptor
tu peux utiliser le resultat de I- 2) et puis le theoreme de Gausse
Je le fais déjà mrc comme même
near raptor
2)a)
wispy iris
2)a)
P diff de 5 ghadir ghir verification
Of 5^p - 2^p atst3ml fermat
7it p o 5^p-2^p premier
near raptor
P diff de 5 ghadir ghir verification
how?
obtuse pebbleBOT
@near raptor Has your question been resolved?
obtuse pebbleBOT
@near raptor Has your question been resolved?
acoustic garnet
my evasion is 55 and a mob has 40 accuracy . every attack i roll my evasion from 0-55 and the mob rolls 0-40 . if my evasion is higher than their accuracy i dodge the hit, what is my chance of dodging?
obtuse pebbleBOT
my evasion is 55 and a mob has 40 accuracy . every attack i roll my evasion from...
ocean ingot
Number of rolls where you dodge divided by total ways to roll
zinc marten
no total outcome is 56*41
ocean ingot
So that'd be like (55 + 54 + 53 + ... + 15) / 56*41, depending on whether 0 is a possible roll and whether you need a greater roll or greater than or equal
drifting wraith
no, it would start with 41
41 + 41 + 41 ...
oh
yeah, either one works
it should be 15/56 + (41/56)(1/2 − 1/41)
,calc 41(35) / 56 / 41
,calc 15/56 + (41/56)(1/2 - 1/41)
warm shaleBOT
Result:
0.625
yes, but which
acoustic garnet
if the roll is equal . the chance you get hit is 50%
and yes. its possible to roll a 0
drifting wraith
Result:
```
0.61607142857143
```
ok calc gets it wrong somehow
,calc 41(35) / 56 / 41
warm shaleBOT
Result:
0.625
ok, we'll never know
acoustic garnet
thanks guys. may you always dodge succubus hits whilst freerunning 😘😘
tranquil flume
,calc 41/56 * 1/2 + 15/56 * 1
warm shaleBOT
Result:
0.63392857142857
,calc 41/56 * 1/2 + 15/56 * 1
warm shaleBOT
Result:
0.63392857142857
yeah
obtuse pebbleBOT
solar stump
thanks guys. may you always dodge succubus hits whilst freerunning 😘😘
wild valediction 
zenith raft
,w valediction
warm shaleBOT
solar stump
,w valediction
any sign-off message
obtuse pebbleBOT
Available help channel!
toxic harbor
please @ me
obtuse pebbleBOT
please @ me
haughty stump
please @ me
are you trying to check ur work?
toxic harbor
haughty stump
oh lol you cross multiplied incorrectly
toxic harbor
im an idiot
haughty stump
u good dawg
toxic harbor
lets start from scratch
gaunt current
And sin45 is 1 and sin 30 is 1/2
haughty stump
just go from after the cross multiplication but do it right
gaunt current
Why don't you substitute
toxic harbor
gaunt current
Correct
toxic harbor
And sin45 is 1 and sin 30 is 1/2
idk that i dont even know what is sin
gaunt current
👍
toxic harbor
so are my steps correct?
gaunt current
Sin is the ratio of the side opposite to the angle over the hypotenuse
toxic harbor
but wait if i move everything to one side then i will get a negative sin, and sin cant go under -1, can it?
toxic harbor
While cos is side adjacent to angle over hypotenuse
ik whats cosahtoa, i just dont know the real meaning
gaunt current
but wait if i move everything to one side then i will get a negative sin, and si...
Sin well can be negative. You'll learn that in higher classes
toxic harbor
Sin well can be negative. You'll learn that in higher classes
so if i move everything to one side its a correct step?
gaunt current
Are you in 10th
toxic harbor
11
gaunt current
so if i move everything to one side its a correct step?
Yes
toxic harbor
ok thanks
gaunt current
Wait in 11 then sin is as follows
toxic harbor
im doing 11 methods, last year i was in 10 general thats why this is a bit challenging
gaunt current
Let there be a circle in coordinate plane with r = 1 and center (0,0) each point on it is in form cosx, sinx
With angle 0 on positive x axis
Its the real meaning of sin
gaunt current
Anyways in 12th you'll learn
sin(x) = x -( x^3)/6+(x^5)/120.....
toxic harbor
wait if i remove sin 45 to other side wouldnt it be (all)/sin 45 ?
toxic harbor
i dont wanna use stuff that i didnt learn
gaunt current
i dont wanna use stuff that i didnt learn
Ok
gaunt current
Yes
gaunt current
See sin 45- sin 30 is not sin15
toxic harbor
i put sin (-15)
gaunt current
Sin does not work like this
toxic harbor
but heres the thing sin isnt being added its being multiplied, and opposite of multiplication is division
so do i divide?
stoic breach
please @ me
This is wrong.
gaunt current
i put sin (-15)
Sin 15 is in fact sin45cos30-cos45sin30
toxic harbor
yeh were trying to solve it rn
stoic breach
From the third line.
toxic harbor
Sin 15 is in fact sin45*cos30-cos45*sin30
how should ik
gaunt current
how should ik
Basically you can't write it like that
stoic breach
Wait what no this is wrong.
stoic breach
Expand this.
toxic harbor
wait if i remove sin 45 to other side wouldnt it be (all)/sin 45 ?
@stoic breach this is ma question
gaunt current
Wait what no this is wrong.
Exactly thats what I'm explaining
stoic breach
wait if i remove sin 45 to other side wouldnt it be (all)/sin 45 ?
Yes, it is.
toxic harbor
thank u
gaunt current
But sin a+b is not sin a + sin b
toxic harbor
gaunt current
How?
toxic harbor
-5-3=-8
stoic breach
It would be: $\frac{\sin{30}}{\sin{45}}(2x-5)=x+3$
warm shaleBOT
Mercury (ヤフォダ)
stoic breach
@toxic harbor
gaunt current
x+3 is multiplication
toxic harbor
<@1476553835060265104>
can u explain
stoic breach
Because you cancel out $\sin{45}$ from $(x+3)(\sin{45})$
warm shaleBOT
Mercury (ヤフォダ)
gaunt current
You don't know simple cross multiplication
warm shaleBOT
Mercury (ヤフォダ)
toxic harbor
yes but i assumed you divide the left side by sin 45
stoic breach
yes but i assumed you divide the left side by sin 45
You divide both side by sin 45.
gaunt current
Yes
toxic harbor
now it makes lots of sense
gaunt current
Sorry
stoic breach
Nah it's fine.
toxic harbor
gaunt current
What about I suggest using partial fractions
toxic harbor
now do i do (all)-x+3
toxic harbor
What about I suggest using partial fractions
so im wrong?
gaunt current
so im wrong?
No
stoic breach
Yes.
gaunt current
You're right
toxic harbor
do i really need it?
stoic breach
It must be $\frac{\sin{30}}{\sin{45}}(2x-5)$
warm shaleBOT
Mercury (ヤフォダ)
gaunt current
It is 2+(1/x+3)
stoic breach
Else it can be understood as $\frac{2x-(5\sin{30})}{\sin{45}}$
toxic harbor
so are we multiplying everything by 2x-5?
warm shaleBOT
Mercury (ヤフォダ)
stoic breach
Correct.
gaunt current
**Mercury (ヤフォダ)**
Incorrect
stoic breach
but why tho, its a*b i cant just split them
if you split them you have to multiply sin 30/sin 45 to both 2x and -5
toxic harbor
idk whose right, but i trust mercury
gaunt current
$(2*x-5) \sin{ 30}$
warm shaleBOT
Coder decoder
stoic breach
$\frac{\sin{30}}{\sin{45}}(2x-5)=x+3$ here.
warm shaleBOT
Mercury (ヤフォダ)
toxic harbor
what i dont get is why isnt 2x-5 next to sin 30, they a part of each other
stoic breach
You can write: $\frac{\sin{30}(2x-5)}{\sin{45}} = x+3$
gaunt current
$\frac{\sin{30}}{\sin{45}}(2x-5)=x+3$ here.
You wrote $2x-(5 \sin 30)$
warm shaleBOT
Mercury (ヤフォダ)
stoic breach
It is still the same though.
toxic harbor
thats what i had
warm shaleBOT
Coder decoder
stoic breach
You wrote $2x-(5 \sin 30)$
Because Moey didn't use bracket, and could lead to that possibilities?
stoic breach
thats what i had
Can you calculate sin 30 / sin 45?
gaunt current
2/√2.
warm shaleBOT
toxic harbor
yeh that
stoic breach
Then $2\sqrt{2} (2x-5)=x-3$.
warm shaleBOT
Mercury (ヤフォダ)
stoic breach
Can you expand it and solve normally?
toxic harbor
is this really different from this
can u answer this pls
stoic breach
is this really different from this
No, it is the same.
toxic harbor
i believe im very wrong
gaunt current
i believe im very wrong
You told me you don't want to use sin 45 =1/√2
toxic harbor
You told me you don't want to use sin 45 =1/√2
i didnt we used sin 30/sin 45
toxic harbor
i believe im very wrong
can u just tell me if this is wrong
toxic harbor
u didnt answer my question
gaunt current
a/b or a/c is the same when b = c
gaunt current
u didnt answer my question
Cause you said you didn't want to use it
toxic harbor
Cause you said you didn't want to use it
can u just tell me if im right
gaunt current
Yes
toxic harbor
or wrong
toxic harbor
and how do i get rid of x
gaunt current
You're supposed to find it I presume