? (2y-3)^2 = 49 find the square root of both sides and you get 2y-3 = +-7 which xan be seperated into the two equations i mentioned before
#help-13
crimson sedge
shrewd blaze
Wait, 2y=4? I transfer 3 to 7
crimson sedge
2y-3=7
2y=10 , y=5
2y-3=-7
2y=-4
y=-2
y=-2 and 5
shrewd blaze
Wait, 2y=4? I transfer 3 to 7
Yay im correct
crimson sedge
transfer what
shrewd blaze
33
shrewd blaze
-33
crimson sedge
No
shrewd blaze
😭😭😭
crimson sedge
what is -41-8
shrewd blaze
So i will not answer it?
shrewd blaze
Okiee
crimson sedge
because you cant multiply any real number by itself to get a negative number
shrewd blaze
Thankk
shrewd blaze
because you cant multiply any real number by itself to get a negative number
But do we square it with -1 to make it positive?
Anyway
Lets do 4
crimson sedge
You have number 4 right you just forgot the +- sign
crimson sedge
You forgot the +- sign
shrewd blaze
Ahhh okayy
Thankkk
Thank you very very muchhh
Heheheh
Is it done, did i forget something?
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
wooden heart
Name one pair of rays that are not opposite rays
cedar kilnBOT
Name one pair of rays that are not opposite rays
wooden heart
I don’t get what it wants me to do?the way they said kinda confusin
crimson sedge
Name one pair of rays that are not opposite rays
first, What is an opposite ray
opposite rays are rays that share an endpoint and go opposite directions
wooden heart
But don’t rays go forever?
crimson sedge
Not in both directions
rays start at one point and continue on forever in the other
LINES go on forever in both directions
wooden heart
So would B,E,C be a opposite rays?
crimson sedge
No also thats not the correct terminology
B, E, C is naming three points
Yoo need to name two rays that are not opposite
wooden heart
So
crimson sedge
Do you know what a ray is
wooden heart
S and T
crimson sedge
Where is s and t
also thats not how you name a ray
Example of a ray: Ray BD, Ray CA , etc
wooden heart
wooden heart
Ok
crimson sedge
Ok so @wooden heart s and t are naming the line not the ray pretty sure
you need to find two rays that are not opposite
wooden heart
Ye
wooden heart
I thought u said those were points?
crimson sedge
They dont share an endpoint and dont go opposite ways
crimson sedge
I thought u said those were points?
two points make a line, segment, or ray
wooden heart
Oh ye…
And I’m just trying to find a one that’s not opposites
So would Ray AE and Ray BE be opposite rays then?
crimson sedge
not necessarily. AE and EB dont go the same direction or opposite directions
and they're also not opposite rays
btw you need to name a ray with the endpoint first
tepid quiver
Conditional probability, wondering if P(H3 x A) is the same as P(A x H3)
mental trail
cedar kilnBOT
honest inlet
I found the total area to be 40ln(2.5)+20ln(4)-32 in exact form
<@&286206848099549185>
cedar kilnBOT
@honest inlet Has your question been resolved?
brave nacelle
How do i evaluate this?(my topic is functions and relation)
1.+7x² +35x-45
A.10
B.3
C.-4
General Mathematics
humble karma
Define "evaluate". Your question statement is missing something.
brave nacelle
I think i wrote it wrong.
F(x) +7x²+35x-45
A.10
B.3
C.-4
surreal cave
evaluate $7x^2+35x-45$ at $x=10,3,-4$?
wraith daggerBOT
MrFancy
humble karma
Still missing something. You need to evaluate something AT some point
Ohh
I thought it was MCQ
brave nacelle
What's MCQ
humble karma
multi-choice question
surreal cave
multiple choice question(s)
humble karma
that
brave nacelle
Idk if it's a multiple choice question or not...
humble karma
It's probably not, what MrFancy wrote makes sense
brave nacelle
I can understand pre-calculus but not general math....
humble karma
Idk if it's a multiple choice question or not...
If you're doing an exam and you have to circle the answer amongst some other answers, then that's a MCQ. Otherwise not.
Here it looks like they're asking to evaluate your expression for different values of x
So for A., you want to evaluate F(10)
So plug in 10 in your expression wherever you see x
brave nacelle
Could you give me an example on how to evaluate F(10)?
humble karma
Where you see x
You put 10
F(2) = 7 * (2)^2 + 35(2) - 45
F(banana) = 7* (banana)^2 + 35*banana - 45
brave nacelle
Ohh
So if there isn't any ^2 then i multiply by the number inside the parentheses?
humble karma
Yeah I put parentheses there to avoid confusion, but it's just multiplication
brave nacelle
Sooo for A will be
F(10) = +7(10)^2 +35(10) -45
= +7(100) + 350 - 45
=(?) 700 + 350 - 45
= 1050 - 45
= 1005
Is this right or wrong?....
@humble karma
humble karma
10^2 is not equal to 20
brave nacelle
It's 100 isn't it?
humble karma
Yes
humble karma
Yes
brave nacelle
Alright ima do B and C please tell me if it's right
humble karma
Ok
I mean it's just evaluation at this point. You can ask WolframAlpha https://www.wolframalpha.com/input?i=7*x**2%2B35x-45+at+x+%3D+10
brave nacelle
@humble karma
cedar kilnBOT
<@125307464647180288>
brave nacelle
I need another help...
Identify whether it is odd even or neither
- F(x) -3x^2 -5x
What the heck
How did you compute that
celest ledge
For any polynomial f, f(x)=odd_f(x)+even_f(x). Like f(x)=3x^2-7x+4 even_f(x)=3x^2+4, odd_f(x)=-7x
I use o(x) e(x) respectively for shorter expressions
f being odd <-> o(-x)+e(-x)=-(o(x)+e(x))<-> e(x)=e(-x)=-e(x) <-> f(x) itself equals o(x)
Similar f is even <-> f itself equals e(x).
So whenever your f has both odd power terms and even power terms, it is neither odd nor even
brave nacelle
I still don't get it...
Where did 3 go
This is functions right?
Can u explain it to me
celest ledge
For any polynomial f, f(x)=odd_f(x)+even_f(x). Like f(x)=3x^2-7x+4 even_f(x)=3x^...
Your polynomial -3x^2-5x has both odd power term -5x and even power term -3x^2, so it’s neither odd nor even by this
Why?
brave nacelle
I got a note here saying
Nothing changed = even
All changed formula = odd
Some changed = neither
celest ledge
y(x)=-3(x-5/6)^2+25/12
brave nacelle
But idk
celest ledge
Your polynomial -3x^2-5x has both odd power term -5x and even power term -3x^2, ...
And here is my answer
brave nacelle
Is there like a solution im supposed to see orr just straight up look for odd and even numbers
celest ledge
Like I explained
Any polynomial f
Can be break into sum of two parts
One is sum of odd power terms , denote it by o(x)
Another one is sum of even power terms denoted by e(x)
Like I proved
f being odd <-> e(x)=0
f being even <-> o(x)=0
Now for you f, neither o(x)=-5x nor e(x)=-3x^2 is zero
Therefore it’s neither odd nor even
Again, -3x^2-5x=-3(x-5/6)^2+25/12
+/-3x^2+/-5x is neither , similarly
brave nacelle
I do not understand
celest ledge
Read what I sent
Whatever you are typing must be very long. As I said, ax^2+bx+c , a non-zero, is symmetric by x=-b/2a. So symmetric by x=0 iff b=0. Now whatever your b is, 5 or -5 is not zero, therefore you saying it’s even is wrong
Just to confirm , what is your f(x) again?
The expression of f(x) I mean
I am just making sure of it
celest ledge
Again, -3x^2-5x=-3(x-5/6)^2+25/12
So see?
You want to draw this on paper or , wolfram ?
brave nacelle
My brain is having a seizure
celest ledge
That paragraph is to show you saying f being even is wrong
brave nacelle
Wait
celest ledge
Any polynomial f
My proof starts from here
brave nacelle
What about this
brave nacelle
f(w) = 4w +21
celest ledge
odd+odd or odd-odd is still odd?
And do you agree that
even+even or even-even is still even?
(Easy to prove)
brave nacelle
Even + odd is neither?
celest ledge
Just tell me whether you agree the things said above
And do you agree that a function both odd and even must be constant 0?
brave nacelle
No?
celest ledge
No?
Which one you disagree
addition or subtraction of two odd is still odd
Two even still even
Or both odd and even has to be 0.
These three sentences, which one you disagree?
brave nacelle
And do you agree that a function both odd and even must be constant 0?
I disagree on this one?
celest ledge
I disagree on this one?
Okay g(x) is both even and odd. then -g(-x)=g(x) since it’s odd
g(-x)=g(x) since it’s even
Add these two equations, 2g(x)=0, so g(x)=0, for any x
So now you agree with these three sentences?
Real values
I am waiting for him to confirm the three statements I gave him
brave nacelle
celest ledge
Irrelevant with his original question. I will use these three to make him understand what I proved
celest ledge
Can you please confirm you got that three statements I said
celest ledge
addition or subtraction of two odd is still odd
Two even still even
Or both odd ...
These three
celest ledge
Okay g(x) is both even and odd. then -g(-x)=g(x) since it’s odd
g(-x)=g(x) since...
This is proof of the third
brave nacelle
You're talking about this odd+odd = odd being the first statement right?
celest ledge
Yeah first odd+odd or odd-odd is still odd
Second : even +even or even-even are still even
Third a function being both even and odd can only be 0
celest ledge
Okay g(x) is both even and odd. then -g(-x)=g(x) since it’s odd
g(-x)=g(x) since...
You said you didn’t get the third , I proved it. Please read it and confirm that you get it now
brave nacelle
Okay g(x) is both even and odd. then -g(-x)=g(x) since it’s odd
g(-x)=g(x) since...
I still don't understand this
brave nacelle
I don't know what that -g(-x)=g(X) is supposed to mean
celest ledge
g being an odd function
Means g(-x)=-g(x) for any x
So -g(-x)=g(x)
g being an even function
Means g(-x)=g(x)
Combine these two, since g is both even and odd, 2g(x)=0 therefore g(x)=0, so g can only be 0
You get it now? I need to move on and continue
brave nacelle
Ohhhhh
celest ledge
Good I move on:
Polynomial f(x), write f(x) as o(x)+e(x). Where o(x) is sum of odd power terms of f(x). e(x) is sum of even power terms of f(x).
Clearly o(x) is odd and e(x) is even
f(x) is odd <-> e(x)=f(x)-o(x) is odd <-> e(x) is both even and odd <-> e(x)=0
f(x) is even <-> o(x)=f(x)-e(x) is even <-> o(x) is both even and odd <-> o(x)=0
QED
Apply to your case : in your case neither o(x)=-5x nor e(x)=-3x^2 is zero, therefore your f(x)=-3x^2-5x is neither odd nor even
celest ledge
No . Short for polynomial f(x)
Edited for your convenience
I already made it the easiest possible way
celest ledge
Odd-odd being odd is used in where “e(x)=f(x)-o(x) is odd”
Even-even being even is used in where “o(x)=f(x)-e(x) is even”
No
celest ledge
This one's odd + odd right?
f(w) = 4w +21
Neither odd nor even
this case o(w)=4w, e(w)=21
remember 0 is an even number
celest ledge
Polynomial f(x), write f(x) as o(x)+e(x). Where o(x) is sum of odd power terms o...
So get it now or you want to read one more time
brave nacelle
how did f(x) become o(x)
celest ledge
<-> means if and only if by the way
Because I just proved f(x) is odd if and only if e(x)=0, this case f(x)=o(x)+e(x)=o(x)+0=o(x)
brave nacelle
Because I just proved f(x) is odd if and only if e(x)=0, this case f(x)=o(x)+e(x...
This solution, are you talking about 4w +21 or 3x²-5x
celest ledge
For general case
Any polynomial f(x)
f(x) is odd if and only if the even part of it e(x)=0
f(x) is even if and only if the odd part of it o(x)=0
celest ledge
f(w)=4w+21 you said
celest ledge
Is f(w)=4w+21 or f(w)=4w
brave nacelle
I just didn't include the +21
celest ledge
Are you talking about this function f(w)=4w?
brave nacelle
Yes
brave nacelle
4 is odd?
celest ledge
It has nothing to do with coefficients being odd or even
o(w)=4w, not 0, e(w)=0, is 0, so f(w) is odd
celest ledge
f(x) is odd if and only if the even part of it e(x)=0
f(x) is even if and only i...
Again, this
brave nacelle
this case o(w)=4w, e(w)=0
Does this mean you just removed the parentheses?
celest ledge
What parentheses it has nothing to do with parentheses
$$f(x)=\sum_{k}a_{k}x^{k}$$
Then
$$o(x)=\sum_{k, k \text{odd}}a_{k}x^{k}=\sum_{j}a_{2j+1}x^{2j+1}$$
$$e(x)=\sum_{k, k \text{even}}a_{k}x^{k}=\sum_{j}a_{2j}x^{2j}$$
brave nacelle
Ok if you said f(x) -3x² -5x is neither, how is it neither?
wraith daggerBOT
Cogwheels of the mind
celest ledge
f(x)=-3x^2-5x
o(x)=-5x, e(x)=-3x^2
Neither o(x) nor e(x) is zero, therefore f(x) is neither odd nor even
Don’t overthink it.
It’s just o(x) is you put all odd power terms a_1x, a_3x^3,… together, o(x)=a_1 x+a_3 x^3+…
e(x)=a_0+a_2 x^2+a_4 x^4+…
Put all even power terms together
celest ledge
f(x)=-3x^2-5x
a_0=0, a_1=-5, a_2=-3, a_3=a_4=…=0
So f(x) has no even power term in it <-> f(x) is odd
f(x) has no odd power term in it <-> f(x) is even
f(x) has both odd and even power terms in it <-> f(x) is neither odd nor even
brave nacelle
I still can't understand how you got neither
celest ledge
No, all high school stuffs
brave nacelle
Senior secondary school
celest ledge
I am already being more patient than I usually am. Because I guessed you are a high school student
Usually I walk away
brave nacelle
I am really sorry if I am getting on your nerves
celest ledge
A little bit, but doesn’t bother
brave nacelle
Cause the first time i went here and asked how to compute the
+7x² +35x -45
A.10
B.3
C.-4
Turns out you just need to put the 10 to the x
Pretty simple right, but then this even odd or neither pops up
brave nacelle
The teacher just straight up put it as a homework
celest ledge
You see power 0, power 1, power 2 in it
-45 is power 0 term
35x is power 1 term
7x^2 is power 2 term
If you have only odd power term -> it is odd
If you have only even power term-> it is even
brave nacelle
celest ledge
You have both-> neither
brave nacelle
This is right?
brave nacelle
Nono i already got that answered
celest ledge
Let’s finish your original question, odd even things then
brave nacelle
Yes
celest ledge
Good
celest ledge
Power 0 and 1
brave nacelle
Okay last one
celest ledge
Give me one, whatever polynomial you can think of
celest ledge
Which powers appear?
celest ledge
There isn’t power 1
celest ledge
f(n)=23n^3-11
Again it has nothing to do with coefficients Being odd or even
Just whether coefficients being non-zero or zero
celest ledge
No…
I thought you finally got it
23n^3, so power 3
-11, power 0
Powers are 0, 3
celest ledge
To make sure you get it. I make up one example:
4x-7x^2+100x^6-279x^8
Powers are?
celest ledge
Not enough
brave nacelle
Is there something im not seeing?
celest ledge
1,2,6,8
brave nacelle
5 and 11
celest ledge
Not enough…
brave nacelle
WHAT
celest ledge
0,5,11
brave nacelle
27482 is 0
brave nacelle
Okay try me one more time
celest ledge
f(x)=21-x+8x^3+5x^5
brave nacelle
0,1,3,5
celest ledge
And are there odd numbers among these power? And Are there even among them?
celest ledge
Good
brave nacelle
This is neither
celest ledge
Good
brave nacelle
3,7
celest ledge
Continue
brave nacelle
Odd
celest ledge
Great
celest ledge
Yes
brave nacelle
Thank you so much
celest ledge
Np
cedar kilnBOT
@brave nacelle Has your question been resolved?
frank bronze
jus was wondering how to do this
crimson sedge
suppose it exists
then you use limit laws for division
and gets contradiction
it's an analysis class?
or calculus?
frank bronze
its calc
frank bronze
then you use limit laws for division
limit laws?
cedar kilnBOT
Available help channel!
crimson sedge
limit laws?
cedar kilnBOT
wraith daggerBOT
IllIIIllIlIIl
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
.close
cedar kilnBOT
Available help channel!
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
Available help channel!
prisma gull
cedar kilnBOT
prisma gull
Is it correct?
celest ledge
Checking
But first it will help me speed up if you
Give me the prime factorization of 2860
And 4165 respectively
celest ledge
Okay I use online calculator
prisma gull
yes
prisma gull
49 divides 4165 right?
prisma gull
oh but 49 isnt prime
celest ledge
Actually the counterexample is unique in this case
Yeah
I mean yeah it isn’t
So you know the counterexample?
prisma gull
yess
celest ledge
(Finite group G of order n, p^k|n, there always exist subgroups of order p^k, by sylow theorem)
Oh
celest ledge
I mean, I would like to know
Direct product of Z/5Z, Z/7Z, Z/7Z, Z/17Z
There are only two cases actually
The another that does have an element of order 49, is the direct product of Z/5Z, Z/49Z, Z/17Z by the way.
prisma gull
i see
celest ledge
So get it?
celest ledge
(a,b,c) in Z/5Z times (Z/7Z times Z/7Z) times Z/17Z
order of (a,b,c) in this product, is lcm(order(a),order(b),order(c)) . So if it equals 49, then order(a)=order(c)=1, meaning order(b)=49 which is impossible
Because Z/7Z times Z/7Z, orders of elements is either 1 or 7
prisma gull
Let me go through
cedar kilnBOT
@prisma gull Has your question been resolved?
celest ledge
I am going to take a shower… you can DM me if you have further questions…
empty locust
can someone please guide me through this question
cedar kilnBOT
can someone please guide me through this question
empty locust
i get how we can just multiply with the rotation matrix
but i wanted to understand it in terms of diagram
so can someone help with a part then maybe i can buil up further on that
cedar kilnBOT
@empty locust Has your question been resolved?
cedar kilnBOT
@empty locust Has your question been resolved?
cedar kilnBOT
@empty locust Has your question been resolved?
cedar kilnBOT
@empty locust Has your question been resolved?
worldly chasm
@empty locust it's isn't clear to me what your question is. Are you just having difficulty visualizing the rotation?
empty locust
<@793385686354755615> it's isn't clear to me what your question is. Are you just...
I can visualise and I can just sub in the formula and get the answer but I am not getting why
worldly chasm
Why what?
worldly chasm
@empty locust
empty locust
<@793385686354755615>
sorry i was in a class
okay so this is the diagram i have made
empty locust
That looks correct to me
but how do I proceed further?
i know the answer is
$\mathbf{\hat{\epsilon}_1'}=\cos\theta\mathbf{\hat{\epsilon}_1}+\sin\theta\mathbf{\hat{\epsilon}_2}$
$\mathbf{\hat{\epsilon}_2'}=-\sin\theta\mathbf{\hat{\epsilon}_1}+\cos\theta\mathbf{\hat{\epsilon}_2}$
wraith daggerBOT
Heisenberg.
empty locust
and we can get that by multiply with rotation matrix?
worldly chasm
Yeah
empty locust
but like that just doesnt sit with me. I mean if I only had this diagram then how would i proceed to get the answer?
worldly chasm
I assume that you're uncertain how to construct a rotation matrix from a diagram?
empty locust
I assume that you're uncertain how to construct a rotation matrix from a diagram...
yeaaa
worldly chasm
So a basic two dimensional rotation matrix is given by
$$\begin{pmatrix}
\cos \theta & -\sin \theta \
\sin \theta & \cos \theta
\end{pmatrix}$$
Right?
wraith daggerBOT
OmnipotentEntity
worldly chasm
You're comfortable with this I'm assuming
This rotates x and y about the origin of the xy plane
@empty locust ^
empty locust
yesss
worldly chasm
Ok cool, we have 3 dimensions though
So we can make a matrix that just leaves the last component alone
empty locust
since e3= e3prime so rotation in that direction will be 0 right
worldly chasm
$$\begin{pmatrix}
\cos \theta & -\sin \theta & 0 \
\sin \theta & \cos \theta & 0 \
0 & 0 & 1 \
\end{pmatrix}$$
wraith daggerBOT
OmnipotentEntity
worldly chasm
Now if we multiply this matrix by the vector (e1, e2, e3)^T we get our transformed e1' and e2' but e3 is left alone
empty locust
Now if we multiply this matrix by the vector (e1, e2, e3)^T we get our transform...
yeaaa I get that but I dont get how we can figure out the matrix. I mean we can easily answer this question by knowing the rotation matrix but what if i we didnt know it then how will we derive the rotation matrix from this question??
worldly chasm
Oh
You don't want to know how to use the rotation matrix but how to derive it.
Ok, do you know much about complex numbers?
I know this sounds like it's out of left field, but if you know about them it helps a lot
empty locust
Ok, do you know much about complex numbers?
not a lot. I mean i have studied it but forgotten
i looked at some derivations online
and they used trig
but they all were for vectors
not for coordinate system
worldly chasm
Well a coordinate system is literally just a collection of vectors
e1 is the vector (1, 0, 0)^T for instance
So when you write, for instance, (3, 6, -1)^T you are writing 3e1 + 6e2 - e3.
$$\begin{pmatrix} 3 \ 6 \ -1 \end{pmatrix} = 3 \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} + 6 \begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix} + (-1) \begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix}$$
wraith daggerBOT
OmnipotentEntity
worldly chasm
So a rotation that applies to any vector will apply also to these specific vectors.
@empty locust
worldly chasm
👍
simple bane
$CD=2a^2+3a^2-2\sqrt{3}\sqrt{2}a^2cos(75)$
cedar kilnBOT
$CD=2a^2+3a^2-2\sqrt{3}\sqrt{2}a^2cos(75)$
simple bane
how do i simplify this
wraith daggerBOT
张元英
umbral dew
you know the value of cos75?
simple bane
no
cannot use any kind of aid
$CD=2a^2+3a^2-2\sqrt{3}\sqrt{2}a^\frac{\sqrt{6}-\sqrt{2}}{4}$
wraith daggerBOT
张元英
umbral dew
you can learn this tho, if you want to
simple bane
what is that
simple bane
i mean the probability of getting 7.5 degrees is not good
umbral dew
we just need to be ready, we dont know whats about to come in exams, these are some obervational values, it can obv be finded out, but doint all this takes a lot of time and no body be wanting to waste thier time, specially in a test where any kind of question can be given
i mean its not neccesary to learn all these, but i makes you better than others
simple bane
agree with that statement
but, memorizing that seems a little far fetched
and excessive
umbral dew
i mean i can simplify this ques now because i know its value
i dont know how i can help you with another way
simple bane
$5a^2-2\sqrt{3}\sqrt{2}a^2*\frac{\sqrt{6}-\sqrt{2}}{4}$
wraith daggerBOT
张元英
simple bane
$5a^2-2a^2\frac{6-\sqrt{2}}{4}$
wraith daggerBOT
张元英
umbral dew
wait what?
simple bane
$\sqrt{6}\sqrt{6}=6$
wraith daggerBOT
张元英
umbral dew
wait i messed up
yeah
simple bane
$5a^2-2\sqrt{6}a^2*\frac{\sqrt{6}-\sqrt{2}}{4}$
wraith daggerBOT
张元英
umbral dew
yes now?
simple bane
$5a^2-2a^2*\frac{6-2\sqrt{3}}{4}$
wraith daggerBOT
张元英
simple bane
$5a^2-2a^2*\frac{2(3-\sqrt{3})}{2*2}$
wraith daggerBOT
张元英
simple bane
$5a^2-2a^2*\frac{3-\sqrt{3}}{2}$
umbral dew
cancel the 2's now
wraith daggerBOT
张元英
umbral dew
again
simple bane
$5a^2-a^2*\frac{3-\sqrt{3}$
wraith daggerBOT
张元英
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
umbral dew
$5a^2-a^2*\frac{3-\sqrt{3}}{1}$
wraith daggerBOT
yajatk07
simple bane
$5a^2-a^2*({3-\sqrt{3})$
wraith daggerBOT
张元英
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
umbral dew
yeah now open the bracket and then just simplyfi it a little bit and youre done
simple bane
$5a^2-3a^2+\sqrt{3}a^2$
wraith daggerBOT
张元英
simple bane
$2a^2+\sqrt{3}a^2$
wraith daggerBOT
张元英
umbral dew
yeaah, youre done
simple bane
i think i got the wrong answer...
umbral dew
we got the second term wrong
simple bane
yes
umbral dew
and we were to find CD?
simple bane
and we were to find CD?
thank you for helpin though
i really appreciate it
enough math for today
.close
.close
deft arch
in the next questions im gonna refer to words in lengthe 9 built from the charcters : A ,A , B, B, B, C, C, C, C.
Q1 true or false :
the number of words will grow twice if we will add one more C to the given charcters ?
cedar kilnBOT
in the next questions im gonna refer to words in lengthe 9 built from the charct...
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thin torrent
how do i sove for t if 16 = (-6t) + 1/2 x 2 x t^2
cedar kilnBOT
how do i sove for t if 16 = (-6t) + 1/2 x 2 x t^2
@thin torrent Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
finite raven
What is your reasoning
cedar kilnBOT
@cyan void Has your question been resolved?
finite raven
What is your reasoning @cyan void
cyan void
What is your reasoning <@1072266627497852988>
idk
cyan void
So you just guessed
kinda
cedar kilnBOT
@cyan void Has your question been resolved?
cyan void
What is your reasoning
is this right
finite raven
yes
cedar kilnBOT
Available help channel!
cyan void
I didn’t mean to close
Whatd I get wrong here
cyan void
<@&286206848099549185>
surreal temple
I didn’t mean to close
Isn't it -4, 1
The lowest point is x=-5 y=-4
And the highest point y=1
cyan void
And the highest point y=1
so this?
oh shit
i was looking at the dots
not the highest and lowest
@surreal temple
surreal temple
Yes
cyan void
-6 is less than 4
the smaller one goes first?
surreal temple
Yes
surreal temple
Probably not
You find f-1 (x) by f(f-1(x)) = x
so f-1($(x^1/3-1)/9$) = x
$f^-1$
f'
$f'((x^(1/3)-1)/9)=x$
wraith daggerBOT
Minyuan
cyan void
Bruh I don't know how to use this ting
crimson sedge
would i get a answer if i graph this
you know how to get the inverse function?
surreal temple
Yeah
cyan void
you just switch f(x) with x and solve for f(x)
is this right @surreal temple
surreal temple
I don't think so
I think it's 9x+1 ^ 3
Because 9x makes x^1/3-1, then 9x+1 is x^1/3, then ^3 is x
crimson sedge
I think it's 9x+1 ^ 3
dont give out answers
glossy tangle
hi need some help adding and simplifying \frac{x^2-2x}{x^2+4x}+\frac{x^2+x}{x^2+4x}
glossy tangle
\frac{x^2-2x}{x^2+4x}+\frac{x^2+x}{x^2+4x}
smoky idol
wrap your query with $$
astral bay
$\frac{x^2-2x}{x^2+4x}+\frac{x^2+x}{x^2+4x}$
wraith daggerBOT
bee [it/its]
glossy tangle
thanks
I can add it so its 2x^2 -1x/x^2+4 but i am having trouble simplifying it
?
never using latex again 
<@&286206848099549185>
flint meteor
if 4 converted to 2 square and then make it in form same as numerator
something like that
glossy tangle
if 4 converted to 2 square and then make it in form same as numerator
wdym?
.close
jolly sable
F(x) = sin (x^2)/x
What should I say for this function
Trigonometric function/polynomial?
muted bear
Neither
upper abyss
Definitely not a polynomial, as it's not a finite sum of x^n, with natural n
I wouldn't personally call it a trig function but that's not a well defined thing afaik
muted bear
i would consider a trig function solely based off the functions sin x, cos x, tan x, etc.
probably sum and products, but idk that seems to be pushing it
lime gyro
Can I get help understanding what I need to do to set up the problem??
drifting marlin
What's your class's definition of average velocity?
(Or more generally average rate of change)
lime gyro
What's your class's definition of average velocity?
basically slope ( its Cal 1)
drifting marlin
I'd prefer something more specific
lime gyro
I'd prefer something more specific
that is what my professor told me lol
drifting marlin
Can I see exactly what they showed you?
The average rate of change of a function is related to a slope, but "basically slope" is most certainly not what they told you
lime gyro
The average rate of change of a function is related to a slope, but "basically s...
lemme see if i can find it, one second
I couldnt find her exact notes but here is mine from that day where we defined it
it is equal to slope with distance being on top and time on bottom
<@&286206848099549185>
cedar kilnBOT
@lime gyro Has your question been resolved?
cedar kilnBOT
@lime gyro Has your question been resolved?
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Available help channel!
vocal harness
Hey ya'll, wanted some help on understanding this problem, I've already solved it, I just want to double check with someone for understanding!
vocal harness
I set it up like
$6-2.9(x-6)+0.5(y-6)$
Which simplifies down to
$-2.9x+0.5y+20.4$
wraith daggerBOT
Huntifer
vocal harness
My question kinda lies in the original setup, I understand that the 6 on its own represents Z, the 6 million they're selling per year in this example
I guess my question is, why the (x-6) and (y-6)?
wraith daggerBOT
Huntifer
vocal harness
Sorry had to fix the variable, so its below the other equation now
I sort of understand that 20.4 is supposed to be the "fixed" value in this case, is this meant to be for the current year, where the 6 million units sold in x caused a 17.4 million decline in sales and 6 million units of y sold causes a 3 million increase in sales?
So it levels out whatever the extra 1 input in x and y would be to give an answer of z that models 6 million units of z sold already, and then subtracts and adds whatever the extra millions of x and y are sold that year past 6?
cedar kilnBOT
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Available help channel!
vapid sand
how am I suppose to start this
cedar kilnBOT
how am I suppose to start this
crimson delta
try to find some a,b so that the RHS is (a+b)^n
vapid sand
is the binomial theorem (1+x)^n
crimson sedge
that's a binomial that can be expanded using the binomial theorem
vapid sand
oh my bad
crimson delta
"(1+x)^n" is an expression, not a theorem
crimson sedge
not the binomial theorem itself
vapid sand
uhh
(n k) (1)^k x^n-k
I know I have to do something with (-1)^n but what exactly is my problem
crimson sedge
\darkmode
\[
(a+b)^n =\sum_{j=0}^n \binom n j a^{n-j} b^j
\]
is what you mean
oh so now I use the sum in this context?
crimson delta
(RHS has x,y instead of a,b)
wraith daggerBOT
crimson sedge
oops nice catch
crimson sedge
oh so now I use the sum in this context?
can you try writing the RHS of the question you sent above in sum notation?
crimson sedge
how am I suppose to start this
\darkmode
as in, [
\binom n 0 - \binom n 1 + \hdots + (-1)^n \binom n n = \sum ???
]
wraith daggerBOT
crimson sedge
n sum k = 0 (n k) 1^k * x^(n-k)
please just write on paper because this is very hard to parse
vapid sand
crimson sedge
okay... what are the contents of the sum?
vapid sand
oh you want all of it
sorry
I really do not know what I am suppose to do with the (-1)^n
crimson sedge
you're saying that represents this?
vapid sand
..does it not?
crimson sedge
well you kind of summoned that x from nirvana
vapid sand
good point
crimson sedge
and also how can that sum ever have negative terms if it is 1^k?
vapid sand
well I kind know how to do it one way from (1+x)^n but I never done it the other way...
crimson sedge
okay
so
let's do it simpler first
\darkmode
can you represent [
\binom n 0 + \binom n 1 + \dots + \binom n n
]
in sum notation?
wraith daggerBOT
vapid sand
no
crimson sedge
\darkmode okay do you understand what something like [
\sum_{k = 1}^n k
]
is doing
wraith daggerBOT
vapid sand
yes, its going to sum each value of k until it reaches n
vapid sand
yes
crimson sedge
so for this
lyric scaffold
sorry to interject, but the sum notation stuff is not really taught within the hsc extension 1 course
crimson sedge
you see how the n at the top is constant throughout, and the only thing changing is the bottom part?
lyric scaffold
sorry to interject, but the sum notation stuff is not really taught within the h...
i think the purpose of the question is to identify the binomial expansion stuff
crimson sedge
sorry to interject, but the sum notation stuff is not really taught within the h...
they still should know it. It is not like it is particularly difficult to learn the meaning of what a $\sum$ is
wraith daggerBOT
lyric scaffold
they still should know it. It is not like it is particularly difficult to learn ...
agreed
vapid sand
lyric scaffold
...
vapid sand
I am actually clueless on this
crimson sedge
right. those are correct bounds for the expression
now what would be the contents of the sum?
crimson sedge
yes, its going to sum each value of k until it reaches n
it is exactly the same logic as this btw
riiiiight
perfect
vapid sand
I just realised that
crimson sedge
now let's go back to this
\darkmode
[
\binom n 0 - \binom n 1 + \hdots + (-1)^n \binom n n
]
tropic oxide
what's the original problem
wraith daggerBOT
vapid sand
what's the original problem
this #help-13 message
tropic oxide
also btw @vapid sand is this like, your first exposure to the summation symbol
crimson sedge
can you represent that in sum notation?
(notice that it becomes negative at odd values of k)
vapid sand
also btw <@310000360976809984> is this like, your first exposure to the summatio...
no, I am trying to revise this crap and I realise how clueless I am when looking at this
tropic oxide
maybe it would be better if you went to revise some less heavy duty big-sigma stuff
like maybe try working with shit like $\sum_{k=1}^n k$ and stuff of that caliber
wraith daggerBOT
Ann
vapid sand
my syllabus does not use sigma in any form other than this
I am trapped in this tourmented hell
crimson sedge
you still need to understand it. It will not go away in your future classes
lyric scaffold
my syllabus does not use sigma in any form other than this
for the question, the syllabus dot point that is being target is the binomial expansion stuff
lyric scaffold
you still need to understand it. It will not go away in your future classes
... the hsc course is the year 12 course for NSW Australia
vapid sand
lyric scaffold
so consider $(x-1)^n$
wraith daggerBOT
Editmond
vapid sand
x-1?
lyric scaffold
yeah becuase of the -1 coefficeint at the end
vapid sand
shouldn't it be (1 +x)^n
lyric scaffold
shouldn't it be (1 +x)^n
same difference
crimson sedge
it's not n on the exponent of (-1)
vapid sand
k?
crimson sedge
so consider $(x-1)^n$
there are no x's in the expression
vapid sand
it doesn't matter because the x will disappear
lyric scaffold
there are no x's in the expression
i know but consider it and then figure out an x so that it satifies RHS
vapid sand
but thats the line that fades for me, what the hell do you do to get rid of the x
lyric scaffold
i know but consider it and then figure out an x so that it satifies RHS
in this case it is 1
crimson sedge
\darkmode
Now compare
\[
\sum_{j=0}^n \binom n j a^{n-j} b^j \tss{with} \sum_{j=0}^n \binom n j (-1)^j
\]
For what values of $a$ and $b$ are the above sums equal?
vapid sand
crimson sedge
the left is the binomial theorem. the right is the binomial you have
vapid sand
yes
crimson sedge
so what's the a and b that would make them the same you think?
vapid sand
what do you exactly mean by the same?
crimson sedge
equal
\darkmode
\[
\sum_{j=0}^n \binom n j a^{n-j} b^j = \sum_{j=0}^n \binom n j (-1)^j
\]
Find $a$ and $b$
vapid sand
well my intuition would just say a=1 and b=-1
crimson sedge
yes!
Correct!!
\darkmode
so we said [
(a+b)^n = \sum_{j=0}^n a^{n-j}b^j
]
and you have deduced that $a = 1$ and $b=-1$. So that means that[
(a+b)^n = (\mathord ? + \mathord ?)^n
]
wraith daggerBOT
crimson sedge
how am I suppose to start this
you have shown that the sum is equal to 0 using the binomial theorem
vapid sand
thats it
huh
alright
thanks for the help alex, sorry for taking so much of your time 
crimson sedge
it's okay
vapid sand
you literally taught me a whole different method lol
but thank you so much for the help. I am very grateful
.close
cloud kiln
cedar kilnBOT
spice kraken
cloud kiln
what is a??
latent bloom
Factor that accounts for how wide the parabola is
cloud kiln
how do I find the a?
latent bloom
Well you know that 50ft below the vertex, the parabola goes right by 60ft right?
Right and left actually
latent bloom
Now you can use coordinates and plug in into your y=ax^2 + 50 equation
cloud kiln
Now you can use coordinates and plug in into your y=ax^2 + 50 equation
is it not y=-ax^2+50??
latent bloom
Well a will be negative so it will still include the sign :)
cloud kiln
ahh okey
latent bloom
So (x,y) = (+or- 60, 0)
latent bloom
upper ruin
So (x,y) = (+or- 60, 0)
Have you plugged this into the equation?
latent bloom
Let's pick the positive side and say that we will use (60,0)
cloud kiln
is it y=a(60)^2+50
latent bloom
is it y=a(60)^2+50
Yep
upper ruin
is it y=a(60)^2+50
What was the y of that point?
latent bloom
Oops
latent bloom
Yep
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
\darkmode
The Gauss kernel \[
\map G{t,x,y} =\f1{\s{4\pi t}}\map[\bigg] \exp{-\f{(x-y)^2}{4t}}
\]
is the fundamental solution of the heat equation \[
G_t = G_{xx}, \quad \map G{0,x,y}= \map \delta{x-y}
\]
By analogy with the heat equation, find the fundamental solution $\map H{t,x,y}$ of the Schrödinger equation \[
H_t = iH_{xx}, \quad \map H{0,x,y} = \map \delta{x-y}
\]
crimson sedge
I managed to find the fundamental solution of the heat equation by means of the Fourier transform
the Schrödinger equation in one dimension is pretty straightforward too. But I cannot for the life of me rationalise how I'm supposed to do the above
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
dire geode
I managed to find the fundamental solution of the heat equation by means of the ...
show your work for the heat eqn
do you have something like this?
crimson sedge
show your work for the heat eqn
maybe tomorrow I can latex it
crimson sedge
do you have something like this?
yes exactly
dire geode
yea i think the only thing you need to find the inverse fourier transform of the delta function
cedar kilnBOT
@crimson sedge Has your question been resolved?
silent tendon
i need help with removeable discontinuity and piecewise functions
silent tendon
the question i am confused on ^
i genuinely just dont understand where to start
<@&286206848099549185>
bro hello
.close
rich sandal
cedar kilnBOT
cedar kilnBOT