A Lonely Bean
#help-0
ocean sealBOT
echo socket
Makes sense?
echo socket
**A Lonely Bean**
Right, so the domain would be $[-6, 6]$
ocean sealBOT
A Lonely Bean
upper flame
yeees
echo socket
Now, you may ask why did they write $0 < x < 6$ instead of $0 \le x \le 6$ for the domain of the function giving the area of a rectangle
ocean sealBOT
A Lonely Bean
echo socket
Well, before I explain, can you see what happens to the rectangle when $x = 0$ or $x = 6$?
ocean sealBOT
A Lonely Bean
upper flame
oh wai tthis whole time ive just been thinking of the equation and completely forgot about the rectangle
when x = 6 that point is not in the rectangle?
and x=0 it's the orgin....?
echo socket
When x = 0 or x = 6, the shape is no longer a rectangle, it's a line
upper flame
wiat how does the rectangle relate to the function
echo socket
Well, we wanted to construct a function which gives us the area of the rectangle
And we got 2x sqrt(36 - x^2)
upper flame
yes i think even tho i cant see the texit thingy
echo socket
Which, sure, is defined for -6 <= x <= 6, but when x = 6, -6 or 0, the shape is no longer a rectangle, so we exclude those (I don't know why they didn't exclude 0 alongside with 6 and -6)
upper flame
when you say that when x = 6 or -6 or 0 do you mean if we were to take the side of the shape and stretch it out/compress it to those points
you mean the x value line of the rectangle right (the one that shows height)
echo socket
when you say that when x = 6 or -6 or 0 do you mean if we were to take the side ...
Yeah, you can imagine it like that
upper flame
okay i get this concept but can you explain why my math was wrong ;-;
here
how do i get to plus and negetive 6 by solving it out?
echo socket
It would be correct if we had x^2 = 36
But we have inequalities here and there's no such step which lets you imply x < +-6
The expression x < +-6 in and of itself is ambiguous
upper flame
then what do i doooo....
once i reach the x^2 less than or equal to 36 do i just have to think it out without using equation?
echo socket
Yeah, you just use this and that's it
elfin vector
Hi! I just need help checking whether this answer is correct. Thx.
tardy stag
i think you're confused about what the question is asking
the answer should be 6 different numbers
one for each of {5, 6, 7, 8, 9, 10}
little blade
<@&286206848099549185>
lone heartBOT
@elfin vector Has your question been resolved?
elfin vector
<@&286206848099549185>
crisp pine
That looks right to me
fluid venture
That looks right to me
not to me though
elfin vector
i think you're confused about what the question is asking
do you think it's correct now?
tardy stag
denominator isn't right on that i think
like
if i tell you that i rolled two dice and got a 10
do you think it's likely or unlikely that one of them was a 6?
elfin vector
oh the denominator should be resspective to the sum for each right?
elfin vector
denominator isn't right on that i think
like for 5 the denominator would be how many sample points that would add up to 5, not 36 which is all the possibilities
tardy stag
yeah exacly
elfin vector
ah i see
limpid shore
If $c\geq 0$, then $\sup cA=c\sup A$. However, how should one interpret the formula if $c=0$ and $\sup A=\infty$?
ocean sealBOT
sunside
maiden glen
if $cA = {ca:a\in A}$
ocean sealBOT
Desync
maiden glen
then for $c=0$, we have $$\sup(0A)=\sup({0})=0=0\sup(A)$$
ocean sealBOT
Desync
limpid shore
then for $c=0$, we have $$\sup(0A)=\sup(\{0\})=0=0\sup(A)$$
and yes, what is $0\sup(A)$ if $\sup A=\infty$?
ocean sealBOT
sunside
maiden glen
not defined I suppose?
you don't get sup(A) being infinite if you plug in c=0 to the formula though
limpid shore
you don't get sup(A) being infinite if you plug in c=0 to the formula though
well, you don't get that $\sup(cA)$ is infinite if $c=0$, but $\sup A$ could still be infinite
ocean sealBOT
sunside
maiden glen
if sup(A) is infinite, then A is empty or unbounded above; in the former case, sup(0A) is still empty and we have equality
thinking about the unbounded above case
well, if we take 0 * infty to be zero
then it still holds
because we'd have sup{0}=0 on the left and 0*infty = 0 on the right
limpid shore
thinking about the unbounded above case
the sup of the empty set is negative infinity
maiden glen
then disregard that case
short goblet
Need some help with sets and proofs
lone heartBOT
Need some help with sets and proofs
short goblet
How does the pythagorean identity relate to this?
short goblet
something like this?
echo socket
No you can't assume c = 1
short goblet
ah
echo socket
Isolate $\cos{x}$ in $\left(\frac{a}{c}\right)^2 + \cos^2{x} = 1$
ocean sealBOT
A Lonely Bean
short goblet
?
echo socket
Yeah, now make the denominator common in $1 - \frac{a^2}{c^2}$
ocean sealBOT
A Lonely Bean
short goblet
b^2
oh
so
b^2 / c^2
and since b and c are both natural numbers per definition of Set P, b^2/c^2 should be a rational number
short goblet
and since set C is the set of real numbers x, for which cos(x) is rational, set A is a subset of set C
would it be correct to say it like that?
echo socket
I don't think you need to mention that the sets are subsets of R, you've shown that x being an element of A means that x is also an element of C, so A is a subset of C by definition
upbeat eagle
Hia
upbeat eagle
Simultaneous equations- Ezie Pezie
I am confused on part C
I decided to Replace all k's with 1/16
in this
and then solve the equation for X's but it gives me imaginary numbers
I am confused on why it does not want me to do that
But rather simply do
Why is my method wrong? It should be the same
NVM
GOT IT
I made a mistake
.close
torn locust
The region on the second and third quadrants of the curve x ^ 2 + y ^ 2 = 9 is revolved about the line x - 3 = 0 What is the volume generated?
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!status 1
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
The correct answer is 379.58 but I dont know the solution
<@&286206848099549185> <@&268886789983436800>
karmic grove
Do you know the cylindrical shell's method ?
lone heartBOT
@torn locust Has your question been resolved?
jagged plume
lone heartBOT
jagged plume
How to go from the first to 2nd line?
lone heartBOT
@jagged plume Has your question been resolved?
lone heartBOT
@jagged plume Has your question been resolved?
thorn monolith
How to go from the first to 2nd line?
Hi, have you done any work or still there?
Get dx on the RHS(Right Hand Side)
Then take integral of both sides
Integral cancels out $d$ of $$d \left ( \frac{u^2}{2} \right )$$
ocean sealBOT
Cyrenux
thorn monolith
And on right side, you take integral with respect to x
lone heartBOT
@jagged plume Has your question been resolved?
somber steppe
Just a quick question, I'm always confused when it comes to operations on finite fields. So when calculating the determinant of a matrix in $\mathbb{Z}_2$ for example, should I apply mod 2 to all the operations while calculating or only apply mod 2 to the resulting equation terms? And in the case of a linear system in the same finite field, when I get the solutions (after using Gauss method with mod 2 operations), i.e. $x_1 + x_4 = 1$, is the following form permitted $x_1 = 1 - x_4$ or should I remove the $-$ sign in front of $x_4$ and replace it by a $+$ because of the mod 2?
ocean sealBOT
froud
somber steppe
@echo socket
somber steppe
is $-x_4$ considered valid in $\mathbb{Z}_2$?
echo socket
You can pretend like you are calculating a determinant of a matrix with real entries and at the end reduce modulo 2
ocean sealBOT
froud
ocean sealBOT
A Lonely Bean
somber steppe
Oh but isn't the finite field composed of only 0 and 1?
echo socket
Oh but isn't the finite field composed of only 0 and 1?
What doesn't change anything though
They are not 0 and 1 as in the numbers 0 and 1 just in case
They denote equivalence classes
somber steppe
oh, what do you mean by that?
I thought this finite field contained only the null vector and 1
echo socket
One way you can construct $\bZ_2$ is by taking $\bZ / \equiv$ where $\equiv$ is the equivalence relation defined by $a \equiv b$ iff $2 \mid (a - b)$
ocean sealBOT
A Lonely Bean
echo socket
What you get is a set of two equivalence classes
One contains the even integers and the other contains the odd integers
somber steppe
what is the "/" in "Z/"?
echo socket
And they can be identified with 0 and 1
echo socket
what is the "/" in "Z/"?
Quotient ring
You could also do $\bZ / (2)$ which I think would be more appropriate way of defining $\bZ_2$
ocean sealBOT
A Lonely Bean
echo socket
Where (2) denotes the ideal generated by 2
somber steppe
what's the ideal here?
echo socket
Ideal is a subset of a ring which contains the additive identity, is closed under addition and multiplying an element from the ideal by any element of the ring still gets you an element of the ideal
Anyway, you will learn about these soon enough in the abstract algebra course
somber steppe
Oh ok, but what does it mean that 2 generates the ideal?
echo socket
Ideal generated by some element r means the smallest ideal that contains 2
So the ideal generated by 2 is the set of even numbers
In Z
somber steppe
if its the smallest ideal then shouldn't it just contain zero, one and two and no other numbers?
echo socket
Like I said, the ideal should be closed under addition
So 2 + 2 should also be present
And then 4 + 2
6 + 2
So on
echo socket
What do you mean?
somber steppe
Is 2*2 permitted for the idea?
somber steppe
ok, so how would I summarize what we talked about the ideal generated by 2 with the concept of a finite field?
Like what would be the quotient ring of the ideal?
echo socket
When you take a quotient by some ideal I, each element a gets mapped to a + I
a + I denoting {a + i where i is an element of I}
somber steppe
ohhh, I think I got it, the quotient bý an ideal concept is still unclear for me, but I understand what you meant by equivalence classes. Z_2 contains the whole elements of Z, but since it contains operations modulo 2, then each element < 0 and > 2 gets mapped to an equivalent class of 0 and 1
echo socket
Okay wait I might as well connect this with why talking about -1 in modulo 2 makes sense every though Z_2 contains only 0 and 1
echo socket
ohhh, I think I got it, the quotient bý an ideal concept is still unclear for me...
Yes
So -1 gets mapped to -1 + (2)
Which is the same as 1 + (2)
Making 1 and -1 equivalent mod 2
somber steppe
I see
so when you do 1 + 2 this maps it to 3, which is in the equivalence class of 1 so it maps it to 1, or am I confused?
somber steppe
When you take a quotient by some ideal I, each element a gets mapped to a + I
Refering this
somber steppe
oh sorry
So to get back to $-x_4$. Is it correct if I write for my solution $S = {(-x_4, 2x_3, x_3, x_4) | x_3,x_4 \in \mathbb{Z}_2$}?
ocean sealBOT
froud
echo socket
Should be, yeah, what's the question though?
somber steppe
To determine the affine subvector space of an equation system in Z_2
echo socket
Yeah, that's a valid answer
Although I would rewrite it as (x4, 0, x3, x4), but it doesn't make it more right
somber steppe
why?
echo socket
Looks nicer
somber steppe
but how did you come up with that?
echo socket
All I did was replace -x4 by x4 since they are congruent and 2x3 with 0 because 2 = 0 mod 2
somber steppe
Ok I see, so that was what I wondered, which form should I put S in for an exam, given that the question is to find the solution subspace in Z_2?
echo socket
Although I would rewrite it as (x4, 0, x3, x4), but it doesn't make it *more* ri...
Well, if you wanted to give an answer simplified as possible, I would suggest writing this
somber steppe
ok I see
somber steppe
So to get back to $-x_4$. Is it correct if I write for my solution $S = \{(-x_4,...
Also if I were to write this, then this would mean that if I were to plug in values for x_3 and x_4 I would have to calculate the mod before determining the particular solution?
echo socket
It's not really necessary, but I think you are expected to do that, yeah
somber steppe
Is it not necessary because we already know we are working on a finite field?
echo socket
Yeah what you have before and after reducing mod n is equivalent
It's just that reducing mod n makes it more simplified/conventional so to speak
somber steppe
ok great, thanks again, you really helped me clear it up in my head. In the course, the teacher as she introduced finite fields made me think it was a particular field with only two elements, I didn't really think of it with equivalence classes as we talked about
.close
rustic cairn
Im looking for help verifying my answer for question 5. I feel like my approach is correct but the probability is so low im thinking i messed up somewhere.
I mean there are only 4 possible outcomes for this even right?
win lose
lose win
win win
lose lose
so why is (win lose) + (lose win) + (win win) 4.5%? can't be right?
tardy stag
you're not using conditional probability right
rustic cairn
not for 5, but i have the conditional probabilities for 2 and 3
tardy stag
"imagine that the team has won their previous game" so the first lines in each scenario should be conditioned on P=1 and H=1
rustic cairn
Im not quite sure what you mean, the calculation for probability of each scenario (win win, win lose, lose win) will involve conditional probability in this case?
tardy stag
Im not quite sure what you mean, the calculation for probability of each scenari...
yeah, every line will involve some conditional probability
WW, WL, LW, and LL should add up to 1
rustic cairn
okay thats a helpful tip, i will keep trying until i run into this
right now the probability i am describing is something else entirely?
cause im still a little blur about the nuance between conditional probability and joint
tardy stag
what you are using is like P(H=1 and P=1 and W=1) which is "the probability that we are playing a home game, and we won our previous game, and we win this game" which is very low because half the time we're playing away games
what you want is P(W=1 | H=1 and P=1) which is "ok i know we're playing a home game and that we won our previous game; what's the probability that we win this game?"
rustic cairn
oh that makes a lot of sense, thank you so much
yes i see, since the pool of states is so big yeah the probability of that is gonna be miniscule, that makes alot of sense
so for example the lose win case would be:
P(W=0 | H=1 and P=1) * P(W=1 | H=0 and P=0) right?
tardy stag
yeah!
tardy stag
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
So I'm supposed to express this series 4+2+0+(-2)+(-4)+(-6) into a sigma notation and I dont understand why it gets arranged like this: [-4+(-2)+0+2+4+6]
naive valley
can you give more context?
alpine sable
i will send a pic
naive valley
addition is commutative, so as long as you're summing finitely many things, you can put them in any order you like
i guess they just wanted to express it in terms of a finite series in ascending order
-4, -2, 0, 2, 4, 6 is sorted
naive valley
notice the minus sign in front of the brackets on the second line
they factored out a -1 from everything
naive valley
they basically multiplied everything by -1 twice
which is the same as doing nothing
6 = -(-6)
same with the other numbers
naive valley
they're trying to get it into a form that involves a sequence of numbers that are ascending with steps of 1
like on the last line: -2, -1, 0, 1, 2, 3
that's easy to write using summation notation
as $\sum_{n=-2}^3 n$
ocean sealBOT
Bungo
naive valley
so they did some factoring to get something with that form
alpine sable
my mind isn't catching up sorry
naive valley
basically factored out a -2 from everything
it's probably easier to understand without all the intermediate steps which imo are just adding confusion
4 + 2 + 0 + (-2) + (-4) + (-6)
these are all divisble by 2
so i can factor out a 2
to get:
2 (2 + 1 + 0 + (-1) + (-2) + (-3))
so now I can write that as $2\sum_{n=-3}^2 n$
ocean sealBOT
Bungo
alpine sable
so i just divide 2 to all of them?
naive valley
4 + 2 + 0 + (-2) + (-4) + (-6) also equals -2(-2 + (-1) + 0 + 1 + 2 + 3)
which is $-2\sum_{n=-2}^3 n$
ocean sealBOT
Bungo
naive valley
either of those solutions is correct
alpine sable
ok thanks i wasnt able to understad much cuz im not so smart but thanks for the explanation
naive valley
nw, i suggest just trying it yourself and ignoring what they wrote, it might become clearer
lone heartBOT
lone heartBOT
Available help channel!
west ivy
how do i start this
lone heartBOT
how do i start this
wind cloak
Squeeze theorem probably
wind cloak
what have you learnt
wind cloak
Do you need to prove/disprove convergence or evaluate the sum
west ivy
we just have to find what the limit of this series is
wind cloak
I probably sound stupider
wind cloak
You need to evaluate it basically
wind cloak
Well that's simply proving convergence and it should get the job done if that's what you need to do
west ivy
its divergent
wind cloak
also btw
west ivy
yeah
wind cloak
Yeah you said it before me
wind cloak
lim a_n = 0 does not imply that it's convergent
the limit does not exist in that case
wind cloak
,w sum from n = 0 to infinity n^5/(6n^6 + 1)
ocean sealBOT
wind cloak
limit does not exist I suppose
west ivy
but im supposed to write a fraction in s as the answer
also the numerator is 3n^5
if that makes a difference
west ivy
so when n approaches inf
west ivy
Are you sure this is the full question
yeah
wind cloak
Doss the box not allow characters other than numbers in it
alpine sable
it allows any number
-1/12
west ivy
huh
alpine sable
Reference to infinity 
west ivy
im so lost
alpine sable
1+2+3+...
wind cloak
it allows any number
Can you not write "does not exist" or "dne" in it?
west ivy
no
also
its the only question that mentions anything about the answer being in a fraction
so im sure the answer is supposed to be a fraction
west ivy
would it be 1/2?
west ivy
limit comparison test
wind cloak
What series did you use
native cloud
How do I solve this?
$\frac{\sin\left(x\right)+\tan\left(x\right)}{1+\sec\left(x\right)} = \frac{\sin\left(x\right)+\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\frac{\cos\left(x\right)+1}{\cos\left(x\right)}} = \frac{\frac{\sin\left(x\right)\cos\left(x\right)+\sin\left(x\right)}{\cos\left(x\right)}}{\frac{\cos\left(x\right)+1}{\cos\left(x\right)}} = \frac{\left(\sin\left(x\right)\cos\left(x\right)+\sin\left(x\right)\right)}{\left(\cos\left(x\right)+1\right)}$
ocean sealBOT
LE SSERAFIM
native cloud
This is what I've done so far
tardy stag
$\frac{SC + S}{C + 1}$
ocean sealBOT
haγly
tardy stag
do you see an opportunity here?
native cloud
Oh
Yes
lol
Sorry my brain isn't braining at 3 am
$\frac{\sin\left(x\right)\left(\cos\left(x\right)+1\right)}{\left(\cos\left(x\right)+1\right)}$
ocean sealBOT
LE SSERAFIM
ocean sealBOT
Dissrupt
tardy stag
sure
tardy tapir
native cloud
Thanks for the heads up though
Should watch out if there isn't the term, admissible
.close
lone heartBOT
lone heartBOT
Available help channel!
vague oxide
Can anyone easily explain me what's affine geometry and why Z/3Z plane is an affine plane?
(ps. I'm not good at math, don't know vectors and university leveled math a lot.)
native cloud
평행선 기하학 아닌가요?
oak perch
I can’t read Korean
native cloud
I wasn't sure so that's why I asked him in Korean
vague oxide
I mean the plane with quotient group Z/3Z X Z/3Z
vague oxide
Z/3Z is the set of all equivalence classes of the equivalence relation "x ≡ y mod 3"
oak perch
I know that, I am asking what your sentence means
vague oxide
So, there's only 9 integar points to the Z/3Z X Z/3Z plane.
vague oxide
I know that, I am asking what your sentence means
Oh
I saw that Z/3Z X Z/3Z plane is an affine plane.
I want to know why that is true.
Also the easy explanation what affine geometry is.
I don't exactly know what affine geometry is since my math skills aren't enough 😅
oak perch
vague oxide
I want to know the relationship between the Z/3Z X Z/3Z plane and affine geometry
oak perch
No idea. To define an affine plane you need to give me a set of points, a set of lines. And you didn’t give me those. You gave me a group instead
vague oxide
There's 9 points x={0,1,2}, y={0,1,2} in Z/3Z X Z/3Z plane which is a set of points.
oak perch
So points are (0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2) in R^2
And what are the lines
vague oxide
Uh, you may refer this.
https://www.geogebra.org/m/fHExMhpP#material/dC3WFZUe
AG(2, 3) is basically the same as Z/3Z X Z/3Z plane right?
oak perch
I understand AG(2,3) now. I’ve never seen Z/3Z times Z/3Z to denote it
vague oxide
Okay..?
oak perch
And what do you want to know?
vague oxide
An easy explanation what affine geometry is and why AG(2,3) is an affine plane.
oak perch
Affine space is just
You have two set
One set, you call the elements of it points
Another set you call the elements of it lines
vague oxide
Okay
oak perch
Given a point x and a line y, you assign one of two states for this pair (x,y). Those two states, you name them by “x is on y” and “x is not on y” respectively
It’s like give a mapping from {set of points} times {set of lines} to {0,1}. Image of (x,y) being 1 you call this “x is on y”
A point x is an intersection point of line y and line z means that
“x is on y”, “x is on z” are both satisfied
If y and z have such intersection point we say y and z meet
Two lines y and z are called being parallel to each other, if y=z or y and z don’t meet
Now you have these two sets and these notations,
These form an affine line, if
These conditions are satisfied for your set of points and set of lines
vague oxide
So it's like extended version of euclidean?
oak perch
You can say that
vague oxide
I see
oak perch
But they can be anything
vague oxide
Thanks for explaining. Internet explains it so difficult with vectors and stuffs.
oak perch
The set of points is not necessarily really a set of points in a Euclidean space
Just the name “point” and a name “lines”
vague oxide
I don't get that.
oak perch
Like I said you have these two sets
You call the elements in the first set “points”
It’s just a name
vague oxide
But the euclidean doesn't have lines set?
oak perch
Not necessarily really points In Euclidean spaces that’s what I meant
Again, line is just a name
You call an element of the second set a line
vague oxide
Ok
oak perch
You just call it this way, it doesn’t have to be a real line in a space
oak perch
AG(2,3)=(V,E) where
V={(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)}, just the underlying set Z/3Z times Z/3Z. Now I see why you call it this way
vague oxide
What's E then?
oak perch
E={y0, y1, y2, x0, x1, x2, l0, l1, l2, r0, r1, r2}
vague oxide
The lines in the space?
oak perch
Just 12 abstract elements
They don’t need to have any meaning
I can replace them with
{cat A, cat B, cat C, dog A, dog B, dog C…}
vague oxide
Then what's E for?
oak perch
Elements of E are called lines
To define the set of “lines”
And the relation given by:
(a,0), (a,1), (a,2) are on x_a;
(0, a) (1,a), (2,a) are on y_a;
(i,j): i+j=a mod 3 are on l_a, (i,j);
i-j=a mod 3 are on r_a.
oak perch
For a=0 or 1 or 2
oak perch
Yeah
vague oxide
Oh
oak perch
Can be imagined as strange lines, but points mod 3
lone heartBOT
lone heartBOT
Available help channel!
lethal citrus
Determine the maximum value of $P(0)$ among all polynomials $P\in\mathbb{R}[X]$ verifying
$P$ is of degree less than or equal to $5$.
$P(1),P(2),P(3),P(4),P(5),P(6)$ is a permutation of 1,2,3,4,5,6.
ocean sealBOT
joseph.P
lethal citrus
I did Lagrange interpolation and found five polynomials but I don’t know how to choose the values of y_i
lethal citrus
I’ll show you
oak perch
Lagrange polynomial, use that method
azure swan
So now you have to evaluate them all at 0
lethal citrus
That’s it ?
azure swan
No
lethal citrus
I evaluate it at 0 And then I try the value of y
azure swan
You want to maximize
$P(0) = \sum_{i=1}^6 P_i(0) P(i)$
lethal citrus
Okay I’ll try
oak perch
You can plug in x=0 at the beginning actually, make calculations easier…
For example (-1)(-2)(-3)(-4)(-5)/(6-1)(6-2)(6-3)(6-4)(6-5)
lone heartBOT
@lethal citrus Has your question been resolved?
oak perch
And how are you going to deal with the cases when the degree is <=4?
oak perch
Then done, 83. But the thing is
This is just the case when degree is 5
Your question asked <=5
Degree of P
How are you going to conclude that for degree <=4 P, P(0)<=83?
lethal citrus
It’s telling me 83 is wrong
oak perch
Then probably there exists a lower degree polynomial whose P(0) is greater than 83
oak perch
Thank you
lethal citrus
Then probably there exists a lower degree polynomial whose P(0) is greater than ...
I’ll find it
oak perch
I hope so, because I have no idea… looks complicated.
You know the issue is
You also need to examine whether a lower degree polynomial can satisfy these conditions
lethal citrus
I don’t think you have to do it with Lagrange interpolation because it’s not in the theory
oak perch
For example, you define P of degree 4, such that P(1)=1, … P(5)=5 , it could happen that P doesn’t satisfy P(6)=6 so you need to discard this one
So not only you need to check whether your polynomial satisfies the condition, and also need to calculate its value at 0…
oak perch
Never seen this symbol, {n top k down}…
You know the name of it? This symbol or the name of polynomial of this form?
rose sigil
stirling numbers of the second kind?
oak perch
Oh I see
lethal citrus
Yes
oak perch
Well I hope you can make it…. I can only do this far, to obtain 83 for the degree=5 case…
lethal citrus
Thanks
lethal citrus
Well I hope you can make it…. I can only do this far, to obtain 83 for the degre...
How did you obtain 83 by the way
oak perch
The upper right corner, 6 times 5 + 20 times 6 +…
Bigger number needs to be multiplied with bigger numbers. Like Biggest number 20 with biggest 6, smallest -15 with smallest 1
lethal citrus
It’s minus 1 not one
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
3
south fox
<@&286206848099549185>
lethal citrus
Why did you ping the helpers again ??
azure swan
So now you have to multiply each of those numbers with one number from 1 to 6, such that you use each number once and such that the sum is maximized
azure swan
You want to maximize
$P(0) = \sum_{i=1}^6 P_i(0) P(i)$
As this is what you want to maximize
lethal citrus
I just did 20x6+15x5+7x4+6x3-1-15=225 but it’s wrong
lethal citrus
Yes just saw it
azure swan
Does it work?
lethal citrus
It’s wrong again
lethal citrus
Does it work?
No
azure swan
So 224 is wrong? Weird
lethal citrus
Maybe my polynomial are false ?
azure swan
It could be, as this should be a correct way to solve it
So it could be that one of the steps has an error
Im checking it now by myself
lethal citrus
Didn’t find any error in my work so I don’t know
lethal citrus
I’m dumb
azure swan
Nah
lethal citrus
You won’t believe me it’s wrong again
azure swan
220 is wrong?
lethal citrus
Yes
lethal citrus
I don’t know why but for x=1 I find l_1=1 and the other 0
azure swan
That's correct, because that is how the basis works
The first basis polynomial only changes the value at x_1. It stays the same for the other x_i
azure swan
This is why we use computers for interpolations and stuff xd
azure swan
Sure, why not xd
azure swan
I read it
lethal citrus
It was a lot faster than doing the interpolation but that’s okay
Thanks for the help
.close
jolly glacier
hey can anyone help me in solving this
lone heartBOT
hey can anyone help me in solving this
jolly glacier
i distributed but i don’t know what to do after
alpine sable
i distributed but i don’t know what to do after
bring the unknown to one side and then set the unknown's coefficient to 1
lone heartBOT
i distributed but i don’t know what to do after
Show your work, and if possible, explain where you are stuck.
jolly glacier
alpine sable
=rotate
jolly glacier
how do i combine the as
alpine sable
,rotate
ocean sealBOT
jolly glacier
do i give them a gcf
jolly glacier
mb that’s what i meant
alpine sable
do i give them a gcf
ah i see so your problem is adding fractions
jolly glacier
ah i see so your problem is adding fractions
it’s been like 2 years since i done this
wary stream
You can do that, or in my opinion, multiply all the terms by that lcd, to remove fractions
jolly glacier
wait
wary stream
it’s been like 2 years since i done this
What's the lcd of the fractions?
jolly glacier
can i just multiply 16 on both sides
wary stream
Yes
alpine sable
yeah but if you're having trouble with fractions find the gcd
alpine sable
if you multiply by 16 you must multiply everything
jolly glacier
yeah
wary stream
and make 3/4 into 12/16
Are you trying to find the lcd or multiply by 16 to all the terms?
Because you found a common denominator for 3/4
alpine sable
and make 3/4 into 12/16
yeah you can do that and then multiply by 16 so it's just 12
lone heartBOT
jolly glacier
.reopen
lone heartBOT
✅
jolly glacier
how would i set this up
jolly glacier
how would i set this up
,rotate
ocean sealBOT
wary stream
Cross multiply
jolly glacier
is that all?
bold tree
Flip it and multiply by 2 ig
lethal citrus
A/B=C/D==> AD=CB
wary stream
is that all?
Yes, cross multiplication is the easier way to do it
wary stream
Looks good
wary stream
then i got -14/5
Fractions are numbers too, why doesn't it work?
You can have fractions as answers
tacit arch
yeah i know but it doesn’t work when i plug it back in
why not
are you using parentheses
lone heartBOT
yeah i know but it doesn’t work when i plug it back in
Show your work, and if possible, explain where you are stuck.
wary stream
How are you doing the math to check it
lethal citrus
You can plug -2.8 instead
jolly glacier
You can plug -2.8 instead
ye that worked
so i just cross multiply
on most of them
lethal citrus
You can
jolly glacier
and for absolute value do i calculate what’s inside first and then convert it
lethal citrus
Show me the question
jolly glacier
lethal citrus
Is it $|15-(|-6+2|+\sqrt{9})|^2$or just $15-(|6+2|+\sqrt{9})^2$ on the top
jolly glacier
also do i treat absolute value like a parentheses
so like if there’s a negative outside
ocean sealBOT
unmatheux
jolly glacier
it’s a bracket
lethal citrus
also do i treat absolute value like a parentheses
Treat it as a parentheses
grave orbit
-6 + 2= -4
jolly glacier
like if there’s something like -|-8|
lethal citrus
When you have a minus before a number and nothing in front of it you can put it behind the other number
-6+2=2-6
=-4
And no matter what’s inside the absolute value, the result will always be positive
lethal citrus
Yea
jolly glacier
wait would the outcome of square root 9
be negative
bc there’s minus outside of the parentheses
so it distributes in
lethal citrus
When you don’t have any variables just do the calculations before treating the minus
lethal citrus
wait would the outcome of square root 9
But yes square root of nine can be negative
grave orbit
15-(-1)
jolly glacier
wait let me show u
lethal citrus
Go ahead
jolly glacier
grave orbit
Better
jolly glacier
wdym
lethal citrus
Square root nine
grave orbit
When √9 = -3,3
lethal citrus
Square root nine
It’s 3 or -3
fossil pecan
sqrts are generally assumed to be positive unless stated otherwise
grave orbit
That's what we do in my school
jolly glacier
It’s 3 or -3
yeah but u said to do the minus times parentheses last
lethal citrus
sqrts are generally assumed to be positive unless stated otherwise
My teacher would kill you if you said that to him
fossil pecan
idk that's what I've learned
grave orbit
My teacher would failed me if I used -3
lethal citrus
yeah but u said to do the minus times parentheses last
You don’t distribute the minus I’m just telling you that square root 9 is equal to 3 or -3
You have either $\dfrac{\Big(15-(4\pm3)\Big)^2}{-24}$
ocean sealBOT
unmatheux
grave orbit
**unmatheux**
May I ask how you do this?
lethal citrus
The latex ?
grave orbit
Yeah
grave orbit
Thanks
lethal citrus
yeah but u said to do the minus times parentheses last
So did you find the other solution?
chilly tree
Can someone help me with these problems I got wrong
lethal citrus
Sorry this channel is already occupied by someone else
You can take one in #❓how-to-get-help
lethal citrus
Can someone help me with these problems I got wrong
!help
lone heartBOT
Can someone help me with these problems I got wrong
Please read #❓how-to-get-help
lethal citrus
If you count square root 9=-3 as a solution yes there’s two
lethal citrus
**unmatheux**
.
lone heartBOT
@jolly glacier Has your question been resolved?
civic stream
yes
mental flame
granite badger
first 3 look good
ocean sealBOT
riemann
tacit arch
3rd row
alpine sable
Yep, that'd be right
somber eagle
should be
full helm
by the way, are you writing an exam
lone heartBOT
paper mango
ys
wary stream
Not quite
Do you know what least common multiple means?
Also what is an "unproctored placement assessment"
Is it a test?
lone heartBOT
lone heartBOT
Available help channel!
manic matrix
How would i find the domain of this in my head
alpine sable
How would i find the domain of this in my head
split it into two parts
$$\sqrt{x+5}$$ $$ \frac{1}{(x+2)(x-7)}$$
What can't the top one be?
What can't the bottom one be?
manic matrix
well ik the top is x>= -5 yeah?
ocean sealBOT
One person
somber eagle
yeah
manic matrix
and i see the bottom as asymptotes
somber eagle
so whats the bottom part
manic matrix
x cannot equal -2 and positive 7
somber eagle
yeah
manic matrix
and thats as far as I get
alpine sable
yeah, you're done
manic matrix
...
somber eagle
those are the values for x that would make this valid
manic matrix
ive seen what the graph looks like and what the domain looks like
but idk how i assume that
So i just have to know the graph will look like this bs when i get a function like that?
somber eagle
yeah that shows you what you just worked out
manic matrix
but without a calculator i wouldnt realize thats what it would look like
somber eagle
the question didnt ask you to sketch it did it?
somber eagle
you just worked it out
manic matrix
how do i close this shit
somber eagle
you dont always need a graphical representation
lone heartBOT
@manic matrix Has your question been resolved?
manic matrix
.close
dapper lynx
I've got come to ask a few questions about changing bases with respect to matrices and transformations
dapper lynx
I understand the basic concept - its a matter of expressing a vector in terms of different coordinate systems such that the actual intrinsic length and direction of the vector doesn't change
What's giving me trouble is the mechanics behind the math
I guess my first question is
With respect to a change of basis - is there a difference when working with a matrix versus when working with a transformation?
visual nest
hello
visual nest
I need help with functions, domain and range
this one is tricky
So the question is asking me to list the domains and range, (1,2,4,6 etc.) or (#<x<#)
Its a parabola line with its middle being (2,-2)
And I put - Infinite < x < infinite
and for y its -2 < y < Infinite
alpine sable
Its a parabola line with its middle being (2,-2)
can you share a picture of the problem
visual nest
can you share a picture of the problem
k
@alpine sable
the pink cross is where that parabola is
i just dont know how to like make the parabola move
alpine sable
are you sure that's the right one?
visual nest
are you sure that's the right one?
yes
visual nest
you said the middle was (2,-2)
no like the midpoint of the parabola was (2,-2)
alpine sable
alpine sable
$$ (x-h)^2 + k$$
ocean sealBOT
One person
visual nest
**One person**
k
alpine sable
your answer for the domain is correct
visual nest
so anyway
alpine sable
but the range is wrong
alpine sable
does it look like it's the same
visual nest
does the line ever go under ~~2~~ -2?
yeah
i meant no
it doesnt go under -2
-2 all the way up to infinite
alpine sable
yeah
visual nest
so -2 < y < infinte?
alpine sable
no
alpine sable
do you know what < means
visual nest
you told me that the vertex is (2,-2)
yeah
alpine sable
-2 is not less than -2
alpine sable
less than or equal to
visual nest
our teacher said dont worry about it lol but anyways
Is this my answer?
-2 ≤ y < infinite?
alpine sable
yes
alpine sable
picture
visual nest
picture
k
@alpine sable
srry if its blurry
basically the points are going by 1
and the circles are empty ones
not the filled in ones
alpine sable
yes
alpine sable
idk how to do this one
what is the lowest x value
what is the highest x value
what is the lowest y value
what is the highest y value
visual nest
what is the lowest x value
the lowest x value is -4 and the highest is 2
alpine sable
the lowest x value is -4 and the highest is 2
so what's your domain
visual nest
and lowest y value is -5 and and highest is 5
visual nest
so what's your domain
-4 < x < 2?
alpine sable
and lowest y value is -5 and and highest is 5
so what's your range
visual nest
so what's your range
-5 < x < 5
alpine sable
-4 < x < 2?
wrong
alpine sable
-5 < x < 5
correct
alpine sable
-4 < x < 2?
only one side has an open circle
visual nest
oh wait the lowest x value is -4 and the highest is 3
visual nest
only one side has an open circle
theres both
both of them are open circle
i told u that
alpine sable
both of them are open circle
there is no open circle at x = -4
alpine sable
?
visual nest
theres a line that goes to -4
visual nest
and then goes up
alpine sable
no
alpine sable
no
visual nest
now?
alpine sable
yes
alpine sable
if it's defined at that point
visual nest
k
ty
WAIT
one more
i just want to make sure this one is right
@alpine sable
so for this one
i put
- infinite ≤ x ≤ infinite
-3 ≤ y ≤ infinite
visual nest
sure
and als
also
i hope you dont min
mind*
i have this other problem not similiar to that
which idk the answer to it
idk whats the answer to number 14
it says a(#)/a(#) = -2
so im trying to find #
visual nest
i did