this dude kuro gave up on me
#help-13
hidden fog
subtle gulch
Nah i m here
I was trying to find a better way. I couldnt. The others did a better job
median lantern
also, without the discrinimant, we can see that the coefficient of the leading term is positive
so the parabola points upwards
and we can use the constant to determine the rest
hidden fog
so 121-4ac?
median lantern
4 * a * c
median lantern
yep
hidden fog
oh oops
median lantern
the discriminant is?
median lantern
$\sqrt{161}$
wraith daggerBOT
w
median lantern
~ 12
hidden fog
now i gotta find the number of real solutions of the equation
wait so now what
cuz i got the discriminant
median lantern
@hidden fog
median lantern
161 > 0
hidden fog
median lantern
so we have 2 real solutions
since we take the square root of the discriminant
we need to make sure it is greater than zero
or we get imaginary term
subtle gulch
Last 3 lines
median lantern
if it is zero, we have a double root
hidden fog
since we take the square root of the discriminant
12.6
hidden fog
yuh
hidden fog
so double 12.6?
median lantern
wdym
hidden fog
wym double the root
median lantern
if it is zero, we have a double root
^
hidden fog
oh gotchu
median lantern
its only if the discriminant is zero
subtle gulch
wym double the root
2 real soln
subtle gulch
Ya
hidden fog
damn
subtle gulch
so there’s 2 solutions?
This
median lantern
prolly more than one
subtle gulch
1 ques per channel
median lantern
oh
hidden fog
damn
subtle gulch
Pls start a new channel for a new ques
subtle gulch
Ya caden pls . Close
hidden fog
.close
cedar kilnBOT
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half glacier
hello
half glacier
Your favorite authors from the 17th century are Molière, Racine and Corneille! Of the first, you have 5 books; of the second, 3 pounds; of the third, 4 pounds. How many ways can you arrange them on a shelf in your library? books by the same author must necessarily remain together. and books by the same author are indistinguishable.
i need help for this
turbid mesa
Okay, firstly consider books by same author as one batch
How many batches do you have?
half glacier
3
turbid mesa
Correct. How many ways can you arrange 3 items in a shelf?
half glacier
6 ?
turbid mesa
Yes
Now since in one batch, all books are indistinguishable, so it shouldn't matter how you arrange books in one batch
So the total number of ways must be only in how many ways can you arrange the batches
turbid mesa
Correct. How many ways can you arrange 3 items in a shelf?
^
cedar kilnBOT
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half glacier
Ok ty
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still rover
Please help me understand how the answer is C
cedar kilnBOT
Please help me understand how the answer is C
tranquil atlas
2 log x = log(x^2)
-3/2 log y = log (1/y^(3/2))
So 2 log x - 3/2 log y = log (x^2/y^(3/2))
Then if the base of the log is 10, 2 = log 100
That's it
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frail sphinx
Hey, I am doing vectors now and I understand that d=c+b+a , but why is there - in front of all vectors ? didn`t get the explanation in the video
hollow totem
Its the direction of vector
frail sphinx
Its the direction of vector
but I understand if c were negative because the direction is going under, why a and b are negative too?
Idk doesn`t make sense for me, are all vector directions negative?
hollow totem
No
vector d is defined as goes from point D to A
The negative part is just saying goes from D to C to B to A = goes from D to A
frail sphinx
So it means if the direction of d would be positive then all other Vektors would be positive too ?
hollow totem
So it means if the direction of d would be positive then all other Vektors would...
Your drawing is missing the direction of vector c, b and a
frail sphinx
Your drawing is missing the direction of vector c, b and a
it`s jsut for understanding if the vector is positive all others positive too?
hollow totem
frail sphinx
idk hahahha I try my best
hollow totem
The statement is true if the direction is like this
frail sphinx
okay I know now
frail sphinx
it`s jsut for understanding if the vector is positive all others positive too?
so the statement is true ?
hollow totem
frail sphinx
I know where was my mistake in drawing thank you
hollow totem
If the direction like this, the vector d will be defined as this
hollow totem
Hey, I am doing vectors now and I understand that d=c+b+a , but why is there - i...
For this question
The original vector direction doesnt lign up as we want, so we - it, so it flips its direction
frail sphinx
Hey, I am doing vectors now and I understand that d=c+b+a , but why is there - i...
so if the vector d would go from A to D it would be positive, right, or I am wrong
hollow totem
so if the vector d would go from A to D it would be positive, right, or I am wro...
Yep
cedar kilnBOT
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worn geode
Is this function odd?
cedar kilnBOT
Is this function odd?
mighty shuttle
I think so, yes
worn geode
I think so, yes
Here is how I graphed it, I'm unsure because the situation with the discontinuity points isn't symmetric
worn geode
Would it have to be open at -pi?
mighty shuttle
didn't notice that it's open at π
idle tusk
Is this function odd?
if you really meant to write $-\pi \leq x$ then no it's not symmetric
wraith daggerBOT
artemetra
idle tusk
$h(-x) = -h(x) \iff h(x)$ is odd
wraith daggerBOT
artemetra
cedar kilnBOT
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fervent pike
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fervent pike
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royal loom
question 36, why is [T]c the inverse of the matrix?
I'm confused by your question. All they did was take the matrix, and put an inverse sign on it and claim that is the inverse. What's your doubt about that?
it's invertible because it has 3 pivot columns
dawn junco
no that's not what they're saying
[T]c = (C^-1 * [T]e * C) = diag(1, 3, 9) [C is the matrix whose columns are the vectors in basis "fancy C"]
adding the parentheses for clarity
@royal loom @fervent pike
wide scroll
fervent pike
yup
fervent pike
[T]c = (C^-1 * [T]e * C) = diag(1, 3, 9) [C is the matrix whose columns ar...
C is the matrix formed by vectors in the basis C?
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silver sleet
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silver sleet
how do i go about solving this
i was thinking negative binomial distribution but im not sure how to use it
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twilit thunder
I don't understand how the points of intersection we get are 4a,4a can someone explain
rigid lava
you have y^2 = 4ax, x^2 = 4ay
you can solve the system however you want for (x,y)
for example, solving eqn 1 for x, then substituing it in for eq2
cedar kilnBOT
gusty wraith
Aerospace engineering major (not much of a mathematics major background) working in classical mechanics and optimal control theory, need to get a deep understanding of several topics and need textbook recommendations:
- Euclidean space, real space, and vector space and defining these terms
- Motions in Euclidean space
- Manifolds
- Total derivative vs gradient
- The concept of mapping
cedar kilnBOT
@gusty wraith Has your question been resolved?
nocturne reef
Had everything I needed for my engineering maths at least - at various points in there should feature matrix analysis, vector calc, functions of complex variables, which I think covers most of your list
gusty wraith
https://drive.google.com/file/d/0B0kR9wWYP7oBcGZkTkhnemVkRFk/preview?resourcekey...
Already own this but ty
nocturne reef
Fair enough haha
gusty wraith
I need stuff more leaning towards Euclidean geometry
nocturne reef
Hmm let me see if I can dig out my old reading lists
gusty wraith
Something along the lines of this article in content
And this one
<@&286206848099549185> Just in case other ppl have any interesting suggestions as well
vernal minnow
total derivative vs gradient should be explained in any multivariable calculus textbook, really
vernal minnow
a partial derivative is a function that has exactly the same incline with regards to ONE variable, at ALL points of your original function. it's usually represented as rhe Jacobian matrix.
the total derivative is the best possible linear approximation of the rate of change of a function in ALL variables at ALL points. You can write that as a row matrix of all partial derivative matrices.
also a partial derivative is always exact (if the function is differentiable in that variable). A total derivative is often not.
cedar kilnBOT
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crimson sedge
cedar kilnBOT
crimson sedge
all unanswered questions
livid hound
focus on one question at a time
livid hound
what have you tried
crimson sedge
using > <
livid hound
show what you've tried
cedar kilnBOT
@crimson sedge Has your question been resolved?
robust lagoon
cedar kilnBOT
robust lagoon
ik what a minimum is
shouldnt it be when the equation is positive
in tp form its (x+4)^2 - 7
i would have thought its a range of values but it just gave a singular one
<@&286206848099549185>
fallen jasper
u should take the first derivative
fallen jasper
so bro
robust lagoon
sorry go
fallen jasper
x^2 is postive right ?
robust lagoon
yes
for it to be a minimum it needs to be positive
which is why i thought the answer might be a range for x, but instead the answer is just -4
fallen jasper
because the x value of a lowest point of a qudratic function is given by the formula
-b/2a
here b =8 , a=1
so your x value is -4
robust lagoon
ah ok
thanks
could you also help me with this too please?
im not sure how to re arrange it
its not anywhere in the textbook
ive tried factoring
@fallen jasper
fallen jasper
i think you should use long division here
there is a certian formula but i forgot
it
robust lagoon
like divide 4x-7 by x+1
fallen jasper
yes
robust lagoon
i get -7
fallen jasper
gimme 5 minutes
robust lagoon
correct
robust lagoon
so theres no way to work it out or did u just do it that way
fallen jasper
there is a way but i forgot
robust lagoon
where did i go wrong in my division because my calculator gives the right answer
fallen jasper
lemme see
soo
u did the division right
but why did you continue afterg getting
-11
robust lagoon
yeah coz u divide the remainder by the thing ur dividing by
and have the quotent in front of that
robust lagoon
??
fallen jasper
and then ( the thing left after the division )/the denominator + the result of the division
bro didnt we get 4 from the devision
?
fallen jasper
the -11 is wrong
fallen jasper
-11 is just the thing left while divising
robust lagoon
why did i put it up there
fallen jasper
yes exactly
robust lagoon
now i understand
fallen jasper
good shit
fallen jasper
happens bro
robust lagoon
😂
fallen jasper
have a good one bro
fallen jasper
xd
robust lagoon
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bleak glen
cedar kilnBOT
bleak glen
helps pls
runic garnet
What’ve u tried
@bleak glen
Remember that f is a function of x
And thus ‘e’ is just a constant
And what happens when u differentiate constants?
There’s ur answer
bleak glen
Thanks @runic garnet could you please provide the answer as well
frigid escarp
It’s basically just the graph of x = A
bleak glen
It’s basically just the graph of x = A
that makes sense
frigid escarp
how about this
¯_(ツ)_/¯
smoky idol
I don‘t get why I‘m picking up a negative sign. The result is supposed to be positive :\
smoky idol
<@&286206848099549185>
cedar kilnBOT
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hard mirage
hi
cedar kilnBOT
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north smelt
Hello
north smelt
How should I solve 2 square root 15 and -2 square root 15?
Do the 2s cancel out?
Oh
I should multiply ?
cedar kilnBOT
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✅
vagrant elbow
north smelt
Add
limpid ice
do you mean $$2\sqrt{15}-2\sqrt{15}$$
north smelt
Yeah
limpid ice
a-a =0 for any a
north smelt
Okay thx
wraith daggerBOT
dabeastmode_the_wannabe_nerd
river veldt
is it possible to calculate the vertexX(-(b / (2 * a))) of a parabola if the discriminant is greater than 0?
ember geode
whether or not the discriminant is zero should have no bearing on if the vertex is able to be calculated
river veldt
whether or not the discriminant is zero should have no bearing on if the vertex ...
but if the discriminant is zero, then the x of the vertex of the parabola is b/2a and y is 0. when the discriminant is greater, then there are only formulas for finding the roots. or even if the discriminant is greater than zero, i can simply calculate the vertex x and y using the same formula -(b / (2 * a)) for x and -(discriminant/4*a)) for y?
dusk finch
but if the discriminant is zero, then the x of the vertex of the parabola is b/2...
-b/2a
not b/2a
dusk finch
and yes, you can use this formula
even if the discriminant is 0
or negative
And yes, the y coordinate of vertex is always 0 when discriminant is 0
river veldt
that is, when I find the vertex of the parabola, I do not pay attention to the discriminant
dusk finch
that is, when I find the vertex of the parabola, I do not pay attention to the d...
idk what you're asking now
river veldt
idk what you're asking now
and if I substitute the vertex of the parabola x instead of x(ax^2+bx+c), will I get the vertex of the parabola y?
dusk finch
and if I substitute the vertex of the parabola x instead of x(ax^2+bx+c), will I...
yes
if the x coordinate was e.g. 6, then 36a+6b+c would give the y coordinate of the vertex
river veldt
if the x coordinate was e.g. 6, then 36a+6b+c would give the y coordinate of the...
So it's the same as -(discriminant/4*a))?
dusk finch
Yep
if you want to verify this fact, you would need to show that this equality is right
$-\frac{b^{2}-4ac}{4a}=a\left(-\frac{b}{2a}\right)^{2}+b\left(-\frac{b}{2a}\right)+c$
wraith daggerBOT
MethIsAlwaysRight
dusk finch
oh waait
this is not ur channel
if u have any further questions, open ur own
im closing this one
.cloe
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lavish spire
cedar kilnBOT
lavish spire
lavish spire
^
In the second picture and while proving that kerf + ker(f-ide)(X) is direct, my questions:How did we get to the 2nd step? (F(X)=0 intercesection (f-ide)[(f-ide)(f(X)-x)]?2nd step and 3rd step aren't clear for me...
<@&286206848099549185>
cedar kilnBOT
@lavish spire Has your question been resolved?
lean cave
Hey! I need some help on (b).
cedar kilnBOT
Hey! I need some help on (b).
lean cave
I have no idea how to calculate f'(0)
the value of f'(0) = -5/2 for context
just no idea how though
teal tendon
so do you find b0
lean cave
yeah b_0 is 1 which makes f continious at 0
wraith daggerBOT
lean cave
and how does that lead to -5/2?
teal tendon
lim x to 0 f'(x)
lean cave
so the lim x to 0 of this?
teal tendon
yes
lean cave
ahhh i see
lean cave
,w differentiate ((ln(1+3 x)-ln(1+2 x))/(x))
how come we only do it with this?
how come we don't use b_0 = 1 in any of it
teal tendon
b_0 = 1 make it differentiable at 0
muted ember
how do i go around to solving this? i removed the parentheses $x^4 +2x^3 +2x^2 +x -42 =0$ and im not sure what to do next, cant find a way to group them
wraith daggerBOT
medioqre
idle tusk
how do i go around to solving this? i removed the parentheses $x^4 +2x^3 +2x^2 +...
is x an integer?
terse sigil
You would solve when each of the factors is equal to 40, no?
muted ember
im not sure, its not stated that it is
terse sigil
e.g. x^2 + x - 1 = 40 and x^2 + x + 2 = 40
muted ember
e.g. x^2 + x - 1 = 40 and x^2 + x + 2 = 40
oh and then i can move the 40 to the other side to solve it easily?
livid hound
i'd probs just rat root the expanded form
livid hound
that's a better idea
muted ember
that seems plausible imma try that'
yep i got the answer thank you all so much
.close
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ivory meadow
hi
ivory meadow
this is the solution for b)
I dont get how they went from the second line to the third one
This step
how did they get (1-2c)??
Or where did -cu*v go
chilly warren
how did they get (1-2c)??
Notice the first and the last term both contains $\bold{u}\cdot\bold{v}$
wraith daggerBOT
Xwtek
ivory meadow
oh
lmao
Yeah okay i dont know how i missed that
Wait just to clarify
((1-c)-c) * u cdot v?
ivory meadow
Surround the equation with $ and begin the command with \
tyy
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uneven axle
how to give the expression of an odd function on a given interval from its curve?
uneven axle
@here
coral jewel
insane
coral jewel
how to give the expression of an odd function on a given interval from its curve...
!xy
cedar kilnBOT
how to give the expression of an odd function on a given interval from its curve...
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
mental trail
Please show the original problem, **exactly as it was stated to you**, with the ...
@uneven axle
hearty arch
slate lintel
why not?
cedar kilnBOT
@uneven axle Has your question been resolved?
marsh lake
If i have points A,B,C (6,4) (3,7) (17,18) and i know that AB is perpendicular to BC, and A,B,C lie on the same circle, how do i find its equation of circle?
marsh lake
is there like a property relating one of the lines to be a diameter of the circle
grand raft
Yeah AC is the diameter
marsh lake
Yeah AC is the diameter
how to know this
grand raft
how to know this
It's a theorem
marsh lake
It's a theorem
so its always true if theres two perpendicular lines with points that pass through a circle?
grand raft
so its always true if theres two perpendicular lines with points that pass throu...
It's called thales theorem
And yes
stiff vigil
If i have points A,B,C (6,4) (3,7) (17,18) and i know that AB is perpendicular t...
also it would be in the form of (x-a)^2+(x-b)^2=r^2, right? once you find the diameter, divide by 2 to find the radius which is r, and then you would have to find what centre coordinate (a,b) is, which can be found by calculating the coordinates for the circumcenter of that triangle
marsh lake
also it would be in the form of (x-a)^2+(x-b)^2=r^2, right? once you find the di...
yeah i just have trouble identifying the diameter
cedar kilnBOT
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blissful gale
Does anyone know how to prove this. It's mainly combinatorics. But I'm not sure what part of the two sums I can equate
blissful gale
Like I'm not sure if I'm allowed to pull out the pi sum and then equate the insides
chilly warren
Wait, what is $\epsilon(\sigma)$
wraith daggerBOT
Xwtek
blissful gale
It's the sign of a permutation
chilly warren
Oh. It felt like something determinant.
chilly warren
You might want to look at Vandermonde matrix
blissful gale
You might want to look at Vandermonde matrix
There's no geometric progression. The notation may be confusing. The superscript is the row of A
chilly warren
Oops. I thought it's "to the power of $\sigma(i)$"
wraith daggerBOT
Xwtek
blissful gale
It's just different notation. It's multilinear algebra so it's more general for a set of super and sub scripts
chilly warren
So, basically B=A+I, right?
chilly warren
And what is A? Any matrix?
blissful gale
It's a representation of a linear function f
chilly warren
And what result do you want to prove?
chilly warren
Oh, the picture is the identity you want to prove.
cedar kilnBOT
@blissful gale Has your question been resolved?
chilly warren
I have an idea. First prove that
$$|B| = |B-I_{i}| + |B_{i}|$$
Where
$I_{S}(x, y)=1$ if $x = y \in S$ or $0$ otherwise
$B_{S}$ is $B$ without column and row whose index is in $S$
blissful gale
I'm not sure what you mean
chilly warren
Essentially, we're going back to using determinant
blissful gale
Just not sure how to use this with the sum identity
wraith daggerBOT
Xwtek
chilly warren
Essentially we want to prove that
$$|B| = \sum_{S \in P(0, 1, ..., n-1)} |A_S|$$
cedar kilnBOT
blissful gale
.reopen
cedar kilnBOT
✅
blissful gale
I'm just not sure how this helps
wraith daggerBOT
Xwtek
blissful gale
Essentially we want to prove that
$$|B| = \sum_{S \in P(0, 1, ..., n-1)} |A_S|$...
I'm not sure what to do with this
chilly warren
I'm not sure what to do with this
We're basically relating the formula to determinant.
blissful gale
So take the determinate of each side
chilly warren
No, the left hand is just a formula of a determinant.
And the right side of the equation is a summation of determinants in a disguise.
blissful gale
Ah okay
chilly warren
Wait, my notation gets confusing fast. Let's change it.
$B_S$ as the matrix $B$ whose column and index is included in $S$
wraith daggerBOT
Xwtek
chilly warren
So, $$|B_S| = |B_S - I_i| + |B_{S-{i}}|$$
wraith daggerBOT
Xwtek
chilly warren
Where
$I_i(x,y) = 1$ if $x=y=i$ or $0$ otherwise
wraith daggerBOT
Xwtek
chilly warren
Yeah, something like that. And, I forgot that it's supposed to be $(B-I_i)_S$
wraith daggerBOT
Xwtek
blissful gale
I'll try that thanks
cedar kilnBOT
@blissful gale Has your question been resolved?
cedar kilnBOT
@blissful gale Has your question been resolved?
blissful gale
The goal now is to write a permutation of n elements as permutations of n-1 elements with n added in different spots
Ie
<@&286206848099549185>
cedar kilnBOT
@blissful gale Has your question been resolved?
blissful gale
Does anyone have any ideas
blissful gale
Anyone
cedar kilnBOT
@blissful gale Has your question been resolved?
cedar kilnBOT
@blissful gale Has your question been resolved?
wooden barn
cedar kilnBOT
wraith daggerBOT
Renz
stone mountain
where $(x_1,y_1)$ is a point on the graph
wraith daggerBOT
Renz
stone mountain
what do you think $x_1$ and $y_1$ are
wraith daggerBOT
Renz
cedar kilnBOT
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cedar kilnBOT
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thick portal
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ornate rune
How do you get confidence coefficient?
cedar kilnBOT
How do you get confidence coefficient?
hollow totem
of what exactly?
ornate rune
of what exactly?
in stats and probability
ornate rune
hollow totem
Basically, in reality, you first choose a confidence level or significant level, then use this formula to get the sample size, then u get the data that = to the sample size
The confidence simply said: "its 92% confident that the sample size prepresent the average population"
ornate rune
uh then what is this table
hollow totem
Thats z value?
hollow totem
yea how do u get that
Dont worry, the teacher will allow cheat sheet for z value
Or at least the problem will provide it for u
ornate rune
Dont worry, the teacher will allow cheat sheet for z value
i wanna know where did it come from
hollow totem
U dont need to know how to calculate it
hollow totem
i wanna know where did it come from
A bit complex
Search YT: Where z value come from and its relationship with confidence level
ornate rune
Search YT: Where z value come from and its relationship with confidence level
ok will do
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gusty lotus
i have the taylor series expansion of a function , how do i find its 6th derivative ( not g''''''(0) but g''''''(x) )
limpid ice
um, depends on the function
limpid ice
um unfortunately my French kind of sucks, but I believe you just have to find derivative of the function 6 times. There might be a faster method though
what does sh(x) mean?
gusty lotus
um unfortunately my French kind of sucks, but I believe you just have to find de...
they asked us to deduce from the the first question tho
gusty lotus
what does sh(x) mean?
hyperbolic sine (x)
limpid ice
sorry I probably can't help you
gusty lotus
sorry I probably can't help you
No worries
cedar kilnBOT
@gusty lotus Has your question been resolved?
glad peak
Use substitution and chain rule
Let $u=\sin^{-1}(x)$
[ g(u) = \sinh^{4}(u) ]
[ g’(u)= 4\cosh (u)\sinh^3(u) \frac{du}{dx}]
wraith daggerBOT
shsgd
glad peak
Wow 6th derivative will be painful to reach
gusty lotus
**shsgd**
so i do that six times ?
they asked us to deduce from the first question wich is the taylor expansion of f
could they have meant to find g''''''(0) instead of g''''''(x) ?
glad peak
If you have already got the taylor expansion, then g^(6)(x) will be one of the terms
glad peak
It will be slightly different since it looks like you got the taylor expansion of f not g
Although it looks like you were only asked to expand up to 4 terms
gusty lotus
but would that term give us the 6th derivative and not just the image of 0 through the 6th derivative
gusty lotus
Although it looks like you were only asked to expand up to 4 terms
if we multiply it by x^3 it gives us g(x) up to 7 terms i suppose
glad peak
Did it ask to expand at the point 0?
gusty lotus
Did it ask to expand at the point 0?
yes
glad peak
Hmm
I’m not sure then, because I doubt they want you to differentiate 6 times as that would be very involved
I have a feeling there is a trick you are supposed to use
gusty lotus
I have a feeling there is a trick you are supposed to use
yeah i can't figure it out 😔
is there a way to call in the math avengers cuz i kinda need it asap
glad peak
is there a way to call in the math avengers cuz i kinda need it asap
I do not believe they expect you to get this
,w [//number:6//]th derivative of [//math:sinh^4(arcsin(x))//]
wraith daggerBOT
glad peak
That is a ridiculous amount of work to do
gusty lotus
okey you have convinced me that they might have made a mistake 💀
they probably just want g^6(0)
glad peak
Maybe ask your professor about that q
gusty lotus
Maybe ask your professor about that q
yes thx for helping
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gaunt fern
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gaunt fern
<@&286206848099549185>
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lost wagon
What is the question
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lofty lily
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lofty lily
i literally cannot figure this out
even with desmos
symbolab
anything etc
ive retaken the problem (it changes the stuff around) like 8 times i dont even care anymore i just want to eradicate this thing out of my incomplete problems
crimson sedge
Bro these type of problems r so stupid wish I could help
stone mountain
what do they say
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small igloo
Consider A to be a 2024 × 2024 matrix such that det A = 2. Find det(adjA)
cedar kilnBOT
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rare magnet
Could someone help me with this problem using the epsilon-delta limit definition?
rare magnet
I have gotten to here.
however, this does not match the formula
usually for these problems i get a perfect match at the end like, x-7 or x-2, but for this I am left with 6-x, so I'm not sure if there is more work to be done or not.
ohh I see
I can rewrite it and then divide both sides by -1
leaving me with my desired: x-c
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wheat rain
i was very late for class and have no idea how to do find the range for this function. all of them tbh
f(x)=(x+1)/(x+2)
domain equals {-1, 0, 3}
wheat rain
like what do i solve
south tundra
Here range of f is simply {f(-1), f(0), f(3)}, so start by calculating f(-1), f(0), f(3)
native rain
f(-1)=(-1+1)/(-1+2)?
yes
wheat rain
0/-1
native rain
=0
wheat rain
oh okay
thank u
if i have another question do i open another help or js ask again here
native rain
up to you
wheat rain
oh okay
well
if the domain= {0,2,4} what is the range for g of x?
whats they asking me
native rain
this question is asking you about the range of a function g(x) for the given domain {0,2,4}
this means you are to find the outputs of the function g(x) when the inputs are specifically 0, 2, and 4
not sure how one would find the range if we do not know the function
did the question state the function g(x)?
wheat rain
yeah its at the too
top
i js didnt need to add more words i js needed to know what they were asking
native rain
oh ok
wheat rain
native rain
yes, you can just do the same things you did earlier
wheat rain
okok
native rain
it is the same type of question
wheat rain
last question
native rain
the set of values you obtain should be {5, 9, 21}
wheat rain
thanks
wheat rain
last question
f of x is the same as any other letter
right
like it could be z(m)= m+1/m+2
native rain
yes
"f" is just the label for the function
it can be replaced by any other letter or symbol
f is just very commonly used
wheat rain
why
native rain
it is the first letter of the word function
native rain
it would be a good idea to sleep more if you want your brain to absorb and retain more information
native rain
np
wheat rain
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cedar kilnBOT
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crimson sedge
what's the length of a 3d line projected onto a plane?
cedar kilnBOT
what's the length of a 3d line projected onto a plane?
crimson sedge
the line's length L probably equals sqrt(x²+y²+z²), so...
wraith daggerBOT
.doc
prisma gull
to get the projection, you will just set z=0
crimson sedge
if the normal vector of the plane projected onto is exactly aligned with the x-axis, then is the formula sqrt(y²+z²)=sqrt(L²-x²)?
prisma gull
if the normal vector of a plane is aligned to the x axis then the plane is perpendicular to xy plane
crimson sedge
ok nice thanks
it feels like there's some kind of connection to partial derivatives there.. ehh I'll just worry about it another time
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lethal lichen
.reopen
I’m kind of struggling to do some of the basic absolutely value graph questions I don’t understand what and why my y- values are
cedar kilnBOT
I’m kind of struggling to do some of the basic absolutely value graph questions ...
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south turtle
I have a problem related to the convergence of Gauss-Seidel and Jacobi iterative methods. I am asked to evaluate, without calculating the spectral rays, the convergence of these iterative methods.
I know that by the theorem:
if A is a strictly row- or column-dominant diagonal matrix, or irreducibly row- or column-dominant diagonal matrix, then:
- Jacobi's method converges
- the Gauss-Seidel method converges and ||G||_inf <= ||J||_inf
and therefore considering that the matrix is strictly diagonal dominant I can already say that
- both iterative methods converge
- the Gauss-Seidel method converges before Jacobi.
in the solution it does exactly this step. but before using the theorem I mentioned above, check if the matrix is symmetric and tridiagonal.
Can you tell me why this step was taken? A thousand thanks
I attach the question and the solution
south turtle
Question:
Consider the following matrix M and the following vector z,
Given the system Mx = b, establish whether and which iterative methods are convergent, without calculating the spectral radii and carefully motivating the answers.
Solution:
The matrix M is symmetric, not tridiagonal. We immediately see that it is strictly diagonal dominant (both for rows and columns, being symmetric): Therefore the Jacobi and Gauss-Seidel iterative methods are convergent.
I can imagine that perhaps the fact that the matrix is strictly diagonally dominant has been seen using the symmetry property, although it would seem more convenient to me to control the value of the elements on the diagonal. and I didn't understand why it was evaluated that the matrix is not tridiagonal
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wheat raven
can someone help me to do this problem
bright moss
!status
cedar kilnBOT
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
distant wyvern
i couldve sworn someone asked this exact problem earlier today
bright moss
xD
cedar kilnBOT
wheat raven
wheat raven
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
@bright moss I don't know where to begin
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split pier
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split pier
i am doing this exercise in baby rudin. it's clear to me that E is bounded since E ⊂ [1, 3]. i am trying to prove it is closed. since 2 < p² < 3 for p in E, it can be equivalently interpreted as √2 < p < √3 for p in E so that it is a set consisting of all rational elements between √2 and √3. note although it doesn't make sense to write √2, √3 when we're only given the metric space Q and these elements are not members of Q, i just considered it for simplicity's sake for me.
if x is a limit point that is not in E, then x can be 1) irrationals between √2 and √3,
2) x < √2
3) x > √3
irrationals are not members of this metric space so forget about 1. In 2nd and 3rd case just there must exist some rational r and r' such that x < r < √2 for 2nd case and √3 < r' < x for the 3rd case by density property. take half times d(r,x) and d(r',x) respectively for these respective cases. then nbds with this radius will invalidate x as a limit point of E. this says no limit points outside of √2 and √3.
for p in E, there exists a rational a/b and m/n such that √2 < a/b < p < m/n < √3 by density property. just take the nbd with inf{d(p, m/n), d(p, a/b)} so that this nbd can be allowed to be contained in E. E must be open. these also act like limit points so i think E is also closed.
is this right way of thinking but wrong way of proving or can it be taken as a proof
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native rain
i agree with your interpretation for the closedness of E, but i think your method for checking the openness of E needs some adjustment
the way you used it here is more relevant to discussing closedness than openness
split pier
the way you used it here is more relevant to discussing closedness than openness
uhh is that so? then how can i adjust the openness nicely enough??? i just thought these rationals in E are also limit points as well as interior points
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sinful dirge
x+y+xy=63
y+z+y=24
z+x+xz=48
x+y+z+xyz=?
cedar kilnBOT
x+y+xy=63
y+z+y=24
z+x+xz=48
x+y+z+xyz=?
sinful dirge
i came accross this math problem in a random book and couldnt solve it can some one walk me through explanations?
ashen sable
Have u tried anything?
sinful dirge
yes i tried finding values separately, unfortunately didnt match the choices provided
there were 4 choices to it (cant remember them distinctively tho)
ashen sable
What were your steps?
ashen sable
x(1+y) + y = 63
z + 2y = 24
x(1+z) + z = 48
get two equations for x in terms of y and z
solve using the 2nd one?
sinful dirge
lemme try real quick
slate solstice
wait are you sure it isnt y+z+zy=24?
sinful dirge
yes sure
slate solstice
ok
sinful dirge
least it wrote that way
ashen sable
Your solution may differ, if the question's different
sinful dirge
I still have quite near answers to my doing
Gosh, with typo hypothesis, my answer seems closer to their answer.
What u guys think (btw im really curious is there a magical equation arrangement way to solve this question)
u guys bios are hilarious haha
fiery valley
whats the difference between $$\log_{e}$$ and $$\ln$$?
cedar kilnBOT
whats the difference between $$\log_{e}$$ and $$\ln$$?
wraith daggerBOT
Maladroit
crimson sedge
it is the same
hollow trail
just different notation for the same function
cedar kilnBOT
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north smelt
Hello
elfin minnow
we have the value of time which is 4 hours, and the speed the sis was driving right?
elfin minnow
Only the dads speed
yes
so we can find the distance travelled
since the dad caught up with her, their distances travelled must be the same right?
north smelt
Yes
elfin minnow
so let's find the distance travelled first
elfin minnow
do you know the equation for speed?
north smelt
No?
elfin minnow
u alr found it, i didnt see
elfin minnow
no, u just have to do 300=5x
elfin minnow
yup
north smelt
Ok what should I do next
elfin minnow
u alr got it
north smelt
Oh
elfin minnow
60 km/h is the answer
north smelt
But it’s asking for speed not distance right
elfin minnow
here u found the distances value for each person
for dad it is 300 km
and it is 5x for mom
x represents the rate right?
elfin minnow
since the dad caught up with her, their distances travelled must be the same rig...
and since this, we can equal the two distances
elfin minnow
X is the rate idk
u set the rate of mom to be x is ur table
elfin minnow
and since this, we can equal the two distances
so it will be 5x=300, so x=60 km/h
elfin minnow
u used it to find the distance of the dad
distance = rate * time
so 75 * 4
which is 300
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jaunty heath
Can one of you fellow nerds possibly solve this pattern for me? My friend sent it to me. It was for a test she had to do for a job application. It’s really bothering me that I can’t figure it out. She couldn’t either - failed the test sadly.
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inland jackal
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sage forge
Do you have a math question?
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frigid sinew
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frigid sinew
whcih theorem do they mean
cerulean sail
whcih theorem do they mean
I'd think you'd know the theorem, do they not have like notes that refer to theorems there?
frigid sinew
<:catGiggle:668948717772079128> I'd think you'd know the theorem, do they not ha...
they dont lol
i jsut googled theorem sequence
and a bunch of stuff popped up
cerulean sail
well, I have no idea which theorem they're referring to, not very nice of them to state theorem numbers but not explain what they actually are 
I'm guessing something like algebra of limits? 
[tl;dr "limit of the sum/product of convergent sequences is the sum/product of the limits"]
Do you have an idea of how you'd find the limit at least?
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frigid sinew
<:catBruh:715619607431610418> well, I have no idea which theorem they're referri...
Yeahhh rip
frigid sinew
Do you have an idea of how you'd find the limit at least?
Yeah it’s easy just the theorem is weird
Anyway ry
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edgy sun
Help
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blazing leaf
What is the phase shift for this?
cedar kilnBOT
What is the phase shift for this?
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