Right, so composition of f with itself doesn't exist
#help-17
river minnow
sharp sinew
old niche
what is a pivot in gaussian elimination, i always sorta just did the process without paying attention to a pivot
vocal sleetBOT
what is a pivot in gaussian elimination, i always sorta just did the process wit...
old niche
and why is it significant
like when i do gaussian elimination i sorta just
eyeball what to do
karmic imp
and why is it significant
Idk if this is helpful
hard atlas
after the elimination, the first entries in the rows are the pivots
by counting them you can read off the number of free variables for example
vocal sleetBOT
@old niche Has your question been resolved?
old niche
after the elimination, the first entries in the rows are the pivots
so you can only know after elimination?
hard atlas
yes
old niche
.close
vast shale
help pls
wary mantle
Yes
vast shale
so c?
wary mantle
Btw, is this an exam?
vast shale
Btw, is this an exam?
no just practice exams
wary mantle
Wait
vast shale
ok
strange crater
could you clarify what you mean? because sin(0) is not 1/2
oh. well angles will be expressed in degrees or radians
I don't think I'd say it's either one by default. you can choose how you want to express theta
and you don't "convert" 1/2 to degrees/radians
karmic imp
That 1/2 is based on the unit circle
What theta equals, can be degrees or radians
Like sin(45 degrees) = sin(pi/4 radians) = sqrt(2)/2
strange crater
it is whichever you choose it to be. they can be expressed equivalently
loud pivot
Degrees should have the unit written next to it (°), radians usually don't
karmic imp
Science is degrees unless stated otherwise
Even without the degree symbol, default is math uses radians, science/physics uses degrees, unless it's stated what to use
loud pivot
Of course
But haven't seen anyone writing in degrees if there's no unit symbol next to the number
Natively 🙃
210 rad is quite a bit
Probably don't have 12.032 degrees in mind
But I'm just speaking generally
humble current
Hello!
If you have to dismiss a negative value in an answer that has either positive or negative values (e.g. taking the square root of a number) what’s the formatting to do so?
humble current
I thought it was something like “- is dismissed” but it’s been a few months since calc so I can’t remember
loud pivot
If I understand correctly, can't you just write a restriction next to the answer?
humble current
Like saying x is between 0 and positive infinity?
humble current
Ye sure
Just basically, if a question went like this “y=sqrt(9)” then y=+/- 3
But if the question requires a positive answer
Then I needed to put a statement to show that dismissal of the negative
But I can’t remember the exact wording of it
humble current
Yea that’s what we did but my teacher would make us use a certain word to describe it
It’s not too big of a deal I just wanted to see if it was used elsewhere
rancid blaze
discard?
loud pivot
$y \in \mathbb{R}^+, y \neq -3$
twin meteorBOT
USS-Enterprise
loud pivot
maybe, or the symbol for therefore (3 dots arranged in a triangle)
loud pivot
Just means "y belongs to positive reals, so y can't equal -3"
loud pivot
No problem
humble current
.close
sweet cargo
How did Newton, and other early Calculus discoverers, know their values for a derivative were correct? This is one of those super novice questions so perhaps someone could give me some context as well. I understand that a derivative is a special kind of limit. When evaluating a derivative at a certain point and seeing how the value gets closer and closer to a given value, do we just assume that number is the exact derivative?
vast shale
Anything that was invented in their time was crude af, they solved and solved things till they refined it further and further into things you know today. And it was work of centuries and many minds that you see as Calculus. And yeah, you should approximate to a certain value like maybeyou can go on and on but then after a while it wont matter.
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
Any ideas how I can start with Q4
dull maple
Well, follow on the hint.
vast shale
And then?
vocal sleetBOT
@vast shale Has your question been resolved?
tender mantle
Hello Bosses I need your help on Fourier series
vocal sleetBOT
Hello Bosses I need your help on Fourier series
tender mantle
Help me please
vocal sleetBOT
@tender mantle Has your question been resolved?
warped mountain
vocal sleetBOT
warped mountain
Why did I lose a point here for justification?
rough depot
Before looking at any logic, did you +c at the end?
warped mountain
Same thing happened here
No +C
I mean yes at the very end
But the error happened around where the red marks are
Both say "proper?"
woops
But u can see at the top
warped mountain
You can see the purple box at the top of that last ss. It also says "not proper"
rough depot
Shoot, your form looks good to me for a set up. The only idea I could think of is that you didn't go A/2x-1) +B/(x-1). I'd ping a different helper to gain some insight
open hornet
U0 = 0
Un+1 = sqrt(4Un +5)
0<Un < 5
prove : 5-Un+1 < 4/5 * (5-Un)
Please give me the answer line by line , i've been stuck on this question for a solid 2h (i'm garbage at algebra)
flat whale
U0 = 0
Un+1 = sqrt(4Un +5)
0<Un < 5
prove : 5-Un+1 < 4/5 * (5-Un)
Please give...
no one's gonna give away the solution
vocal sleetBOT
@open hornet Has your question been resolved?
rancid ibex
can someone explain how the joining process works
vocal sleetBOT
can someone explain how the joining process works
grizzled halo
common denominating: $\frac1{9+h}-\frac19=\frac9{9(9+h)}-\frac{9+h}{9(9+h)}=\frac{9-(9+h)}{9(9+h)}$
twin meteorBOT
chlamydia
zenith ore
Can someone help me figure out where I messed up? It says the correct answer is supposed to be -5ln|x+2| + 5ln|x+1| + 4/(x+1) + C
vocal sleetBOT
Can someone help me figure out where I messed up? It says the correct answer is ...
grizzled halo
check this
vocal sleetBOT
@zenith ore Has your question been resolved?
zenith ore
Ooh I see, so those numerators would be plus (x+1) and then it would be -2 right?
grizzled halo
$-\frac{x-3}{(x+1)^2}=-\frac{x+1-4}{(x+1)^2}=-\frac{x+1}{(x+1)^2}--\frac4{(x+1)^2}$
twin meteorBOT
chlamydia
mild raven
the derivitave of this is 2x + k right
vocal sleetBOT
the derivitave of this is 2x + k right
mild raven
im new to these so im just checking to make sure im on the right track
karmic imp
No
karmic imp
Yes
mild raven
🙏
livid tapir
was a pleasure helping u
mild raven
.close
wispy patio
vocal sleetBOT
wispy patio
hi, i need help with this question
grizzled halo
what part
grizzled halo
recall Area$=\frac12ab\sin C$
twin meteorBOT
chlamydia
grizzled halo
for angle C between sides a and b
grizzled halo
yeah
grizzled halo
a line can be described with a gradient and a point it passes through
this can be applied to vectors
wispy patio
yeah?
wispy patio
a line can be described with a gradient and a point it passes through
this can b...
so what should i do here?
grizzled halo
did you learn anything like this for lines
with a direction vector and position vector?
wispy patio
yes
grizzled halo
so we're told that:
- L1 is parallel to AB (direction) and passes through (2,-1,0) (position)
- L2 is parallel to AC and passes through (-1,1,1)
wispy patio
so we're told that:
- L1 is parallel to AB (**direction**) and passes through (2...
okay
so for the equation of L1
it should be:
(2, -1, 0) + (AB)lambda
?
grizzled halo
yes
wispy patio
oh okay
wispy patio
yes
for cii) i think i know how to do, just make them equals each other and solve simultaneois euqatiion, if there is no answer they do not intersect
what about d) how do you do it?
@grizzled halo?
hard kraken
I don't know what bearing 143° means
vocal sleetBOT
I don't know what bearing 143° means
worthy citrus
lean merlin
Are these correct and how do I proceed to find {u\geq a}?
vocal sleetBOT
@lean merlin Has your question been resolved?
lean merlin
<@&286206848099549185>
fleet ember
solve u(x) >= a for each of these cases
vocal sleetBOT
@lean merlin Has your question been resolved?
lean merlin
solve u(x) >= a for each of these cases
are these correct?
fleet ember
what
how did an inequation become that
no idea what you're doing
???
it's not even closely related to your exercise
lean merlin
It is the exact same but with another function?
fleet ember
you're just supposed to solve 3 inequations
lean merlin
Im supposed to {u\geq a} to then use it argue that u is a borel function. I thought this was the approach for such a question
lean merlin
thats what im trying lol. It is part a) to then use to argue it is Borel which follows easily from this question a)
fleet ember
but did you already do question a) ?
if not start by that
why you skipping questions
lean merlin
To prove that the function u is Borel measurable, it suffices to show that each preimage {u\geq a}=u^−1([a,\infty)) is a Borel set for all a since the intervals {[a,infty)} generate the Borel sigma-algebra. (or any other generator set rather)
part a which is the question i am asking is {u\geq a}=u^−1([a,\infty)) which I am trying to do
fleet ember
dude you just have to solve u >= a in your 3 cases what you doing
first case a < - 2 and u > -2 so it's (-inf, inf) for this case
2 cases left
lean merlin
so the first one is correct no?
fleet ember
if a > -1 then it's (1/2, inf)
lean merlin
forgot the minus in my picture yes and it should be 1/2 i see
fleet ember
and also >= and > are different
because if a = -1 then (-inf, 0) counts too
like, stop reading a forum and focus on your 3 inequations
lean merlin
I need some guide lines. Relax
lean merlin
because if a = -1 then (-inf, 0) counts too
so actually it would be 3 cases being a<-2, a>-1 and -2 <a <=-1
fleet ember
then you're forgetting to put the case a = -2 somewhere
you should put it with a < -2
because these are the same
lean merlin
ah so a=<-2, a>-1 and -2 <a <=-1 and then everything should be covered
fleet ember
yeah
lean merlin
yeah
so we have for case 1: (-inf,inf), case 2: (1/2,inf) and case 3: (-inf,0] U [a,inf) (?)
fleet ember
wait no case 2 is missing something important, it should depend on a, I must have misread
and case 3 have a problem with the [a, inf)
if a > -1
then it we need to solve 2x-2 >= a
it's ((a+2)/2, inf)
that's case 2
and then case 3 has the same problem, it should be (a+2)/2 and not a
lean merlin
I am not sure anymore. Looking at the sketch of the piecewise function it would seem like at a>-1 that the x's that result in u(x)>=a would be (1/2,infty)
lean merlin
yes that makes sense
fleet ember
despite 0 being in the case a > -1
so it has to depend on a
because it's the interval of R+ which is solution of 2x-2 >= a
it can only be ((a+2)/2, inf)
lean merlin
a=<-2, a>-1 and -2 <a <=-1 a and the solutions are now 1: (-inf,inf) 2: ((a+2)/2, inf) and 3: (-inf,0] U [(a+2)/2,inf) I guess because the piecewise consists constant and linear meaning it has to depend on a for cases involving x>=0?
fleet ember
yes and no, for x >= 0, it depends on a only if a is relevant
for example in case 1
a didn't not matter
because u(x) > -2
so the whole interval x >= 0 worked too
but in case 2 and 3, a was relevant because x >= 0 is not sufficient to say that u >= a or not
it depends on a
lean merlin
makes sense. I'll run with a=<-2, a>-1 and -2 <a <=-1 with 1: (-inf,inf) 2: ((a+2)/2, inf) and 3: (-inf,0] U [(a+2)/2,inf)
fleet ember
you can immediately notice that (-inf, inf) is open, and ((a+2)/2, inf) too
so then you need to find why (-inf,0] U [(a+2)/2,inf) is a Borel set, despite not being open
hint: it's equal to R \ (0, (a+2)/2)
lean merlin
what about this: The union of borel sets is again borel and we have that both the sets generate the borel sigma algebra:
Therefore it must be a borel set?
fleet ember
yes if you already know that semi open intervals are borel set you're good
my hint was just in case you don't have cases like:
in your lesson
lean merlin
I have shown that before so I am allowed to use it. Got both of the sets from in the union from case 3 in remark 3.9
honest pollen
vocal sleetBOT
honest pollen
So I took the derivative of r(t) which gave me the velocity vector
To find where the speed is minimum, I needed to find the critical points for the velocity vector
To do that, I took the derivative of the velocity vector and got the acceleration vector
However, after taking the derivative a second time, all values of t are now gone
Idk how to find where t equals zero to get the critical points, and I'm lost here
vocal sleetBOT
@honest pollen Has your question been resolved?
exotic quarry
u dont need the acceleration vector
minimize the length of velocity vector, which is speed
its a function of t to real numbers
or equivalently find minimum of whats under the square root when calculating the length
honest pollen
u dont need the acceleration vector
To find the critical points I tried to take the derivative of speed (acceleration) and use it to find the critical points. Do you mean that there's a different method?
Based on the velocity vector that I have, the lower the input for t, the lower the velocity.
Can you elaborate more? Idk where to go from here
exotic quarry
To find the critical points I tried to take the derivative of speed (acceleratio...
length of velocity vector is speed
honest pollen
Oh, magnitude
honest pollen
I simplified it to √ 4(5t^2+4t+1) or √ 20t^2+16t+4
After plotting this on a graph, I found the lowest value to be 0.4 and it was correct!
Thanks @exotic quarry , I appreciate the help!
.close
barren kindle
\sqrt{\tan^{2}x+1}
vocal sleetBOT
\sqrt{\tan^{2}x+1}
vocal sleetBOT
@barren kindle Has your question been resolved?
vapid gorge
help!
gritty spade
You need to use exponent rules to simplify this.
vapid gorge
Whats the exponent rule?
gritty spade
karmic imp
vapid gorge
Ok ty let me see
one question so i worked it out and io was wondering if i have -8a to the power of 12 times 16a to the power of 8
do i multiply the base numbers too>
which would be -8 x 16
js wondering what ii would do with these
gritty spade
You would do (-2)^-3 and (-2)^4
vapid gorge
That gave me -8 and 16
gritty spade
Ok, give me a second to check
vapid gorge
I had that but when u multiply -2 times -3 u gotta take it to decnominotor
vapid gorge
And the B that was below, i added those up to b^31
and now i js needa figure out how to solve the a's together
which is a^-5 x -.125a^12 x 16 a^8
gritty spade
Can you show your work? I'm too slow...
vapid gorge
my works a bit all over the place but yeah one second
gritty spade
An image or photo would do
vapid gorge
gritty spade
,rotate
vapid gorge
I can show u the while page but it def wont help..
twin meteorBOT
gritty spade
I think i see a mistake
vapid gorge
Oh rlly
gritty spade
In the first step you did (-2)^-3 which got you -8
Thats incorrect its supposed to be 1/ (2)^3
The negative exponent rule applies here
gritty spade
Oh ok
gritty spade
itd be .125a^12
Oh you turned it into a decimal
gritty spade
But in case you didn't notice, we can multiply that 1/8 to 16 which gets us 2, (this is without the exponents and other variables involved)
vapid gorge
i didnt guess though
because
i arleady added b
which gave me b31
i was js a bit ocnfused
but now i know that we multiply the two coefficients
so .125 x 16 which gave us 2
i was js confused what to do with that
gritty spade
Yeah
gritty spade
ok
vapid gorge
You too
@gritty spade One questiopn
On my next problem its (2u^2v^0)5
in case of v^0
would it just be 1
gritty spade
Yes
gritty spade
np
vapid gorge
have a good evening/afternoon/morning
vapid gorge
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
rugged orchid
If $Y\sim\text{MVN}(\mu, \Sigma)$ what would be the distribution of $||Y||^2$?
$$\Sigma^{1/2}(Y-\mu)\sim\text{MVN}(0,I_n)$$
Then $||\Sigma^{1/2}(Y-\mu)||\sim\chi^2_n$ but that’s not norm squared of $Y$
vocal sleetBOT
If $Y\sim\text{MVN}(\mu, \Sigma)$ what would be the distribution of $||Y||^2$?
$...
twin meteorBOT
Frosst
rugged orchid
The best I’ve found was https://en.m.wikipedia.org/wiki/Noncentral_chi-squared_distribution
But that doesn’t help if my Covariance matrix isn’t σ²I
I want to get to the purple line
But I don’t know how the non I covariance gets transformed
vocal sleetBOT
@rugged orchid Has your question been resolved?
lucid furnace
vast shale
.help
vocal sleetBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
vocal sleetBOT
lucid furnace
I think my teacher made a mistake
the answer is "C" but as x->0+ y can't be infinity because there's an asymptote at y=2
did my teacher make a mistake or am i crazy
vocal sleetBOT
@lucid furnace Has your question been resolved?
lucid furnace
<@&286206848099549185>
vocal sleetBOT
@lucid furnace Has your question been resolved?
humble adder
Hi, i just need some clarification for boolean algebra... this function is being represented in a table. my only concern is why does the x become x̄ in the last collum
vocal sleetBOT
Hi, i just need some clarification for boolean algebra... this function is being...
river minnow
I would suppose because that's the function they are presenting the table of
Does the book refer to that as the table of just xy?
vocal sleetBOT
@humble adder Has your question been resolved?
humble adder
Does the book refer to that as the table of just xy?
yeah but wouldn’t it just be F(x, y)
also how do you figure out what numbers go in the last collum? is it + , x or?
river minnow
The order of inputs is up to you, just make sure you go through every case
And there's no problem with writing the expression that F(x, y) is instead of "F(x, y)" in the table if that's what confuses you
humble adder
what confuses me is why the x becomes x bar
humble adder
The order of inputs is up to you, just make sure you go through every case
also wdym by this you’ve lost me
river minnow
If I defined a function f(x) = x^2, would you question why x becomes x^2?
humble adder
no but it never said it was defined as x bar
river minnow
Ah, so the book doesn't define x̄?
humble adder
isn’t x bar (not x) ?
humble adder
Ah, so the book doesn't define x̄?
yeah exactly
hold up i’ll show the full question
river minnow
x̄ is the same as (not x), yeah, or negation of x, complement of x
Basically 0 bar = 1 and 1 bar = 0, that's the definition
humble adder
humble adder
Basically 0 bar = 1 and 1 bar = 0, that's the definition
yeah that’s what i mean, how does x become not x
that’s the complete opposite
river minnow
,rotate
twin meteorBOT
humble adder
mkay, forget the x bar
in the first pic
how did they get the numbers in the last collum?
like for example
x y xy
1 1 0
nevermind i’m stupid, would be 1 x 1 = 0
river minnow
[ \overline{1} \cdot 1 = 0 \cdot 1 = 0 ]
[ \overline{1} \cdot 0 = 0 \cdot 0 = 0 ]
[ \overline{0} \cdot 1 = 1 \cdot 1 = 1 ]
[ \overline{0} \cdot 0 = 1 \cdot 0 = 0 ]
twin meteorBOT
A Lonely Bean
humble adder
legend
and then they combine the two functions to make the last collum i’m assuming? (picture 2)
i got all these numbers just don’t know how to get the last one since there’s no operator
,rotate
twin meteorBOT
river minnow
i got all these numbers just don’t know how to get the last one since there’s no...
From here you just add each z bar and xy
And make a new column for xy + z bar
humble adder
yeah i split the two earlier into
F(x, y, z) and xy+z bar
and i got values
but then i don’t know how to combine them
like to make them into 1 collum
vocal sleetBOT
@humble adder Has your question been resolved?
vocal sleetBOT
@humble adder Has your question been resolved?
rugged orchid
yeah i split the two earlier into
F(x, y, z) and xy+z bar
No they are the same thing
Look at the xy column and look at the z bar column
Add them together
humble adder
Add them together
what do you mean add them together though
rugged orchid
Use the definition of the addition operator
humble adder
Use the definition of the addition operator
like it would make sense if it was
F(x,y,z) + (xy+z bar)
but it’s not
rugged orchid
No?
F(x, y, z) is a function
xy + z bar is a Boolean variable
You can’t add a function to a Boolean variable that’s not defined
humble adder
but you just said add them together
rugged orchid
I said add xy and z bar together
As is indicated by the + symbol between those 2 terms
rugged orchid
Show it
twin meteorBOT
rugged orchid
You can’t just go remove equal signs
And besides
They should have the same truth values
Since they are equal
But also
F(x, y, z) does not admit a truth value
It is not a Boolean variable
Well, technically F(x, y, z) is but F itself is not
humble adder
i’m so confused man
humble adder
right yeah
rugged orchid
Let’s look here
Ignore F
Let’s just have a look at the z bar column
What is z bar
rugged orchid
It’s also a Boolean variable
It can take on values of 0 or 1
And you can do Boolean algebra on it
rugged orchid
Like z bar + z bar
Or z bar * z bar
Ok
So when z is 0, z bar is 1
You’ve got that down
humble adder
yeah 100%
humble adder
x times y
humble adder
i was gonna say something but idk if it’s right
rugged orchid
(The more you say the more I can see if you understand correctly)
humble adder
times is the same as “and” but for boolean instead right?
rugged orchid
Don’t be afraid to say something wrong
humble adder
so T and T is like saying 1 x 1
rugged orchid
times is the same as “and” but for boolean instead right?
Yes
It’s not “the same” but it pretty much is
“And” does not exist in Boolean algebra
Boolean algebra has just (*, +, bar)
Everything else you don’t know what it means
humble adder
It’s not “the same” but it pretty much is
“logically equivalent to” ?
rugged orchid
“Or” is not something that makes sense in Boolean algebra
rugged orchid
“logically equivalent to” ?
Pretty much yeah
humble adder
“Or” is not something that makes sense in Boolean algebra
instead it’s + yeah?
rugged orchid
Yeah
humble adder
1 x 1 = 1
1 x 0 = 0
0 x 1 = 0
0 x 0 = 0
rugged orchid
What about it
humble adder
isn’t that what you meant by walk me through it?
rugged orchid
No I want you to describe in detail how you decided to write down the 0’s and 1’s in the xy column
(This is important for the column with F, that’s why I’m making you explain in detail)
humble adder
No I want you to describe in detail how you decided to write down the 0’s and 1’...
i think of the 1’s as T , the 0’s as F and the x as and
then i just fill it out like i would for logical truth tables
rugged orchid
1 x 1 = 1
1 x 0 = 0
0 x 1 = 0
0 x 0 = 0
Then what’s the point of this
humble adder
just a simplified version, don’t wanna bug you by writing too much
rugged orchid
i think of the 1’s as T , the 0’s as F and the x as and
First off yoy should get comfortable doing algebra with + * bar and 1 0
And secondly, I still need more details
rugged orchid
i think of the 1’s as T , the 0’s as F and the x as and
Where are you looking for the 1’s and 0’s and how does that affect what you write down in the xy column
rugged orchid
It’s implicit but I like to write the dot still
rugged orchid
the x collum and the y collum
Why are you looking at the x and y columns
humble adder
Why are you looking at the x and y columns
coz isn’t that what the xy is made of? the output of x . y ?
humble adder
the output we got for collum xy and now we + z bar onto that output
rugged orchid
Ok do that and send a picture
rugged orchid
Sure
twin meteorBOT
humble adder
that’s what i got for xy+z bar
rugged orchid
Now instead of going around having to call it xy + z bar
We can just call it F(x, y, z)
rugged orchid
👍
You should now realise that I can have G(x, y, z) = xy
Then put that in the top of the xy column
And then I can say F(x, y, z) = G(x, y, z) + z bar
And that makes perfect sense
humble adder
You should now realise that I can have G(x, y, z) = xy
wait what 🤣
where did G come from
humble adder
Just like the question made F up
how come G (x, y, z) = xy instead of = xy + z bar ?
rugged orchid
And then I can say F(x, y, z) = G(x, y, z) + z bar
Look at this
humble adder
yeah u added it on at the end
so theoretically i could define it with the z bar at the end ye?
rugged orchid
Well I could have H(x, y, z) = z bar
And then I can say F(x, y, z) = G(x, y, z) + H(x, y, z)
And that’s also perfectly fine
humble adder
ohhhhh i get ya mate
rugged orchid
I can also have K(x, y, z) = y bar
And never use it
But it’s a bit silly to do that
But there’s nothing wrong with it
rugged orchid
Exactly
I just made it up
But I’m not using it
And there’s nothing wrong with that
It’s a bit silly to do that because you’ve just defined something for the sake of defining it and not to use it
humble adder
Hi, i just need some clarification for boolean algebra... this function is being...
is that why they changed x to x bar here?
rugged orchid
But nothing says you can’t do that
humble adder
i didn’t mean to reply to the message ignore that sry
rugged orchid
is that why they changed x to x bar here?
They’ve just skipped the Xbar column
You can add it in if you want
But they’ve just skipped it
humble adder
i’m gonna ask this but it might be stupid
would the function here be
F(x,y)
and u can make it F(x, y) = x bar y
rugged orchid
Yes
When I write on paper I like to have the dot in between
Just so it is absolutely clear that they are multipled
humble adder
between x bar and y?
rugged orchid
Yes
rugged orchid
Just look at the expressions
You might not have seen this yet but it doesn’t matter
I like to put my brackets and dots and plus signs between everything so there is absolutely no ambiguity as to what I’m writing
(The ones without dots I’m copying from the question so it’s a bit different imo)
humble adder
I like to put my brackets and dots and plus signs between everything so there is...
i’m doing that from now on
makes everything so much easier to read
rugged orchid
It’s just nice yeah
Making it clear for yourself and the reader is a blessing for all parties involved
rugged orchid
Cool :3 I’m only just studying this as well hehe
humble adder
it’s scary
humble adder
Cool :3 I’m only just studying this as well hehe
man u explained it like you’ve done it for decades, well done seriously 😂
rugged orchid
It really isn’t all that scary if you just wrestle with it and understand what’s happening
But it does take a bit to wrap your head around
humble adder
It really isn’t all that scary if you just wrestle with it and understand what’s...
glad you’re taking it well champ 😅
vocal trench
I need help with a line-plane question in 3 dimention
vocal sleetBOT
I need help with a line-plane question in 3 dimention
vocal trench
line D: x = (y-2)/-1 = z
line D': (x-2)/2 = (y-3)/1 = (z+5)/-1
find plane (α) for (α) contain D and the angle between (α) and D' is 60 degree
this is my translated version, the question is not originally in english
let v,v' be the vector for line D,D' respectately
I got v = ( 1, -1, 1) ; v' = ( 2, 1, -1), which is perpendicular meaning D and D' is perpendicular.
α and D' intersection
Therefore D and D' don't intersec
<@&286206848099549185>
vocal sleetBOT
@vocal trench Has your question been resolved?
vocal sleetBOT
@vocal trench Has your question been resolved?
static sand
vocal sleetBOT
static sand
Sorry if this isn't concise but, my question is, why is this written as "What is the value of A..." rather than, what I wrote in the first pic? If anyone can articulate with different verbiage I'd appreciate it.
pallid forge
you wrote the question to the right of the top red arrow? and you're wondering what the difference is between what you wrote and the given question?
static sand
I was a bit confused by the way it was written. I understand all the rules of exponents, but was looking for maybe some more elaboration as to why the question is written this way. It might be an odd question.
Or maybe they could have mentioned in the work that you're looking to cancel out the denominator, in the other part that I marked in red.
But yes, I rewrote the question in the top with the arrow
Me attempting to word it differently as an example
pallid forge
well you're not looking to find the value of x in 6^x, you're trying to figure out what value of A would make the two expressions equivalent.
static sand
So it would probably make more sense for me to move that sentance down to the second arrow as an explanation of what/why they're doing that work?
Basically, I'm trying to show more of what's happening like this:
pallid forge
right yeah. the whole point is to get something that has an exponent of x/4. your second step with what you wrote in red is enough. you get to 6^(4*(x/4)), or (6^4)^(x/4), which gives you 6^4 as the answer since that matches up with A^(x/4)
you're not finding x
static sand
I think that helps
pallid forge
you're rewriting 6^x such that x has a factor of x/4
static sand
So how would you write the white sentance?
"rewrite 6^x such that x has a factor of x/4" ?
I guess that's full circle
pallid forge
yeah i suppose so. it's tough to explain without just restating the original question
static sand
I might be too used to evaluating them, is how it's usually been presented up until this unit
but it's okay, thanks for the help
pallid forge
no problem.
static sand
Is what I wrote in red correct for what happened between the steps here in the work?
vocal sleetBOT
Is what I wrote in red correct for what happened between the steps here in the w...
merry python
yes
harsh forge
The length of a rectangular piece of paper is three times its width. The paper is folded so that one vertex lies on top of the opposite vertex, thus forming a pentagonal shape.
What is the area of the pentagon as a fraction of the area of the original rectangle?
vocal sleetBOT
The length of a rectangular piece of paper is three times its width. The paper i...
@harsh forge Has your question been resolved?
vocal sleetBOT
@harsh forge Has your question been resolved?
vocal sleetBOT
@harsh forge Has your question been resolved?
solemn cape
The length of a rectangular piece of paper is three times its width. The paper i...
!status
vocal sleetBOT
The length of a rectangular piece of paper is three times its width. The paper i...
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
@harsh forge Has your question been resolved?
gusty torrent
how do i evaluate the definite integral? i keep trying with calculators but they say its due to the cauchy principal value. please explain how i could solve this with a calculus II knowledge?
vocal sleetBOT
how do i evaluate the definite integral? i keep trying with calculators but they...
grizzled halo
it's an odd function.
hybrid flicker
it's an odd function.
yes but the integral doesn't even converge so this won't work
mild flower
it's a fairly simple u-substitution
"simple" idk it gets weird with infinite limits
and disconnected domains
hybrid flicker
yeah, the integral diverges oddly enough
visual ravine
yes but the integral doesn't even converge so this won't work
why wouldn't it converge ?
hybrid flicker
why wouldn't it converge ?
when x-> infinity for example, 2x/(1+x^2) is equivalent to 2/x
And the integral of 2/x diverges
so our starting integral diverges
visual ravine
hmmmm, ok, that makes sense
nevertheless, isn't the "oddliness" of the function tells as that this specific integral would be 0?
hybrid flicker
$\int_{-\infty}^\infty ... \neq \lim_{A\to \infty}\int_{-A}^A...$
twin meteorBOT
rafilou2003
naive herald
the Cauchy principal value = 0
visual ravine
**rafilou2003**
wait, really?
hybrid flicker
**rafilou2003**
this is only true if the infinite integral converges
gusty torrent
how would you determine the cauchy principal value?
hybrid flicker
For example, if I take $\lim_{A\to \infty}\int_{-A}^{A^2}\frac{2x}{1+x^2}dx$, what does that give me?
twin meteorBOT
rafilou2003
hybrid flicker
(spoiler alert : it gives me +infinity)
whereas IF the integral converged, it should give me exactly the infinite integral
visual ravine
ok, i will need to make rest my head on that 🧐 , thanks!
visual ravine
p.s. so i our case, the result of that is unknown(the integral diverge)?
kind jetty
so the integral diverges, but its cauchy principal value is 0?
hybrid flicker
so the integral diverges, but its cauchy principal value is 0?
yes
According to the cauchy principal value theorem (which sounds like bollocks but ok), we define $\int_{-\infty}^\infty \frac{2x}{1+x^2}dx$ as $\lim_{A\to \infty}\int_{-A}^A\frac{2x}{1+x^2}dx$
twin meteorBOT
rafilou2003
kind jetty
is the cauchy principal value ever implied in a math problem? Or does it always have to be denoted with p. v.?
hybrid flicker
I suggest always indicating when we're referring to it as p.v
hybrid flicker
Can you find how to integrate 2x/(1+x^2)?
so hint for @gusty torrent : try the u-sub ||u = 1+x^2||
gusty torrent
wouldnt that be ln |1+x^2|
gusty torrent
so ln 1+x^2
kind jetty
yeah
but if you didnt use p. v., then you would have to split the integral
which would result in undefined
rugged portal
can someone write this for me I can't seem to be able to copy and paste it into word or write it
vocal sleetBOT
can someone write this for me I can't seem to be able to copy and paste it into ...
vocal sleetBOT
vocal sleetBOT
Available help channel!
rough zenith
vocal sleetBOT
rough zenith
i think you use angle bisector theorm but i feel like my answer is wrong
scarlet lichen
i hate these questions so much
rough zenith
i did 2.5/4.6=4.6/x
rough zenith
the triangle CAB and CAD is similar right
scarlet lichen
this is the way i learnt it
rough zenith
yeah
scarlet lichen
4.6 / 6.8 = 2.5/x
rough zenith
huh
unreal dove
vocal sleetBOT
pale perch
tut tut
unreal dove
.reopen
pale perch
gotta open a new one
past mural
ur done
unreal dove
alr
karmic imp
.
blissful sentinel
Just ignore this channel
vocal sleetBOT
Available help channel!
vast shale
can someone tell me if my thinking is right? Is it 3 because i would end up with a zero in the denominator? And before anyone asks.. this is not a real quiz. It is a homework assignment.
vocal sleetBOT
can someone tell me if my thinking is right? Is it 3 because i would end up with...
vast shale
Is it because it cannot factor out?
scarlet lichen
removable happens when you can cancel an x term from the numerator and denominator
no CF
yep your right
vast shale
.close
vocal sleetBOT
vast shale
can someone tell me if my thinking is right? Is it 3 because i would end up with...
Isn't this a test? nvm
.reopen
vocal sleetBOT
✅
vast shale
@scarlet lichen This is also none right? Couldn't factor.
oh wait it says nonremovable lemme check
Is it 3?
scarlet lichen
<@782977640747106375> This is also none right? Couldn't factor.
thats the same equation
vast shale
because 3-3 would be 0 aka a vertical asymptote
scarlet lichen
yep
vast shale
it's saying nonremovable, not removable
vast shale
the first question said removable
vocal sleetBOT
vocal sleetBOT
Available help channel!
lone vale
I need help on how to solve the question
vocal sleetBOT
I need help on how to solve the question
lone vale
I didn’t understand it in class and I’m so confused
vocal sleetBOT
@lone vale Has your question been resolved?
nova delta
Do you know what standard form is
They’re asking you to write the equation such that ax^2 + bx + c. The chart that you were given are clues as to what each element is
If you’re struggling, graph each point on paper/ a graphing calculator.
A is your multiplier (how much it stretches)
B is your x axis shifter ( does it move left or right? By how much?)
C is your y shifter (how much does it move up or down)
eager furnace
vocal sleetBOT
grizzled halo
dude what
karmic imp
wrong image
Don't include the g(x) = and f(x) = parts
Because it already declares it
And it's f(t) btw, meaning the variable is t, not x
trim sparrow
does the set of natural number include 0 ?
vocal sleetBOT
does the set of natural number include 0 ?
trim sparrow
plush sage
does the set of natural number include 0 ?
It doesn't
trim sparrow
non-negative integers as the set of natural numbers denote as N. But i see google , the set doesnt include 0
plush sage
am i misinterpreting the text then or are they just wrong?
0 is neither positive nor negative
trim sparrow
oh it continues: "other authors call only the positive integers natural numbers. To prevent confusion, we simply avoid using the phrase natural numbers in this book."
plush sage
But according to what I know, the set of non negative integers and that of Natural numbers are different
trim sparrow
damn this ambiguity.
plush sage
oh it continues: "other authors call only the positive integers natural numbers....
It might be used for convenience otherwise I am pretty sure that they are different
It should have been whole numbers set
strange crater
I have seen 0 included in the set of natural numbers
trim sparrow
mmm
trim sparrow
I have seen 0 included in the set of natural numbers
doesn't this trip up people a lot
plush sage
doesn't this trip up people a lot
Fr i also was confused at first when I was taught these
strange crater
yes, which is why it should be stated in whatever text you're reading, or by the professor
see here, the answer is "it depends": https://math.stackexchange.com/a/293/993372
plush sage
yes, which is why it should be stated in whatever text you're reading, or by the...
Yes, I mean they can refer that for the sake of convinience but that doens't make that correct
strange crater
Yes, I mean they can refer that for the sake of convinience but that doens't mak...
it doesn't make it "incorrect", either. see other answers to the MSE post, and some comments as well
vocal sleetBOT
@trim sparrow Has your question been resolved?
boreal escarp
can someone double check if this is corect?
vocal sleetBOT
can someone double check if this is corect?
regal bane
Note the limit also distributes over the subtraction, which is necessary
I'm not marking you, I'm not sure if your marker will want to see that specifically
The steps are good otherwise
boreal escarp
Note the limit also distributes over the subtraction, which is necessary
are you saying there should be another step in between the two to show that
regal bane
In a perfect proof, that step would exist, or acknowledge that this limit property is necessary.
Consult the person who is marking you, on whether or not they want that explicitly shown.
jaunty coral
Hello, could I recieve help on my trigonometry work?
vocal sleetBOT
Hello, could I recieve help on my trigonometry work?
jaunty coral
For this one I got y=tan(4x)
I used the equation b=pi/P = pi/(pi/4) = 4
As for the rest, I'm pretty clueluess but will try and continue working on them. Any assistance would be appreciative. Thanks 🙂
<@&286206848099549185>
vast shale
0 is not a natural number , natural number are those number which occurs in nature
yes
nullity
jaunty coral
That won't apply to any of my questions
vast shale
have u seen 0 cats ?
jaunty coral
lol
What I got for this equation was -4cos(2(x--1.5707)+-3. Could a helper check this?
jaunty coral
What I got for this equation was -4cos(2(x--1.5707)+-3. Could a helper check thi...
<@&286206848099549185>
shy willow
What I got for this equation was -4cos(2(x--1.5707)+-3. Could a helper check thi...
its a positive cosine graph, in the form Acos(B(x+c))+D
graph has a period of pi
B = 2pi/period=2pi/pi=2
A= amplitude = 3 (positive 3 cuz graph is positive and not flipped)
graph appears to be a sin graph, which is just a shifted cosin graph, graph is shifted left by pi/4 to the righ so C = -pi/4
note: sin(x) = cos(x-(period)/2))
graph is shifted down by 3 (hence why the middle line is -3 and not 0) therefore D = -3
therefore
y= 3cos(2(x-pi/4)-3
jaunty coral
Oh wait, you're right. It would take -3 to go from -3 to -6. I'm not exactly sure where I got my -4.
shy willow
if youre unfamiliar or uncomfortable with the theory relating to graphs with general equations:
Acos(B(x+c))+D and Asin(B(x+c))+D, how they can be transformed into eachother, how to find the midline and how the midline, maximum, and minimum relate to values A, B, C and D i can explain in more detail
jaunty coral
where did you get the pi/4?
shy willow
where did you get the pi/4?
so the graph appears to be a sine graph, but is they want a cosine graph
cosine graphs begin at the maximum, while sine graphs begin at the midpoint
since the graph in the image has its nearest maximum at pi/4, if it were a cosine graph, begining at that maximum, to make it the graph in the image we would need to shift it by pi/4 to the right
do you see how shifting the cosine graph by half its period results in a sine graph
x + a shifts a to the left by a factor of a
so to shift to the right by pi/4, thats (-pi/4)
which is inside the bracket, remember
cos(B(X+C))
C = -pi/4
did this help?
jaunty coral
gimme a minute
jaunty coral
For this one I got y=tan(4x)
Also, can you check if this is correct @shy willow
jaunty coral
This makes sense. I appreciate your help!
Wait, if we were to convert the pi/4, we would just get .78. So the equation would be 3cos(2(x-.78))-3 .... is that correct?
shy willow
For this one I got y=tan(4x)
this appears to be a regular tan graph but with a different period
since your answer is tan(_x) its clear the only modification thats been made a regular tan graph is a stretch
whats the period of a regular tan graph?
shy willow
Wait, if we were to convert the pi/4, we would just get .78. So the equation wou...
keep it exact. pi/4
some webworks dont accept decimal answers
unless it says it does
shy willow
whats the period of a regular tan graph?
^
jaunty coral
keep it exact. pi/4
I will not be able to since they want it to be in decimal rounded to the two decimal. so it should be .79
shy willow
I will not be able to since they want it to be in decimal rounded to the two dec...
ah alr then that should work
shy willow
whats the period of a regular tan graph?
@jaunty coral do you recall?
jaunty coral
whats the period of a regular tan graph?
around every pi which is why I used the equation b=pi/P