because p(0) must be equal to 0?
#help-0
tawny fable
chrome salmon
because p(0) must be equal to 0?
Yes
chrome salmon
Wait
Let me check them first
Yes I think first three are subspaces need to think about 4th
tawny fable
I mean
Arent the first 3 easy to say? I think I am missing something
isnt it just like this one
and also for p(0)
chrome salmon
isnt it just like this one
Yes
All go on the same line
The last one won't be
Not gonna think bout it yet
tawny fable
what do you mean?
do they mean it must be either 3 or 1?
why do the point out that {0} is in it?
chrome salmon
do they mean it must be either 3 or 1?
3 or 1?
chrome salmon
Idk what that {0} is for 
tawny fable
O.o
chrome salmon
Is that 0 in R or some Rⁿ
tawny fable
Someone asked my teacher
chrome salmon
Someone asked my teacher
Yes what
tawny fable
he said:
R4[x] is a vector space, which is why there exists a unique vector which will be additive identity and it will be 0v.
That doesnt say anything...
xD
chrome salmon
he said:
R4[x] is a vector space, which is why there exists a unique vector whic...
Zero polynomial but that's already done
So here in last problem
Since they gave degree is odd
We won't get zero polynomial in set that's why they added union of {0}
We will get x,x³,x⁵, and such polynomiqls
chrome salmon
In all other cases they gave p(a)=0 that means p(x)=0 was one case too but here they gave
"Polynomial with odd degree"
Is some constant like c is polynomial of odd degree?
chrome salmon
Pls ranz you need to see the difference in both sets
tawny fable
I see that it is an odd degree...
chrome salmon
Then a constant won't be in the last set
tawny fable
then they had to put {0} inside
chrome salmon
Yup
tawny fable
so it wont be easy xD
chrome salmon
In other cases we could have constant polynomials
tawny fable
yeah
chrome salmon
In here we can have degree 1,3,5,...
tawny fable
you mean as counter example right?
if they wouldnt have put the {0} in
we could just say that {0} is not a part of p this time because it does not have a odd degree
chrome salmon
No need
tawny fable
oh really?
chrome salmon
What two cases?
tawny fable
but how do you know from what degree it will be?
it could be x^3 + 3x^2 -2x^1 and also 2x^3
or
-2x^1
itselft
chrome salmon
Let degree of p be m and degree of q be n
Then degree of p+q =< max{m,n}
chrome salmon
Let me think of this example
chrome salmon
Say p=x³+2x²+x and q=-x³+x²+x
When we add both we get p+q=3x²+2x
Which is of even degree
Oh well we found a counter then
That didn't came to me before
Are you following?
tawny fable
yeah
when the odd degree canceles it self
it is a counter example
that it right yeah..
when proving (c)
do I have to show 3 cases?
chrome salmon
3 cases for what
chrome salmon
Doing p(-2)=0 separately and p(0) separately is enough
tawny fable
do you mean like b?
chrome salmon
See p such that p(-2)=0 and p(0)=0 have factor (x+2)x
Right
If you show separately that p with factor x+2 and p with factor x form subspace then it's enough
chrome salmon
Yes
tawny fable
once for -2 and once for 0
chrome salmon
Doing it in 3 cases as you said will be right too but there's no need to go the hard way
chrome salmon
once for -2 and once for 0
Yes
tawny fable
but that is exactly what I did in (b)
was I wrong there then?
usually they dont let us do the exact same things..
chrome salmon
The and or difference
You see in 2nd one you need polynomial with zeros -2,0
Polynomials like x(x-2)
But in 3rd one
You can have polynomials like
x , x-2 , x(x-2)
tawny fable
I do see the difference
which is applicable because of distributivity we can factor x out and it will be in the form of x(x......number)
chrome salmon
Ranz I think you should analyze the rest yourself
First try it properly and if you have any more doubt then ask it
tawny fable
ok
lethal lichen
lone heartBOT
lethal lichen
how to integrate this by parts?
solar merlin
scarlet mango
Can someone help me with this one?
lone heartBOT
Can someone help me with this one?
scarlet mango
I like half understand it, solving these has always been somewhat ambiguous to me
<@&286206848099549185>
Mb lmao
In a similar vein, I don't feel like I really understand these either
I understand how to get the fundamental set of solutions for all of them, but I don't understand how that translates to a particular solution and how to use the right side of the equation
placid zinc
See "method of undetermined coefficients"
scarlet mango
That would be for determining the actual A, B, C values no?
I just want to know how to get the equation shown as the answer
Okay now I should be able to ping lmao
<@&286206848099549185> ping me when you can help
I'm sure you guys are busy 👍
lone heartBOT
@scarlet mango Has your question been resolved?
short pumice
There is a distinguishable professors and b distinguishable exercises to grade. There is more professors than exercises. How many ways are there to distribute the grading assuming every exercise is graded by exactly one lecturer and each lecturer grades at most one exercise?
lone heartBOT
@short pumice Has your question been resolved?
short pumice
short pumice
There is a distinguishable professors and b distinguishable exercises to grade. ...
Do you think I picked the right answer for this question ?
because if there is a professors then they can grade a! exercises but since there is not that many exercises we have to divide by (a-b)!?
do my answer now would be the 6th option
lone heartBOT
@short pumice Has your question been resolved?
short pumice
<@&286206848099549185>
young violet
because if there is a professors then they can grade a! exercises but since ther...
Your logic checks out. With b different exercises, the first one can be graded by a different professors. The second one could be graded by a-1, third by a-2, and so on. There would be a-b professors who don't grade an exercise. a!/(a-b)! would therefore be correct.
Example: 5 professors, 3 tests.
First test: 5 possible professors. Second: 4. Third: 3.
If we multiply them together to get the number of permutations, we get 5*4*3 = 5!/(5-3)! = 60
frosty sparrow
lone heartBOT
frosty sparrow
green line follows the curve of a circle
lone heartBOT
@frosty sparrow Has your question been resolved?
frosty sparrow
no
lone heartBOT
@frosty sparrow Has your question been resolved?
bleak ridge
I mean theres many ways you could go about doing that
You could create n angles from arctan(c.y/c.x) to arctan(a.y/a.x) for example
Then just (|c-b| cos(ang),|c-b| sin(ang)) for each angle
Where |c-b| is the distance between c and b
That comes with its own problems though
Theres prob a better way to do it with complex numbers
Do you have an application for this problem? @frosty sparrow
frosty sparrow
that’s exactly what i’m doing rn
and yeah it’s for rasterizing line loops with rounded corners
i think i found a solution that’s fast computationally
use dot product to find angle between a and b
compute the matrix that rotates a point clockwise angle/(n+1) degrees
lone heartBOT
frosty sparrow
and then rotate A around B n+1 times and plot each of those
that way u only call sin and cos once each
bleak ridge
Yeah that sounds like itd work
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lime kiln
I am having hard time to understand vacuous proof.
From the book I am reading, it states that vacuous proof happens when the hypothesis of the implication is always false and from the example in the book kinds of throw me off a little...
The example in book:
"Prove that if n is an integer with 10 <=n<=15 which is a perfect square, then n is also a perfect cube"
According to the solution in book:
"There are no perfect squares n with 10<=n<=15 because 3^2 = 9 and 4^2 = 16. Hence the statement that n is an integer with 10<=n<=15 which is a perfect square is false. Consequently the statement to be proved is true for all integers"
but I can't find any number between 10<=n<=15 to have perfect cube?
so what I understand from vacuous proof is that if p is not true, ~P -> Q is true?
Can someone maybe explain it in super layman style for me to understand or tell me if what I understood is wrong etc.?
lime kiln
As can be seen on the truth table for →
uhh meaning? sweat
placid zinc
Have you seen a truth table for → before?
lime kiln
no
bleak ridge
Thats one weird truth table
lime kiln
so we can kinda say that
If P = I live in Paris
and Q = I live in France
this P->Q is true but at the same time
if P not true = I do not live in Paris
but Q = I live in France (because I can still live in france but just not Paris)
If so, then the statement above is proven by using vacuous proof?
placid zinc
So you've detailed why → is not ⇔
Which is also very important to get, but is not an example of vacuous truth
Let's say:
P = You live on the moon
Q = You live on Jupiter
Then P → Q is true, because you don't live on the moon.
If P is false, then P → Q is true
Which is given by the bottom two rows
lime kiln
I am having hard time to understand vacuous proof.
From the book I am reading, ...
so like the example given by the book. the P is false but isn't the Q also false? how would that fall under vacuous proof? 
placid zinc
Because P is false
lime kiln
so as long P is false it doesn't matter if Q is true or false, it can be proven P→Q true by vacuous proof?
thanks!
.close
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dense compass
How would I go about evaluating this integral? Thank you
lone heartBOT
How would I go about evaluating this integral? Thank you
@dense compass Has your question been resolved?
atomic lodge
Question 8
lone heartBOT
Question 8
atomic lodge
<@&286206848099549185>
I found the derivative and set that equal to 0
I got 30x-300 =0
X=10
So at 10 there’s a min or max
I got a min because I got the profit As -1500
i need to find max
lime kiln
you need to 2nd derivative it to check for min or max.
d^2y/dx^2 < 0 is max
lime kiln
if that's the case, from what I get from reading the question is that the profit of the company is P(x). the number of units sold can be from 0<=x<=40 and it wants the greatest profit of the company. After plotting the graph of this equation, the min point is a x=10 (where the company will have it's lowest profit which is 0) and the max can be infinite. And since we want the max profit within the number of items sold. I would substitute x=40 into p(x) to get my max profit for the company since the company sold at most 40 units
atomic lodge
ya that's what i thought ok i don't what the correct answer is
lime kiln
oh wait sorry (min profit would be -1500)
atomic lodge
oh wait sorry (min profit would be -1500)
yes
lime kiln
ya that's what i thought ok i don't what the correct answer is
sub 40 into the equation and you will get an answer which is also the answer option
substitute*
alpine sable
hi
atomic lodge
X+Y=34
atomic lodge
Take the number of $5 as x and $10 as Y
alpine sable
oh ok
atomic lodge
It is saying there are a total of 34 notes (only 5 and 10 dollar notes)
alpine sable
o
atomic lodge
The other equation would be 5x+10Y =235
One is telling u the value the other is telling u the number of notes
Solve both the solutions by substituting
U will get ur answer
minor yacht
Hi, im trying to find what this topic is called
lone heartBOT
Hi, im trying to find what this topic is called
minor yacht
and, if you can also suggest videos for this topic that would be great
lone heartBOT
@minor yacht Has your question been resolved?
minor yacht
<@&286206848099549185>
remote heron
looks like multivar?
minor yacht
What is the specific topic?
remote heron
What is the specific topic?
im not sure 
maybe calculus in different coordinate systems
minor yacht
That is kinda broad, im looking for the specific topic. Still, thanks
minor yacht
yea that is in the scope of that, but what I want to know is the specific topic for this.
maybe im wrong lol
what i mean is that how can i know what i have to do for this, like do i use dot product or cross product and to what unit vector do I have to use dot/cross product
^what is this topic called(if there is a specific topic)
knotty sleet
I think it's just general problem solving in geometry
minor yacht
Its in my vector analysis class, so i dont think its in ggeometry
knotty sleet
You should be able to do things like this with a good grasp of resolving vectors and different coordinate systems
minor yacht
but it can probably be solved through geometry as well
knotty sleet
Its in my vector analysis class, so i dont think its in ggeometry
Oh well could you just review the materials from class?
minor yacht
I tried but its not really helping that much
hence im trying to find videos but i dont know what topic this is to search lol
if you can suggest videos, i'll really appreciate it
knotty sleet
I guess you've tried searching the name of your class
Vector analysis
Perhaps search up spherical coordinates
Because this uses it
minor yacht
yes, i tried but I could not find something that answers a similar question to this
knotty sleet
Unfortunately idrk video resources for university material
Oh 😰
Then probably just do something else and find a chance to ask a friend/professor?
minor yacht
most video resources just tackles the basic, converting, gradients, etc
ill try but maybe someone here knows
ima repost my question so people can see
Hi, im trying to find what this topic is called
visual iris
Maybe Tangent, Normal, and Binormal Vectors?
frosty sparrow
probably polar coordinates too
lone heartBOT
@minor yacht Has your question been resolved?
fresh tide
anyone know why this isn’t right?
lone heartBOT
anyone know why this isn’t right?
fresh tide
raw shard
u = 9t+5, du = 9t dt, (1/9)du = dt \ $\frac{1}{9} \cdot \int u^{2.4} \dd{u}$
@fresh tide did you do this
ocean sealBOT
quantum
raw shard
well your coefficient is wrong
1/9 = 0.1111111…
either way it should be kept as a fraction
fresh tide
it says 1/9 is wrong too lol
raw shard
,w integral of (9t+5)^(2.4)
ocean sealBOT
fresh tide
lol
raw shard
wolfram alpha is drunk
anyways, (1/9)*(9t+5)^3.4 + C is correct
oh darn wait
i’m so dumb
fresh tide
raw shard
i forgot the integral power rule
(1/9)(10/34)*(9t+5)^3.4 + C
(10/306)*(9t+5)^3.4 + C
fresh tide
boom
raw shard
me dumb
raw shard
no problem
fresh tide
what’s command to clsoe
raw shard
it’s .close
fresh tide
.close
royal trench
lone heartBOT
royal trench
need help with this problem, i have tried doing ln1.8/0.024 but its not right?
got from using continuous interest formula but not sure if i should be using another
chrome salmon
need help with this problem, i have tried doing ln1.8/0.024 but its not right?
You need to use ln(1.8)/0.024
royal trench
You need to use ln(1.8)/0.024
i did that but its not right
ocean sealBOT
it's Sam
onyx hatch
how do i show that $f_s : \mathbb{C} \backslash {0} \to \mathbb{C}, ; f_s = \frac{\overline{z}}{|z|^s}$ is boundless for $s>1$
ocean sealBOT
lewis
onyx hatch
My argument would have been: \
Let $z_0 \in \mathbb{C} \backslash {0}$ be arbitrary. Choose $(z_n){n \geq 1}$ such that $z_n := \frac{1}{n}$ and $z_n \to \infty$ for $n \to \infty$. Then, we have: $$f_s(z_n) = \frac{\overline{1/n}}{(1/n)^s} = \frac{1}{n} \cdot \left(\frac{1}{n}\right)^{-s} = \left(\frac{1}{n}\right)^{-(s-1)}$$
So, there exists a $q \geq 1$ such that $q = s-1$. It follows that $f_s(z_n) = \left(\frac{1}{n}\right)^{-q} = n^q$. Since $q \geq 1$, it obviously diverges. So we get: $\lim{n \to \infty} n^q \neq z_0$. The limit cannot exist.
ocean sealBOT
lewis
onyx hatch
.close
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Available help channel!
potent rain
How can I know where the midline intersection and extrama should be for a sinusoidal equation? Khan academy wants me to differentiate between the points and depending on which one I use it is wrong -- what am I doing wrong?
supple tundra
The midline is the horizontal line that cuts through the middle of a periodic function right?
Do you know how to graph $\sin(x)$?
ocean sealBOT
azeem321
potent rain
The midline is the horizontal line that cuts through the middle of a periodic fu...
I haven't tried to graph sin x yet I don't have graphing paper though
I could probably do it easily if I tried
Are you suggesting that I graph the functions on paper before answering?
Could work
supple tundra
I'm not even sure what your question is tbh
do you need help graphing the function
or
potent rain
I'm not even sure what your question is tbh
Well if you look at the pics basically I sometimes answer wrong because the graph looks wrong based off which point I use.
I'm not sure how I'm supposed to know unless like you say I graph multiple points
Idk which is the extrema point that's probably my main issue
From for example y = 3sin(1/3(x)) + 4 I know that one point is (0, 1)
supple tundra
You should think about graphing this function by starting with $f(x) = \sin(x)$ and then applying transformations to the graph
ocean sealBOT
azeem321
supple tundra
What does $f(\frac{\pi}{2}x)$ do to a graph?
ocean sealBOT
azeem321
supple tundra
= f(1.57x)
supple tundra
Nooo
potent rain
Ok
supple tundra
Right. So under this transformation $sin(1) \mapsto sin(1.57)$
ocean sealBOT
azeem321
supple tundra
You get to points faster
supple tundra
That's just one of the transformations. So $f(\frac{\pi}{2}x)$ compresses the function. What happens when you do $f(\frac{\pi}{2}x) + 2$ ?
ocean sealBOT
azeem321
supple tundra
If you added 2 to $\sin(x)$ what would happen?
ocean sealBOT
azeem321
potent rain
It's minimum value would be 2
supple tundra
??
potent rain
3.57 for the first one
supple tundra
nope
potent rain
The y value
supple tundra
$-1\leq \sin(x) \leq 1$
ocean sealBOT
azeem321
supple tundra
$-1\leq \sin(\frac{\pi x}{2}) \leq 1$
ocean sealBOT
azeem321
supple tundra
$1\leq \sin(\frac{\pi x}{2}) + 2 \leq 3$
ocean sealBOT
azeem321
supple tundra
Do you get that so far?
supple tundra
Just think about applying graph transformations to the basic graph one by one
potent rain
So like with -3cos(pi*x/6)-6 I can focus on cos(pix/6) first
supple tundra
$f(x) + a$ lifts the graph up if it's positive and down if it's negative. $f(x-a)$ moves the graph to the right if it's positive and to the left it's negative. $af(x)$ stretches the y coordinates if it's positive and greater than 1 and compresses the y coordinates if it's between 0 and 1. $f(ax)$ compresses the graph in the x direction
potent rain
Then do * -3 and -6
ocean sealBOT
azeem321
supple tundra
With $-3\cos(\frac{\pi x}{6})-6$. I would start by graphing $\cos(x)$
ocean sealBOT
azeem321
supple tundra
and then I would graph $\cos(\frac{\pi x}{6})$
ocean sealBOT
azeem321
supple tundra
and then I would do $-3\cos(\frac{\pi x}{6})$
ocean sealBOT
azeem321
supple tundra
and finally $-3\cos(\frac{\pi x}{6})-6$
ocean sealBOT
azeem321
supple tundra
Ok
Also, note $\frac{\pi}{6} \approx 0.5$ So instead of compressing the graph in the x direction, it would stretch it out
ocean sealBOT
azeem321
supple tundra
I'm gonna use a calculator lol
Review graph transformations it will help you with trigonometry and make it really easy to understand when you start with solving trig equations and stuff
potent rain
Ok. It's just taking time to plot out these points.
lone heartBOT
@potent rain Has your question been resolved?
alpine sable
Discrete Math
How many bit strings of length 10 have
a) exactly three 0s?
Why is it 10 C 3?
lone heartBOT
Why is it 10 C 3?
@alpine sable Has your question been resolved?
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fringe robin
lone heartBOT
fringe robin
can anyone help
buoyant kayak
keep following the pattern?
cinder mantle
im just learnign this topic so dont take my advice to heart. But i think this involves finding the series sum. Looking at this im assuming it is a geometric sequence. to make sure check if t2/t1=t4/t3
i dont remember the formula series sum for a geometric sequence but u just have to use that formula and slap it in
ill try and see if i can solve it but i doubt it, since i as well am learning this cancer of a topic
@fringe robin
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@fringe robin Has your question been resolved?
cinder mantle
soz
couldnt solve it
but i do know it would have something to do along the lines of what i have explained
that much im confident in
lone heartBOT
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Available help channel!
alpine sable
Determine each rule below is a function or not with the given domain
T/F
f: R-> R
f(x) = f(x) = x+1 if x >= 0 and x-1 if x <= 10
It's F but I don't know why
vale wigeon
...is that the exact wording of the question?
or did you omit something you thought was unimportant but actually was?
@alpine sable
vale wigeon
,rccw
ocean sealBOT
vale wigeon
okay, so you think part e is a valid function definition, yes?
vale wigeon
the definition contradicts itself for inputs between 0 and 10
for example, f(5) should be 6 according to the first piece but 4 according to the second
can't be both at once
vale wigeon
this is the reason why it's not a valid function definition.
muted briar
Hello, I'm trying to understand basics statistics, the F value in linear regression - https://youtu.be/nk2CQITm_eo?t=1089 in this example here he says that F equals variation in mouse size explained by weight divided by variation in mouse size not explained by weight and then the equation is {[sumOfSquares(mean)-SumOfSquares(fit)]/(pfit-pmean)}/[SS(fit)/(n-pfit)] but im confused, should it be something like [sumOfSquares(mean)-SumOfSquares(fit)]/n instead of sumOfSquares(mean)-SumOfSquares(fit), because now its not variation in mouse size explained by weight but sum of squares in mouse size explained by weight?
lone heartBOT
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@muted briar Has your question been resolved?
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@muted briar Has your question been resolved?
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@muted briar Has your question been resolved?
unkempt umbra
How would you show this?
these are properties of a subspace
α) 0 ∈ S;
β) ∀x, y ∈ S , x + y ∈ S;
γ) ∀k ∈ K , ∀x ∈ S , kx ∈ S
But how would they apply here?
Let's first take only Re - even functions
x+y would be g o f ?
glass lichen
How would you show this?
these are properties of a subspace
```
α) 0 ∈ S;
β) ∀x,...
f+g is f+g
they haven't defined explicitly vector addition and scaling, so it's assumed the standard operations
unkempt umbra
ok, and how would I prove that f+g is in Re if f, g ∈ Re?
glass lichen
The definition of a function being even and or odd
you're showing that the sum of even functions is even.
unkempt umbra
well we know that
f(-x) = -f(x) (1)
and
g(-x) = -g(x) (2)
then we have to show that
f(-x) + g(-x) = -(f(x) + g(x))
(1), (2) -> f(-x) + g(-x) = -f(x) - g(x) = -(f(x) + g(x))
Is this alright?
unkempt umbra
f(-x) = -f(x) (1)
(1) -> k * f(-x) = -k * f(x)
does this prove the third property?
chrome salmon
Ok
chrome salmon
Yes
unkempt umbra
but it's pretty similar for even i think
glass lichen
yes, $(f+g)(-x)=f(-x)+g(-x)=-f(x)-g(x)=-(f+g)(x)$
ocean sealBOT
Mosh
glass lichen
so odd functions are closed under addition
glass lichen
yes.
unkempt umbra
f(-x) = f(x) (1)
(1) -> k * f(-x) = k * f(x)
also 0 has to be an element of both Re and Ro
glass lichen
is it?
unkempt umbra
it is
i'm thinking about how to prove that
glass lichen
just show the 0 function is odd and even.
unkempt umbra
so it's enought to say that
f(x) = 0
f(-x) = -f(x) = -0 = 0 in Ro
and
f(x) = 0
f(-x) = f(x)= 0 in Re
```?Mosh
glass lichen
you want 0 in the middle of the string of equality not at the end
you assumed it was odd and even in your proof
unkempt umbra
yes you're right
R^Ro ⊕ R^Re = {f + g | f ∈ R^Ro, g ∈ R^Re }
And we have to show that
R^Ro ⊕ R^Re = R^R
yep
unkempt umbra
Well I'm not exactly sure how to start this proof
Could you give me a hint?
glass lichen
It's probably a shit hint if you don't know sinh and cosh but:
Take inspiration from the exponential definition of sinh and cosh
$\sinh(x):=\frac{e^x-e^{-x}}{2}\ \cosh(x):=\frac{e^x+e^{-x}}{2}$
ocean sealBOT
Mosh
glass lichen
alternatively, you want to somehow introduce f(-x) in somehow to use even and odd proprties
(also note that the sum of those is e^x)
unkempt umbra
i think i have seen something like this a few years ago in highschool
i'll try
$\g(x) = \frac{f(x) + f(-x)}{2}
\
h(x) = \frac{f(x) - f(-x)}{2}
\
g(x) + h(x) = \frac{f(x) + f(-x) + f(x) - f(-x)}{2}
\
g(x) + h(x) = \frac{2 f(x)}{2}
\
g(x) + h(x) = f(x)
\\\
g(x) = \frac{f(x) + f(-x)}{2} = \frac{f(-x) + f(x)}{2} = g(-x) \rightarrow even
\\\
h(x) = \frac{f(x) - f(-x)}{2} = -frac{f(-x) + f(x)}{2} = -h(x) \rightarrow odd$
ocean sealBOT
xbr
unkempt umbra
basically f(x) is a sum of an even and an odd function
glass lichen
unkempt umbra
and does this directly imply that R^Ro ⊕ R^Re = R^R?
glass lichen
yes, as long as f is in R^R
cause you've shown f is a sum of an odd function and an even function
chrome salmon
Close
unkempt umbra
.close
thorny sentinel
does a real valued function of one real variable exist whose antiderivative is a complex velued function?
thorny sentinel
I've done some googling but didn't find anything (probably due to my mathematical immaturity :/ )
lone heartBOT
@thorny sentinel Has your question been resolved?
thorny sentinel
<@&286206848099549185>
lone heartBOT
@thorny sentinel Has your question been resolved?
velvet magnet
does a real valued function of one real variable exist whose antiderivative is a...
Not one that i have come across so far, but im no expert at calculus
¯\_(ツ)_/¯
thorny sentinel
Not one that i have come across so far, but im no expert at calculus
have you maybe taken complex analysis?
velvet magnet
Nah im not even in college lol
thorny sentinel
cuz I suppose you would've came across one if you did and it does exist and it has been discovered
oh
ok
guess I'll just wait for someone with more insight 🙂
lone heartBOT
@thorny sentinel Has your question been resolved?
thorny sentinel
Could you please state your question?
does a real valued function of one real variable exist whose antiderivative is a complex velued function?
hope it's not a stupid question
glass lichen
Does anti derivative mean partial derivative?
no.
glass lichen
does a real valued function of one real variable exist whose antiderivative is a...
Yes, y=x
you can plug complex numbers into 0.5x^2+C.
thorny sentinel
you can plug complex numbers into 0.5x^2+C.
I see. I gues it wasn't clear in the question. I'm looking for the case where the only antiderivative is non real
glass lichen
sine and cosine can be written as complex functions.
thorny sentinel
but they have a real antiderivative
I'm looking for a function that doesn't have one
glass lichen
Yeah, which can be written as a complex function.
thorny sentinel
Yeah, which can be written as a complex function.
Ok, let me restate my question: does a real valued function of one real variable exist which doesn't have a real valued antiderivative, but has the complex-valued antiderivative?
glass lichen
what are you defining as a complex valued function..?
glass lichen
then no
cause you're not satisfied with the fact R to R functions are a subset of C to C functions.
thorny sentinel
oh right, by complex i mean it has nonzero imaginary unit
glass lichen
Then no
thorny sentinel
Is there a proof or a reference you can give? or at least an intuitive explanation
glass lichen
integration maintains domain I suppose.
misty bobcat
Decide if it's possible to find four vectors in $\mathbb{R}^4$ such that, every 3 of them are basis.
ocean sealBOT
Michal
misty bobcat
Any ideas ?
glass lichen
those arent R^4 vectors
glass lichen
then yes, as long as each 3-vector subset is independent
glass lichen
it should by extremal properties of bases
gaunt eagle
lone heartBOT
gaunt eagle
Hello! So this question is from calculus a full cource but I dont get how they come to the conclusion that B=0
I get everything else though!
bleak dune
so your factors are (A+1) and (x(A-1) + B)
if either of those is 0, then that whole side of the equation becomes 0
(if A+1 = 0, then it becomes 0*[x(A-1) + B] which is 0)
gaunt eagle
yup
bleak dune
right, so for the factor on the right, it's [x(A-1) + B] = 0
So it has to be that x(A-1) = -B no matter what x is. The only way for that to happen is if x(A-1) and B are both worth 0
Let's say you pick any other value for A. Let's say -2. The factor becomes -3x + B = 0. But you can't make it so B is always equal to -3x, because B is a constant.
So it doesn't work.
the only time that right hand factor will be zero is when A = -1 and B = 0
does that help?
gaunt eagle
but
cant B be another number?
since the whole term will become 0 anyways when A=-1?
lone heartBOT
@gaunt eagle Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
raven ravine
Hello I’m having trouble isolating my variables to get the inverse
buoyant kayak
so what do you think you should do next
wait it's a take home test
can't get help with tests here
raven ravine
no my teacher said it was review
buoyant kayak
it says take home test at the top
raven ravine
Ik but he said it was a review. I promise it’s not a test.
We have an exam next Wednesday
I understand the confusion and I apologize for how this may look. Can you close my ticket as completed.
.close
lost steeple
How do I find the derivative of log(3x-2)?
lone heartBOT
How do I find the derivative of log(3x-2)?
lost steeple
According to my notes, it's g'(x) / g(x) * ln(b)
Which I got 3 / (3x-2)*ln(10)
But using the derivative calculator it's not right
How do I do it
jagged imp
How do I find the derivative of log(3x-2)?
is the base of this log meant to be 10 or e
The calculator assumes its base is e, and your answer assumes its base is 10
so it depends on that
jagged imp
yes
well actually, it depends on if your answer is 3/((3x-2)ln10) or 3/(3x-2) *ln10
Should be the former(the log is in the denominator)
cold meadow
if i have
vague coral
no
cold meadow
why
raw shard
this is basically spam
cold meadow
i mis said it wrong
I said it wrong
wait
so if i have the odds, 3133507531 out of 436116003068178632599586304885865102436987283273192588087066946205825385420102245537617641171508064231363006853389201952225629937253532766998346708022315458543404066186915809029438078922052852453720811267502691138577239348756804955313693393091406303393978608038048294775593159201377364139187142305434603252709617151318958922901417601677040658907901408937709530384849660728157676437361951488873238454079633326062998564370475129597220298716911739158299214865235291416480348618758676919027696256066573122899301892912081375412160180698274455765997411725112824776559729034126511125728785207316456433746195093026529168420804699808556231371820824328024241019054519605469721555033733292097536/6197148516394364188900141323882322297210558701995146720297131484855101557855486731958221825570944947984004858553140186641155182016082966859736962550177180088600405321238825249746403835469727033342501800712896634341355449588496565230819852486507103432027694702173423912538079766299114717526424477880616639449302766419689877623466381205865605118390274355471509815278332251971759244543740352243076811277717664865760571719052087465244804777251295251995674217073974490490639368917793497383548456310727391232146480195472325811180553427557484142696840113044630459874629946903509481288793101524546602637214862483656004358674999005683914545225086663429140282193350054143291262884451455852063961426683890652699785527976797456599012104868536777488904438653913152719206119693088299602007397720839957389279772575408178106779022036761970796031083638898838300999211395119392678116082151174675257415694403682741632963982317824529718557167903433530955641359259898743752340961013280091956109688607349893209675381881203380524958393734988046719982595235111430847956368856989676534079417326438466595922976484817758530826916589148548056446877738990
whats the percent
Its not spam its a real question i swear
raw shard
0
vague coral
<@&268886789983436800>
raw shard
now go away
cold meadow
how
what is your problem
i need help
why are you so butthurt because i asked for help with a big number
.close
rain crypt
Not sure how to start? A unit length stick is broken into two pieces at a uniformly distributed random point. Then the left
piece is broken again into two pieces at a uniformly distributed random point, and one takes the left
one of the resulting two. Find the expectation of its length.
lone heartBOT
Not sure how to start? A unit length stick is broken into two pieces at a unifor...
@rain crypt Has your question been resolved?
lone heartBOT
@rain crypt Has your question been resolved?
bleak dune
are you looking for the average length of the left most stick?
rain crypt
yes
bleak dune
so i'm not sure how you're supposed to go about this, but I would start by adding up all possible values of the length of the stick after the first break, then divide that by the amount of possible values
and then do that again for the second break
have you seen integrals?
rain crypt
yes
bleak dune
do you know how to add up all the possible lengths of the left stick?
rain crypt
not really kind of abstract to me
bleak dune
it's basically just an integral in this case
varies from 0 to u (u being the length of a unit stick)
rain crypt
random experiment consists in tossing three fair coins. If the result is three heads or three tails,
it is considered to be a success; any other result is a failure. This experiment is repeated 1000 times.
Find the expectation of the number of successes.
what about this one ?
bleak dune
what are the chances one of the experiments succeeds?
rain crypt
1/2
bleak dune
not quite
the first coin can land either way, sure, but there are two other coins that need to land on the same side
rain crypt
oh I meant 1/8
rain crypt
the first coin is 1/2 right?
bleak dune
it can be either heads or tails
as long as the other two land on the same thing as the first one
rain crypt
.close
alpine sable
lone heartBOT
alpine sable
Gotta need some help right here at let's try
I do not understand the question at all on how to solve it
.close
radiant lantern
Hello I need help
lone heartBOT
Hello I need help
bleak dune
alright, what are the parameters you're looking for?
radiant lantern
I really don’t know, because im not sure what form is the best for this problem
Like general factorised or cannonic
bleak dune
Well what are the pros and cons
radiant lantern
General= i got c, factorised = i got the zeros of the function and cannonic: I got h,k
But im not sure how to find cannonic because I dont have h and k
bleak dune
how do you find the h and k usually?
radiant lantern
And also I dont have the zeros of the function so I can’t use factorised
radiant lantern
how do you find the h and k usually?
h by doing like -b/2a or (x1+x2)/2
But I don’t understand how to find it on a table of number like this
alpine sable
try starting with the equation ax^2+bx+c and putting in the information that can be found from the table
radiant lantern
I can only get the c
And one random point
But I still can’t find a and b
Like c is 12
radiant lantern
How ?
alpine sable
ok, well let's start from the very beginning
radiant lantern
What do I need to do ?
alpine sable
the first logical step would be to find the difference between each point subsequently
so on a scratch sheet of paper, remember that the table does skip a few numbers
radiant lantern
Like to find the reflexion axis ?
bleak dune
you know
in this particular case
it might be easier to place the points on a graph and see what it looks like
bleak dune
there is an algebraic way, but I'm not sure you've seen it yet
radiant lantern
Could you just explain to me, maybe ive seen it
alpine sable
the algebraic way is to find 2nd difference
radiant lantern
Like doing (0+4)/2 ?
I think it might give the h
Because 0 and 4 give the value of 12
alpine sable
if you don't want to graph
you have to find 2nd difference
and solve with a system of 3 linear equations
bleak dune
well if you consider Ax^2 + Bx + C = y, then you could just make three equations and treat it like a système d'équations linéaires
alpine sable
well if you consider Ax^2 + Bx + C = y, then you could just make three equations...
that's how you are supposed to solve
bleak dune
¯_(ツ)_/¯
radiant lantern
Like when you substitute the variables to find others
bleak dune
yep
radiant lantern
Oh yeah I see ok I will try
bleak dune
or you could say that this looks very much like a parabola
radiant lantern
And so I do this for a in b right ?
bleak dune
and that it has the same y value in x= 0 and x = 4
so the reflection axis is probably straight in the middle
bleak dune
And so I do this for a in b right ?
yes
radiant lantern
Wait but when I do it, a or b cancel out so I can’t find them
celest root
is this taken....
radiant lantern
Yes but you can take 10
celest root
thank your kind sir
radiant lantern
No problem
bleak dune
Wait but when I do it, a or b cancel out so I can’t find them
they shouldn't. what coordinates did you pick?
radiant lantern
2 and -4
For x and y in respect order
I find that a=(-8-b)/2
And when I replace it in -4=4a+2b+12 it cancel out
bleak dune
you need to use a different point
you have 2 unknown variables
that means you need to use two different equations to solve it
so you need two different coordinate pairs
radiant lantern
Oh like the other method of substracting an equation from an other ?
bleak dune
ye
radiant lantern
Ok I will try
radiant lantern
Well substitution didn’t worked
That’s what I used when all the variables canceled out
Well thank you for your help
I will try it by myself
.close
nocturne beacon
lone heartBOT
nocturne beacon
I took this a while ago so not at the moment
I can start something
I’ll share it in a few
buoyant kayak
alright
dense niche
maybe 6 I am not sure
buoyant kayak
don't do people's work for them, and "6" is not a radius of convergence
lone heartBOT
@nocturne beacon Has your question been resolved?
wary stream
What did you try?
I believe what you need to do instead, use the rational root theorem, find a root of that expression, then use long division
Have you done polynomial long division before?
I suggest watching some videos
alpine sable
I got a question
lone heartBOT
I got a question
velvet magnet
long division
lone heartBOT
normal chasm
lone heartBOT
normal chasm
Can someone explain how i do this? Im kinda confused
velvet magnet
They r asking for what values of x is y=0
normal chasm
What
velvet magnet
Lemme try and phrase it better
The question that they are asking is
"What values of x can you substitute so that y will become equal to 0?"
velvet magnet
Theres 3 factors on the rhs
We know that y will become 0 if at least one of these factors is 0
5 con never be zero for any value of x
Can (30-1.5x) be 0 for some value of x?
normal chasm
Yes i think?
velvet magnet
What is that value?
velvet magnet
12+2x=0
velvet magnet
Sorry im a bit confused
Its ok thats y im here lol
normal chasm
What about the 5 at the start? Do i do anything to that?
velvet magnet
U cant because 5 cannot become 0 for any value of x
velvet magnet
Yes
normal chasm
Okay. I got it, thanks!!! :D
velvet magnet
Glad i could help 😀
lone heartBOT
@normal chasm Has your question been resolved?
uncut frost
I have a couple questions about vectors.
- If you are told to write a vector in i+j+k form, are you just supposed to calculate the unit vector version of that? For example, if the components are <3,4>, are you supposed to write the vector in ijk form like 3/5i+ 4/5k?
uncut frost
- If you are given a vector in ijk form, are you supposed to assume that it is a unit vector?
pearl jasper
- if the components are <3, 4>, i think you're supposed to write it as 3i + 4j
lone heartBOT
@uncut frost Has your question been resolved?
manic pike
question: find the length of XY
lone heartBOT
question: find the length of XY
manic pike
I know pythagoras theorem, how do I use it and solve the question?
copper pond
First you can use the pythagorean theorem to find XB, and see if you can work it out from there.
You can find XB by first finding AB and then subtracting 8cm.
glad tide
Once you've gotten XB, you can work out XC
manic pike
got both XB and XC
glad tide
hmm
manic pike
.close
proven hedge
someone help im stuck for abt 3 hrs already
lone heartBOT
someone help im stuck for abt 3 hrs already
lone heartBOT
@proven hedge Has your question been resolved?
proven hedge
<@&286206848099549185>
i need to use the ping because my problem was already here for abt 20 mins
<@&286206848099549185>
alpine sable
stop pinging
lone heartBOT
@proven hedge Has your question been resolved?
lethal dock
arranging an algebraic equation in an ascending order in the regards of y, it will start from the smallest variation of y to the biggest and if there is a variation of x there, will it come at the end as we are doing it in the regards of y?
lone heartBOT
arranging an algebraic equation in an ascending order in the regards of y, it wi...
@lethal dock Has your question been resolved?
alpine sable
in this-then equations when we are trying to solve: If P, Then Find Q
alpine sable
then we minipulate P so that it becomes Q=(something)
smoky jacinth
Can someone explain how to solve this...?
alpine sable
Can someone explain how to solve this...?
i am already in this channel, go to a avalable channel
now could a this-then equation be solved like this too
inner pine
Hello
alpine sable
where we manipulate P so that, it looks like a part of Q but not the whole Q; Q(piece)=(something)
and we take that (something) that the Piece of Q is equal to. and plug it into the original Q to find the answer
for ex; if 153=2(x+x)y, then find 2y(2x)-193
rewrite; 153=2y(2x), then plug 153 into 2y(2x)-193
153-193
=-40
TLDR; if we have a; If P, then find Q equation
so we take P and do we make one side of the P completely look like Q, Or do we can just make one side of p just equal to partially look like q
<@&286206848099549185>
is anyone there?
OR, if the problem says If (p), then find (q), then we have to make one side of p completely look like q
and , if the problem says, if (p), then find the value of (q), then we can make one side of p look like a part of q, and then plug the value into the original Q to find the value
TLDR AGAIN: IS THERE A DIFFERENCE BETWEEN "IF P, THEN FIND Q" and "IF P, THEN FIND THE VALUE OF Q"
.close
shadow stream
How would I approach this problem? I'm a little clueless about it 
lone heartBOT
How would I approach this problem? I'm a little clueless about it <:sad:76720136...
@shadow stream Has your question been resolved?
gentle flame
. Find the longest pole length that can be put in a room of 10m ×5m
wth? is this question right?
chrome salmon
. Find the longest pole length that can be put in a room of 10m ×5m
wth? is thi...
So you are given with only two dimensions? 
chrome salmon
How would I approach this problem? I'm a little clueless about it <:sad:76720136...
Is fx pmf?
shadow stream
uh idk if i have the wrong understanding but if its continuous then its a pdf right?
i believe it is continuous between 2 and 3？
chrome salmon
Yeah typo from me
shadow stream
it should be a pdf
shadow stream
im not sure how to approach this question 
chrome salmon
im not sure how to approach this question <:B_Dead:664215008116211713>
You know how to change variables in integration?
shadow stream
You know how to change variables in integration?
not really